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— Tahák pro R",{"type":1096,"value":1097,"toc":4138},"minimark",[1098,1102,1135,1140,1143,1234,1296,1300,1309,1539,1545,1549,1559,2219,2407,2416,2652,2661,2790,2799,3229,3238,3314,3323,3679,3683,4068,4072,4109,4112,4120,4127,4134],[1099,1100,1094],"h1",{"id":1101},"mask-tahák-pro-r",[1103,1104,1109,1123],"aside",{"className":1105,"dataCallout":1108},[1106,1107],"callout","callout-abstract","abstract",[1110,1111,1114,1122],"p",{"className":1112},[1113],"callout-title",[1115,1116],"span",{"className":1117,"ariaHidden":1121},[1118,1119,1120],"iconify","i-lucide:clipboard-list","callout-icon","true","TL;DR",[1110,1124,1125,1126,1134],{},"Referenční přehled příkazů R používaných v kurzu ",[1127,1128,1133],"a",{"className":1129,"dataFsResolvedFilePath":1131,"href":1132},[1130],"wikilink","courses\u002Fmask.md","\u002Fwiki\u002Fmask","Metody aplikované statistiky",": načtení dat, volba statistického testu podle situace, funkce jednotlivých kapitol a výchozí hodnoty parametrů R, které mění výsledek.",[1136,1137,1139],"h2",{"id":1138},"načtení-dat","Načtení dat",[1110,1141,1142],{},"Data se do R zadávají buď přímo jako vektor, nebo se načtou ze souboru v pracovním adresáři či vybraného v dialogovém okně:",[1144,1145,1149],"pre",{"className":1146,"code":1147,"language":71,"meta":1148,"style":1148},"language-r shiki shiki-themes github-light github-light github-dark","x \u003C- c(4.1, 4.0, 3.8, 3.9, 3.8, 3.8, 3.5, 3.7, 4.0, 4.0)   # přímé zadání hodnot\n# x \u003C- read.table(\"data.txt\")[, 1]     # první sloupec souboru v pracovním adresáři\n# x \u003C- read.table(file.choose())[, 1]  # první sloupec souboru vybraného v dialogovém okně\n","",[1150,1151,1152,1224,1229],"code",{"__ignoreMap":1148},[1115,1153,1155,1159,1163,1167,1171,1175,1178,1181,1183,1186,1188,1191,1193,1195,1197,1199,1201,1204,1206,1209,1211,1213,1215,1217,1220],{"class":1154,"line":10},"line",[1115,1156,1158],{"class":1157},"sP4rz","x",[1115,1160,1162],{"class":1161},"s8jYJ"," \u003C-",[1115,1164,1166],{"class":1165},"snPdu"," c",[1115,1168,1170],{"class":1169},"sxrX7","(",[1115,1172,1174],{"class":1173},"sBjJW","4.1",[1115,1176,1177],{"class":1161},",",[1115,1179,1180],{"class":1173}," 4.0",[1115,1182,1177],{"class":1161},[1115,1184,1185],{"class":1173}," 3.8",[1115,1187,1177],{"class":1161},[1115,1189,1190],{"class":1173}," 3.9",[1115,1192,1177],{"class":1161},[1115,1194,1185],{"class":1173},[1115,1196,1177],{"class":1161},[1115,1198,1185],{"class":1173},[1115,1200,1177],{"class":1161},[1115,1202,1203],{"class":1173}," 3.5",[1115,1205,1177],{"class":1161},[1115,1207,1208],{"class":1173}," 3.7",[1115,1210,1177],{"class":1161},[1115,1212,1180],{"class":1173},[1115,1214,1177],{"class":1161},[1115,1216,1180],{"class":1173},[1115,1218,1219],{"class":1169},")   ",[1115,1221,1223],{"class":1222},"sCsY4","# přímé zadání hodnot\n",[1115,1225,1226],{"class":1154,"line":27},[1115,1227,1228],{"class":1222},"# x \u003C- read.table(\"data.txt\")[, 1]     # první sloupec souboru v pracovním adresáři\n",[1115,1230,1231],{"class":1154,"line":148},[1115,1232,1233],{"class":1222},"# x \u003C- read.table(file.choose())[, 1]  # první sloupec souboru vybraného v dialogovém okně\n",[1110,1235,1236,1237,1240,1241,1244,1245,1248,1249,1252,1253,1256,1257,1260,1261,1264,1265,1268,1269,1260,1272,1275,1276,1279,1280,1283,1284,1287,1288,1291,1292,1295],{},"Řádky s načtením ze souboru jsou zakomentované znakem ",[1150,1238,1239],{},"#",", protože soubor musí ležet v pracovním adresáři R. ",[1150,1242,1243],{},"read.table()"," vrací datovou tabulku (",[1150,1246,1247],{},"data.frame","), ne vektor. Bez výběru sloupce ",[1150,1250,1251],{},"[, 1]"," vrátí ",[1150,1254,1255],{},"mean(x)"," hodnotu ",[1150,1258,1259],{},"NA"," a ",[1150,1262,1263],{},"shapiro.test(x)"," skončí chybou. Soubor s více proměnnými ve sloupcích (např. u regrese) se načte celý a sloupce se vyberou podle pořadí: ",[1150,1266,1267],{},"d \u003C- read.table(\"data.txt\")",", pak ",[1150,1270,1271],{},"x \u003C- d[, 1]",[1150,1273,1274],{},"y \u003C- d[, 2]",". Soubor bez řádku se jmény sloupců dostane jména ",[1150,1277,1278],{},"V1",", ",[1150,1281,1282],{},"V2",", …; jména z prvního řádku souboru načte ",[1150,1285,1286],{},"read.table(\"data.txt\", header = TRUE)"," a sloupec se pak vybere přes ",[1150,1289,1290],{},"$"," (např. ",[1150,1293,1294],{},"d$x",").",[1136,1297,1299],{"id":1298},"volba-testu-podle-počtu-výběrů-závislosti-a-normality-dat","Volba testu podle počtu výběrů, závislosti a normality dat",[1110,1301,1302],{},[1303,1304],"img",{"alt":1305,"className":1306,"src":1308},"mask-ilu-volba-testu",[1130,1307],"wikilink-broken","\u002Fwiki-assets\u002Fmask-ilu-volba-testu.png",[1310,1311,1312,1331],"table",{},[1313,1314,1315],"thead",{},[1316,1317,1318,1322,1325,1328],"tr",{},[1319,1320,1321],"th",{},"Situace",[1319,1323,1324],{},"Test",[1319,1326,1327],{},"R volání",[1319,1329,1330],{},"Co odečíst z výstupu",[1332,1333,1334,1357,1374,1394,1411,1433,1455,1472,1489,1506,1522],"tbody",{},[1316,1335,1336,1340,1343,1348],{},[1337,1338,1339],"td",{},"Jeden výběr, normální data — test střední hodnoty",[1337,1341,1342],{},"jednovýběrový t-test",[1337,1344,1345],{},[1150,1346,1347],{},"t.test(x, mu = ..., alternative = ...)",[1337,1349,1350,1353,1354],{},[1150,1351,1352],{},"p-value",", interval spolehlivosti, ",[1150,1355,1356],{},"mean of x",[1316,1358,1359,1362,1365,1370],{},[1337,1360,1361],{},"Jeden výběr, data nejsou normální — test mediánu",[1337,1363,1364],{},"jednovýběrový Wilcoxonův test",[1337,1366,1367],{},[1150,1368,1369],{},"wilcox.test(x, mu = c, alternative = ...)",[1337,1371,1372],{},[1150,1373,1352],{},[1316,1375,1376,1379,1382,1387],{},[1337,1377,1378],{},"Párová měření, diference normální",[1337,1380,1381],{},"párový t-test",[1337,1383,1384],{},[1150,1385,1386],{},"t.test(x, y, paired = TRUE)",[1337,1388,1389,1279,1391],{},[1150,1390,1352],{},[1150,1392,1393],{},"mean difference",[1316,1395,1396,1399,1402,1407],{},[1337,1397,1398],{},"Párová měření, diference nejsou normální",[1337,1400,1401],{},"párový Wilcoxonův test",[1337,1403,1404],{},[1150,1405,1406],{},"wilcox.test(x, y, paired = TRUE, mu = c)",[1337,1408,1409],{},[1150,1410,1352],{},[1316,1412,1413,1416,1419,1424],{},[1337,1414,1415],{},"Dva nezávislé výběry — shoda rozptylů (krok 1)",[1337,1417,1418],{},"F-test",[1337,1420,1421],{},[1150,1422,1423],{},"var.test(x, y)",[1337,1425,1426,1428,1429,1432],{},[1150,1427,1352],{}," → volba ",[1150,1430,1431],{},"var.equal"," pro následující t-test",[1316,1434,1435,1438,1441,1446],{},[1337,1436,1437],{},"Dva nezávislé výběry, normální data — shoda středních hodnot (krok 2)",[1337,1439,1440],{},"dvouvýběrový t-test",[1337,1442,1443],{},[1150,1444,1445],{},"t.test(x, y, var.equal = TRUE\u002FFALSE)",[1337,1447,1448,1279,1450,1279,1452],{},[1150,1449,1352],{},[1150,1451,1356],{},[1150,1453,1454],{},"mean of y",[1316,1456,1457,1460,1463,1468],{},[1337,1458,1459],{},"Dva nezávislé výběry, data nejsou normální",[1337,1461,1462],{},"dvouvýběrový Wilcoxonův test",[1337,1464,1465],{},[1150,1466,1467],{},"wilcox.test(x, y)",[1337,1469,1470],{},[1150,1471,1352],{},[1316,1473,1474,1477,1480,1485],{},[1337,1475,1476],{},"Víc než dva nezávislé výběry, data nejsou normální",[1337,1478,1479],{},"Kruskalův-Wallisův test",[1337,1481,1482],{},[1150,1483,1484],{},"kruskal.test(y ~ faktor, data)",[1337,1486,1487],{},[1150,1488,1352],{},[1316,1490,1491,1494,1497,1502],{},[1337,1492,1493],{},"Víc než dva závislé výběry (dvojné třídění)",[1337,1495,1496],{},"Friedmanův test",[1337,1498,1499],{},[1150,1500,1501],{},"friedman.test(y ~ A | B, data)",[1337,1503,1504],{},[1150,1505,1352],{},[1316,1507,1508,1511,1514,1518],{},[1337,1509,1510],{},"Ověření normality dat před volbou testu",[1337,1512,1513],{},"Shapiro-Wilkův test",[1337,1515,1516],{},[1150,1517,1263],{},[1337,1519,1520],{},[1150,1521,1352],{},[1316,1523,1524,1527,1530,1535],{},[1337,1525,1526],{},"Shoda dat se zadaným typem rozdělení",[1337,1528,1529],{},"Kolmogorovův-Smirnovův test",[1337,1531,1532],{},[1150,1533,1534],{},"ks.test(x, \"pnorm\", mu, sigma)",[1337,1536,1537],{},[1150,1538,1352],{},[1110,1540,1541,1542,1544],{},"H0 se na hladině významnosti 0,05 zamítá, pokud je ",[1150,1543,1352],{}," nejvýše 0,05, a nezamítá, pokud je vyšší; nezamítnutí neznamená, že H0 platí, jen že data proti ní nejsou v rozporu. U testů normality to znamená, že normalitu dat lze předpokládat, ne že data jsou normální.",[1136,1546,1548],{"id":1547},"funkce-podle-kapitol","Funkce podle kapitol",[1550,1551,1553],"h3",{"id":1552},"náhodné-veličiny-a-rozdělení-pravděpodobnosti",[1127,1554,1558],{"className":1555,"dataFsResolvedFilePath":1556,"href":1557},[1130],"topics\u002Fnahodne-veliciny-a-rozdeleni.md","\u002Fwiki\u002Fnahodne-veliciny-a-rozdeleni","Náhodné veličiny a rozdělení pravděpodobnosti",[1310,1560,1561,1755],{},[1313,1562,1563],{},[1316,1564,1565,1568,1631,1679,1733],{},[1319,1566,1567],{},"Rozdělení",[1319,1569,1570,1609,1610],{},[1115,1571,1574],{"className":1572},[1573],"katex",[1575,1576,1578],"math",{"xmlns":1577},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1579,1580,1581,1604],"semantics",{},[1582,1583,1584,1588,1592,1595,1598,1601],"mrow",{},[1585,1586,1587],"mi",{},"P",[1589,1590,1170],"mo",{"stretchy":1591},"false",[1585,1593,1594],{},"X",[1589,1596,1597],{},"=",[1585,1599,1600],{},"k",[1589,1602,1603],{"stretchy":1591},")",[1605,1606,1608],"annotation",{"encoding":1607},"application\u002Fx-tex","P(X = k)",", hustota ",[1115,1611,1613],{"className":1612},[1573],[1575,1614,1615],{"xmlns":1577},[1579,1616,1617,1628],{},[1582,1618,1619,1622,1624,1626],{},[1585,1620,1621],{},"f",[1589,1623,1170],{"stretchy":1591},[1585,1625,1158],{},[1589,1627,1603],{"stretchy":1591},[1605,1629,1630],{"encoding":1607},"f(x)",[1319,1632,1633,1279,1658],{},[1115,1634,1636],{"className":1635},[1573],[1575,1637,1638],{"xmlns":1577},[1579,1639,1640,1655],{},[1582,1641,1642,1644,1646,1648,1651,1653],{},[1585,1643,1587],{},[1589,1645,1170],{"stretchy":1591},[1585,1647,1594],{},[1589,1649,1650],{},"≤",[1585,1652,1600],{},[1589,1654,1603],{"stretchy":1591},[1605,1656,1657],{"encoding":1607},"P(X \\le k)",[1115,1659,1661],{"className":1660},[1573],[1575,1662,1663],{"xmlns":1577},[1579,1664,1665,1676],{},[1582,1666,1667,1670,1672,1674],{},[1585,1668,1669],{},"F",[1589,1671,1170],{"stretchy":1591},[1585,1673,1158],{},[1589,1675,1603],{"stretchy":1591},[1605,1677,1678],{"encoding":1607},"F(x)",[1319,1680,1681,1279,1706],{},[1115,1682,1684],{"className":1683},[1573],[1575,1685,1686],{"xmlns":1577},[1579,1687,1688,1703],{},[1582,1689,1690,1692,1694,1696,1699,1701],{},[1585,1691,1587],{},[1589,1693,1170],{"stretchy":1591},[1585,1695,1594],{},[1589,1697,1698],{},">",[1585,1700,1600],{},[1589,1702,1603],{"stretchy":1591},[1605,1704,1705],{"encoding":1607},"P(X > k)",[1115,1707,1709],{"className":1708},[1573],[1575,1710,1711],{"xmlns":1577},[1579,1712,1713,1730],{},[1582,1714,1715,1719,1722,1724,1726,1728],{},[1716,1717,1718],"mn",{},"1",[1589,1720,1721],{},"−",[1585,1723,1669],{},[1589,1725,1170],{"stretchy":1591},[1585,1727,1158],{},[1589,1729,1603],{"stretchy":1591},[1605,1731,1732],{"encoding":1607},"1 - F(x)",[1319,1734,1735,1736],{},"Kvantil ",[1115,1737,1739],{"className":1738},[1573],[1575,1740,1741],{"xmlns":1577},[1579,1742,1743,1752],{},[1582,1744,1745],{},[1746,1747,1748,1750],"msub",{},[1585,1749,1158],{},[1585,1751,1587],{},[1605,1753,1754],{"encoding":1607},"x_P",[1332,1756,1757,1811,1860,1906,1962,2019,2066,2112,2162],{},[1316,1758,1759,1791,1796,1801,1806],{},[1337,1760,1761,1762],{},"Binomické ",[1115,1763,1765],{"className":1764},[1573],[1575,1766,1767],{"xmlns":1577},[1579,1768,1769,1788],{},[1582,1770,1771,1774,1777,1779,1782,1784,1786],{},[1585,1772,1773],{},"B",[1585,1775,1776],{},"i",[1589,1778,1170],{"stretchy":1591},[1585,1780,1781],{},"n",[1589,1783,1177],{"separator":1121},[1585,1785,1110],{},[1589,1787,1603],{"stretchy":1591},[1605,1789,1790],{"encoding":1607},"Bi(n,p)",[1337,1792,1793],{},[1150,1794,1795],{},"dbinom(k, n, p)",[1337,1797,1798],{},[1150,1799,1800],{},"pbinom(k, n, p)",[1337,1802,1803],{},[1150,1804,1805],{},"pbinom(k, n, p, FALSE)",[1337,1807,1808],{},[1150,1809,1810],{},"qbinom(P, n, p)",[1316,1812,1813,1840,1845,1850,1855],{},[1337,1814,1815,1816],{},"Poissonovo ",[1115,1817,1819],{"className":1818},[1573],[1575,1820,1821],{"xmlns":1577},[1579,1822,1823,1837],{},[1582,1824,1825,1827,1830,1832,1835],{},[1585,1826,1587],{},[1585,1828,1829],{},"o",[1589,1831,1170],{"stretchy":1591},[1585,1833,1834],{},"λ",[1589,1836,1603],{"stretchy":1591},[1605,1838,1839],{"encoding":1607},"Po(\\lambda)",[1337,1841,1842],{},[1150,1843,1844],{},"dpois(k, lambda)",[1337,1846,1847],{},[1150,1848,1849],{},"ppois(k, lambda)",[1337,1851,1852],{},[1150,1853,1854],{},"ppois(k, lambda, FALSE)",[1337,1856,1857],{},[1150,1858,1859],{},"qpois(P, lambda)",[1316,1861,1862,1886,1891,1896,1901],{},[1337,1863,1864,1865],{},"Geometrické ",[1115,1866,1868],{"className":1867},[1573],[1575,1869,1870],{"xmlns":1577},[1579,1871,1872,1883],{},[1582,1873,1874,1877,1879,1881],{},[1585,1875,1876],{},"G",[1589,1878,1170],{"stretchy":1591},[1585,1880,1110],{},[1589,1882,1603],{"stretchy":1591},[1605,1884,1885],{"encoding":1607},"G(p)",[1337,1887,1888],{},[1150,1889,1890],{},"dgeom(k, p)",[1337,1892,1893],{},[1150,1894,1895],{},"pgeom(k, p)",[1337,1897,1898],{},[1150,1899,1900],{},"pgeom(k, p, FALSE)",[1337,1902,1903],{},[1150,1904,1905],{},"qgeom(P, p)",[1316,1907,1908,1942,1947,1952,1957],{},[1337,1909,1910,1911],{},"Hypergeometrické ",[1115,1912,1914],{"className":1913},[1573],[1575,1915,1916],{"xmlns":1577},[1579,1917,1918,1939],{},[1582,1919,1920,1923,1925,1928,1930,1933,1935,1937],{},[1585,1921,1922],{},"H",[1589,1924,1170],{"stretchy":1591},[1585,1926,1927],{},"N",[1589,1929,1177],{"separator":1121},[1585,1931,1932],{},"M",[1589,1934,1177],{"separator":1121},[1585,1936,1781],{},[1589,1938,1603],{"stretchy":1591},[1605,1940,1941],{"encoding":1607},"H(N,M,n)",[1337,1943,1944],{},[1150,1945,1946],{},"dhyper(k, M, N-M, n)",[1337,1948,1949],{},[1150,1950,1951],{},"phyper(k, M, N-M, n)",[1337,1953,1954],{},[1150,1955,1956],{},"phyper(k, M, N-M, n, FALSE)",[1337,1958,1959],{},[1150,1960,1961],{},"qhyper(P, M, N-M, n)",[1316,1963,1964,1999,2004,2009,2014],{},[1337,1965,1966,1967],{},"Normální ",[1115,1968,1970],{"className":1969},[1573],[1575,1971,1972],{"xmlns":1577},[1579,1973,1974,1996],{},[1582,1975,1976,1978,1980,1983,1985,1994],{},[1585,1977,1927],{},[1589,1979,1170],{"stretchy":1591},[1585,1981,1982],{},"μ",[1589,1984,1177],{"separator":1121},[1986,1987,1988,1991],"msup",{},[1585,1989,1990],{},"σ",[1716,1992,1993],{},"2",[1589,1995,1603],{"stretchy":1591},[1605,1997,1998],{"encoding":1607},"N(\\mu,\\sigma^2)",[1337,2000,2001],{},[1150,2002,2003],{},"dnorm(x, mu, sigma)",[1337,2005,2006],{},[1150,2007,2008],{},"pnorm(x, mu, sigma)",[1337,2010,2011],{},[1150,2012,2013],{},"pnorm(x, mu, sigma, FALSE)",[1337,2015,2016],{},[1150,2017,2018],{},"qnorm(P, mu, sigma)",[1316,2020,2021,2046,2051,2056,2061],{},[1337,2022,2023,2024],{},"Exponenciální ",[1115,2025,2027],{"className":2026},[1573],[1575,2028,2029],{"xmlns":1577},[1579,2030,2031,2043],{},[1582,2032,2033,2036,2038,2041],{},[1585,2034,2035],{},"E",[1589,2037,1170],{"stretchy":1591},[1585,2039,2040],{},"δ",[1589,2042,1603],{"stretchy":1591},[1605,2044,2045],{"encoding":1607},"E(\\delta)",[1337,2047,2048],{},[1150,2049,2050],{},"dexp(x, 1\u002Fdelta)",[1337,2052,2053],{},[1150,2054,2055],{},"pexp(x, 1\u002Fdelta)",[1337,2057,2058],{},[1150,2059,2060],{},"pexp(x, 1\u002Fdelta, FALSE)",[1337,2062,2063],{},[1150,2064,2065],{},"qexp(P, 1\u002Fdelta)",[1316,2067,2068,2092,2097,2102,2107],{},[1337,2069,2070,2071],{},"Studentovo ",[1115,2072,2074],{"className":2073},[1573],[1575,2075,2076],{"xmlns":1577},[1579,2077,2078,2089],{},[1582,2079,2080,2083,2085,2087],{},[1585,2081,2082],{},"t",[1589,2084,1170],{"stretchy":1591},[1585,2086,1600],{},[1589,2088,1603],{"stretchy":1591},[1605,2090,2091],{"encoding":1607},"t(k)",[1337,2093,2094],{},[1150,2095,2096],{},"dt(x, df = k)",[1337,2098,2099],{},[1150,2100,2101],{},"pt(x, df = k)",[1337,2103,2104],{},[1150,2105,2106],{},"pt(x, df = k, lower.tail = FALSE)",[1337,2108,2109],{},[1150,2110,2111],{},"qt(P, df = k)",[1316,2113,2114,2142,2147,2152,2157],{},[1337,2115,2116,2117],{},"Pearsonovo ",[1115,2118,2120],{"className":2119},[1573],[1575,2121,2122],{"xmlns":1577},[1579,2123,2124,2139],{},[1582,2125,2126,2133,2135,2137],{},[1986,2127,2128,2131],{},[1585,2129,2130],{},"χ",[1716,2132,1993],{},[1589,2134,1170],{"stretchy":1591},[1585,2136,1600],{},[1589,2138,1603],{"stretchy":1591},[1605,2140,2141],{"encoding":1607},"\\chi^2(k)",[1337,2143,2144],{},[1150,2145,2146],{},"dchisq(x, df = k)",[1337,2148,2149],{},[1150,2150,2151],{},"pchisq(x, df = k)",[1337,2153,2154],{},[1150,2155,2156],{},"pchisq(x, df = k, lower.tail = FALSE)",[1337,2158,2159],{},[1150,2160,2161],{},"qchisq(P, df = k)",[1316,2163,2164,2199,2204,2209,2214],{},[1337,2165,2166,2167],{},"Fisherovo-Snedecorovo ",[1115,2168,2170],{"className":2169},[1573],[1575,2171,2172],{"xmlns":1577},[1579,2173,2174,2196],{},[1582,2175,2176,2178,2180,2186,2188,2194],{},[1585,2177,1669],{},[1589,2179,1170],{"stretchy":1591},[1746,2181,2182,2184],{},[1585,2183,1600],{},[1716,2185,1718],{},[1589,2187,1177],{"separator":1121},[1746,2189,2190,2192],{},[1585,2191,1600],{},[1716,2193,1993],{},[1589,2195,1603],{"stretchy":1591},[1605,2197,2198],{"encoding":1607},"F(k_1,k_2)",[1337,2200,2201],{},[1150,2202,2203],{},"df(x, df1 = k1, df2 = k2)",[1337,2205,2206],{},[1150,2207,2208],{},"pf(x, df1 = k1, df2 = k2)",[1337,2210,2211],{},[1150,2212,2213],{},"pf(x, df1 = k1, df2 = k2, lower.tail = FALSE)",[1337,2215,2216],{},[1150,2217,2218],{},"qf(P, df1 = k1, df2 = k2)",[2220,2221,2222,2265,2287,2306,2370],"ul",{},[2223,2224,2225,2226,2230,2231,2245,2246,2264],"li",{},"Normální rozdělení se v R zadává ",[2227,2228,2229],"strong",{},"směrodatnou odchylkou"," ",[1115,2232,2234],{"className":2233},[1573],[1575,2235,2236],{"xmlns":1577},[1579,2237,2238,2242],{},[1582,2239,2240],{},[1585,2241,1990],{},[1605,2243,2244],{"encoding":1607},"\\sigma",", ne rozptylem ",[1115,2247,2249],{"className":2248},[1573],[1575,2250,2251],{"xmlns":1577},[1579,2252,2253,2261],{},[1582,2254,2255],{},[1986,2256,2257,2259],{},[1585,2258,1990],{},[1716,2260,1993],{},[1605,2262,2263],{"encoding":1607},"\\sigma^2",".",[2223,2266,2267,2268,2271,2272,2286],{},"Exponenciální rozdělení se zadává parametrem ",[1150,2269,2270],{},"1\u002Fdelta",", kde ",[1115,2273,2275],{"className":2274},[1573],[1575,2276,2277],{"xmlns":1577},[1579,2278,2279,2283],{},[1582,2280,2281],{},[1585,2282,2040],{},[1605,2284,2285],{"encoding":1607},"\\delta"," je střední hodnota.",[2223,2288,2289,2291,2292,2305],{},[1150,2290,1890],{}," počítá pravděpodobnost ",[1115,2293,2295],{"className":2294},[1573],[1575,2296,2297],{"xmlns":1577},[1579,2298,2299,2303],{},[1582,2300,2301],{},[1585,2302,1600],{},[1605,2304,1600],{"encoding":1607}," neúspěchů před prvním úspěchem.",[2223,2307,2308,2309,2312,2313,2316,2317,1279,2330,1260,2348,2361,2362,2365,2366,2369],{},"Pravý ocas vrací argument ",[1150,2310,2311],{},"lower.tail = FALSE",". Bez jména (jen ",[1150,2314,2315],{},"FALSE",") musí stát přesně na jeho pozici, tedy hned za parametry rozdělení. U ",[1115,2318,2320],{"className":2319},[1573],[1575,2321,2322],{"xmlns":1577},[1579,2323,2324,2328],{},[1582,2325,2326],{},[1585,2327,2082],{},[1605,2329,2082],{"encoding":1607},[1115,2331,2333],{"className":2332},[1573],[1575,2334,2335],{"xmlns":1577},[1579,2336,2337,2345],{},[1582,2338,2339],{},[1986,2340,2341,2343],{},[1585,2342,2130],{},[1716,2344,1993],{},[1605,2346,2347],{"encoding":1607},"\\chi^2",[1115,2349,2351],{"className":2350},[1573],[1575,2352,2353],{"xmlns":1577},[1579,2354,2355,2359],{},[1582,2356,2357],{},[1585,2358,1669],{},[1605,2360,1669],{"encoding":1607}," je na této pozici parametr necentrality ",[1150,2363,2364],{},"ncp",", proto se tam ",[1150,2367,2368],{},"lower.tail"," píše vždy jménem.",[2223,2371,2372,2373,2402,2403,2406],{},"U spojitých rozdělení je ",[1115,2374,2376],{"className":2375},[1573],[1575,2377,2378],{"xmlns":1577},[1579,2379,2380,2399],{},[1582,2381,2382,2384,2386,2388,2390,2392,2394,2396],{},[1585,2383,1587],{},[1589,2385,1170],{"stretchy":1591},[1585,2387,1594],{},[1589,2389,1597],{},[1585,2391,1158],{},[1589,2393,1603],{"stretchy":1591},[1589,2395,1597],{},[1716,2397,2398],{},"0",[1605,2400,2401],{"encoding":1607},"P(X = x) = 0","; ",[1150,2404,2405],{},"d*"," vrací hodnotu hustoty, ne pravděpodobnost.",[1550,2408,2410],{"id":2409},"popisná-statistika-a-datové-soubory",[1127,2411,2415],{"className":2412,"dataFsResolvedFilePath":2413,"href":2414},[1130],"topics\u002Fpopisna-statistika.md","\u002Fwiki\u002Fpopisna-statistika","Popisná statistika a datové soubory",[1310,2417,2418,2428],{},[1313,2419,2420],{},[1316,2421,2422,2425],{},[1319,2423,2424],{},"Funkce",[1319,2426,2427],{},"Co vrací",[1332,2429,2430,2453,2466,2475,2485,2495,2508,2532,2546,2556,2569,2585,2609,2619,2642],{},[1316,2431,2432,2437],{},[1337,2433,2434],{},[1150,2435,2436],{},"length(x)",[1337,2438,2439,2440],{},"rozsah souboru ",[1115,2441,2443],{"className":2442},[1573],[1575,2444,2445],{"xmlns":1577},[1579,2446,2447,2451],{},[1582,2448,2449],{},[1585,2450,1781],{},[1605,2452,1781],{"encoding":1607},[1316,2454,2455,2463],{},[1337,2456,2457,1279,2460],{},[1150,2458,2459],{},"min(x)",[1150,2461,2462],{},"max(x)",[1337,2464,2465],{},"nejmenší a největší hodnota",[1316,2467,2468,2472],{},[1337,2469,2470],{},[1150,2471,1255],{},[1337,2473,2474],{},"výběrový průměr",[1316,2476,2477,2482],{},[1337,2478,2479],{},[1150,2480,2481],{},"var(x)",[1337,2483,2484],{},"výběrový rozptyl",[1316,2486,2487,2492],{},[1337,2488,2489],{},[1150,2490,2491],{},"sd(x)",[1337,2493,2494],{},"výběrová směrodatná odchylka",[1316,2496,2497,2502],{},[1337,2498,2499],{},[1150,2500,2501],{},"median(x)",[1337,2503,2504,2505,1603],{},"výběrový medián (stejně jako ",[1150,2506,2507],{},"quantile(x, 0.5, type = 6)",[1316,2509,2510,2515],{},[1337,2511,2512],{},[1150,2513,2514],{},"quantile(x, p, type = 6)",[1337,2516,2517,2518,2531],{},"výběrový ",[1115,2519,2521],{"className":2520},[1573],[1575,2522,2523],{"xmlns":1577},[1579,2524,2525,2529],{},[1582,2526,2527],{},[1585,2528,1110],{},[1605,2530,1110],{"encoding":1607},"-kvantil, jak se počítá v kurzu",[1316,2533,2534,2543],{},[1337,2535,2536,2539,2540],{},[1150,2537,2538],{},"sort(x)"," \u002F ",[1150,2541,2542],{},"sort(x, decreasing = TRUE)",[1337,2544,2545],{},"hodnoty seřazené vzestupně\u002Fsestupně",[1316,2547,2548,2553],{},[1337,2549,2550],{},[1150,2551,2552],{},"boxplot(x)",[1337,2554,2555],{},"krabicový graf",[1316,2557,2558,2563],{},[1337,2559,2560],{},[1150,2561,2562],{},"h \u003C- hist(x, br = seq(38, 46, by = 1))",[1337,2564,2565,2566],{},"histogram s danými hranicemi tříd; výsledek třídění v ",[1150,2567,2568],{},"h",[1316,2570,2571,2582],{},[1337,2572,2573,1279,2576,1279,2579],{},[1150,2574,2575],{},"h$counts",[1150,2577,2578],{},"h$breaks",[1150,2580,2581],{},"h$mids",[1337,2583,2584],{},"četnosti tříd, hranice tříd, středy tříd",[1316,2586,2587,2592],{},[1337,2588,2589],{},[1150,2590,2591],{},"h$density",[1337,2593,2594,2595,2608],{},"četnost třídy dělená ",[1115,2596,2598],{"className":2597},[1573],[1575,2599,2600],{"xmlns":1577},[1579,2601,2602,2606],{},[1582,2603,2604],{},[1585,2605,1781],{},[1605,2607,1781],{"encoding":1607}," a šířkou třídy (při šířce 1 relativní četnost)",[1316,2610,2611,2616],{},[1337,2612,2613],{},[1150,2614,2615],{},"f \u003C- ecdf(x)",[1337,2617,2618],{},"empirická distribuční funkce",[1316,2620,2621,2626],{},[1337,2622,2623],{},[1150,2624,2625],{},"f(k)",[1337,2627,2628,2629],{},"hodnota empirické distribuční funkce v bodě ",[1115,2630,2632],{"className":2631},[1573],[1575,2633,2634],{"xmlns":1577},[1579,2635,2636,2640],{},[1582,2637,2638],{},[1585,2639,1600],{},[1605,2641,1600],{"encoding":1607},[1316,2643,2644,2649],{},[1337,2645,2646],{},[1150,2647,2648],{},"knots(f)",[1337,2650,2651],{},"vzestupně seřazené různé hodnoty souboru",[1550,2653,2655],{"id":2654},"testování-statistických-hypotéz",[1127,2656,2660],{"className":2657,"dataFsResolvedFilePath":2658,"href":2659},[1130],"topics\u002Ftestovani-hypotez.md","\u002Fwiki\u002Ftestovani-hypotez","Testování statistických hypotéz",[1310,2662,2663,2672],{},[1313,2664,2665],{},[1316,2666,2667,2669],{},[1319,2668,2424],{},[1319,2670,2671],{},"Použití",[1332,2673,2674,2682,2690,2698,2707,2716,2725,2735,2743,2751,2759,2767,2777],{},[1316,2675,2676,2680],{},[1337,2677,2678],{},[1150,2679,1347],{},[1337,2681,1342],{},[1316,2683,2684,2688],{},[1337,2685,2686],{},[1150,2687,1386],{},[1337,2689,1381],{},[1316,2691,2692,2696],{},[1337,2693,2694],{},[1150,2695,1445],{},[1337,2697,1440],{},[1316,2699,2700,2704],{},[1337,2701,2702],{},[1150,2703,1423],{},[1337,2705,2706],{},"F-test shody rozptylů",[1316,2708,2709,2713],{},[1337,2710,2711],{},[1150,2712,1263],{},[1337,2714,2715],{},"Shapiro-Wilkův test normality",[1316,2717,2718,2722],{},[1337,2719,2720],{},[1150,2721,1534],{},[1337,2723,2724],{},"Kolmogorovův-Smirnovův test shody s normálním rozdělením",[1316,2726,2727,2732],{},[1337,2728,2729],{},[1150,2730,2731],{},"ks.test(x, \"pexp\", 1\u002Fdelta)",[1337,2733,2734],{},"Kolmogorovův-Smirnovův test shody s exponenciálním rozdělením",[1316,2736,2737,2741],{},[1337,2738,2739],{},[1150,2740,1369],{},[1337,2742,1364],{},[1316,2744,2745,2749],{},[1337,2746,2747],{},[1150,2748,1406],{},[1337,2750,1401],{},[1316,2752,2753,2757],{},[1337,2754,2755],{},[1150,2756,1467],{},[1337,2758,1462],{},[1316,2760,2761,2765],{},[1337,2762,2763],{},[1150,2764,1484],{},[1337,2766,1479],{},[1316,2768,2769,2774],{},[1337,2770,2771],{},[1150,2772,2773],{},"library(agricolae); Median.test(y, faktor)",[1337,2775,2776],{},"mediánový test (alternativa ke Kruskalovu-Wallisovu)",[1316,2778,2779,2783],{},[1337,2780,2781],{},[1150,2782,1501],{},[1337,2784,2785,2786,2789],{},"Friedmanův test (",[1150,2787,2788],{},"friedman.test(y, A, B)"," jen pro samostatné vektory)",[1550,2791,2793],{"id":2792},"regresní-a-korelační-analýza",[1127,2794,2798],{"className":2795,"dataFsResolvedFilePath":2796,"href":2797},[1130],"topics\u002Fregresni-a-korelacni-analyza.md","\u002Fwiki\u002Fregresni-a-korelacni-analyza","Regresní a korelační analýza",[1310,2800,2801,2809],{},[1313,2802,2803],{},[1316,2804,2805,2807],{},[1319,2806,2424],{},[1319,2808,2671],{},[1332,2810,2811,2821,2831,2841,2890,2932,2942,2983,3036,3084,3094,3122,3145,3169,3179,3189,3199,3209,3219],{},[1316,2812,2813,2818],{},[1337,2814,2815],{},[1150,2816,2817],{},"lm(y ~ x)",[1337,2819,2820],{},"lineární regrese (přímka)",[1316,2822,2823,2828],{},[1337,2824,2825],{},[1150,2826,2827],{},"lm(y ~ x + I(x^2))",[1337,2829,2830],{},"parabolická regrese",[1316,2832,2833,2838],{},[1337,2834,2835],{},[1150,2836,2837],{},"lm(y ~ I(1\u002Fx))",[1337,2839,2840],{},"hyperbolická regrese",[1316,2842,2843,2848],{},[1337,2844,2845],{},[1150,2846,2847],{},"library(nls2); nls2(y ~ b1 * exp(b2 * x))",[1337,2849,2850,2851],{},"exponenciální regrese ",[1115,2852,2854],{"className":2853},[1573],[1575,2855,2856],{"xmlns":1577},[1579,2857,2858,2887],{},[1582,2859,2860,2863,2865,2872],{},[1585,2861,2862],{},"y",[1589,2864,1597],{},[1746,2866,2867,2870],{},[1585,2868,2869],{},"b",[1716,2871,1718],{},[1986,2873,2874,2877],{},[1585,2875,2876],{},"e",[1582,2878,2879,2885],{},[1746,2880,2881,2883],{},[1585,2882,2869],{},[1716,2884,1993],{},[1585,2886,1158],{},[1605,2888,2889],{"encoding":1607},"y = b_1 e^{b_2 x}",[1316,2891,2892,2897],{},[1337,2893,2894],{},[1150,2895,2896],{},"nls2(y ~ b1 * b2^x)",[1337,2898,2899,2900,2931],{},"regrese ",[1115,2901,2903],{"className":2902},[1573],[1575,2904,2905],{"xmlns":1577},[1579,2906,2907,2928],{},[1582,2908,2909,2911,2913,2919],{},[1585,2910,2862],{},[1589,2912,1597],{},[1746,2914,2915,2917],{},[1585,2916,2869],{},[1716,2918,1718],{},[2920,2921,2922,2924,2926],"msubsup",{},[1585,2923,2869],{},[1716,2925,1993],{},[1585,2927,1158],{},[1605,2929,2930],{"encoding":1607},"y = b_1 b_2^{x}"," (v kurzu „mocninná funkce“)",[1316,2933,2934,2939],{},[1337,2935,2936],{},[1150,2937,2938],{},"summary(model)",[1337,2940,2941],{},"odhady parametrů, jejich významnost, koeficient determinace",[1316,2943,2944,2949],{},[1337,2945,2946],{},[1150,2947,2948],{},"coef(model)",[1337,2950,2951,2952],{},"odhadnuté parametry ",[1115,2953,2955],{"className":2954},[1573],[1575,2956,2957],{"xmlns":1577},[1579,2958,2959,2980],{},[1582,2960,2961,2967,2969,2975,2977],{},[1746,2962,2963,2965],{},[1585,2964,2869],{},[1716,2966,2398],{},[1589,2968,1177],{"separator":1121},[1746,2970,2971,2973],{},[1585,2972,2869],{},[1716,2974,1718],{},[1589,2976,1177],{"separator":1121},[1589,2978,2979],{},"…",[1605,2981,2982],{"encoding":1607},"b_0, b_1, \\dots",[1316,2984,2985,2990],{},[1337,2986,2987],{},[1150,2988,2989],{},"fitted(model)",[1337,2991,2992,2993,3017,3018],{},"predikce ",[1115,2994,2996],{"className":2995},[1573],[1575,2997,2998],{"xmlns":1577},[1579,2999,3000,3014],{},[1582,3001,3002],{},[1746,3003,3004,3012],{},[3005,3006,3007,3009],"mover",{"accent":1121},[1585,3008,2862],{},[1589,3010,3011],{},"^",[1585,3013,1776],{},[1605,3015,3016],{"encoding":1607},"\\hat y_i"," pro pozorované ",[1115,3019,3021],{"className":3020},[1573],[1575,3022,3023],{"xmlns":1577},[1579,3024,3025,3033],{},[1582,3026,3027],{},[1746,3028,3029,3031],{},[1585,3030,1158],{},[1585,3032,1776],{},[1605,3034,3035],{"encoding":1607},"x_i",[1316,3037,3038,3043],{},[1337,3039,3040],{},[1150,3041,3042],{},"residuals(model)",[1337,3044,3045,3046],{},"rezidua ",[1115,3047,3049],{"className":3048},[1573],[1575,3050,3051],{"xmlns":1577},[1579,3052,3053,3081],{},[1582,3054,3055,3061,3063,3069,3071],{},[1746,3056,3057,3059],{},[1585,3058,2876],{},[1585,3060,1776],{},[1589,3062,1597],{},[1746,3064,3065,3067],{},[1585,3066,2862],{},[1585,3068,1776],{},[1589,3070,1721],{},[1746,3072,3073,3079],{},[3005,3074,3075,3077],{"accent":1121},[1585,3076,2862],{},[1589,3078,3011],{},[1585,3080,1776],{},[1605,3082,3083],{"encoding":1607},"e_i = y_i - \\hat y_i",[1316,3085,3086,3091],{},[1337,3087,3088],{},[1150,3089,3090],{},"confint(model, level = 0.95)",[1337,3092,3093],{},"intervaly spolehlivosti pro parametry modelu",[1316,3095,3096,3101],{},[1337,3097,3098],{},[1150,3099,3100],{},"predict(model, interval = \"confidence\", level = 0.95)",[1337,3102,3103,3104],{},"interval spolehlivosti pro střední hodnotu ",[1115,3105,3107],{"className":3106},[1573],[1575,3108,3109],{"xmlns":1577},[1579,3110,3111,3119],{},[1582,3112,3113],{},[3005,3114,3115,3117],{"accent":1121},[1585,3116,2862],{},[1589,3118,3011],{},[1605,3120,3121],{"encoding":1607},"\\hat y",[1316,3123,3124,3129],{},[1337,3125,3126],{},[1150,3127,3128],{},"predict(model, interval = \"prediction\", level = 0.95)",[1337,3130,3131,3132],{},"predikční interval pro jednotlivou hodnotu ",[1115,3133,3135],{"className":3134},[1573],[1575,3136,3137],{"xmlns":1577},[1579,3138,3139,3143],{},[1582,3140,3141],{},[1585,3142,2862],{},[1605,3144,2862],{"encoding":1607},[1316,3146,3147,3152],{},[1337,3148,3149],{},[1150,3150,3151],{},"predict(model, newdata = data.frame(x = c(7, 8)), interval = \"confidence\")",[1337,3153,3154,3155,3168],{},"totéž pro nové hodnoty ",[1115,3156,3158],{"className":3157},[1573],[1575,3159,3160],{"xmlns":1577},[1579,3161,3162,3166],{},[1582,3163,3164],{},[1585,3165,1158],{},[1605,3167,1158],{"encoding":1607},"; sloupec se musí jmenovat jako proměnná v modelu",[1316,3170,3171,3176],{},[1337,3172,3173],{},[1150,3174,3175],{},"cor(x, y)",[1337,3177,3178],{},"korelační koeficient",[1316,3180,3181,3186],{},[1337,3182,3183],{},[1150,3184,3185],{},"step(model, direction = \"both\")",[1337,3187,3188],{},"stepwise výběr proměnných podle AIC",[1316,3190,3191,3196],{},[1337,3192,3193],{},[1150,3194,3195],{},"library(car); vif(model)",[1337,3197,3198],{},"Variance Inflation Factor (multikolinearita)",[1316,3200,3201,3206],{},[1337,3202,3203],{},[1150,3204,3205],{},"library(lmtest); dwtest(model)",[1337,3207,3208],{},"Durbin-Watsonův test autokorelace reziduí",[1316,3210,3211,3216],{},[1337,3212,3213],{},[1150,3214,3215],{},"library(whitestrap); white_test(model)",[1337,3217,3218],{},"Whiteův test homoskedasticity reziduí",[1316,3220,3221,3226],{},[1337,3222,3223],{},[1150,3224,3225],{},"shapiro.test(residuals(model))",[1337,3227,3228],{},"test normality reziduí",[1550,3230,3232],{"id":3231},"kontingenční-tabulky",[1127,3233,3237],{"className":3234,"dataFsResolvedFilePath":3235,"href":3236},[1130],"topics\u002Fkontingencni-tabulky.md","\u002Fwiki\u002Fkontingencni-tabulky","Kontingenční tabulky",[1310,3239,3240,3248],{},[1313,3241,3242],{},[1316,3243,3244,3246],{},[1319,3245,2424],{},[1319,3247,2671],{},[1332,3249,3250,3260,3270,3280,3304],{},[1316,3251,3252,3257],{},[1337,3253,3254],{},[1150,3255,3256],{},"chisq.test(tab)",[1337,3258,3259],{},"test nezávislosti dvou kvalitativních znaků",[1316,3261,3262,3267],{},[1337,3263,3264],{},[1150,3265,3266],{},"chisq.test(tab, correct = FALSE)",[1337,3268,3269],{},"totéž pro čtyřpolní tabulku 2 × 2 bez Yatesovy korekce, jak se počítá v kurzu",[1316,3271,3272,3277],{},[1337,3273,3274],{},[1150,3275,3276],{},"chisq.test(tab)$expected",[1337,3278,3279],{},"očekávané četnosti za platnosti nezávislosti",[1316,3281,3282,3287],{},[1337,3283,3284],{},[1150,3285,3286],{},"sqrt(chisq.test(tab, correct = FALSE)$statistic \u002F (sum(tab) * (min(dim(tab)) - 1)))",[1337,3288,3289,3290],{},"Cramérův koeficient kontingence ",[1115,3291,3293],{"className":3292},[1573],[1575,3294,3295],{"xmlns":1577},[1579,3296,3297,3302],{},[1582,3298,3299],{},[1585,3300,3301],{},"V",[1605,3303,3301],{"encoding":1607},[1316,3305,3306,3311],{},[1337,3307,3308],{},[1150,3309,3310],{},"mcnemar.test(tab, correct = FALSE)",[1337,3312,3313],{},"McNemarův test pro párovaná kvalitativní data",[1550,3315,3317],{"id":3316},"regulační-diagramy-a-indexy-způsobilosti",[1127,3318,3322],{"className":3319,"dataFsResolvedFilePath":3320,"href":3321},[1130],"topics\u002Fregulacni-diagramy-a-indexy-zpusobilosti.md","\u002Fwiki\u002Fregulacni-diagramy-a-indexy-zpusobilosti","Regulační diagramy a indexy způsobilosti",[1310,3324,3325,3333],{},[1313,3326,3327],{},[1316,3328,3329,3331],{},[1319,3330,2424],{},[1319,3332,2671],{},[1332,3334,3335,3345,3355,3383,3412,3436,3478,3502,3530,3570,3594,3604],{},[1316,3336,3337,3342],{},[1337,3338,3339],{},[1150,3340,3341],{},"library(qcc)",[1337,3343,3344],{},"balíček pro regulační diagramy a indexy způsobilosti",[1316,3346,3347,3352],{},[1337,3348,3349],{},[1150,3350,3351],{},"qcc.groups(x, sample)",[1337,3353,3354],{},"sestavení logických podskupin z dlouhého formátu dat",[1316,3356,3357,3362],{},[1337,3358,3359],{},[1150,3360,3361],{},"qcc(data, type = \"R\")",[1337,3363,3364,3365,2402,3379,3382],{},"regulační diagram rozpětí ",[1115,3366,3368],{"className":3367},[1573],[1575,3369,3370],{"xmlns":1577},[1579,3371,3372,3377],{},[1582,3373,3374],{},[1585,3375,3376],{},"R",[1605,3378,3376],{"encoding":1607},[1150,3380,3381],{},"data"," je matice, řádek = logická podskupina",[1316,3384,3385,3390],{},[1337,3386,3387],{},[1150,3388,3389],{},"qcc(data, type = \"xbar\")",[1337,3391,3392,3393],{},"regulační diagram průměrů ",[1115,3394,3396],{"className":3395},[1573],[1575,3397,3398],{"xmlns":1577},[1579,3399,3400,3409],{},[1582,3401,3402],{},[3005,3403,3404,3406],{"accent":1121},[1585,3405,1158],{},[1589,3407,3408],{},"ˉ",[1605,3410,3411],{"encoding":1607},"\\bar x",[1316,3413,3414,3419],{},[1337,3415,3416],{},[1150,3417,3418],{},"qcc(data, type = \"S\")",[1337,3420,3421,3422],{},"regulační diagram výběrových směrodatných odchylek ",[1115,3423,3425],{"className":3424},[1573],[1575,3426,3427],{"xmlns":1577},[1579,3428,3429,3434],{},[1582,3430,3431],{},[1585,3432,3433],{},"s",[1605,3435,3433],{"encoding":1607},[1316,3437,3438,3443],{},[1337,3439,3440],{},[1150,3441,3442],{},"qcc(x, type = \"xbar.one\")",[1337,3444,3445,3446,3463,3464,3477],{},"diagram individuálních hodnot ",[1115,3447,3449],{"className":3448},[1573],[1575,3450,3451],{"xmlns":1577},[1579,3452,3453,3461],{},[1582,3454,3455],{},[1746,3456,3457,3459],{},[1585,3458,1158],{},[1585,3460,1776],{},[1605,3462,3035],{"encoding":1607}," (jedno měření v podskupině, ",[1115,3465,3467],{"className":3466},[1573],[1575,3468,3469],{"xmlns":1577},[1579,3470,3471,3475],{},[1582,3472,3473],{},[1585,3474,1990],{},[1605,3476,2244],{"encoding":1607}," z klouzavých rozpětí)",[1316,3479,3480,3485],{},[1337,3481,3482],{},[1150,3483,3484],{},"qcc(c_i, type = \"c\")",[1337,3486,3487,3488],{},"diagram počtu neshod ",[1115,3489,3491],{"className":3490},[1573],[1575,3492,3493],{"xmlns":1577},[1579,3494,3495,3500],{},[1582,3496,3497],{},[1585,3498,3499],{},"c",[1605,3501,3499],{"encoding":1607},[1316,3503,3504,3509],{},[1337,3505,3506],{},[1150,3507,3508],{},"qcc(u_i, type = \"u\", sizes = ...)",[1337,3510,3511,3512,2402,3526,3529],{},"diagram počtu neshod na jednotku ",[1115,3513,3515],{"className":3514},[1573],[1575,3516,3517],{"xmlns":1577},[1579,3518,3519,3524],{},[1582,3520,3521],{},[1585,3522,3523],{},"u",[1605,3525,3523],{"encoding":1607},[1150,3527,3528],{},"sizes"," = rozsahy podskupin",[1316,3531,3532,3537],{},[1337,3533,3534],{},[1150,3535,3536],{},"qcc(np_i, type = \"np\", sizes = n)",[1337,3538,3539,3540,3556,3557,1603],{},"diagram počtu neshodných jednotek ",[1115,3541,3543],{"className":3542},[1573],[1575,3544,3545],{"xmlns":1577},[1579,3546,3547,3553],{},[1582,3548,3549,3551],{},[1585,3550,1781],{},[1585,3552,1110],{},[1605,3554,3555],{"encoding":1607},"np"," (stejné rozsahy ",[1115,3558,3560],{"className":3559},[1573],[1575,3561,3562],{"xmlns":1577},[1579,3563,3564,3568],{},[1582,3565,3566],{},[1585,3567,1781],{},[1605,3569,1781],{"encoding":1607},[1316,3571,3572,3577],{},[1337,3573,3574],{},[1150,3575,3576],{},"qcc(np_i, type = \"p\", sizes = ...)",[1337,3578,3579,3580,3593],{},"diagram podílu neshodných jednotek ",[1115,3581,3583],{"className":3582},[1573],[1575,3584,3585],{"xmlns":1577},[1579,3586,3587,3591],{},[1582,3588,3589],{},[1585,3590,1110],{},[1605,3592,1110],{"encoding":1607}," (rozsahy smějí být různé)",[1316,3595,3596,3601],{},[1337,3597,3598],{},[1150,3599,3600],{},"q \u003C- qcc(data, type = \"xbar\")",[1337,3602,3603],{},"uložení diagramu pro výpočet indexů způsobilosti",[1316,3605,3606,3611],{},[1337,3607,3608],{},[1150,3609,3610],{},"process.capability(q, spec.limits = c(LSL, USL), target = T, std.dev = sd(data))",[1337,3612,3613,3614,1279,3633,1260,3655,3678],{},"indexy ",[1115,3615,3617],{"className":3616},[1573],[1575,3618,3619],{"xmlns":1577},[1579,3620,3621,3630],{},[1582,3622,3623],{},[1746,3624,3625,3628],{},[1585,3626,3627],{},"C",[1585,3629,1110],{},[1605,3631,3632],{"encoding":1607},"C_p",[1115,3634,3636],{"className":3635},[1573],[1575,3637,3638],{"xmlns":1577},[1579,3639,3640,3652],{},[1582,3641,3642],{},[1746,3643,3644,3646],{},[1585,3645,3627],{},[1582,3647,3648,3650],{},[1585,3649,1110],{},[1585,3651,1600],{},[1605,3653,3654],{"encoding":1607},"C_{pk}",[1115,3656,3658],{"className":3657},[1573],[1575,3659,3660],{"xmlns":1577},[1579,3661,3662,3675],{},[1582,3663,3664],{},[1746,3665,3666,3668],{},[1585,3667,3627],{},[1582,3669,3670,3672],{},[1585,3671,1110],{},[1585,3673,3674],{},"m",[1605,3676,3677],{"encoding":1607},"C_{pm}"," s výběrovou směrodatnou odchylkou všech dat, jak se počítá v kurzu",[1136,3680,3682],{"id":3681},"výchozí-nastavení-r-která-mění-výsledek","Výchozí nastavení R, která mění výsledek",[1310,3684,3685,3698],{},[1313,3686,3687],{},[1316,3688,3689,3692,3695],{},[1319,3690,3691],{},"Parametr",[1319,3693,3694],{},"Výchozí hodnota v R",[1319,3696,3697],{},"Co se změní při jiném nastavení",[1332,3699,3700,3723,3742,3761,3808,3828,3866,3891,3912,3933,3954,3977],{},[1316,3701,3702,3711,3717],{},[1337,3703,3704,3707,3708],{},[1150,3705,3706],{},"correct"," v ",[1150,3709,3710],{},"mcnemar.test()",[1337,3712,3713,3716],{},[1150,3714,3715],{},"TRUE"," (Yatesova korekce na kontinuitu)",[1337,3718,3719,3722],{},[1150,3720,3721],{},"correct = FALSE"," odpovídá nekorigovanému vzorci počítanému v kurzu ručně",[1316,3724,3725,3732,3737],{},[1337,3726,3727,3707,3729],{},[1150,3728,3706],{},[1150,3730,3731],{},"chisq.test()",[1337,3733,3734,3736],{},[1150,3735,3715],{},", uplatní se jen u tabulky 2 × 2",[1337,3738,3739,3741],{},[1150,3740,3721],{}," dá hodnotu vzorce pro čtyřpolní tabulku z kurzu",[1316,3743,3744,3751,3756],{},[1337,3745,3746,3707,3748],{},[1150,3747,1431],{},[1150,3749,3750],{},"t.test()",[1337,3752,3753,3755],{},[1150,3754,2315],{}," (Welchova varianta)",[1337,3757,3758,3760],{},[1150,3759,3715],{}," použije klasickou dvouvýběrovou statistiku se společným rozptylem — volí se podle výsledku F-testu",[1316,3762,3763,3776,3781],{},[1337,3764,3765,3707,3768,2539,3770,2539,3773],{},[1150,3766,3767],{},"alternative",[1150,3769,3750],{},[1150,3771,3772],{},"wilcox.test()",[1150,3774,3775],{},"var.test()",[1337,3777,3778],{},[1150,3779,3780],{},"\"two.sided\"",[1337,3782,3783,2539,3786,3789,3790],{},[1150,3784,3785],{},"\"greater\"",[1150,3787,3788],{},"\"less\""," testuje jednostrannou alternativu — musí odpovídat formulaci ",[1115,3791,3793],{"className":3792},[1573],[1575,3794,3795],{"xmlns":1577},[1579,3796,3797,3805],{},[1582,3798,3799],{},[1746,3800,3801,3803],{},[1585,3802,1922],{},[1716,3804,1718],{},[1605,3806,3807],{"encoding":1607},"H_1",[1316,3809,3810,3819,3823],{},[1337,3811,3812,3707,3815,2539,3817],{},[1150,3813,3814],{},"paired",[1150,3816,3750],{},[1150,3818,3772],{},[1337,3820,3821],{},[1150,3822,2315],{},[1337,3824,3825,3827],{},[1150,3826,3715],{}," testuje dvojice závislých měření (diference), ne dva nezávislé výběry",[1316,3829,3830,3839,3844],{},[1337,3831,3832,3707,3835,2539,3837],{},[1150,3833,3834],{},"conf.level",[1150,3836,3750],{},[1150,3838,3775],{},[1337,3840,3841],{},[1150,3842,3843],{},"0.95",[1337,3845,3846,3847,1603],{},"určuje spolehlivost intervalu uvedeného ve výstupu testu (",[1115,3848,3850],{"className":3849},[1573],[1575,3851,3852],{"xmlns":1577},[1579,3853,3854,3863],{},[1582,3855,3856,3858,3860],{},[1716,3857,1718],{},[1589,3859,1721],{},[1585,3861,3862],{},"α",[1605,3864,3865],{"encoding":1607},"1 - \\alpha",[1316,3867,3868,3875,3879],{},[1337,3869,3870,3707,3873],{},[1150,3871,3872],{},"conf.int",[1150,3874,3772],{},[1337,3876,3877],{},[1150,3878,2315],{},[1337,3880,3881,3883,3884,3887,3888,3890],{},[1150,3882,3772],{}," vypíše interval spolehlivosti jen s ",[1150,3885,3886],{},"conf.int = TRUE","; samotné ",[1150,3889,3834],{}," výstup nezmění",[1316,3892,3893,3901,3906],{},[1337,3894,3895,3707,3898],{},[1150,3896,3897],{},"type",[1150,3899,3900],{},"quantile()",[1337,3902,3903],{},[1150,3904,3905],{},"7",[1337,3907,3908,3911],{},[1150,3909,3910],{},"type = 6"," odpovídá ručnímu výpočtu kvantilů použitému v kurzu",[1316,3913,3914,3922,3927],{},[1337,3915,3916,3707,3919],{},[1150,3917,3918],{},"right",[1150,3920,3921],{},"hist()",[1337,3923,3924,3926],{},[1150,3925,3715],{}," (třídy zleva otevřené, zprava uzavřené)",[1337,3928,3929,3932],{},[1150,3930,3931],{},"right = FALSE"," otočí hranice tříd na zleva uzavřené, zprava otevřené",[1316,3934,3935,3943,3948],{},[1337,3936,3937,3707,3940],{},[1150,3938,3939],{},"plot",[1150,3941,3942],{},"qcc()",[1337,3944,3945,3947],{},[1150,3946,3715],{}," (diagram se vykreslí)",[1337,3949,3950,3953],{},[1150,3951,3952],{},"plot = FALSE"," jen spočítá meze a vrátí objekt bez vykreslení grafu",[1316,3955,3956,3964,3971],{},[1337,3957,3958,3707,3961],{},[1150,3959,3960],{},"std.dev",[1150,3962,3963],{},"process.capability()",[1337,3965,3966,3967,3970],{},"směrodatná odchylka z regulačního diagramu ",[1150,3968,3969],{},"q"," (z rozpětí nebo směrodatných odchylek v podskupinách)",[1337,3972,3973,3976],{},[1150,3974,3975],{},"std.dev = sd(data)"," použije výběrovou směrodatnou odchylku všech dat; indexy vyjdou jinak",[1316,3978,3979,3986,4029],{},[1337,3980,3981,3707,3984],{},[1150,3982,3983],{},"target",[1150,3985,3963],{},[1337,3987,3988,3989],{},"střed tolerance ",[1115,3990,3992],{"className":3991},[1573],[1575,3993,3994],{"xmlns":1577},[1579,3995,3996,4026],{},[1582,3997,3998,4000,4003,4006,4008,4011,4014,4016,4018,4020,4024],{},[1589,3999,1170],{"stretchy":1591},[1585,4001,4002],{},"L",[1585,4004,4005],{},"S",[1585,4007,4002],{},[1589,4009,4010],{},"+",[1585,4012,4013],{},"U",[1585,4015,4005],{},[1585,4017,4002],{},[1589,4019,1603],{"stretchy":1591},[1585,4021,4023],{"mathvariant":4022},"normal","\u002F",[1716,4025,1993],{},[1605,4027,4028],{"encoding":1607},"(LSL + USL)\u002F2",[1337,4030,4031,4032,4046,4047],{},"jiná cílová hodnota ",[1115,4033,4035],{"className":4034},[1573],[1575,4036,4037],{"xmlns":1577},[1579,4038,4039,4044],{},[1582,4040,4041],{},[1585,4042,4043],{},"T",[1605,4045,4043],{"encoding":1607}," změní ",[1115,4048,4050],{"className":4049},[1573],[1575,4051,4052],{"xmlns":1577},[1579,4053,4054,4066],{},[1582,4055,4056],{},[1746,4057,4058,4060],{},[1585,4059,3627],{},[1582,4061,4062,4064],{},[1585,4063,1110],{},[1585,4065,3674],{},[1605,4067,3677],{"encoding":1607},[1136,4069,4071],{"id":4070},"související-stránky","Související stránky",[2220,4073,4074,4079,4084,4089,4094,4099,4104],{},[2223,4075,4076],{},[1127,4077,1133],{"className":4078,"dataFsResolvedFilePath":1131,"href":1132},[1130],[2223,4080,4081],{},[1127,4082,1558],{"className":4083,"dataFsResolvedFilePath":1556,"href":1557},[1130],[2223,4085,4086],{},[1127,4087,2415],{"className":4088,"dataFsResolvedFilePath":2413,"href":2414},[1130],[2223,4090,4091],{},[1127,4092,2660],{"className":4093,"dataFsResolvedFilePath":2658,"href":2659},[1130],[2223,4095,4096],{},[1127,4097,2798],{"className":4098,"dataFsResolvedFilePath":2796,"href":2797},[1130],[2223,4100,4101],{},[1127,4102,3237],{"className":4103,"dataFsResolvedFilePath":3235,"href":3236},[1130],[2223,4105,4106],{},[1127,4107,3322],{"className":4108,"dataFsResolvedFilePath":3320,"href":3321},[1130],[1136,4110,4111],{"id":934},"Reference",[1110,4113,4114,4115,4119],{},"KROPÁČ, J. ",[4116,4117,4118],"em",{},"Statistika A",". 4. vyd. Brno: Fakulta podnikatelská VUT, 2011.",[1110,4121,4122,4123,4126],{},"MONTGOMERY, D. C. ",[4116,4124,4125],{},"Introduction to Statistical Quality Control",". 6. vyd. Hoboken: Wiley, 2009.",[1110,4128,4129,4130,4133],{},"KUPKA, K. ",[4116,4131,4132],{},"Statistické řízení jakosti",". Pardubice: TriloByte, 1997.",[4135,4136,4137],"style",{},"html pre.shiki code .sP4rz, html code.shiki .sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sCsY4, html code.shiki .sCsY4{--shiki-light:#6A737D;--shiki-default:#6A737D;--shiki-dark:#6A737D}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":1148,"searchDepth":27,"depth":27,"links":4139},[4140,4141,4142,4150,4151,4152],{"id":1138,"depth":27,"text":1139},{"id":1298,"depth":27,"text":1299},{"id":1547,"depth":27,"text":1548,"children":4143},[4144,4145,4146,4147,4148,4149],{"id":1552,"depth":148,"text":1558},{"id":2409,"depth":148,"text":2415},{"id":2654,"depth":148,"text":2660},{"id":2792,"depth":148,"text":2798},{"id":3231,"depth":148,"text":3237},{"id":3316,"depth":148,"text":3322},{"id":3681,"depth":27,"text":3682},{"id":4070,"depth":27,"text":4071},{"id":934,"depth":27,"text":4111},null,"2026-10-02","md",{},true,"\u002Foutputs\u002Fmask-r-tahak",{"title":1094,"description":1148},[4161,4162,4163,4164,4165,4166,4167],"raw\u002Fmask\u002F01 náhodné veličiny - 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Kvalitativní znaky dále dělíme na\n",[2227,4385,4386],{},"alternativní"," (dvě varianty, např. vada ano\u002Fne) a ",[2227,4389,4390],{},"množné"," (více než dvě varianty, např. svobodný\u002Frozvedený\u002Fženatý).",[1110,4393,4394,4395,4408,4409,4423,4424,4454,4455,4468,4469,4499,4500,4503,4504,4527,4528,2230,4531,4553,4554,4572,4573,4591,4592,4595],{},"Mějme ",[1115,4396,4398],{"className":4397},[1573],[1575,4399,4400],{"xmlns":1577},[1579,4401,4402,4406],{},[1582,4403,4404],{},[1585,4405,1781],{},[1605,4407,1781],{"encoding":1607}," opakování pokusu, při nichž sledujeme dva kvalitativní znaky ",[1115,4410,4412],{"className":4411},[1573],[1575,4413,4414],{"xmlns":1577},[1579,4415,4416,4421],{},[1582,4417,4418],{},[1585,4419,4420],{},"A",[1605,4422,4420],{"encoding":1607}," (varianty ",[1115,4425,4427],{"className":4426},[1573],[1575,4428,4429],{"xmlns":1577},[1579,4430,4431,4451],{},[1582,4432,4433,4439,4441,4443,4445],{},[1746,4434,4435,4437],{},[1585,4436,4420],{},[1716,4438,1718],{},[1589,4440,1177],{"separator":1121},[1589,4442,2979],{},[1589,4444,1177],{"separator":1121},[1746,4446,4447,4449],{},[1585,4448,4420],{},[1585,4450,71],{},[1605,4452,4453],{"encoding":1607},"A_1,\\dots,A_r",") a ",[1115,4456,4458],{"className":4457},[1573],[1575,4459,4460],{"xmlns":1577},[1579,4461,4462,4466],{},[1582,4463,4464],{},[1585,4465,1773],{},[1605,4467,1773],{"encoding":1607},"\n(varianty ",[1115,4470,4472],{"className":4471},[1573],[1575,4473,4474],{"xmlns":1577},[1579,4475,4476,4496],{},[1582,4477,4478,4484,4486,4488,4490],{},[1746,4479,4480,4482],{},[1585,4481,1773],{},[1716,4483,1718],{},[1589,4485,1177],{"separator":1121},[1589,4487,2979],{},[1589,4489,1177],{"separator":1121},[1746,4491,4492,4494],{},[1585,4493,1773],{},[1585,4495,3433],{},[1605,4497,4498],{"encoding":1607},"B_1,\\dots,B_s","). Výsledky zapíšeme do ",[2227,4501,4502],{},"kontingenční tabulky",": v políčku ",[1115,4505,4507],{"className":4506},[1573],[1575,4508,4509],{"xmlns":1577},[1579,4510,4511,4524],{},[1582,4512,4513,4515,4517,4519,4522],{},[1589,4514,1170],{"stretchy":1591},[1585,4516,1776],{},[1589,4518,1177],{"separator":1121},[1585,4520,4521],{},"j",[1589,4523,1603],{"stretchy":1591},[1605,4525,4526],{"encoding":1607},"(i,j)"," je ",[2227,4529,4530],{},"simultánní\nčetnost",[1115,4532,4534],{"className":4533},[1573],[1575,4535,4536],{"xmlns":1577},[1579,4537,4538,4550],{},[1582,4539,4540],{},[1746,4541,4542,4544],{},[1585,4543,1781],{},[1582,4545,4546,4548],{},[1585,4547,1776],{},[1585,4549,4521],{},[1605,4551,4552],{"encoding":1607},"n_{ij}",", tedy počet pokusů s variantou ",[1115,4555,4557],{"className":4556},[1573],[1575,4558,4559],{"xmlns":1577},[1579,4560,4561,4569],{},[1582,4562,4563],{},[1746,4564,4565,4567],{},[1585,4566,4420],{},[1585,4568,1776],{},[1605,4570,4571],{"encoding":1607},"A_i"," zároveň s variantou ",[1115,4574,4576],{"className":4575},[1573],[1575,4577,4578],{"xmlns":1577},[1579,4579,4580,4588],{},[1582,4581,4582],{},[1746,4583,4584,4586],{},[1585,4585,1773],{},[1585,4587,4521],{},[1605,4589,4590],{"encoding":1607},"B_j",". Řádkové a sloupcové součty\njsou ",[2227,4593,4594],{},"marginální četnosti",":",[1115,4597,4599],{"className":4598},[1573],[1575,4600,4602],{"xmlns":1577,"display":4601},"block",[1579,4603,4604,4733],{},[1582,4605,4606,4617,4619,4635,4645,4647,4651,4661,4663,4677,4687,4689,4691,4693,4695,4709,4723],{},[1746,4607,4608,4610],{},[1585,4609,1781],{},[1582,4611,4612,4614],{},[1585,4613,1776],{},[1589,4615,4616],{},"∙",[1589,4618,1597],{},[4620,4621,4622,4625,4633],"munderover",{},[1589,4623,4624],{},"∑",[1582,4626,4627,4629,4631],{},[1585,4628,4521],{},[1589,4630,1597],{},[1716,4632,1718],{},[1585,4634,3433],{},[1746,4636,4637,4639],{},[1585,4638,1781],{},[1582,4640,4641,4643],{},[1585,4642,1776],{},[1585,4644,4521],{},[1589,4646,1177],{"separator":1121},[4648,4649],"mspace",{"width":4650},"2em",[1746,4652,4653,4655],{},[1585,4654,1781],{},[1582,4656,4657,4659],{},[1589,4658,4616],{},[1585,4660,4521],{},[1589,4662,1597],{},[4620,4664,4665,4667,4675],{},[1589,4666,4624],{},[1582,4668,4669,4671,4673],{},[1585,4670,1776],{},[1589,4672,1597],{},[1716,4674,1718],{},[1585,4676,71],{},[1746,4678,4679,4681],{},[1585,4680,1781],{},[1582,4682,4683,4685],{},[1585,4684,1776],{},[1585,4686,4521],{},[1589,4688,1177],{"separator":1121},[4648,4690],{"width":4650},[1585,4692,1781],{},[1589,4694,1597],{},[4620,4696,4697,4699,4707],{},[1589,4698,4624],{},[1582,4700,4701,4703,4705],{},[1585,4702,1776],{},[1589,4704,1597],{},[1716,4706,1718],{},[1585,4708,71],{},[4620,4710,4711,4713,4721],{},[1589,4712,4624],{},[1582,4714,4715,4717,4719],{},[1585,4716,4521],{},[1589,4718,1597],{},[1716,4720,1718],{},[1585,4722,3433],{},[1746,4724,4725,4727],{},[1585,4726,1781],{},[1582,4728,4729,4731],{},[1585,4730,1776],{},[1585,4732,4521],{},[1605,4734,4735],{"encoding":1607},"n_{i\\bullet} = \\sum_{j=1}^{s} n_{ij}, \\qquad n_{\\bullet j} = \\sum_{i=1}^{r} n_{ij}, \\qquad n = \\sum_{i=1}^r\\sum_{j=1}^s n_{ij}",[1310,4737,4738,4849],{},[1313,4739,4740],{},[1316,4741,4742,4763,4783,4803,4805,4825],{},[1319,4743,4744],{},[1115,4745,4747],{"className":4746},[1573],[1575,4748,4749],{"xmlns":1577},[1579,4750,4751,4760],{},[1582,4752,4753,4755,4758],{},[1585,4754,4420],{},[1585,4756,4757],{"mathvariant":4022},"\\",[1585,4759,1773],{},[1605,4761,4762],{"encoding":1607},"A \\backslash B",[1319,4764,4765],{},[1115,4766,4768],{"className":4767},[1573],[1575,4769,4770],{"xmlns":1577},[1579,4771,4772,4780],{},[1582,4773,4774],{},[1746,4775,4776,4778],{},[1585,4777,1773],{},[1716,4779,1718],{},[1605,4781,4782],{"encoding":1607},"B_1",[1319,4784,4785],{},[1115,4786,4788],{"className":4787},[1573],[1575,4789,4790],{"xmlns":1577},[1579,4791,4792,4800],{},[1582,4793,4794],{},[1746,4795,4796,4798],{},[1585,4797,1773],{},[1716,4799,1993],{},[1605,4801,4802],{"encoding":1607},"B_2",[1319,4804,2979],{},[1319,4806,4807],{},[1115,4808,4810],{"className":4809},[1573],[1575,4811,4812],{"xmlns":1577},[1579,4813,4814,4822],{},[1582,4815,4816],{},[1746,4817,4818,4820],{},[1585,4819,1773],{},[1585,4821,3433],{},[1605,4823,4824],{"encoding":1607},"B_s",[1319,4826,4827],{},[1115,4828,4830],{"className":4829},[1573],[1575,4831,4832],{"xmlns":1577},[1579,4833,4834,4846],{},[1582,4835,4836],{},[1746,4837,4838,4840],{},[1585,4839,1781],{},[1582,4841,4842,4844],{},[1585,4843,1776],{},[1589,4845,4616],{},[1605,4847,4848],{"encoding":1607},"n_{i\\bullet}",[1332,4850,4851,4965,5079,5095,5215],{},[1316,4852,4853,4873,4894,4915,4917,4941],{},[1337,4854,4855],{},[1115,4856,4858],{"className":4857},[1573],[1575,4859,4860],{"xmlns":1577},[1579,4861,4862,4870],{},[1582,4863,4864],{},[1746,4865,4866,4868],{},[1585,4867,4420],{},[1716,4869,1718],{},[1605,4871,4872],{"encoding":1607},"A_1",[1337,4874,4875],{},[1115,4876,4878],{"className":4877},[1573],[1575,4879,4880],{"xmlns":1577},[1579,4881,4882,4891],{},[1582,4883,4884],{},[1746,4885,4886,4888],{},[1585,4887,1781],{},[1716,4889,4890],{},"11",[1605,4892,4893],{"encoding":1607},"n_{11}",[1337,4895,4896],{},[1115,4897,4899],{"className":4898},[1573],[1575,4900,4901],{"xmlns":1577},[1579,4902,4903,4912],{},[1582,4904,4905],{},[1746,4906,4907,4909],{},[1585,4908,1781],{},[1716,4910,4911],{},"12",[1605,4913,4914],{"encoding":1607},"n_{12}",[1337,4916,2979],{},[1337,4918,4919],{},[1115,4920,4922],{"className":4921},[1573],[1575,4923,4924],{"xmlns":1577},[1579,4925,4926,4938],{},[1582,4927,4928],{},[1746,4929,4930,4932],{},[1585,4931,1781],{},[1582,4933,4934,4936],{},[1716,4935,1718],{},[1585,4937,3433],{},[1605,4939,4940],{"encoding":1607},"n_{1s}",[1337,4942,4943],{},[1115,4944,4946],{"className":4945},[1573],[1575,4947,4948],{"xmlns":1577},[1579,4949,4950,4962],{},[1582,4951,4952],{},[1746,4953,4954,4956],{},[1585,4955,1781],{},[1582,4957,4958,4960],{},[1716,4959,1718],{},[1589,4961,4616],{},[1605,4963,4964],{"encoding":1607},"n_{1\\bullet}",[1316,4966,4967,4987,5008,5029,5031,5055],{},[1337,4968,4969],{},[1115,4970,4972],{"className":4971},[1573],[1575,4973,4974],{"xmlns":1577},[1579,4975,4976,4984],{},[1582,4977,4978],{},[1746,4979,4980,4982],{},[1585,4981,4420],{},[1716,4983,1993],{},[1605,4985,4986],{"encoding":1607},"A_2",[1337,4988,4989],{},[1115,4990,4992],{"className":4991},[1573],[1575,4993,4994],{"xmlns":1577},[1579,4995,4996,5005],{},[1582,4997,4998],{},[1746,4999,5000,5002],{},[1585,5001,1781],{},[1716,5003,5004],{},"21",[1605,5006,5007],{"encoding":1607},"n_{21}",[1337,5009,5010],{},[1115,5011,5013],{"className":5012},[1573],[1575,5014,5015],{"xmlns":1577},[1579,5016,5017,5026],{},[1582,5018,5019],{},[1746,5020,5021,5023],{},[1585,5022,1781],{},[1716,5024,5025],{},"22",[1605,5027,5028],{"encoding":1607},"n_{22}",[1337,5030,2979],{},[1337,5032,5033],{},[1115,5034,5036],{"className":5035},[1573],[1575,5037,5038],{"xmlns":1577},[1579,5039,5040,5052],{},[1582,5041,5042],{},[1746,5043,5044,5046],{},[1585,5045,1781],{},[1582,5047,5048,5050],{},[1716,5049,1993],{},[1585,5051,3433],{},[1605,5053,5054],{"encoding":1607},"n_{2s}",[1337,5056,5057],{},[1115,5058,5060],{"className":5059},[1573],[1575,5061,5062],{"xmlns":1577},[1579,5063,5064,5076],{},[1582,5065,5066],{},[1746,5067,5068,5070],{},[1585,5069,1781],{},[1582,5071,5072,5074],{},[1716,5073,1993],{},[1589,5075,4616],{},[1605,5077,5078],{"encoding":1607},"n_{2\\bullet}",[1316,5080,5081,5084,5086,5088,5091,5093],{},[1337,5082,5083],{},"⋮",[1337,5085,5083],{},[1337,5087,5083],{},[1337,5089,5090],{},"⋱",[1337,5092,5083],{},[1337,5094,5083],{},[1316,5096,5097,5117,5141,5165,5167,5191],{},[1337,5098,5099],{},[1115,5100,5102],{"className":5101},[1573],[1575,5103,5104],{"xmlns":1577},[1579,5105,5106,5114],{},[1582,5107,5108],{},[1746,5109,5110,5112],{},[1585,5111,4420],{},[1585,5113,71],{},[1605,5115,5116],{"encoding":1607},"A_r",[1337,5118,5119],{},[1115,5120,5122],{"className":5121},[1573],[1575,5123,5124],{"xmlns":1577},[1579,5125,5126,5138],{},[1582,5127,5128],{},[1746,5129,5130,5132],{},[1585,5131,1781],{},[1582,5133,5134,5136],{},[1585,5135,71],{},[1716,5137,1718],{},[1605,5139,5140],{"encoding":1607},"n_{r1}",[1337,5142,5143],{},[1115,5144,5146],{"className":5145},[1573],[1575,5147,5148],{"xmlns":1577},[1579,5149,5150,5162],{},[1582,5151,5152],{},[1746,5153,5154,5156],{},[1585,5155,1781],{},[1582,5157,5158,5160],{},[1585,5159,71],{},[1716,5161,1993],{},[1605,5163,5164],{"encoding":1607},"n_{r2}",[1337,5166,2979],{},[1337,5168,5169],{},[1115,5170,5172],{"className":5171},[1573],[1575,5173,5174],{"xmlns":1577},[1579,5175,5176,5188],{},[1582,5177,5178],{},[1746,5179,5180,5182],{},[1585,5181,1781],{},[1582,5183,5184,5186],{},[1585,5185,71],{},[1585,5187,3433],{},[1605,5189,5190],{"encoding":1607},"n_{rs}",[1337,5192,5193],{},[1115,5194,5196],{"className":5195},[1573],[1575,5197,5198],{"xmlns":1577},[1579,5199,5200,5212],{},[1582,5201,5202],{},[1746,5203,5204,5206],{},[1585,5205,1781],{},[1582,5207,5208,5210],{},[1585,5209,71],{},[1589,5211,4616],{},[1605,5213,5214],{"encoding":1607},"n_{r\\bullet}",[1316,5216,5217,5241,5265,5289,5291,5315],{},[1337,5218,5219],{},[1115,5220,5222],{"className":5221},[1573],[1575,5223,5224],{"xmlns":1577},[1579,5225,5226,5238],{},[1582,5227,5228],{},[1746,5229,5230,5232],{},[1585,5231,1781],{},[1582,5233,5234,5236],{},[1589,5235,4616],{},[1585,5237,4521],{},[1605,5239,5240],{"encoding":1607},"n_{\\bullet j}",[1337,5242,5243],{},[1115,5244,5246],{"className":5245},[1573],[1575,5247,5248],{"xmlns":1577},[1579,5249,5250,5262],{},[1582,5251,5252],{},[1746,5253,5254,5256],{},[1585,5255,1781],{},[1582,5257,5258,5260],{},[1589,5259,4616],{},[1716,5261,1718],{},[1605,5263,5264],{"encoding":1607},"n_{\\bullet 1}",[1337,5266,5267],{},[1115,5268,5270],{"className":5269},[1573],[1575,5271,5272],{"xmlns":1577},[1579,5273,5274,5286],{},[1582,5275,5276],{},[1746,5277,5278,5280],{},[1585,5279,1781],{},[1582,5281,5282,5284],{},[1589,5283,4616],{},[1716,5285,1993],{},[1605,5287,5288],{"encoding":1607},"n_{\\bullet 2}",[1337,5290,2979],{},[1337,5292,5293],{},[1115,5294,5296],{"className":5295},[1573],[1575,5297,5298],{"xmlns":1577},[1579,5299,5300,5312],{},[1582,5301,5302],{},[1746,5303,5304,5306],{},[1585,5305,1781],{},[1582,5307,5308,5310],{},[1589,5309,4616],{},[1585,5311,3433],{},[1605,5313,5314],{"encoding":1607},"n_{\\bullet s}",[1337,5316,5317],{},[1115,5318,5320],{"className":5319},[1573],[1575,5321,5322],{"xmlns":1577},[1579,5323,5324,5328],{},[1582,5325,5326],{},[1585,5327,1781],{},[1605,5329,1781],{"encoding":1607},[1110,5331,5332,5333,5346],{},"Vydělením četností počtem opakování ",[1115,5334,5336],{"className":5335},[1573],[1575,5337,5338],{"xmlns":1577},[1579,5339,5340,5344],{},[1582,5341,5342],{},[1585,5343,1781],{},[1605,5345,1781],{"encoding":1607}," dostaneme odhady pravděpodobností:",[1115,5348,5350],{"className":5349},[1573],[1575,5351,5352],{"xmlns":1577,"display":4601},[1579,5353,5354,5455],{},[1582,5355,5356,5370,5372,5387,5389,5391,5405,5407,5421,5423,5425,5439,5441],{},[1746,5357,5358,5364],{},[3005,5359,5360,5362],{"accent":1121},[1585,5361,1110],{},[1589,5363,3011],{},[1582,5365,5366,5368],{},[1585,5367,1776],{},[1585,5369,4521],{},[1589,5371,1597],{},[5373,5374,5375,5385],"mfrac",{},[1746,5376,5377,5379],{},[1585,5378,1781],{},[1582,5380,5381,5383],{},[1585,5382,1776],{},[1585,5384,4521],{},[1585,5386,1781],{},[1589,5388,1177],{"separator":1121},[4648,5390],{"width":4650},[1746,5392,5393,5399],{},[3005,5394,5395,5397],{"accent":1121},[1585,5396,1110],{},[1589,5398,3011],{},[1582,5400,5401,5403],{},[1585,5402,1776],{},[1589,5404,4616],{},[1589,5406,1597],{},[5373,5408,5409,5419],{},[1746,5410,5411,5413],{},[1585,5412,1781],{},[1582,5414,5415,5417],{},[1585,5416,1776],{},[1589,5418,4616],{},[1585,5420,1781],{},[1589,5422,1177],{"separator":1121},[4648,5424],{"width":4650},[1746,5426,5427,5433],{},[3005,5428,5429,5431],{"accent":1121},[1585,5430,1110],{},[1589,5432,3011],{},[1582,5434,5435,5437],{},[1589,5436,4616],{},[1585,5438,4521],{},[1589,5440,1597],{},[5373,5442,5443,5453],{},[1746,5444,5445,5447],{},[1585,5446,1781],{},[1582,5448,5449,5451],{},[1589,5450,4616],{},[1585,5452,4521],{},[1585,5454,1781],{},[1605,5456,5457],{"encoding":1607},"\\hat p_{ij} = \\frac{n_{ij}}{n}, \\qquad \\hat p_{i\\bullet} = \\frac{n_{i\\bullet}}{n}, \\qquad \\hat p_{\\bullet j} = \\frac{n_{\\bullet j}}{n}",[1136,5459,5461],{"id":5460},"test-nezávislosti-dvou-kvalitativních-znaků","Test nezávislosti dvou kvalitativních znaků",[1110,5463,5464,5465,5478,5479,5492],{},"Test ověřuje, zda varianty znaku ",[1115,5466,5468],{"className":5467},[1573],[1575,5469,5470],{"xmlns":1577},[1579,5471,5472,5476],{},[1582,5473,5474],{},[1585,5475,4420],{},[1605,5477,4420],{"encoding":1607}," a varianty znaku ",[1115,5480,5482],{"className":5481},[1573],[1575,5483,5484],{"xmlns":1577},[1579,5485,5486,5490],{},[1582,5487,5488],{},[1585,5489,1773],{},[1605,5491,1773],{"encoding":1607}," jsou na sobě nezávislé, tedy zda simultánní\npravděpodobnost je součinem marginálních pravděpodobností.",[1110,5494,5495],{},[2227,5496,5497],{},"Postup testu:",[5499,5500,5501,5631,5948,6028],"ol",{},[2223,5502,5503,5559,5560,1279,5586,5612,5613,5630],{},[1115,5504,5506],{"className":5505},[1573],[1575,5507,5508],{"xmlns":1577},[1579,5509,5510,5556],{},[1582,5511,5512,5518,5520,5530,5532,5542,5546],{},[1746,5513,5514,5516],{},[1585,5515,1922],{},[1716,5517,2398],{},[1589,5519,4595],{},[1746,5521,5522,5524],{},[1585,5523,1110],{},[1582,5525,5526,5528],{},[1585,5527,1776],{},[1585,5529,4521],{},[1589,5531,1597],{},[1746,5533,5534,5536],{},[1585,5535,1110],{},[1582,5537,5538,5540],{},[1585,5539,1776],{},[1589,5541,4616],{},[5543,5544,5545],"mtext",{}," ",[1746,5547,5548,5550],{},[1585,5549,1110],{},[1582,5551,5552,5554],{},[1589,5553,4616],{},[1585,5555,4521],{},[1605,5557,5558],{"encoding":1607},"H_0: p_{ij} = p_{i\\bullet}\\,p_{\\bullet j}"," pro všechna ",[1115,5561,5563],{"className":5562},[1573],[1575,5564,5565],{"xmlns":1577},[1579,5566,5567,5583],{},[1582,5568,5569,5571,5573,5575,5577,5579,5581],{},[1585,5570,1776],{},[1589,5572,1597],{},[1716,5574,1718],{},[1589,5576,1177],{"separator":1121},[1589,5578,2979],{},[1589,5580,1177],{"separator":1121},[1585,5582,71],{},[1605,5584,5585],{"encoding":1607},"i = 1,\\dots,r",[1115,5587,5589],{"className":5588},[1573],[1575,5590,5591],{"xmlns":1577},[1579,5592,5593,5609],{},[1582,5594,5595,5597,5599,5601,5603,5605,5607],{},[1585,5596,4521],{},[1589,5598,1597],{},[1716,5600,1718],{},[1589,5602,1177],{"separator":1121},[1589,5604,2979],{},[1589,5606,1177],{"separator":1121},[1585,5608,3433],{},[1605,5610,5611],{"encoding":1607},"j = 1,\\dots,s"," (znaky jsou na sobě\nnezávislé) proti ",[1115,5614,5616],{"className":5615},[1573],[1575,5617,5618],{"xmlns":1577},[1579,5619,5620,5628],{},[1582,5621,5622],{},[1746,5623,5624,5626],{},[1585,5625,1922],{},[1716,5627,1718],{},[1605,5629,3807],{"encoding":1607},": znaky jsou závislé.",[2223,5632,5633,5634,5790,5793,5794,5811,5812,5844,5845,4527,5904,5907,5908,5929,5930,5947],{},"Testové kritérium",[1115,5635,5637],{"className":5636},[1573],[1575,5638,5639],{"xmlns":1577,"display":4601},[1579,5640,5641,5787],{},[1582,5642,5643,5649,5651,5665,5679,5737,5739,5741,5755,5757,5771,5773],{},[1986,5644,5645,5647],{},[1585,5646,2130],{},[1716,5648,1993],{},[1589,5650,1597],{},[4620,5652,5653,5655,5663],{},[1589,5654,4624],{},[1582,5656,5657,5659,5661],{},[1585,5658,1776],{},[1589,5660,1597],{},[1716,5662,1718],{},[1585,5664,71],{},[4620,5666,5667,5669,5677],{},[1589,5668,4624],{},[1582,5670,5671,5673,5675],{},[1585,5672,4521],{},[1589,5674,1597],{},[1716,5676,1718],{},[1585,5678,3433],{},[5373,5680,5681,5719],{},[1582,5682,5683,5685,5695,5697,5699,5713],{},[1589,5684,1170],{"stretchy":1591},[1746,5686,5687,5689],{},[1585,5688,1781],{},[1582,5690,5691,5693],{},[1585,5692,1776],{},[1585,5694,4521],{},[1589,5696,1721],{},[1585,5698,1781],{},[1746,5700,5701,5707],{},[3005,5702,5703,5705],{"accent":1121},[1585,5704,1110],{},[1589,5706,3011],{},[1582,5708,5709,5711],{},[1585,5710,1776],{},[1585,5712,4521],{},[1986,5714,5715,5717],{},[1589,5716,1603],{"stretchy":1591},[1716,5718,1993],{},[1582,5720,5721,5723],{},[1585,5722,1781],{},[1746,5724,5725,5731],{},[3005,5726,5727,5729],{"accent":1121},[1585,5728,1110],{},[1589,5730,3011],{},[1582,5732,5733,5735],{},[1585,5734,1776],{},[1585,5736,4521],{},[1589,5738,1177],{"separator":1121},[4648,5740],{"width":4650},[1746,5742,5743,5749],{},[3005,5744,5745,5747],{"accent":1121},[1585,5746,1110],{},[1589,5748,3011],{},[1582,5750,5751,5753],{},[1585,5752,1776],{},[1585,5754,4521],{},[1589,5756,1597],{},[1746,5758,5759,5765],{},[3005,5760,5761,5763],{"accent":1121},[1585,5762,1110],{},[1589,5764,3011],{},[1582,5766,5767,5769],{},[1585,5768,1776],{},[1589,5770,4616],{},[5543,5772,5545],{},[1746,5774,5775,5781],{},[3005,5776,5777,5779],{"accent":1121},[1585,5778,1110],{},[1589,5780,3011],{},[1582,5782,5783,5785],{},[1589,5784,4616],{},[1585,5786,4521],{},[1605,5788,5789],{"encoding":1607},"\\chi^2 = \\sum_{i=1}^{r}\\sum_{j=1}^{s} \\frac{(n_{ij} - n\\hat p_{ij})^2}{n\\hat p_{ij}}, \\qquad \\hat p_{ij} = \\hat p_{i\\bullet}\\,\\hat p_{\\bullet j}",[5791,5792],"br",{},"má asymptoticky Pearsonovo (",[1115,5795,5797],{"className":5796},[1573],[1575,5798,5799],{"xmlns":1577},[1579,5800,5801,5809],{},[1582,5802,5803],{},[1986,5804,5805,5807],{},[1585,5806,2130],{},[1716,5808,1993],{},[1605,5810,2347],{"encoding":1607},") rozdělení o ",[1115,5813,5815],{"className":5814},[1573],[1575,5816,5817],{"xmlns":1577},[1579,5818,5819,5841],{},[1582,5820,5821,5823,5825,5827,5829,5831,5833,5835,5837,5839],{},[1589,5822,1170],{"stretchy":1591},[1585,5824,71],{},[1589,5826,1721],{},[1716,5828,1718],{},[1589,5830,1603],{"stretchy":1591},[1589,5832,1170],{"stretchy":1591},[1585,5834,3433],{},[1589,5836,1721],{},[1716,5838,1718],{},[1589,5840,1603],{"stretchy":1591},[1605,5842,5843],{"encoding":1607},"(r-1)(s-1)"," stupních volnosti. Hodnota ",[1115,5846,5848],{"className":5847},[1573],[1575,5849,5850],{"xmlns":1577},[1579,5851,5852,5901],{},[1582,5853,5854,5856,5870,5872],{},[1585,5855,1781],{},[1746,5857,5858,5864],{},[3005,5859,5860,5862],{"accent":1121},[1585,5861,1110],{},[1589,5863,3011],{},[1582,5865,5866,5868],{},[1585,5867,1776],{},[1585,5869,4521],{},[1589,5871,1597],{},[5873,5874,5875],"mstyle",{"scriptlevel":2398,"displaystyle":1121},[5373,5876,5877,5899],{},[1582,5878,5879,5889],{},[1746,5880,5881,5883],{},[1585,5882,1781],{},[1582,5884,5885,5887],{},[1585,5886,1776],{},[1589,5888,4616],{},[1746,5890,5891,5893],{},[1585,5892,1781],{},[1582,5894,5895,5897],{},[1589,5896,4616],{},[1585,5898,4521],{},[1585,5900,1781],{},[1605,5902,5903],{"encoding":1607},"n\\hat p_{ij} = \\dfrac{n_{i\\bullet}n_{\\bullet j}}{n}",[2227,5905,5906],{},"očekávaná četnost"," políčka ",[1115,5909,5911],{"className":5910},[1573],[1575,5912,5913],{"xmlns":1577},[1579,5914,5915,5927],{},[1582,5916,5917,5919,5921,5923,5925],{},[1589,5918,1170],{"stretchy":1591},[1585,5920,1776],{},[1589,5922,1177],{"separator":1121},[1585,5924,4521],{},[1589,5926,1603],{"stretchy":1591},[1605,5928,4526],{"encoding":1607}," — četnost, kterou bychom čekali, kdyby ",[1115,5931,5933],{"className":5932},[1573],[1575,5934,5935],{"xmlns":1577},[1579,5936,5937,5945],{},[1582,5938,5939],{},[1746,5940,5941,5943],{},[1585,5942,1922],{},[1716,5944,2398],{},[1605,5946,4225],{"encoding":1607}," platila.",[2223,5949,5950,5951,2264],{},"Kritický obor: ",[1115,5952,5954],{"className":5953},[1573],[1575,5955,5956],{"xmlns":1577},[1579,5957,5958,6025],{},[1582,5959,5960,5962,5964,5967,5973,5975,5981,5984,5998,6000,6002,6004,6006,6008,6010,6012,6014,6016,6018,6020,6022],{},[1585,5961,4256],{},[1589,5963,1597],{},[1589,5965,5966],{"stretchy":1591},"{",[1986,5968,5969,5971],{},[1585,5970,2130],{},[1716,5972,1993],{},[1589,5974,4595],{},[1986,5976,5977,5979],{},[1585,5978,2130],{},[1716,5980,1993],{},[1589,5982,5983],{},"≥",[2920,5985,5986,5988,5996],{},[1585,5987,2130],{},[1582,5989,5990,5992,5994],{},[1716,5991,1718],{},[1589,5993,1721],{},[1585,5995,3862],{},[1716,5997,1993],{},[1589,5999,1170],{"stretchy":1591},[1589,6001,1170],{"stretchy":1591},[1585,6003,71],{},[1589,6005,1721],{},[1716,6007,1718],{},[1589,6009,1603],{"stretchy":1591},[1589,6011,1170],{"stretchy":1591},[1585,6013,3433],{},[1589,6015,1721],{},[1716,6017,1718],{},[1589,6019,1603],{"stretchy":1591},[1589,6021,1603],{"stretchy":1591},[1589,6023,6024],{"stretchy":1591},"}",[1605,6026,6027],{"encoding":1607},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}((r-1)(s-1))\\}",[2223,6029,6030,6031,6044,6045,6059,6060,6077,6078,6095],{},"Padne-li testové kritérium do ",[1115,6032,6034],{"className":6033},[1573],[1575,6035,6036],{"xmlns":1577},[1579,6037,6038,6042],{},[1582,6039,6040],{},[1585,6041,4256],{},[1605,6043,4256],{"encoding":1607},", zamítáme na hladině ",[1115,6046,6048],{"className":6047},[1573],[1575,6049,6050],{"xmlns":1577},[1579,6051,6052,6056],{},[1582,6053,6054],{},[1585,6055,3862],{},[1605,6057,6058],{"encoding":1607},"\\alpha"," nulovou hypotézu o nezávislosti a přijímáme\n",[1115,6061,6063],{"className":6062},[1573],[1575,6064,6065],{"xmlns":1577},[1579,6066,6067,6075],{},[1582,6068,6069],{},[1746,6070,6071,6073],{},[1585,6072,1922],{},[1716,6074,1718],{},[1605,6076,3807],{"encoding":1607},"; jinak nemáme důvod ",[1115,6079,6081],{"className":6080},[1573],[1575,6082,6083],{"xmlns":1577},[1579,6084,6085,6093],{},[1582,6086,6087],{},[1746,6088,6089,6091],{},[1585,6090,1922],{},[1716,6092,2398],{},[1605,6094,4225],{"encoding":1607}," zamítnout.",[1110,6097,6098,6099,2264],{},"V R počítá test i očekávané četnosti funkce ",[1150,6100,3731],{},[1103,6102,6106,6114,6117,6120,6266],{"className":6103,"dataCallout":6105},[1106,6104],"callout-example","example",[1110,6107,6109,6113],{"className":6108},[1113],[1115,6110],{"className":6111,"ariaHidden":1121},[1118,6112,1120],"i-lucide:flask-conical","Příklad: nákup potravin na internetu a vzdělání",[1110,6115,6116],{},"Testujte hypotézu, zda se vzájemně ovlivňuje zkušenost s nákupem potravin na internetu a vzdělání respondenta\n(n = 385 respondentů).",[1110,6118,6119],{},"Základní soubor: respondenti; výběrový soubor: respondenti, kteří odpověděli; měřený znak A: vzdělání, měřený\nznak B: způsob nákupu.",[1310,6121,6122,6161],{},[1313,6123,6124],{},[1316,6125,6126,6129,6132,6135,6138],{},[1319,6127,6128],{},"vzdělání \\ nákup",[1319,6130,6131],{},"ano",[1319,6133,6134],{},"ne, ale plánuji",[1319,6136,6137],{},"ne, neplánuji",[1319,6139,6140],{},[1115,6141,6143],{"className":6142},[1573],[1575,6144,6145],{"xmlns":1577},[1579,6146,6147,6159],{},[1582,6148,6149],{},[1746,6150,6151,6153],{},[1585,6152,1781],{},[1582,6154,6155,6157],{},[1585,6156,1776],{},[1589,6158,4616],{},[1605,6160,4848],{"encoding":1607},[1332,6162,6163,6179,6196,6213,6229],{},[1316,6164,6165,6168,6171,6174,6176],{},[1337,6166,6167],{},"SŠ bez maturity",[1337,6169,6170],{},"4",[1337,6172,6173],{},"13",[1337,6175,4911],{},[1337,6177,6178],{},"29",[1316,6180,6181,6184,6187,6190,6193],{},[1337,6182,6183],{},"SŠ s maturitou, VOŠ",[1337,6185,6186],{},"31",[1337,6188,6189],{},"62",[1337,6191,6192],{},"71",[1337,6194,6195],{},"164",[1316,6197,6198,6201,6204,6207,6210],{},[1337,6199,6200],{},"VŠ",[1337,6202,6203],{},"44",[1337,6205,6206],{},"58",[1337,6208,6209],{},"66",[1337,6211,6212],{},"168",[1316,6214,6215,6218,6221,6224,6226],{},[1337,6216,6217],{},"ZŠ",[1337,6219,6220],{},"3",[1337,6222,6223],{},"9",[1337,6225,4911],{},[1337,6227,6228],{},"24",[1316,6230,6231,6254,6257,6260,6263],{},[1337,6232,6233],{},[1115,6234,6236],{"className":6235},[1573],[1575,6237,6238],{"xmlns":1577},[1579,6239,6240,6252],{},[1582,6241,6242],{},[1746,6243,6244,6246],{},[1585,6245,1781],{},[1582,6247,6248,6250],{},[1589,6249,4616],{},[1585,6251,4521],{},[1605,6253,5240],{"encoding":1607},[1337,6255,6256],{},"82",[1337,6258,6259],{},"142",[1337,6261,6262],{},"161",[1337,6264,6265],{},"385",[1110,6267,6268,6320],{},[1115,6269,6271],{"className":6270},[1573],[1575,6272,6273],{"xmlns":1577},[1579,6274,6275,6317],{},[1582,6276,6277,6283,6285,6295,6297,6307],{},[1746,6278,6279,6281],{},[1585,6280,1922],{},[1716,6282,2398],{},[1589,6284,4595],{},[1746,6286,6287,6289],{},[1585,6288,1110],{},[1582,6290,6291,6293],{},[1585,6292,1776],{},[1585,6294,4521],{},[1589,6296,1597],{},[1746,6298,6299,6301],{},[1585,6300,1110],{},[1582,6302,6303,6305],{},[1585,6304,1776],{},[1589,6306,4616],{},[1746,6308,6309,6311],{},[1585,6310,1110],{},[1582,6312,6313,6315],{},[1589,6314,4616],{},[1585,6316,4521],{},[1605,6318,6319],{"encoding":1607},"H_0: p_{ij} = p_{i\\bullet}p_{\\bullet j}"," — vzdělání a způsob nákupu jsou na sobě nezávislé.",[1144,6322,6324],{"className":1146,"code":6323,"language":71,"meta":1148,"style":1148},"tab1 \u003C- matrix(c(4, 13, 12,\n                 31, 62, 71,\n                 44, 58, 66,\n                 3,  9, 12),\n               nrow = 4, byrow = TRUE,\n               dimnames = list(\n                 vzdelani = c(\"SS bez maturity\", \"SS s maturitou nebo VOS\", \"VS\", \"ZS\"),\n                 nakup    = c(\"ano\", \"ne, ale planuji\", \"ne, neplanuji\")))\nchisq.test(tab1)\nchisq.test(tab1)$expected\n",[1150,6325,6326,6357,6374,6391,6409,6432,6445,6479,6507,6520],{"__ignoreMap":1148},[1115,6327,6328,6331,6333,6336,6338,6340,6342,6344,6346,6349,6351,6354],{"class":1154,"line":10},[1115,6329,6330],{"class":1157},"tab1",[1115,6332,1162],{"class":1161},[1115,6334,6335],{"class":1165}," matrix",[1115,6337,1170],{"class":1169},[1115,6339,3499],{"class":1165},[1115,6341,1170],{"class":1169},[1115,6343,6170],{"class":1173},[1115,6345,1177],{"class":1161},[1115,6347,6348],{"class":1173}," 13",[1115,6350,1177],{"class":1161},[1115,6352,6353],{"class":1173}," 12",[1115,6355,6356],{"class":1161},",\n",[1115,6358,6359,6362,6364,6367,6369,6372],{"class":1154,"line":27},[1115,6360,6361],{"class":1173},"                 31",[1115,6363,1177],{"class":1161},[1115,6365,6366],{"class":1173}," 62",[1115,6368,1177],{"class":1161},[1115,6370,6371],{"class":1173}," 71",[1115,6373,6356],{"class":1161},[1115,6375,6376,6379,6381,6384,6386,6389],{"class":1154,"line":148},[1115,6377,6378],{"class":1173},"                 44",[1115,6380,1177],{"class":1161},[1115,6382,6383],{"class":1173}," 58",[1115,6385,1177],{"class":1161},[1115,6387,6388],{"class":1173}," 66",[1115,6390,6356],{"class":1161},[1115,6392,6393,6396,6398,6401,6403,6405,6407],{"class":1154,"line":111},[1115,6394,6395],{"class":1173},"                 3",[1115,6397,1177],{"class":1161},[1115,6399,6400],{"class":1173},"  9",[1115,6402,1177],{"class":1161},[1115,6404,6353],{"class":1173},[1115,6406,1603],{"class":1169},[1115,6408,6356],{"class":1161},[1115,6410,6411,6414,6417,6420,6422,6425,6427,6430],{"class":1154,"line":96},[1115,6412,6413],{"class":1157},"               nrow",[1115,6415,6416],{"class":1161}," =",[1115,6418,6419],{"class":1173}," 4",[1115,6421,1177],{"class":1161},[1115,6423,6424],{"class":1157}," byrow",[1115,6426,6416],{"class":1161},[1115,6428,6429],{"class":1173}," TRUE",[1115,6431,6356],{"class":1161},[1115,6433,6434,6437,6439,6442],{"class":1154,"line":89},[1115,6435,6436],{"class":1157},"               dimnames",[1115,6438,6416],{"class":1161},[1115,6440,6441],{"class":1165}," list",[1115,6443,6444],{"class":1169},"(\n",[1115,6446,6447,6450,6452,6454,6456,6460,6462,6465,6467,6470,6472,6475,6477],{"class":1154,"line":82},[1115,6448,6449],{"class":1157},"                 vzdelani",[1115,6451,6416],{"class":1161},[1115,6453,1166],{"class":1165},[1115,6455,1170],{"class":1169},[1115,6457,6459],{"class":6458},"sIIMD","\"SS bez maturity\"",[1115,6461,1177],{"class":1161},[1115,6463,6464],{"class":6458}," \"SS s maturitou nebo VOS\"",[1115,6466,1177],{"class":1161},[1115,6468,6469],{"class":6458}," \"VS\"",[1115,6471,1177],{"class":1161},[1115,6473,6474],{"class":6458}," \"ZS\"",[1115,6476,1603],{"class":1169},[1115,6478,6356],{"class":1161},[1115,6480,6481,6484,6487,6489,6491,6494,6496,6499,6501,6504],{"class":1154,"line":75},[1115,6482,6483],{"class":1157},"                 nakup",[1115,6485,6486],{"class":1161},"    =",[1115,6488,1166],{"class":1165},[1115,6490,1170],{"class":1169},[1115,6492,6493],{"class":6458},"\"ano\"",[1115,6495,1177],{"class":1161},[1115,6497,6498],{"class":6458}," \"ne, ale planuji\"",[1115,6500,1177],{"class":1161},[1115,6502,6503],{"class":6458}," \"ne, neplanuji\"",[1115,6505,6506],{"class":1169},")))\n",[1115,6508,6510,6513,6515,6517],{"class":1154,"line":6509},9,[1115,6511,6512],{"class":1165},"chisq.test",[1115,6514,1170],{"class":1169},[1115,6516,6330],{"class":1157},[1115,6518,6519],{"class":1169},")\n",[1115,6521,6522,6524,6526,6528,6530,6532],{"class":1154,"line":72},[1115,6523,6512],{"class":1165},[1115,6525,1170],{"class":1169},[1115,6527,6330],{"class":1157},[1115,6529,1603],{"class":1169},[1115,6531,1290],{"class":1161},[1115,6533,6534],{"class":1157},"expected\n",[1144,6536,6541],{"className":6537,"code":6539,"language":6540,"meta":1148},[6538],"language-text","    Pearson's Chi-squared test\n\ndata:  tab1\nX-squared = 5.4875, df = 6, p-value = 0.483\n\n                         nakup\nvzdelani                        ano ne, ale planuji ne, neplanuji\n  SS bez maturity          6.176623       10.696104      12.12727\n  SS s maturitou nebo VOS 34.929870       60.488312      68.58182\n  VS                      35.781818       61.963636      70.25455\n  ZS                       5.111688        8.851948      10.03636\n","text",[1150,6542,6539],{"__ignoreMap":1148},[1110,6544,6545,6546,6569,6570,6584,6585,6605,6606,6623],{},"Všechny očekávané četnosti jsou nad 5, aproximace je v pořádku. Testové kritérium ",[1115,6547,6549],{"className":6548},[1573],[1575,6550,6551],{"xmlns":1577},[1579,6552,6553,6566],{},[1582,6554,6555,6561,6563],{},[1986,6556,6557,6559],{},[1585,6558,2130],{},[1716,6560,1993],{},[1589,6562,1597],{},[1716,6564,6565],{},"5,49",[1605,6567,6568],{"encoding":1607},"\\chi^2 = 5{,}49"," s ",[1115,6571,6573],{"className":6572},[1573],[1575,6574,6575],{"xmlns":1577},[1579,6576,6577,6582],{},[1582,6578,6579],{},[1716,6580,6581],{},"6",[1605,6583,6581],{"encoding":1607}," stupni\nvolnosti dává p-hodnotu ",[1115,6586,6588],{"className":6587},[1573],[1575,6589,6590],{"xmlns":1577},[1579,6591,6592,6602],{},[1582,6593,6594,6597,6599],{},[1716,6595,6596],{},"0,483",[1589,6598,1698],{},[1716,6600,6601],{},"0,05",[1605,6603,6604],{"encoding":1607},"0{,}483 > 0{,}05",": ",[1115,6607,6609],{"className":6608},[1573],[1575,6610,6611],{"xmlns":1577},[1579,6612,6613,6621],{},[1582,6614,6615],{},[1746,6616,6617,6619],{},[1585,6618,1922],{},[1716,6620,2398],{},[1605,6622,4225],{"encoding":1607}," nezamítáme, závislost mezi zkušeností s nákupem potravin na\ninternetu a vzděláním respondenta se neprokázala.",[1103,6625,6627,6634,6637,6682],{"className":6626,"dataCallout":6105},[1106,6104],[1110,6628,6630,6633],{"className":6629},[1113],[1115,6631],{"className":6632,"ariaHidden":1121},[1118,6112,1120],"Příklad: vzdělání a zveřejňování citlivých údajů na Facebooku",[1110,6635,6636],{},"Mezi 221 osobami bylo zaznamenáno vzdělání a zda zveřejňují na Facebooku citlivé údaje. Proveďte test\nnezávislosti.",[1310,6638,6639,6653],{},[1313,6640,6641],{},[1316,6642,6643,6646,6649,6651],{},[1319,6644,6645],{},"zveřejňuje \\ vzdělání",[1319,6647,6648],{},"SŠ",[1319,6650,6200],{},[1319,6652,6217],{},[1332,6654,6655,6669],{},[1316,6656,6657,6660,6663,6666],{},[1337,6658,6659],{},"ne",[1337,6661,6662],{},"20",[1337,6664,6665],{},"33",[1337,6667,6668],{},"39",[1316,6670,6671,6673,6676,6679],{},[1337,6672,6131],{},[1337,6674,6675],{},"25",[1337,6677,6678],{},"28",[1337,6680,6681],{},"76",[1110,6683,6684,6735],{},[1115,6685,6687],{"className":6686},[1573],[1575,6688,6689],{"xmlns":1577},[1579,6690,6691,6733],{},[1582,6692,6693,6699,6701,6711,6713,6723],{},[1746,6694,6695,6697],{},[1585,6696,1922],{},[1716,6698,2398],{},[1589,6700,4595],{},[1746,6702,6703,6705],{},[1585,6704,1110],{},[1582,6706,6707,6709],{},[1585,6708,1776],{},[1585,6710,4521],{},[1589,6712,1597],{},[1746,6714,6715,6717],{},[1585,6716,1110],{},[1582,6718,6719,6721],{},[1585,6720,1776],{},[1589,6722,4616],{},[1746,6724,6725,6727],{},[1585,6726,1110],{},[1582,6728,6729,6731],{},[1589,6730,4616],{},[1585,6732,4521],{},[1605,6734,6319],{"encoding":1607}," — vzdělání a zveřejňování citlivých údajů jsou na sobě nezávislé.",[1144,6737,6739],{"className":1146,"code":6738,"language":71,"meta":1148,"style":1148},"tab2 \u003C- matrix(c(20, 33, 39,\n                 25, 28, 76),\n               nrow = 2, byrow = TRUE,\n               dimnames = list(\n                 zverejnuje = c(\"ne\", \"ano\"),\n                 vzdelani   = c(\"SS\", \"VS\", \"ZS\")))\nchisq.test(tab2)\nchisq.test(tab2)$expected\n",[1150,6740,6741,6770,6789,6808,6818,6841,6865,6875],{"__ignoreMap":1148},[1115,6742,6743,6746,6748,6750,6752,6754,6756,6758,6760,6763,6765,6768],{"class":1154,"line":10},[1115,6744,6745],{"class":1157},"tab2",[1115,6747,1162],{"class":1161},[1115,6749,6335],{"class":1165},[1115,6751,1170],{"class":1169},[1115,6753,3499],{"class":1165},[1115,6755,1170],{"class":1169},[1115,6757,6662],{"class":1173},[1115,6759,1177],{"class":1161},[1115,6761,6762],{"class":1173}," 33",[1115,6764,1177],{"class":1161},[1115,6766,6767],{"class":1173}," 39",[1115,6769,6356],{"class":1161},[1115,6771,6772,6775,6777,6780,6782,6785,6787],{"class":1154,"line":27},[1115,6773,6774],{"class":1173},"                 25",[1115,6776,1177],{"class":1161},[1115,6778,6779],{"class":1173}," 28",[1115,6781,1177],{"class":1161},[1115,6783,6784],{"class":1173}," 76",[1115,6786,1603],{"class":1169},[1115,6788,6356],{"class":1161},[1115,6790,6791,6793,6795,6798,6800,6802,6804,6806],{"class":1154,"line":148},[1115,6792,6413],{"class":1157},[1115,6794,6416],{"class":1161},[1115,6796,6797],{"class":1173}," 2",[1115,6799,1177],{"class":1161},[1115,6801,6424],{"class":1157},[1115,6803,6416],{"class":1161},[1115,6805,6429],{"class":1173},[1115,6807,6356],{"class":1161},[1115,6809,6810,6812,6814,6816],{"class":1154,"line":111},[1115,6811,6436],{"class":1157},[1115,6813,6416],{"class":1161},[1115,6815,6441],{"class":1165},[1115,6817,6444],{"class":1169},[1115,6819,6820,6823,6825,6827,6829,6832,6834,6837,6839],{"class":1154,"line":96},[1115,6821,6822],{"class":1157},"                 zverejnuje",[1115,6824,6416],{"class":1161},[1115,6826,1166],{"class":1165},[1115,6828,1170],{"class":1169},[1115,6830,6831],{"class":6458},"\"ne\"",[1115,6833,1177],{"class":1161},[1115,6835,6836],{"class":6458}," \"ano\"",[1115,6838,1603],{"class":1169},[1115,6840,6356],{"class":1161},[1115,6842,6843,6845,6848,6850,6852,6855,6857,6859,6861,6863],{"class":1154,"line":89},[1115,6844,6449],{"class":1157},[1115,6846,6847],{"class":1161},"   =",[1115,6849,1166],{"class":1165},[1115,6851,1170],{"class":1169},[1115,6853,6854],{"class":6458},"\"SS\"",[1115,6856,1177],{"class":1161},[1115,6858,6469],{"class":6458},[1115,6860,1177],{"class":1161},[1115,6862,6474],{"class":6458},[1115,6864,6506],{"class":1169},[1115,6866,6867,6869,6871,6873],{"class":1154,"line":82},[1115,6868,6512],{"class":1165},[1115,6870,1170],{"class":1169},[1115,6872,6745],{"class":1157},[1115,6874,6519],{"class":1169},[1115,6876,6877,6879,6881,6883,6885,6887],{"class":1154,"line":75},[1115,6878,6512],{"class":1165},[1115,6880,1170],{"class":1169},[1115,6882,6745],{"class":1157},[1115,6884,1603],{"class":1169},[1115,6886,1290],{"class":1161},[1115,6888,6534],{"class":1157},[1144,6890,6893],{"className":6891,"code":6892,"language":6540,"meta":1148},[6538],"    Pearson's Chi-squared test\n\ndata:  tab2\nX-squared = 6.8677, df = 2, p-value = 0.03226\n\n          vzdelani\nzverejnuje       SS       VS      ZS\n       ne  18.73303 25.39367 47.8733\n       ano 26.26697 35.60633 67.1267\n",[1150,6894,6892],{"__ignoreMap":1148},[1110,6896,6897,6898,6569,6921,6934,6935,6605,6955,6972,6973,2264],{},"I zde jsou všechny očekávané četnosti nad 5. Testové kritérium ",[1115,6899,6901],{"className":6900},[1573],[1575,6902,6903],{"xmlns":1577},[1579,6904,6905,6918],{},[1582,6906,6907,6913,6915],{},[1986,6908,6909,6911],{},[1585,6910,2130],{},[1716,6912,1993],{},[1589,6914,1597],{},[1716,6916,6917],{},"6,87",[1605,6919,6920],{"encoding":1607},"\\chi^2 = 6{,}87",[1115,6922,6924],{"className":6923},[1573],[1575,6925,6926],{"xmlns":1577},[1579,6927,6928,6932],{},[1582,6929,6930],{},[1716,6931,1993],{},[1605,6933,1993],{"encoding":1607}," stupni volnosti dává\np-hodnotu ",[1115,6936,6938],{"className":6937},[1573],[1575,6939,6940],{"xmlns":1577},[1579,6941,6942,6952],{},[1582,6943,6944,6947,6950],{},[1716,6945,6946],{},"0,032",[1589,6948,6949],{},"\u003C",[1716,6951,6601],{},[1605,6953,6954],{"encoding":1607},"0{,}032 \u003C 0{,}05",[1115,6956,6958],{"className":6957},[1573],[1575,6959,6960],{"xmlns":1577},[1579,6961,6962,6970],{},[1582,6963,6964],{},[1746,6965,6966,6968],{},[1585,6967,1922],{},[1716,6969,2398],{},[1605,6971,4225],{"encoding":1607}," zamítáme — na rozdíl od předchozího příkladu tady vzdělání a zveřejňování\ncitlivých údajů na Facebooku na sobě ",[2227,6974,6975],{},"závisí",[1110,6977,6978,6979,6996],{},"Srovnání pozorovaných a očekávaných četností ukazuje, proč jeden příklad ",[1115,6980,6982],{"className":6981},[1573],[1575,6983,6984],{"xmlns":1577},[1579,6985,6986,6994],{},[1582,6987,6988],{},[1746,6989,6990,6992],{},[1585,6991,1922],{},[1716,6993,2398],{},[1605,6995,4225],{"encoding":1607}," nezamítá a druhý ano — ve druhém\nse pozorované sloupce (zejména u ZŠ) systematicky odchylují od očekávaných, v prvním kolísají jen náhodně kolem nich:",[1110,6998,6999],{},[1303,7000],{"alt":7001,"className":7002,"src":7003},"mask-kt-observed-expected",[1130,1307],"\u002Fwiki-assets\u002Fmask-kt-observed-expected.png",[1110,7005,7006,7007,7024,7025,4595],{},"Totéž je vidět na rozdělení testového kritéria: u prvního příkladu leží ",[1115,7008,7010],{"className":7009},[1573],[1575,7011,7012],{"xmlns":1577},[1579,7013,7014,7022],{},[1582,7015,7016],{},[1986,7017,7018,7020],{},[1585,7019,2130],{},[1716,7021,1993],{},[1605,7023,2347],{"encoding":1607}," hluboko pod kritickou hodnotou,\nu druhého uvnitř kritického oboru ",[1115,7026,7028],{"className":7027},[1573],[1575,7029,7030],{"xmlns":1577},[1579,7031,7032,7036],{},[1582,7033,7034],{},[1585,7035,4256],{},[1605,7037,4256],{"encoding":1607},[1110,7039,7040],{},[1303,7041],{"alt":7042,"className":7043,"src":7044},"mask-kt-chi2-kriticky-obor",[1130,1307],"\u002Fwiki-assets\u002Fmask-kt-chi2-kriticky-obor.png",[1136,7046,4304],{"id":7047},"cramérův-koeficient-kontingence",[1110,7049,7050,7051,4595],{},"Test nezávislosti pouze rozhodne, zda jsou znaky závislé, nebo ne. Sílu závislosti měří ",[2227,7052,7053],{},"Cramérův koeficient\nkontingence",[1115,7055,7057],{"className":7056},[1573],[1575,7058,7059],{"xmlns":1577,"display":4601},[1579,7060,7061,7116],{},[1582,7062,7063,7065,7067,7092,7094,7096,7098,7100,7103,7106,7108,7110,7112,7114],{},[1585,7064,3301],{},[1589,7066,1597],{},[7068,7069,7070],"msqrt",{},[5373,7071,7072,7078],{},[1986,7073,7074,7076],{},[1585,7075,2130],{},[1716,7077,1993],{},[1582,7079,7080,7082,7084,7086,7088,7090],{},[1585,7081,1781],{},[1589,7083,1170],{"stretchy":1591},[1585,7085,3674],{},[1589,7087,1721],{},[1716,7089,1718],{},[1589,7091,1603],{"stretchy":1591},[1589,7093,1177],{"separator":1121},[4648,7095],{"width":4650},[1585,7097,3674],{},[1589,7099,1597],{},[1585,7101,7102],{},"min",[1589,7104,7105],{},"⁡",[1589,7107,1170],{"stretchy":1591},[1585,7109,71],{},[1589,7111,1177],{"separator":1121},[1585,7113,3433],{},[1589,7115,1603],{"stretchy":1591},[1605,7117,7118],{"encoding":1607},"V = \\sqrt{\\frac{\\chi^2}{n(m-1)}}, \\qquad m = \\min(r, s)",[1110,7120,7121,7122,7139,7140,7158,7159,7177],{},"kde ",[1115,7123,7125],{"className":7124},[1573],[1575,7126,7127],{"xmlns":1577},[1579,7128,7129,7137],{},[1582,7130,7131],{},[1986,7132,7133,7135],{},[1585,7134,2130],{},[1716,7136,1993],{},[1605,7138,2347],{"encoding":1607}," je hodnota testového kritéria z testu nezávislosti. ",[1115,7141,7143],{"className":7142},[1573],[1575,7144,7145],{"xmlns":1577},[1579,7146,7147,7155],{},[1582,7148,7149,7151,7153],{},[1585,7150,3301],{},[1589,7152,1597],{},[1716,7154,2398],{},[1605,7156,7157],{"encoding":1607},"V = 0"," odpovídá úplné nezávislosti znaků,\n",[1115,7160,7162],{"className":7161},[1573],[1575,7163,7164],{"xmlns":1577},[1579,7165,7166,7174],{},[1582,7167,7168,7170,7172],{},[1585,7169,3301],{},[1589,7171,1597],{},[1716,7173,1718],{},[1605,7175,7176],{"encoding":1607},"V = 1"," jejich úplné závislosti.",[1144,7179,7181],{"className":1146,"code":7180,"language":71,"meta":1148,"style":1148},"V1 \u003C- sqrt(as.numeric(chisq.test(tab1)$statistic) \u002F (sum(tab1) * (min(dim(tab1)) - 1)))\nV2 \u003C- sqrt(as.numeric(chisq.test(tab2)$statistic) \u002F (sum(tab2) * (min(dim(tab2)) - 1)))\nV1\nV2\n",[1150,7182,7183,7256,7318,7323],{"__ignoreMap":1148},[1115,7184,7185,7187,7189,7192,7194,7197,7199,7201,7203,7205,7207,7209,7212,7215,7217,7220,7223,7225,7227,7229,7232,7234,7236,7238,7241,7243,7245,7248,7251,7254],{"class":1154,"line":10},[1115,7186,1278],{"class":1157},[1115,7188,1162],{"class":1161},[1115,7190,7191],{"class":1165}," sqrt",[1115,7193,1170],{"class":1169},[1115,7195,7196],{"class":1165},"as.numeric",[1115,7198,1170],{"class":1169},[1115,7200,6512],{"class":1165},[1115,7202,1170],{"class":1169},[1115,7204,6330],{"class":1157},[1115,7206,1603],{"class":1169},[1115,7208,1290],{"class":1161},[1115,7210,7211],{"class":1157},"statistic",[1115,7213,7214],{"class":1169},") ",[1115,7216,4023],{"class":1161},[1115,7218,7219],{"class":1169}," (",[1115,7221,7222],{"class":1165},"sum",[1115,7224,1170],{"class":1169},[1115,7226,6330],{"class":1157},[1115,7228,7214],{"class":1169},[1115,7230,7231],{"class":1161},"*",[1115,7233,7219],{"class":1169},[1115,7235,7102],{"class":1165},[1115,7237,1170],{"class":1169},[1115,7239,7240],{"class":1165},"dim",[1115,7242,1170],{"class":1169},[1115,7244,6330],{"class":1157},[1115,7246,7247],{"class":1169},")) ",[1115,7249,7250],{"class":1161},"-",[1115,7252,7253],{"class":1173}," 1",[1115,7255,6506],{"class":1169},[1115,7257,7258,7260,7262,7264,7266,7268,7270,7272,7274,7276,7278,7280,7282,7284,7286,7288,7290,7292,7294,7296,7298,7300,7302,7304,7306,7308,7310,7312,7314,7316],{"class":1154,"line":27},[1115,7259,1282],{"class":1157},[1115,7261,1162],{"class":1161},[1115,7263,7191],{"class":1165},[1115,7265,1170],{"class":1169},[1115,7267,7196],{"class":1165},[1115,7269,1170],{"class":1169},[1115,7271,6512],{"class":1165},[1115,7273,1170],{"class":1169},[1115,7275,6745],{"class":1157},[1115,7277,1603],{"class":1169},[1115,7279,1290],{"class":1161},[1115,7281,7211],{"class":1157},[1115,7283,7214],{"class":1169},[1115,7285,4023],{"class":1161},[1115,7287,7219],{"class":1169},[1115,7289,7222],{"class":1165},[1115,7291,1170],{"class":1169},[1115,7293,6745],{"class":1157},[1115,7295,7214],{"class":1169},[1115,7297,7231],{"class":1161},[1115,7299,7219],{"class":1169},[1115,7301,7102],{"class":1165},[1115,7303,1170],{"class":1169},[1115,7305,7240],{"class":1165},[1115,7307,1170],{"class":1169},[1115,7309,6745],{"class":1157},[1115,7311,7247],{"class":1169},[1115,7313,7250],{"class":1161},[1115,7315,7253],{"class":1173},[1115,7317,6506],{"class":1169},[1115,7319,7320],{"class":1154,"line":148},[1115,7321,7322],{"class":1157},"V1\n",[1115,7324,7325],{"class":1154,"line":111},[1115,7326,7327],{"class":1157},"V2\n",[1144,7329,7332],{"className":7330,"code":7331,"language":6540,"meta":1148},[6538],"[1] 0.08441958\n[1] 0.1762822\n",[1150,7333,7331],{"__ignoreMap":1148},[1110,7335,7336],{},[1303,7337],{"alt":7338,"className":7339,"src":7340},"mask-kt-cramerovo-v",[1130,1307],"\u002Fwiki-assets\u002Fmask-kt-cramerovo-v.png",[1110,7342,7343,7344,7363,7364,7381,7382,6605,7401,7418],{},"U nákupu potravin je ",[1115,7345,7347],{"className":7346},[1573],[1575,7348,7349],{"xmlns":1577},[1579,7350,7351,7360],{},[1582,7352,7353,7355,7357],{},[1585,7354,3301],{},[1589,7356,1597],{},[1716,7358,7359],{},"0,084",[1605,7361,7362],{"encoding":1607},"V = 0{,}084"," zanedbatelné — ostatně ",[1115,7365,7367],{"className":7366},[1573],[1575,7368,7369],{"xmlns":1577},[1579,7370,7371,7379],{},[1582,7372,7373],{},[1746,7374,7375,7377],{},[1585,7376,1922],{},[1716,7378,2398],{},[1605,7380,4225],{"encoding":1607}," jsme ani nezamítli. U zveřejňování údajů je ",[1115,7383,7385],{"className":7384},[1573],[1575,7386,7387],{"xmlns":1577},[1579,7388,7389,7398],{},[1582,7390,7391,7393,7395],{},[1585,7392,3301],{},[1589,7394,1597],{},[1716,7396,7397],{},"0,176",[1605,7399,7400],{"encoding":1607},"V = 0{,}176",[1115,7402,7404],{"className":7403},[1573],[1575,7405,7406],{"xmlns":1577},[1579,7407,7408,7416],{},[1582,7409,7410],{},[1746,7411,7412,7414],{},[1585,7413,1922],{},[1716,7415,2398],{},[1605,7417,4225],{"encoding":1607},"\njsme zamítli, ale samotná závislost je stále slabá.",[1136,7420,4322],{"id":7421},"čtyřpolní-tabulka",[1110,7423,7424,7426,7427,7440,7441,7454,7455,7477],{},[2227,7425,4322],{}," je speciální případ kontingenční tabulky, kdy oba znaky ",[1115,7428,7430],{"className":7429},[1573],[1575,7431,7432],{"xmlns":1577},[1579,7433,7434,7438],{},[1582,7435,7436],{},[1585,7437,4420],{},[1605,7439,4420],{"encoding":1607}," i ",[1115,7442,7444],{"className":7443},[1573],[1575,7445,7446],{"xmlns":1577},[1579,7447,7448,7452],{},[1582,7449,7450],{},[1585,7451,1773],{},[1605,7453,1773],{"encoding":1607}," mají jen dvě varianty\n(",[1115,7456,7458],{"className":7457},[1573],[1575,7459,7460],{"xmlns":1577},[1579,7461,7462,7474],{},[1582,7463,7464,7466,7468,7470,7472],{},[1585,7465,71],{},[1589,7467,1597],{},[1585,7469,3433],{},[1589,7471,1597],{},[1716,7473,1993],{},[1605,7475,7476],{"encoding":1607},"r = s = 2","):",[1310,7479,7480,7564],{},[1313,7481,7482],{},[1316,7483,7484,7503,7522,7541],{},[1319,7485,7486],{},[1115,7487,7489],{"className":7488},[1573],[1575,7490,7491],{"xmlns":1577},[1579,7492,7493,7501],{},[1582,7494,7495,7497,7499],{},[1585,7496,4420],{},[1585,7498,4757],{"mathvariant":4022},[1585,7500,1773],{},[1605,7502,4762],{"encoding":1607},[1319,7504,7505],{},[1115,7506,7508],{"className":7507},[1573],[1575,7509,7510],{"xmlns":1577},[1579,7511,7512,7520],{},[1582,7513,7514],{},[1746,7515,7516,7518],{},[1585,7517,1773],{},[1716,7519,1718],{},[1605,7521,4782],{"encoding":1607},[1319,7523,7524],{},[1115,7525,7527],{"className":7526},[1573],[1575,7528,7529],{"xmlns":1577},[1579,7530,7531,7539],{},[1582,7532,7533],{},[1746,7534,7535,7537],{},[1585,7536,1773],{},[1716,7538,1993],{},[1605,7540,4802],{"encoding":1607},[1319,7542,7543],{},[1115,7544,7546],{"className":7545},[1573],[1575,7547,7548],{"xmlns":1577},[1579,7549,7550,7562],{},[1582,7551,7552],{},[1746,7553,7554,7556],{},[1585,7555,1781],{},[1582,7557,7558,7560],{},[1585,7559,1776],{},[1589,7561,4616],{},[1605,7563,4848],{"encoding":1607},[1332,7565,7566,7648,7730],{},[1316,7567,7568,7587,7606,7625],{},[1337,7569,7570],{},[1115,7571,7573],{"className":7572},[1573],[1575,7574,7575],{"xmlns":1577},[1579,7576,7577,7585],{},[1582,7578,7579],{},[1746,7580,7581,7583],{},[1585,7582,4420],{},[1716,7584,1718],{},[1605,7586,4872],{"encoding":1607},[1337,7588,7589],{},[1115,7590,7592],{"className":7591},[1573],[1575,7593,7594],{"xmlns":1577},[1579,7595,7596,7604],{},[1582,7597,7598],{},[1746,7599,7600,7602],{},[1585,7601,1781],{},[1716,7603,4890],{},[1605,7605,4893],{"encoding":1607},[1337,7607,7608],{},[1115,7609,7611],{"className":7610},[1573],[1575,7612,7613],{"xmlns":1577},[1579,7614,7615,7623],{},[1582,7616,7617],{},[1746,7618,7619,7621],{},[1585,7620,1781],{},[1716,7622,4911],{},[1605,7624,4914],{"encoding":1607},[1337,7626,7627],{},[1115,7628,7630],{"className":7629},[1573],[1575,7631,7632],{"xmlns":1577},[1579,7633,7634,7646],{},[1582,7635,7636],{},[1746,7637,7638,7640],{},[1585,7639,1781],{},[1582,7641,7642,7644],{},[1716,7643,1718],{},[1589,7645,4616],{},[1605,7647,4964],{"encoding":1607},[1316,7649,7650,7669,7688,7707],{},[1337,7651,7652],{},[1115,7653,7655],{"className":7654},[1573],[1575,7656,7657],{"xmlns":1577},[1579,7658,7659,7667],{},[1582,7660,7661],{},[1746,7662,7663,7665],{},[1585,7664,4420],{},[1716,7666,1993],{},[1605,7668,4986],{"encoding":1607},[1337,7670,7671],{},[1115,7672,7674],{"className":7673},[1573],[1575,7675,7676],{"xmlns":1577},[1579,7677,7678,7686],{},[1582,7679,7680],{},[1746,7681,7682,7684],{},[1585,7683,1781],{},[1716,7685,5004],{},[1605,7687,5007],{"encoding":1607},[1337,7689,7690],{},[1115,7691,7693],{"className":7692},[1573],[1575,7694,7695],{"xmlns":1577},[1579,7696,7697,7705],{},[1582,7698,7699],{},[1746,7700,7701,7703],{},[1585,7702,1781],{},[1716,7704,5025],{},[1605,7706,5028],{"encoding":1607},[1337,7708,7709],{},[1115,7710,7712],{"className":7711},[1573],[1575,7713,7714],{"xmlns":1577},[1579,7715,7716,7728],{},[1582,7717,7718],{},[1746,7719,7720,7722],{},[1585,7721,1781],{},[1582,7723,7724,7726],{},[1716,7725,1993],{},[1589,7727,4616],{},[1605,7729,5078],{"encoding":1607},[1316,7731,7732,7755,7778,7801],{},[1337,7733,7734],{},[1115,7735,7737],{"className":7736},[1573],[1575,7738,7739],{"xmlns":1577},[1579,7740,7741,7753],{},[1582,7742,7743],{},[1746,7744,7745,7747],{},[1585,7746,1781],{},[1582,7748,7749,7751],{},[1589,7750,4616],{},[1585,7752,4521],{},[1605,7754,5240],{"encoding":1607},[1337,7756,7757],{},[1115,7758,7760],{"className":7759},[1573],[1575,7761,7762],{"xmlns":1577},[1579,7763,7764,7776],{},[1582,7765,7766],{},[1746,7767,7768,7770],{},[1585,7769,1781],{},[1582,7771,7772,7774],{},[1589,7773,4616],{},[1716,7775,1718],{},[1605,7777,5264],{"encoding":1607},[1337,7779,7780],{},[1115,7781,7783],{"className":7782},[1573],[1575,7784,7785],{"xmlns":1577},[1579,7786,7787,7799],{},[1582,7788,7789],{},[1746,7790,7791,7793],{},[1585,7792,1781],{},[1582,7794,7795,7797],{},[1589,7796,4616],{},[1716,7798,1993],{},[1605,7800,5288],{"encoding":1607},[1337,7802,7803],{},[1115,7804,7806],{"className":7805},[1573],[1575,7807,7808],{"xmlns":1577},[1579,7809,7810,7814],{},[1582,7811,7812],{},[1585,7813,1781],{},[1605,7815,1781],{"encoding":1607},[1110,7817,4345,7818,7836],{},[1115,7819,7821],{"className":7820},[1573],[1575,7822,7823],{"xmlns":1577},[1579,7824,7825,7833],{},[1582,7826,7827,7829,7831],{},[1585,7828,1781],{},[1589,7830,1698],{},[1716,7832,4339],{},[1605,7834,7835],{"encoding":1607},"n > 40"," se místo obecného vzorce používá zjednodušená varianta testového kritéria:",[1115,7838,7840],{"className":7839},[1573],[1575,7841,7842],{"xmlns":1577,"display":4601},[1579,7843,7844,7938],{},[1582,7845,7846,7852,7854,7856,7858],{},[1986,7847,7848,7850],{},[1585,7849,2130],{},[1716,7851,1993],{},[1589,7853,1597],{},[1585,7855,1781],{},[5543,7857,5545],{},[5373,7859,7860,7896],{},[1582,7861,7862,7864,7870,7876,7878,7884,7890],{},[1589,7863,1170],{"stretchy":1591},[1746,7865,7866,7868],{},[1585,7867,1781],{},[1716,7869,4890],{},[1746,7871,7872,7874],{},[1585,7873,1781],{},[1716,7875,5025],{},[1589,7877,1721],{},[1746,7879,7880,7882],{},[1585,7881,1781],{},[1716,7883,4911],{},[1746,7885,7886,7888],{},[1585,7887,1781],{},[1716,7889,5004],{},[1986,7891,7892,7894],{},[1589,7893,1603],{"stretchy":1591},[1716,7895,1993],{},[1582,7897,7898,7908,7918,7928],{},[1746,7899,7900,7902],{},[1585,7901,1781],{},[1582,7903,7904,7906],{},[1716,7905,1718],{},[1589,7907,4616],{},[1746,7909,7910,7912],{},[1585,7911,1781],{},[1582,7913,7914,7916],{},[1716,7915,1993],{},[1589,7917,4616],{},[1746,7919,7920,7922],{},[1585,7921,1781],{},[1582,7923,7924,7926],{},[1589,7925,4616],{},[1716,7927,1718],{},[1746,7929,7930,7932],{},[1585,7931,1781],{},[1582,7933,7934,7936],{},[1589,7935,4616],{},[1716,7937,1993],{},[1605,7939,7940],{"encoding":1607},"\\chi^2 = n\\,\\frac{(n_{11}n_{22} - n_{12}n_{21})^2}{n_{1\\bullet}n_{2\\bullet}n_{\\bullet 1}n_{\\bullet 2}}",[1110,7942,7943,7944,8004,8005,8041,8042,8044,8045,8047],{},"s kritickým oborem ",[1115,7945,7947],{"className":7946},[1573],[1575,7948,7949],{"xmlns":1577},[1579,7950,7951,8001],{},[1582,7952,7953,7959,7961,7963,7969,7971,7977,7979,7993,7995,7997,7999],{},[1746,7954,7955,7957],{},[1585,7956,4256],{},[1585,7958,3862],{},[1589,7960,1597],{},[1589,7962,5966],{"stretchy":1591},[1986,7964,7965,7967],{},[1585,7966,2130],{},[1716,7968,1993],{},[1589,7970,4595],{},[1986,7972,7973,7975],{},[1585,7974,2130],{},[1716,7976,1993],{},[1589,7978,5983],{},[2920,7980,7981,7983,7991],{},[1585,7982,2130],{},[1582,7984,7985,7987,7989],{},[1716,7986,1718],{},[1589,7988,1721],{},[1585,7990,3862],{},[1716,7992,1993],{},[1589,7994,1170],{"stretchy":1591},[1716,7996,1718],{},[1589,7998,1603],{"stretchy":1591},[1589,8000,6024],{"stretchy":1591},[1605,8002,8003],{"encoding":1607},"W_\\alpha = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}(1)\\}"," — formálně jde o stejný test\nnezávislosti jako výše, jen dosazený do zjednodušeného tvaru pro ",[1115,8006,8008],{"className":8007},[1573],[1575,8009,8010],{"xmlns":1577},[1579,8011,8012,8038],{},[1582,8013,8014,8016,8018,8020,8022,8024,8026,8028,8030,8032,8034,8036],{},[1589,8015,1170],{"stretchy":1591},[1585,8017,71],{},[1589,8019,1721],{},[1716,8021,1718],{},[1589,8023,1603],{"stretchy":1591},[1589,8025,1170],{"stretchy":1591},[1585,8027,3433],{},[1589,8029,1721],{},[1716,8031,1718],{},[1589,8033,1603],{"stretchy":1591},[1589,8035,1597],{},[1716,8037,1718],{},[1605,8039,8040],{"encoding":1607},"(r-1)(s-1) = 1"," stupeň volnosti. V R dává tuto hodnotu ",[1150,8043,3266],{},". Bez ",[1150,8046,3721],{}," R u tabulky 2 × 2 použije Yatesovu korekci na kontinuitu a testové kritérium vyjde menší.",[1136,8049,4352],{"id":8050},"mcnemarův-test",[1110,8052,8053,8054,8057,8058,8060,8061,8064,8065,8068,8069,8071],{},"Čtyřpolní tabulka z předchozí sekce porovnává dva ",[2227,8055,8056],{},"různé"," znaky na stejném souboru. ",[2227,8059,4352],{}," řeší\njinou situaci: na prvcích základního souboru se měří ",[2227,8062,8063],{},"jeden"," alternativní znak, a to ",[2227,8066,8067],{},"dvakrát"," — před a po\nnějakém zásahu. Cílem je zjistit, zda zásah změnil pravděpodobnostní rozdělení variant tohoto znaku. Jde tedy o\n",[2227,8070,4348],{}," (stejné prvky měřené opakovaně), ne o dva nezávisle naměřené znaky.",[1110,8073,8074],{},"Kontingenční tabulka před\u002Fpo má tvar:",[1310,8076,8077,8111],{},[1313,8078,8079],{},[1316,8080,8081,8084,8086,8088],{},[1319,8082,8083],{},"před \\ po",[1319,8085,4010],{},[1319,8087,1721],{},[1319,8089,8090],{},[1115,8091,8093],{"className":8092},[1573],[1575,8094,8095],{"xmlns":1577},[1579,8096,8097,8109],{},[1582,8098,8099],{},[1746,8100,8101,8103],{},[1585,8102,1781],{},[1582,8104,8105,8107],{},[1585,8106,1776],{},[1589,8108,4616],{},[1605,8110,4848],{"encoding":1607},[1332,8112,8113,8178,8243],{},[1316,8114,8115,8117,8136,8155],{},[1337,8116,4010],{},[1337,8118,8119],{},[1115,8120,8122],{"className":8121},[1573],[1575,8123,8124],{"xmlns":1577},[1579,8125,8126,8134],{},[1582,8127,8128],{},[1746,8129,8130,8132],{},[1585,8131,1781],{},[1716,8133,4890],{},[1605,8135,4893],{"encoding":1607},[1337,8137,8138],{},[1115,8139,8141],{"className":8140},[1573],[1575,8142,8143],{"xmlns":1577},[1579,8144,8145,8153],{},[1582,8146,8147],{},[1746,8148,8149,8151],{},[1585,8150,1781],{},[1716,8152,4911],{},[1605,8154,4914],{"encoding":1607},[1337,8156,8157],{},[1115,8158,8160],{"className":8159},[1573],[1575,8161,8162],{"xmlns":1577},[1579,8163,8164,8176],{},[1582,8165,8166],{},[1746,8167,8168,8170],{},[1585,8169,1781],{},[1582,8171,8172,8174],{},[1716,8173,1718],{},[1589,8175,4616],{},[1605,8177,4964],{"encoding":1607},[1316,8179,8180,8182,8201,8220],{},[1337,8181,1721],{},[1337,8183,8184],{},[1115,8185,8187],{"className":8186},[1573],[1575,8188,8189],{"xmlns":1577},[1579,8190,8191,8199],{},[1582,8192,8193],{},[1746,8194,8195,8197],{},[1585,8196,1781],{},[1716,8198,5004],{},[1605,8200,5007],{"encoding":1607},[1337,8202,8203],{},[1115,8204,8206],{"className":8205},[1573],[1575,8207,8208],{"xmlns":1577},[1579,8209,8210,8218],{},[1582,8211,8212],{},[1746,8213,8214,8216],{},[1585,8215,1781],{},[1716,8217,5025],{},[1605,8219,5028],{"encoding":1607},[1337,8221,8222],{},[1115,8223,8225],{"className":8224},[1573],[1575,8226,8227],{"xmlns":1577},[1579,8228,8229,8241],{},[1582,8230,8231],{},[1746,8232,8233,8235],{},[1585,8234,1781],{},[1582,8236,8237,8239],{},[1716,8238,1993],{},[1589,8240,4616],{},[1605,8242,5078],{"encoding":1607},[1316,8244,8245,8268,8291,8314],{},[1337,8246,8247],{},[1115,8248,8250],{"className":8249},[1573],[1575,8251,8252],{"xmlns":1577},[1579,8253,8254,8266],{},[1582,8255,8256],{},[1746,8257,8258,8260],{},[1585,8259,1781],{},[1582,8261,8262,8264],{},[1589,8263,4616],{},[1585,8265,4521],{},[1605,8267,5240],{"encoding":1607},[1337,8269,8270],{},[1115,8271,8273],{"className":8272},[1573],[1575,8274,8275],{"xmlns":1577},[1579,8276,8277,8289],{},[1582,8278,8279],{},[1746,8280,8281,8283],{},[1585,8282,1781],{},[1582,8284,8285,8287],{},[1589,8286,4616],{},[1716,8288,1718],{},[1605,8290,5264],{"encoding":1607},[1337,8292,8293],{},[1115,8294,8296],{"className":8295},[1573],[1575,8297,8298],{"xmlns":1577},[1579,8299,8300,8312],{},[1582,8301,8302],{},[1746,8303,8304,8306],{},[1585,8305,1781],{},[1582,8307,8308,8310],{},[1589,8309,4616],{},[1716,8311,1993],{},[1605,8313,5288],{"encoding":1607},[1337,8315,8316],{},[1115,8317,8319],{"className":8318},[1573],[1575,8320,8321],{"xmlns":1577},[1579,8322,8323,8327],{},[1582,8324,8325],{},[1585,8326,1781],{},[1605,8328,1781],{"encoding":1607},[1110,8330,8331,8332,1260,8349,8366,8367,8370,8371,1260,8388,8405,8406,8409],{},"Pole ",[1115,8333,8335],{"className":8334},[1573],[1575,8336,8337],{"xmlns":1577},[1579,8338,8339,8347],{},[1582,8340,8341],{},[1746,8342,8343,8345],{},[1585,8344,1781],{},[1716,8346,4890],{},[1605,8348,4893],{"encoding":1607},[1115,8350,8352],{"className":8351},[1573],[1575,8353,8354],{"xmlns":1577},[1579,8355,8356,8364],{},[1582,8357,8358],{},[1746,8359,8360,8362],{},[1585,8361,1781],{},[1716,8363,5025],{},[1605,8365,5028],{"encoding":1607}," jsou ",[2227,8368,8369],{},"shodná"," (prvek zůstal ve stejné variantě), pole ",[1115,8372,8374],{"className":8373},[1573],[1575,8375,8376],{"xmlns":1577},[1579,8377,8378,8386],{},[1582,8379,8380],{},[1746,8381,8382,8384],{},[1585,8383,1781],{},[1716,8385,4911],{},[1605,8387,4914],{"encoding":1607},[1115,8389,8391],{"className":8390},[1573],[1575,8392,8393],{"xmlns":1577},[1579,8394,8395,8403],{},[1582,8396,8397],{},[1746,8398,8399,8401],{},[1585,8400,1781],{},[1716,8402,5004],{},[1605,8404,5007],{"encoding":1607}," jsou\n",[2227,8407,8408],{},"diskordantní"," (prvek mezi měřeními variantu změnil) — jen ta rozhodují o výsledku testu:",[1110,8411,8412],{},[1303,8413],{"alt":8414,"className":8415,"src":8416},"mask-kt-mcnemar-tabulka",[1130,1307],"\u002Fwiki-assets\u002Fmask-kt-mcnemar-tabulka.png",[1110,8418,8419],{},[2227,8420,5497],{},[5499,8422,8423,8460,8541,8599],{},[2223,8424,8425,8459],{},[1115,8426,8428],{"className":8427},[1573],[1575,8429,8430],{"xmlns":1577},[1579,8431,8432,8456],{},[1582,8433,8434,8440,8442,8448,8450],{},[1746,8435,8436,8438],{},[1585,8437,1922],{},[1716,8439,2398],{},[1589,8441,4595],{},[1746,8443,8444,8446],{},[1585,8445,1110],{},[1716,8447,4911],{},[1589,8449,1597],{},[1746,8451,8452,8454],{},[1585,8453,1110],{},[1716,8455,5004],{},[1605,8457,8458],{"encoding":1607},"H_0: p_{12} = p_{21}"," — pravděpodobnost přechodu z varianty (+) do (−) je stejná jako pravděpodobnost\npřechodu z (−) do (+); zásah tedy nemá na rozdělení variant žádný vliv.",[2223,8461,5633,8462,8524,8526,8527,8540],{},[1115,8463,8465],{"className":8464},[1573],[1575,8466,8467],{"xmlns":1577,"display":4601},[1579,8468,8469,8521],{},[1582,8470,8471,8477,8479],{},[1986,8472,8473,8475],{},[1585,8474,2130],{},[1716,8476,1993],{},[1589,8478,1597],{},[5373,8480,8481,8505],{},[1582,8482,8483,8485,8491,8493,8499],{},[1589,8484,1170],{"stretchy":1591},[1746,8486,8487,8489],{},[1585,8488,1781],{},[1716,8490,4911],{},[1589,8492,1721],{},[1746,8494,8495,8497],{},[1585,8496,1781],{},[1716,8498,5004],{},[1986,8500,8501,8503],{},[1589,8502,1603],{"stretchy":1591},[1716,8504,1993],{},[1582,8506,8507,8513,8515],{},[1746,8508,8509,8511],{},[1585,8510,1781],{},[1716,8512,4911],{},[1589,8514,4010],{},[1746,8516,8517,8519],{},[1585,8518,1781],{},[1716,8520,5004],{},[1605,8522,8523],{"encoding":1607},"\\chi^2 = \\frac{(n_{12} - n_{21})^2}{n_{12} + n_{21}}",[5791,8525],{},"má asymptoticky Pearsonovo rozdělení o ",[1115,8528,8530],{"className":8529},[1573],[1575,8531,8532],{"xmlns":1577},[1579,8533,8534,8538],{},[1582,8535,8536],{},[1716,8537,1718],{},[1605,8539,1718],{"encoding":1607}," stupni volnosti.",[2223,8542,5950,8543,2264],{},[1115,8544,8546],{"className":8545},[1573],[1575,8547,8548],{"xmlns":1577},[1579,8549,8550,8596],{},[1582,8551,8552,8554,8556,8558,8564,8566,8572,8574,8588,8590,8592,8594],{},[1585,8553,4256],{},[1589,8555,1597],{},[1589,8557,5966],{"stretchy":1591},[1986,8559,8560,8562],{},[1585,8561,2130],{},[1716,8563,1993],{},[1589,8565,4595],{},[1986,8567,8568,8570],{},[1585,8569,2130],{},[1716,8571,1993],{},[1589,8573,5983],{},[2920,8575,8576,8578,8586],{},[1585,8577,2130],{},[1582,8579,8580,8582,8584],{},[1716,8581,1718],{},[1589,8583,1721],{},[1585,8585,3862],{},[1716,8587,1993],{},[1589,8589,1170],{"stretchy":1591},[1716,8591,1718],{},[1589,8593,1603],{"stretchy":1591},[1589,8595,6024],{"stretchy":1591},[1605,8597,8598],{"encoding":1607},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}(1)\\}",[2223,8600,6030,8601,8614,8615,8632,8633,8650],{},[1115,8602,8604],{"className":8603},[1573],[1575,8605,8606],{"xmlns":1577},[1579,8607,8608,8612],{},[1582,8609,8610],{},[1585,8611,4256],{},[1605,8613,4256],{"encoding":1607},", zamítáme ",[1115,8616,8618],{"className":8617},[1573],[1575,8619,8620],{"xmlns":1577},[1579,8621,8622,8630],{},[1582,8623,8624],{},[1746,8625,8626,8628],{},[1585,8627,1922],{},[1716,8629,2398],{},[1605,8631,4225],{"encoding":1607}," a přijímáme ",[1115,8634,8636],{"className":8635},[1573],[1575,8637,8638],{"xmlns":1577},[1579,8639,8640,8648],{},[1582,8641,8642],{},[1746,8643,8644,8646],{},[1585,8645,1922],{},[1716,8647,1718],{},[1605,8649,3807],{"encoding":1607},": zásah rozdělení variant změnil.",[1110,8652,8653,8654,8656,8657,8660,8661,8663],{},"V R počítá tento test funkce ",[1150,8655,3710],{},". Vzorec výše ",[2227,8658,8659],{},"neobsahuje korekci na kontinuitu"," — aby R vrátilo\npřesně tuto hodnotu, musí se volat s ",[1150,8662,3721],{}," (viz Časté chyby níže).",[1103,8665,8667,8674,8677,8680,8777],{"className":8666,"dataCallout":6105},[1106,6104],[1110,8668,8670,8673],{"className":8669},[1113],[1115,8671],{"className":8672,"ariaHidden":1121},[1118,6112,1120],"Příklad: informační kampaň a zveřejňování na Facebooku",[1110,8675,8676],{},"U 170 studentů bylo zjišťováno, zda zveřejňují své údaje na Facebooku. Poté proběhla informační kampaň o\nrizicích zveřejňování a zjišťování se opakovalo. Posuďte, zda měla kampaň vliv na změnu chování studentů.",[1110,8678,8679],{},"Základní soubor: všichni studenti; výběrový soubor: vybraní studenti; měřený znak: zveřejňování (ano \u002F ne).",[1310,8681,8682,8717],{},[1313,8683,8684],{},[1316,8685,8686,8688,8691,8694],{},[1319,8687,8083],{},[1319,8689,8690],{},"nezveřejňuje",[1319,8692,8693],{},"zveřejňuje",[1319,8695,8696],{},[1115,8697,8699],{"className":8698},[1573],[1575,8700,8701],{"xmlns":1577},[1579,8702,8703,8715],{},[1582,8704,8705],{},[1746,8706,8707,8709],{},[1585,8708,1781],{},[1582,8710,8711,8713],{},[1585,8712,1776],{},[1589,8714,4616],{},[1605,8716,4848],{"encoding":1607},[1332,8718,8719,8731,8743],{},[1316,8720,8721,8723,8725,8728],{},[1337,8722,8690],{},[1337,8724,6228],{},[1337,8726,8727],{},"68",[1337,8729,8730],{},"92",[1316,8732,8733,8735,8737,8740],{},[1337,8734,8693],{},[1337,8736,6678],{},[1337,8738,8739],{},"50",[1337,8741,8742],{},"78",[1316,8744,8745,8768,8771,8774],{},[1337,8746,8747],{},[1115,8748,8750],{"className":8749},[1573],[1575,8751,8752],{"xmlns":1577},[1579,8753,8754,8766],{},[1582,8755,8756],{},[1746,8757,8758,8760],{},[1585,8759,1781],{},[1582,8761,8762,8764],{},[1589,8763,4616],{},[1585,8765,4521],{},[1605,8767,5240],{"encoding":1607},[1337,8769,8770],{},"52",[1337,8772,8773],{},"118",[1337,8775,8776],{},"170",[1110,8778,8779,8812],{},[1115,8780,8782],{"className":8781},[1573],[1575,8783,8784],{"xmlns":1577},[1579,8785,8786,8810],{},[1582,8787,8788,8794,8796,8802,8804],{},[1746,8789,8790,8792],{},[1585,8791,1922],{},[1716,8793,2398],{},[1589,8795,4595],{},[1746,8797,8798,8800],{},[1585,8799,1110],{},[1716,8801,4911],{},[1589,8803,1597],{},[1746,8805,8806,8808],{},[1585,8807,1110],{},[1716,8809,5004],{},[1605,8811,8458],{"encoding":1607}," — informační kampaň nemá na chování vliv.",[1144,8814,8816],{"className":1146,"code":8815,"language":71,"meta":1148,"style":1148},"tab3 \u003C- matrix(c(24, 68,\n                 28, 50),\n               nrow = 2, byrow = TRUE,\n               dimnames = list(\n                 pred = c(\"nezverejnuje\", \"zverejnuje\"),\n                 po   = c(\"nezverejnuje\", \"zverejnuje\")))\nmcnemar.test(tab3, correct = FALSE)\n",[1150,8817,8818,8842,8856,8874,8884,8907,8926],{"__ignoreMap":1148},[1115,8819,8820,8823,8825,8827,8829,8831,8833,8835,8837,8840],{"class":1154,"line":10},[1115,8821,8822],{"class":1157},"tab3",[1115,8824,1162],{"class":1161},[1115,8826,6335],{"class":1165},[1115,8828,1170],{"class":1169},[1115,8830,3499],{"class":1165},[1115,8832,1170],{"class":1169},[1115,8834,6228],{"class":1173},[1115,8836,1177],{"class":1161},[1115,8838,8839],{"class":1173}," 68",[1115,8841,6356],{"class":1161},[1115,8843,8844,8847,8849,8852,8854],{"class":1154,"line":27},[1115,8845,8846],{"class":1173},"                 28",[1115,8848,1177],{"class":1161},[1115,8850,8851],{"class":1173}," 50",[1115,8853,1603],{"class":1169},[1115,8855,6356],{"class":1161},[1115,8857,8858,8860,8862,8864,8866,8868,8870,8872],{"class":1154,"line":148},[1115,8859,6413],{"class":1157},[1115,8861,6416],{"class":1161},[1115,8863,6797],{"class":1173},[1115,8865,1177],{"class":1161},[1115,8867,6424],{"class":1157},[1115,8869,6416],{"class":1161},[1115,8871,6429],{"class":1173},[1115,8873,6356],{"class":1161},[1115,8875,8876,8878,8880,8882],{"class":1154,"line":111},[1115,8877,6436],{"class":1157},[1115,8879,6416],{"class":1161},[1115,8881,6441],{"class":1165},[1115,8883,6444],{"class":1169},[1115,8885,8886,8889,8891,8893,8895,8898,8900,8903,8905],{"class":1154,"line":96},[1115,8887,8888],{"class":1157},"                 pred",[1115,8890,6416],{"class":1161},[1115,8892,1166],{"class":1165},[1115,8894,1170],{"class":1169},[1115,8896,8897],{"class":6458},"\"nezverejnuje\"",[1115,8899,1177],{"class":1161},[1115,8901,8902],{"class":6458}," \"zverejnuje\"",[1115,8904,1603],{"class":1169},[1115,8906,6356],{"class":1161},[1115,8908,8909,8912,8914,8916,8918,8920,8922,8924],{"class":1154,"line":89},[1115,8910,8911],{"class":1157},"                 po",[1115,8913,6847],{"class":1161},[1115,8915,1166],{"class":1165},[1115,8917,1170],{"class":1169},[1115,8919,8897],{"class":6458},[1115,8921,1177],{"class":1161},[1115,8923,8902],{"class":6458},[1115,8925,6506],{"class":1169},[1115,8927,8928,8931,8933,8935,8937,8940,8942,8945],{"class":1154,"line":82},[1115,8929,8930],{"class":1165},"mcnemar.test",[1115,8932,1170],{"class":1169},[1115,8934,8822],{"class":1157},[1115,8936,1177],{"class":1161},[1115,8938,8939],{"class":1157}," correct",[1115,8941,6416],{"class":1161},[1115,8943,8944],{"class":1173}," FALSE",[1115,8946,6519],{"class":1169},[1144,8948,8951],{"className":8949,"code":8950,"language":6540,"meta":1148},[6538],"    McNemar's Chi-squared test\n\ndata:  tab3\nMcNemar's chi-squared = 16.667, df = 1, p-value = 4.456e-05\n",[1150,8952,8950],{"__ignoreMap":1148},[1110,8954,8955,8956,6605,8975,8992,8993,9010],{},"P-hodnota ",[1115,8957,8959],{"className":8958},[1573],[1575,8960,8961],{"xmlns":1577},[1579,8962,8963,8972],{},[1582,8964,8965,8968,8970],{},[1716,8966,8967],{},"0,00004456",[1589,8969,6949],{},[1716,8971,6601],{},[1605,8973,8974],{"encoding":1607},"0{,}00004456 \u003C 0{,}05",[1115,8976,8978],{"className":8977},[1573],[1575,8979,8980],{"xmlns":1577},[1579,8981,8982,8990],{},[1582,8983,8984],{},[1746,8985,8986,8988],{},[1585,8987,1922],{},[1716,8989,2398],{},[1605,8991,4225],{"encoding":1607}," zamítáme, přijímáme ",[1115,8994,8996],{"className":8995},[1573],[1575,8997,8998],{"xmlns":1577},[1579,8999,9000,9008],{},[1582,9001,9002],{},[1746,9003,9004,9006],{},[1585,9005,1922],{},[1716,9007,1718],{},[1605,9009,3807],{"encoding":1607}," — informační kampaň měla vliv na změnu\nchování studentů ve zveřejňování údajů na Facebooku.",[1136,9012,9014],{"id":9013},"časté-chyby","Časté chyby",[1103,9016,9020,9028],{"className":9017,"dataCallout":9019},[1106,9018],"callout-warning","warning",[1110,9021,9023,9027],{"className":9022},[1113],[1115,9024],{"className":9025,"ariaHidden":1121},[1118,9026,1120],"i-lucide:triangle-alert","Test nezávislosti na párovaných datech",[1110,9029,9030,9031,9033],{},"Tabulka před\u002Fpo vypadá jako obyčejná kontingenční tabulka, ale ",[1150,9032,3731],{}," na ní předpokládá dva nezávislé\nvýběry a ignoruje, že jde o tytéž studenty měřené dvakrát. Na datech z předchozího příkladu to vede k úplně\njinému (a chybnému) závěru.",[1144,9035,9037],{"className":1146,"code":9036,"language":71,"meta":1148,"style":1148},"chisq.test(tab3)\n",[1150,9038,9039],{"__ignoreMap":1148},[1115,9040,9041,9043,9045,9047],{"class":1154,"line":10},[1115,9042,6512],{"class":1165},[1115,9044,1170],{"class":1169},[1115,9046,8822],{"class":1157},[1115,9048,6519],{"class":1169},[1144,9050,9053],{"className":9051,"code":9052,"language":6540,"meta":1148},[6538],"    Pearson's Chi-squared test with Yates' continuity correction\n\ndata:  tab3\nX-squared = 1.4793, df = 1, p-value = 0.2239\n",[1150,9054,9052],{"__ignoreMap":1148},[1110,9056,8955,9057,9076,9077,9094,9095,9097,9098,2264],{},[1115,9058,9060],{"className":9059},[1573],[1575,9061,9062],{"xmlns":1577},[1579,9063,9064,9073],{},[1582,9065,9066,9069,9071],{},[1716,9067,9068],{},"0,224",[1589,9070,1698],{},[1716,9072,6601],{},[1605,9074,9075],{"encoding":1607},"0{,}224 > 0{,}05"," by vedla k nezamítnutí ",[1115,9078,9080],{"className":9079},[1573],[1575,9081,9082],{"xmlns":1577},[1579,9083,9084,9092],{},[1582,9085,9086],{},[1746,9087,9088,9090],{},[1585,9089,1922],{},[1716,9091,2398],{},[1605,9093,4225],{"encoding":1607}," — opačný závěr než správný McNemarův test. Na\npárovaná data (stejné prvky měřené dvakrát) vždy patří ",[1150,9096,3710],{},", nikdy ",[1150,9099,3731],{},[1103,9101,9103,9112],{"className":9102,"dataCallout":9019},[1106,9018],[1110,9104,9106,9109,9110],{"className":9105},[1113],[1115,9107],{"className":9108,"ariaHidden":1121},[1118,9026,1120],"Výchozí korekce na kontinuitu v ",[1150,9111,3710],{},[1110,9113,9114,9115,9117],{},"Bez argumentu ",[1150,9116,3706],{}," R ve výchozím nastavení použije Yatesovu korekci na kontinuitu, která dá jinou\np-hodnotu než nekorigovaný vzorec uvedený výše.",[1144,9119,9121],{"className":1146,"code":9120,"language":71,"meta":1148,"style":1148},"mcnemar.test(tab3)\n",[1150,9122,9123],{"__ignoreMap":1148},[1115,9124,9125,9127,9129,9131],{"class":1154,"line":10},[1115,9126,8930],{"class":1165},[1115,9128,1170],{"class":1169},[1115,9130,8822],{"class":1157},[1115,9132,6519],{"class":1169},[1144,9134,9137],{"className":9135,"code":9136,"language":6540,"meta":1148},[6538],"    McNemar's Chi-squared test with continuity correction\n\ndata:  tab3\nMcNemar's chi-squared = 15.844, df = 1, p-value = 6.879e-05\n",[1150,9138,9136],{"__ignoreMap":1148},[1110,9140,9141,9142,9160,9161,9180,9181,9194,9195,2264],{},"Oproti nekorigované hodnotě ",[1115,9143,9145],{"className":9144},[1573],[1575,9146,9147],{"xmlns":1577},[1579,9148,9149,9157],{},[1582,9150,9151,9153,9155],{},[1585,9152,1110],{},[1589,9154,1597],{},[1716,9156,8967],{},[1605,9158,9159],{"encoding":1607},"p = 0{,}00004456"," vyjde ",[1115,9162,9164],{"className":9163},[1573],[1575,9165,9166],{"xmlns":1577},[1579,9167,9168,9177],{},[1582,9169,9170,9172,9174],{},[1585,9171,1110],{},[1589,9173,1597],{},[1716,9175,9176],{},"0,00006879",[1605,9178,9179],{"encoding":1607},"p = 0{,}00006879"," — v tomto příkladu obě vedou ke\nstejnému rozhodnutí, ale u hodnot blíž hranici ",[1115,9182,9184],{"className":9183},[1573],[1575,9185,9186],{"xmlns":1577},[1579,9187,9188,9192],{},[1582,9189,9190],{},[1585,9191,3862],{},[1605,9193,6058],{"encoding":1607}," by korekce mohla rozhodnutí změnit. Aby R reprodukovalo\nnekorigovaný vzorec, je třeba vždy volat ",[1150,9196,9197],{},"mcnemar.test(x, correct = FALSE)",[1136,9199,4071],{"id":4070},[2220,9201,9202,9207,9212,9217,9222,9227,9232],{},[2223,9203,9204],{},[1127,9205,1133],{"className":9206,"dataFsResolvedFilePath":1131,"href":1132},[1130],[2223,9208,9209],{},[1127,9210,2660],{"className":9211,"dataFsResolvedFilePath":2658,"href":2659},[1130],[2223,9213,9214],{},[1127,9215,2415],{"className":9216,"dataFsResolvedFilePath":2413,"href":2414},[1130],[2223,9218,9219],{},[1127,9220,1558],{"className":9221,"dataFsResolvedFilePath":1556,"href":1557},[1130],[2223,9223,9224],{},[1127,9225,2798],{"className":9226,"dataFsResolvedFilePath":2796,"href":2797},[1130],[2223,9228,9229],{},[1127,9230,3322],{"className":9231,"dataFsResolvedFilePath":3320,"href":3321},[1130],[2223,9233,9234],{},[1127,9235,9239],{"className":9236,"dataFsResolvedFilePath":9237,"href":9238},[1130],"outputs\u002Fmask-r-tahak.md","\u002Fwiki\u002Fmask-r-tahak","Tahák pro R",[1136,9241,4111],{"id":934},[1110,9243,4114,9244,4119],{},[4116,9245,4118],{},[4135,9247,9248],{},"html pre.shiki code .sP4rz, html code.shiki .sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: 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05.docx","topics\u002Fkontingencni-tabulky",[23,67,714,486,768,71],"topic","E-gDO0c3LOdVy6YB6I-h8KKMQKlrqjomMSQWFmOANZE",{"id":9270,"title":1558,"body":9271,"course":23,"courses":4153,"created":4154,"description":1148,"extension":4155,"meta":13654,"navigation":4157,"path":13655,"seo":13656,"sources":13657,"stem":13660,"tags":13661,"type":9267,"updated":4154,"__hash__":13662},"topics\u002Ftopics\u002Fnahodne-veliciny-a-rozdeleni.md",{"type":1096,"value":9272,"toc":13642},[9273,9275,9549,9553,9783,9786,9853,9857,9864,9871,10029,10068,10071,10304,10307,10385,10439,10537,10541,10643,10646,10650,10656,10711,10714,10722,10873,10880,10933,10963,11082,11085,11133,11294,11349,11356,11463,11525,11529,11632,11635,11672,11678,11737,11786,11793,11829,11835,11838,11886,11893,11955,11961,11964,12028,12035,12074,12080,12083,12087,12109,12410,12446,12501,12631,12637,12641,12648,12667,12772,12816,12835,12930,12947,12989,13164,13171,13174,13177,13320,13323,13398,13404,13406,13592,13594,13633,13635,13639],[1099,9274,1558],{"id":1552},[1103,9276,9278,9284],{"className":9277,"dataCallout":4184},[1106,4183],[1110,9279,9281,4192],{"className":9280},[1113],[1115,9282],{"className":9283,"ariaHidden":1121},[1118,4191,1120],[2220,9285,9286,9297,9394,9461,9537],{},[2223,9287,9288,9289,9292,9293,9296],{},"Náhodná veličina je funkce, která výsledkům pokusu přiřazuje reálná čísla; rozlišujeme ",[2227,9290,9291],{},"diskrétní"," (izolované hodnoty s nenulovou pravděpodobností) a ",[2227,9294,9295],{},"spojité"," (hodnoty z intervalu, každý bod má nulovou pravděpodobnost).",[2223,9298,9299,9300,2230,9303,9337,9338,2271,9374,9393],{},"Každou náhodnou veličinu popisuje ",[2227,9301,9302],{},"distribuční funkce",[1115,9304,9306],{"className":9305},[1573],[1575,9307,9308],{"xmlns":1577},[1579,9309,9310,9334],{},[1582,9311,9312,9314,9316,9318,9320,9322,9324,9326,9328,9330,9332],{},[1585,9313,1669],{},[1589,9315,1170],{"stretchy":1591},[1585,9317,1158],{},[1589,9319,1603],{"stretchy":1591},[1589,9321,1597],{},[1585,9323,1587],{},[1589,9325,1170],{"stretchy":1591},[1585,9327,1594],{},[1589,9329,1650],{},[1585,9331,1158],{},[1589,9333,1603],{"stretchy":1591},[1605,9335,9336],{"encoding":1607},"F(x) = P(X \\le x)","; u spojité veličiny platí ",[1115,9339,9341],{"className":9340},[1573],[1575,9342,9343],{"xmlns":1577},[1579,9344,9345,9371],{},[1582,9346,9347,9355,9357,9359,9361,9363,9365,9367,9369],{},[1986,9348,9349,9351],{},[1585,9350,1669],{},[1589,9352,9354],{"mathvariant":4022,"lspace":9353,"rspace":9353},"0em","′",[1589,9356,1170],{"stretchy":1591},[1585,9358,1158],{},[1589,9360,1603],{"stretchy":1591},[1589,9362,1597],{},[1585,9364,1621],{},[1589,9366,1170],{"stretchy":1591},[1585,9368,1158],{},[1589,9370,1603],{"stretchy":1591},[1605,9372,9373],{"encoding":1607},"F'(x) = f(x)",[1115,9375,9377],{"className":9376},[1573],[1575,9378,9379],{"xmlns":1577},[1579,9380,9381,9391],{},[1582,9382,9383,9385,9387,9389],{},[1585,9384,1621],{},[1589,9386,1170],{"stretchy":1591},[1585,9388,1158],{},[1589,9390,1603],{"stretchy":1591},[1605,9392,1630],{"encoding":1607}," je hustota pravděpodobnosti.",[2223,9395,9396,9397,2264],{},"Pravděpodobnost na intervalu se počítá jako ",[1115,9398,9400],{"className":9399},[1573],[1575,9401,9402],{"xmlns":1577},[1579,9403,9404,9458],{},[1582,9405,9406,9408,9410,9416,9418,9420,9422,9428,9430,9432,9434,9436,9442,9444,9446,9448,9450,9456],{},[1585,9407,1587],{},[1589,9409,1170],{"stretchy":1591},[1746,9411,9412,9414],{},[1585,9413,1158],{},[1716,9415,1718],{},[1589,9417,6949],{},[1585,9419,1594],{},[1589,9421,6949],{},[1746,9423,9424,9426],{},[1585,9425,1158],{},[1716,9427,1993],{},[1589,9429,1603],{"stretchy":1591},[1589,9431,1597],{},[1585,9433,1669],{},[1589,9435,1170],{"stretchy":1591},[1746,9437,9438,9440],{},[1585,9439,1158],{},[1716,9441,1993],{},[1589,9443,1603],{"stretchy":1591},[1589,9445,1721],{},[1585,9447,1669],{},[1589,9449,1170],{"stretchy":1591},[1746,9451,9452,9454],{},[1585,9453,1158],{},[1716,9455,1718],{},[1589,9457,1603],{"stretchy":1591},[1605,9459,9460],{"encoding":1607},"P(x_1 \u003C X \u003C x_2) = F(x_2) - F(x_1)",[2223,9462,9463,2230,9466,9495,9496,1279,9499,1279,9502,9505,9506,9519,9520,2264],{},[2227,9464,9465],{},"Normální rozdělení",[1115,9467,9469],{"className":9468},[1573],[1575,9470,9471],{"xmlns":1577},[1579,9472,9473,9492],{},[1582,9474,9475,9477,9479,9481,9484,9490],{},[1585,9476,1927],{},[1589,9478,1170],{"stretchy":1591},[1585,9480,1982],{},[1589,9482,9483],{"separator":1121},";",[1986,9485,9486,9488],{},[1585,9487,1990],{},[1716,9489,1993],{},[1589,9491,1603],{"stretchy":1591},[1605,9493,9494],{"encoding":1607},"N(\\mu; \\sigma^2)"," je nejdůležitější spojité rozdělení; v R ho počítáme funkcemi ",[1150,9497,9498],{},"dnorm",[1150,9500,9501],{},"pnorm",[1150,9503,9504],{},"qnorm"," — R jako parametr očekává směrodatnou odchylku ",[1115,9507,9509],{"className":9508},[1573],[1575,9510,9511],{"xmlns":1577},[1579,9512,9513,9517],{},[1582,9514,9515],{},[1585,9516,1990],{},[1605,9518,2244],{"encoding":1607},", ne rozptyl ",[1115,9521,9523],{"className":9522},[1573],[1575,9524,9525],{"xmlns":1577},[1579,9526,9527,9535],{},[1582,9528,9529],{},[1986,9530,9531,9533],{},[1585,9532,1990],{},[1716,9534,1993],{},[1605,9536,2263],{"encoding":1607},[2223,9538,9539,1279,9542,1260,9545,9548],{},[2227,9540,9541],{},"Studentovo",[2227,9543,9544],{},"Pearsonovo (χ²)",[2227,9546,9547],{},"Fisherovo-Snedecorovo"," rozdělení slouží jako nástroj pro pozdější konstrukci intervalů spolehlivosti a testování hypotéz.",[1136,9550,9552],{"id":9551},"náhodná-veličina","Náhodná veličina",[1110,9554,9555,9558,9559,9574,9575,2230,9577,9590,9591,9611,9612,2271,9625,9649,9650,1279,9663,1279,9677,9690,9691,1279,9704,1279,9717,9730,9731,9744,9745,9758,9759,2264],{},[1127,9556,1133],{"className":9557,"dataFsResolvedFilePath":1131,"href":1132},[1130]," pracuje s veličinami, jejichž hodnota závisí na náhodě. Formálně: uvažujeme základní prostor ",[1115,9560,9562],{"className":9561},[1573],[1575,9563,9564],{"xmlns":1577},[1579,9565,9566,9571],{},[1582,9567,9568],{},[1585,9569,9570],{"mathvariant":4022},"Ω",[1605,9572,9573],{"encoding":1607},"\\Omega"," přiřazený výsledkům pokusu. ",[2227,9576,9552],{},[1115,9578,9580],{"className":9579},[1573],[1575,9581,9582],{"xmlns":1577},[1579,9583,9584,9588],{},[1582,9585,9586],{},[1585,9587,1594],{},[1605,9589,1594],{"encoding":1607}," je funkce, která prvkům ",[1115,9592,9594],{"className":9593},[1573],[1575,9595,9596],{"xmlns":1577},[1579,9597,9598,9608],{},[1582,9599,9600,9603,9606],{},[1585,9601,9602],{},"ω",[1589,9604,9605],{},"∈",[1585,9607,9570],{"mathvariant":4022},[1605,9609,9610],{"encoding":1607},"\\omega \\in \\Omega"," přiřazuje reálná čísla ",[1115,9613,9615],{"className":9614},[1573],[1575,9616,9617],{"xmlns":1577},[1579,9618,9619,9623],{},[1582,9620,9621],{},[1585,9622,1158],{},[1605,9624,1158],{"encoding":1607},[1115,9626,9628],{"className":9627},[1573],[1575,9629,9630],{"xmlns":1577},[1579,9631,9632,9646],{},[1582,9633,9634,9636,9638,9640,9642,9644],{},[1585,9635,1158],{},[1589,9637,1597],{},[1585,9639,1594],{},[1589,9641,1170],{"stretchy":1591},[1585,9643,9602],{},[1589,9645,1603],{"stretchy":1591},[1605,9647,9648],{"encoding":1607},"x = X(\\omega)",". Náhodné veličiny značíme velkými písmeny (",[1115,9651,9653],{"className":9652},[1573],[1575,9654,9655],{"xmlns":1577},[1579,9656,9657,9661],{},[1582,9658,9659],{},[1585,9660,1594],{},[1605,9662,1594],{"encoding":1607},[1115,9664,9666],{"className":9665},[1573],[1575,9667,9668],{"xmlns":1577},[1579,9669,9670,9675],{},[1582,9671,9672],{},[1585,9673,9674],{},"Y",[1605,9676,9674],{"encoding":1607},[1115,9678,9680],{"className":9679},[1573],[1575,9681,9682],{"xmlns":1577},[1579,9683,9684,9688],{},[1582,9685,9686],{},[1585,9687,4043],{},[1605,9689,4043],{"encoding":1607},"), jejich konkrétní hodnoty odpovídajícími malými písmeny (",[1115,9692,9694],{"className":9693},[1573],[1575,9695,9696],{"xmlns":1577},[1579,9697,9698,9702],{},[1582,9699,9700],{},[1585,9701,1158],{},[1605,9703,1158],{"encoding":1607},[1115,9705,9707],{"className":9706},[1573],[1575,9708,9709],{"xmlns":1577},[1579,9710,9711,9715],{},[1582,9712,9713],{},[1585,9714,2862],{},[1605,9716,2862],{"encoding":1607},[1115,9718,9720],{"className":9719},[1573],[1575,9721,9722],{"xmlns":1577},[1579,9723,9724,9728],{},[1582,9725,9726],{},[1585,9727,2082],{},[1605,9729,2082],{"encoding":1607},"); pravděpodobnost, že ",[1115,9732,9734],{"className":9733},[1573],[1575,9735,9736],{"xmlns":1577},[1579,9737,9738,9742],{},[1582,9739,9740],{},[1585,9741,1594],{},[1605,9743,1594],{"encoding":1607}," nabyla hodnoty ",[1115,9746,9748],{"className":9747},[1573],[1575,9749,9750],{"xmlns":1577},[1579,9751,9752,9756],{},[1582,9753,9754],{},[1585,9755,1158],{},[1605,9757,1158],{"encoding":1607},", zapisujeme ",[1115,9760,9762],{"className":9761},[1573],[1575,9763,9764],{"xmlns":1577},[1579,9765,9766,9780],{},[1582,9767,9768,9770,9772,9774,9776,9778],{},[1585,9769,1587],{},[1589,9771,1170],{"stretchy":1591},[1585,9773,1594],{},[1589,9775,1597],{},[1585,9777,1158],{},[1589,9779,1603],{"stretchy":1591},[1605,9781,9782],{"encoding":1607},"P(X = x)",[1110,9784,9785],{},"Podle typu hodnot, kterých náhodná veličina nabývá, rozlišujeme dva typy:",[2220,9787,9788,9847],{},[2223,9789,9790,9793,9794,9807,9808,9846],{},[2227,9791,9792],{},"Diskrétní náhodná veličina"," — prvky ",[1115,9795,9797],{"className":9796},[1573],[1575,9798,9799],{"xmlns":1577},[1579,9800,9801,9805],{},[1582,9802,9803],{},[1585,9804,9570],{"mathvariant":4022},[1605,9806,9573],{"encoding":1607}," se zobrazí na osu reálných čísel jako izolované body ",[1115,9809,9811],{"className":9810},[1573],[1575,9812,9813],{"xmlns":1577},[1579,9814,9815,9843],{},[1582,9816,9817,9823,9825,9831,9833,9835,9837],{},[1746,9818,9819,9821],{},[1585,9820,1158],{},[1716,9822,1718],{},[1589,9824,1177],{"separator":1121},[1746,9826,9827,9829],{},[1585,9828,1158],{},[1716,9830,1993],{},[1589,9832,1177],{"separator":1121},[1589,9834,2979],{},[1589,9836,1177],{"separator":1121},[1746,9838,9839,9841],{},[1585,9840,1158],{},[1585,9842,1600],{},[1605,9844,9845],{"encoding":1607},"x_1, x_2, \\dots, x_k",", přičemž každý z nich má nenulovou pravděpodobnost. Příklad: počet bodů při hodu kostkou, počet studentů na cvičení.",[2223,9848,9849,9852],{},[2227,9850,9851],{},"Spojitá náhodná veličina"," — hodnoty tvoří interval na ose reálných čísel, přičemž každý bod intervalu má nulovou pravděpodobnost. Příklad: velikost výrobku, doba psaní testu, výška dětí v populaci.",[1136,9854,9856],{"id":9855},"distribuční-funkce","Distribuční funkce",[1110,9858,9859,9860,9863],{},"Náhodná veličina nabývá při pokusu určité hodnoty, aniž bychom předem věděli, které. Při opakování pokusu se ale projevují zákonitosti, které popisují ",[2227,9861,9862],{},"zákony rozdělení",". Nejobecnějším z nich je distribuční funkce.",[1110,9865,9866],{},[1303,9867],{"alt":9868,"className":9869,"src":9870},"mask-nv-distribucni-funkce",[1130,1307],"\u002Fwiki-assets\u002Fmask-nv-distribucni-funkce.png",[1103,9872,9875,9882],{"className":9873,"dataCallout":654},[1106,9874],"callout-info",[1110,9876,9878,9881],{"className":9877},[1113],[1115,9879],{"className":9880,"ariaHidden":1121},[1118,4191,1120],"Definice",[1110,9883,9884,9885,9898,9899,9918,9919,9932,9933,9969,9988,9989,10002,10003,2264],{},"Distribuční funkcí náhodné veličiny ",[1115,9886,9888],{"className":9887},[1573],[1575,9889,9890],{"xmlns":1577},[1579,9891,9892,9896],{},[1582,9893,9894],{},[1585,9895,1594],{},[1605,9897,1594],{"encoding":1607}," nazýváme reálnou funkci ",[1115,9900,9902],{"className":9901},[1573],[1575,9903,9904],{"xmlns":1577},[1579,9905,9906,9916],{},[1582,9907,9908,9910,9912,9914],{},[1585,9909,1669],{},[1589,9911,1170],{"stretchy":1591},[1585,9913,1158],{},[1589,9915,1603],{"stretchy":1591},[1605,9917,1678],{"encoding":1607}," definovanou pro každé reálné číslo ",[1115,9920,9922],{"className":9921},[1573],[1575,9923,9924],{"xmlns":1577},[1579,9925,9926,9930],{},[1582,9927,9928],{},[1585,9929,1158],{},[1605,9931,1158],{"encoding":1607}," jako\n",[1115,9934,9936],{"className":9935},[1573],[1575,9937,9938],{"xmlns":1577},[1579,9939,9940,9966],{},[1582,9941,9942,9944,9946,9948,9950,9952,9954,9956,9958,9960,9962,9964],{},[1585,9943,1669],{},[1589,9945,1170],{"stretchy":1591},[1585,9947,1158],{},[1589,9949,1603],{"stretchy":1591},[1589,9951,1597],{},[1585,9953,1587],{},[1589,9955,1170],{"stretchy":1591},[1585,9957,1594],{},[1589,9959,1650],{},[1585,9961,1158],{},[1589,9963,1603],{"stretchy":1591},[1585,9965,2264],{"mathvariant":4022},[1605,9967,9968],{"encoding":1607},"F(x) = P(X \\le x).",[1115,9970,9972],{"className":9971},[1573],[1575,9973,9974],{"xmlns":1577},[1579,9975,9976,9986],{},[1582,9977,9978,9980,9982,9984],{},[1585,9979,1669],{},[1589,9981,1170],{"stretchy":1591},[1585,9983,1158],{},[1589,9985,1603],{"stretchy":1591},[1605,9987,1678],{"encoding":1607}," tedy vyjadřuje pravděpodobnost, s jakou ",[1115,9990,9992],{"className":9991},[1573],[1575,9993,9994],{"xmlns":1577},[1579,9995,9996,10000],{},[1582,9997,9998],{},[1585,9999,1594],{},[1605,10001,1594],{"encoding":1607}," nabude hodnoty z intervalu ",[1115,10004,10006],{"className":10005},[1573],[1575,10007,10008],{"xmlns":1577},[1579,10009,10010,10026],{},[1582,10011,10012,10014,10016,10019,10021,10023],{},[1589,10013,1170],{"stretchy":1591},[1589,10015,1721],{},[1585,10017,10018],{"mathvariant":4022},"∞",[1589,10020,1177],{"separator":1121},[1585,10022,1158],{},[1589,10024,10025],{"stretchy":1591},"⟩",[1605,10027,10028],{"encoding":1607},"(-\\infty, x\\rangle",[1110,10030,10031,10032,10045,10046,10067],{},"Značí-li například ",[1115,10033,10035],{"className":10034},[1573],[1575,10036,10037],{"xmlns":1577},[1579,10038,10039,10043],{},[1582,10040,10041],{},[1585,10042,1594],{},[1605,10044,1594],{"encoding":1607}," výšku mužů v populaci, pak ",[1115,10047,10049],{"className":10048},[1573],[1575,10050,10051],{"xmlns":1577},[1579,10052,10053,10064],{},[1582,10054,10055,10057,10059,10062],{},[1585,10056,1669],{},[1589,10058,1170],{"stretchy":1591},[1716,10060,10061],{},"175",[1589,10063,1603],{"stretchy":1591},[1605,10065,10066],{"encoding":1607},"F(175)"," je pravděpodobnost, že muž měří nejvýše 175 cm.",[1110,10069,10070],{},"Pro distribuční funkci vždy platí:",[2220,10072,10073,10103,10161,10220],{},[2223,10074,10075,1177],{},[1115,10076,10078],{"className":10077},[1573],[1575,10079,10080],{"xmlns":1577},[1579,10081,10082,10100],{},[1582,10083,10084,10086,10088,10090,10092,10094,10096,10098],{},[1716,10085,2398],{},[1589,10087,1650],{},[1585,10089,1669],{},[1589,10091,1170],{"stretchy":1591},[1585,10093,1158],{},[1589,10095,1603],{"stretchy":1591},[1589,10097,1650],{},[1716,10099,1718],{},[1605,10101,10102],{"encoding":1607},"0 \\le F(x) \\le 1",[2223,10104,10105,10106,1177],{},"je neklesající: ",[1115,10107,10109],{"className":10108},[1573],[1575,10110,10111],{"xmlns":1577},[1579,10112,10113,10158],{},[1582,10114,10115,10121,10123,10129,10132,10134,10136,10142,10144,10146,10148,10150,10156],{},[1746,10116,10117,10119],{},[1585,10118,1158],{},[1716,10120,1718],{},[1589,10122,1650],{},[1746,10124,10125,10127],{},[1585,10126,1158],{},[1716,10128,1993],{},[1589,10130,10131],{},"⇒",[1585,10133,1669],{},[1589,10135,1170],{"stretchy":1591},[1746,10137,10138,10140],{},[1585,10139,1158],{},[1716,10141,1718],{},[1589,10143,1603],{"stretchy":1591},[1589,10145,1650],{},[1585,10147,1669],{},[1589,10149,1170],{"stretchy":1591},[1746,10151,10152,10154],{},[1585,10153,1158],{},[1716,10155,1993],{},[1589,10157,1603],{"stretchy":1591},[1605,10159,10160],{"encoding":1607},"x_1 \\le x_2 \\Rightarrow F(x_1) \\le F(x_2)",[2223,10162,10163,10164,1177],{},"je spojitá zprava: ",[1115,10165,10167],{"className":10166},[1573],[1575,10168,10169],{"xmlns":1577},[1579,10170,10171,10217],{},[1582,10172,10173,10195,10197,10199,10201,10203,10205,10207,10209,10211,10213,10215],{},[1746,10174,10175,10182],{},[1582,10176,10177,10180],{},[1585,10178,10179],{},"lim",[1589,10181,7105],{},[1582,10183,10184,10186,10189],{},[1585,10185,2568],{},[1589,10187,10188],{},"→",[1986,10190,10191,10193],{},[1716,10192,2398],{},[1589,10194,4010],{},[1585,10196,1669],{},[1589,10198,1170],{"stretchy":1591},[1585,10200,1158],{},[1589,10202,4010],{},[1585,10204,2568],{},[1589,10206,1603],{"stretchy":1591},[1589,10208,1597],{},[1585,10210,1669],{},[1589,10212,1170],{"stretchy":1591},[1585,10214,1158],{},[1589,10216,1603],{"stretchy":1591},[1605,10218,10219],{"encoding":1607},"\\lim_{h \\to 0^+} F(x+h) = F(x)",[2223,10221,10222,1279,10264,2264],{},[1115,10223,10225],{"className":10224},[1573],[1575,10226,10227],{"xmlns":1577},[1579,10228,10229,10261],{},[1582,10230,10231,10249,10251,10253,10255,10257,10259],{},[1746,10232,10233,10239],{},[1582,10234,10235,10237],{},[1585,10236,10179],{},[1589,10238,7105],{},[1582,10240,10241,10243,10245,10247],{},[1585,10242,1158],{},[1589,10244,10188],{},[1589,10246,1721],{},[1585,10248,10018],{"mathvariant":4022},[1585,10250,1669],{},[1589,10252,1170],{"stretchy":1591},[1585,10254,1158],{},[1589,10256,1603],{"stretchy":1591},[1589,10258,1597],{},[1716,10260,2398],{},[1605,10262,10263],{"encoding":1607},"\\lim_{x \\to -\\infty} F(x) = 0",[1115,10265,10267],{"className":10266},[1573],[1575,10268,10269],{"xmlns":1577},[1579,10270,10271,10301],{},[1582,10272,10273,10289,10291,10293,10295,10297,10299],{},[1746,10274,10275,10281],{},[1582,10276,10277,10279],{},[1585,10278,10179],{},[1589,10280,7105],{},[1582,10282,10283,10285,10287],{},[1585,10284,1158],{},[1589,10286,10188],{},[1585,10288,10018],{"mathvariant":4022},[1585,10290,1669],{},[1589,10292,1170],{"stretchy":1591},[1585,10294,1158],{},[1589,10296,1603],{"stretchy":1591},[1589,10298,1597],{},[1716,10300,1718],{},[1605,10302,10303],{"encoding":1607},"\\lim_{x \\to \\infty} F(x) = 1",[1110,10305,10306],{},"U spojité náhodné veličiny je distribuční funkce svázaná s hustotou pravděpodobnosti vztahem",[1115,10308,10310],{"className":10309},[1573],[1575,10311,10312],{"xmlns":1577,"display":4601},[1579,10313,10314,10382],{},[1582,10315,10316,10322,10324,10326,10328,10330,10332,10334,10336,10338,10340,10342,10344,10346,10348,10350,10352,10365,10367,10369,10371,10373,10375,10378,10380],{},[1986,10317,10318,10320],{},[1585,10319,1669],{},[1589,10321,9354],{"mathvariant":4022,"lspace":9353,"rspace":9353},[1589,10323,1170],{"stretchy":1591},[1585,10325,1158],{},[1589,10327,1603],{"stretchy":1591},[1589,10329,1597],{},[1585,10331,1621],{},[1589,10333,1170],{"stretchy":1591},[1585,10335,1158],{},[1589,10337,1603],{"stretchy":1591},[1589,10339,1177],{"separator":1121},[4648,10341],{"width":4650},[1585,10343,1669],{},[1589,10345,1170],{"stretchy":1591},[1585,10347,1158],{},[1589,10349,1603],{"stretchy":1591},[1589,10351,1597],{},[2920,10353,10354,10357,10363],{},[1589,10355,10356],{},"∫",[1582,10358,10359,10361],{},[1589,10360,1721],{},[1585,10362,10018],{"mathvariant":4022},[1585,10364,1158],{},[1585,10366,1621],{},[1589,10368,1170],{"stretchy":1591},[1585,10370,2082],{},[1589,10372,1603],{"stretchy":1591},[5543,10374,5545],{},[1585,10376,10377],{},"d",[1585,10379,2082],{},[1585,10381,2264],{"mathvariant":4022},[1605,10383,10384],{"encoding":1607},"F'(x) = f(x), \\qquad F(x) = \\int_{-\\infty}^{x} f(t)\\,dt.",[1110,10386,10387,10388,10401,10402,1260,10420,10438],{},"Pravděpodobnost, že ",[1115,10389,10391],{"className":10390},[1573],[1575,10392,10393],{"xmlns":1577},[1579,10394,10395,10399],{},[1582,10396,10397],{},[1585,10398,1594],{},[1605,10400,1594],{"encoding":1607}," padne mezi body ",[1115,10403,10405],{"className":10404},[1573],[1575,10406,10407],{"xmlns":1577},[1579,10408,10409,10417],{},[1582,10410,10411],{},[1746,10412,10413,10415],{},[1585,10414,1158],{},[1716,10416,1718],{},[1605,10418,10419],{"encoding":1607},"x_1",[1115,10421,10423],{"className":10422},[1573],[1575,10424,10425],{"xmlns":1577},[1579,10426,10427,10435],{},[1582,10428,10429],{},[1746,10430,10431,10433],{},[1585,10432,1158],{},[1716,10434,1993],{},[1605,10436,10437],{"encoding":1607},"x_2",", se pak počítá jako",[1115,10440,10442],{"className":10441},[1573],[1575,10443,10444],{"xmlns":1577,"display":4601},[1579,10445,10446,10534],{},[1582,10447,10448,10450,10452,10458,10460,10462,10464,10470,10472,10474,10490,10492,10494,10496,10498,10500,10502,10504,10506,10508,10510,10516,10518,10520,10522,10524,10530,10532],{},[1585,10449,1587],{},[1589,10451,1170],{"stretchy":1591},[1746,10453,10454,10456],{},[1585,10455,1158],{},[1716,10457,1718],{},[1589,10459,6949],{},[1585,10461,1594],{},[1589,10463,6949],{},[1746,10465,10466,10468],{},[1585,10467,1158],{},[1716,10469,1993],{},[1589,10471,1603],{"stretchy":1591},[1589,10473,1597],{},[2920,10475,10476,10478,10484],{},[1589,10477,10356],{},[1746,10479,10480,10482],{},[1585,10481,1158],{},[1716,10483,1718],{},[1746,10485,10486,10488],{},[1585,10487,1158],{},[1716,10489,1993],{},[1585,10491,1621],{},[1589,10493,1170],{"stretchy":1591},[1585,10495,2082],{},[1589,10497,1603],{"stretchy":1591},[5543,10499,5545],{},[1585,10501,10377],{},[1585,10503,2082],{},[1589,10505,1597],{},[1585,10507,1669],{},[1589,10509,1170],{"stretchy":1591},[1746,10511,10512,10514],{},[1585,10513,1158],{},[1716,10515,1993],{},[1589,10517,1603],{"stretchy":1591},[1589,10519,1721],{},[1585,10521,1669],{},[1589,10523,1170],{"stretchy":1591},[1746,10525,10526,10528],{},[1585,10527,1158],{},[1716,10529,1718],{},[1589,10531,1603],{"stretchy":1591},[1585,10533,2264],{"mathvariant":4022},[1605,10535,10536],{"encoding":1607},"P(x_1 \u003C X \u003C x_2) = \\int_{x_1}^{x_2} f(t)\\,dt = F(x_2) - F(x_1).",[1136,10538,10540],{"id":10539},"hustota-pravděpodobnosti","Hustota pravděpodobnosti",[1103,10542,10544,10550],{"className":10543,"dataCallout":654},[1106,9874],[1110,10545,10547,9881],{"className":10546},[1113],[1115,10548],{"className":10549,"ariaHidden":1121},[1118,4191,1120],[1110,10551,10552,10553,10572,10573,10586,10587,10600,10601,2264],{},"Hustota pravděpodobnosti ",[1115,10554,10556],{"className":10555},[1573],[1575,10557,10558],{"xmlns":1577},[1579,10559,10560,10570],{},[1582,10561,10562,10564,10566,10568],{},[1585,10563,1621],{},[1589,10565,1170],{"stretchy":1591},[1585,10567,1158],{},[1589,10569,1603],{"stretchy":1591},[1605,10571,1630],{"encoding":1607}," určuje, jak jsou hodnoty spojité náhodné veličiny ",[1115,10574,10576],{"className":10575},[1573],[1575,10577,10578],{"xmlns":1577},[1579,10579,10580,10584],{},[1582,10581,10582],{},[1585,10583,1594],{},[1605,10585,1594],{"encoding":1607}," nahuštěny v okolí bodu ",[1115,10588,10590],{"className":10589},[1573],[1575,10591,10592],{"xmlns":1577},[1579,10593,10594,10598],{},[1582,10595,10596],{},[1585,10597,1158],{},[1605,10599,1158],{"encoding":1607},". Je vždy nezáporná a platí pro ni ",[1115,10602,10604],{"className":10603},[1573],[1575,10605,10606],{"xmlns":1577},[1579,10607,10608,10640],{},[1582,10609,10610,10622,10624,10626,10628,10630,10632,10634,10636,10638],{},[2920,10611,10612,10614,10620],{},[1589,10613,10356],{},[1582,10615,10616,10618],{},[1589,10617,1721],{},[1585,10619,10018],{"mathvariant":4022},[1585,10621,10018],{"mathvariant":4022},[1585,10623,1621],{},[1589,10625,1170],{"stretchy":1591},[1585,10627,1158],{},[1589,10629,1603],{"stretchy":1591},[5543,10631,5545],{},[1585,10633,10377],{},[1585,10635,1158],{},[1589,10637,1597],{},[1716,10639,1718],{},[1605,10641,10642],{"encoding":1607},"\\int_{-\\infty}^{\\infty} f(x)\\,dx = 1",[1110,10644,10645],{},"Intuitivně: rozdělíme-li hodnoty náhodné veličiny (např. výšku mužů v populaci) do stejně širokých intervalů, bude v intervalech blízko průměru nahuštěno víc pozorování než v krajních intervalech — hustota tam bude vyšší.",[1136,10647,10649],{"id":10648},"charakteristiky-spojité-náhodné-veličiny","Charakteristiky spojité náhodné veličiny",[1110,10651,10652,10655],{},[2227,10653,10654],{},"Střední hodnota"," je nejdůležitější charakteristika náhodné veličiny:",[1115,10657,10659],{"className":10658},[1573],[1575,10660,10661],{"xmlns":1577,"display":4601},[1579,10662,10663,10708],{},[1582,10664,10665,10667,10669,10671,10673,10675,10687,10689,10692,10694,10696,10698,10700,10702,10704,10706],{},[1585,10666,2035],{},[1589,10668,1170],{"stretchy":1591},[1585,10670,1594],{},[1589,10672,1603],{"stretchy":1591},[1589,10674,1597],{},[2920,10676,10677,10679,10685],{},[1589,10678,10356],{},[1582,10680,10681,10683],{},[1589,10682,1721],{},[1585,10684,10018],{"mathvariant":4022},[1585,10686,10018],{"mathvariant":4022},[1585,10688,1158],{},[1589,10690,10691],{},"⋅",[1585,10693,1621],{},[1589,10695,1170],{"stretchy":1591},[1585,10697,1158],{},[1589,10699,1603],{"stretchy":1591},[5543,10701,5545],{},[1585,10703,10377],{},[1585,10705,1158],{},[1585,10707,2264],{"mathvariant":4022},[1605,10709,10710],{"encoding":1607},"E(X) = \\int_{-\\infty}^{\\infty} x \\cdot f(x)\\,dx.",[1110,10712,10713],{},"Je to číslo, kolem něhož kolísají výběrové průměry vypočtené ze sérií pozorovaných hodnot náhodné veličiny.",[1110,10715,10716,1260,10719,4595],{},[2227,10717,10718],{},"Rozptyl",[2227,10720,10721],{},"směrodatná odchylka",[1115,10723,10725],{"className":10724},[1573],[1575,10726,10727],{"xmlns":1577,"display":4601},[1579,10728,10729,10870],{},[1582,10730,10731,10734,10736,10738,10740,10742,10754,10757,10759,10761,10763,10765,10767,10769,10776,10778,10780,10782,10784,10786,10788,10790,10792,10804,10810,10812,10814,10816,10818,10820,10822,10824,10826,10828,10830,10832,10834,10836,10842,10844,10846,10848,10850,10852,10854,10856,10868],{},[1585,10732,10733],{},"D",[1589,10735,1170],{"stretchy":1591},[1585,10737,1594],{},[1589,10739,1603],{"stretchy":1591},[1589,10741,1597],{},[2920,10743,10744,10746,10752],{},[1589,10745,10356],{},[1582,10747,10748,10750],{},[1589,10749,1721],{},[1585,10751,10018],{"mathvariant":4022},[1585,10753,10018],{"mathvariant":4022},[1589,10755,10756],{"stretchy":1591},"[",[1585,10758,1158],{},[1589,10760,1721],{},[1585,10762,2035],{},[1589,10764,1170],{"stretchy":1591},[1585,10766,1594],{},[1589,10768,1603],{"stretchy":1591},[1986,10770,10771,10774],{},[1589,10772,10773],{"stretchy":1591},"]",[1716,10775,1993],{},[1585,10777,1621],{},[1589,10779,1170],{"stretchy":1591},[1585,10781,1158],{},[1589,10783,1603],{"stretchy":1591},[5543,10785,5545],{},[1585,10787,10377],{},[1585,10789,1158],{},[1589,10791,1597],{},[2920,10793,10794,10796,10802],{},[1589,10795,10356],{},[1582,10797,10798,10800],{},[1589,10799,1721],{},[1585,10801,10018],{"mathvariant":4022},[1585,10803,10018],{"mathvariant":4022},[1986,10805,10806,10808],{},[1585,10807,1158],{},[1716,10809,1993],{},[1585,10811,1621],{},[1589,10813,1170],{"stretchy":1591},[1585,10815,1158],{},[1589,10817,1603],{"stretchy":1591},[5543,10819,5545],{},[1585,10821,10377],{},[1585,10823,1158],{},[1589,10825,1721],{},[1589,10827,10756],{"stretchy":1591},[1585,10829,2035],{},[1589,10831,1170],{"stretchy":1591},[1585,10833,1594],{},[1589,10835,1603],{"stretchy":1591},[1986,10837,10838,10840],{},[1589,10839,10773],{"stretchy":1591},[1716,10841,1993],{},[1589,10843,1177],{"separator":1121},[4648,10845],{"width":4650},[1585,10847,1990],{},[1589,10849,1170],{"stretchy":1591},[1585,10851,1594],{},[1589,10853,1603],{"stretchy":1591},[1589,10855,1597],{},[7068,10857,10858],{},[1582,10859,10860,10862,10864,10866],{},[1585,10861,10733],{},[1589,10863,1170],{"stretchy":1591},[1585,10865,1594],{},[1589,10867,1603],{"stretchy":1591},[1585,10869,2264],{"mathvariant":4022},[1605,10871,10872],{"encoding":1607},"D(X) = \\int_{-\\infty}^{\\infty} [x - E(X)]^2 f(x)\\,dx = \\int_{-\\infty}^{\\infty} x^2 f(x)\\,dx - [E(X)]^2, \\qquad \\sigma(X) = \\sqrt{D(X)}.",[1110,10874,10875,10876,10879],{},"Směrodatná odchylka udává, jak moc jsou hodnoty náhodné veličiny rozptýlené kolem střední hodnoty. (Pro odhad těchto charakteristik z naměřených dat viz empirické protějšky v ",[1127,10877,886],{"className":10878,"dataFsResolvedFilePath":2413,"href":2414},[1130],".)",[1110,10881,10882,10885,10886,10899,10900,10918,10919,10932],{},[2227,10883,10884],{},"Kvantily"," udávají, jak jsou hodnoty náhodné veličiny ",[1115,10887,10889],{"className":10888},[1573],[1575,10890,10891],{"xmlns":1577},[1579,10892,10893,10897],{},[1582,10894,10895],{},[1585,10896,1594],{},[1605,10898,1594],{"encoding":1607}," rozděleny na ose reálných čísel v určitém pravděpodobnostním poměru. 100p%-ní kvantil ",[1115,10901,10903],{"className":10902},[1573],[1575,10904,10905],{"xmlns":1577},[1579,10906,10907,10915],{},[1582,10908,10909],{},[1746,10910,10911,10913],{},[1585,10912,1158],{},[1585,10914,1110],{},[1605,10916,10917],{"encoding":1607},"x_p"," je číslo, pro které při zvolené pravděpodobnosti ",[1115,10920,10922],{"className":10921},[1573],[1575,10923,10924],{"xmlns":1577},[1579,10925,10926,10930],{},[1582,10927,10928],{},[1585,10929,1110],{},[1605,10931,1110],{"encoding":1607}," platí",[1115,10934,10936],{"className":10935},[1573],[1575,10937,10938],{"xmlns":1577,"display":4601},[1579,10939,10940,10960],{},[1582,10941,10942,10944,10946,10952,10954,10956,10958],{},[1585,10943,1669],{},[1589,10945,1170],{"stretchy":1591},[1746,10947,10948,10950],{},[1585,10949,1158],{},[1585,10951,1110],{},[1589,10953,1603],{"stretchy":1591},[1589,10955,1597],{},[1585,10957,1110],{},[1585,10959,2264],{"mathvariant":4022},[1605,10961,10962],{"encoding":1607},"F(x_p) = p.",[1110,10964,10965,10966,10994,10995,11022,11023,11042,11043,11062,11063,2264],{},"V intervalu ",[1115,10967,10969],{"className":10968},[1573],[1575,10970,10971],{"xmlns":1577},[1579,10972,10973,10991],{},[1582,10974,10975,10977,10979,10981,10983,10989],{},[1589,10976,1170],{"stretchy":1591},[1589,10978,1721],{},[1585,10980,10018],{"mathvariant":4022},[1589,10982,9483],{"separator":1121},[1746,10984,10985,10987],{},[1585,10986,1158],{},[1585,10988,1110],{},[1589,10990,1603],{"stretchy":1591},[1605,10992,10993],{"encoding":1607},"(-\\infty; x_p)"," leží 100p % hodnot, v intervalu ",[1115,10996,10998],{"className":10997},[1573],[1575,10999,11000],{"xmlns":1577},[1579,11001,11002,11019],{},[1582,11003,11004,11007,11013,11015,11017],{},[1589,11005,11006],{"stretchy":1591},"⟨",[1746,11008,11009,11011],{},[1585,11010,1158],{},[1585,11012,1110],{},[1589,11014,9483],{"separator":1121},[1585,11016,10018],{"mathvariant":4022},[1589,11018,1603],{"stretchy":1591},[1605,11020,11021],{"encoding":1607},"\\langle x_p; \\infty)"," leží 100(1-p) % hodnot. Nejdůležitější kvantily jsou medián ",[1115,11024,11026],{"className":11025},[1573],[1575,11027,11028],{"xmlns":1577},[1579,11029,11030,11039],{},[1582,11031,11032],{},[1746,11033,11034,11036],{},[1585,11035,1158],{},[1716,11037,11038],{},"0,5",[1605,11040,11041],{"encoding":1607},"x_{0{,}5}",", dolní kvartil ",[1115,11044,11046],{"className":11045},[1573],[1575,11047,11048],{"xmlns":1577},[1579,11049,11050,11059],{},[1582,11051,11052],{},[1746,11053,11054,11056],{},[1585,11055,1158],{},[1716,11057,11058],{},"0,25",[1605,11060,11061],{"encoding":1607},"x_{0{,}25}"," a horní kvartil ",[1115,11064,11066],{"className":11065},[1573],[1575,11067,11068],{"xmlns":1577},[1579,11069,11070,11079],{},[1582,11071,11072],{},[1746,11073,11074,11076],{},[1585,11075,1158],{},[1716,11077,11078],{},"0,75",[1605,11080,11081],{"encoding":1607},"x_{0{,}75}",[1136,11083,9465],{"id":11084},"normální-rozdělení",[1110,11086,11087,11088,11101,11102,2230,11105,11132],{},"Spojitá náhodná veličina ",[1115,11089,11091],{"className":11090},[1573],[1575,11092,11093],{"xmlns":1577},[1579,11094,11095,11099],{},[1582,11096,11097],{},[1585,11098,1594],{},[1605,11100,1594],{"encoding":1607}," má ",[2227,11103,11104],{},"normální rozdělení",[1115,11106,11108],{"className":11107},[1573],[1575,11109,11110],{"xmlns":1577},[1579,11111,11112,11130],{},[1582,11113,11114,11116,11118,11120,11122,11128],{},[1585,11115,1927],{},[1589,11117,1170],{"stretchy":1591},[1585,11119,1982],{},[1589,11121,9483],{"separator":1121},[1986,11123,11124,11126],{},[1585,11125,1990],{},[1716,11127,1993],{},[1589,11129,1603],{"stretchy":1591},[1605,11131,9494],{"encoding":1607},", jestliže její hustota pravděpodobnosti a distribuční funkce jsou dány předpisy",[1115,11134,11136],{"className":11135},[1573],[1575,11137,11138],{"xmlns":1577,"display":4601},[1579,11139,11140,11291],{},[1582,11141,11142,11144,11146,11148,11150,11152,11169,11205,11207,11209,11211,11213,11215,11217,11219,11235,11247,11283,11285,11287,11289],{},[1585,11143,1621],{},[1589,11145,1170],{"stretchy":1591},[1585,11147,1158],{},[1589,11149,1603],{"stretchy":1591},[1589,11151,1597],{},[5373,11153,11154,11156],{},[1716,11155,1718],{},[1582,11157,11158,11160],{},[1585,11159,1990],{},[7068,11161,11162],{},[1582,11163,11164,11166],{},[1716,11165,1993],{},[1585,11167,11168],{},"π",[1986,11170,11171,11173],{},[1585,11172,2876],{},[1582,11174,11175,11177],{},[1589,11176,1721],{},[5373,11178,11179,11195],{},[1582,11180,11181,11183,11185,11187,11189],{},[1589,11182,1170],{"stretchy":1591},[1585,11184,1158],{},[1589,11186,1721],{},[1585,11188,1982],{},[1986,11190,11191,11193],{},[1589,11192,1603],{"stretchy":1591},[1716,11194,1993],{},[1582,11196,11197,11199],{},[1716,11198,1993],{},[1986,11200,11201,11203],{},[1585,11202,1990],{},[1716,11204,1993],{},[1589,11206,1177],{"separator":1121},[4648,11208],{"width":4650},[1585,11210,1669],{},[1589,11212,1170],{"stretchy":1591},[1585,11214,1158],{},[1589,11216,1603],{"stretchy":1591},[1589,11218,1597],{},[5373,11220,11221,11223],{},[1716,11222,1718],{},[1582,11224,11225,11227],{},[1585,11226,1990],{},[7068,11228,11229],{},[1582,11230,11231,11233],{},[1716,11232,1993],{},[1585,11234,11168],{},[2920,11236,11237,11239,11245],{},[1589,11238,10356],{},[1582,11240,11241,11243],{},[1589,11242,1721],{},[1585,11244,10018],{"mathvariant":4022},[1585,11246,1158],{},[1986,11248,11249,11251],{},[1585,11250,2876],{},[1582,11252,11253,11255],{},[1589,11254,1721],{},[5373,11256,11257,11273],{},[1582,11258,11259,11261,11263,11265,11267],{},[1589,11260,1170],{"stretchy":1591},[1585,11262,2082],{},[1589,11264,1721],{},[1585,11266,1982],{},[1986,11268,11269,11271],{},[1589,11270,1603],{"stretchy":1591},[1716,11272,1993],{},[1582,11274,11275,11277],{},[1716,11276,1993],{},[1986,11278,11279,11281],{},[1585,11280,1990],{},[1716,11282,1993],{},[5543,11284,5545],{},[1585,11286,10377],{},[1585,11288,2082],{},[1589,11290,1177],{"separator":1121},[1605,11292,11293],{"encoding":1607},"f(x) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}, \\qquad F(x) = \\frac{1}{\\sigma\\sqrt{2\\pi}} \\int_{-\\infty}^{x} e^{-\\frac{(t-\\mu)^2}{2\\sigma^2}}\\,dt,",[1110,11295,11296,11297,1279,11321,2264],{},"přičemž ",[1115,11298,11300],{"className":11299},[1573],[1575,11301,11302],{"xmlns":1577},[1579,11303,11304,11318],{},[1582,11305,11306,11308,11310,11312,11314,11316],{},[1585,11307,2035],{},[1589,11309,1170],{"stretchy":1591},[1585,11311,1594],{},[1589,11313,1603],{"stretchy":1591},[1589,11315,1597],{},[1585,11317,1982],{},[1605,11319,11320],{"encoding":1607},"E(X) = \\mu",[1115,11322,11324],{"className":11323},[1573],[1575,11325,11326],{"xmlns":1577},[1579,11327,11328,11346],{},[1582,11329,11330,11332,11334,11336,11338,11340],{},[1585,11331,10733],{},[1589,11333,1170],{"stretchy":1591},[1585,11335,1594],{},[1589,11337,1603],{"stretchy":1591},[1589,11339,1597],{},[1986,11341,11342,11344],{},[1585,11343,1990],{},[1716,11345,1993],{},[1605,11347,11348],{"encoding":1607},"D(X) = \\sigma^2",[1110,11350,11351],{},[1303,11352],{"alt":11353,"className":11354,"src":11355},"mask-nv-normalni",[1130,1307],"\u002Fwiki-assets\u002Fmask-nv-normalni.png",[1110,11357,11358,11359,11362,11363,11377,11378,11397,11398,11414,11415,11428,11429,2264],{},"Křivka hustoty se nazývá ",[2227,11360,11361],{},"Gaussova křivka",": je symetrická kolem svislé přímky procházející ",[1115,11364,11366],{"className":11365},[1573],[1575,11367,11368],{"xmlns":1577},[1579,11369,11370,11374],{},[1582,11371,11372],{},[1585,11373,1982],{},[1605,11375,11376],{"encoding":1607},"\\mu",", kde má ",[1115,11379,11381],{"className":11380},[1573],[1575,11382,11383],{"xmlns":1577},[1579,11384,11385,11395],{},[1582,11386,11387,11389,11391,11393],{},[1585,11388,1621],{},[1589,11390,1170],{"stretchy":1591},[1585,11392,1158],{},[1589,11394,1603],{"stretchy":1591},[1605,11396,1630],{"encoding":1607}," globální maximum, a ve vzdálenosti ",[1115,11399,11401],{"className":11400},[1573],[1575,11402,11403],{"xmlns":1577},[1579,11404,11405,11411],{},[1582,11406,11407,11409],{},[1716,11408,6220],{},[1585,11410,1990],{},[1605,11412,11413],{"encoding":1607},"3\\sigma"," od ",[1115,11416,11418],{"className":11417},[1573],[1575,11419,11420],{"xmlns":1577},[1579,11421,11422,11426],{},[1582,11423,11424],{},[1585,11425,1982],{},[1605,11427,11376],{"encoding":1607}," se téměř dotýká osy x — zhruba 99,73 % hodnot leží v intervalu ",[1115,11430,11432],{"className":11431},[1573],[1575,11433,11434],{"xmlns":1577},[1579,11435,11436,11460],{},[1582,11437,11438,11440,11442,11444,11446,11448,11450,11452,11454,11456,11458],{},[1589,11439,1170],{"stretchy":1591},[1585,11441,1982],{},[1589,11443,1721],{},[1716,11445,6220],{},[1585,11447,1990],{},[1589,11449,9483],{"separator":1121},[1585,11451,1982],{},[1589,11453,4010],{},[1716,11455,6220],{},[1585,11457,1990],{},[1589,11459,1603],{"stretchy":1591},[1605,11461,11462],{"encoding":1607},"(\\mu - 3\\sigma; \\mu + 3\\sigma)",[1110,11464,11465,11466,2230,11469,11493,11494,2264],{},"Zvláštní postavení má ",[2227,11467,11468],{},"normované normální rozdělení",[1115,11470,11472],{"className":11471},[1573],[1575,11473,11474],{"xmlns":1577},[1579,11475,11476,11490],{},[1582,11477,11478,11480,11482,11484,11486,11488],{},[1585,11479,1927],{},[1589,11481,1170],{"stretchy":1591},[1716,11483,2398],{},[1589,11485,9483],{"separator":1121},[1716,11487,1718],{},[1589,11489,1603],{"stretchy":1591},[1605,11491,11492],{"encoding":1607},"N(0; 1)",", na které se dá libovolné normální rozdělení převést standardizací ",[1115,11495,11497],{"className":11496},[1573],[1575,11498,11499],{"xmlns":1577},[1579,11500,11501,11522],{},[1582,11502,11503,11506,11508,11510,11512,11514,11516,11518,11520],{},[1585,11504,11505],{},"Z",[1589,11507,1597],{},[1589,11509,1170],{"stretchy":1591},[1585,11511,1594],{},[1589,11513,1721],{},[1585,11515,1982],{},[1589,11517,1603],{"stretchy":1591},[1585,11519,4023],{"mathvariant":4022},[1585,11521,1990],{},[1605,11523,11524],{"encoding":1607},"Z = (X-\\mu)\u002F\\sigma",[11526,11527],"graph-mount",{"spec":11528},"{\"title\":\"Hustota normálního rozdělení N(μ; σ²)\",\"alt\":\"Hustota normálního rozdělení f(x) = 1\u002F(σ√(2π)) krát exp(−(x−μ)²\u002F(2σ²)) s nastavitelnou střední hodnotou μ a směrodatnou odchylkou σ. Se zvyšujícím se σ se křivka zplošťuje a rozšiřuje, se změnou μ se posouvá po ose x.\",\"engine\":\"function-plot\",\"xAxis\":{\"label\":\"x\",\"domain\":[-15,15]},\"yAxis\":{\"label\":\"f(x)\",\"domain\":[0,0.9]},\"params\":[{\"name\":\"mu\",\"label\":\"střední hodnota μ\",\"min\":-3,\"max\":3,\"step\":0.5,\"default\":0},{\"name\":\"s\",\"label\":\"směrodatná odchylka σ\",\"min\":0.5,\"max\":3,\"step\":0.25,\"default\":1}],\"curves\":[{\"fn\":\"(1\u002F(s*sqrt(2*PI)))*exp(-((x-mu)^2)\u002F(2*s^2))\",\"label\":\"f(x) = N(μ; σ²)\",\"color\":\"fp-purple\"}],\"markers\":[{\"x\":\"mu\",\"label\":\"μ\"}]}",[1103,11530,11532,11539],{"className":11531,"dataCallout":9019},[1106,9018],[1110,11533,11535,11538],{"className":11534},[1113],[1115,11536],{"className":11537,"ariaHidden":1121},[1118,9026,1120],"R očekává směrodatnou odchylku, ne rozptyl",[1110,11540,11541,11542,11569,11570,11573,11574,1279,11576,1260,11578,11580,11581,2230,11584,11597,11598,11624,11625,11628,11629,2264],{},"Zápis ",[1115,11543,11545],{"className":11544},[1573],[1575,11546,11547],{"xmlns":1577},[1579,11548,11549,11567],{},[1582,11550,11551,11553,11555,11557,11559,11565],{},[1585,11552,1927],{},[1589,11554,1170],{"stretchy":1591},[1585,11556,1982],{},[1589,11558,9483],{"separator":1121},[1986,11560,11561,11563],{},[1585,11562,1990],{},[1716,11564,1993],{},[1589,11566,1603],{"stretchy":1591},[1605,11568,9494],{"encoding":1607}," v definici používá ",[2227,11571,11572],{},"rozptyl",". Funkce ",[1150,11575,9498],{},[1150,11577,9501],{},[1150,11579,9504],{}," v R ale jako třetí argument berou ",[2227,11582,11583],{},"směrodatnou odchylku",[1115,11585,11587],{"className":11586},[1573],[1575,11588,11589],{"xmlns":1577},[1579,11590,11591,11595],{},[1582,11592,11593],{},[1585,11594,1990],{},[1605,11596,2244],{"encoding":1607},". Má-li náhodná veličina rozdělení ",[1115,11599,11601],{"className":11600},[1573],[1575,11602,11603],{"xmlns":1577},[1579,11604,11605,11621],{},[1582,11606,11607,11609,11611,11614,11616,11619],{},[1585,11608,1927],{},[1589,11610,1170],{"stretchy":1591},[1716,11612,11613],{},"10",[1589,11615,9483],{"separator":1121},[1716,11617,11618],{},"0,12",[1589,11620,1603],{"stretchy":1591},[1605,11622,11623],{"encoding":1607},"N(10; 0{,}12)",", je ",[1150,11626,11627],{},"sd = sqrt(0.12)",", ne ",[1150,11630,11631],{},"sd = 0.12",[1110,11633,11634],{},"V R:",[1144,11636,11638],{"className":1146,"code":11637,"language":71,"meta":1148,"style":1148},"dnorm(0)\npnorm(1.96)\nqnorm(0.975)\n",[1150,11639,11640,11650,11661],{"__ignoreMap":1148},[1115,11641,11642,11644,11646,11648],{"class":1154,"line":10},[1115,11643,9498],{"class":1165},[1115,11645,1170],{"class":1169},[1115,11647,2398],{"class":1173},[1115,11649,6519],{"class":1169},[1115,11651,11652,11654,11656,11659],{"class":1154,"line":27},[1115,11653,9501],{"class":1165},[1115,11655,1170],{"class":1169},[1115,11657,11658],{"class":1173},"1.96",[1115,11660,6519],{"class":1169},[1115,11662,11663,11665,11667,11670],{"class":1154,"line":148},[1115,11664,9504],{"class":1165},[1115,11666,1170],{"class":1169},[1115,11668,11669],{"class":1173},"0.975",[1115,11671,6519],{"class":1169},[1144,11673,11676],{"className":11674,"code":11675,"language":6540,"meta":1148},[6538],"[1] 0.3989423\n[1] 0.9750021\n[1] 1.959964\n",[1150,11677,11675],{"__ignoreMap":1148},[1110,11679,11680,11683,11684,11708,11709,4527,11712,1260,11733,11736],{},[1150,11681,11682],{},"dnorm(0)"," je hodnota hustoty ",[1115,11685,11687],{"className":11686},[1573],[1575,11688,11689],{"xmlns":1577},[1579,11690,11691,11705],{},[1582,11692,11693,11695,11697,11699,11701,11703],{},[1585,11694,1927],{},[1589,11696,1170],{"stretchy":1591},[1716,11698,2398],{},[1589,11700,9483],{"separator":1121},[1716,11702,1718],{},[1589,11704,1603],{"stretchy":1591},[1605,11706,11707],{"encoding":1607},"N(0;1)"," v bodě 0, ",[1150,11710,11711],{},"pnorm(1.96)",[1115,11713,11715],{"className":11714},[1573],[1575,11716,11717],{"xmlns":1577},[1579,11718,11719,11730],{},[1582,11720,11721,11723,11725,11728],{},[1585,11722,1669],{},[1589,11724,1170],{"stretchy":1591},[1716,11726,11727],{},"1,96",[1589,11729,1603],{"stretchy":1591},[1605,11731,11732],{"encoding":1607},"F(1{,}96)",[1150,11734,11735],{},"qnorm(0.975)"," je 97,5%-ní kvantil — hodnota, pod kterou leží 97,5 % pravděpodobnosti.",[1103,11738,11740,11747],{"className":11739,"dataCallout":6105},[1106,6104],[1110,11741,11743,11746],{"className":11742},[1113],[1115,11744],{"className":11745,"ariaHidden":1121},[1118,6112,1120],"Příklad: Návštěvnost zábavního parku",[1110,11748,11749,11750,11785],{},"Denní návštěvnost zábavního parku je náhodná veličina s normálním rozdělením, průměrnou hodnotou 230 a směrodatnou odchylkou 27,5 návštěvníků: ",[1115,11751,11753],{"className":11752},[1573],[1575,11754,11755],{"xmlns":1577},[1579,11756,11757,11782],{},[1582,11758,11759,11761,11764,11766,11768,11771,11773,11780],{},[1585,11760,1594],{},[1589,11762,11763],{},"∼",[1585,11765,1927],{},[1589,11767,1170],{"stretchy":1591},[1716,11769,11770],{},"230",[1589,11772,9483],{"separator":1121},[1986,11774,11775,11778],{},[1716,11776,11777],{},"27,5",[1716,11779,1993],{},[1589,11781,1603],{"stretchy":1591},[1605,11783,11784],{"encoding":1607},"X \\sim N(230; 27{,}5^2)",". Přijde-li za den méně než 180 návštěvníků, je park ztrátový. Kolik procent dní je ztrátových?",[1110,11787,11788],{},[1303,11789],{"alt":11790,"className":11791,"src":11792},"mask-nv-priklad-park",[1130,1307],"\u002Fwiki-assets\u002Fmask-nv-priklad-park.png",[1144,11794,11796],{"className":1146,"code":11795,"language":71,"meta":1148,"style":1148},"pnorm(180, mean = 230, sd = 27.5)\n",[1150,11797,11798],{"__ignoreMap":1148},[1115,11799,11800,11802,11804,11807,11809,11812,11814,11817,11819,11822,11824,11827],{"class":1154,"line":10},[1115,11801,9501],{"class":1165},[1115,11803,1170],{"class":1169},[1115,11805,11806],{"class":1173},"180",[1115,11808,1177],{"class":1161},[1115,11810,11811],{"class":1157}," mean",[1115,11813,6416],{"class":1161},[1115,11815,11816],{"class":1173}," 230",[1115,11818,1177],{"class":1161},[1115,11820,11821],{"class":1157}," sd",[1115,11823,6416],{"class":1161},[1115,11825,11826],{"class":1173}," 27.5",[1115,11828,6519],{"class":1169},[1144,11830,11833],{"className":11831,"code":11832,"language":6540,"meta":1148},[6538],"[1] 0.03451817\n",[1150,11834,11832],{"__ignoreMap":1148},[1110,11836,11837],{},"Park je ztrátový přibližně v 3,45 % dní.",[1103,11839,11841,11848],{"className":11840,"dataCallout":6105},[1106,6104],[1110,11842,11844,11847],{"className":11843},[1113],[1115,11845],{"className":11846,"ariaHidden":1121},[1118,6112,1120],"Příklad: Délka výrobku",[1110,11849,11850,11851,11885],{},"Automat je seřízen tak, aby střední hodnota délky výrobku byla 42 mm, s přesností charakterizovanou směrodatnou odchylkou 1,2 mm: ",[1115,11852,11854],{"className":11853},[1573],[1575,11855,11856],{"xmlns":1577},[1579,11857,11858,11882],{},[1582,11859,11860,11862,11864,11866,11868,11871,11873,11880],{},[1585,11861,1594],{},[1589,11863,11763],{},[1585,11865,1927],{},[1589,11867,1170],{"stretchy":1591},[1716,11869,11870],{},"42",[1589,11872,9483],{"separator":1121},[1986,11874,11875,11878],{},[1716,11876,11877],{},"1,2",[1716,11879,1993],{},[1589,11881,1603],{"stretchy":1591},[1605,11883,11884],{"encoding":1607},"X \\sim N(42; 1{,}2^2)",". Výrobky s délkou 41 až 43 mm jsou zařazeny do 1. jakostní třídy. Jaké je procento výrobků v 1. jakostní třídě?",[1110,11887,11888],{},[1303,11889],{"alt":11890,"className":11891,"src":11892},"mask-nv-priklad-delka",[1130,1307],"\u002Fwiki-assets\u002Fmask-nv-priklad-delka.png",[1144,11894,11896],{"className":1146,"code":11895,"language":71,"meta":1148,"style":1148},"pnorm(43, mean = 42, sd = 1.2) - pnorm(41, mean = 42, sd = 1.2)\n",[1150,11897,11898],{"__ignoreMap":1148},[1115,11899,11900,11902,11904,11907,11909,11911,11913,11916,11918,11920,11922,11925,11927,11929,11932,11934,11937,11939,11941,11943,11945,11947,11949,11951,11953],{"class":1154,"line":10},[1115,11901,9501],{"class":1165},[1115,11903,1170],{"class":1169},[1115,11905,11906],{"class":1173},"43",[1115,11908,1177],{"class":1161},[1115,11910,11811],{"class":1157},[1115,11912,6416],{"class":1161},[1115,11914,11915],{"class":1173}," 42",[1115,11917,1177],{"class":1161},[1115,11919,11821],{"class":1157},[1115,11921,6416],{"class":1161},[1115,11923,11924],{"class":1173}," 1.2",[1115,11926,7214],{"class":1169},[1115,11928,7250],{"class":1161},[1115,11930,11931],{"class":1165}," pnorm",[1115,11933,1170],{"class":1169},[1115,11935,11936],{"class":1173},"41",[1115,11938,1177],{"class":1161},[1115,11940,11811],{"class":1157},[1115,11942,6416],{"class":1161},[1115,11944,11915],{"class":1173},[1115,11946,1177],{"class":1161},[1115,11948,11821],{"class":1157},[1115,11950,6416],{"class":1161},[1115,11952,11924],{"class":1173},[1115,11954,6519],{"class":1169},[1144,11956,11959],{"className":11957,"code":11958,"language":6540,"meta":1148},[6538],"[1] 0.5953432\n",[1150,11960,11958],{"__ignoreMap":1148},[1110,11962,11963],{},"Do 1. jakostní třídy spadá přibližně 59,53 % výrobků.",[1103,11965,11967,11974],{"className":11966,"dataCallout":6105},[1106,6104],[1110,11968,11970,11973],{"className":11969},[1113],[1115,11971],{"className":11972,"ariaHidden":1121},[1118,6112,1120],"Příklad: Obsah ampulky",[1110,11975,11976,11977,12000,12001,12027],{},"Obsah ampulky s lékem (v cm³) má rozdělení ",[1115,11978,11980],{"className":11979},[1573],[1575,11981,11982],{"xmlns":1577},[1579,11983,11984,11998],{},[1582,11985,11986,11988,11990,11992,11994,11996],{},[1585,11987,1927],{},[1589,11989,1170],{"stretchy":1591},[1716,11991,11613],{},[1589,11993,9483],{"separator":1121},[1716,11995,11618],{},[1589,11997,1603],{"stretchy":1591},[1605,11999,11623],{"encoding":1607},", tedy střední hodnota 10 a rozptyl 0,12 (",[1115,12002,12004],{"className":12003},[1573],[1575,12005,12006],{"xmlns":1577},[1579,12007,12008,12024],{},[1582,12009,12010,12012,12014,12018,12021],{},[1585,12011,1990],{},[1589,12013,1597],{},[7068,12015,12016],{},[1716,12017,11618],{},[1589,12019,12020],{},"≈",[1716,12022,12023],{},"0,346",[1605,12025,12026],{"encoding":1607},"\\sigma = \\sqrt{0{,}12} \\approx 0{,}346","). Kolik procent ampulek má obsah menší než 9,8 cm³?",[1110,12029,12030],{},[1303,12031],{"alt":12032,"className":12033,"src":12034},"mask-nv-priklad-ampulka",[1130,1307],"\u002Fwiki-assets\u002Fmask-nv-priklad-ampulka.png",[1144,12036,12038],{"className":1146,"code":12037,"language":71,"meta":1148,"style":1148},"pnorm(9.8, mean = 10, sd = sqrt(0.12))\n",[1150,12039,12040],{"__ignoreMap":1148},[1115,12041,12042,12044,12046,12049,12051,12053,12055,12058,12060,12062,12064,12066,12068,12071],{"class":1154,"line":10},[1115,12043,9501],{"class":1165},[1115,12045,1170],{"class":1169},[1115,12047,12048],{"class":1173},"9.8",[1115,12050,1177],{"class":1161},[1115,12052,11811],{"class":1157},[1115,12054,6416],{"class":1161},[1115,12056,12057],{"class":1173}," 10",[1115,12059,1177],{"class":1161},[1115,12061,11821],{"class":1157},[1115,12063,6416],{"class":1161},[1115,12065,7191],{"class":1165},[1115,12067,1170],{"class":1169},[1115,12069,12070],{"class":1173},"0.12",[1115,12072,12073],{"class":1169},"))\n",[1144,12075,12078],{"className":12076,"code":12077,"language":6540,"meta":1148},[6538],"[1] 0.2818514\n",[1150,12079,12077],{"__ignoreMap":1148},[1110,12081,12082],{},"Obsah menší než 9,8 cm³ má přibližně 28,19 % ampulek.",[1136,12084,12086],{"id":12085},"další-rozdělení-dostupná-v-r","Další rozdělení dostupná v R",[1110,12088,12089,12090,12092,12093,12096,12097,12099,12100,4023,12102,12104,12105,12108],{},"Vedle normálního rozdělení R přímo nabízí hustotu, distribuční funkci a kvantilovou funkci i pro další běžná rozdělení. Pojmenování funkcí je jednotné: ",[1150,12091,2405],{}," je hustota\u002Fpravděpodobnostní funkce, ",[1150,12094,12095],{},"p*"," distribuční funkce (s ",[1150,12098,2311],{},", případně čtvrtým argumentem ",[1150,12101,3715],{},[1150,12103,2315],{},", pro horní chvost) a ",[1150,12106,12107],{},"q*"," kvantilová funkce.",[1310,12110,12111,12214],{},[1313,12112,12113],{},[1316,12114,12115,12117,12162,12187],{},[1319,12116,1567],{},[1319,12118,12119,2539,12143],{},[1115,12120,12122],{"className":12121},[1573],[1575,12123,12124],{"xmlns":1577},[1579,12125,12126,12140],{},[1582,12127,12128,12130,12132,12134,12136,12138],{},[1585,12129,1587],{},[1589,12131,1170],{"stretchy":1591},[1585,12133,1594],{},[1589,12135,1597],{},[1585,12137,1600],{},[1589,12139,1603],{"stretchy":1591},[1605,12141,12142],{"encoding":1607},"P(X=k)",[1115,12144,12146],{"className":12145},[1573],[1575,12147,12148],{"xmlns":1577},[1579,12149,12150,12160],{},[1582,12151,12152,12154,12156,12158],{},[1585,12153,1621],{},[1589,12155,1170],{"stretchy":1591},[1585,12157,1158],{},[1589,12159,1603],{"stretchy":1591},[1605,12161,1630],{"encoding":1607},[1319,12163,12164],{},[1115,12165,12167],{"className":12166},[1573],[1575,12168,12169],{"xmlns":1577},[1579,12170,12171,12185],{},[1582,12172,12173,12175,12177,12179,12181,12183],{},[1585,12174,1587],{},[1589,12176,1170],{"stretchy":1591},[1585,12178,1594],{},[1589,12180,1650],{},[1585,12182,1600],{},[1589,12184,1603],{"stretchy":1591},[1605,12186,1657],{"encoding":1607},[1319,12188,12189,12190],{},"horní chvost ",[1115,12191,12193],{"className":12192},[1573],[1575,12194,12195],{"xmlns":1577},[1579,12196,12197,12211],{},[1582,12198,12199,12201,12203,12205,12207,12209],{},[1585,12200,1587],{},[1589,12202,1170],{"stretchy":1591},[1585,12204,1594],{},[1589,12206,1698],{},[1585,12208,1600],{},[1589,12210,1603],{"stretchy":1591},[1605,12212,12213],{"encoding":1607},"P(X>k)",[1332,12215,12216,12257,12294,12329,12372],{},[1316,12217,12218,12245,12249,12253],{},[1337,12219,1761,12220],{},[1115,12221,12223],{"className":12222},[1573],[1575,12224,12225],{"xmlns":1577},[1579,12226,12227,12243],{},[1582,12228,12229,12231,12233,12235,12237,12239,12241],{},[1585,12230,1773],{},[1585,12232,1776],{},[1589,12234,1170],{"stretchy":1591},[1585,12236,1781],{},[1589,12238,1177],{"separator":1121},[1585,12240,1110],{},[1589,12242,1603],{"stretchy":1591},[1605,12244,1790],{"encoding":1607},[1337,12246,12247],{},[1150,12248,1795],{},[1337,12250,12251],{},[1150,12252,1800],{},[1337,12254,12255],{},[1150,12256,1805],{},[1316,12258,12259,12282,12286,12290],{},[1337,12260,1815,12261],{},[1115,12262,12264],{"className":12263},[1573],[1575,12265,12266],{"xmlns":1577},[1579,12267,12268,12280],{},[1582,12269,12270,12272,12274,12276,12278],{},[1585,12271,1587],{},[1585,12273,1829],{},[1589,12275,1170],{"stretchy":1591},[1585,12277,1834],{},[1589,12279,1603],{"stretchy":1591},[1605,12281,1839],{"encoding":1607},[1337,12283,12284],{},[1150,12285,1844],{},[1337,12287,12288],{},[1150,12289,1849],{},[1337,12291,12292],{},[1150,12293,1854],{},[1316,12295,12296,12317,12321,12325],{},[1337,12297,1864,12298],{},[1115,12299,12301],{"className":12300},[1573],[1575,12302,12303],{"xmlns":1577},[1579,12304,12305,12315],{},[1582,12306,12307,12309,12311,12313],{},[1585,12308,1876],{},[1589,12310,1170],{"stretchy":1591},[1585,12312,1110],{},[1589,12314,1603],{"stretchy":1591},[1605,12316,1885],{"encoding":1607},[1337,12318,12319],{},[1150,12320,1890],{},[1337,12322,12323],{},[1150,12324,1895],{},[1337,12326,12327],{},[1150,12328,1900],{},[1316,12330,12331,12360,12364,12368],{},[1337,12332,1910,12333],{},[1115,12334,12336],{"className":12335},[1573],[1575,12337,12338],{"xmlns":1577},[1579,12339,12340,12358],{},[1582,12341,12342,12344,12346,12348,12350,12352,12354,12356],{},[1585,12343,1922],{},[1589,12345,1170],{"stretchy":1591},[1585,12347,1927],{},[1589,12349,1177],{"separator":1121},[1585,12351,1932],{},[1589,12353,1177],{"separator":1121},[1585,12355,1781],{},[1589,12357,1603],{"stretchy":1591},[1605,12359,1941],{"encoding":1607},[1337,12361,12362],{},[1150,12363,1946],{},[1337,12365,12366],{},[1150,12367,1951],{},[1337,12369,12370],{},[1150,12371,1956],{},[1316,12373,12374,12395,12400,12405],{},[1337,12375,2023,12376],{},[1115,12377,12379],{"className":12378},[1573],[1575,12380,12381],{"xmlns":1577},[1579,12382,12383,12393],{},[1582,12384,12385,12387,12389,12391],{},[1585,12386,2035],{},[1589,12388,1170],{"stretchy":1591},[1585,12390,2040],{},[1589,12392,1603],{"stretchy":1591},[1605,12394,2045],{"encoding":1607},[1337,12396,12397],{},[1150,12398,12399],{},"dexp(k, 1\u002Fdelta)",[1337,12401,12402],{},[1150,12403,12404],{},"pexp(k, 1\u002Fdelta)",[1337,12406,12407],{},[1150,12408,12409],{},"pexp(k, 1\u002Fdelta, FALSE)",[1103,12411,12413,12420],{"className":12412,"dataCallout":9019},[1106,9018],[1110,12414,12416,12419],{"className":12415},[1113],[1115,12417],{"className":12418,"ariaHidden":1121},[1118,9026,1120],"Exponenciální rozdělení: R bere intenzitu, ne střední hodnotu",[1110,12421,12422,12423,12426,12427,12440,12441,11628,12443,2264],{},"R parametrizuje exponenciální rozdělení intenzitou (",[1150,12424,12425],{},"rate","). Je-li ",[1115,12428,12430],{"className":12429},[1573],[1575,12431,12432],{"xmlns":1577},[1579,12433,12434,12438],{},[1582,12435,12436],{},[1585,12437,2040],{},[1605,12439,2285],{"encoding":1607}," střední doba do události, do R se dosazuje ",[1150,12442,2270],{},[1150,12444,12445],{},"delta",[1110,12447,12448,12449,12481,12482,12500],{},"V R (pravděpodobnostní a distribuční funkce diskrétní náhodné veličiny ",[1115,12450,12452],{"className":12451},[1573],[1575,12453,12454],{"xmlns":1577},[1579,12455,12456,12478],{},[1582,12457,12458,12460,12462,12464,12466,12468,12471,12473,12476],{},[1585,12459,1594],{},[1589,12461,11763],{},[1585,12463,1773],{},[1585,12465,1776],{},[1589,12467,1170],{"stretchy":1591},[1716,12469,12470],{},"5",[1589,12472,9483],{"separator":1121},[1716,12474,12475],{},"0,95",[1589,12477,1603],{"stretchy":1591},[1605,12479,12480],{"encoding":1607},"X \\sim Bi(5; 0{,}95)",", a pravděpodobnost, že u exponenciálního rozdělení se střední hodnotou ",[1115,12483,12485],{"className":12484},[1573],[1575,12486,12487],{"xmlns":1577},[1579,12488,12489,12497],{},[1582,12490,12491,12493,12495],{},[1585,12492,2040],{},[1589,12494,1597],{},[1716,12496,12470],{},[1605,12498,12499],{"encoding":1607},"\\delta = 5"," nastane událost do 3 jednotek času):",[1144,12502,12504],{"className":1146,"code":12503,"language":71,"meta":1148,"style":1148},"x \u003C- 0:5\nround(dbinom(x, 5, 0.95), 4)\nround(pbinom(x, 5, 0.95), 4)\n\ndelta \u003C- 5\nround(pexp(3, rate = 1 \u002F delta), 4)\n",[1150,12505,12506,12520,12552,12581,12586,12595],{"__ignoreMap":1148},[1115,12507,12508,12510,12512,12515,12517],{"class":1154,"line":10},[1115,12509,1158],{"class":1157},[1115,12511,1162],{"class":1161},[1115,12513,12514],{"class":1173}," 0",[1115,12516,4595],{"class":1161},[1115,12518,12519],{"class":1173},"5\n",[1115,12521,12522,12525,12527,12530,12532,12534,12536,12539,12541,12544,12546,12548,12550],{"class":1154,"line":27},[1115,12523,12524],{"class":1165},"round",[1115,12526,1170],{"class":1169},[1115,12528,12529],{"class":1165},"dbinom",[1115,12531,1170],{"class":1169},[1115,12533,1158],{"class":1157},[1115,12535,1177],{"class":1161},[1115,12537,12538],{"class":1173}," 5",[1115,12540,1177],{"class":1161},[1115,12542,12543],{"class":1173}," 0.95",[1115,12545,1603],{"class":1169},[1115,12547,1177],{"class":1161},[1115,12549,6419],{"class":1173},[1115,12551,6519],{"class":1169},[1115,12553,12554,12556,12558,12561,12563,12565,12567,12569,12571,12573,12575,12577,12579],{"class":1154,"line":148},[1115,12555,12524],{"class":1165},[1115,12557,1170],{"class":1169},[1115,12559,12560],{"class":1165},"pbinom",[1115,12562,1170],{"class":1169},[1115,12564,1158],{"class":1157},[1115,12566,1177],{"class":1161},[1115,12568,12538],{"class":1173},[1115,12570,1177],{"class":1161},[1115,12572,12543],{"class":1173},[1115,12574,1603],{"class":1169},[1115,12576,1177],{"class":1161},[1115,12578,6419],{"class":1173},[1115,12580,6519],{"class":1169},[1115,12582,12583],{"class":1154,"line":111},[1115,12584,12585],{"emptyLinePlaceholder":4157},"\n",[1115,12587,12588,12590,12592],{"class":1154,"line":96},[1115,12589,12445],{"class":1157},[1115,12591,1162],{"class":1161},[1115,12593,12594],{"class":1173}," 5\n",[1115,12596,12597,12599,12601,12604,12606,12608,12610,12613,12615,12617,12620,12623,12625,12627,12629],{"class":1154,"line":89},[1115,12598,12524],{"class":1165},[1115,12600,1170],{"class":1169},[1115,12602,12603],{"class":1165},"pexp",[1115,12605,1170],{"class":1169},[1115,12607,6220],{"class":1173},[1115,12609,1177],{"class":1161},[1115,12611,12612],{"class":1157}," rate",[1115,12614,6416],{"class":1161},[1115,12616,7253],{"class":1173},[1115,12618,12619],{"class":1161}," \u002F",[1115,12621,12622],{"class":1157}," delta",[1115,12624,1603],{"class":1169},[1115,12626,1177],{"class":1161},[1115,12628,6419],{"class":1173},[1115,12630,6519],{"class":1169},[1144,12632,12635],{"className":12633,"code":12634,"language":6540,"meta":1148},[6538],"[1] 0.0000 0.0000 0.0011 0.0214 0.2036 0.7738\n[1] 0.0000 0.0000 0.0012 0.0226 0.2262 1.0000\n[1] 0.4512\n",[1150,12636,12634],{"__ignoreMap":1148},[1136,12638,12640],{"id":12639},"studentovo-pearsonovo-a-fisherovo-snedecorovo-rozdělení","Studentovo, Pearsonovo a Fisherovo-Snedecorovo rozdělení",[1110,12642,12643,12644,12647],{},"Tato tři rozdělení mají statistiky, které se dále používají při konstrukci intervalů spolehlivosti a testování hypotéz (viz ",[1127,12645,141],{"className":12646,"dataFsResolvedFilePath":2658,"href":2659},[1130],") — na rozdíl od normálního rozdělení se v příkladech této kapitoly samostatně nepočítají, jsou to nástroje pro další kapitoly.",[1110,12649,12650,6569,12653,12666],{},[2227,12651,12652],{},"Studentovo rozdělení",[1115,12654,12656],{"className":12655},[1573],[1575,12657,12658],{"xmlns":1577},[1579,12659,12660,12664],{},[1582,12661,12662],{},[1585,12663,1600],{},[1605,12665,1600],{"encoding":1607}," stupni volnosti má hustotu pravděpodobnosti",[1115,12668,12670],{"className":12669},[1573],[1575,12671,12672],{"xmlns":1577,"display":4601},[1579,12673,12674,12769],{},[1582,12675,12676,12678,12680,12682,12684,12686,12718,12756,12758,12760,12762,12764,12767],{},[1585,12677,1621],{},[1589,12679,1170],{"stretchy":1591},[1585,12681,1158],{},[1589,12683,1603],{"stretchy":1591},[1589,12685,1597],{},[5373,12687,12688,12690],{},[1716,12689,1718],{},[1582,12691,12692,12694,12714],{},[1585,12693,1773],{},[1582,12695,12696,12698,12704,12706,12712],{},[1589,12697,1170],{"fence":1121},[5373,12699,12700,12702],{},[1716,12701,1718],{},[1716,12703,1993],{},[1589,12705,1177],{"separator":1121},[5373,12707,12708,12710],{},[1585,12709,1600],{},[1716,12711,1993],{},[1589,12713,1603],{"fence":1121},[7068,12715,12716],{},[1585,12717,1600],{},[1986,12719,12720,12740],{},[1582,12721,12722,12724,12726,12728,12738],{},[1589,12723,1170],{"fence":1121},[1716,12725,1718],{},[1589,12727,4010],{},[5373,12729,12730,12736],{},[1986,12731,12732,12734],{},[1585,12733,1158],{},[1716,12735,1993],{},[1585,12737,1600],{},[1589,12739,1603],{"fence":1121},[1582,12741,12742,12744],{},[1589,12743,1721],{},[5373,12745,12746,12754],{},[1582,12747,12748,12750,12752],{},[1585,12749,1600],{},[1589,12751,4010],{},[1716,12753,1718],{},[1716,12755,1993],{},[1589,12757,1177],{"separator":1121},[4648,12759],{"width":4650},[1585,12761,1158],{},[1589,12763,9605],{},[1585,12765,3376],{"mathvariant":12766},"double-struck",[1589,12768,1177],{"separator":1121},[1605,12770,12771],{"encoding":1607},"f(x) = \\frac{1}{B\\left(\\frac12, \\frac{k}{2}\\right)\\sqrt{k}} \\left(1 + \\frac{x^2}{k}\\right)^{-\\frac{k+1}{2}}, \\qquad x \\in \\mathbb{R},",[1110,12773,7121,12774,12787,12788,12801,12802,12815],{},[1115,12775,12777],{"className":12776},[1573],[1575,12778,12779],{"xmlns":1577},[1579,12780,12781,12785],{},[1582,12782,12783],{},[1585,12784,1773],{},[1605,12786,1773],{"encoding":1607}," je funkce beta. Je symetrické kolem nuly; číslo ",[1115,12789,12791],{"className":12790},[1573],[1575,12792,12793],{"xmlns":1577},[1579,12794,12795,12799],{},[1582,12796,12797],{},[1585,12798,1600],{},[1605,12800,1600],{"encoding":1607}," určuje tvar křivky — s rostoucím ",[1115,12803,12805],{"className":12804},[1573],[1575,12806,12807],{"xmlns":1577},[1579,12808,12809,12813],{},[1582,12810,12811],{},[1585,12812,1600],{},[1605,12814,1600],{"encoding":1607}," se rozdělení blíží normálnímu.",[1110,12817,12818,6569,12821,12834],{},[2227,12819,12820],{},"Pearsonovo (chí-kvadrát) rozdělení",[1115,12822,12824],{"className":12823},[1573],[1575,12825,12826],{"xmlns":1577},[1579,12827,12828,12832],{},[1582,12829,12830],{},[1585,12831,1600],{},[1605,12833,1600],{"encoding":1607}," stupni volnosti:",[1115,12836,12838],{"className":12837},[1573],[1575,12839,12840],{"xmlns":1577,"display":4601},[1579,12841,12842,12927],{},[1582,12843,12844,12846,12848,12850,12852,12854,12885,12901,12915,12917,12919,12921,12923,12925],{},[1585,12845,1621],{},[1589,12847,1170],{"stretchy":1591},[1585,12849,1158],{},[1589,12851,1603],{"stretchy":1591},[1589,12853,1597],{},[5373,12855,12856,12858],{},[1716,12857,1718],{},[1582,12859,12860,12872,12875,12877,12879,12881,12883],{},[1986,12861,12862,12864],{},[1716,12863,1993],{},[1582,12865,12866,12868,12870],{},[1585,12867,1600],{},[1585,12869,4023],{"mathvariant":4022},[1716,12871,1993],{},[1585,12873,12874],{"mathvariant":4022},"Γ",[1589,12876,1170],{"stretchy":1591},[1585,12878,1600],{},[1585,12880,4023],{"mathvariant":4022},[1716,12882,1993],{},[1589,12884,1603],{"stretchy":1591},[1986,12886,12887,12889],{},[1585,12888,1158],{},[1582,12890,12891,12893,12895,12897,12899],{},[1585,12892,1600],{},[1585,12894,4023],{"mathvariant":4022},[1716,12896,1993],{},[1589,12898,1721],{},[1716,12900,1718],{},[1986,12902,12903,12905],{},[1585,12904,2876],{},[1582,12906,12907,12909,12911,12913],{},[1589,12908,1721],{},[1585,12910,1158],{},[1585,12912,4023],{"mathvariant":4022},[1716,12914,1993],{},[1589,12916,1177],{"separator":1121},[4648,12918],{"width":4650},[1585,12920,1158],{},[1589,12922,1698],{},[1716,12924,2398],{},[1589,12926,1177],{"separator":1121},[1605,12928,12929],{"encoding":1607},"f(x) = \\frac{1}{2^{k\u002F2}\\Gamma(k\u002F2)} x^{k\u002F2-1} e^{-x\u002F2}, \\qquad x > 0,",[1110,12931,7121,12932,12946],{},[1115,12933,12935],{"className":12934},[1573],[1575,12936,12937],{"xmlns":1577},[1579,12938,12939,12943],{},[1582,12940,12941],{},[1585,12942,12874],{"mathvariant":4022},[1605,12944,12945],{"encoding":1607},"\\Gamma"," je funkce gama.",[1110,12948,12949,12952,12953,1260,12971,4595],{},[2227,12950,12951],{},"Fisherovo-Snedecorovo rozdělení"," se stupni volnosti ",[1115,12954,12956],{"className":12955},[1573],[1575,12957,12958],{"xmlns":1577},[1579,12959,12960,12968],{},[1582,12961,12962],{},[1746,12963,12964,12966],{},[1585,12965,1600],{},[1716,12967,1718],{},[1605,12969,12970],{"encoding":1607},"k_1",[1115,12972,12974],{"className":12973},[1573],[1575,12975,12976],{"xmlns":1577},[1579,12977,12978,12986],{},[1582,12979,12980],{},[1746,12981,12982,12984],{},[1585,12983,1600],{},[1716,12985,1993],{},[1605,12987,12988],{"encoding":1607},"k_2",[1115,12990,12992],{"className":12991},[1573],[1575,12993,12994],{"xmlns":1577,"display":4601},[1579,12995,12996,13161],{},[1582,12997,12998,13000,13002,13004,13006,13008,13044,13078,13098,13150,13152,13154,13156,13158],{},[1585,12999,1621],{},[1589,13001,1170],{"stretchy":1591},[1585,13003,1158],{},[1589,13005,1603],{"stretchy":1591},[1589,13007,1597],{},[5373,13009,13010,13012],{},[1716,13011,1718],{},[1582,13013,13014,13016],{},[1585,13015,1773],{},[1582,13017,13018,13020,13030,13032,13042],{},[1589,13019,1170],{"fence":1121},[5373,13021,13022,13028],{},[1746,13023,13024,13026],{},[1585,13025,1600],{},[1716,13027,1718],{},[1716,13029,1993],{},[1589,13031,1177],{"separator":1121},[5373,13033,13034,13040],{},[1746,13035,13036,13038],{},[1585,13037,1600],{},[1716,13039,1993],{},[1716,13041,1993],{},[1589,13043,1603],{"fence":1121},[1986,13045,13046,13066],{},[1582,13047,13048,13050,13064],{},[1589,13049,1170],{"fence":1121},[5373,13051,13052,13058],{},[1746,13053,13054,13056],{},[1585,13055,1600],{},[1716,13057,1718],{},[1746,13059,13060,13062],{},[1585,13061,1600],{},[1716,13063,1993],{},[1589,13065,1603],{"fence":1121},[1582,13067,13068,13074,13076],{},[1746,13069,13070,13072],{},[1585,13071,1600],{},[1716,13073,1718],{},[1585,13075,4023],{"mathvariant":4022},[1716,13077,1993],{},[1986,13079,13080,13082],{},[1585,13081,1158],{},[1582,13083,13084,13090,13092,13094,13096],{},[1746,13085,13086,13088],{},[1585,13087,1600],{},[1716,13089,1718],{},[1585,13091,4023],{"mathvariant":4022},[1716,13093,1993],{},[1589,13095,1721],{},[1716,13097,1718],{},[1986,13099,13100,13126],{},[1582,13101,13102,13104,13106,13108,13122,13124],{},[1589,13103,1170],{"fence":1121},[1716,13105,1718],{},[1589,13107,4010],{},[5373,13109,13110,13116],{},[1746,13111,13112,13114],{},[1585,13113,1600],{},[1716,13115,1718],{},[1746,13117,13118,13120],{},[1585,13119,1600],{},[1716,13121,1993],{},[1585,13123,1158],{},[1589,13125,1603],{"fence":1121},[1582,13127,13128,13130],{},[1589,13129,1721],{},[5373,13131,13132,13148],{},[1582,13133,13134,13140,13142],{},[1746,13135,13136,13138],{},[1585,13137,1600],{},[1716,13139,1718],{},[1589,13141,4010],{},[1746,13143,13144,13146],{},[1585,13145,1600],{},[1716,13147,1993],{},[1716,13149,1993],{},[1589,13151,1177],{"separator":1121},[4648,13153],{"width":4650},[1585,13155,1158],{},[1589,13157,1698],{},[1716,13159,13160],{},"0.",[1605,13162,13163],{"encoding":1607},"f(x) = \\frac{1}{B\\left(\\frac{k_1}{2}, \\frac{k_2}{2}\\right)} \\left(\\frac{k_1}{k_2}\\right)^{k_1\u002F2} x^{k_1\u002F2 - 1} \\left(1 + \\frac{k_1}{k_2}x\\right)^{-\\frac{k_1+k_2}{2}}, \\qquad x > 0.",[1110,13165,13166],{},[1303,13167],{"alt":13168,"className":13169,"src":13170},"mask-nv-specialni-rozdeleni",[1130,1307],"\u002Fwiki-assets\u002Fmask-nv-specialni-rozdeleni.png",[11526,13172],{"spec":13173},"{\"title\":\"Studentovo rozdělení a jeho konvergence k normálnímu rozdělení\",\"alt\":\"Srovnání hustoty standardizovaného normálního rozdělení N(0;1) s hustotou Studentova rozdělení pro k = 1, 2 a 4 stupně volnosti. S rostoucím k se Studentovo rozdělení přibližuje normálnímu — má méně těžké konce a vyšší vrchol.\",\"engine\":\"function-plot\",\"xAxis\":{\"label\":\"x\",\"domain\":[-6,6]},\"yAxis\":{\"label\":\"f(x)\",\"domain\":[0,0.42]},\"params\":[],\"curves\":[{\"fn\":\"exp(-x^2\u002F2)\u002Fsqrt(2*PI)\",\"label\":\"N(0; 1)\",\"color\":\"ink\"},{\"fn\":\"(1\u002FPI)*(1+x^2)^(-1)\",\"label\":\"t, k = 1\",\"color\":\"fp-red\"},{\"fn\":\"(1\u002F(2*sqrt(2)))*(1+x^2\u002F2)^(-1.5)\",\"label\":\"t, k = 2\",\"color\":\"fp-purple\"},{\"fn\":\"(3\u002F8)*(1+x^2\u002F4)^(-2.5)\",\"label\":\"t, k = 4\",\"color\":\"paper-500\"}],\"markers\":[]}",[1110,13175,13176],{},"R funkce pro tato tři rozdělení:",[1310,13178,13179,13193],{},[1313,13180,13181],{},[1316,13182,13183,13185,13188,13190],{},[1319,13184,1567],{},[1319,13186,13187],{},"hustota",[1319,13189,9302],{},[1319,13191,13192],{},"kvantil",[1332,13194,13195,13231,13271],{},[1316,13196,13197,13218,13222,13226],{},[1337,13198,2070,13199],{},[1115,13200,13202],{"className":13201},[1573],[1575,13203,13204],{"xmlns":1577},[1579,13205,13206,13216],{},[1582,13207,13208,13210,13212,13214],{},[1585,13209,2082],{},[1589,13211,1170],{"stretchy":1591},[1585,13213,1600],{},[1589,13215,1603],{"stretchy":1591},[1605,13217,2091],{"encoding":1607},[1337,13219,13220],{},[1150,13221,2096],{},[1337,13223,13224],{},[1150,13225,2101],{},[1337,13227,13228],{},[1150,13229,13230],{},"qt(p, df = k)",[1316,13232,13233,13258,13262,13266],{},[1337,13234,2116,13235],{},[1115,13236,13238],{"className":13237},[1573],[1575,13239,13240],{"xmlns":1577},[1579,13241,13242,13256],{},[1582,13243,13244,13250,13252,13254],{},[1986,13245,13246,13248],{},[1585,13247,2130],{},[1716,13249,1993],{},[1589,13251,1170],{"stretchy":1591},[1585,13253,1600],{},[1589,13255,1603],{"stretchy":1591},[1605,13257,2141],{"encoding":1607},[1337,13259,13260],{},[1150,13261,2146],{},[1337,13263,13264],{},[1150,13265,2151],{},[1337,13267,13268],{},[1150,13269,13270],{},"qchisq(p, df = k)",[1316,13272,13273,13307,13311,13315],{},[1337,13274,2166,13275],{},[1115,13276,13278],{"className":13277},[1573],[1575,13279,13280],{"xmlns":1577},[1579,13281,13282,13304],{},[1582,13283,13284,13286,13288,13294,13296,13302],{},[1585,13285,1669],{},[1589,13287,1170],{"stretchy":1591},[1746,13289,13290,13292],{},[1585,13291,1600],{},[1716,13293,1718],{},[1589,13295,1177],{"separator":1121},[1746,13297,13298,13300],{},[1585,13299,1600],{},[1716,13301,1993],{},[1589,13303,1603],{"stretchy":1591},[1605,13305,13306],{"encoding":1607},"F(k_1, k_2)",[1337,13308,13309],{},[1150,13310,2203],{},[1337,13312,13313],{},[1150,13314,2208],{},[1337,13316,13317],{},[1150,13318,13319],{},"qf(p, df1 = k1, df2 = k2)",[1110,13321,13322],{},"V R (97,5%-ní kvantil Studentova rozdělení s 9 stupni volnosti, 95%-ní kvantily Pearsonova a Fisherova-Snedecorova rozdělení):",[1144,13324,13326],{"className":1146,"code":13325,"language":71,"meta":1148,"style":1148},"qt(0.975, df = 9)\nqchisq(0.95, df = 9)\nqf(0.95, df1 = 3, df2 = 10)\n",[1150,13327,13328,13349,13368],{"__ignoreMap":1148},[1115,13329,13330,13333,13335,13337,13339,13342,13344,13347],{"class":1154,"line":10},[1115,13331,13332],{"class":1165},"qt",[1115,13334,1170],{"class":1169},[1115,13336,11669],{"class":1173},[1115,13338,1177],{"class":1161},[1115,13340,13341],{"class":1157}," df",[1115,13343,6416],{"class":1161},[1115,13345,13346],{"class":1173}," 9",[1115,13348,6519],{"class":1169},[1115,13350,13351,13354,13356,13358,13360,13362,13364,13366],{"class":1154,"line":27},[1115,13352,13353],{"class":1165},"qchisq",[1115,13355,1170],{"class":1169},[1115,13357,3843],{"class":1173},[1115,13359,1177],{"class":1161},[1115,13361,13341],{"class":1157},[1115,13363,6416],{"class":1161},[1115,13365,13346],{"class":1173},[1115,13367,6519],{"class":1169},[1115,13369,13370,13373,13375,13377,13379,13382,13384,13387,13389,13392,13394,13396],{"class":1154,"line":148},[1115,13371,13372],{"class":1165},"qf",[1115,13374,1170],{"class":1169},[1115,13376,3843],{"class":1173},[1115,13378,1177],{"class":1161},[1115,13380,13381],{"class":1157}," df1",[1115,13383,6416],{"class":1161},[1115,13385,13386],{"class":1173}," 3",[1115,13388,1177],{"class":1161},[1115,13390,13391],{"class":1157}," df2",[1115,13393,6416],{"class":1161},[1115,13395,12057],{"class":1173},[1115,13397,6519],{"class":1169},[1144,13399,13402],{"className":13400,"code":13401,"language":6540,"meta":1148},[6538],"[1] 2.262157\n[1] 16.91898\n[1] 3.708265\n",[1150,13403,13401],{"__ignoreMap":1148},[1136,13405,9014],{"id":9013},[2220,13407,13408,13494,13544],{},[2223,13409,13410,13413,13414,13441,13442,4023,13444,4023,13446,13448,13449,13469,13470,13493],{},[2227,13411,13412],{},"Rozptyl vs. směrodatná odchylka v R."," Zápis ",[1115,13415,13417],{"className":13416},[1573],[1575,13418,13419],{"xmlns":1577},[1579,13420,13421,13439],{},[1582,13422,13423,13425,13427,13429,13431,13437],{},[1585,13424,1927],{},[1589,13426,1170],{"stretchy":1591},[1585,13428,1982],{},[1589,13430,9483],{"separator":1121},[1986,13432,13433,13435],{},[1585,13434,1990],{},[1716,13436,1993],{},[1589,13438,1603],{"stretchy":1591},[1605,13440,9494],{"encoding":1607}," používá rozptyl, ale ",[1150,13443,9498],{},[1150,13445,9501],{},[1150,13447,9504],{}," očekávají směrodatnou odchylku. Dosazení rozptylu místo ",[1115,13450,13452],{"className":13451},[1573],[1575,13453,13454],{"xmlns":1577},[1579,13455,13456,13466],{},[1582,13457,13458],{},[7068,13459,13460],{},[1986,13461,13462,13464],{},[1585,13463,1990],{},[1716,13465,1993],{},[1605,13467,13468],{"encoding":1607},"\\sqrt{\\sigma^2}"," dává jiný — a pro ",[1115,13471,13473],{"className":13472},[1573],[1575,13474,13475],{"xmlns":1577},[1579,13476,13477,13490],{},[1582,13478,13479,13485,13488],{},[1986,13480,13481,13483],{},[1585,13482,1990],{},[1716,13484,1993],{},[1589,13486,13487],{"mathvariant":4022},"≠",[1716,13489,1718],{},[1605,13491,13492],{"encoding":1607},"\\sigma^2 \\ne 1"," výrazně odlišný — výsledek (viz příklad s ampulkou).",[2223,13495,13496,13523,13524,13543],{},[2227,13497,13498,13522],{},[1115,13499,13501],{"className":13500},[1573],[1575,13502,13503],{"xmlns":1577},[1579,13504,13505,13519],{},[1582,13506,13507,13509,13511,13513,13515,13517],{},[1585,13508,1587],{},[1589,13510,1170],{"stretchy":1591},[1585,13512,1594],{},[1589,13514,1597],{},[1585,13516,1158],{},[1589,13518,1603],{"stretchy":1591},[1605,13520,13521],{"encoding":1607},"P(X=x)"," u spojité veličiny je vždy 0."," Hustota ",[1115,13525,13527],{"className":13526},[1573],[1575,13528,13529],{"xmlns":1577},[1579,13530,13531,13541],{},[1582,13532,13533,13535,13537,13539],{},[1585,13534,1621],{},[1589,13536,1170],{"stretchy":1591},[1585,13538,1158],{},[1589,13540,1603],{"stretchy":1591},[1605,13542,1630],{"encoding":1607}," sama o sobě pravděpodobnost neudává — pravděpodobnost dává až plocha pod křivkou na intervalu.",[2223,13545,13546,2230,13549,13566,13567,13584,13585,13588,13589,2264],{},[2227,13547,13548],{},"Záměna stupňů volnosti u Fisherova-Snedecorova rozdělení.",[1115,13550,13552],{"className":13551},[1573],[1575,13553,13554],{"xmlns":1577},[1579,13555,13556,13564],{},[1582,13557,13558],{},[1746,13559,13560,13562],{},[1585,13561,1600],{},[1716,13563,1718],{},[1605,13565,12970],{"encoding":1607}," (čitatel) a ",[1115,13568,13570],{"className":13569},[1573],[1575,13571,13572],{"xmlns":1577},[1579,13573,13574,13582],{},[1582,13575,13576],{},[1746,13577,13578,13580],{},[1585,13579,1600],{},[1716,13581,1993],{},[1605,13583,12988],{"encoding":1607}," (jmenovatel) nejsou zaměnitelné — ",[1150,13586,13587],{},"qf(p, df1, df2)"," dá jiný výsledek než ",[1150,13590,13591],{},"qf(p, df2, df1)",[1136,13593,4071],{"id":4070},[2220,13595,13596,13601,13606,13611,13617,13622,13628],{},[2223,13597,13598],{},[1127,13599,1133],{"className":13600,"dataFsResolvedFilePath":1131,"href":1132},[1130],[2223,13602,13603],{},[1127,13604,886],{"className":13605,"dataFsResolvedFilePath":2413,"href":2414},[1130],[2223,13607,13608],{},[1127,13609,141],{"className":13610,"dataFsResolvedFilePath":2658,"href":2659},[1130],[2223,13612,13613],{},[1127,13614,13616],{"className":13615,"dataFsResolvedFilePath":2796,"href":2797},[1130],"regresni-a-korelacni-analyza",[2223,13618,13619],{},[1127,13620,716],{"className":13621,"dataFsResolvedFilePath":3235,"href":3236},[1130],[2223,13623,13624],{},[1127,13625,13627],{"className":13626,"dataFsResolvedFilePath":3320,"href":3321},[1130],"regulacni-diagramy-a-indexy-zpusobilosti",[2223,13629,13630],{},[1127,13631,9239],{"className":13632,"dataFsResolvedFilePath":9237,"href":9238},[1130],[1136,13634,4111],{"id":934},[1110,13636,4114,13637,4119],{},[4116,13638,4118],{},[4135,13640,13641],{},"html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: 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.sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}",{"title":1148,"searchDepth":27,"depth":27,"links":13643},[13644,13645,13646,13647,13648,13649,13650,13651,13652,13653],{"id":9551,"depth":27,"text":9552},{"id":9855,"depth":27,"text":9856},{"id":10539,"depth":27,"text":10540},{"id":10648,"depth":27,"text":10649},{"id":11084,"depth":27,"text":9465},{"id":12085,"depth":27,"text":12086},{"id":12639,"depth":27,"text":12640},{"id":9013,"depth":27,"text":9014},{"id":4070,"depth":27,"text":4071},{"id":934,"depth":27,"text":4111},{},"\u002Ftopics\u002Fnahodne-veliciny-a-rozdeleni",{"title":1558,"description":1148},[13658,4161,13659],"raw\u002Fmask\u002F01 náhodné veličiny.pdf","raw\u002Fmask\u002Fpříklady 01 a 02.docx","topics\u002Fnahodne-veliciny-a-rozdeleni",[23,67,812,332,532,71],"y7MCWBwmskoGgsMoqVPhRRaL6YYTo3Cf-R4Yf-89eMs",{"id":13664,"title":2415,"body":13665,"course":23,"courses":4153,"created":4154,"description":1148,"extension":4155,"meta":18389,"navigation":4157,"path":18390,"seo":18391,"sources":18392,"stem":18398,"tags":18399,"type":9267,"updated":4154,"__hash__":18400},"topics\u002Ftopics\u002Fpopisna-statistika.md",{"type":1096,"value":13666,"toc":18380},[13667,13669,13763,13767,13777,13903,13910,13921,13925,13968,13973,14072,14082,14087,14226,14302,14306,14406,14487,14494,14556,14570,14572,14788,14794,14803,14810,14813,14867,14873,14883,14896,15042,15045,15058,15377,15383,15386,15390,15469,15503,15532,15534,15611,15617,15678,15685,15698,15775,15890,15940,15953,16108,16114,16141,16145,16170,16173,16386,16453,16553,16560,16573,17076,17082,17114,17374,17527,17638,17667,17673,17680,17686,17699,18129,18135,18138,18140,18333,18335,18372,18374,18378],[1099,13668,2415],{"id":2409},[1103,13670,13672,13678],{"className":13671,"dataCallout":4184},[1106,4183],[1110,13673,13675,4192],{"className":13674},[1113],[1115,13676],{"className":13677,"ariaHidden":1121},[1118,4191,1120],[2220,13679,13680,13683,13686,13713,13760],{},[2223,13681,13682],{},"Rozlišit základní a výběrový soubor, typ statistického znaku (kvantitativní\u002Fkvalitativní, diskrétní\u002Fspojitý) a požadavek reprezentativity a nezávislého výběru.",[2223,13684,13685],{},"Spočítat výběrový průměr, rozptyl, směrodatnou odchylku a variační rozpětí; interpretovat je jako bodové odhady charakteristik náhodné veličiny.",[2223,13687,13688,13689,2264],{},"Určit medián a kvartily a číst empirickou distribuční funkci ",[1115,13690,13692],{"className":13691},[1573],[1575,13693,13694],{"xmlns":1577},[1579,13695,13696,13710],{},[1582,13697,13698,13704,13706,13708],{},[1746,13699,13700,13702],{},[1585,13701,1669],{},[1585,13703,1781],{},[1589,13705,1170],{"stretchy":1591},[1585,13707,1158],{},[1589,13709,1603],{"stretchy":1591},[1605,13711,13712],{"encoding":1607},"F_n(x)",[2223,13714,13715,13716,13759],{},"Roztřídit velký datový soubor do tříd (intervalové rozdělení četností), sestavit tabulku ",[1115,13717,13719],{"className":13718},[1573],[1575,13720,13721],{"xmlns":1577},[1579,13722,13723,13756],{},[1582,13724,13725,13732,13734,13740,13742,13748,13750],{},[1746,13726,13727,13730],{},[1585,13728,13729],{},"I",[1585,13731,4521],{},[1589,13733,1177],{"separator":1121},[1746,13735,13736,13738],{},[1585,13737,11505],{},[1585,13739,4521],{},[1589,13741,1177],{"separator":1121},[1746,13743,13744,13746],{},[1585,13745,1621],{},[1585,13747,4521],{},[1589,13749,1177],{"separator":1121},[1746,13751,13752,13754],{},[1585,13753,1110],{},[1585,13755,4521],{},[1605,13757,13758],{"encoding":1607},"I_j, Z_j, f_j, p_j"," a nakreslit histogram.",[2223,13761,13762],{},"Z histogramu odhadnout zákon rozdělení dat; formální test shody patří do testování hypotéz.",[1136,13764,13766],{"id":13765},"základní-pojmy","Základní pojmy",[1110,13768,13769,13772,13773,13776],{},[1127,13770,1133],{"className":13771,"dataFsResolvedFilePath":1131,"href":1132},[1130]," pracuje s ",[2227,13774,13775],{},"datovými soubory"," — konkrétními hodnotami, které popisují vlastnost zkoumaných prvků.",[2220,13778,13779,13785,13809,13815,13890],{},[2223,13780,13781,13784],{},[2227,13782,13783],{},"Základní soubor"," — množina prvků, na nichž provádíme šetření (např. všichni výdělečně činní obyvatelé ČR).",[2223,13786,13787,13790,13791],{},[2227,13788,13789],{},"Statistický znak"," — funkce, která vyjadřuje určitou vlastnost prvku (např. velikost platu). Znaky dělíme na:\n",[2220,13792,13793,13804],{},[2223,13794,13795,13797,13798,13800,13801,13803],{},[2227,13796,4379],{}," (vyjádřitelné číslem) — dále ",[2227,13799,9291],{}," (spočetně mnoho hodnot) nebo ",[2227,13802,9295],{}," (libovolná hodnota v intervalu);",[2223,13805,13806,13808],{},[2227,13807,4372],{}," (vyjádřitelné slovně).",[2223,13810,13811,13814],{},[2227,13812,13813],{},"Výběrový soubor"," — podmnožina prvků základního souboru, na níž znak skutečně zjišťujeme (např. 5 náhodně vybraných obyvatel).",[2223,13816,13817,13820,13821,2264],{},[2227,13818,13819],{},"Datový soubor"," — n-tice naměřených hodnot zkoumaného znaku, např. ",[1115,13822,13824],{"className":13823},[1573],[1575,13825,13826],{"xmlns":1577},[1579,13827,13828,13887],{},[1582,13829,13830,13832,13834,13836,13839,13841,13844,13847,13849,13852,13854,13856,13859,13861,13864,13866,13868,13870,13872,13874,13876,13878,13880,13882,13885],{},[1589,13831,1170],{"stretchy":1591},[1716,13833,6178],{},[5543,13835,5545],{},[1716,13837,13838],{},"500",[1589,13840,1177],{"separator":1121},[5543,13842,13843],{}," ",[1716,13845,13846],{},"38",[5543,13848,5545],{},[1716,13850,13851],{},"000",[1589,13853,1177],{"separator":1121},[5543,13855,13843],{},[1716,13857,13858],{},"37",[5543,13860,5545],{},[1716,13862,13863],{},"800",[1589,13865,1177],{"separator":1121},[5543,13867,13843],{},[1716,13869,11936],{},[5543,13871,5545],{},[1716,13873,13851],{},[1589,13875,1177],{"separator":1121},[5543,13877,13843],{},[1716,13879,6186],{},[5543,13881,5545],{},[1716,13883,13884],{},"200",[1589,13886,1603],{"stretchy":1591},[1605,13888,13889],{"encoding":1607},"(29\\,500,\\ 38\\,000,\\ 37\\,800,\\ 41\\,000,\\ 31\\,200)",[2223,13891,13892,13893,1279,13896,1260,13899,13902],{},"Podle počtu sledovaných znaků rozlišujeme ",[2227,13894,13895],{},"jednorozměrné",[2227,13897,13898],{},"dvourozměrné",[2227,13900,13901],{},"vícerozměrné"," datové soubory.",[1110,13904,13905],{},[1303,13906],{"alt":13907,"className":13908,"src":13909},"mask-ilu-zakladni-soubor-vyber",[1130,1307],"\u002Fwiki-assets\u002Fmask-ilu-zakladni-soubor-vyber.png",[1110,13911,13912,13913,13916,13917,13920],{},"Aby výběrový soubor dobře vypovídal o základním souboru, měl by být ",[2227,13914,13915],{},"reprezentativní"," (podobný základnímu souboru svým složením). Není-li to možné zajistit přímo, volí se prvky do výběru náhodně — ",[2227,13918,13919],{},"nezávislý výběr",". Bez náhodnosti výběru nelze vlastnosti základního souboru správně vystihnout.",[1136,13922,13924],{"id":13923},"empirické-charakteristiky","Empirické charakteristiky",[1110,13926,13927,13928,13931,13932,13935,13936,13949,13950,13953,13954,13967],{},"Zpracováním datového souboru získáme ",[2227,13929,13930],{},"empirické charakteristiky"," a odhad ",[2227,13933,13934],{},"zákona rozdělení"," zkoumané náhodné veličiny ",[1115,13937,13939],{"className":13938},[1573],[1575,13940,13941],{"xmlns":1577},[1579,13942,13943,13947],{},[1582,13944,13945],{},[1585,13946,1594],{},[1605,13948,1594],{"encoding":1607},". Jde o ",[2227,13951,13952],{},"bodové odhady"," charakteristik ",[1115,13955,13957],{"className":13956},[1573],[1575,13958,13959],{"xmlns":1577},[1579,13960,13961,13965],{},[1582,13962,13963],{},[1585,13964,1594],{},[1605,13966,1594],{"encoding":1607},"; ruční výpočet podle vzorců níže je potřeba jen bez dostupného softwaru.",[1110,13969,13970],{},[2227,13971,13972],{},"Míry polohy",[1115,13974,13976],{"className":13975},[1573],[1575,13977,13978],{"xmlns":1577,"display":4601},[1579,13979,13980,14069],{},[1582,13981,13982,13988,13990,13996,14010,14016,14018],{},[3005,13983,13984,13986],{"accent":1121},[1585,13985,1158],{},[1589,13987,3408],{},[1589,13989,1597],{},[5373,13991,13992,13994],{},[1716,13993,1718],{},[1585,13995,1781],{},[4620,13997,13998,14000,14008],{},[1589,13999,4624],{},[1582,14001,14002,14004,14006],{},[1585,14003,1776],{},[1589,14005,1597],{},[1716,14007,1718],{},[1585,14009,1781],{},[1746,14011,14012,14014],{},[1585,14013,1158],{},[1585,14015,1776],{},[4648,14017],{"width":4650},[1582,14019,14020,14023,14030,14032,14039,14042,14048,14051,14058,14060,14066],{},[5543,14021,14022],{},"(v",[3005,14024,14025,14027],{"accent":1121},[5543,14026,2862],{},[1589,14028,14029],{},"ˊ",[5543,14031,2869],{},[3005,14033,14034,14036],{"accent":1121},[5543,14035,2876],{},[1589,14037,14038],{},"ˇ",[5543,14040,14041],{},"rov",[3005,14043,14044,14046],{"accent":1121},[5543,14045,2862],{},[1589,14047,14029],{},[5543,14049,14050],{}," pr",[3005,14052,14053,14055],{"accent":1121},[5543,14054,3523],{},[1589,14056,14057],{},"˚",[5543,14059,3674],{},[3005,14061,14062,14064],{"accent":1121},[5543,14063,2876],{},[1589,14065,14038],{},[5543,14067,14068],{},"r)",[1605,14070,14071],{"encoding":1607},"\\bar{x} = \\frac{1}{n}\\sum_{i=1}^{n} x_i \\qquad \\text{(výběrový průměr)}",[1110,14073,14074,14075,1260,14078,14081],{},"Dalšími mírami polohy jsou ",[2227,14076,14077],{},"medián",[2227,14079,14080],{},"modus"," (nejčetnější hodnota výběru).",[1110,14083,14084],{},[2227,14085,14086],{},"Míry variability",[1115,14088,14090],{"className":14089},[1573],[1575,14091,14092],{"xmlns":1577,"display":4601},[1579,14093,14094,14223],{},[1582,14095,14096,14102,14104,14116,14158,14160,14162,14164,14166,14174,14176],{},[1986,14097,14098,14100],{},[1585,14099,3433],{},[1716,14101,1993],{},[1589,14103,1597],{},[5373,14105,14106,14108],{},[1716,14107,1718],{},[1582,14109,14110,14112,14114],{},[1585,14111,1781],{},[1589,14113,1721],{},[1716,14115,1718],{},[1582,14117,14118,14120,14134,14142,14144,14146,14156],{},[1589,14119,1170],{"fence":1121},[4620,14121,14122,14124,14132],{},[1589,14123,4624],{},[1582,14125,14126,14128,14130],{},[1585,14127,1776],{},[1589,14129,1597],{},[1716,14131,1718],{},[1585,14133,1781],{},[2920,14135,14136,14138,14140],{},[1585,14137,1158],{},[1585,14139,1776],{},[1716,14141,1993],{},[1589,14143,1721],{},[1585,14145,1781],{},[1986,14147,14148,14154],{},[3005,14149,14150,14152],{"accent":1121},[1585,14151,1158],{},[1589,14153,3408],{},[1716,14155,1993],{},[1589,14157,1603],{"fence":1121},[1589,14159,1177],{"separator":1121},[4648,14161],{"width":4650},[1585,14163,3433],{},[1589,14165,1597],{},[7068,14167,14168],{},[1986,14169,14170,14172],{},[1585,14171,3433],{},[1716,14173,1993],{},[4648,14175],{"width":4650},[1582,14177,14178,14180,14186,14188,14194,14196,14202,14205,14211,14214,14220],{},[5543,14179,14022],{},[3005,14181,14182,14184],{"accent":1121},[5543,14183,2862],{},[1589,14185,14029],{},[5543,14187,2869],{},[3005,14189,14190,14192],{"accent":1121},[5543,14191,2876],{},[1589,14193,14038],{},[5543,14195,14041],{},[3005,14197,14198,14200],{"accent":1121},[5543,14199,2862],{},[1589,14201,14029],{},[5543,14203,14204],{}," rozptyl, sm",[3005,14206,14207,14209],{"accent":1121},[5543,14208,2876],{},[1589,14210,14038],{},[5543,14212,14213],{},"rodatn",[3005,14215,14216,14218],{"accent":1121},[5543,14217,1127],{},[1589,14219,14029],{},[5543,14221,14222],{}," odchylka)",[1605,14224,14225],{"encoding":1607},"s^2 = \\frac{1}{n-1}\\left(\\sum_{i=1}^{n} x_i^2 - n\\bar{x}^2\\right), \\qquad s=\\sqrt{s^2} \\qquad \\text{(výběrový rozptyl, směrodatná odchylka)}",[1115,14227,14229],{"className":14228},[1573],[1575,14230,14231],{"xmlns":1577,"display":4601},[1579,14232,14233,14299],{},[1582,14234,14235,14237,14239,14248,14250,14258,14260],{},[1585,14236,3376],{},[1589,14238,1597],{},[1746,14240,14241,14243,14246],{},[1585,14242,1158],{},[1585,14244,14245],{},"max",[1589,14247,7105],{},[1589,14249,1721],{},[1746,14251,14252,14254,14256],{},[1585,14253,1158],{},[1585,14255,7102],{},[1589,14257,7105],{},[4648,14259],{"width":4650},[1582,14261,14262,14265,14271,14273,14280,14283,14289,14291,14297],{},[5543,14263,14264],{},"(varia",[3005,14266,14267,14269],{"accent":1121},[5543,14268,3499],{},[1589,14270,14038],{},[5543,14272,1781],{},[3005,14274,14275,14278],{"accent":1121},[5543,14276,14277],{},"ı",[1589,14279,14029],{},[5543,14281,14282],{}," rozp",[3005,14284,14285,14287],{"accent":1121},[5543,14286,2876],{},[1589,14288,14038],{},[5543,14290,2082],{},[3005,14292,14293,14295],{"accent":1121},[5543,14294,14277],{},[1589,14296,14029],{},[5543,14298,1603],{},[1605,14300,14301],{"encoding":1607},"R = x_{\\max} - x_{\\min} \\qquad \\text{(variační rozpětí)}",[1110,14303,14304],{},[2227,14305,10884],{},[1110,14307,1735,14308,14331,14332,14354,14355,14376,14377,14405],{},[1115,14309,14311],{"className":14310},[1573],[1575,14312,14313],{"xmlns":1577},[1579,14314,14315,14328],{},[1582,14316,14317],{},[1746,14318,14319,14326],{},[3005,14320,14321,14323],{"accent":1121},[1585,14322,1158],{},[1589,14324,14325],{},"~",[1585,14327,1110],{},[1605,14329,14330],{"encoding":1607},"\\tilde{x}_p"," dělí hodnoty datového souboru na dvě části: ",[1115,14333,14335],{"className":14334},[1573],[1575,14336,14337],{"xmlns":1577},[1579,14338,14339,14351],{},[1582,14340,14341,14344,14346,14348],{},[1716,14342,14343],{},"100",[1585,14345,1110],{},[5543,14347,5545],{},[1585,14349,14350],{"mathvariant":4022},"%",[1605,14352,14353],{"encoding":1607},"100p\\,\\%"," hodnot je menších nebo rovných ",[1115,14356,14358],{"className":14357},[1573],[1575,14359,14360],{"xmlns":1577},[1579,14361,14362,14374],{},[1582,14363,14364],{},[1746,14365,14366,14372],{},[3005,14367,14368,14370],{"accent":1121},[1585,14369,1158],{},[1589,14371,14325],{},[1585,14373,1110],{},[1605,14375,14330],{"encoding":1607},", zbylých ",[1115,14378,14380],{"className":14379},[1573],[1575,14381,14382],{"xmlns":1577},[1579,14383,14384,14402],{},[1582,14385,14386,14388,14390,14392,14394,14396,14398,14400],{},[1716,14387,14343],{},[1589,14389,1170],{"stretchy":1591},[1716,14391,1718],{},[1589,14393,1721],{},[1585,14395,1110],{},[1589,14397,1603],{"stretchy":1591},[5543,14399,5545],{},[1585,14401,14350],{"mathvariant":4022},[1605,14403,14404],{"encoding":1607},"100(1-p)\\,\\%"," je větších. Nejdůležitější kvantily:",[2220,14407,14408,14435],{},[2223,14409,14410,2230,14412,14434],{},[2227,14411,14077],{},[1115,14413,14415],{"className":14414},[1573],[1575,14416,14417],{"xmlns":1577},[1579,14418,14419,14431],{},[1582,14420,14421],{},[1746,14422,14423,14429],{},[3005,14424,14425,14427],{"accent":1121},[1585,14426,1158],{},[1589,14428,14325],{},[1716,14430,11038],{},[1605,14432,14433],{"encoding":1607},"\\tilde{x}_{0{,}5}"," — pro lichý počet prvků uspořádaného souboru prostřední prvek, pro sudý počet průměr dvou prostředních prvků;",[2223,14436,14437,2230,14440,1260,14462,2230,14465,2264],{},[2227,14438,14439],{},"dolní kvartil",[1115,14441,14443],{"className":14442},[1573],[1575,14444,14445],{"xmlns":1577},[1579,14446,14447,14459],{},[1582,14448,14449],{},[1746,14450,14451,14457],{},[3005,14452,14453,14455],{"accent":1121},[1585,14454,1158],{},[1589,14456,14325],{},[1716,14458,11058],{},[1605,14460,14461],{"encoding":1607},"\\tilde{x}_{0{,}25}",[2227,14463,14464],{},"horní kvartil",[1115,14466,14468],{"className":14467},[1573],[1575,14469,14470],{"xmlns":1577},[1579,14471,14472,14484],{},[1582,14473,14474],{},[1746,14475,14476,14482],{},[3005,14477,14478,14480],{"accent":1121},[1585,14479,1158],{},[1589,14481,14325],{},[1716,14483,11078],{},[1605,14485,14486],{"encoding":1607},"\\tilde{x}_{0{,}75}",[1110,14488,14489,14490,14493],{},"Datový soubor se do R zadává buď přímo (",[1150,14491,14492],{},"x \u003C- c(...)","), nebo načtením ze souboru:",[1144,14495,14497],{"className":1146,"code":14496,"language":71,"meta":1148,"style":1148},"x \u003C- c(4.1, 4.0, 3.8, 3.9, 3.8, 3.8, 3.5, 3.7, 4.0, 4.0)   # přímé zadání hodnot\n# x \u003C- read.table(\"data.txt\")[, 1]                       # načtení prvního sloupce ze souboru\n",[1150,14498,14499,14551],{"__ignoreMap":1148},[1115,14500,14501,14503,14505,14507,14509,14511,14513,14515,14517,14519,14521,14523,14525,14527,14529,14531,14533,14535,14537,14539,14541,14543,14545,14547,14549],{"class":1154,"line":10},[1115,14502,1158],{"class":1157},[1115,14504,1162],{"class":1161},[1115,14506,1166],{"class":1165},[1115,14508,1170],{"class":1169},[1115,14510,1174],{"class":1173},[1115,14512,1177],{"class":1161},[1115,14514,1180],{"class":1173},[1115,14516,1177],{"class":1161},[1115,14518,1185],{"class":1173},[1115,14520,1177],{"class":1161},[1115,14522,1190],{"class":1173},[1115,14524,1177],{"class":1161},[1115,14526,1185],{"class":1173},[1115,14528,1177],{"class":1161},[1115,14530,1185],{"class":1173},[1115,14532,1177],{"class":1161},[1115,14534,1203],{"class":1173},[1115,14536,1177],{"class":1161},[1115,14538,1208],{"class":1173},[1115,14540,1177],{"class":1161},[1115,14542,1180],{"class":1173},[1115,14544,1177],{"class":1161},[1115,14546,1180],{"class":1173},[1115,14548,1219],{"class":1169},[1115,14550,1223],{"class":1222},[1115,14552,14553],{"class":1154,"line":27},[1115,14554,14555],{"class":1222},"# x \u003C- read.table(\"data.txt\")[, 1]                       # načtení prvního sloupce ze souboru\n",[1110,14557,14558,14559,14561,14562,1244,14564,14566,14567,14569],{},"Řádek s načtením ze souboru je zakomentovaný znakem ",[1150,14560,1239],{},": soubor musí ležet v pracovním adresáři R. ",[1150,14563,1243],{},[1150,14565,1247],{},"), proto ",[1150,14568,1251],{}," vybere její první sloupec jako vektor.",[1110,14571,11634],{},[1144,14573,14575],{"className":1146,"code":14574,"language":71,"meta":1148,"style":1148},"x \u003C- c(11.1, 12.7, 10.8, 13.2, 12.7, 13.4, 12.7, 14.4, 14.7, 14.4)\nlength(x)\nmean(x)\nvar(x)\nsd(x)\nmin(x); max(x); max(x) - min(x)\nquantile(x, 0.5, type = 6)\nquantile(x, 0.25, type = 6)\nquantile(x, 0.75, type = 6)\n",[1150,14576,14577,14634,14645,14656,14667,14678,14716,14742,14765],{"__ignoreMap":1148},[1115,14578,14579,14581,14583,14585,14587,14590,14592,14595,14597,14600,14602,14605,14607,14609,14611,14614,14616,14618,14620,14623,14625,14628,14630,14632],{"class":1154,"line":10},[1115,14580,1158],{"class":1157},[1115,14582,1162],{"class":1161},[1115,14584,1166],{"class":1165},[1115,14586,1170],{"class":1169},[1115,14588,14589],{"class":1173},"11.1",[1115,14591,1177],{"class":1161},[1115,14593,14594],{"class":1173}," 12.7",[1115,14596,1177],{"class":1161},[1115,14598,14599],{"class":1173}," 10.8",[1115,14601,1177],{"class":1161},[1115,14603,14604],{"class":1173}," 13.2",[1115,14606,1177],{"class":1161},[1115,14608,14594],{"class":1173},[1115,14610,1177],{"class":1161},[1115,14612,14613],{"class":1173}," 13.4",[1115,14615,1177],{"class":1161},[1115,14617,14594],{"class":1173},[1115,14619,1177],{"class":1161},[1115,14621,14622],{"class":1173}," 14.4",[1115,14624,1177],{"class":1161},[1115,14626,14627],{"class":1173}," 14.7",[1115,14629,1177],{"class":1161},[1115,14631,14622],{"class":1173},[1115,14633,6519],{"class":1169},[1115,14635,14636,14639,14641,14643],{"class":1154,"line":27},[1115,14637,14638],{"class":1165},"length",[1115,14640,1170],{"class":1169},[1115,14642,1158],{"class":1157},[1115,14644,6519],{"class":1169},[1115,14646,14647,14650,14652,14654],{"class":1154,"line":148},[1115,14648,14649],{"class":1165},"mean",[1115,14651,1170],{"class":1169},[1115,14653,1158],{"class":1157},[1115,14655,6519],{"class":1169},[1115,14657,14658,14661,14663,14665],{"class":1154,"line":111},[1115,14659,14660],{"class":1165},"var",[1115,14662,1170],{"class":1169},[1115,14664,1158],{"class":1157},[1115,14666,6519],{"class":1169},[1115,14668,14669,14672,14674,14676],{"class":1154,"line":96},[1115,14670,14671],{"class":1165},"sd",[1115,14673,1170],{"class":1169},[1115,14675,1158],{"class":1157},[1115,14677,6519],{"class":1169},[1115,14679,14680,14682,14684,14686,14689,14691,14693,14695,14697,14699,14701,14703,14705,14707,14710,14712,14714],{"class":1154,"line":89},[1115,14681,7102],{"class":1165},[1115,14683,1170],{"class":1169},[1115,14685,1158],{"class":1157},[1115,14687,14688],{"class":1169},"); ",[1115,14690,14245],{"class":1165},[1115,14692,1170],{"class":1169},[1115,14694,1158],{"class":1157},[1115,14696,14688],{"class":1169},[1115,14698,14245],{"class":1165},[1115,14700,1170],{"class":1169},[1115,14702,1158],{"class":1157},[1115,14704,7214],{"class":1169},[1115,14706,7250],{"class":1161},[1115,14708,14709],{"class":1165}," min",[1115,14711,1170],{"class":1169},[1115,14713,1158],{"class":1157},[1115,14715,6519],{"class":1169},[1115,14717,14718,14721,14723,14725,14727,14730,14732,14735,14737,14740],{"class":1154,"line":82},[1115,14719,14720],{"class":1165},"quantile",[1115,14722,1170],{"class":1169},[1115,14724,1158],{"class":1157},[1115,14726,1177],{"class":1161},[1115,14728,14729],{"class":1173}," 0.5",[1115,14731,1177],{"class":1161},[1115,14733,14734],{"class":1157}," type",[1115,14736,6416],{"class":1161},[1115,14738,14739],{"class":1173}," 6",[1115,14741,6519],{"class":1169},[1115,14743,14744,14746,14748,14750,14752,14755,14757,14759,14761,14763],{"class":1154,"line":75},[1115,14745,14720],{"class":1165},[1115,14747,1170],{"class":1169},[1115,14749,1158],{"class":1157},[1115,14751,1177],{"class":1161},[1115,14753,14754],{"class":1173}," 0.25",[1115,14756,1177],{"class":1161},[1115,14758,14734],{"class":1157},[1115,14760,6416],{"class":1161},[1115,14762,14739],{"class":1173},[1115,14764,6519],{"class":1169},[1115,14766,14767,14769,14771,14773,14775,14778,14780,14782,14784,14786],{"class":1154,"line":6509},[1115,14768,14720],{"class":1165},[1115,14770,1170],{"class":1169},[1115,14772,1158],{"class":1157},[1115,14774,1177],{"class":1161},[1115,14776,14777],{"class":1173}," 0.75",[1115,14779,1177],{"class":1161},[1115,14781,14734],{"class":1157},[1115,14783,6416],{"class":1161},[1115,14785,14739],{"class":1173},[1115,14787,6519],{"class":1169},[1144,14789,14792],{"className":14790,"code":14791,"language":6540,"meta":1148},[6538],"[1] 10\n[1] 13.01\n[1] 1.747667\n[1] 1.321993\n[1] 10.8\n[1] 14.7\n[1] 3.9\n  50% \n12.95 \n 25% \n12.3 \n 75% \n14.4 \n",[1150,14793,14791],{"__ignoreMap":1148},[1110,14795,14796,14798,14799,14802],{},[1150,14797,2514],{}," je potřeba zadat explicitně — výchozí typ v R (",[1150,14800,14801],{},"type = 7",") by u některých souborů dal mírně odlišné hodnoty kvantilů než ruční výpočet použitý v této kapitole.",[1110,14804,14805],{},[1303,14806],{"alt":14807,"className":14808,"src":14809},"mask-ps-kvantily",[1130,1307],"\u002Fwiki-assets\u002Fmask-ps-kvantily.png",[1110,14811,14812],{},"Seřazení souboru a krabicový graf:",[1144,14814,14816],{"className":1146,"code":14815,"language":71,"meta":1148,"style":1148},"sort(x)                     # vzestupně\nsort(x, decreasing = TRUE)  # sestupně\nboxplot(x)\n",[1150,14817,14818,14833,14856],{"__ignoreMap":1148},[1115,14819,14820,14823,14825,14827,14830],{"class":1154,"line":10},[1115,14821,14822],{"class":1165},"sort",[1115,14824,1170],{"class":1169},[1115,14826,1158],{"class":1157},[1115,14828,14829],{"class":1169},")                     ",[1115,14831,14832],{"class":1222},"# vzestupně\n",[1115,14834,14835,14837,14839,14841,14843,14846,14848,14850,14853],{"class":1154,"line":27},[1115,14836,14822],{"class":1165},[1115,14838,1170],{"class":1169},[1115,14840,1158],{"class":1157},[1115,14842,1177],{"class":1161},[1115,14844,14845],{"class":1157}," decreasing",[1115,14847,6416],{"class":1161},[1115,14849,6429],{"class":1173},[1115,14851,14852],{"class":1169},")  ",[1115,14854,14855],{"class":1222},"# sestupně\n",[1115,14857,14858,14861,14863,14865],{"class":1154,"line":148},[1115,14859,14860],{"class":1165},"boxplot",[1115,14862,1170],{"class":1169},[1115,14864,1158],{"class":1157},[1115,14866,6519],{"class":1169},[1144,14868,14871],{"className":14869,"code":14870,"language":6540,"meta":1148},[6538]," [1] 10.8 11.1 12.7 12.7 12.7 13.2 13.4 14.4 14.4 14.7\n [1] 14.7 14.4 14.4 13.4 13.2 12.7 12.7 12.7 11.1 10.8\n",[1150,14872,14870],{"__ignoreMap":1148},[1110,14874,14875,14878,14879,14882],{},[1150,14876,14877],{},"boxplot()"," kreslí krabici mezi hodnotami ",[1150,14880,14881],{},"fivenum(x)"," (zde 12,7 a 14,4), které se od kvartilů typu 6 mohou mírně lišit.",[1103,14884,14886,14893],{"className":14885,"dataCallout":6105},[1106,6104],[1110,14887,14889,14892],{"className":14888},[1113],[1115,14890],{"className":14891,"ariaHidden":1121},[1118,6112,1120],"Příklad: Empirické charakteristiky",[1110,14894,14895],{},"Na deseti náhodně vybraných mechanicích byla měřena doba opravy vadné součástky (v minutách):\n11,1  12,7  10,8  13,2  12,7  13,4  12,7  14,4  14,7  14,4.\nUrčete empirické charakteristiky a kvantily.",[1110,14897,14898,14899,1279,14922,1279,14945,1279,14964,14983,14984,11042,15011,15026,15027,2264],{},"Výstup R kódu výše dává ",[1115,14900,14902],{"className":14901},[1573],[1575,14903,14904],{"xmlns":1577},[1579,14905,14906,14919],{},[1582,14907,14908,14914,14916],{},[3005,14909,14910,14912],{"accent":1121},[1585,14911,1158],{},[1589,14913,3408],{},[1589,14915,1597],{},[1716,14917,14918],{},"13,01",[1605,14920,14921],{"encoding":1607},"\\bar{x}=13{,}01",[1115,14923,14925],{"className":14924},[1573],[1575,14926,14927],{"xmlns":1577},[1579,14928,14929,14942],{},[1582,14930,14931,14937,14939],{},[1986,14932,14933,14935],{},[1585,14934,3433],{},[1716,14936,1993],{},[1589,14938,1597],{},[1716,14940,14941],{},"1,75",[1605,14943,14944],{"encoding":1607},"s^2=1{,}75",[1115,14946,14948],{"className":14947},[1573],[1575,14949,14950],{"xmlns":1577},[1579,14951,14952,14961],{},[1582,14953,14954,14956,14958],{},[1585,14955,3433],{},[1589,14957,1597],{},[1716,14959,14960],{},"1,32",[1605,14962,14963],{"encoding":1607},"s=1{,}32",[1115,14965,14967],{"className":14966},[1573],[1575,14968,14969],{"xmlns":1577},[1579,14970,14971,14980],{},[1582,14972,14973,14975,14977],{},[1585,14974,3376],{},[1589,14976,1597],{},[1716,14978,14979],{},"3,9",[1605,14981,14982],{"encoding":1607},"R=3{,}9",", medián ",[1115,14985,14987],{"className":14986},[1573],[1575,14988,14989],{"xmlns":1577},[1579,14990,14991,15008],{},[1582,14992,14993,15003,15005],{},[1746,14994,14995,15001],{},[3005,14996,14997,14999],{"accent":1121},[1585,14998,1158],{},[1589,15000,14325],{},[1716,15002,11038],{},[1589,15004,1597],{},[1716,15006,15007],{},"12,95",[1605,15009,15010],{"encoding":1607},"\\tilde{x}_{0{,}5}=12{,}95",[1115,15012,15014],{"className":15013},[1573],[1575,15015,15016],{"xmlns":1577},[1579,15017,15018,15023],{},[1582,15019,15020],{},[1716,15021,15022],{},"12,3",[1605,15024,15025],{"encoding":1607},"12{,}3",", horní kvartil ",[1115,15028,15030],{"className":15029},[1573],[1575,15031,15032],{"xmlns":1577},[1579,15033,15034,15039],{},[1582,15035,15036],{},[1716,15037,15038],{},"14,4",[1605,15040,15041],{"encoding":1607},"14{,}4",[1110,15043,15044],{},"Odhad střední doby opravy je přibližně 13 minut, odhad směrodatné odchylky přibližně 1,32 minuty. Odchylka je vzhledem k průměru nízká — data kolísají kolem průměru jen málo. Uspořádaný soubor má medián 12,95: polovina oprav trvala méně, polovina více; 25 % oprav bylo kratších než 12,3 minuty a 75 % kratších než 14,4 minuty.",[1103,15046,15048,15055],{"className":15047,"dataCallout":6105},[1106,6104],[1110,15049,15051,15054],{"className":15050},[1113],[1115,15052],{"className":15053,"ariaHidden":1121},[1118,6112,1120],"Příklad: Doba oprav televizorů",[1110,15056,15057],{},"Při 50 opravách určité závady televizoru byly naměřeny časy (v minutách). Určete empirické charakteristiky.",[1144,15059,15061],{"className":1146,"code":15060,"language":71,"meta":1148,"style":1148},"x6 \u003C- c(44, 40.2, 41.9, 43.4, 42.8, 42.3, 43.2, 45, 41.5, 42.7,\n        43.9, 40.1, 43.3, 41.1, 42.5, 42.4, 41.4, 40.8, 42, 44.7,\n        41.2, 41.9, 42.4, 44.4, 40.5, 39.7, 41.1, 41, 41.9, 40.8,\n        43, 42.8, 42.9, 42.7, 43.3, 42.2, 39.2, 41.5, 41.6, 42.7,\n        45, 42.3, 43.6, 43.2, 38.8, 43, 44.2, 43, 40, 44.4)\nlength(x6)\nmean(x6)\nsd(x6)\nmax(x6) - min(x6)\nmedian(x6)\n",[1150,15062,15063,15123,15174,15221,15268,15316,15326,15336,15346,15366],{"__ignoreMap":1148},[1115,15064,15065,15068,15070,15072,15074,15076,15078,15081,15083,15086,15088,15091,15093,15096,15098,15101,15103,15106,15108,15111,15113,15116,15118,15121],{"class":1154,"line":10},[1115,15066,15067],{"class":1157},"x6",[1115,15069,1162],{"class":1161},[1115,15071,1166],{"class":1165},[1115,15073,1170],{"class":1169},[1115,15075,6203],{"class":1173},[1115,15077,1177],{"class":1161},[1115,15079,15080],{"class":1173}," 40.2",[1115,15082,1177],{"class":1161},[1115,15084,15085],{"class":1173}," 41.9",[1115,15087,1177],{"class":1161},[1115,15089,15090],{"class":1173}," 43.4",[1115,15092,1177],{"class":1161},[1115,15094,15095],{"class":1173}," 42.8",[1115,15097,1177],{"class":1161},[1115,15099,15100],{"class":1173}," 42.3",[1115,15102,1177],{"class":1161},[1115,15104,15105],{"class":1173}," 43.2",[1115,15107,1177],{"class":1161},[1115,15109,15110],{"class":1173}," 45",[1115,15112,1177],{"class":1161},[1115,15114,15115],{"class":1173}," 41.5",[1115,15117,1177],{"class":1161},[1115,15119,15120],{"class":1173}," 42.7",[1115,15122,6356],{"class":1161},[1115,15124,15125,15128,15130,15133,15135,15138,15140,15143,15145,15148,15150,15153,15155,15158,15160,15163,15165,15167,15169,15172],{"class":1154,"line":27},[1115,15126,15127],{"class":1173},"        43.9",[1115,15129,1177],{"class":1161},[1115,15131,15132],{"class":1173}," 40.1",[1115,15134,1177],{"class":1161},[1115,15136,15137],{"class":1173}," 43.3",[1115,15139,1177],{"class":1161},[1115,15141,15142],{"class":1173}," 41.1",[1115,15144,1177],{"class":1161},[1115,15146,15147],{"class":1173}," 42.5",[1115,15149,1177],{"class":1161},[1115,15151,15152],{"class":1173}," 42.4",[1115,15154,1177],{"class":1161},[1115,15156,15157],{"class":1173}," 41.4",[1115,15159,1177],{"class":1161},[1115,15161,15162],{"class":1173}," 40.8",[1115,15164,1177],{"class":1161},[1115,15166,11915],{"class":1173},[1115,15168,1177],{"class":1161},[1115,15170,15171],{"class":1173}," 44.7",[1115,15173,6356],{"class":1161},[1115,15175,15176,15179,15181,15183,15185,15187,15189,15192,15194,15197,15199,15202,15204,15206,15208,15211,15213,15215,15217,15219],{"class":1154,"line":148},[1115,15177,15178],{"class":1173},"        41.2",[1115,15180,1177],{"class":1161},[1115,15182,15085],{"class":1173},[1115,15184,1177],{"class":1161},[1115,15186,15152],{"class":1173},[1115,15188,1177],{"class":1161},[1115,15190,15191],{"class":1173}," 44.4",[1115,15193,1177],{"class":1161},[1115,15195,15196],{"class":1173}," 40.5",[1115,15198,1177],{"class":1161},[1115,15200,15201],{"class":1173}," 39.7",[1115,15203,1177],{"class":1161},[1115,15205,15142],{"class":1173},[1115,15207,1177],{"class":1161},[1115,15209,15210],{"class":1173}," 41",[1115,15212,1177],{"class":1161},[1115,15214,15085],{"class":1173},[1115,15216,1177],{"class":1161},[1115,15218,15162],{"class":1173},[1115,15220,6356],{"class":1161},[1115,15222,15223,15226,15228,15230,15232,15235,15237,15239,15241,15243,15245,15248,15250,15253,15255,15257,15259,15262,15264,15266],{"class":1154,"line":111},[1115,15224,15225],{"class":1173},"        43",[1115,15227,1177],{"class":1161},[1115,15229,15095],{"class":1173},[1115,15231,1177],{"class":1161},[1115,15233,15234],{"class":1173}," 42.9",[1115,15236,1177],{"class":1161},[1115,15238,15120],{"class":1173},[1115,15240,1177],{"class":1161},[1115,15242,15137],{"class":1173},[1115,15244,1177],{"class":1161},[1115,15246,15247],{"class":1173}," 42.2",[1115,15249,1177],{"class":1161},[1115,15251,15252],{"class":1173}," 39.2",[1115,15254,1177],{"class":1161},[1115,15256,15115],{"class":1173},[1115,15258,1177],{"class":1161},[1115,15260,15261],{"class":1173}," 41.6",[1115,15263,1177],{"class":1161},[1115,15265,15120],{"class":1173},[1115,15267,6356],{"class":1161},[1115,15269,15270,15273,15275,15277,15279,15282,15284,15286,15288,15291,15293,15296,15298,15301,15303,15305,15307,15310,15312,15314],{"class":1154,"line":96},[1115,15271,15272],{"class":1173},"        45",[1115,15274,1177],{"class":1161},[1115,15276,15100],{"class":1173},[1115,15278,1177],{"class":1161},[1115,15280,15281],{"class":1173}," 43.6",[1115,15283,1177],{"class":1161},[1115,15285,15105],{"class":1173},[1115,15287,1177],{"class":1161},[1115,15289,15290],{"class":1173}," 38.8",[1115,15292,1177],{"class":1161},[1115,15294,15295],{"class":1173}," 43",[1115,15297,1177],{"class":1161},[1115,15299,15300],{"class":1173}," 44.2",[1115,15302,1177],{"class":1161},[1115,15304,15295],{"class":1173},[1115,15306,1177],{"class":1161},[1115,15308,15309],{"class":1173}," 40",[1115,15311,1177],{"class":1161},[1115,15313,15191],{"class":1173},[1115,15315,6519],{"class":1169},[1115,15317,15318,15320,15322,15324],{"class":1154,"line":89},[1115,15319,14638],{"class":1165},[1115,15321,1170],{"class":1169},[1115,15323,15067],{"class":1157},[1115,15325,6519],{"class":1169},[1115,15327,15328,15330,15332,15334],{"class":1154,"line":82},[1115,15329,14649],{"class":1165},[1115,15331,1170],{"class":1169},[1115,15333,15067],{"class":1157},[1115,15335,6519],{"class":1169},[1115,15337,15338,15340,15342,15344],{"class":1154,"line":75},[1115,15339,14671],{"class":1165},[1115,15341,1170],{"class":1169},[1115,15343,15067],{"class":1157},[1115,15345,6519],{"class":1169},[1115,15347,15348,15350,15352,15354,15356,15358,15360,15362,15364],{"class":1154,"line":6509},[1115,15349,14245],{"class":1165},[1115,15351,1170],{"class":1169},[1115,15353,15067],{"class":1157},[1115,15355,7214],{"class":1169},[1115,15357,7250],{"class":1161},[1115,15359,14709],{"class":1165},[1115,15361,1170],{"class":1169},[1115,15363,15067],{"class":1157},[1115,15365,6519],{"class":1169},[1115,15367,15368,15371,15373,15375],{"class":1154,"line":72},[1115,15369,15370],{"class":1165},"median",[1115,15372,1170],{"class":1169},[1115,15374,15067],{"class":1157},[1115,15376,6519],{"class":1169},[1144,15378,15381],{"className":15379,"code":15380,"language":6540,"meta":1148},[6538],"[1] 50\n[1] 42.27\n[1] 1.48052\n[1] 6.2\n[1] 42.4\n",[1150,15382,15380],{"__ignoreMap":1148},[1110,15384,15385],{},"Průměrná doba opravy je 42,27 minuty se směrodatnou odchylkou 1,48 minuty a mediánem 42,4 minuty; průměr a medián téměř splývají, data jsou kolem středu rozložena souměrně.",[1136,15387,15389],{"id":15388},"empirická-distribuční-funkce","Empirická distribuční funkce",[1110,15391,15392,15393,15406,15407,2230,15410,15433,15434,15468],{},"Pro libovolný rozsah datového souboru, diskrétní i spojitou náhodnou veličinu ",[1115,15394,15396],{"className":15395},[1573],[1575,15397,15398],{"xmlns":1577},[1579,15399,15400,15404],{},[1582,15401,15402],{},[1585,15403,1594],{},[1605,15405,1594],{"encoding":1607},", lze sestrojit ",[2227,15408,15409],{},"empirickou distribuční funkci",[1115,15411,15413],{"className":15412},[1573],[1575,15414,15415],{"xmlns":1577},[1579,15416,15417,15431],{},[1582,15418,15419,15425,15427,15429],{},[1746,15420,15421,15423],{},[1585,15422,1669],{},[1585,15424,1781],{},[1589,15426,1170],{"stretchy":1591},[1585,15428,1158],{},[1589,15430,1603],{"stretchy":1591},[1605,15432,13712],{"encoding":1607},". Pro datový soubor ",[1115,15435,15437],{"className":15436},[1573],[1575,15438,15439],{"xmlns":1577},[1579,15440,15441,15465],{},[1582,15442,15443,15445,15451,15453,15455,15457,15463],{},[1589,15444,1170],{"stretchy":1591},[1746,15446,15447,15449],{},[1585,15448,1158],{},[1716,15450,1718],{},[1589,15452,1177],{"separator":1121},[1589,15454,2979],{},[1589,15456,1177],{"separator":1121},[1746,15458,15459,15461],{},[1585,15460,1158],{},[1585,15462,1781],{},[1589,15464,1603],{"stretchy":1591},[1605,15466,15467],{"encoding":1607},"(x_1,\\dots,x_n)"," je",[1115,15470,15472],{"className":15471},[1573],[1575,15473,15474],{"xmlns":1577,"display":4601},[1579,15475,15476,15500],{},[1582,15477,15478,15484,15486,15488,15490,15492,15498],{},[1746,15479,15480,15482],{},[1585,15481,1669],{},[1585,15483,1781],{},[1589,15485,1170],{"stretchy":1591},[1585,15487,1158],{},[1589,15489,1603],{"stretchy":1591},[1589,15491,1597],{},[5373,15493,15494,15496],{},[1585,15495,1600],{},[1585,15497,1781],{},[1589,15499,1177],{"separator":1121},[1605,15501,15502],{"encoding":1607},"F_n(x) = \\frac{k}{n},",[1110,15504,7121,15505,15518,15519,2264],{},[1115,15506,15508],{"className":15507},[1573],[1575,15509,15510],{"xmlns":1577},[1579,15511,15512,15516],{},[1582,15513,15514],{},[1585,15515,1600],{},[1605,15517,1600],{"encoding":1607}," je počet prvků datového souboru menších nebo rovných číslu ",[1115,15520,15522],{"className":15521},[1573],[1575,15523,15524],{"xmlns":1577},[1579,15525,15526,15530],{},[1582,15527,15528],{},[1585,15529,1158],{},[1605,15531,1158],{"encoding":1607},[1110,15533,11634],{},[1144,15535,15537],{"className":1146,"code":15536,"language":71,"meta":1148,"style":1148},"f \u003C- ecdf(x)\nknots(f)        # vzestupně seřazené různé hodnoty datového souboru\nf(knots(f))      # hodnoty Fn(x) v těchto bodech\nf(13)            # Fn v libovolném bodě\nplot(f)\n",[1150,15538,15539,15554,15569,15587,15601],{"__ignoreMap":1148},[1115,15540,15541,15543,15545,15548,15550,15552],{"class":1154,"line":10},[1115,15542,1621],{"class":1157},[1115,15544,1162],{"class":1161},[1115,15546,15547],{"class":1165}," ecdf",[1115,15549,1170],{"class":1169},[1115,15551,1158],{"class":1157},[1115,15553,6519],{"class":1169},[1115,15555,15556,15559,15561,15563,15566],{"class":1154,"line":27},[1115,15557,15558],{"class":1165},"knots",[1115,15560,1170],{"class":1169},[1115,15562,1621],{"class":1157},[1115,15564,15565],{"class":1169},")        ",[1115,15567,15568],{"class":1222},"# vzestupně seřazené různé hodnoty datového souboru\n",[1115,15570,15571,15573,15575,15577,15579,15581,15584],{"class":1154,"line":148},[1115,15572,1621],{"class":1165},[1115,15574,1170],{"class":1169},[1115,15576,15558],{"class":1165},[1115,15578,1170],{"class":1169},[1115,15580,1621],{"class":1157},[1115,15582,15583],{"class":1169},"))      ",[1115,15585,15586],{"class":1222},"# hodnoty Fn(x) v těchto bodech\n",[1115,15588,15589,15591,15593,15595,15598],{"class":1154,"line":111},[1115,15590,1621],{"class":1165},[1115,15592,1170],{"class":1169},[1115,15594,6173],{"class":1173},[1115,15596,15597],{"class":1169},")            ",[1115,15599,15600],{"class":1222},"# Fn v libovolném bodě\n",[1115,15602,15603,15605,15607,15609],{"class":1154,"line":96},[1115,15604,3939],{"class":1165},[1115,15606,1170],{"class":1169},[1115,15608,1621],{"class":1157},[1115,15610,6519],{"class":1169},[1144,15612,15615],{"className":15613,"code":15614,"language":6540,"meta":1148},[6538],"[1] 10.8 11.1 12.7 13.2 13.4 14.4 14.7\n[1] 0.1 0.2 0.5 0.6 0.7 0.9 1.0\n[1] 0.5\n",[1150,15616,15614],{"__ignoreMap":1148},[1110,15618,15619,15622,15623,15641,15642,15645,15646,15659,15660,2264],{},[1150,15620,15621],{},"knots()"," vrací jen různé hodnoty (opakující se hodnota 12,7 je ve výpočtu ",[1115,15624,15626],{"className":15625},[1573],[1575,15627,15628],{"xmlns":1577},[1579,15629,15630,15638],{},[1582,15631,15632],{},[1746,15633,15634,15636],{},[1585,15635,1669],{},[1585,15637,1781],{},[1605,15639,15640],{"encoding":1607},"F_n"," započtena třikrát, v seznamu uzlů je ale jen jednou); ",[1150,15643,15644],{},"plot(f)"," nakreslí schodovitý graf, který v každém uzlu skáče o ",[1115,15647,15649],{"className":15648},[1573],[1575,15650,15651],{"xmlns":1577},[1579,15652,15653,15657],{},[1582,15654,15655],{},[1585,15656,1600],{},[1605,15658,1600],{"encoding":1607},"-násobek ",[1115,15661,15663],{"className":15662},[1573],[1575,15664,15665],{"xmlns":1577},[1579,15666,15667,15675],{},[1582,15668,15669,15671,15673],{},[1716,15670,1718],{},[1585,15672,4023],{"mathvariant":4022},[1585,15674,1781],{},[1605,15676,15677],{"encoding":1607},"1\u002Fn",[1110,15679,15680],{},[1303,15681],{"alt":15682,"className":15683,"src":15684},"mask-ps-ecdf",[1130,1307],"\u002Fwiki-assets\u002Fmask-ps-ecdf.png",[1103,15686,15688,15695],{"className":15687,"dataCallout":6105},[1106,6104],[1110,15689,15691,15694],{"className":15690},[1113],[1115,15692],{"className":15693,"ariaHidden":1121},[1118,6112,1120],"Příklad: Empirická distribuční funkce",[1110,15696,15697],{},"Pro předchozí datový soubor (doba opravy součástky) určete empirickou distribuční funkci.",[1110,15699,15700,15701,2264],{},"Uspořádaný soubor je ",[1115,15702,15704],{"className":15703},[1573],[1575,15705,15706],{"xmlns":1577},[1579,15707,15708,15772],{},[1582,15709,15710,15713,15715,15717,15720,15722,15724,15727,15729,15731,15733,15735,15737,15739,15741,15743,15746,15748,15750,15753,15755,15757,15759,15761,15763,15765,15767,15769],{},[1716,15711,15712],{},"10,8",[1589,15714,9483],{"separator":1121},[5543,15716,13843],{},[1716,15718,15719],{},"11,1",[1589,15721,9483],{"separator":1121},[5543,15723,13843],{},[1716,15725,15726],{},"12,7",[1589,15728,9483],{"separator":1121},[5543,15730,13843],{},[1716,15732,15726],{},[1589,15734,9483],{"separator":1121},[5543,15736,13843],{},[1716,15738,15726],{},[1589,15740,9483],{"separator":1121},[5543,15742,13843],{},[1716,15744,15745],{},"13,2",[1589,15747,9483],{"separator":1121},[5543,15749,13843],{},[1716,15751,15752],{},"13,4",[1589,15754,9483],{"separator":1121},[5543,15756,13843],{},[1716,15758,15038],{},[1589,15760,9483],{"separator":1121},[5543,15762,13843],{},[1716,15764,15038],{},[1589,15766,9483],{"separator":1121},[5543,15768,13843],{},[1716,15770,15771],{},"14,7",[1605,15773,15774],{"encoding":1607},"10{,}8;\\ 11{,}1;\\ 12{,}7;\\ 12{,}7;\\ 12{,}7;\\ 13{,}2;\\ 13{,}4;\\ 14{,}4;\\ 14{,}4;\\ 14{,}7",[1310,15776,15777,15810],{},[1313,15778,15779],{},[1316,15780,15781,15796,15798,15800,15802,15804,15806,15808],{},[1319,15782,15783],{},[1115,15784,15786],{"className":15785},[1573],[1575,15787,15788],{"xmlns":1577},[1579,15789,15790,15794],{},[1582,15791,15792],{},[1585,15793,1158],{},[1605,15795,1158],{"encoding":1607},[1319,15797,15712],{},[1319,15799,15719],{},[1319,15801,15726],{},[1319,15803,15745],{},[1319,15805,15752],{},[1319,15807,15038],{},[1319,15809,15771],{},[1332,15811,15812,15843],{},[1316,15813,15814,15829,15831,15833,15835,15837,15839,15841],{},[1337,15815,15816],{},[1115,15817,15819],{"className":15818},[1573],[1575,15820,15821],{"xmlns":1577},[1579,15822,15823,15827],{},[1582,15824,15825],{},[1585,15826,1600],{},[1605,15828,1600],{"encoding":1607},[1337,15830,1718],{},[1337,15832,1993],{},[1337,15834,12470],{},[1337,15836,6581],{},[1337,15838,3905],{},[1337,15840,6223],{},[1337,15842,11613],{},[1316,15844,15845,15870,15873,15876,15878,15881,15884,15887],{},[1337,15846,15847],{},[1115,15848,15850],{"className":15849},[1573],[1575,15851,15852],{"xmlns":1577},[1579,15853,15854,15868],{},[1582,15855,15856,15862,15864,15866],{},[1746,15857,15858,15860],{},[1585,15859,1669],{},[1585,15861,1781],{},[1589,15863,1170],{"stretchy":1591},[1585,15865,1158],{},[1589,15867,1603],{"stretchy":1591},[1605,15869,13712],{"encoding":1607},[1337,15871,15872],{},"0,1",[1337,15874,15875],{},"0,2",[1337,15877,11038],{},[1337,15879,15880],{},"0,6",[1337,15882,15883],{},"0,7",[1337,15885,15886],{},"0,9",[1337,15888,15889],{},"1,0",[1110,15891,15892,15893,15915,15916,15939],{},"Graf (levý panel výše) odpovídá tabulce: funkce je nulová pod 10,8, skáče o ",[1115,15894,15896],{"className":15895},[1573],[1575,15897,15898],{"xmlns":1577},[1579,15899,15900,15912],{},[1582,15901,15902,15904,15906,15908,15910],{},[1716,15903,1718],{},[1585,15905,4023],{"mathvariant":4022},[1585,15907,1781],{},[1589,15909,1597],{},[1716,15911,15872],{},[1605,15913,15914],{"encoding":1607},"1\u002Fn = 0{,}1"," v každé jednoduché hodnotě a o ",[1115,15917,15919],{"className":15918},[1573],[1575,15920,15921],{"xmlns":1577},[1579,15922,15923,15936],{},[1582,15924,15925,15927,15929,15931,15933],{},[1716,15926,6220],{},[1585,15928,4023],{"mathvariant":4022},[1585,15930,1781],{},[1589,15932,1597],{},[1716,15934,15935],{},"0,3",[1605,15937,15938],{"encoding":1607},"3\u002Fn = 0{,}3"," v bodě 12,7, kde se hodnota opakuje třikrát.",[1103,15941,15943,15950],{"className":15942,"dataCallout":6105},[1106,6104],[1110,15944,15946,15949],{"className":15945},[1113],[1115,15947],{"className":15948,"ariaHidden":1121},[1118,6112,1120],"Příklad: Odpad materiálu",[1110,15951,15952],{},"Na deseti obráběných kusech byly naměřeny hodnoty odpadu materiálu (v %):\n4,1  4,0  3,8  3,9  3,8  3,8  3,5  3,7  4,0  4,0.\nUrčete empirické charakteristiky a nakreslete empirickou distribuční funkci.",[1144,15954,15956],{"className":1146,"code":15955,"language":71,"meta":1148,"style":1148},"x4 \u003C- c(4.1, 4.0, 3.8, 3.9, 3.8, 3.8, 3.5, 3.7, 4.0, 4.0)\nlength(x4)\nmean(x4)\nsd(x4)\nmax(x4) - min(x4)\nmedian(x4)\nf4 \u003C- ecdf(x4)\nknots(f4)\nf4(knots(f4))\n",[1150,15957,15958,16009,16019,16029,16039,16059,16069,16084,16094],{"__ignoreMap":1148},[1115,15959,15960,15963,15965,15967,15969,15971,15973,15975,15977,15979,15981,15983,15985,15987,15989,15991,15993,15995,15997,15999,16001,16003,16005,16007],{"class":1154,"line":10},[1115,15961,15962],{"class":1157},"x4",[1115,15964,1162],{"class":1161},[1115,15966,1166],{"class":1165},[1115,15968,1170],{"class":1169},[1115,15970,1174],{"class":1173},[1115,15972,1177],{"class":1161},[1115,15974,1180],{"class":1173},[1115,15976,1177],{"class":1161},[1115,15978,1185],{"class":1173},[1115,15980,1177],{"class":1161},[1115,15982,1190],{"class":1173},[1115,15984,1177],{"class":1161},[1115,15986,1185],{"class":1173},[1115,15988,1177],{"class":1161},[1115,15990,1185],{"class":1173},[1115,15992,1177],{"class":1161},[1115,15994,1203],{"class":1173},[1115,15996,1177],{"class":1161},[1115,15998,1208],{"class":1173},[1115,16000,1177],{"class":1161},[1115,16002,1180],{"class":1173},[1115,16004,1177],{"class":1161},[1115,16006,1180],{"class":1173},[1115,16008,6519],{"class":1169},[1115,16010,16011,16013,16015,16017],{"class":1154,"line":27},[1115,16012,14638],{"class":1165},[1115,16014,1170],{"class":1169},[1115,16016,15962],{"class":1157},[1115,16018,6519],{"class":1169},[1115,16020,16021,16023,16025,16027],{"class":1154,"line":148},[1115,16022,14649],{"class":1165},[1115,16024,1170],{"class":1169},[1115,16026,15962],{"class":1157},[1115,16028,6519],{"class":1169},[1115,16030,16031,16033,16035,16037],{"class":1154,"line":111},[1115,16032,14671],{"class":1165},[1115,16034,1170],{"class":1169},[1115,16036,15962],{"class":1157},[1115,16038,6519],{"class":1169},[1115,16040,16041,16043,16045,16047,16049,16051,16053,16055,16057],{"class":1154,"line":96},[1115,16042,14245],{"class":1165},[1115,16044,1170],{"class":1169},[1115,16046,15962],{"class":1157},[1115,16048,7214],{"class":1169},[1115,16050,7250],{"class":1161},[1115,16052,14709],{"class":1165},[1115,16054,1170],{"class":1169},[1115,16056,15962],{"class":1157},[1115,16058,6519],{"class":1169},[1115,16060,16061,16063,16065,16067],{"class":1154,"line":89},[1115,16062,15370],{"class":1165},[1115,16064,1170],{"class":1169},[1115,16066,15962],{"class":1157},[1115,16068,6519],{"class":1169},[1115,16070,16071,16074,16076,16078,16080,16082],{"class":1154,"line":82},[1115,16072,16073],{"class":1157},"f4",[1115,16075,1162],{"class":1161},[1115,16077,15547],{"class":1165},[1115,16079,1170],{"class":1169},[1115,16081,15962],{"class":1157},[1115,16083,6519],{"class":1169},[1115,16085,16086,16088,16090,16092],{"class":1154,"line":75},[1115,16087,15558],{"class":1165},[1115,16089,1170],{"class":1169},[1115,16091,16073],{"class":1157},[1115,16093,6519],{"class":1169},[1115,16095,16096,16098,16100,16102,16104,16106],{"class":1154,"line":6509},[1115,16097,16073],{"class":1165},[1115,16099,1170],{"class":1169},[1115,16101,15558],{"class":1165},[1115,16103,1170],{"class":1169},[1115,16105,16073],{"class":1157},[1115,16107,12073],{"class":1169},[1144,16109,16112],{"className":16110,"code":16111,"language":6540,"meta":1148},[6538],"[1] 10\n[1] 3.86\n[1] 0.1776388\n[1] 0.6\n[1] 3.85\n[1] 3.5 3.7 3.8 3.9 4.0 4.1\n[1] 0.1 0.2 0.5 0.6 0.9 1.0\n",[1150,16113,16111],{"__ignoreMap":1148},[1110,16115,16116,16117,16140],{},"Průměrný odpad je 3,86 % se směrodatnou odchylkou 0,18 % a mediánem 3,85 %. Pravý panel obrázku výše ukazuje tvar ",[1115,16118,16120],{"className":16119},[1573],[1575,16121,16122],{"xmlns":1577},[1579,16123,16124,16138],{},[1582,16125,16126,16132,16134,16136],{},[1746,16127,16128,16130],{},[1585,16129,1669],{},[1585,16131,1781],{},[1589,16133,1170],{"stretchy":1591},[1585,16135,1158],{},[1589,16137,1603],{"stretchy":1591},[1605,16139,13712],{"encoding":1607},": hodnota 3,8 se v souboru opakuje třikrát, proto zde funkce skáče o 0,3 najednou, stejně jako hodnota 4,0.",[1136,16142,16144],{"id":16143},"třídění-datového-souboru-do-tříd","Třídění datového souboru do tříd",[1110,16146,16147,16148,16151,16152,16165,16166,16169],{},"Je-li rozsah datového souboru velký (řádově přes 30 až 50 pozorování), hodnoty se před dalším zpracováním ",[2227,16149,16150],{},"roztřídí",": variační rozpětí ",[1115,16153,16155],{"className":16154},[1573],[1575,16156,16157],{"xmlns":1577},[1579,16158,16159,16163],{},[1582,16160,16161],{},[1585,16162,3376],{},[1605,16164,3376],{"encoding":1607}," se rozdělí na určitý počet ",[2227,16167,16168],{},"tříd"," (intervalů) a zjistí se, kolik hodnot do které třídy padne. Na počet ani šířku tříd neexistuje obecný předpis — počet by neměl být ani příliš malý, ani příliš velký.",[1110,16171,16172],{},"Výsledkem je tabulka četností se sloupci:",[2220,16174,16175,16255,16276,16297],{},[2223,16176,16177,16195,16196,16209,16210,16254],{},[1115,16178,16180],{"className":16179},[1573],[1575,16181,16182],{"xmlns":1577},[1579,16183,16184,16192],{},[1582,16185,16186],{},[1746,16187,16188,16190],{},[1585,16189,13729],{},[1585,16191,4521],{},[1605,16193,16194],{"encoding":1607},"I_j"," — ",[1115,16197,16199],{"className":16198},[1573],[1575,16200,16201],{"xmlns":1577},[1579,16202,16203,16207],{},[1582,16204,16205],{},[1585,16206,4521],{},[1605,16208,4521],{"encoding":1607},"-tý interval (v této kapitole vždy zleva uzavřený a zprava otevřený, ",[1115,16211,16213],{"className":16212},[1573],[1575,16214,16215],{"xmlns":1577},[1579,16216,16217,16251],{},[1582,16218,16219,16225,16227,16229,16235,16237,16249],{},[1746,16220,16221,16223],{},[1585,16222,13729],{},[1585,16224,4521],{},[1589,16226,1597],{},[1589,16228,11006],{"stretchy":1591},[1746,16230,16231,16233],{},[1585,16232,3499],{},[1585,16234,4521],{},[1589,16236,9483],{"separator":1121},[1746,16238,16239,16241],{},[1585,16240,3499],{},[1582,16242,16243,16245,16247],{},[1585,16244,4521],{},[1589,16246,4010],{},[1716,16248,1718],{},[1589,16250,1603],{"stretchy":1591},[1605,16252,16253],{"encoding":1607},"I_j = \\langle c_j; c_{j+1})","),",[2223,16256,16257,16275],{},[1115,16258,16260],{"className":16259},[1573],[1575,16261,16262],{"xmlns":1577},[1579,16263,16264,16272],{},[1582,16265,16266],{},[1746,16267,16268,16270],{},[1585,16269,11505],{},[1585,16271,4521],{},[1605,16273,16274],{"encoding":1607},"Z_j"," — střed (reprezentant) intervalu,",[2223,16277,16278,16296],{},[1115,16279,16281],{"className":16280},[1573],[1575,16282,16283],{"xmlns":1577},[1579,16284,16285,16293],{},[1582,16286,16287],{},[1746,16288,16289,16291],{},[1585,16290,1621],{},[1585,16292,4521],{},[1605,16294,16295],{"encoding":1607},"f_j"," — četnost, počet hodnot v intervalu,",[2223,16298,16299,16329,16330,1260,16358,2264],{},[1115,16300,16302],{"className":16301},[1573],[1575,16303,16304],{"xmlns":1577},[1579,16305,16306,16326],{},[1582,16307,16308,16314,16316,16322,16324],{},[1746,16309,16310,16312],{},[1585,16311,1110],{},[1585,16313,4521],{},[1589,16315,1597],{},[1746,16317,16318,16320],{},[1585,16319,1621],{},[1585,16321,4521],{},[1585,16323,4023],{"mathvariant":4022},[1585,16325,1781],{},[1605,16327,16328],{"encoding":1607},"p_j = f_j\u002Fn"," — relativní četnost, přičemž ",[1115,16331,16333],{"className":16332},[1573],[1575,16334,16335],{"xmlns":1577},[1579,16336,16337,16355],{},[1582,16338,16339,16345,16351,16353],{},[1746,16340,16341,16343],{},[1589,16342,4624],{},[1585,16344,4521],{},[1746,16346,16347,16349],{},[1585,16348,1621],{},[1585,16350,4521],{},[1589,16352,1597],{},[1585,16354,1781],{},[1605,16356,16357],{"encoding":1607},"\\sum_j f_j = n",[1115,16359,16361],{"className":16360},[1573],[1575,16362,16363],{"xmlns":1577},[1579,16364,16365,16383],{},[1582,16366,16367,16373,16379,16381],{},[1746,16368,16369,16371],{},[1589,16370,4624],{},[1585,16372,4521],{},[1746,16374,16375,16377],{},[1585,16376,1110],{},[1585,16378,4521],{},[1589,16380,1597],{},[1716,16382,1718],{},[1605,16384,16385],{"encoding":1607},"\\sum_j p_j = 1",[1110,16387,16388,16389,16391,16392,16395,16396,16399,16400,16403,16404,7219,16407,16424,16425,16428,16429,7219,16432,4454,16449,16452],{},"V R se třídění provádí příkazem ",[1150,16390,3921],{}," — buď necháme R zvolit třídy samo (",[1150,16393,16394],{},"hist(x)","), nebo zadáme hranice přímo (",[1150,16397,16398],{},"hist(x, br = seq(0, 550, by = 50))","). Uložením výsledku do proměnné (",[1150,16401,16402],{},"y \u003C- hist(...)",") získáme jednotlivé sloupce tabulky: ",[1150,16405,16406],{},"y$counts",[1115,16408,16410],{"className":16409},[1573],[1575,16411,16412],{"xmlns":1577},[1579,16413,16414,16422],{},[1582,16415,16416],{},[1746,16417,16418,16420],{},[1585,16419,1621],{},[1585,16421,4521],{},[1605,16423,16295],{"encoding":1607},"), ",[1150,16426,16427],{},"y$breaks"," (hranice tříd), ",[1150,16430,16431],{},"y$mids",[1115,16433,16435],{"className":16434},[1573],[1575,16436,16437],{"xmlns":1577},[1579,16438,16439,16447],{},[1582,16440,16441],{},[1746,16442,16443,16445],{},[1585,16444,11505],{},[1585,16446,4521],{},[1605,16448,16274],{"encoding":1607},[1150,16450,16451],{},"y$density"," (relativní četnosti na škále hustoty).",[1110,16454,16455,16456,16473,16474,16476,16477,16513,16514,16516,16517,2264],{},"Interval ",[1115,16457,16459],{"className":16458},[1573],[1575,16460,16461],{"xmlns":1577},[1579,16462,16463,16471],{},[1582,16464,16465],{},[1746,16466,16467,16469],{},[1585,16468,13729],{},[1585,16470,4521],{},[1605,16472,16194],{"encoding":1607}," je ve výchozím nastavení ",[1150,16475,3921],{}," zleva otevřený a zprava uzavřený, ",[1115,16478,16480],{"className":16479},[1573],[1575,16481,16482],{"xmlns":1577},[1579,16483,16484,16510],{},[1582,16485,16486,16488,16494,16496,16508],{},[1589,16487,1170],{"stretchy":1591},[1746,16489,16490,16492],{},[1585,16491,3499],{},[1585,16493,4521],{},[1589,16495,9483],{"separator":1121},[1746,16497,16498,16500],{},[1585,16499,3499],{},[1582,16501,16502,16504,16506],{},[1585,16503,4521],{},[1589,16505,4010],{},[1716,16507,1718],{},[1589,16509,10025],{"stretchy":1591},[1605,16511,16512],{"encoding":1607},"(c_j; c_{j+1}\\rangle"," — opačně, než jak třídy zapisujeme v této kapitole. Parametr ",[1150,16515,3931],{}," třídy obrátí na ",[1115,16518,16520],{"className":16519},[1573],[1575,16521,16522],{"xmlns":1577},[1579,16523,16524,16550],{},[1582,16525,16526,16528,16534,16536,16548],{},[1589,16527,11006],{"stretchy":1591},[1746,16529,16530,16532],{},[1585,16531,3499],{},[1585,16533,4521],{},[1589,16535,9483],{"separator":1121},[1746,16537,16538,16540],{},[1585,16539,3499],{},[1582,16541,16542,16544,16546],{},[1585,16543,4521],{},[1589,16545,4010],{},[1716,16547,1718],{},[1589,16549,1603],{"stretchy":1591},[1605,16551,16552],{"encoding":1607},"\\langle c_j; c_{j+1})",[1110,16554,16555],{},[1303,16556],{"alt":16557,"className":16558,"src":16559},"mask-ps-histogram-trideni",[1130,1307],"\u002Fwiki-assets\u002Fmask-ps-histogram-trideni.png",[1103,16561,16563,16570],{"className":16562,"dataCallout":6105},[1106,6104],[1110,16564,16566,16569],{"className":16565},[1113],[1115,16567],{"className":16568,"ariaHidden":1121},[1118,6112,1120],"Příklad: Třídění datového souboru",[1110,16571,16572],{},"Byly provedeny zkoušky životnosti nového výrobku. Datový soubor obsahuje 68 hodnot doby do poruchy (v minutách). Určete odhady charakteristik a zákona rozdělení.",[1144,16574,16576],{"className":1146,"code":16575,"language":71,"meta":1148,"style":1148},"x9 \u003C- c(101, 338, 150, 47, 10, 2, 12, 392, 5, 73,\n        367, 54, 114, 213, 71, 341, 313, 112, 343, 151,\n        9, 160, 18, 113, 77, 71, 159, 12, 119, 130,\n        140, 161, 379, 54, 373, 168, 365, 110, 145, 88,\n        74, 46, 246, 259, 19, 119, 48, 3, 163, 179,\n        194, 33, 49, 501, 193, 19, 5, 2, 221, 300,\n        88, 13, 428, 249, 25, 209, 54, 91)\nlength(x9)\nmax(x9) - min(x9)\ny9 \u003C- hist(x9, br = seq(0, 550, by = 50), right = FALSE, plot = FALSE)\ny9$counts\nround(y9$counts \u002F length(x9), 3)\nmean(x9); sd(x9)\n",[1150,16577,16578,16635,16686,16736,16787,16837,16885,16925,16935,16955,17019,17028,17058],{"__ignoreMap":1148},[1115,16579,16580,16583,16585,16587,16589,16592,16594,16597,16599,16602,16604,16607,16609,16611,16613,16615,16617,16619,16621,16624,16626,16628,16630,16633],{"class":1154,"line":10},[1115,16581,16582],{"class":1157},"x9",[1115,16584,1162],{"class":1161},[1115,16586,1166],{"class":1165},[1115,16588,1170],{"class":1169},[1115,16590,16591],{"class":1173},"101",[1115,16593,1177],{"class":1161},[1115,16595,16596],{"class":1173}," 338",[1115,16598,1177],{"class":1161},[1115,16600,16601],{"class":1173}," 150",[1115,16603,1177],{"class":1161},[1115,16605,16606],{"class":1173}," 47",[1115,16608,1177],{"class":1161},[1115,16610,12057],{"class":1173},[1115,16612,1177],{"class":1161},[1115,16614,6797],{"class":1173},[1115,16616,1177],{"class":1161},[1115,16618,6353],{"class":1173},[1115,16620,1177],{"class":1161},[1115,16622,16623],{"class":1173}," 392",[1115,16625,1177],{"class":1161},[1115,16627,12538],{"class":1173},[1115,16629,1177],{"class":1161},[1115,16631,16632],{"class":1173}," 73",[1115,16634,6356],{"class":1161},[1115,16636,16637,16640,16642,16645,16647,16650,16652,16655,16657,16659,16661,16664,16666,16669,16671,16674,16676,16679,16681,16684],{"class":1154,"line":27},[1115,16638,16639],{"class":1173},"        367",[1115,16641,1177],{"class":1161},[1115,16643,16644],{"class":1173}," 54",[1115,16646,1177],{"class":1161},[1115,16648,16649],{"class":1173}," 114",[1115,16651,1177],{"class":1161},[1115,16653,16654],{"class":1173}," 213",[1115,16656,1177],{"class":1161},[1115,16658,6371],{"class":1173},[1115,16660,1177],{"class":1161},[1115,16662,16663],{"class":1173}," 341",[1115,16665,1177],{"class":1161},[1115,16667,16668],{"class":1173}," 313",[1115,16670,1177],{"class":1161},[1115,16672,16673],{"class":1173}," 112",[1115,16675,1177],{"class":1161},[1115,16677,16678],{"class":1173}," 343",[1115,16680,1177],{"class":1161},[1115,16682,16683],{"class":1173}," 151",[1115,16685,6356],{"class":1161},[1115,16687,16688,16691,16693,16696,16698,16701,16703,16706,16708,16711,16713,16715,16717,16720,16722,16724,16726,16729,16731,16734],{"class":1154,"line":148},[1115,16689,16690],{"class":1173},"        9",[1115,16692,1177],{"class":1161},[1115,16694,16695],{"class":1173}," 160",[1115,16697,1177],{"class":1161},[1115,16699,16700],{"class":1173}," 18",[1115,16702,1177],{"class":1161},[1115,16704,16705],{"class":1173}," 113",[1115,16707,1177],{"class":1161},[1115,16709,16710],{"class":1173}," 77",[1115,16712,1177],{"class":1161},[1115,16714,6371],{"class":1173},[1115,16716,1177],{"class":1161},[1115,16718,16719],{"class":1173}," 159",[1115,16721,1177],{"class":1161},[1115,16723,6353],{"class":1173},[1115,16725,1177],{"class":1161},[1115,16727,16728],{"class":1173}," 119",[1115,16730,1177],{"class":1161},[1115,16732,16733],{"class":1173}," 130",[1115,16735,6356],{"class":1161},[1115,16737,16738,16741,16743,16746,16748,16751,16753,16755,16757,16760,16762,16765,16767,16770,16772,16775,16777,16780,16782,16785],{"class":1154,"line":111},[1115,16739,16740],{"class":1173},"        140",[1115,16742,1177],{"class":1161},[1115,16744,16745],{"class":1173}," 161",[1115,16747,1177],{"class":1161},[1115,16749,16750],{"class":1173}," 379",[1115,16752,1177],{"class":1161},[1115,16754,16644],{"class":1173},[1115,16756,1177],{"class":1161},[1115,16758,16759],{"class":1173}," 373",[1115,16761,1177],{"class":1161},[1115,16763,16764],{"class":1173}," 168",[1115,16766,1177],{"class":1161},[1115,16768,16769],{"class":1173}," 365",[1115,16771,1177],{"class":1161},[1115,16773,16774],{"class":1173}," 110",[1115,16776,1177],{"class":1161},[1115,16778,16779],{"class":1173}," 145",[1115,16781,1177],{"class":1161},[1115,16783,16784],{"class":1173}," 88",[1115,16786,6356],{"class":1161},[1115,16788,16789,16792,16794,16797,16799,16802,16804,16807,16809,16812,16814,16816,16818,16821,16823,16825,16827,16830,16832,16835],{"class":1154,"line":96},[1115,16790,16791],{"class":1173},"        74",[1115,16793,1177],{"class":1161},[1115,16795,16796],{"class":1173}," 46",[1115,16798,1177],{"class":1161},[1115,16800,16801],{"class":1173}," 246",[1115,16803,1177],{"class":1161},[1115,16805,16806],{"class":1173}," 259",[1115,16808,1177],{"class":1161},[1115,16810,16811],{"class":1173}," 19",[1115,16813,1177],{"class":1161},[1115,16815,16728],{"class":1173},[1115,16817,1177],{"class":1161},[1115,16819,16820],{"class":1173}," 48",[1115,16822,1177],{"class":1161},[1115,16824,13386],{"class":1173},[1115,16826,1177],{"class":1161},[1115,16828,16829],{"class":1173}," 163",[1115,16831,1177],{"class":1161},[1115,16833,16834],{"class":1173}," 179",[1115,16836,6356],{"class":1161},[1115,16838,16839,16842,16844,16846,16848,16851,16853,16856,16858,16861,16863,16865,16867,16869,16871,16873,16875,16878,16880,16883],{"class":1154,"line":89},[1115,16840,16841],{"class":1173},"        194",[1115,16843,1177],{"class":1161},[1115,16845,6762],{"class":1173},[1115,16847,1177],{"class":1161},[1115,16849,16850],{"class":1173}," 49",[1115,16852,1177],{"class":1161},[1115,16854,16855],{"class":1173}," 501",[1115,16857,1177],{"class":1161},[1115,16859,16860],{"class":1173}," 193",[1115,16862,1177],{"class":1161},[1115,16864,16811],{"class":1173},[1115,16866,1177],{"class":1161},[1115,16868,12538],{"class":1173},[1115,16870,1177],{"class":1161},[1115,16872,6797],{"class":1173},[1115,16874,1177],{"class":1161},[1115,16876,16877],{"class":1173}," 221",[1115,16879,1177],{"class":1161},[1115,16881,16882],{"class":1173}," 300",[1115,16884,6356],{"class":1161},[1115,16886,16887,16890,16892,16894,16896,16899,16901,16904,16906,16909,16911,16914,16916,16918,16920,16923],{"class":1154,"line":82},[1115,16888,16889],{"class":1173},"        88",[1115,16891,1177],{"class":1161},[1115,16893,6348],{"class":1173},[1115,16895,1177],{"class":1161},[1115,16897,16898],{"class":1173}," 428",[1115,16900,1177],{"class":1161},[1115,16902,16903],{"class":1173}," 249",[1115,16905,1177],{"class":1161},[1115,16907,16908],{"class":1173}," 25",[1115,16910,1177],{"class":1161},[1115,16912,16913],{"class":1173}," 209",[1115,16915,1177],{"class":1161},[1115,16917,16644],{"class":1173},[1115,16919,1177],{"class":1161},[1115,16921,16922],{"class":1173}," 91",[1115,16924,6519],{"class":1169},[1115,16926,16927,16929,16931,16933],{"class":1154,"line":75},[1115,16928,14638],{"class":1165},[1115,16930,1170],{"class":1169},[1115,16932,16582],{"class":1157},[1115,16934,6519],{"class":1169},[1115,16936,16937,16939,16941,16943,16945,16947,16949,16951,16953],{"class":1154,"line":6509},[1115,16938,14245],{"class":1165},[1115,16940,1170],{"class":1169},[1115,16942,16582],{"class":1157},[1115,16944,7214],{"class":1169},[1115,16946,7250],{"class":1161},[1115,16948,14709],{"class":1165},[1115,16950,1170],{"class":1169},[1115,16952,16582],{"class":1157},[1115,16954,6519],{"class":1169},[1115,16956,16957,16960,16962,16965,16967,16969,16971,16974,16976,16979,16981,16983,16985,16988,16990,16993,16995,16997,16999,17001,17004,17006,17008,17010,17013,17015,17017],{"class":1154,"line":72},[1115,16958,16959],{"class":1157},"y9",[1115,16961,1162],{"class":1161},[1115,16963,16964],{"class":1165}," hist",[1115,16966,1170],{"class":1169},[1115,16968,16582],{"class":1157},[1115,16970,1177],{"class":1161},[1115,16972,16973],{"class":1157}," br",[1115,16975,6416],{"class":1161},[1115,16977,16978],{"class":1165}," seq",[1115,16980,1170],{"class":1169},[1115,16982,2398],{"class":1173},[1115,16984,1177],{"class":1161},[1115,16986,16987],{"class":1173}," 550",[1115,16989,1177],{"class":1161},[1115,16991,16992],{"class":1157}," by",[1115,16994,6416],{"class":1161},[1115,16996,8851],{"class":1173},[1115,16998,1603],{"class":1169},[1115,17000,1177],{"class":1161},[1115,17002,17003],{"class":1157}," right",[1115,17005,6416],{"class":1161},[1115,17007,8944],{"class":1173},[1115,17009,1177],{"class":1161},[1115,17011,17012],{"class":1157}," plot",[1115,17014,6416],{"class":1161},[1115,17016,8944],{"class":1173},[1115,17018,6519],{"class":1169},[1115,17020,17021,17023,17025],{"class":1154,"line":25},[1115,17022,16959],{"class":1157},[1115,17024,1290],{"class":1161},[1115,17026,17027],{"class":1157},"counts\n",[1115,17029,17030,17032,17034,17036,17038,17041,17043,17046,17048,17050,17052,17054,17056],{"class":1154,"line":65},[1115,17031,12524],{"class":1165},[1115,17033,1170],{"class":1169},[1115,17035,16959],{"class":1157},[1115,17037,1290],{"class":1161},[1115,17039,17040],{"class":1157},"counts",[1115,17042,12619],{"class":1161},[1115,17044,17045],{"class":1165}," length",[1115,17047,1170],{"class":1169},[1115,17049,16582],{"class":1157},[1115,17051,1603],{"class":1169},[1115,17053,1177],{"class":1161},[1115,17055,13386],{"class":1173},[1115,17057,6519],{"class":1169},[1115,17059,17060,17062,17064,17066,17068,17070,17072,17074],{"class":1154,"line":63},[1115,17061,14649],{"class":1165},[1115,17063,1170],{"class":1169},[1115,17065,16582],{"class":1157},[1115,17067,14688],{"class":1169},[1115,17069,14671],{"class":1165},[1115,17071,1170],{"class":1169},[1115,17073,16582],{"class":1157},[1115,17075,6519],{"class":1169},[1144,17077,17080],{"className":17078,"code":17079,"language":6540,"meta":1148},[6538],"[1] 68\n[1] 499\n [1] 19 11 10 10  5  1  5  5  1  0  1\n [1] 0.279 0.162 0.147 0.147 0.074 0.015 0.074 0.074 0.015 0.000 0.015\n[1] 145.4412\n[1] 126.1283\n",[1150,17081,17079],{"__ignoreMap":1148},[1110,17083,17084,17085,17113],{},"Variační rozpětí je ",[1115,17086,17088],{"className":17087},[1573],[1575,17089,17090],{"xmlns":1577},[1579,17091,17092,17110],{},[1582,17093,17094,17096,17098,17101,17103,17105,17107],{},[1585,17095,3376],{},[1589,17097,1597],{},[1716,17099,17100],{},"501",[1589,17102,1721],{},[1716,17104,1993],{},[1589,17106,1597],{},[1716,17108,17109],{},"499",[1605,17111,17112],{"encoding":1607},"R = 501 - 2 = 499"," minut; rozdělit je na 11 tříd po 50 minutách je rozumná volba (ani moc málo, ani moc tříd). Výsledná tabulka četností:",[1310,17115,17116,17212],{},[1313,17117,17118],{},[1316,17119,17120,17135,17154,17173,17192],{},[1319,17121,17122],{},[1115,17123,17125],{"className":17124},[1573],[1575,17126,17127],{"xmlns":1577},[1579,17128,17129,17133],{},[1582,17130,17131],{},[1585,17132,4521],{},[1605,17134,4521],{"encoding":1607},[1319,17136,17137],{},[1115,17138,17140],{"className":17139},[1573],[1575,17141,17142],{"xmlns":1577},[1579,17143,17144,17152],{},[1582,17145,17146],{},[1746,17147,17148,17150],{},[1585,17149,13729],{},[1585,17151,4521],{},[1605,17153,16194],{"encoding":1607},[1319,17155,17156],{},[1115,17157,17159],{"className":17158},[1573],[1575,17160,17161],{"xmlns":1577},[1579,17162,17163,17171],{},[1582,17164,17165],{},[1746,17166,17167,17169],{},[1585,17168,11505],{},[1585,17170,4521],{},[1605,17172,16274],{"encoding":1607},[1319,17174,17175],{},[1115,17176,17178],{"className":17177},[1573],[1575,17179,17180],{"xmlns":1577},[1579,17181,17182,17190],{},[1582,17183,17184],{},[1746,17185,17186,17188],{},[1585,17187,1621],{},[1585,17189,4521],{},[1605,17191,16295],{"encoding":1607},[1319,17193,17194],{},[1115,17195,17197],{"className":17196},[1573],[1575,17198,17199],{"xmlns":1577},[1579,17200,17201,17209],{},[1582,17202,17203],{},[1746,17204,17205,17207],{},[1585,17206,1110],{},[1585,17208,4521],{},[1605,17210,17211],{"encoding":1607},"p_j",[1332,17213,17214,17229,17244,17259,17272,17287,17302,17316,17331,17345,17360],{},[1316,17215,17216,17218,17221,17223,17226],{},[1337,17217,1718],{},[1337,17219,17220],{},"⟨0; 50)",[1337,17222,6675],{},[1337,17224,17225],{},"19",[1337,17227,17228],{},"0,279",[1316,17230,17231,17233,17236,17239,17241],{},[1337,17232,1993],{},[1337,17234,17235],{},"⟨50; 100)",[1337,17237,17238],{},"75",[1337,17240,4890],{},[1337,17242,17243],{},"0,162",[1316,17245,17246,17248,17251,17254,17256],{},[1337,17247,6220],{},[1337,17249,17250],{},"⟨100; 150)",[1337,17252,17253],{},"125",[1337,17255,11613],{},[1337,17257,17258],{},"0,147",[1316,17260,17261,17263,17266,17268,17270],{},[1337,17262,6170],{},[1337,17264,17265],{},"⟨150; 200)",[1337,17267,10061],{},[1337,17269,11613],{},[1337,17271,17258],{},[1316,17273,17274,17276,17279,17282,17284],{},[1337,17275,12470],{},[1337,17277,17278],{},"⟨200; 250)",[1337,17280,17281],{},"225",[1337,17283,12470],{},[1337,17285,17286],{},"0,074",[1316,17288,17289,17291,17294,17297,17299],{},[1337,17290,6581],{},[1337,17292,17293],{},"⟨250; 300)",[1337,17295,17296],{},"275",[1337,17298,1718],{},[1337,17300,17301],{},"0,015",[1316,17303,17304,17306,17309,17312,17314],{},[1337,17305,3905],{},[1337,17307,17308],{},"⟨300; 350)",[1337,17310,17311],{},"325",[1337,17313,12470],{},[1337,17315,17286],{},[1316,17317,17318,17321,17324,17327,17329],{},[1337,17319,17320],{},"8",[1337,17322,17323],{},"⟨350; 400)",[1337,17325,17326],{},"375",[1337,17328,12470],{},[1337,17330,17286],{},[1316,17332,17333,17335,17338,17341,17343],{},[1337,17334,6223],{},[1337,17336,17337],{},"⟨400; 450)",[1337,17339,17340],{},"425",[1337,17342,1718],{},[1337,17344,17301],{},[1316,17346,17347,17349,17352,17355,17357],{},[1337,17348,11613],{},[1337,17350,17351],{},"⟨450; 500)",[1337,17353,17354],{},"475",[1337,17356,2398],{},[1337,17358,17359],{},"0,000",[1316,17361,17362,17364,17367,17370,17372],{},[1337,17363,4890],{},[1337,17365,17366],{},"⟨500; ∞)",[1337,17368,17369],{},"525",[1337,17371,1718],{},[1337,17373,17301],{},[1110,17375,17376,17377,17394,17395,17412,17413,1279,17436,1279,17464,17483,17484,1279,17507,17526],{},"Asi 27,9 % výrobků vydrželo méně než 50 minut, jen asi 1,5 % mezi 250 a 300 minutami. Charakteristiky spočtené ze středů tříd ",[1115,17378,17380],{"className":17379},[1573],[1575,17381,17382],{"xmlns":1577},[1579,17383,17384,17392],{},[1582,17385,17386],{},[1746,17387,17388,17390],{},[1585,17389,11505],{},[1585,17391,4521],{},[1605,17393,16274],{"encoding":1607}," (vážený průměr a rozptyl se střední hodnotou nahrazenou ",[1115,17396,17398],{"className":17397},[1573],[1575,17399,17400],{"xmlns":1577},[1579,17401,17402,17410],{},[1582,17403,17404],{},[1746,17405,17406,17408],{},[1585,17407,11505],{},[1585,17409,4521],{},[1605,17411,16274],{"encoding":1607},") vycházejí ",[1115,17414,17416],{"className":17415},[1573],[1575,17417,17418],{"xmlns":1577},[1579,17419,17420,17433],{},[1582,17421,17422,17428,17430],{},[3005,17423,17424,17426],{"accent":1121},[1585,17425,1158],{},[1589,17427,3408],{},[1589,17429,12020],{},[1716,17431,17432],{},"149,26",[1605,17434,17435],{"encoding":1607},"\\bar{x} \\approx 149{,}26",[1115,17437,17439],{"className":17438},[1573],[1575,17440,17441],{"xmlns":1577},[1579,17442,17443,17461],{},[1582,17444,17445,17451,17453,17456,17458],{},[1986,17446,17447,17449],{},[1585,17448,3433],{},[1716,17450,1993],{},[1589,17452,12020],{},[1716,17454,17455],{},"15",[5543,17457,5545],{},[1716,17459,17460],{},"484,5",[1605,17462,17463],{"encoding":1607},"s^2 \\approx 15\\,484{,}5",[1115,17465,17467],{"className":17466},[1573],[1575,17468,17469],{"xmlns":1577},[1579,17470,17471,17480],{},[1582,17472,17473,17475,17477],{},[1585,17474,3433],{},[1589,17476,12020],{},[1716,17478,17479],{},"124,44",[1605,17481,17482],{"encoding":1607},"s \\approx 124{,}44"," — blízko hodnotám ",[1115,17485,17487],{"className":17486},[1573],[1575,17488,17489],{"xmlns":1577},[1579,17490,17491,17504],{},[1582,17492,17493,17499,17501],{},[3005,17494,17495,17497],{"accent":1121},[1585,17496,1158],{},[1589,17498,3408],{},[1589,17500,1597],{},[1716,17502,17503],{},"145,44",[1605,17505,17506],{"encoding":1607},"\\bar{x}=145{,}44",[1115,17508,17510],{"className":17509},[1573],[1575,17511,17512],{"xmlns":1577},[1579,17513,17514,17523],{},[1582,17515,17516,17518,17520],{},[1585,17517,3433],{},[1589,17519,1597],{},[1716,17521,17522],{},"126,13",[1605,17524,17525],{"encoding":1607},"s=126{,}13"," spočteným přímo z nerozdělených dat; malý rozdíl vzniká tím, že třídění nahrazuje skutečné hodnoty středy tříd.",[1110,17528,17529,17530,17533,17534,17570,17571,17589,17590,17604,17605,17631,17632,17634,17635,7477],{},"Tvar histogramu — vysoká četnost u krátkých dob, rychlý pokles — odpovídá ",[2227,17531,17532],{},"exponenciálnímu rozdělení",", které se pro dobu do poruchy používá nejčastěji. Jeho hustota je ",[1115,17535,17537],{"className":17536},[1573],[1575,17538,17539],{"xmlns":1577},[1579,17540,17541,17567],{},[1582,17542,17543,17545,17547,17549,17551,17553,17555],{},[1585,17544,1621],{},[1589,17546,1170],{"stretchy":1591},[1585,17548,1158],{},[1589,17550,1603],{"stretchy":1591},[1589,17552,1597],{},[1585,17554,1834],{},[1986,17556,17557,17559],{},[1585,17558,2876],{},[1582,17560,17561,17563,17565],{},[1589,17562,1721],{},[1585,17564,1834],{},[1585,17566,1158],{},[1605,17568,17569],{"encoding":1607},"f(x) = \\lambda e^{-\\lambda x}"," pro ",[1115,17572,17574],{"className":17573},[1573],[1575,17575,17576],{"xmlns":1577},[1579,17577,17578,17586],{},[1582,17579,17580,17582,17584],{},[1585,17581,1158],{},[1589,17583,5983],{},[1716,17585,2398],{},[1605,17587,17588],{"encoding":1607},"x \\ge 0",", s parametrem ",[1115,17591,17593],{"className":17592},[1573],[1575,17594,17595],{"xmlns":1577},[1579,17596,17597,17601],{},[1582,17598,17599],{},[1585,17600,1834],{},[1605,17602,17603],{"encoding":1607},"\\lambda"," odhadnutým jako ",[1115,17606,17608],{"className":17607},[1573],[1575,17609,17610],{"xmlns":1577},[1579,17611,17612,17628],{},[1582,17613,17614,17616,17618,17620,17622],{},[1585,17615,1834],{},[1589,17617,1597],{},[1716,17619,1718],{},[1585,17621,4023],{"mathvariant":4022},[3005,17623,17624,17626],{"accent":1121},[1585,17625,1158],{},[1589,17627,3408],{},[1605,17629,17630],{"encoding":1607},"\\lambda = 1\u002F\\bar{x}"," (v R je ",[1150,17633,12425],{}," parametrem ",[1150,17636,17637],{},"dexp()",[1144,17639,17641],{"className":1146,"code":17640,"language":71,"meta":1148,"style":1148},"rate9 \u003C- 1 \u002F mean(x9)\nrate9\n",[1150,17642,17643,17662],{"__ignoreMap":1148},[1115,17644,17645,17648,17650,17652,17654,17656,17658,17660],{"class":1154,"line":10},[1115,17646,17647],{"class":1157},"rate9",[1115,17649,1162],{"class":1161},[1115,17651,7253],{"class":1173},[1115,17653,12619],{"class":1161},[1115,17655,11811],{"class":1165},[1115,17657,1170],{"class":1169},[1115,17659,16582],{"class":1157},[1115,17661,6519],{"class":1169},[1115,17663,17664],{"class":1154,"line":27},[1115,17665,17666],{"class":1157},"rate9\n",[1144,17668,17671],{"className":17669,"code":17670,"language":6540,"meta":1148},[6538],"[1] 0.006875632\n",[1150,17672,17670],{"__ignoreMap":1148},[1110,17674,17675],{},[1303,17676],{"alt":17677,"className":17678,"src":17679},"mask-ps-hustota-fit",[1130,1307],"\u002Fwiki-assets\u002Fmask-ps-hustota-fit.png",[1110,17681,17682,17683,2264],{},"Proložená křivka dobře sleduje tvar sloupců. Zda data odpovídají exponenciálnímu rozdělení formálně, posuzuje test dobré shody popsaný v ",[1127,17684,2660],{"className":17685,"dataFsResolvedFilePath":2658,"href":2659},[1130],[1103,17687,17689,17696],{"className":17688,"dataCallout":6105},[1106,6104],[1110,17690,17692,17695],{"className":17691},[1113],[1115,17693],{"className":17694,"ariaHidden":1121},[1118,6112,1120],"Příklad: Doba života výrobku",[1110,17697,17698],{},"Sledováním doby života výrobku bylo naměřeno 50 hodnot (v minutách). Určete empirické charakteristiky, roztřiďte datový soubor a nakreslete histogram četností.",[1144,17700,17702],{"className":1146,"code":17701,"language":71,"meta":1148,"style":1148},"x5 \u003C- c(63, 156, 184, 786, 822, 278, 15, 561, 229, 8,\n        4, 35, 73, 203, 178, 323, 275, 176, 427, 196,\n        415, 140, 17, 293, 991, 100, 189, 176, 672, 134,\n        529, 310, 22, 69, 130, 272, 117, 169, 466, 286,\n        46, 236, 387, 92, 177, 188, 124, 385, 174, 23)\nlength(x5)\nmean(x5); sd(x5); median(x5)\nmax(x5) - min(x5)\ny5 \u003C- hist(x5, br = seq(0, 1050, by = 150), right = FALSE, plot = FALSE)\ny5$mids\ny5$counts\nround(y5$counts \u002F length(x5), 3)\n",[1150,17703,17704,17765,17816,17867,17918,17970,17980,18006,18026,18084,18093,18101],{"__ignoreMap":1148},[1115,17705,17706,17709,17711,17713,17715,17718,17720,17723,17725,17728,17730,17733,17735,17738,17740,17743,17745,17748,17750,17753,17755,17758,17760,17763],{"class":1154,"line":10},[1115,17707,17708],{"class":1157},"x5",[1115,17710,1162],{"class":1161},[1115,17712,1166],{"class":1165},[1115,17714,1170],{"class":1169},[1115,17716,17717],{"class":1173},"63",[1115,17719,1177],{"class":1161},[1115,17721,17722],{"class":1173}," 156",[1115,17724,1177],{"class":1161},[1115,17726,17727],{"class":1173}," 184",[1115,17729,1177],{"class":1161},[1115,17731,17732],{"class":1173}," 786",[1115,17734,1177],{"class":1161},[1115,17736,17737],{"class":1173}," 822",[1115,17739,1177],{"class":1161},[1115,17741,17742],{"class":1173}," 278",[1115,17744,1177],{"class":1161},[1115,17746,17747],{"class":1173}," 15",[1115,17749,1177],{"class":1161},[1115,17751,17752],{"class":1173}," 561",[1115,17754,1177],{"class":1161},[1115,17756,17757],{"class":1173}," 229",[1115,17759,1177],{"class":1161},[1115,17761,17762],{"class":1173}," 8",[1115,17764,6356],{"class":1161},[1115,17766,17767,17770,17772,17775,17777,17779,17781,17784,17786,17789,17791,17794,17796,17799,17801,17804,17806,17809,17811,17814],{"class":1154,"line":27},[1115,17768,17769],{"class":1173},"        4",[1115,17771,1177],{"class":1161},[1115,17773,17774],{"class":1173}," 35",[1115,17776,1177],{"class":1161},[1115,17778,16632],{"class":1173},[1115,17780,1177],{"class":1161},[1115,17782,17783],{"class":1173}," 203",[1115,17785,1177],{"class":1161},[1115,17787,17788],{"class":1173}," 178",[1115,17790,1177],{"class":1161},[1115,17792,17793],{"class":1173}," 323",[1115,17795,1177],{"class":1161},[1115,17797,17798],{"class":1173}," 275",[1115,17800,1177],{"class":1161},[1115,17802,17803],{"class":1173}," 176",[1115,17805,1177],{"class":1161},[1115,17807,17808],{"class":1173}," 427",[1115,17810,1177],{"class":1161},[1115,17812,17813],{"class":1173}," 196",[1115,17815,6356],{"class":1161},[1115,17817,17818,17821,17823,17826,17828,17831,17833,17836,17838,17841,17843,17846,17848,17851,17853,17855,17857,17860,17862,17865],{"class":1154,"line":148},[1115,17819,17820],{"class":1173},"        415",[1115,17822,1177],{"class":1161},[1115,17824,17825],{"class":1173}," 140",[1115,17827,1177],{"class":1161},[1115,17829,17830],{"class":1173}," 17",[1115,17832,1177],{"class":1161},[1115,17834,17835],{"class":1173}," 293",[1115,17837,1177],{"class":1161},[1115,17839,17840],{"class":1173}," 991",[1115,17842,1177],{"class":1161},[1115,17844,17845],{"class":1173}," 100",[1115,17847,1177],{"class":1161},[1115,17849,17850],{"class":1173}," 189",[1115,17852,1177],{"class":1161},[1115,17854,17803],{"class":1173},[1115,17856,1177],{"class":1161},[1115,17858,17859],{"class":1173}," 672",[1115,17861,1177],{"class":1161},[1115,17863,17864],{"class":1173}," 134",[1115,17866,6356],{"class":1161},[1115,17868,17869,17872,17874,17877,17879,17882,17884,17887,17889,17891,17893,17896,17898,17901,17903,17906,17908,17911,17913,17916],{"class":1154,"line":111},[1115,17870,17871],{"class":1173},"        529",[1115,17873,1177],{"class":1161},[1115,17875,17876],{"class":1173}," 310",[1115,17878,1177],{"class":1161},[1115,17880,17881],{"class":1173}," 22",[1115,17883,1177],{"class":1161},[1115,17885,17886],{"class":1173}," 69",[1115,17888,1177],{"class":1161},[1115,17890,16733],{"class":1173},[1115,17892,1177],{"class":1161},[1115,17894,17895],{"class":1173}," 272",[1115,17897,1177],{"class":1161},[1115,17899,17900],{"class":1173}," 117",[1115,17902,1177],{"class":1161},[1115,17904,17905],{"class":1173}," 169",[1115,17907,1177],{"class":1161},[1115,17909,17910],{"class":1173}," 466",[1115,17912,1177],{"class":1161},[1115,17914,17915],{"class":1173}," 286",[1115,17917,6356],{"class":1161},[1115,17919,17920,17923,17925,17928,17930,17933,17935,17938,17940,17943,17945,17948,17950,17953,17955,17958,17960,17963,17965,17968],{"class":1154,"line":96},[1115,17921,17922],{"class":1173},"        46",[1115,17924,1177],{"class":1161},[1115,17926,17927],{"class":1173}," 236",[1115,17929,1177],{"class":1161},[1115,17931,17932],{"class":1173}," 387",[1115,17934,1177],{"class":1161},[1115,17936,17937],{"class":1173}," 92",[1115,17939,1177],{"class":1161},[1115,17941,17942],{"class":1173}," 177",[1115,17944,1177],{"class":1161},[1115,17946,17947],{"class":1173}," 188",[1115,17949,1177],{"class":1161},[1115,17951,17952],{"class":1173}," 124",[1115,17954,1177],{"class":1161},[1115,17956,17957],{"class":1173}," 385",[1115,17959,1177],{"class":1161},[1115,17961,17962],{"class":1173}," 174",[1115,17964,1177],{"class":1161},[1115,17966,17967],{"class":1173}," 23",[1115,17969,6519],{"class":1169},[1115,17971,17972,17974,17976,17978],{"class":1154,"line":89},[1115,17973,14638],{"class":1165},[1115,17975,1170],{"class":1169},[1115,17977,17708],{"class":1157},[1115,17979,6519],{"class":1169},[1115,17981,17982,17984,17986,17988,17990,17992,17994,17996,17998,18000,18002,18004],{"class":1154,"line":82},[1115,17983,14649],{"class":1165},[1115,17985,1170],{"class":1169},[1115,17987,17708],{"class":1157},[1115,17989,14688],{"class":1169},[1115,17991,14671],{"class":1165},[1115,17993,1170],{"class":1169},[1115,17995,17708],{"class":1157},[1115,17997,14688],{"class":1169},[1115,17999,15370],{"class":1165},[1115,18001,1170],{"class":1169},[1115,18003,17708],{"class":1157},[1115,18005,6519],{"class":1169},[1115,18007,18008,18010,18012,18014,18016,18018,18020,18022,18024],{"class":1154,"line":75},[1115,18009,14245],{"class":1165},[1115,18011,1170],{"class":1169},[1115,18013,17708],{"class":1157},[1115,18015,7214],{"class":1169},[1115,18017,7250],{"class":1161},[1115,18019,14709],{"class":1165},[1115,18021,1170],{"class":1169},[1115,18023,17708],{"class":1157},[1115,18025,6519],{"class":1169},[1115,18027,18028,18031,18033,18035,18037,18039,18041,18043,18045,18047,18049,18051,18053,18056,18058,18060,18062,18064,18066,18068,18070,18072,18074,18076,18078,18080,18082],{"class":1154,"line":6509},[1115,18029,18030],{"class":1157},"y5",[1115,18032,1162],{"class":1161},[1115,18034,16964],{"class":1165},[1115,18036,1170],{"class":1169},[1115,18038,17708],{"class":1157},[1115,18040,1177],{"class":1161},[1115,18042,16973],{"class":1157},[1115,18044,6416],{"class":1161},[1115,18046,16978],{"class":1165},[1115,18048,1170],{"class":1169},[1115,18050,2398],{"class":1173},[1115,18052,1177],{"class":1161},[1115,18054,18055],{"class":1173}," 1050",[1115,18057,1177],{"class":1161},[1115,18059,16992],{"class":1157},[1115,18061,6416],{"class":1161},[1115,18063,16601],{"class":1173},[1115,18065,1603],{"class":1169},[1115,18067,1177],{"class":1161},[1115,18069,17003],{"class":1157},[1115,18071,6416],{"class":1161},[1115,18073,8944],{"class":1173},[1115,18075,1177],{"class":1161},[1115,18077,17012],{"class":1157},[1115,18079,6416],{"class":1161},[1115,18081,8944],{"class":1173},[1115,18083,6519],{"class":1169},[1115,18085,18086,18088,18090],{"class":1154,"line":72},[1115,18087,18030],{"class":1157},[1115,18089,1290],{"class":1161},[1115,18091,18092],{"class":1157},"mids\n",[1115,18094,18095,18097,18099],{"class":1154,"line":25},[1115,18096,18030],{"class":1157},[1115,18098,1290],{"class":1161},[1115,18100,17027],{"class":1157},[1115,18102,18103,18105,18107,18109,18111,18113,18115,18117,18119,18121,18123,18125,18127],{"class":1154,"line":65},[1115,18104,12524],{"class":1165},[1115,18106,1170],{"class":1169},[1115,18108,18030],{"class":1157},[1115,18110,1290],{"class":1161},[1115,18112,17040],{"class":1157},[1115,18114,12619],{"class":1161},[1115,18116,17045],{"class":1165},[1115,18118,1170],{"class":1169},[1115,18120,17708],{"class":1157},[1115,18122,1603],{"class":1169},[1115,18124,1177],{"class":1161},[1115,18126,13386],{"class":1173},[1115,18128,6519],{"class":1169},[1144,18130,18133],{"className":18131,"code":18132,"language":6540,"meta":1148},[6538],"[1] 50\n[1] 246.42\n[1] 220.0209\n[1] 181\n[1] 987\n[1]   75 225 375 525 675 825 975\n[1] 18 19  6  3  1  2  1\n[1] 0.36 0.38 0.12 0.06 0.02 0.04 0.02\n",[1150,18134,18132],{"__ignoreMap":1148},[1110,18136,18137],{},"Variační rozpětí 987 minut rozdělené do 7 tříd po 150 minutách dává podobný tvar jako u předchozího příkladu: 74 % výrobků vydrželo méně než 300 minut, ojedinělé hodnoty sahají až k 991 minutám. Průměr 246,4 minuty leží výrazně nad mediánem 181 minut — rozdělení je zešikmené k vyšším hodnotám stejně jako u doby do poruchy výše.",[1136,18139,9014],{"id":9013},[2220,18141,18142,18158,18259,18327],{},[2223,18143,18144,2230,18147,18149,18150,18152,18153,18155,18156,2264],{},[2227,18145,18146],{},"Výchozí typ kvantilu v R.",[1150,18148,3900],{}," bez argumentu ",[1150,18151,3897],{}," používá jiný výpočetní vzorec (",[1150,18154,14801],{},") než ruční postup v této kapitole — u některých souborů se hodnoty liší. Pro shodu s ručním výpočtem zadávejte ",[1150,18157,2514],{},[2223,18159,18160,18165,18166,18168,18169,18204,18205,18240,18241,18258],{},[2227,18161,18162,18163,2264],{},"Výchozí ohraničení tříd v ",[1150,18164,3921],{}," Bez ",[1150,18167,3931],{}," jsou třídy zprava uzavřené, ",[1115,18170,18172],{"className":18171},[1573],[1575,18173,18174],{"xmlns":1577},[1579,18175,18176,18202],{},[1582,18177,18178,18180,18186,18188,18200],{},[1589,18179,1170],{"stretchy":1591},[1746,18181,18182,18184],{},[1585,18183,3499],{},[1585,18185,4521],{},[1589,18187,9483],{"separator":1121},[1746,18189,18190,18192],{},[1585,18191,3499],{},[1582,18193,18194,18196,18198],{},[1585,18195,4521],{},[1589,18197,4010],{},[1716,18199,1718],{},[1589,18201,10025],{"stretchy":1591},[1605,18203,16512],{"encoding":1607}," — opačně než konvence ",[1115,18206,18208],{"className":18207},[1573],[1575,18209,18210],{"xmlns":1577},[1579,18211,18212,18238],{},[1582,18213,18214,18216,18222,18224,18236],{},[1589,18215,11006],{"stretchy":1591},[1746,18217,18218,18220],{},[1585,18219,3499],{},[1585,18221,4521],{},[1589,18223,9483],{"separator":1121},[1746,18225,18226,18228],{},[1585,18227,3499],{},[1582,18229,18230,18232,18234],{},[1585,18231,4521],{},[1589,18233,4010],{},[1716,18235,1718],{},[1589,18237,1603],{"stretchy":1591},[1605,18239,16552],{"encoding":1607}," použitá v tabulkách výše. Hodnota ležící přesně na hranici pak spadne do jiné třídy a četnosti ",[1115,18242,18244],{"className":18243},[1573],[1575,18245,18246],{"xmlns":1577},[1579,18247,18248,18256],{},[1582,18249,18250],{},[1746,18251,18252,18254],{},[1585,18253,1621],{},[1585,18255,4521],{},[1605,18257,16295],{"encoding":1607}," vyjdou jinak.",[2223,18260,18261,2230,18264,18282,18283,18296,18297,11628,18310,2264],{},[2227,18262,18263],{},"Rozptyl vs. směrodatná odchylka.",[1115,18265,18267],{"className":18266},[1573],[1575,18268,18269],{"xmlns":1577},[1579,18270,18271,18279],{},[1582,18272,18273],{},[1986,18274,18275,18277],{},[1585,18276,3433],{},[1716,18278,1993],{},[1605,18280,18281],{"encoding":1607},"s^2"," se udává v jednotkách znaku na druhou, ",[1115,18284,18286],{"className":18285},[1573],[1575,18287,18288],{"xmlns":1577},[1579,18289,18290,18294],{},[1582,18291,18292],{},[1585,18293,3433],{},[1605,18295,3433],{"encoding":1607}," ve stejných jednotkách jako data — pro interpretaci (např. „kolísání kolem průměru\") patří vždy ",[1115,18298,18300],{"className":18299},[1573],[1575,18301,18302],{"xmlns":1577},[1579,18303,18304,18308],{},[1582,18305,18306],{},[1585,18307,3433],{},[1605,18309,3433],{"encoding":1607},[1115,18311,18313],{"className":18312},[1573],[1575,18314,18315],{"xmlns":1577},[1579,18316,18317,18325],{},[1582,18318,18319],{},[1986,18320,18321,18323],{},[1585,18322,3433],{},[1716,18324,1993],{},[1605,18326,18281],{"encoding":1607},[2223,18328,18329,18332],{},[2227,18330,18331],{},"Příliš mnoho nebo příliš málo tříd."," Málo tříd skryje tvar rozdělení, moc tříd rozmělní četnosti na jednotky a histogram je nečitelný; volí se kompromis, ne pevné pravidlo.",[1136,18334,4071],{"id":4070},[2220,18336,18337,18342,18347,18352,18357,18362,18367],{},[2223,18338,18339],{},[1127,18340,1133],{"className":18341,"dataFsResolvedFilePath":1131,"href":1132},[1130],[2223,18343,18344],{},[1127,18345,1558],{"className":18346,"dataFsResolvedFilePath":1556,"href":1557},[1130],[2223,18348,18349],{},[1127,18350,2660],{"className":18351,"dataFsResolvedFilePath":2658,"href":2659},[1130],[2223,18353,18354],{},[1127,18355,2798],{"className":18356,"dataFsResolvedFilePath":2796,"href":2797},[1130],[2223,18358,18359],{},[1127,18360,3237],{"className":18361,"dataFsResolvedFilePath":3235,"href":3236},[1130],[2223,18363,18364],{},[1127,18365,3322],{"className":18366,"dataFsResolvedFilePath":3320,"href":3321},[1130],[2223,18368,18369],{},[1127,18370,9239],{"className":18371,"dataFsResolvedFilePath":9237,"href":9238},[1130],[1136,18373,4111],{"id":934},[1110,18375,4114,18376,4119],{},[4116,18377,4118],{},[4135,18379,4137],{},{"title":1148,"searchDepth":27,"depth":27,"links":18381},[18382,18383,18384,18385,18386,18387,18388],{"id":13765,"depth":27,"text":13766},{"id":13923,"depth":27,"text":13924},{"id":15388,"depth":27,"text":15389},{"id":16143,"depth":27,"text":16144},{"id":9013,"depth":27,"text":9014},{"id":4070,"depth":27,"text":4071},{"id":934,"depth":27,"text":4111},{},"\u002Ftopics\u002Fpopisna-statistika",{"title":2415,"description":1148},[18393,4162,13659,18394,18395,18396,18397],"raw\u002Fmask\u002F02 datové soubory.pdf","raw\u002Fmask\u002Fdata k příkladům\u002F4.txt","raw\u002Fmask\u002Fdata k příkladům\u002F5.txt","raw\u002Fmask\u002Fdata k příkladům\u002F6.txt","raw\u002Fmask\u002Fdata k příkladům\u002F9.txt","topics\u002Fpopisna-statistika",[23,67,886,624,732,71],"S7Mr0W_asypsa_HGrO-Qlzv4HzQm_pC2nyjSomTKbnk",{"id":18402,"title":2798,"body":18403,"course":23,"courses":4153,"created":4154,"description":1148,"extension":4155,"meta":23086,"navigation":4157,"path":23087,"seo":23088,"sources":23089,"stem":23091,"tags":23092,"type":9267,"updated":4154,"__hash__":23093},"topics\u002Ftopics\u002Fregresni-a-korelacni-analyza.md",{"type":1096,"value":18404,"toc":23059},[18405,18407,18634,18636,18704,18710,18713,18791,18802,18806,19025,19032,19092,19095,19102,19124,19128,19134,19196,19246,19250,19260,19373,19379,19509,19512,19550,19556,19672,19689,19816,19822,19866,19870,19883,19911,19917,19974,20001,20007,20063,20083,20089,20110,20117,20120,20359,20363,20475,20795,20852,20894,20901,20905,20911,21035,21041,21090,21094,21100,21161,21167,21206,21250,21256,21349,21353,21359,21401,21407,21467,21578,21684,21688,21693,21771,21806,21837,21897,21934,21941,22004,22007,22028,22034,22064,22107,22111,22128,22248,22252,22274,22278,22289,22390,22394,22466,22473,22476,22479,22490,22557,22560,22564,22587,22590,22593,22796,22805,22835,22837,22972,22985,22998,23011,23013,23050,23052,23056],[1099,18406,2798],{"id":2792},[1103,18408,18410,18416],{"className":18409,"dataCallout":4184},[1106,4183],[1110,18411,18413,4192],{"className":18412},[1113],[1115,18414],{"className":18415,"ariaHidden":1121},[1118,4191,1120],[2220,18417,18418,18456,18503,18581,18595,18601],{},[2223,18419,18420,18423,18424,18437,18438,18451,18452,18455],{},[2227,18421,18422],{},"Regresní analýza"," zkoumá jednostrannou závislost vysvětlované proměnné ",[1115,18425,18427],{"className":18426},[1573],[1575,18428,18429],{"xmlns":1577},[1579,18430,18431,18435],{},[1582,18432,18433],{},[1585,18434,2862],{},[1605,18436,2862],{"encoding":1607}," na vysvětlujících proměnných ",[1115,18439,18441],{"className":18440},[1573],[1575,18442,18443],{"xmlns":1577},[1579,18444,18445,18449],{},[1582,18446,18447],{},[1585,18448,1158],{},[1605,18450,1158],{"encoding":1607}," (příčina → následek); ",[2227,18453,18454],{},"korelační analýza"," měří intenzitu (těsnost) vzájemné závislosti.",[2223,18457,18458,18459,18462,18463,2264],{},"Parametry regresní funkce se odhadují ",[2227,18460,18461],{},"metodou nejmenších čtverců"," — minimalizací součtu čtverců reziduí ",[1115,18464,18466],{"className":18465},[1573],[1575,18467,18468],{"xmlns":1577},[1579,18469,18470,18500],{},[1582,18471,18472,18474,18476,18482,18484,18494],{},[1589,18473,4624],{},[1589,18475,1170],{"stretchy":1591},[1746,18477,18478,18480],{},[1585,18479,2862],{},[1585,18481,1776],{},[1589,18483,1721],{},[1746,18485,18486,18492],{},[3005,18487,18488,18490],{"accent":1121},[1585,18489,2862],{},[1589,18491,3011],{},[1585,18493,1776],{},[1986,18495,18496,18498],{},[1589,18497,1603],{"stretchy":1591},[1716,18499,1993],{},[1605,18501,18502],{"encoding":1607},"\\sum(y_i-\\hat y_i)^2",[2223,18504,18505,18506,2230,18509,18527,18528,2230,18531,18555,18556,2230,18559,2264],{},"Kvalitu fitu měří ",[2227,18507,18508],{},"index determinace",[1115,18510,18512],{"className":18511},[1573],[1575,18513,18514],{"xmlns":1577},[1579,18515,18516,18524],{},[1582,18517,18518],{},[1986,18519,18520,18522],{},[1585,18521,3376],{},[1716,18523,1993],{},[1605,18525,18526],{"encoding":1607},"R^2","; obecnou těsnost závislosti ",[2227,18529,18530],{},"index korelace",[1115,18532,18534],{"className":18533},[1573],[1575,18535,18536],{"xmlns":1577},[1579,18537,18538,18552],{},[1582,18539,18540,18542,18544],{},[1585,18541,13729],{},[1589,18543,1597],{},[7068,18545,18546],{},[1986,18547,18548,18550],{},[1585,18549,3376],{},[1716,18551,1993],{},[1605,18553,18554],{"encoding":1607},"I=\\sqrt{R^2}",", který je pro regresní přímku roven ",[2227,18557,18558],{},"koeficientu korelace",[1115,18560,18562],{"className":18561},[1573],[1575,18563,18564],{"xmlns":1577},[1579,18565,18566,18578],{},[1582,18567,18568],{},[1746,18569,18570,18572],{},[1585,18571,71],{},[1582,18573,18574,18576],{},[1585,18575,1158],{},[1585,18577,2862],{},[1605,18579,18580],{"encoding":1607},"r_{xy}",[2223,18582,18583,18584,18587,18588,18591,18592,1295],{},"Když přímka nestačí, volí se ",[2227,18585,18586],{},"parabolická, polynomická, hyperbolická nebo logaritmická"," regrese (stále lineární v parametrech, odhad metodou nejmenších čtverců) nebo ",[2227,18589,18590],{},"exponenciální"," regrese (nelineární v parametrech, odhad přes ",[1150,18593,18594],{},"nls2",[2223,18596,18597,18600],{},[2227,18598,18599],{},"Vícenásobná regrese"," rozšiřuje model o více regresorů; vyžaduje výběr proměnných (ENTER\u002Fstepwise), ověření šesti předpokladů modelu a kontrolu multikolinearity přes VIF.",[2223,18602,18603,18604,1279,18607,1279,18610,1279,18613,1279,18616,1279,18619,1279,18622,1279,18625,1279,18628,1279,18631,2264],{},"V R: ",[1150,18605,18606],{},"lm()",[1150,18608,18609],{},"nls2()",[1150,18611,18612],{},"summary()",[1150,18614,18615],{},"confint()",[1150,18617,18618],{},"predict()",[1150,18620,18621],{},"step()",[1150,18623,18624],{},"car::vif()",[1150,18626,18627],{},"lmtest::dwtest()",[1150,18629,18630],{},"whitestrap::white_test()",[1150,18632,18633],{},"shapiro.test()",[1136,18635,13766],{"id":13765},[1110,18637,18638,18641,18642,1260,18655,18668,18669,18671,18672,18685,18686,18699,18700,18703],{},[1127,18639,1133],{"className":18640,"dataFsResolvedFilePath":1131,"href":1132},[1130]," pracuje se dvěma znaky ",[1115,18643,18645],{"className":18644},[1573],[1575,18646,18647],{"xmlns":1577},[1579,18648,18649,18653],{},[1582,18650,18651],{},[1585,18652,1158],{},[1605,18654,1158],{"encoding":1607},[1115,18656,18658],{"className":18657},[1573],[1575,18659,18660],{"xmlns":1577},[1579,18661,18662,18666],{},[1582,18663,18664],{},[1585,18665,2862],{},[1605,18667,2862],{"encoding":1607}," zjištěnými na stejných jednotkách. ",[2227,18670,18422],{}," se zabývá jednostrannými závislostmi, kdy proti sobě stojí vysvětlující (nezávisle) proměnná ",[1115,18673,18675],{"className":18674},[1573],[1575,18676,18677],{"xmlns":1577},[1579,18678,18679,18683],{},[1582,18680,18681],{},[1585,18682,1158],{},[1605,18684,1158],{"encoding":1607}," v úloze příčiny a vysvětlovaná (závisle) proměnná ",[1115,18687,18689],{"className":18688},[1573],[1575,18690,18691],{"xmlns":1577},[1579,18692,18693,18697],{},[1582,18694,18695],{},[1585,18696,2862],{},[1605,18698,2862],{"encoding":1607}," v úloze následku. ",[2227,18701,18702],{},"Korelační analýza"," se zabývá vzájemnými, většinou lineárními závislostmi; důraz je kladen na intenzitu vztahu. Oba přístupy se v praxi prolínají — nejdřív se zvolí a odhadne regresní funkce, pak se její kvalita vyjádří korelační charakteristikou.",[1110,18705,18706,18707,1295],{},"Hlavním úkolem obou analýz je přispět k poznání vztahů mezi znaky — podat matematický popis systematických okolností, které závislost provázejí, a nalézt funkci, která nejlépe vystihuje její charakter (",[2227,18708,18709],{},"regresní funkce",[1110,18711,18712],{},"Druh regresní analýzy určuje struktura datového souboru:",[2220,18714,18715,18752],{},[2223,18716,18717,18720,18721,18734,18735,18748,18749,1177],{},[2227,18718,18719],{},"dvourozměrný datový soubor"," (jedna ",[1115,18722,18724],{"className":18723},[1573],[1575,18725,18726],{"xmlns":1577},[1579,18727,18728,18732],{},[1582,18729,18730],{},[1585,18731,1158],{},[1605,18733,1158],{"encoding":1607},", jedna ",[1115,18736,18738],{"className":18737},[1573],[1575,18739,18740],{"xmlns":1577},[1579,18741,18742,18746],{},[1582,18743,18744],{},[1585,18745,2862],{},[1605,18747,2862],{"encoding":1607},") → ",[2227,18750,18751],{},"regresní analýza dvou proměnných",[2223,18753,18754,18757,18758,18748,18788,2264],{},[2227,18755,18756],{},"vícerozměrný datový soubor"," (více ",[1115,18759,18761],{"className":18760},[1573],[1575,18762,18763],{"xmlns":1577},[1579,18764,18765,18785],{},[1582,18766,18767,18773,18775,18777,18779],{},[1746,18768,18769,18771],{},[1585,18770,1158],{},[1716,18772,1718],{},[1589,18774,1177],{"separator":1121},[1589,18776,2979],{},[1589,18778,1177],{"separator":1121},[1746,18780,18781,18783],{},[1585,18782,1158],{},[1585,18784,1110],{},[1605,18786,18787],{"encoding":1607},"x_1,\\dots,x_p",[2227,18789,18790],{},"vícenásobná regresní analýza",[1110,18792,18793,18794,18797,18798,18801],{},"Volba konkrétní regresní funkce by měla vycházet jak z ",[2227,18795,18796],{},"ekonomické teorie"," (ta napovídá, zda závislost roste, nebo klesá, zda je přímková, nebo zakřivená), tak z ",[2227,18799,18800],{},"grafické a matematicko-statistické analýzy"," dat — oba přístupy je vhodné kombinovat.",[1136,18803,18805],{"id":18804},"metoda-nejmenších-čtverců","Metoda nejmenších čtverců",[1110,18807,18808,18809,2230,18812,18866,18867,18885,18886,2230,18889,18945,18946,18964,18965,18982,18983,19021,19022,2264],{},"Rozlišují se ",[2227,18810,18811],{},"teoretická regresní funkce",[1115,18813,18815],{"className":18814},[1573],[1575,18816,18817],{"xmlns":1577},[1579,18818,18819,18863],{},[1582,18820,18821,18824,18826,18828,18830,18832,18834,18841,18843,18849,18851,18853,18855,18861],{},[1585,18822,18823],{},"η",[1589,18825,1597],{},[1585,18827,1621],{},[1589,18829,1170],{"stretchy":1591},[1585,18831,1158],{},[1589,18833,9483],{"separator":1121},[1746,18835,18836,18839],{},[1585,18837,18838],{},"β",[1716,18840,2398],{},[1589,18842,1177],{"separator":1121},[1746,18844,18845,18847],{},[1585,18846,18838],{},[1716,18848,1718],{},[1589,18850,1177],{"separator":1121},[1589,18852,2979],{},[1589,18854,1177],{"separator":1121},[1746,18856,18857,18859],{},[1585,18858,18838],{},[1585,18860,1110],{},[1589,18862,1603],{"stretchy":1591},[1605,18864,18865],{"encoding":1607},"\\eta = f(x;\\beta_0,\\beta_1,\\dots,\\beta_p)"," — neznámá, populační, daná neznámými parametry ",[1115,18868,18870],{"className":18869},[1573],[1575,18871,18872],{"xmlns":1577},[1579,18873,18874,18882],{},[1582,18875,18876],{},[1746,18877,18878,18880],{},[1585,18879,18838],{},[1585,18881,1776],{},[1605,18883,18884],{"encoding":1607},"\\beta_i"," — a ",[2227,18887,18888],{},"empirická regresní funkce",[1115,18890,18892],{"className":18891},[1573],[1575,18893,18894],{"xmlns":1577},[1579,18895,18896,18942],{},[1582,18897,18898,18904,18906,18908,18910,18912,18914,18920,18922,18928,18930,18932,18934,18940],{},[3005,18899,18900,18902],{"accent":1121},[1585,18901,2862],{},[1589,18903,3011],{},[1589,18905,1597],{},[1585,18907,1621],{},[1589,18909,1170],{"stretchy":1591},[1585,18911,1158],{},[1589,18913,9483],{"separator":1121},[1746,18915,18916,18918],{},[1585,18917,2869],{},[1716,18919,2398],{},[1589,18921,1177],{"separator":1121},[1746,18923,18924,18926],{},[1585,18925,2869],{},[1716,18927,1718],{},[1589,18929,1177],{"separator":1121},[1589,18931,2979],{},[1589,18933,1177],{"separator":1121},[1746,18935,18936,18938],{},[1585,18937,2869],{},[1585,18939,1110],{},[1589,18941,1603],{"stretchy":1591},[1605,18943,18944],{"encoding":1607},"\\hat y = f(x; b_0,b_1,\\dots,b_p)",", jejíž odhadnuté parametry ",[1115,18947,18949],{"className":18948},[1573],[1575,18950,18951],{"xmlns":1577},[1579,18952,18953,18961],{},[1582,18954,18955],{},[1746,18956,18957,18959],{},[1585,18958,2869],{},[1585,18960,1776],{},[1605,18962,18963],{"encoding":1607},"b_i"," jsou odhadem ",[1115,18966,18968],{"className":18967},[1573],[1575,18969,18970],{"xmlns":1577},[1579,18971,18972,18980],{},[1582,18973,18974],{},[1746,18975,18976,18978],{},[1585,18977,18838],{},[1585,18979,1776],{},[1605,18981,18884],{"encoding":1607}," vypočteným z konkrétních dat. Odchylky skutečných hodnot od empirické funkce, ",[1115,18984,18986],{"className":18985},[1573],[1575,18987,18988],{"xmlns":1577},[1579,18989,18990,19018],{},[1582,18991,18992,18998,19000,19006,19008],{},[1746,18993,18994,18996],{},[1585,18995,2876],{},[1585,18997,1776],{},[1589,18999,1597],{},[1746,19001,19002,19004],{},[1585,19003,2862],{},[1585,19005,1776],{},[1589,19007,1721],{},[1746,19009,19010,19016],{},[3005,19011,19012,19014],{"accent":1121},[1585,19013,2862],{},[1589,19015,3011],{},[1585,19017,1776],{},[1605,19019,19020],{"encoding":1607},"e_i=y_i-\\hat y_i",", se nazývají ",[2227,19023,19024],{},"rezidua",[1110,19026,19027,19028,19031],{},"Nejpoužívanější metodou odhadu parametrů je ",[2227,19029,19030],{},"metoda nejmenších čtverců (OLS)",": hledají se takové parametry, pro které je součet čtverců reziduí minimální,",[1115,19033,19035],{"className":19034},[1573],[1575,19036,19037],{"xmlns":1577,"display":4601},[1579,19038,19039,19089],{},[1582,19040,19041,19055,19057,19063,19065,19075,19081,19083,19085,19087],{},[4620,19042,19043,19045,19053],{},[1589,19044,4624],{},[1582,19046,19047,19049,19051],{},[1585,19048,1776],{},[1589,19050,1597],{},[1716,19052,1718],{},[1585,19054,1781],{},[1589,19056,1170],{"stretchy":1591},[1746,19058,19059,19061],{},[1585,19060,2862],{},[1585,19062,1776],{},[1589,19064,1721],{},[1746,19066,19067,19073],{},[3005,19068,19069,19071],{"accent":1121},[1585,19070,2862],{},[1589,19072,3011],{},[1585,19074,1776],{},[1986,19076,19077,19079],{},[1589,19078,1603],{"stretchy":1591},[1716,19080,1993],{},[1589,19082,10188],{},[1585,19084,7102],{},[1589,19086,7105],{},[1585,19088,2264],{"mathvariant":4022},[1605,19090,19091],{"encoding":1607},"\\sum_{i=1}^n (y_i - \\hat y_i)^2 \\to \\min.",[1110,19093,19094],{},"Odhad probíhá ve čtyřech krocích: (1) posoudit dostupné informace o charakteru závislosti, (2) navrhnout jeden nebo víc typů regresních funkcí, (3) odhadnout jejich parametry metodou nejmenších čtverců, (4) porovnat vhodnost odhadnutých funkcí a při neuspokojivém výsledku zvolit jiný typ.",[1110,19096,19097],{},[1303,19098],{"alt":19099,"className":19100,"src":19101},"mask-ra-primka-rezidua",[1130,1307],"\u002Fwiki-assets\u002Fmask-ra-primka-rezidua.png",[1110,19103,19104,19105,19123],{},"Obrázek ukazuje přesně to, co metoda minimalizuje: délky červených úseček jsou rezidua ",[1115,19106,19108],{"className":19107},[1573],[1575,19109,19110],{"xmlns":1577},[1579,19111,19112,19120],{},[1582,19113,19114],{},[1746,19115,19116,19118],{},[1585,19117,2876],{},[1585,19119,1776],{},[1605,19121,19122],{"encoding":1607},"e_i",", metoda nejmenších čtverců volí přímku tak, aby součet jejich čtverců byl nejmenší možný.",[1136,19125,19127],{"id":19126},"regresní-přímka","Regresní přímka",[1110,19129,19130,19131,4595],{},"Nejjednodušší regresní funkcí je ",[2227,19132,19133],{},"regresní přímka",[1115,19135,19137],{"className":19136},[1573],[1575,19138,19139],{"xmlns":1577,"display":4601},[1579,19140,19141,19193],{},[1582,19142,19143,19145,19147,19153,19155,19161,19163,19165,19167,19173,19175,19181,19183,19189,19191],{},[1585,19144,18823],{},[1589,19146,1597],{},[1746,19148,19149,19151],{},[1585,19150,18838],{},[1716,19152,2398],{},[1589,19154,4010],{},[1746,19156,19157,19159],{},[1585,19158,18838],{},[1716,19160,1718],{},[1585,19162,1158],{},[1589,19164,1177],{"separator":1121},[4648,19166],{"width":4650},[3005,19168,19169,19171],{"accent":1121},[1585,19170,2862],{},[1589,19172,3011],{},[1589,19174,1597],{},[1746,19176,19177,19179],{},[1585,19178,2869],{},[1716,19180,2398],{},[1589,19182,4010],{},[1746,19184,19185,19187],{},[1585,19186,2869],{},[1716,19188,1718],{},[1585,19190,1158],{},[1585,19192,2264],{"mathvariant":4022},[1605,19194,19195],{"encoding":1607},"\\eta = \\beta_0 + \\beta_1 x, \\qquad \\hat y = b_0 + b_1 x.",[1110,19197,19198,19199,19217,19218,19231,19232,19245],{},"Koeficient ",[1115,19200,19202],{"className":19201},[1573],[1575,19203,19204],{"xmlns":1577},[1579,19205,19206,19214],{},[1582,19207,19208],{},[1746,19209,19210,19212],{},[1585,19211,2869],{},[1716,19213,1718],{},[1605,19215,19216],{"encoding":1607},"b_1"," udává změnu průměru ",[1115,19219,19221],{"className":19220},[1573],[1575,19222,19223],{"xmlns":1577},[1579,19224,19225,19229],{},[1582,19226,19227],{},[1585,19228,2862],{},[1605,19230,2862],{"encoding":1607}," při jednotkové změně ",[1115,19233,19235],{"className":19234},[1573],[1575,19236,19237],{"xmlns":1577},[1579,19238,19239,19243],{},[1582,19240,19241],{},[1585,19242,1158],{},[1605,19244,1158],{"encoding":1607},"; jeho znaménko určuje, zda je závislost přímá, nebo nepřímá.",[1550,19247,19249],{"id":19248},"v-r","V R",[1110,19251,19252,19253,19255,19256,19259],{},"Vstupní data se nahrají buď ze souboru (",[1150,19254,1267],{},", případně ",[1150,19257,19258],{},"d \u003C- read.table(file.choose())","), nebo zapíší přímo jako vektory. Na šesti domácnostech sledujeme počet členů domácnosti a jejich týdenní výdaje:",[1144,19261,19263],{"className":1146,"code":19262,"language":71,"meta":1148,"style":1148},"pocet_clenu \u003C- c(1, 2, 3, 4, 5, 6)\ntydenni_vydaje \u003C- c(490, 820, 1230, 1570, 1950, 2320)\nmodel \u003C- lm(tydenni_vydaje ~ pocet_clenu)\nsummary(model)\n",[1150,19264,19265,19300,19341,19362],{"__ignoreMap":1148},[1115,19266,19267,19270,19272,19274,19276,19278,19280,19282,19284,19286,19288,19290,19292,19294,19296,19298],{"class":1154,"line":10},[1115,19268,19269],{"class":1157},"pocet_clenu",[1115,19271,1162],{"class":1161},[1115,19273,1166],{"class":1165},[1115,19275,1170],{"class":1169},[1115,19277,1718],{"class":1173},[1115,19279,1177],{"class":1161},[1115,19281,6797],{"class":1173},[1115,19283,1177],{"class":1161},[1115,19285,13386],{"class":1173},[1115,19287,1177],{"class":1161},[1115,19289,6419],{"class":1173},[1115,19291,1177],{"class":1161},[1115,19293,12538],{"class":1173},[1115,19295,1177],{"class":1161},[1115,19297,14739],{"class":1173},[1115,19299,6519],{"class":1169},[1115,19301,19302,19305,19307,19309,19311,19314,19316,19319,19321,19324,19326,19329,19331,19334,19336,19339],{"class":1154,"line":27},[1115,19303,19304],{"class":1157},"tydenni_vydaje",[1115,19306,1162],{"class":1161},[1115,19308,1166],{"class":1165},[1115,19310,1170],{"class":1169},[1115,19312,19313],{"class":1173},"490",[1115,19315,1177],{"class":1161},[1115,19317,19318],{"class":1173}," 820",[1115,19320,1177],{"class":1161},[1115,19322,19323],{"class":1173}," 1230",[1115,19325,1177],{"class":1161},[1115,19327,19328],{"class":1173}," 1570",[1115,19330,1177],{"class":1161},[1115,19332,19333],{"class":1173}," 1950",[1115,19335,1177],{"class":1161},[1115,19337,19338],{"class":1173}," 2320",[1115,19340,6519],{"class":1169},[1115,19342,19343,19345,19347,19350,19352,19354,19357,19360],{"class":1154,"line":148},[1115,19344,786],{"class":1157},[1115,19346,1162],{"class":1161},[1115,19348,19349],{"class":1165}," lm",[1115,19351,1170],{"class":1169},[1115,19353,19304],{"class":1157},[1115,19355,19356],{"class":1161}," ~",[1115,19358,19359],{"class":1157}," pocet_clenu",[1115,19361,6519],{"class":1169},[1115,19363,19364,19367,19369,19371],{"class":1154,"line":111},[1115,19365,19366],{"class":1165},"summary",[1115,19368,1170],{"class":1169},[1115,19370,786],{"class":1157},[1115,19372,6519],{"class":1169},[1144,19374,19377],{"className":19375,"code":19376,"language":6540,"meta":1148},[6538],"Call:\nlm(formula = tydenni_vydaje ~ pocet_clenu)\n\nResiduals:\n      1       2       3       4       5       6 \n 13.333 -24.667  17.333 -10.667   1.333   3.333 \n\nCoefficients:\n            Estimate Std. Error t value Pr(>|t|)    \n(Intercept)  108.667     16.214   6.702  0.00258 ** \npocet_clenu  368.000      4.163  88.391 9.82e-08 ***\n---\nSignif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 17.42 on 4 degrees of freedom\nMultiple R-squared:  0.9995,    Adjusted R-squared:  0.9994 \nF-statistic:  7813 on 1 and 4 DF,  p-value: 9.821e-08\n",[1150,19378,19376],{"__ignoreMap":1148},[1110,19380,19381,19382,19414,19415,19418,19419,19449,19450,19480,19481,19484,19485,19508],{},"Odhadnutý model je ",[1115,19383,19385],{"className":19384},[1573],[1575,19386,19387],{"xmlns":1577},[1579,19388,19389,19411],{},[1582,19390,19391,19397,19399,19402,19404,19407,19409],{},[3005,19392,19393,19395],{"accent":1121},[1585,19394,2862],{},[1589,19396,3011],{},[1589,19398,1597],{},[1716,19400,19401],{},"108,7",[1589,19403,4010],{},[1716,19405,19406],{},"368,0",[5543,19408,5545],{},[1585,19410,1158],{},[1605,19412,19413],{"encoding":1607},"\\hat y = 108{,}7 + 368{,}0\\,x",". Sloupec ",[1150,19416,19417],{},"Pr(>|t|)"," je p-hodnota t-testu ",[1115,19420,19422],{"className":19421},[1573],[1575,19423,19424],{"xmlns":1577},[1579,19425,19426,19446],{},[1582,19427,19428,19434,19436,19442,19444],{},[1746,19429,19430,19432],{},[1585,19431,1922],{},[1716,19433,2398],{},[1589,19435,4595],{},[1746,19437,19438,19440],{},[1585,19439,18838],{},[1585,19441,1776],{},[1589,19443,1597],{},[1716,19445,2398],{},[1605,19447,19448],{"encoding":1607},"H_0:\\beta_i=0"," proti ",[1115,19451,19453],{"className":19452},[1573],[1575,19454,19455],{"xmlns":1577},[1579,19456,19457,19477],{},[1582,19458,19459,19465,19467,19473,19475],{},[1746,19460,19461,19463],{},[1585,19462,1922],{},[1716,19464,1718],{},[1589,19466,4595],{},[1746,19468,19469,19471],{},[1585,19470,18838],{},[1585,19472,1776],{},[1589,19474,13487],{"mathvariant":4022},[1716,19476,2398],{},[1605,19478,19479],{"encoding":1607},"H_1:\\beta_i\\neq0"," pro každý parametr — obě p-hodnoty jsou hluboko pod 0,05, oba parametry jsou tedy statisticky významné. ",[1150,19482,19483],{},"Multiple R-squared"," je index determinace ",[1115,19486,19488],{"className":19487},[1573],[1575,19489,19490],{"xmlns":1577},[1579,19491,19492,19505],{},[1582,19493,19494,19500,19502],{},[1986,19495,19496,19498],{},[1585,19497,3376],{},[1716,19499,1993],{},[1589,19501,1597],{},[1716,19503,19504],{},"0,9995",[1605,19506,19507],{"encoding":1607},"R^2=0{,}9995",": model vysvětluje 99,95 % rozptylu výdajů.",[1110,19510,19511],{},"Pro doplňkový přehled slouží přímé přístupové funkce:",[1144,19513,19515],{"className":1146,"code":19514,"language":71,"meta":1148,"style":1148},"coef(model)\nfitted(model)\nresiduals(model)\n",[1150,19516,19517,19528,19539],{"__ignoreMap":1148},[1115,19518,19519,19522,19524,19526],{"class":1154,"line":10},[1115,19520,19521],{"class":1165},"coef",[1115,19523,1170],{"class":1169},[1115,19525,786],{"class":1157},[1115,19527,6519],{"class":1169},[1115,19529,19530,19533,19535,19537],{"class":1154,"line":27},[1115,19531,19532],{"class":1165},"fitted",[1115,19534,1170],{"class":1169},[1115,19536,786],{"class":1157},[1115,19538,6519],{"class":1169},[1115,19540,19541,19544,19546,19548],{"class":1154,"line":148},[1115,19542,19543],{"class":1165},"residuals",[1115,19545,1170],{"class":1169},[1115,19547,786],{"class":1157},[1115,19549,6519],{"class":1169},[1144,19551,19554],{"className":19552,"code":19553,"language":6540,"meta":1148},[6538],"(Intercept) pocet_clenu \n   108.6667    368.0000 \n        1         2         3         4         5         6 \n 476.6667  844.6667 1212.6667 1580.6667 1948.6667 2316.6667 \n         1          2          3          4          5          6 \n 13.333333 -24.666667  17.333333 -10.666667   1.333333   3.333333 \n",[1150,19555,19553],{"__ignoreMap":1148},[1110,19557,19558,19561,19562,1279,19588,19591,19592,3017,19613,1279,19630,19633,19634,19671],{},[1150,19559,19560],{},"coef()"," vrací odhadnuté parametry ",[1115,19563,19565],{"className":19564},[1573],[1575,19566,19567],{"xmlns":1577},[1579,19568,19569,19585],{},[1582,19570,19571,19577,19579],{},[1746,19572,19573,19575],{},[1585,19574,2869],{},[1716,19576,2398],{},[1589,19578,1177],{"separator":1121},[1746,19580,19581,19583],{},[1585,19582,2869],{},[1716,19584,1718],{},[1605,19586,19587],{"encoding":1607},"b_0,b_1",[1150,19589,19590],{},"fitted()"," predikce ",[1115,19593,19595],{"className":19594},[1573],[1575,19596,19597],{"xmlns":1577},[1579,19598,19599,19611],{},[1582,19600,19601],{},[1746,19602,19603,19609],{},[3005,19604,19605,19607],{"accent":1121},[1585,19606,2862],{},[1589,19608,3011],{},[1585,19610,1776],{},[1605,19612,3016],{"encoding":1607},[1115,19614,19616],{"className":19615},[1573],[1575,19617,19618],{"xmlns":1577},[1579,19619,19620,19628],{},[1582,19621,19622],{},[1746,19623,19624,19626],{},[1585,19625,1158],{},[1585,19627,1776],{},[1605,19629,3035],{"encoding":1607},[1150,19631,19632],{},"residuals()"," rezidua ",[1115,19635,19637],{"className":19636},[1573],[1575,19638,19639],{"xmlns":1577},[1579,19640,19641,19669],{},[1582,19642,19643,19649,19651,19657,19659],{},[1746,19644,19645,19647],{},[1585,19646,2876],{},[1585,19648,1776],{},[1589,19650,1597],{},[1746,19652,19653,19655],{},[1585,19654,2862],{},[1585,19656,1776],{},[1589,19658,1721],{},[1746,19660,19661,19667],{},[3005,19662,19663,19665],{"accent":1121},[1585,19664,2862],{},[1589,19666,3011],{},[1585,19668,1776],{},[1605,19670,19020],{"encoding":1607}," — stejná čísla, která na obrázku výše tvoří délky červených úseček.",[1110,19673,19674,19675,19688],{},"Intervaly spolehlivosti pro parametry a pro predikci v nových bodech ",[1115,19676,19678],{"className":19677},[1573],[1575,19679,19680],{"xmlns":1577},[1579,19681,19682,19686],{},[1582,19683,19684],{},[1585,19685,1158],{},[1605,19687,1158],{"encoding":1607}," (zde 7 a 8 členů domácnosti):",[1144,19690,19692],{"className":1146,"code":19691,"language":71,"meta":1148,"style":1148},"confint(model, level = 0.95)\nnove \u003C- data.frame(pocet_clenu = c(7, 8))\npredict(model, newdata = nove, interval = \"confidence\", level = 0.95)\npredict(model, newdata = nove, interval = \"prediction\", level = 0.95)\n",[1150,19693,19694,19714,19742,19781],{"__ignoreMap":1148},[1115,19695,19696,19699,19701,19703,19705,19708,19710,19712],{"class":1154,"line":10},[1115,19697,19698],{"class":1165},"confint",[1115,19700,1170],{"class":1169},[1115,19702,786],{"class":1157},[1115,19704,1177],{"class":1161},[1115,19706,19707],{"class":1157}," level",[1115,19709,6416],{"class":1161},[1115,19711,12543],{"class":1173},[1115,19713,6519],{"class":1169},[1115,19715,19716,19719,19721,19724,19726,19728,19730,19732,19734,19736,19738,19740],{"class":1154,"line":27},[1115,19717,19718],{"class":1157},"nove",[1115,19720,1162],{"class":1161},[1115,19722,19723],{"class":1165}," data.frame",[1115,19725,1170],{"class":1169},[1115,19727,19269],{"class":1157},[1115,19729,6416],{"class":1161},[1115,19731,1166],{"class":1165},[1115,19733,1170],{"class":1169},[1115,19735,3905],{"class":1173},[1115,19737,1177],{"class":1161},[1115,19739,17762],{"class":1173},[1115,19741,12073],{"class":1169},[1115,19743,19744,19747,19749,19751,19753,19756,19758,19761,19763,19766,19768,19771,19773,19775,19777,19779],{"class":1154,"line":148},[1115,19745,19746],{"class":1165},"predict",[1115,19748,1170],{"class":1169},[1115,19750,786],{"class":1157},[1115,19752,1177],{"class":1161},[1115,19754,19755],{"class":1157}," newdata",[1115,19757,6416],{"class":1161},[1115,19759,19760],{"class":1157}," nove",[1115,19762,1177],{"class":1161},[1115,19764,19765],{"class":1157}," interval",[1115,19767,6416],{"class":1161},[1115,19769,19770],{"class":6458}," \"confidence\"",[1115,19772,1177],{"class":1161},[1115,19774,19707],{"class":1157},[1115,19776,6416],{"class":1161},[1115,19778,12543],{"class":1173},[1115,19780,6519],{"class":1169},[1115,19782,19783,19785,19787,19789,19791,19793,19795,19797,19799,19801,19803,19806,19808,19810,19812,19814],{"class":1154,"line":111},[1115,19784,19746],{"class":1165},[1115,19786,1170],{"class":1169},[1115,19788,786],{"class":1157},[1115,19790,1177],{"class":1161},[1115,19792,19755],{"class":1157},[1115,19794,6416],{"class":1161},[1115,19796,19760],{"class":1157},[1115,19798,1177],{"class":1161},[1115,19800,19765],{"class":1157},[1115,19802,6416],{"class":1161},[1115,19804,19805],{"class":6458}," \"prediction\"",[1115,19807,1177],{"class":1161},[1115,19809,19707],{"class":1157},[1115,19811,6416],{"class":1161},[1115,19813,12543],{"class":1173},[1115,19815,6519],{"class":1169},[1144,19817,19820],{"className":19818,"code":19819,"language":6540,"meta":1148},[6538],"                2.5 %   97.5 %\n(Intercept)  63.64981 153.6835\npocet_clenu 356.44074 379.5593\n       fit     lwr      upr\n1 2684.667 2639.65 2729.684\n2 3052.667 2997.03 3108.303\n       fit      lwr      upr\n1 2684.667 2618.600 2750.733\n2 3052.667 2978.953 3126.381\n",[1150,19821,19819],{"__ignoreMap":1148},[1110,19823,19824,19827,19828,2230,19831,19844,19845,1279,19858,19861,19862,19865],{},[1150,19825,19826],{},"interval = \"confidence\""," dává interval spolehlivosti pro ",[2227,19829,19830],{},"střední hodnotu",[1115,19832,19834],{"className":19833},[1573],[1575,19835,19836],{"xmlns":1577},[1579,19837,19838,19842],{},[1582,19839,19840],{},[1585,19841,2862],{},[1605,19843,2862],{"encoding":1607}," při daném ",[1115,19846,19848],{"className":19847},[1573],[1575,19849,19850],{"xmlns":1577},[1579,19851,19852,19856],{},[1582,19853,19854],{},[1585,19855,1158],{},[1605,19857,1158],{"encoding":1607},[1150,19859,19860],{},"interval = \"prediction\""," širší interval pro ",[2227,19863,19864],{},"jednotlivé budoucí pozorování"," — ten musí zahrnout i rozptyl kolem regresní přímky, proto je vždy širší.",[1550,19867,19869],{"id":19868},"diagnostika-modelu","Diagnostika modelu",[1110,19871,19872,19873,1279,19876,1260,19879,19882],{},"Platnost závěrů z regresní přímky stojí na předpokladech o reziduích: ",[2227,19874,19875],{},"absenci autokorelace",[2227,19877,19878],{},"stálosti rozptylu (homoskedasticitě)",[2227,19880,19881],{},"normalitě",". V R se ověřují takto:",[1144,19884,19886],{"className":1146,"code":19885,"language":71,"meta":1148,"style":1148},"library(lmtest)\ndwtest(model)\n",[1150,19887,19888,19900],{"__ignoreMap":1148},[1115,19889,19890,19893,19895,19898],{"class":1154,"line":10},[1115,19891,19892],{"class":1161},"library",[1115,19894,1170],{"class":1169},[1115,19896,19897],{"class":1157},"lmtest",[1115,19899,6519],{"class":1169},[1115,19901,19902,19905,19907,19909],{"class":1154,"line":27},[1115,19903,19904],{"class":1165},"dwtest",[1115,19906,1170],{"class":1169},[1115,19908,786],{"class":1157},[1115,19910,6519],{"class":1169},[1144,19912,19915],{"className":19913,"code":19914,"language":6540,"meta":1148},[6538],"    Durbin-Watson test\n\ndata:  model\nDW = 3.4121, p-value = 0.9555\nalternative hypothesis: true autocorrelation is greater than 0\n",[1150,19916,19914],{"__ignoreMap":1148},[1110,19918,19919,19920,19937,19938,19955,19956,19973],{},"Durbinův–Watsonův test má ",[1115,19921,19923],{"className":19922},[1573],[1575,19924,19925],{"xmlns":1577},[1579,19926,19927,19935],{},[1582,19928,19929],{},[1746,19930,19931,19933],{},[1585,19932,1922],{},[1716,19934,2398],{},[1605,19936,4225],{"encoding":1607},": v modelu není problém s autokorelací, proti ",[1115,19939,19941],{"className":19940},[1573],[1575,19942,19943],{"xmlns":1577},[1579,19944,19945,19953],{},[1582,19946,19947],{},[1746,19948,19949,19951],{},[1585,19950,1922],{},[1716,19952,1718],{},[1605,19954,3807],{"encoding":1607},": v modelu problém s autokorelací je. Statistika DW se pohybuje mezi 0 a 4, hodnota blízko 2 znamená žádnou autokorelaci. Zde p-hodnota 0,96 je výrazně nad 0,05, ",[1115,19957,19959],{"className":19958},[1573],[1575,19960,19961],{"xmlns":1577},[1579,19962,19963,19971],{},[1582,19964,19965],{},[1746,19966,19967,19969],{},[1585,19968,1922],{},[1716,19970,2398],{},[1605,19972,4225],{"encoding":1607}," se nezamítá.",[1144,19975,19977],{"className":1146,"code":19976,"language":71,"meta":1148,"style":1148},"library(whitestrap)\nwhite_test(model)\n",[1150,19978,19979,19990],{"__ignoreMap":1148},[1115,19980,19981,19983,19985,19988],{"class":1154,"line":10},[1115,19982,19892],{"class":1161},[1115,19984,1170],{"class":1169},[1115,19986,19987],{"class":1157},"whitestrap",[1115,19989,6519],{"class":1169},[1115,19991,19992,19995,19997,19999],{"class":1154,"line":27},[1115,19993,19994],{"class":1165},"white_test",[1115,19996,1170],{"class":1169},[1115,19998,786],{"class":1157},[1115,20000,6519],{"class":1169},[1144,20002,20005],{"className":20003,"code":20004,"language":6540,"meta":1148},[6538],"White's test results\n\nNull hypothesis: Homoskedasticity of the residuals\nAlternative hypothesis: Heteroskedasticity of the residuals\nTest Statistic: 3.14\nP-value: 0.207817\n",[1150,20006,20004],{"__ignoreMap":1148},[1110,20008,20009,20010,20027,20028,20045,20046,19973],{},"Whiteův test má ",[1115,20011,20013],{"className":20012},[1573],[1575,20014,20015],{"xmlns":1577},[1579,20016,20017,20025],{},[1582,20018,20019],{},[1746,20020,20021,20023],{},[1585,20022,1922],{},[1716,20024,2398],{},[1605,20026,4225],{"encoding":1607},": rozptyl reziduí je stálý (homoskedasticita), proti ",[1115,20029,20031],{"className":20030},[1573],[1575,20032,20033],{"xmlns":1577},[1579,20034,20035,20043],{},[1582,20036,20037],{},[1746,20038,20039,20041],{},[1585,20040,1922],{},[1716,20042,1718],{},[1605,20044,3807],{"encoding":1607},": rozptyl není stálý (heteroskedasticita). P-hodnota 0,21 je nad 0,05, ",[1115,20047,20049],{"className":20048},[1573],[1575,20050,20051],{"xmlns":1577},[1579,20052,20053,20061],{},[1582,20054,20055],{},[1746,20056,20057,20059],{},[1585,20058,1922],{},[1716,20060,2398],{},[1605,20062,4225],{"encoding":1607},[1144,20064,20066],{"className":1146,"code":20065,"language":71,"meta":1148,"style":1148},"shapiro.test(residuals(model))\n",[1150,20067,20068],{"__ignoreMap":1148},[1115,20069,20070,20073,20075,20077,20079,20081],{"class":1154,"line":10},[1115,20071,20072],{"class":1165},"shapiro.test",[1115,20074,1170],{"class":1169},[1115,20076,19543],{"class":1165},[1115,20078,1170],{"class":1169},[1115,20080,786],{"class":1157},[1115,20082,12073],{"class":1169},[1144,20084,20087],{"className":20085,"code":20086,"language":6540,"meta":1148},[6538],"    Shapiro-Wilk normality test\n\ndata:  residuals(model)\nW = 0.94818, p-value = 0.7255\n",[1150,20088,20086],{"__ignoreMap":1148},[1110,20090,20091,20092,20109],{},"Shapiro–Wilkův test má ",[1115,20093,20095],{"className":20094},[1573],[1575,20096,20097],{"xmlns":1577},[1579,20098,20099,20107],{},[1582,20100,20101],{},[1746,20102,20103,20105],{},[1585,20104,1922],{},[1716,20106,2398],{},[1605,20108,4225],{"encoding":1607},": rezidua pocházejí z normálního rozdělení. P-hodnota 0,73 opět nevede k zamítnutí — všechny tři předpoklady model splňuje.",[1110,20111,20112],{},[1303,20113],{"alt":20114,"className":20115,"src":20116},"mask-ra-diagnostika-rezidui",[1130,1307],"\u002Fwiki-assets\u002Fmask-ra-diagnostika-rezidui.png",[1110,20118,20119],{},"Grafická kontrola normality doplňuje Shapiro–Wilkův test: body v levém panelu by měly být rovnoměrně rozptýlené po obou stranách vodorovné osy (bez trychtýře či oblouku), body v Q-Q grafu by měly ležet kolem přímky. U malého počtu pozorování se dává přednost testu; u velkého datového souboru se předpoklad normality reziduí stává méně kritickým díky centrální limitní větě.",[1103,20121,20123,20130,20161,20196,20261],{"className":20122,"dataCallout":6105},[1106,6104],[1110,20124,20126,20129],{"className":20125},[1113],[1115,20127],{"className":20128,"ariaHidden":1121},[1118,6112,1120],"Příklad: Regresní přímka",[1110,20131,20132,20133,20146,20147,20160],{},"V souboru s údaji o hodnotě produkce (v milionech Kč, proměnná ",[1115,20134,20136],{"className":20135},[1573],[1575,20137,20138],{"xmlns":1577},[1579,20139,20140,20144],{},[1582,20141,20142],{},[1585,20143,2862],{},[1605,20145,2862],{"encoding":1607},") a výši investic (ve stovkách tisíc Kč, proměnná ",[1115,20148,20150],{"className":20149},[1573],[1575,20151,20152],{"xmlns":1577},[1579,20153,20154,20158],{},[1582,20155,20156],{},[1585,20157,1158],{},[1605,20159,1158],{"encoding":1607},") za rok 2015 u dvanácti vybraných soukromých firem s více než 30 zaměstnanci byla metodou nejmenších čtverců odhadnuta regresní přímka modelující závislost hodnoty produkce na výši investic.",[1110,20162,20163,20164,2264],{},"Výsledek: ",[1115,20165,20167],{"className":20166},[1573],[1575,20168,20169],{"xmlns":1577},[1579,20170,20171,20193],{},[1582,20172,20173,20179,20181,20184,20186,20189,20191],{},[3005,20174,20175,20177],{"accent":1121},[1585,20176,2862],{},[1589,20178,3011],{},[1589,20180,1597],{},[1716,20182,20183],{},"32,74",[1589,20185,4010],{},[1716,20187,20188],{},"2,15",[5543,20190,5545],{},[1585,20192,1158],{},[1605,20194,20195],{"encoding":1607},"\\hat y = 32{,}74 + 2{,}15\\,x",[1110,20197,19198,20198,20220,20221,20260],{},[1115,20199,20201],{"className":20200},[1573],[1575,20202,20203],{"xmlns":1577},[1579,20204,20205,20217],{},[1582,20206,20207,20213,20215],{},[1746,20208,20209,20211],{},[1585,20210,2869],{},[1716,20212,1718],{},[1589,20214,1597],{},[1716,20216,20188],{},[1605,20218,20219],{"encoding":1607},"b_1=2{,}15"," říká, že se zvýšením investic o 100 000 Kč vzroste produkce v průměru o ",[1115,20222,20224],{"className":20223},[1573],[1575,20225,20226],{"xmlns":1577},[1579,20227,20228,20257],{},[1582,20229,20230,20232,20234,20236,20238,20240,20242,20244,20246,20248,20250,20253,20255],{},[1716,20231,20188],{},[1589,20233,10691],{},[1716,20235,1718],{},[5543,20237,5545],{},[1716,20239,13851],{},[5543,20241,5545],{},[1716,20243,13851],{},[1589,20245,1597],{},[1716,20247,1993],{},[5543,20249,5545],{},[1716,20251,20252],{},"150",[5543,20254,5545],{},[1716,20256,13851],{},[1605,20258,20259],{"encoding":1607},"2{,}15\\cdot 1\\,000\\,000=2\\,150\\,000"," Kč.",[1110,20262,20263,20264,6605,20283,20331,20332,1295],{},"Dosazením libovolné hodnoty investic do empirické regresní funkce dostaneme predikci produkce, například pro třináctou firmu s investicemi ",[1115,20265,20267],{"className":20266},[1573],[1575,20268,20269],{"xmlns":1577},[1579,20270,20271,20280],{},[1582,20272,20273,20275,20277],{},[1585,20274,1158],{},[1589,20276,1597],{},[1716,20278,20279],{},"34",[1605,20281,20282],{"encoding":1607},"x=34",[1115,20284,20286],{"className":20285},[1573],[1575,20287,20288],{"xmlns":1577},[1579,20289,20290,20328],{},[1582,20291,20292,20302,20304,20310,20312,20318,20320,20322,20325],{},[1746,20293,20294,20300],{},[3005,20295,20296,20298],{"accent":1121},[1585,20297,2862],{},[1589,20299,3011],{},[1716,20301,6173],{},[1589,20303,1597],{},[1746,20305,20306,20308],{},[1585,20307,2869],{},[1716,20309,2398],{},[1589,20311,4010],{},[1746,20313,20314,20316],{},[1585,20315,2869],{},[1716,20317,1718],{},[1589,20319,10691],{},[1716,20321,20279],{},[1589,20323,20324],{},"≐",[1716,20326,20327],{},"105,81",[1605,20329,20330],{"encoding":1607},"\\hat y_{13} = b_0 + b_1\\cdot 34 \\doteq 105{,}81"," milionu Kč (se zaokrouhlenými koeficienty ",[1115,20333,20335],{"className":20334},[1573],[1575,20336,20337],{"xmlns":1577},[1579,20338,20339,20356],{},[1582,20340,20341,20343,20345,20347,20349,20351,20353],{},[1716,20342,20183],{},[1589,20344,4010],{},[1716,20346,20188],{},[1589,20348,10691],{},[1716,20350,20279],{},[1589,20352,20324],{},[1716,20354,20355],{},"105,8",[1605,20357,20358],{"encoding":1607},"32{,}74 + 2{,}15\\cdot 34 \\doteq 105{,}8",[1136,20360,20362],{"id":20361},"nelineární-a-vyšší-řády-regresních-funkcí","Nelineární a vyšší řády regresních funkcí",[1110,20364,20365,20366,20369,20370,20437,20438,20456,20457,20474],{},"Když přímka závislost nevystihuje, nabízí se další ",[2227,20367,20368],{},"lineární funkce"," — tedy funkce lineární ve svých parametrech, zapsatelné ve tvaru ",[1115,20371,20373],{"className":20372},[1573],[1575,20374,20375],{"xmlns":1577},[1579,20376,20377,20434],{},[1582,20378,20379,20381,20383,20389,20391,20397,20403,20405,20407,20409,20411,20414,20416,20422,20428,20430,20432],{},[1585,20380,18823],{},[1589,20382,1597],{},[1746,20384,20385,20387],{},[1585,20386,18838],{},[1716,20388,2398],{},[1589,20390,4010],{},[1746,20392,20393,20395],{},[1585,20394,18838],{},[1716,20396,1718],{},[1746,20398,20399,20401],{},[1585,20400,1621],{},[1716,20402,1718],{},[1589,20404,1170],{"stretchy":1591},[1585,20406,1158],{},[1589,20408,1603],{"stretchy":1591},[1589,20410,4010],{},[1589,20412,20413],{},"⋯",[1589,20415,4010],{},[1746,20417,20418,20420],{},[1585,20419,18838],{},[1585,20421,1110],{},[1746,20423,20424,20426],{},[1585,20425,1621],{},[1585,20427,1110],{},[1589,20429,1170],{"stretchy":1591},[1585,20431,1158],{},[1589,20433,1603],{"stretchy":1591},[1605,20435,20436],{"encoding":1607},"\\eta=\\beta_0+\\beta_1 f_1(x)+\\dots+\\beta_p f_p(x)"," se známými funkcemi ",[1115,20439,20441],{"className":20440},[1573],[1575,20442,20443],{"xmlns":1577},[1579,20444,20445,20453],{},[1582,20446,20447],{},[1746,20448,20449,20451],{},[1585,20450,1621],{},[1585,20452,1776],{},[1605,20454,20455],{"encoding":1607},"f_i"," a neznámými parametry ",[1115,20458,20460],{"className":20459},[1573],[1575,20461,20462],{"xmlns":1577},[1579,20463,20464,20472],{},[1582,20465,20466],{},[1746,20467,20468,20470],{},[1585,20469,18838],{},[1585,20471,1776],{},[1605,20473,18884],{"encoding":1607},". I tyto parametry se odhadují metodou nejmenších čtverců, stejně jako u přímky:",[1115,20476,20478],{"className":20477},[1573],[1575,20479,20480],{"xmlns":1577,"display":4601},[1579,20481,20482,20792],{},[20483,20484,20487,20560,20673,20732],"mtable",{"rowspacing":20485,"columnalign":20486,"columnspacing":9353},"0.25em","right left",[20488,20489,20490,20514],"mtr",{},[20491,20492,20493],"mtd",{},[5873,20494,20495],{"scriptlevel":2398,"displaystyle":1121},[1582,20496,20497,20511],{},[1582,20498,20499,20502,20508],{},[5543,20500,20501],{},"parabolick",[3005,20503,20504,20506],{"accent":1121},[5543,20505,1127],{},[1589,20507,14029],{},[5543,20509,20510],{}," regrese: ",[4648,20512],{"width":20513},"1em",[20491,20515,20516],{},[5873,20517,20518],{"scriptlevel":2398,"displaystyle":1121},[1582,20519,20520,20522,20528,20530,20536,20538,20544,20546,20548,20554],{},[1582,20521],{},[3005,20523,20524,20526],{"accent":1121},[1585,20525,2862],{},[1589,20527,3011],{},[1589,20529,1597],{},[1746,20531,20532,20534],{},[1585,20533,2869],{},[1716,20535,2398],{},[1589,20537,4010],{},[1746,20539,20540,20542],{},[1585,20541,2869],{},[1716,20543,1718],{},[1585,20545,1158],{},[1589,20547,4010],{},[1746,20549,20550,20552],{},[1585,20551,2869],{},[1716,20553,1993],{},[1986,20555,20556,20558],{},[1585,20557,1158],{},[1716,20559,1993],{},[20488,20561,20562,20609],{},[20491,20563,20564],{},[5873,20565,20566],{"scriptlevel":2398,"displaystyle":1121},[1582,20567,20568,20607],{},[1582,20569,20570,20573,20579,20582,20586,20589,20595,20598,20604],{},[5543,20571,20572],{},"polynomick",[3005,20574,20575,20577],{"accent":1121},[5543,20576,1127],{},[1589,20578,14029],{},[5543,20580,20581],{}," regrese ",[5873,20583,20584],{"scriptlevel":2398,"displaystyle":1591},[1585,20585,1110],{},[5543,20587,20588],{},"-t",[3005,20590,20591,20593],{"accent":1121},[5543,20592,2876],{},[1589,20594,14029],{},[5543,20596,20597],{},"ho stupn",[3005,20599,20600,20602],{"accent":1121},[5543,20601,2876],{},[1589,20603,14038],{},[5543,20605,20606],{},": ",[4648,20608],{"width":20513},[20491,20610,20611],{},[5873,20612,20613],{"scriptlevel":2398,"displaystyle":1121},[1582,20614,20615,20617,20623,20625,20631,20633,20639,20641,20643,20649,20655,20657,20659,20661,20667],{},[1582,20616],{},[3005,20618,20619,20621],{"accent":1121},[1585,20620,2862],{},[1589,20622,3011],{},[1589,20624,1597],{},[1746,20626,20627,20629],{},[1585,20628,2869],{},[1716,20630,2398],{},[1589,20632,4010],{},[1746,20634,20635,20637],{},[1585,20636,2869],{},[1716,20638,1718],{},[1585,20640,1158],{},[1589,20642,4010],{},[1746,20644,20645,20647],{},[1585,20646,2869],{},[1716,20648,1993],{},[1986,20650,20651,20653],{},[1585,20652,1158],{},[1716,20654,1993],{},[1589,20656,4010],{},[1589,20658,20413],{},[1589,20660,4010],{},[1746,20662,20663,20665],{},[1585,20664,2869],{},[1585,20666,1110],{},[1986,20668,20669,20671],{},[1585,20670,1158],{},[1585,20672,1110],{},[20488,20674,20675,20696],{},[20491,20676,20677],{},[5873,20678,20679],{"scriptlevel":2398,"displaystyle":1121},[1582,20680,20681,20694],{},[1582,20682,20683,20686,20692],{},[5543,20684,20685],{},"hyperbolick",[3005,20687,20688,20690],{"accent":1121},[5543,20689,1127],{},[1589,20691,14029],{},[5543,20693,20510],{},[4648,20695],{"width":20513},[20491,20697,20698],{},[5873,20699,20700],{"scriptlevel":2398,"displaystyle":1121},[1582,20701,20702,20704,20710,20712,20718,20720,20726],{},[1582,20703],{},[3005,20705,20706,20708],{"accent":1121},[1585,20707,2862],{},[1589,20709,3011],{},[1589,20711,1597],{},[1746,20713,20714,20716],{},[1585,20715,2869],{},[1716,20717,2398],{},[1589,20719,4010],{},[1746,20721,20722,20724],{},[1585,20723,2869],{},[1716,20725,1718],{},[5373,20727,20728,20730],{},[1716,20729,1718],{},[1585,20731,1158],{},[20488,20733,20734,20755],{},[20491,20735,20736],{},[5873,20737,20738],{"scriptlevel":2398,"displaystyle":1121},[1582,20739,20740,20753],{},[1582,20741,20742,20745,20751],{},[5543,20743,20744],{},"logaritmick",[3005,20746,20747,20749],{"accent":1121},[5543,20748,1127],{},[1589,20750,14029],{},[5543,20752,20510],{},[4648,20754],{"width":20513},[20491,20756,20757],{},[5873,20758,20759],{"scriptlevel":2398,"displaystyle":1121},[1582,20760,20761,20763,20769,20771,20777,20779,20785,20788,20790],{},[1582,20762],{},[3005,20764,20765,20767],{"accent":1121},[1585,20766,2862],{},[1589,20768,3011],{},[1589,20770,1597],{},[1746,20772,20773,20775],{},[1585,20774,2869],{},[1716,20776,2398],{},[1589,20778,4010],{},[1746,20780,20781,20783],{},[1585,20782,2869],{},[1716,20784,1718],{},[1585,20786,20787],{},"ln",[1589,20789,7105],{},[1585,20791,1158],{},[1605,20793,20794],{"encoding":1607},"\\begin{aligned}\n\\text{parabolická regrese: }\\quad &\\hat y = b_0 + b_1 x + b_2 x^2\\\\\n\\text{polynomická regrese $p$-tého stupně: }\\quad &\\hat y = b_0 + b_1 x + b_2 x^2 + \\dots + b_p x^p\\\\\n\\text{hyperbolická regrese: }\\quad &\\hat y = b_0 + b_1\\frac1x\\\\\n\\text{logaritmická regrese: }\\quad &\\hat y = b_0 + b_1\\ln x\n\\end{aligned}",[1110,20796,20797,20798,20801,20802,20848,20849,4595],{},"Naproti tomu ",[2227,20799,20800],{},"nelineární funkce"," nelze do tvaru ",[1115,20803,20805],{"className":20804},[1573],[1575,20806,20807],{"xmlns":1577},[1579,20808,20809,20845],{},[1582,20810,20811,20813,20815,20821,20823,20829,20835,20837,20839,20841,20843],{},[1585,20812,18823],{},[1589,20814,1597],{},[1746,20816,20817,20819],{},[1585,20818,18838],{},[1716,20820,2398],{},[1589,20822,4010],{},[1746,20824,20825,20827],{},[1585,20826,18838],{},[1716,20828,1718],{},[1746,20830,20831,20833],{},[1585,20832,1621],{},[1716,20834,1718],{},[1589,20836,1170],{"stretchy":1591},[1585,20838,1158],{},[1589,20840,1603],{"stretchy":1591},[1589,20842,4010],{},[1589,20844,2979],{},[1605,20846,20847],{"encoding":1607},"\\eta=\\beta_0+\\beta_1 f_1(x)+\\dots"," převést — je nelineární i ve svých parametrech. Jejich parametry nelze získat přímo metodou nejmenších čtverců, ale vhodnou transformací nebo iterativně. Základní příklad je ",[2227,20850,20851],{},"exponenciální regrese",[1115,20853,20855],{"className":20854},[1573],[1575,20856,20857],{"xmlns":1577,"display":4601},[1579,20858,20859,20891],{},[1582,20860,20861,20867,20869,20875,20877,20889],{},[3005,20862,20863,20865],{"accent":1121},[1585,20864,2862],{},[1589,20866,3011],{},[1589,20868,1597],{},[1746,20870,20871,20873],{},[1585,20872,2869],{},[1716,20874,2398],{},[1589,20876,10691],{},[2920,20878,20879,20881,20883],{},[1585,20880,2869],{},[1716,20882,1718],{},[1582,20884,20885,20887],{},[5543,20886,5545],{},[1585,20888,1158],{},[1585,20890,2264],{"mathvariant":4022},[1605,20892,20893],{"encoding":1607},"\\hat y = b_0 \\cdot b_1^{\\,x}.",[1110,20895,20896],{},[1303,20897],{"alt":20898,"className":20899,"src":20900},"mask-ra-nelinearni-krivky",[1130,1307],"\u002Fwiki-assets\u002Fmask-ra-nelinearni-krivky.png",[1550,20902,20904],{"id":20903},"v-r-parabolická-regrese","V R — parabolická regrese",[1110,20906,20907,20908,4595],{},"Na ročních ziscích firmy (šest let) se parabolická regrese odhadne přidáním kvadratického členu ",[1150,20909,20910],{},"I(x^2)",[1144,20912,20914],{"className":1146,"code":20913,"language":71,"meta":1148,"style":1148},"rok \u003C- c(1, 2, 3, 4, 5, 6)\nzisk \u003C- c(112, 149, 238, 354, 580, 867)\nmodel_parabola \u003C- lm(zisk ~ rok + I(rok^2))\nsummary(model_parabola)\n",[1150,20915,20916,20951,20991,21025],{"__ignoreMap":1148},[1115,20917,20918,20921,20923,20925,20927,20929,20931,20933,20935,20937,20939,20941,20943,20945,20947,20949],{"class":1154,"line":10},[1115,20919,20920],{"class":1157},"rok",[1115,20922,1162],{"class":1161},[1115,20924,1166],{"class":1165},[1115,20926,1170],{"class":1169},[1115,20928,1718],{"class":1173},[1115,20930,1177],{"class":1161},[1115,20932,6797],{"class":1173},[1115,20934,1177],{"class":1161},[1115,20936,13386],{"class":1173},[1115,20938,1177],{"class":1161},[1115,20940,6419],{"class":1173},[1115,20942,1177],{"class":1161},[1115,20944,12538],{"class":1173},[1115,20946,1177],{"class":1161},[1115,20948,14739],{"class":1173},[1115,20950,6519],{"class":1169},[1115,20952,20953,20955,20957,20959,20961,20964,20966,20969,20971,20974,20976,20979,20981,20984,20986,20989],{"class":1154,"line":27},[1115,20954,1088],{"class":1157},[1115,20956,1162],{"class":1161},[1115,20958,1166],{"class":1165},[1115,20960,1170],{"class":1169},[1115,20962,20963],{"class":1173},"112",[1115,20965,1177],{"class":1161},[1115,20967,20968],{"class":1173}," 149",[1115,20970,1177],{"class":1161},[1115,20972,20973],{"class":1173}," 238",[1115,20975,1177],{"class":1161},[1115,20977,20978],{"class":1173}," 354",[1115,20980,1177],{"class":1161},[1115,20982,20983],{"class":1173}," 580",[1115,20985,1177],{"class":1161},[1115,20987,20988],{"class":1173}," 867",[1115,20990,6519],{"class":1169},[1115,20992,20993,20996,20998,21000,21002,21004,21006,21009,21012,21015,21017,21019,21021,21023],{"class":1154,"line":148},[1115,20994,20995],{"class":1157},"model_parabola",[1115,20997,1162],{"class":1161},[1115,20999,19349],{"class":1165},[1115,21001,1170],{"class":1169},[1115,21003,1088],{"class":1157},[1115,21005,19356],{"class":1161},[1115,21007,21008],{"class":1157}," rok",[1115,21010,21011],{"class":1161}," +",[1115,21013,21014],{"class":1165}," I",[1115,21016,1170],{"class":1169},[1115,21018,20920],{"class":1157},[1115,21020,3011],{"class":1161},[1115,21022,1993],{"class":1173},[1115,21024,12073],{"class":1169},[1115,21026,21027,21029,21031,21033],{"class":1154,"line":111},[1115,21028,19366],{"class":1165},[1115,21030,1170],{"class":1169},[1115,21032,20995],{"class":1157},[1115,21034,6519],{"class":1169},[1144,21036,21039],{"className":21037,"code":21038,"language":6540,"meta":1148},[6538],"Call:\nlm(formula = zisk ~ rok + I(rok^2))\n\nResiduals:\n      1       2       3       4       5       6 \n -8.071   9.243  14.343 -17.771  -4.100   6.357 \n\nCoefficients:\n            Estimate Std. Error t value Pr(>|t|)   \n(Intercept)  164.600     27.892   5.901  0.00972 **\nrok          -76.636     18.248  -4.200  0.02464 * \nI(rok^2)      32.107      2.552  12.582  0.00108 **\n---\nSignif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 15.59 on 3 degrees of freedom\nMultiple R-squared:  0.9983,    Adjusted R-squared:  0.9971 \nF-statistic: 868.7 on 2 and 3 DF,  p-value: 7.156e-05\n",[1150,21040,21038],{"__ignoreMap":1148},[1110,21042,21043,21044,21089],{},"Odhadnutá parabola ",[1115,21045,21047],{"className":21046},[1573],[1575,21048,21049],{"xmlns":1577},[1579,21050,21051,21086],{},[1582,21052,21053,21059,21061,21064,21066,21069,21071,21073,21075,21078,21080],{},[3005,21054,21055,21057],{"accent":1121},[1585,21056,2862],{},[1589,21058,3011],{},[1589,21060,1597],{},[1716,21062,21063],{},"164,6",[1589,21065,1721],{},[1716,21067,21068],{},"76,6",[5543,21070,5545],{},[1585,21072,1158],{},[1589,21074,4010],{},[1716,21076,21077],{},"32,1",[5543,21079,5545],{},[1986,21081,21082,21084],{},[1585,21083,1158],{},[1716,21085,1993],{},[1605,21087,21088],{"encoding":1607},"\\hat y = 164{,}6 - 76{,}6\\,x + 32{,}1\\,x^2"," vysvětluje 99,8 % rozptylu zisku — podstatně víc, než by vysvětlila přímka proložená stejně rostoucími daty.",[1550,21091,21093],{"id":21092},"v-r-exponenciální-regrese","V R — exponenciální regrese",[1110,21095,21096,21097,21099],{},"Nelineární funkce se v R odhadují funkcí ",[1150,21098,18609],{}," ze stejnojmenného balíčku. Bez zadaných počátečních hodnot R upozorní, že parametry nastavil na 1, a odhad dopočítá iteračně:",[1144,21101,21103],{"className":1146,"code":21102,"language":71,"meta":1148,"style":1148},"library(nls2)\nmodel_exp \u003C- nls2(zisk ~ b1 * exp(b2 * rok))\nsummary(model_exp)\n",[1150,21104,21105,21115,21151],{"__ignoreMap":1148},[1115,21106,21107,21109,21111,21113],{"class":1154,"line":10},[1115,21108,19892],{"class":1161},[1115,21110,1170],{"class":1169},[1115,21112,18594],{"class":1157},[1115,21114,6519],{"class":1169},[1115,21116,21117,21120,21122,21125,21127,21129,21131,21134,21137,21140,21142,21145,21147,21149],{"class":1154,"line":27},[1115,21118,21119],{"class":1157},"model_exp",[1115,21121,1162],{"class":1161},[1115,21123,21124],{"class":1165}," nls2",[1115,21126,1170],{"class":1169},[1115,21128,1088],{"class":1157},[1115,21130,19356],{"class":1161},[1115,21132,21133],{"class":1157}," b1",[1115,21135,21136],{"class":1161}," *",[1115,21138,21139],{"class":1165}," exp",[1115,21141,1170],{"class":1169},[1115,21143,21144],{"class":1157},"b2",[1115,21146,21136],{"class":1161},[1115,21148,21008],{"class":1157},[1115,21150,12073],{"class":1169},[1115,21152,21153,21155,21157,21159],{"class":1154,"line":148},[1115,21154,19366],{"class":1165},[1115,21156,1170],{"class":1169},[1115,21158,21119],{"class":1157},[1115,21160,6519],{"class":1169},[1144,21162,21165],{"className":21163,"code":21164,"language":6540,"meta":1148},[6538],"Formula: zisk ~ b1 * exp(b2 * rok)\n\nParameters:\n   Estimate Std. Error t value Pr(>|t|)    \nb1 65.35423    3.57542   18.28 5.27e-05 ***\nb2  0.43161    0.01013   42.63 1.81e-06 ***\n---\nSignif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 11.89 on 4 degrees of freedom\n",[1150,21166,21164],{"__ignoreMap":1148},[1110,21168,21169,21170,4595],{},"Stejnou křivku lze zapsat i v mocninném tvaru ",[1115,21171,21173],{"className":21172},[1573],[1575,21174,21175],{"xmlns":1577},[1579,21176,21177,21203],{},[1582,21178,21179,21185,21187,21193,21195],{},[3005,21180,21181,21183],{"accent":1121},[1585,21182,2862],{},[1589,21184,3011],{},[1589,21186,1597],{},[1746,21188,21189,21191],{},[1585,21190,2869],{},[1716,21192,1718],{},[1589,21194,10691],{},[2920,21196,21197,21199,21201],{},[1585,21198,2869],{},[1716,21200,1993],{},[1585,21202,1158],{},[1605,21204,21205],{"encoding":1607},"\\hat y=b_1\\cdot b_2^{x}",[1144,21207,21209],{"className":1146,"code":21208,"language":71,"meta":1148,"style":1148},"model_pow \u003C- nls2(zisk ~ b1 * (b2^rok))\nsummary(model_pow)\n",[1150,21210,21211,21240],{"__ignoreMap":1148},[1115,21212,21213,21216,21218,21220,21222,21224,21226,21228,21230,21232,21234,21236,21238],{"class":1154,"line":10},[1115,21214,21215],{"class":1157},"model_pow",[1115,21217,1162],{"class":1161},[1115,21219,21124],{"class":1165},[1115,21221,1170],{"class":1169},[1115,21223,1088],{"class":1157},[1115,21225,19356],{"class":1161},[1115,21227,21133],{"class":1157},[1115,21229,21136],{"class":1161},[1115,21231,7219],{"class":1169},[1115,21233,21144],{"class":1157},[1115,21235,3011],{"class":1161},[1115,21237,20920],{"class":1157},[1115,21239,12073],{"class":1169},[1115,21241,21242,21244,21246,21248],{"class":1154,"line":27},[1115,21243,19366],{"class":1165},[1115,21245,1170],{"class":1169},[1115,21247,21215],{"class":1157},[1115,21249,6519],{"class":1169},[1144,21251,21254],{"className":21252,"code":21253,"language":6540,"meta":1148},[6538],"Formula: zisk ~ b1 * (b2^rok)\n\nParameters:\n   Estimate Std. Error t value Pr(>|t|)    \nb1 65.35424    3.57542   18.28 5.27e-05 ***\nb2  1.53973    0.01559   98.76 6.30e-08 ***\n---\nSignif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 11.89 on 4 degrees of freedom\n",[1150,21255,21253],{"__ignoreMap":1148},[1110,21257,21258,21259,21323,21324,21348],{},"Obě varianty popisují stejnou křivku (",[1115,21260,21262],{"className":21261},[1573],[1575,21263,21264],{"xmlns":1577},[1579,21265,21266,21320],{},[1582,21267,21268,21285,21287],{},[2920,21269,21270,21272,21274],{},[1585,21271,2869],{},[1716,21273,1993],{},[1582,21275,21276,21279],{},[5543,21277,21278],{},"mocninn",[3005,21280,21281,21283],{"accent":1121},[5543,21282,2862],{},[1589,21284,14029],{},[1589,21286,1597],{},[1986,21288,21289,21291],{},[1585,21290,2876],{},[1582,21292,21293,21295],{},[5543,21294,5545],{},[2920,21296,21297,21299,21301],{},[1585,21298,2869],{},[1716,21300,1993],{},[1582,21302,21303,21306,21312,21314],{},[5543,21304,21305],{},"exponenci",[3005,21307,21308,21310],{"accent":1121},[5543,21309,1127],{},[1589,21311,14029],{},[5543,21313,20787],{},[3005,21315,21316,21318],{"accent":1121},[5543,21317,14277],{},[1589,21319,14029],{},[1605,21321,21322],{"encoding":1607},"b_2^{\\text{mocninný}} = e^{\\,b_2^{\\text{exponenciální}}}",", zde ",[1115,21325,21327],{"className":21326},[1573],[1575,21328,21329],{"xmlns":1577},[1579,21330,21331,21345],{},[1582,21332,21333,21340,21342],{},[1986,21334,21335,21337],{},[1585,21336,2876],{},[1716,21338,21339],{},"0,4316",[1589,21341,12020],{},[1716,21343,21344],{},"1,540",[1605,21346,21347],{"encoding":1607},"e^{0{,}4316}\\approx 1{,}540",") a mají totožnou reziduální chybu — je to jen otázka parametrizace.",[1550,21350,21352],{"id":21351},"v-r-hyperbolická-regrese","V R — hyperbolická regrese",[1110,21354,21355,21356,4595],{},"Hyperbolická regrese se odhadne jako obyčejná lineární regrese na transformované proměnné ",[1150,21357,21358],{},"I(1\u002Fx)",[1144,21360,21362],{"className":1146,"code":21361,"language":71,"meta":1148,"style":1148},"model_hyperbola \u003C- lm(tydenni_vydaje ~ I(1 \u002F pocet_clenu))\nsummary(model_hyperbola)\n",[1150,21363,21364,21391],{"__ignoreMap":1148},[1115,21365,21366,21369,21371,21373,21375,21377,21379,21381,21383,21385,21387,21389],{"class":1154,"line":10},[1115,21367,21368],{"class":1157},"model_hyperbola",[1115,21370,1162],{"class":1161},[1115,21372,19349],{"class":1165},[1115,21374,1170],{"class":1169},[1115,21376,19304],{"class":1157},[1115,21378,19356],{"class":1161},[1115,21380,21014],{"class":1165},[1115,21382,1170],{"class":1169},[1115,21384,1718],{"class":1173},[1115,21386,12619],{"class":1161},[1115,21388,19359],{"class":1157},[1115,21390,12073],{"class":1169},[1115,21392,21393,21395,21397,21399],{"class":1154,"line":27},[1115,21394,19366],{"class":1165},[1115,21396,1170],{"class":1169},[1115,21398,21368],{"class":1157},[1115,21400,6519],{"class":1169},[1144,21402,21405],{"className":21403,"code":21404,"language":6540,"meta":1148},[6538],"Call:\nlm(formula = tydenni_vydaje ~ I(1\u002Fpocet_clenu))\n\nResiduals:\n     1      2      3      4      5      6 \n 229.3 -400.7 -310.7 -130.7  153.3  459.3 \n\nCoefficients:\n                 Estimate Std. Error t value Pr(>|t|)   \n(Intercept)        2180.7      266.5   8.182  0.00122 **\nI(1\u002Fpocet_clenu)  -1920.0      534.6  -3.592  0.02293 * \n---\nSignif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 374.6 on 4 degrees of freedom\nMultiple R-squared:  0.7633,    Adjusted R-squared:  0.7041 \nF-statistic:  12.9 on 1 and 4 DF,  p-value: 0.02293\n",[1150,21406,21404],{"__ignoreMap":1148},[1110,21408,21409,21410,21444,21445,21466],{},"Model ",[1115,21411,21413],{"className":21412},[1573],[1575,21414,21415],{"xmlns":1577},[1579,21416,21417,21441],{},[1582,21418,21419,21425,21427,21430,21432],{},[3005,21420,21421,21423],{"accent":1121},[1585,21422,2862],{},[1589,21424,3011],{},[1589,21426,1597],{},[1716,21428,21429],{},"2180,7",[1589,21431,1721],{},[5873,21433,21434],{"scriptlevel":2398,"displaystyle":1121},[5373,21435,21436,21439],{},[1716,21437,21438],{},"1920,0",[1585,21440,1158],{},[1605,21442,21443],{"encoding":1607},"\\hat y = 2180{,}7 - \\dfrac{1920{,}0}{x}"," vysvětluje jen 76,3 % rozptylu — u těchto dat je hyperbola podstatně horší volbou než přímka (",[1115,21446,21448],{"className":21447},[1573],[1575,21449,21450],{"xmlns":1577},[1579,21451,21452,21464],{},[1582,21453,21454,21460,21462],{},[1986,21455,21456,21458],{},[1585,21457,3376],{},[1716,21459,1993],{},[1589,21461,1597],{},[1716,21463,19504],{},[1605,21465,19507],{"encoding":1607},"). Právě k takovému porovnání slouží index determinace: nízká hodnota signalizuje, že zvolený typ funkce k datům nesedí.",[1103,21468,21470,21477,21508,21556],{"className":21469,"dataCallout":6105},[1106,6104],[1110,21471,21473,21476],{"className":21472},[1113],[1115,21474],{"className":21475,"ariaHidden":1121},[1118,6112,1120],"Příklad: Parabolická regrese",[1110,21478,21479,21480,21493,21494,21507],{},"Prodejna počítačových her nechala prodavače absolvovat kurz prodejních dovedností. Při dvaceti měřeních sledovala, kolik zákazníků navštíví prodejnu během prodejní doby (proměnná ",[1115,21481,21483],{"className":21482},[1573],[1575,21484,21485],{"xmlns":1577},[1579,21486,21487,21491],{},[1582,21488,21489],{},[1585,21490,1158],{},[1605,21492,1158],{"encoding":1607},") a jaká je toho dne tržba v tisících Kč (proměnná ",[1115,21495,21497],{"className":21496},[1573],[1575,21498,21499],{"xmlns":1577},[1579,21500,21501,21505],{},[1582,21502,21503],{},[1585,21504,2862],{},[1605,21506,2862],{"encoding":1607},"). Zároveň chtěla zjistit, zda při rostoucím počtu zákazníků stačí stávající počet prodavačů.",[1110,21509,20163,21510,2264],{},[1115,21511,21513],{"className":21512},[1573],[1575,21514,21515],{"xmlns":1577},[1579,21516,21517,21553],{},[1582,21518,21519,21525,21527,21529,21532,21534,21537,21539,21541,21543,21545,21547],{},[3005,21520,21521,21523],{"accent":1121},[1585,21522,2862],{},[1589,21524,3011],{},[1589,21526,1597],{},[1589,21528,1721],{},[1716,21530,21531],{},"60,3",[1589,21533,4010],{},[1716,21535,21536],{},"4,55",[5543,21538,5545],{},[1585,21540,1158],{},[1589,21542,1721],{},[1716,21544,6601],{},[5543,21546,5545],{},[1986,21548,21549,21551],{},[1585,21550,1158],{},[1716,21552,1993],{},[1605,21554,21555],{"encoding":1607},"\\hat y = -60{,}3 + 4{,}55\\,x - 0{,}05\\,x^2",[1110,21557,21558,21559,21577],{},"Záporný koeficient ",[1115,21560,21562],{"className":21561},[1573],[1575,21563,21564],{"xmlns":1577},[1579,21565,21566,21574],{},[1582,21567,21568],{},[1746,21569,21570,21572],{},[1585,21571,2869],{},[1716,21573,1993],{},[1605,21575,21576],{"encoding":1607},"b_2"," znamená, že tržba s počtem zákazníků neroste neomezeně — funkce má maximum. Derivací a položením rovné nule vychází maximum přibližně při 45 zákaznících: nad tímto počtem zřejmě prodejna další zákazníky obsloužit nestíhá.",[1103,21579,21581,21588,21618,21663],{"className":21580,"dataCallout":6105},[1106,6104],[1110,21582,21584,21587],{"className":21583},[1113],[1115,21585],{"className":21586,"ariaHidden":1121},[1118,6112,1120],"Příklad: Hyperbolická regrese",[1110,21589,21590,21591,21604,21605,1295],{},"V podniku se podle interního účetnictví sledovala závislost vlastních nákladů na jednotku produkce v Kč (proměnná ",[1115,21592,21594],{"className":21593},[1573],[1575,21595,21596],{"xmlns":1577},[1579,21597,21598,21602],{},[1582,21599,21600],{},[1585,21601,2862],{},[1605,21603,2862],{"encoding":1607},") na objemu produkce v tisících kusů (proměnná ",[1115,21606,21608],{"className":21607},[1573],[1575,21609,21610],{"xmlns":1577},[1579,21611,21612,21616],{},[1582,21613,21614],{},[1585,21615,1158],{},[1605,21617,1158],{"encoding":1607},[1110,21619,20163,21620,2264],{},[1115,21621,21623],{"className":21622},[1573],[1575,21624,21625],{"xmlns":1577},[1579,21626,21627,21660],{},[1582,21628,21629,21635,21637,21639,21642,21644],{},[3005,21630,21631,21633],{"accent":1121},[1585,21632,2862],{},[1589,21634,3011],{},[1589,21636,1597],{},[1589,21638,1721],{},[1716,21640,21641],{},"96,78",[1589,21643,4010],{},[5873,21645,21646],{"scriptlevel":2398,"displaystyle":1121},[5373,21647,21648,21658],{},[1582,21649,21650,21653,21655],{},[1716,21651,21652],{},"250",[5543,21654,5545],{},[1716,21656,21657],{},"528,88",[1585,21659,1158],{},[1605,21661,21662],{"encoding":1607},"\\hat y = -96{,}78 + \\dfrac{250\\,528{,}88}{x}",[1110,21664,21665,21666,21683],{},"Záporná hodnota ",[1115,21667,21669],{"className":21668},[1573],[1575,21670,21671],{"xmlns":1577},[1579,21672,21673,21681],{},[1582,21674,21675],{},[1746,21676,21677,21679],{},[1585,21678,2869],{},[1716,21680,1718],{},[1605,21682,19216],{"encoding":1607}," v čitateli ukazuje klesající náklady na jednotku s rostoucím objemem produkce — typický projev úspor z rozsahu, který hyperbola dobře zachycuje.",[1136,21685,21687],{"id":21686},"kvalita-regresní-funkce-a-korelační-analýza","Kvalita regresní funkce a korelační analýza",[1110,21689,21690,21691,4595],{},"Kvalitu odhadnuté regresní funkce vyjadřuje ",[2227,21692,18508],{},[1115,21694,21696],{"className":21695},[1573],[1575,21697,21698],{"xmlns":1577,"display":4601},[1579,21699,21700,21768],{},[1582,21701,21702,21708,21710,21732,21734,21736,21738,21766],{},[1986,21703,21704,21706],{},[1585,21705,3376],{},[1716,21707,1993],{},[1589,21709,1597],{},[5373,21711,21712,21724],{},[2920,21713,21714,21716,21722],{},[1585,21715,3433],{},[3005,21717,21718,21720],{"accent":1121},[1585,21719,2862],{},[1589,21721,3011],{},[1716,21723,1993],{},[2920,21725,21726,21728,21730],{},[1585,21727,3433],{},[1585,21729,2862],{},[1716,21731,1993],{},[1589,21733,1597],{},[1716,21735,1718],{},[1589,21737,1721],{},[5373,21739,21740,21758],{},[2920,21741,21742,21744,21756],{},[1585,21743,3433],{},[1582,21745,21746,21748,21750],{},[1585,21747,2862],{},[1589,21749,1721],{},[3005,21751,21752,21754],{"accent":1121},[1585,21753,2862],{},[1589,21755,3011],{},[1716,21757,1993],{},[2920,21759,21760,21762,21764],{},[1585,21761,3433],{},[1585,21763,2862],{},[1716,21765,1993],{},[1585,21767,2264],{"mathvariant":4022},[1605,21769,21770],{"encoding":1607},"R^2 = \\frac{s^2_{\\hat y}}{s^2_y} = 1 - \\frac{s^2_{y-\\hat y}}{s^2_y}.",[1110,21772,21773,21774,21791,21792,21805],{},"Čím blíž je ",[1115,21775,21777],{"className":21776},[1573],[1575,21778,21779],{"xmlns":1577},[1579,21780,21781,21789],{},[1582,21782,21783],{},[1986,21784,21785,21787],{},[1585,21786,3376],{},[1716,21788,1993],{},[1605,21790,18526],{"encoding":1607}," k 1, tím silnější je závislost; v procentech udává, jakou část rozptylu závisle proměnné ",[1115,21793,21795],{"className":21794},[1573],[1575,21796,21797],{"xmlns":1577},[1579,21798,21799,21803],{},[1582,21800,21801],{},[1585,21802,2862],{},[1605,21804,2862],{"encoding":1607}," se podařilo vysvětlit zvolenou regresní funkcí. Nízký index determinace může signalizovat špatně zvolený typ regresní funkce, ne nutně absenci závislosti.",[1110,21807,21808,21809,2230,21811,21834,21835,4595],{},"Obecnou mírou těsnosti závislosti — platnou pro libovolný typ regresní funkce — je ",[2227,21810,18530],{},[1115,21812,21814],{"className":21813},[1573],[1575,21815,21816],{"xmlns":1577},[1579,21817,21818,21832],{},[1582,21819,21820,21822,21824],{},[1585,21821,13729],{},[1589,21823,1597],{},[7068,21825,21826],{},[1986,21827,21828,21830],{},[1585,21829,3376],{},[1716,21831,1993],{},[1605,21833,18554],{"encoding":1607},". Je-li zvolenou funkcí regresní přímka, index korelace je roven (až na znaménko) ",[2227,21836,18558],{},[1115,21838,21840],{"className":21839},[1573],[1575,21841,21842],{"xmlns":1577,"display":4601},[1579,21843,21844,21894],{},[1582,21845,21846,21856,21858,21892],{},[1746,21847,21848,21850],{},[1585,21849,71],{},[1582,21851,21852,21854],{},[1585,21853,1158],{},[1585,21855,2862],{},[1589,21857,1597],{},[5373,21859,21860,21870],{},[1746,21861,21862,21864],{},[1585,21863,3433],{},[1582,21865,21866,21868],{},[1585,21867,1158],{},[1585,21869,2862],{},[7068,21871,21872],{},[1582,21873,21874,21882,21884],{},[2920,21875,21876,21878,21880],{},[1585,21877,3433],{},[1585,21879,1158],{},[1716,21881,1993],{},[1589,21883,10691],{},[2920,21885,21886,21888,21890],{},[1585,21887,3433],{},[1585,21889,2862],{},[1716,21891,1993],{},[1585,21893,2264],{"mathvariant":4022},[1605,21895,21896],{"encoding":1607},"r_{xy} = \\frac{s_{xy}}{\\sqrt{s^2_x\\cdot s^2_y}}.",[1110,21898,21899,21900,21916,21917,21933],{},"Koeficient korelace nabývá hodnot od ",[1115,21901,21903],{"className":21902},[1573],[1575,21904,21905],{"xmlns":1577},[1579,21906,21907,21913],{},[1582,21908,21909,21911],{},[1589,21910,1721],{},[1716,21912,1718],{},[1605,21914,21915],{"encoding":1607},"-1"," do ",[1115,21918,21920],{"className":21919},[1573],[1575,21921,21922],{"xmlns":1577},[1579,21923,21924,21930],{},[1582,21925,21926,21928],{},[1589,21927,4010],{},[1716,21929,1718],{},[1605,21931,21932],{"encoding":1607},"+1",": znaménko určuje typ závislosti (pozitivní, nebo negativní), absolutní hodnota její sílu — čím blíž k 0, tím je závislost slabší.",[1110,21935,21936],{},[1303,21937],{"alt":21938,"className":21939,"src":21940},"mask-ra-korelace-sila",[1130,1307],"\u002Fwiki-assets\u002Fmask-ra-korelace-sila.png",[1110,21942,21943,21944,21957,21958,21976,21977,1260,21990,22003],{},"S rostoucí absolutní hodnotou ",[1115,21945,21947],{"className":21946},[1573],[1575,21948,21949],{"xmlns":1577},[1579,21950,21951,21955],{},[1582,21952,21953],{},[1585,21954,71],{},[1605,21956,71],{"encoding":1607}," se body v rozptylovém grafu víc blíží přímce; kolem ",[1115,21959,21961],{"className":21960},[1573],[1575,21962,21963],{"xmlns":1577},[1579,21964,21965,21973],{},[1582,21966,21967,21969,21971],{},[1585,21968,71],{},[1589,21970,12020],{},[1716,21972,2398],{},[1605,21974,21975],{"encoding":1607},"r\\approx 0"," je mezi ",[1115,21978,21980],{"className":21979},[1573],[1575,21981,21982],{"xmlns":1577},[1579,21983,21984,21988],{},[1582,21985,21986],{},[1585,21987,1158],{},[1605,21989,1158],{"encoding":1607},[1115,21991,21993],{"className":21992},[1573],[1575,21994,21995],{"xmlns":1577},[1579,21996,21997,22001],{},[1582,21998,21999],{},[1585,22000,2862],{},[1605,22002,2862],{"encoding":1607}," patrná jen náhodná rozptýlenost bez lineárního trendu.",[1550,22005,19249],{"id":22006},"v-r-1",[1144,22008,22010],{"className":1146,"code":22009,"language":71,"meta":1148,"style":1148},"cor(pocet_clenu, tydenni_vydaje)\n",[1150,22011,22012],{"__ignoreMap":1148},[1115,22013,22014,22017,22019,22021,22023,22026],{"class":1154,"line":10},[1115,22015,22016],{"class":1165},"cor",[1115,22018,1170],{"class":1169},[1115,22020,19269],{"class":1157},[1115,22022,1177],{"class":1161},[1115,22024,22025],{"class":1157}," tydenni_vydaje",[1115,22027,6519],{"class":1169},[1144,22029,22032],{"className":22030,"code":22031,"language":6540,"meta":1148},[6538],"[1] 0.9997441\n",[1150,22033,22031],{"__ignoreMap":1148},[1110,22035,22036,22037,22063],{},"Hodnota 0,9997 odpovídá ",[1115,22038,22040],{"className":22039},[1573],[1575,22041,22042],{"xmlns":1577},[1579,22043,22044,22060],{},[1582,22045,22046,22054,22056],{},[7068,22047,22048],{},[1986,22049,22050,22052],{},[1585,22051,3376],{},[1716,22053,1993],{},[1589,22055,1597],{},[7068,22057,22058],{},[1716,22059,19504],{},[1605,22061,22062],{"encoding":1607},"\\sqrt{R^2}=\\sqrt{0{,}9995}"," ze summary regresní přímky výše — přesně tak, jak definice říká: pro přímkovou regresi je koeficient korelace roven indexu korelace.",[1103,22065,22067,22074,22077],{"className":22066,"dataCallout":6105},[1106,6104],[1110,22068,22070,22073],{"className":22069},[1113],[1115,22071],{"className":22072,"ariaHidden":1121},[1118,6112,1120],"Příklad: Koeficient korelace",[1110,22075,22076],{},"Pro stejná data o hodnotě produkce a výši investic dvanácti firem jako u regresní přímky byl spočten koeficient korelace mezi oběma proměnnými.",[1110,22078,20163,22079,22106],{},[1115,22080,22082],{"className":22081},[1573],[1575,22083,22084],{"xmlns":1577},[1579,22085,22086,22103],{},[1582,22087,22088,22098,22100],{},[1746,22089,22090,22092],{},[1585,22091,71],{},[1582,22093,22094,22096],{},[1585,22095,1158],{},[1585,22097,2862],{},[1589,22099,1597],{},[1716,22101,22102],{},"0,739",[1605,22104,22105],{"encoding":1607},"r_{xy} = 0{,}739"," — silná kladná závislost hodnoty produkce na výši investic.",[1136,22108,22110],{"id":22109},"vícenásobná-regrese-a-korelace","Vícenásobná regrese a korelace",[1110,22112,22113,22114,22127],{},"Pokud na závisle proměnnou ",[1115,22115,22117],{"className":22116},[1573],[1575,22118,22119],{"xmlns":1577},[1579,22120,22121,22125],{},[1582,22122,22123],{},[1585,22124,2862],{},[1605,22126,2862],{"encoding":1607}," působí víc vysvětlujících proměnných současně, analyzuje se zvlášť vliv každé z nich a výsledná regresní funkce se konstruuje jako součet jednoduchých regresních funkcí:",[1115,22129,22131],{"className":22130},[1573],[1575,22132,22133],{"xmlns":1577,"display":4601},[1579,22134,22135,22245],{},[1582,22136,22137,22139,22141,22147,22149,22155,22161,22163,22169,22175,22177,22179,22181,22187,22193,22195,22197,22203,22205,22211,22213,22219,22225,22227,22229,22231,22237,22243],{},[1585,22138,18823],{},[1589,22140,1597],{},[1746,22142,22143,22145],{},[1585,22144,18838],{},[1716,22146,2398],{},[1589,22148,4010],{},[1746,22150,22151,22153],{},[1585,22152,18838],{},[1716,22154,1718],{},[1746,22156,22157,22159],{},[1585,22158,1158],{},[1716,22160,1718],{},[1589,22162,4010],{},[1746,22164,22165,22167],{},[1585,22166,18838],{},[1716,22168,1993],{},[1746,22170,22171,22173],{},[1585,22172,1158],{},[1716,22174,1993],{},[1589,22176,4010],{},[1589,22178,20413],{},[1589,22180,4010],{},[1746,22182,22183,22185],{},[1585,22184,18838],{},[1585,22186,1110],{},[1746,22188,22189,22191],{},[1585,22190,1158],{},[1585,22192,1110],{},[1589,22194,1177],{"separator":1121},[4648,22196],{"width":4650},[3005,22198,22199,22201],{"accent":1121},[1585,22200,2862],{},[1589,22202,3011],{},[1589,22204,1597],{},[1746,22206,22207,22209],{},[1585,22208,2869],{},[1716,22210,2398],{},[1589,22212,4010],{},[1746,22214,22215,22217],{},[1585,22216,2869],{},[1716,22218,1718],{},[1746,22220,22221,22223],{},[1585,22222,1158],{},[1716,22224,1718],{},[1589,22226,4010],{},[1589,22228,20413],{},[1589,22230,4010],{},[1746,22232,22233,22235],{},[1585,22234,2869],{},[1585,22236,1110],{},[1746,22238,22239,22241],{},[1585,22240,1158],{},[1585,22242,1110],{},[1585,22244,2264],{"mathvariant":4022},[1605,22246,22247],{"encoding":1607},"\\eta = \\beta_0 + \\beta_1 x_1 + \\beta_2 x_2 + \\dots + \\beta_p x_p, \\qquad \\hat y = b_0 + b_1 x_1 + \\dots + b_p x_p.",[1550,22249,22251],{"id":22250},"výběr-proměnných","Výběr proměnných",[2220,22253,22254,22260],{},[2223,22255,22256,22259],{},[2227,22257,22258],{},"Metoda ENTER"," — vloží do modelu všechny proměnné najednou. Použije se, když jde o index determinace celého modelu, o vliv každé nezávislé proměnné při kontrole vlivu ostatních, nebo o relativní důležitost proměnných. Vyžaduje poměrně vysoký počet pozorování — aspoň 20 na každou proměnnou.",[2223,22261,22262,22265,22266,22269,22270,22273],{},[2227,22263,22264],{},"Metoda stepwise (postupná regrese)"," — hledá „nejlepší\" model (co nejmíň proměnných, co nejkvalitnější predikce) na základě F-testu; pořadí vstupu\u002Fodebrání proměnných řídí program, ne uživatel. Varianta ",[2227,22267,22268],{},"forward"," proměnné postupně přidává, varianta ",[2227,22271,22272],{},"backward"," naopak začíná plným modelem a proměnné postupně odebírá. Pořadí vkládání ovlivňuje odhad důležitosti proměnných, proto je třeba metodu zvolit uvážlivě. Stepwise vyžaduje ještě víc pozorování — aspoň 40 na proměnnou.",[1550,22275,22277],{"id":22276},"postup-odhadu","Postup odhadu",[5499,22279,22280,22283,22286],{},[2223,22281,22282],{},"ověření předpokladů regresního modelu,",[2223,22284,22285],{},"samotný odhad parametrů,",[2223,22287,22288],{},"reziduální analýza výsledného modelu.",[1110,22290,22291,22292,22309,22310,6605,22312,22341,22342,22371,22372,22389],{},"Důležitost každého parametru ",[1115,22293,22295],{"className":22294},[1573],[1575,22296,22297],{"xmlns":1577},[1579,22298,22299,22307],{},[1582,22300,22301],{},[1746,22302,22303,22305],{},[1585,22304,2869],{},[1585,22306,1776],{},[1605,22308,18963],{"encoding":1607}," v modelu ověřuje ",[2227,22311,992],{},[1115,22313,22315],{"className":22314},[1573],[1575,22316,22317],{"xmlns":1577},[1579,22318,22319,22339],{},[1582,22320,22321,22327,22329,22335,22337],{},[1746,22322,22323,22325],{},[1585,22324,1922],{},[1716,22326,2398],{},[1589,22328,4595],{},[1746,22330,22331,22333],{},[1585,22332,18838],{},[1585,22334,1776],{},[1589,22336,1597],{},[1716,22338,2398],{},[1605,22340,19448],{"encoding":1607}," (proměnná je v modelu nevýznamná) proti ",[1115,22343,22345],{"className":22344},[1573],[1575,22346,22347],{"xmlns":1577},[1579,22348,22349,22369],{},[1582,22350,22351,22357,22359,22365,22367],{},[1746,22352,22353,22355],{},[1585,22354,1922],{},[1716,22356,1718],{},[1589,22358,4595],{},[1746,22360,22361,22363],{},[1585,22362,18838],{},[1585,22364,1776],{},[1589,22366,13487],{"mathvariant":4022},[1716,22368,2398],{},[1605,22370,19479],{"encoding":1607}," (proměnná je významná). Při nezamítnutí ",[1115,22373,22375],{"className":22374},[1573],[1575,22376,22377],{"xmlns":1577},[1579,22378,22379,22387],{},[1582,22380,22381],{},[1746,22382,22383,22385],{},[1585,22384,1922],{},[1716,22386,2398],{},[1605,22388,4225],{"encoding":1607}," by proměnná — a s ní spojený regresor — v modelu neměla zůstat.",[1550,22391,22393],{"id":22392},"předpoklady-modelu","Předpoklady modelu",[5499,22395,22396,22413,22446,22452,22455,22458],{},[2223,22397,22398,22399,22412],{},"Závisle proměnná ",[1115,22400,22402],{"className":22401},[1573],[1575,22403,22404],{"xmlns":1577},[1579,22405,22406,22410],{},[1582,22407,22408],{},[1585,22409,2862],{},[1605,22411,2862],{"encoding":1607}," musí být aspoň intervalového typu (ne binární, diskrétní s málo hodnotami apod.) — jinak je na místě logistická regrese.",[2223,22414,22415,22416,22445],{},"Nezávislé proměnné ",[1115,22417,22419],{"className":22418},[1573],[1575,22420,22421],{"xmlns":1577},[1579,22422,22423,22443],{},[1582,22424,22425,22431,22433,22435,22437],{},[1746,22426,22427,22429],{},[1585,22428,1158],{},[1716,22430,1718],{},[1589,22432,1177],{"separator":1121},[1589,22434,2979],{},[1589,22436,1177],{"separator":1121},[1746,22438,22439,22441],{},[1585,22440,1158],{},[1585,22442,1110],{},[1605,22444,18787],{"encoding":1607}," jsou rovněž aspoň intervalového typu, mohou být i alternativní.",[2223,22447,22448,22449,2264],{},"Nezávislé proměnné by mezi sebou neměly být příliš vysoce korelované — ",[2227,22450,22451],{},"multikolinearita",[2223,22453,22454],{},"V datech nesmí být odlehlé či extrémní hodnoty; regresní analýza je na ně citlivá a mohou vážně narušit kvalitu odhadů.",[2223,22456,22457],{},"Proměnné musí být ve vzájemně lineárním vztahu — vícenásobná lineární regrese je založená na Pearsonově koeficientu korelace, takže nelineární vztahy mezi proměnnými zůstanou neodhalené.",[2223,22459,22460,22461,22465],{},"Proměnné mají mít ",[1127,22462,22464],{"className":22463,"dataFsResolvedFilePath":1556,"href":1557},[1130],"normální rozložení","; význam tohoto předpokladu ustupuje do pozadí u dostatečně velkého datového souboru díky centrální limitní větě.",[1110,22467,22468,22469,22472],{},"Normalita se u menšího počtu pozorování ověřuje stejnými testy jako u jiných znaků (viz ",[1127,22470,4368],{"className":22471,"dataFsResolvedFilePath":2658,"href":2659},[1130],") — Shapiro–Wilkovým nebo Kolmogorovovým–Smirnovovým testem — nebo graficky grafem reziduí proti predikovaným hodnotám, kde by body měly být rovnoměrně rozptýlené po obou stranách vodorovné osy.",[1550,22474,22475],{"id":22451},"Multikolinearita",[1110,22477,22478],{},"Multikolinearita vzniká, když vysvětlující proměnné silně závisejí jedna na druhé. Je nežádoucí, protože:",[2220,22480,22481,22484,22487],{},[2223,22482,22483],{},"výsledky regrese jsou pak nespolehlivé,",[2223,22485,22486],{},"zvyšuje pravděpodobnost, že se důležitá proměnná jeví jako statisticky nevýznamná a bude z modelu vyřazena,",[2223,22488,22489],{},"směrodatné odchylky odhadnutých parametrů jsou vysoké, testová kritéria t-testů nízká, p-hodnoty vysoké.",[1110,22491,22492,22493,22496,22497,22520,22521,22539,22540,22556],{},"Pozná se podle vysokých korelačních koeficientů mezi regresory (nad 0,75), podle toho, že celkový F-test modelu je významný, ale jednotlivé t-testy parametrů ne, nebo softwarově přes ",[2227,22494,22495],{},"VIF (Variance Inflation Factor)",": hodnoty ",[1115,22498,22500],{"className":22499},[1573],[1575,22501,22502],{"xmlns":1577},[1579,22503,22504,22517],{},[1582,22505,22506,22508,22510,22513,22515],{},[1716,22507,1718],{},[1589,22509,6949],{},[5543,22511,22512],{},"VIF",[1589,22514,6949],{},[1716,22516,12470],{},[1605,22518,22519],{"encoding":1607},"1\u003C\\text{VIF}\u003C5"," jsou varující, ",[1115,22522,22524],{"className":22523},[1573],[1575,22525,22526],{"xmlns":1577},[1579,22527,22528,22536],{},[1582,22529,22530,22532,22534],{},[5543,22531,22512],{},[1589,22533,1698],{},[1716,22535,12470],{},[1605,22537,22538],{"encoding":1607},"\\text{VIF}>5"," (přísněji ",[1115,22541,22543],{"className":22542},[1573],[1575,22544,22545],{"xmlns":1577},[1579,22546,22547,22553],{},[1582,22548,22549,22551],{},[1589,22550,1698],{},[1716,22552,11613],{},[1605,22554,22555],{"encoding":1607},">10",") značí vysokou multikolinearitu.",[1110,22558,22559],{},"Řešení: je-li multikolinearita způsobená silnou závislostí dvou proměnných, jednu z nich se z modelu vyřadí; je-li způsobená závislostí víc proměnných najednou, použije se metoda hlavních komponent a pracuje se s novými, nekorelovanými proměnnými.",[1550,22561,22563],{"id":22562},"další-ukazatele-kvality-modelu","Další ukazatele kvality modelu",[2220,22565,22566,22571,22577],{},[2223,22567,22568,22570],{},[2227,22569,1418],{}," — testuje hypotézu, že všechny regresní koeficienty jsou rovny nule, proti alternativě, že aspoň jeden v modelu být má (celková významnost modelu).",[2223,22572,22573,22576],{},[2227,22574,22575],{},"RMSE"," (odmocnina z reziduálního rozptylu) — absolutní měřítko vhodnosti funkce (na rozdíl od indexu determinace, který je relativní); nižší hodnota znamená lepší fit.",[2223,22578,22579,22582,22583,22586],{},[2227,22580,22581],{},"AIC"," (Akaikeho informační kritérium) a ",[2227,22584,22585],{},"BIC"," (Bayesovo informační kritérium) — čím nižší hodnoty obou kritérií, tím lepší model; používají se hlavně při stepwise výběru proměnných.",[1550,22588,19249],{"id":22589},"v-r-2",[1110,22591,22592],{},"Pro vícenásobnou regresi je postup v R rozšířením postupu pro regresní přímku — přibývá výběr proměnných a kontrola multikolinearity:",[1144,22594,22596],{"className":1146,"code":22595,"language":71,"meta":1148,"style":1148},"data \u003C- read.table(\"4_4.txt\", header = TRUE)\nmodel_plny \u003C- lm(y ~ x1 + x2 + x3 + x4, data = data)\nmodel_krok \u003C- step(model_plny, direction = \"both\")\nsummary(model_krok)\n\nlibrary(car)\nvif(model_krok)\n\nlibrary(lmtest)\ndwtest(model_krok)\n\nlibrary(whitestrap)\nwhite_test(model_krok)\n\nshapiro.test(residuals(model_krok))\n",[1150,22597,22598,22623,22667,22693,22703,22707,22718,22729,22733,22743,22753,22757,22767,22777,22782],{"__ignoreMap":1148},[1115,22599,22600,22602,22604,22607,22609,22612,22614,22617,22619,22621],{"class":1154,"line":10},[1115,22601,3381],{"class":1157},[1115,22603,1162],{"class":1161},[1115,22605,22606],{"class":1165}," read.table",[1115,22608,1170],{"class":1169},[1115,22610,22611],{"class":6458},"\"4_4.txt\"",[1115,22613,1177],{"class":1161},[1115,22615,22616],{"class":1157}," header",[1115,22618,6416],{"class":1161},[1115,22620,6429],{"class":1173},[1115,22622,6519],{"class":1169},[1115,22624,22625,22628,22630,22632,22634,22636,22638,22641,22643,22646,22648,22651,22653,22656,22658,22661,22663,22665],{"class":1154,"line":27},[1115,22626,22627],{"class":1157},"model_plny",[1115,22629,1162],{"class":1161},[1115,22631,19349],{"class":1165},[1115,22633,1170],{"class":1169},[1115,22635,2862],{"class":1157},[1115,22637,19356],{"class":1161},[1115,22639,22640],{"class":1157}," x1",[1115,22642,21011],{"class":1161},[1115,22644,22645],{"class":1157}," x2",[1115,22647,21011],{"class":1161},[1115,22649,22650],{"class":1157}," x3",[1115,22652,21011],{"class":1161},[1115,22654,22655],{"class":1157}," x4",[1115,22657,1177],{"class":1161},[1115,22659,22660],{"class":1157}," data",[1115,22662,6416],{"class":1161},[1115,22664,22660],{"class":1157},[1115,22666,6519],{"class":1169},[1115,22668,22669,22672,22674,22677,22679,22681,22683,22686,22688,22691],{"class":1154,"line":148},[1115,22670,22671],{"class":1157},"model_krok",[1115,22673,1162],{"class":1161},[1115,22675,22676],{"class":1165}," step",[1115,22678,1170],{"class":1169},[1115,22680,22627],{"class":1157},[1115,22682,1177],{"class":1161},[1115,22684,22685],{"class":1157}," direction",[1115,22687,6416],{"class":1161},[1115,22689,22690],{"class":6458}," \"both\"",[1115,22692,6519],{"class":1169},[1115,22694,22695,22697,22699,22701],{"class":1154,"line":111},[1115,22696,19366],{"class":1165},[1115,22698,1170],{"class":1169},[1115,22700,22671],{"class":1157},[1115,22702,6519],{"class":1169},[1115,22704,22705],{"class":1154,"line":96},[1115,22706,12585],{"emptyLinePlaceholder":4157},[1115,22708,22709,22711,22713,22716],{"class":1154,"line":89},[1115,22710,19892],{"class":1161},[1115,22712,1170],{"class":1169},[1115,22714,22715],{"class":1157},"car",[1115,22717,6519],{"class":1169},[1115,22719,22720,22723,22725,22727],{"class":1154,"line":82},[1115,22721,22722],{"class":1165},"vif",[1115,22724,1170],{"class":1169},[1115,22726,22671],{"class":1157},[1115,22728,6519],{"class":1169},[1115,22730,22731],{"class":1154,"line":75},[1115,22732,12585],{"emptyLinePlaceholder":4157},[1115,22734,22735,22737,22739,22741],{"class":1154,"line":6509},[1115,22736,19892],{"class":1161},[1115,22738,1170],{"class":1169},[1115,22740,19897],{"class":1157},[1115,22742,6519],{"class":1169},[1115,22744,22745,22747,22749,22751],{"class":1154,"line":72},[1115,22746,19904],{"class":1165},[1115,22748,1170],{"class":1169},[1115,22750,22671],{"class":1157},[1115,22752,6519],{"class":1169},[1115,22754,22755],{"class":1154,"line":25},[1115,22756,12585],{"emptyLinePlaceholder":4157},[1115,22758,22759,22761,22763,22765],{"class":1154,"line":65},[1115,22760,19892],{"class":1161},[1115,22762,1170],{"class":1169},[1115,22764,19987],{"class":1157},[1115,22766,6519],{"class":1169},[1115,22768,22769,22771,22773,22775],{"class":1154,"line":63},[1115,22770,19994],{"class":1165},[1115,22772,1170],{"class":1169},[1115,22774,22671],{"class":1157},[1115,22776,6519],{"class":1169},[1115,22778,22780],{"class":1154,"line":22779},14,[1115,22781,12585],{"emptyLinePlaceholder":4157},[1115,22783,22784,22786,22788,22790,22792,22794],{"class":1154,"line":60},[1115,22785,20072],{"class":1165},[1115,22787,1170],{"class":1169},[1115,22789,19543],{"class":1165},[1115,22791,1170],{"class":1169},[1115,22793,22671],{"class":1157},[1115,22795,12073],{"class":1169},[1110,22797,22798,22800,22801,22804],{},[1150,22799,18621],{}," provádí stepwise výběr podle AIC, ",[1150,22802,22803],{},"vif()"," spočítá Variance Inflation Factor pro každý regresor v modelu, zbylé tři volání ověřují stejné tři předpoklady (autokorelace, homoskedasticita, normalita reziduí) jako u regresní přímky výše.",[1103,22806,22808,22815,22818,22821],{"className":22807,"dataCallout":6105},[1106,6104],[1110,22809,22811,22814],{"className":22810},[1113],[1115,22812],{"className":22813,"ariaHidden":1121},[1118,6112,1120],"Příklad: Vícenásobná regrese",[1110,22816,22817],{},"U souboru nemovitostí prodaných v roce 1981 se sledovala prodejní cena v dolarech v závislosti na stáří nemovitosti, počtu sousedících nemovitostí, velikosti podlahové plochy a pozemku, vzdálenosti k mezistátní silnici, vzdálenosti ke spalovně a počtu pokojů a koupelen. Úkolem bylo odhadnout model, který by dobře popisoval data.",[1110,22819,22820],{},"Postup: odhad plného modelu → stepwise analýza podle AIC → ověření předpokladů.",[1110,22822,22823,22824,22827,22828,22830,22831,22834],{},"Diagnostika odhaleného modelu ukázala tři problémy: (1) ",[2227,22825,22826],{},"nelinearita"," — mezi některými vysvětlujícími proměnnými a cenou je zjevně jiný než lineární vztah, řešením je zkusit u nich druhou mocninu; (2) ",[2227,22829,22451],{}," mezi dvojicí proměnných popisujících vzdálenost (k silnici a ke spalovně) — doporučeno jednu z nich vynechat; (3) ",[2227,22832,22833],{},"odlehlá pozorování"," — vhodné je provést ještě test a případně je vyřadit. Výsledný model obsahoval i nevýznamné proměnné, jako celek však byl statisticky významný s přibližně průměrným indexem determinace; dalšího zlepšení šlo dosáhnout snížením AIC pomocí stepwise regrese.",[1136,22836,9014],{"id":9013},[1103,22838,22840,22847],{"className":22839,"dataCallout":9019},[1106,9018],[1110,22841,22843,22846],{"className":22842},[1113],[1115,22844],{"className":22845,"ariaHidden":1121},[1118,9026,1120],"Koeficient korelace jen pro přímku",[1110,22848,22849,22850,22906,22907,22924,22925,22945,22946,1260,22959,2264],{},"Vzorec ",[1115,22851,22853],{"className":22852},[1573],[1575,22854,22855],{"xmlns":1577},[1579,22856,22857,22903],{},[1582,22858,22859,22869,22871,22881,22883],{},[1746,22860,22861,22863],{},[1585,22862,71],{},[1582,22864,22865,22867],{},[1585,22866,1158],{},[1585,22868,2862],{},[1589,22870,1597],{},[1746,22872,22873,22875],{},[1585,22874,3433],{},[1582,22876,22877,22879],{},[1585,22878,1158],{},[1585,22880,2862],{},[1585,22882,4023],{"mathvariant":4022},[7068,22884,22885],{},[1582,22886,22887,22895],{},[2920,22888,22889,22891,22893],{},[1585,22890,3433],{},[1585,22892,1158],{},[1716,22894,1993],{},[2920,22896,22897,22899,22901],{},[1585,22898,3433],{},[1585,22900,2862],{},[1716,22902,1993],{},[1605,22904,22905],{"encoding":1607},"r_{xy}=s_{xy}\u002F\\sqrt{s_x^2 s_y^2}"," měří lineární závislost. Pro nelineární regresní funkci (parabola, hyperbola, exponenciála) se kvalita fitu posuzuje indexem determinace ",[1115,22908,22910],{"className":22909},[1573],[1575,22911,22912],{"xmlns":1577},[1579,22913,22914,22922],{},[1582,22915,22916],{},[1986,22917,22918,22920],{},[1585,22919,3376],{},[1716,22921,1993],{},[1605,22923,18526],{"encoding":1607},", případně obecným indexem korelace ",[1115,22926,22928],{"className":22927},[1573],[1575,22929,22930],{"xmlns":1577},[1579,22931,22932,22942],{},[1582,22933,22934],{},[7068,22935,22936],{},[1986,22937,22938,22940],{},[1585,22939,3376],{},[1716,22941,1993],{},[1605,22943,22944],{"encoding":1607},"\\sqrt{R^2}"," — ne koeficientem korelace mezi ",[1115,22947,22949],{"className":22948},[1573],[1575,22950,22951],{"xmlns":1577},[1579,22952,22953,22957],{},[1582,22954,22955],{},[1585,22956,1158],{},[1605,22958,1158],{"encoding":1607},[1115,22960,22962],{"className":22961},[1573],[1575,22963,22964],{"xmlns":1577},[1579,22965,22966,22970],{},[1582,22967,22968],{},[1585,22969,2862],{},[1605,22971,2862],{"encoding":1607},[1103,22973,22975,22982],{"className":22974,"dataCallout":9019},[1106,9018],[1110,22976,22978,22981],{"className":22977},[1113],[1115,22979],{"className":22980,"ariaHidden":1121},[1118,9026,1120],"Významný F-test, nevýznamné t-testy",[1110,22983,22984],{},"Pokud je celkový F-test modelu významný, ale jednotlivé t-testy parametrů ne, nejde nutně o chybně zvolené proměnné — je to typický příznak multikolinearity. Řešením je zkontrolovat VIF, ne mechanicky vyřazovat „nevýznamné\" proměnné.",[1103,22986,22988,22995],{"className":22987,"dataCallout":9019},[1106,9018],[1110,22989,22991,22994],{"className":22990},[1113],[1115,22992],{"className":22993,"ariaHidden":1121},[1118,9026,1120],"Durbin-Watsonova statistika mimo okolí 2",[1110,22996,22997],{},"DW se pohybuje od 0 do 4; hodnoty blízko 2 znamenají žádnou autokorelaci, blízko 0 pozitivní autokorelaci, blízko 4 negativní autokorelaci. Samotná odchylka od 2 bez pohledu na p-hodnotu testu nic neprokazuje — rozhoduje až test, ne vzdálenost od 2.",[1103,22999,23001,23008],{"className":23000,"dataCallout":9019},[1106,9018],[1110,23002,23004,23007],{"className":23003},[1113],[1115,23005],{"className":23006,"ariaHidden":1121},[1118,9026,1120],"Nízký počet pozorování při stepwise výběru",[1110,23009,23010],{},"Metoda ENTER potřebuje aspoň 20 pozorování na proměnnou, stepwise regrese aspoň 40. Při menším vzorku jsou výsledky výběru proměnných nespolehlivé bez ohledu na to, jak hezky vychází AIC.",[1136,23012,4071],{"id":4070},[2220,23014,23015,23020,23025,23030,23035,23040,23045],{},[2223,23016,23017],{},[1127,23018,1133],{"className":23019,"dataFsResolvedFilePath":1131,"href":1132},[1130],[2223,23021,23022],{},[1127,23023,1558],{"className":23024,"dataFsResolvedFilePath":1556,"href":1557},[1130],[2223,23026,23027],{},[1127,23028,2415],{"className":23029,"dataFsResolvedFilePath":2413,"href":2414},[1130],[2223,23031,23032],{},[1127,23033,2660],{"className":23034,"dataFsResolvedFilePath":2658,"href":2659},[1130],[2223,23036,23037],{},[1127,23038,3237],{"className":23039,"dataFsResolvedFilePath":3235,"href":3236},[1130],[2223,23041,23042],{},[1127,23043,3322],{"className":23044,"dataFsResolvedFilePath":3320,"href":3321},[1130],[2223,23046,23047],{},[1127,23048,9239],{"className":23049,"dataFsResolvedFilePath":9237,"href":9238},[1130],[1136,23051,4111],{"id":934},[1110,23053,4114,23054,4119],{},[4116,23055,4118],{},[4135,23057,23058],{},"html pre.shiki code .sP4rz, html 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diagram zobrazuje vývoj variability procesu v čase a dává signál, že na proces začala působit vymezitelná příčina: bod mimo akční meze UCL a LCL.",[2223,23115,23116,23117,1279,23143,1260,23169,2264],{},"Regulace měřením (spojitá veličina s normálním rozdělením): diagramy ",[1115,23118,23120],{"className":23119},[1573],[1575,23121,23122],{"xmlns":1577},[1579,23123,23124,23140],{},[1582,23125,23126,23128,23134,23136,23138],{},[1589,23127,1170],{"stretchy":1591},[3005,23129,23130,23132],{"accent":1121},[1585,23131,1158],{},[1589,23133,3408],{},[1589,23135,1177],{"separator":1121},[1585,23137,3376],{},[1589,23139,1603],{"stretchy":1591},[1605,23141,23142],{"encoding":1607},"(\\bar{x}, R)",[1115,23144,23146],{"className":23145},[1573],[1575,23147,23148],{"xmlns":1577},[1579,23149,23150,23166],{},[1582,23151,23152,23154,23160,23162,23164],{},[1589,23153,1170],{"stretchy":1591},[3005,23155,23156,23158],{"accent":1121},[1585,23157,1158],{},[1589,23159,3408],{},[1589,23161,1177],{"separator":1121},[1585,23163,3433],{},[1589,23165,1603],{"stretchy":1591},[1605,23167,23168],{"encoding":1607},"(\\bar{x}, s)",[1115,23170,23172],{"className":23171},[1573],[1575,23173,23174],{"xmlns":1577},[1579,23175,23176,23205],{},[1582,23177,23178,23180,23186,23188,23203],{},[1589,23179,1170],{"stretchy":1591},[1746,23181,23182,23184],{},[1585,23183,1158],{},[1585,23185,1776],{},[1589,23187,1177],{"separator":1121},[1746,23189,23190,23192],{},[1585,23191,3376],{},[1582,23193,23194,23196,23199,23201],{},[1585,23195,1600],{},[1585,23197,23198],{},"l",[1589,23200,1177],{"separator":1121},[1585,23202,1776],{},[1589,23204,1603],{"stretchy":1591},[1605,23206,23207],{"encoding":1607},"(x_i, R_{kl,i})",[2223,23209,23210,23211,23224,23225,23238,23239,23254,23255,23268],{},"Regulace srovnáváním (diskrétní veličina): počet neshod ",[1115,23212,23214],{"className":23213},[1573],[1575,23215,23216],{"xmlns":1577},[1579,23217,23218,23222],{},[1582,23219,23220],{},[1585,23221,3499],{},[1605,23223,3499],{"encoding":1607}," (konstantní rozsah) a ",[1115,23226,23228],{"className":23227},[1573],[1575,23229,23230],{"xmlns":1577},[1579,23231,23232,23236],{},[1582,23233,23234],{},[1585,23235,3523],{},[1605,23237,3523],{"encoding":1607}," (nekonstantní rozsah), počet neshodných produktů ",[1115,23240,23242],{"className":23241},[1573],[1575,23243,23244],{"xmlns":1577},[1579,23245,23246,23252],{},[1582,23247,23248,23250],{},[1585,23249,1781],{},[1585,23251,1110],{},[1605,23253,3555],{"encoding":1607}," (konstantní rozsah) a jejich podíl ",[1115,23256,23258],{"className":23257},[1573],[1575,23259,23260],{"xmlns":1577},[1579,23261,23262,23266],{},[1582,23263,23264],{},[1585,23265,1110],{},[1605,23267,1110],{"encoding":1607}," (nekonstantní rozsah).",[2223,23270,23271],{},"Podskupiny s vymezitelnou příčinou se po jejím odstranění z výpočtu vyřadí a meze se přepočítají, dokud jsou všechny body uvnitř mezí.",[2223,23273,23274,23275,1279,23292,1279,23313,1279,23334,23358,23359,23380],{},"Indexy způsobilosti ",[1115,23276,23278],{"className":23277},[1573],[1575,23279,23280],{"xmlns":1577},[1579,23281,23282,23290],{},[1582,23283,23284],{},[1746,23285,23286,23288],{},[1585,23287,3627],{},[1585,23289,1110],{},[1605,23291,3632],{"encoding":1607},[1115,23293,23295],{"className":23294},[1573],[1575,23296,23297],{"xmlns":1577},[1579,23298,23299,23311],{},[1582,23300,23301],{},[1746,23302,23303,23305],{},[1585,23304,3627],{},[1582,23306,23307,23309],{},[1585,23308,1110],{},[1585,23310,1600],{},[1605,23312,3654],{"encoding":1607},[1115,23314,23316],{"className":23315},[1573],[1575,23317,23318],{"xmlns":1577},[1579,23319,23320,23332],{},[1582,23321,23322],{},[1746,23323,23324,23326],{},[1585,23325,3627],{},[1582,23327,23328,23330],{},[1585,23329,1110],{},[1585,23331,3674],{},[1605,23333,3677],{"encoding":1607},[1115,23335,23337],{"className":23336},[1573],[1575,23338,23339],{"xmlns":1577},[1579,23340,23341,23355],{},[1582,23342,23343],{},[1746,23344,23345,23347],{},[1585,23346,3627],{},[1582,23348,23349,23351,23353],{},[1585,23350,1110],{},[1585,23352,3674],{},[1585,23354,1600],{},[1605,23356,23357],{"encoding":1607},"C_{pmk}"," posuzují, zda statisticky zvládnutý proces vyhovuje tolerančním mezím; ",[1115,23360,23362],{"className":23361},[1573],[1575,23363,23364],{"xmlns":1577},[1579,23365,23366,23378],{},[1582,23367,23368],{},[1746,23369,23370,23372],{},[1585,23371,3627],{},[1582,23373,23374,23376],{},[1585,23375,1110],{},[1585,23377,1600],{},[1605,23379,3654],{"encoding":1607}," navíc zohledňuje vychýlení střední hodnoty.",[2223,23382,23383,23384,2264],{},"V R diagramy i indexy počítá balíček ",[1150,23385,360],{},[1136,23387,23389],{"id":23388},"statistická-regulace-procesu","Statistická regulace procesu",[1110,23391,23392,23393,23395,23396,2264],{},"Tradiční zabezpečování jakosti kontroluje výrobky až po jejich vyrobení, což je neekonomické. ",[2227,23394,23389],{}," je preventivní nástroj řízení jakosti: analyzuje chování výrobního procesu, umožňuje včas odhalit odchylky od normy a zasáhnout tak, aby proces zůstal dlouhodobě na požadované a stabilní úrovni — ve ",[2227,23397,23398],{},"statisticky zvládnutém stavu",[1110,23400,23401,23402,23405],{},"Teorie regulace vychází z ",[2227,23403,23404],{},"variability"," procesu, kterou způsobují dva druhy příčin:",[1310,23407,23408,23420],{},[1313,23409,23410],{},[1316,23411,23412,23414,23417],{},[1319,23413],{},[1319,23415,23416],{},"Náhodné příčiny",[1319,23418,23419],{},"Vymezitelné příčiny",[1332,23421,23422,23433,23444],{},[1316,23423,23424,23427,23430],{},[1337,23425,23426],{},"Povaha",[1337,23428,23429],{},"široká skupina neidentifikovatelných vlivů, každý přispívá k variabilitě malou měrou",[1337,23431,23432],{},"vlivy, které za běžných podmínek na proces nepůsobí; vyvolají nepřirozené kolísání údajů",[1316,23434,23435,23438,23441],{},[1337,23436,23437],{},"Stav procesu",[1337,23439,23440],{},"ustálený, jakost výstupů je předvídatelná, není nutné zasahovat — statisticky zvládnutý",[1337,23442,23443],{},"jakost výstupů není předvídatelná, je nutné zasáhnout — proces není statisticky zvládnutý",[1316,23445,23446,23449,23452],{},[1337,23447,23448],{},"Příklady",[1337,23450,23451],{},"psychický stav pracovníka, chvění stroje, teplota ovzduší",[1337,23453,23454],{},"změna materiálu, nezaškolená obsluha",[1110,23456,23457,23458,23461,23462,23465],{},"Vymezitelné příčiny jsou ",[2227,23459,23460],{},"sporadické"," (vznikají náhle, změny trvají krátce) nebo ",[2227,23463,23464],{},"přetrvávající"," (trvají stále nebo se mění).",[1110,23467,23468],{},[1303,23469],{"alt":23470,"className":23471,"src":23472},"mask-ilu-pricin-variability",[1130,1307],"\u002Fwiki-assets\u002Fmask-ilu-pricin-variability.png",[1110,23474,23475],{},"Regulace probíhá ve třech fázích:",[5499,23477,23478,23488,23494],{},[2223,23479,23480,23483,23484,23487],{},[2227,23481,23482],{},"Fáze přípravná"," — stanoví se sledované znaky jakosti (rozměr, hmotnost, počet vad…), délka časového intervalu mezi měřeními, ",[2227,23485,23486],{},"logická podskupina"," (skupina měření, v níž se předpokládá působení pouze náhodných příčin), typ regulačního diagramu a místa kontroly v procesu.",[2223,23489,23490,23493],{},[2227,23491,23492],{},"Fáze zabezpečování statistické zvládnutosti"," — pomocí regulačních diagramů se identifikují vymezitelné příčiny a odstraní se jejich působení.",[2223,23495,23496,23499],{},[2227,23497,23498],{},"Fáze analýzy a zabezpečení způsobilosti"," — zkoumá se, zda statisticky zvládnutý proces vyhovuje požadavkům zákazníka; k tomu slouží indexy způsobilosti (níže).",[1136,23501,23503],{"id":23502},"princip-regulačního-diagramu","Princip regulačního diagramu",[1110,23505,23506,23509],{},[2227,23507,23508],{},"Regulační diagram"," je grafický prostředek pro zobrazení vývoje variability procesu v čase. Popisuje statistickou zvládnutelnost procesu a dává signál, že na proces začala působit vymezitelná příčina; na jeho základě se do procesu zasáhne s cílem příčinu odstranit.",[2220,23511,23512,23518,23524],{},[2223,23513,23514,23517],{},[2227,23515,23516],{},"CL"," — střední přímka, odpovídá požadované (referenční) hodnotě použité charakteristiky,",[2223,23519,23520,23523],{},[2227,23521,23522],{},"UCL"," — horní akční regulační mez,",[2223,23525,23526,23529],{},[2227,23527,23528],{},"LCL"," — dolní akční regulační mez.",[1110,23531,23532],{},"Akční meze vymezují pásmo působení pouze náhodných příčin variability.",[1110,23534,23535],{},[1303,23536],{"alt":23537,"className":23538,"src":23539},"mask-rd-schema",[1130,1307],"\u002Fwiki-assets\u002Fmask-rd-schema.png",[1110,23541,23542,23545],{},[2227,23543,23544],{},"Interpretace:"," jsou-li všechny body uvnitř akčních mezí, je proces statisticky zvládnutý (nepůsobí žádná vymezitelná příčina). Je-li některý bod mimo meze, lze usuzovat, že proces není ve statisticky zvládnutém stavu; je třeba identifikovat vymezitelnou příčinu a přijmout opatření k jejímu odstranění.",[1110,23547,23548,23549,23552,23553,23556],{},"Podle charakteru regulované veličiny se diagramy dělí na diagramy pro ",[2227,23550,23551],{},"regulaci měřením"," (regulovaná veličina je spojitá náhodná veličina) a pro ",[2227,23554,23555],{},"regulaci srovnáváním"," (diskrétní náhodná veličina).",[1110,23558,23559],{},"Postup při konstrukci regulačního diagramu:",[5499,23561,23562,23565,23568,23571,23574,23577,23580,23583,23586],{},[2223,23563,23564],{},"volba regulované veličiny,",[2223,23566,23567],{},"sběr a záznam dat,",[2223,23569,23570],{},"ověření požadovaných předpokladů o datech,",[2223,23572,23573],{},"volba rozsahu logických podskupin,",[2223,23575,23576],{},"volba vhodného regulačního diagramu,",[2223,23578,23579],{},"výpočet hodnot zvoleného testového kritéria pro jednotlivé výběry,",[2223,23581,23582],{},"ověření a zajištění statistické zvládnutosti procesu,",[2223,23584,23585],{},"ověření způsobilosti procesu,",[2223,23587,23588],{},"vlastní regulace procesu.",[1136,23590,23592],{"id":23591},"regulace-měřením","Regulace měřením",[1110,23594,23595],{},"Diagramy pro regulaci měřením se používají, když je regulovaná veličina měřitelná. Požaduje se, aby:",[2220,23597,23598,23601],{},[2223,23599,23600],{},"jednotlivá měření byla vzájemně nezávislá,",[2223,23602,23603,23604,23617,23618,23631,23632,23645,23646,23659],{},"regulovaná veličina byla spojitá náhodná veličina s normálním rozdělením se střední hodnotou ",[1115,23605,23607],{"className":23606},[1573],[1575,23608,23609],{"xmlns":1577},[1579,23610,23611,23615],{},[1582,23612,23613],{},[1585,23614,1982],{},[1605,23616,11376],{"encoding":1607}," a směrodatnou odchylkou ",[1115,23619,23621],{"className":23620},[1573],[1575,23622,23623],{"xmlns":1577},[1579,23624,23625,23629],{},[1582,23626,23627],{},[1585,23628,1990],{},[1605,23630,2244],{"encoding":1607}," — tyto dva parametry charakterizují statistickou stabilitu procesu; ",[1115,23633,23635],{"className":23634},[1573],[1575,23636,23637],{"xmlns":1577},[1579,23638,23639,23643],{},[1582,23640,23641],{},[1585,23642,1982],{},[1605,23644,11376],{"encoding":1607}," je hodnota, na niž je proces nastaven, ",[1115,23647,23649],{"className":23648},[1573],[1575,23650,23651],{"xmlns":1577},[1579,23652,23653,23657],{},[1582,23654,23655],{},[1585,23656,1990],{},[1605,23658,2244],{"encoding":1607}," charakterizuje jeho přesnost.",[1110,23661,23662,23663,1279,23688,1260,23713,23750],{},"Jsou-li předpoklady splněny, volí se diagramy, které současně sledují stabilitu polohy i stabilitu rozptylu: ",[1115,23664,23666],{"className":23665},[1573],[1575,23667,23668],{"xmlns":1577},[1579,23669,23670,23686],{},[1582,23671,23672,23674,23680,23682,23684],{},[1589,23673,1170],{"stretchy":1591},[3005,23675,23676,23678],{"accent":1121},[1585,23677,1158],{},[1589,23679,3408],{},[1589,23681,1177],{"separator":1121},[1585,23683,3376],{},[1589,23685,1603],{"stretchy":1591},[1605,23687,23142],{"encoding":1607},[1115,23689,23691],{"className":23690},[1573],[1575,23692,23693],{"xmlns":1577},[1579,23694,23695,23711],{},[1582,23696,23697,23699,23705,23707,23709],{},[1589,23698,1170],{"stretchy":1591},[3005,23700,23701,23703],{"accent":1121},[1585,23702,1158],{},[1589,23704,3408],{},[1589,23706,1177],{"separator":1121},[1585,23708,3433],{},[1589,23710,1603],{"stretchy":1591},[1605,23712,23168],{"encoding":1607},[1115,23714,23716],{"className":23715},[1573],[1575,23717,23718],{"xmlns":1577},[1579,23719,23720,23748],{},[1582,23721,23722,23724,23730,23732,23746],{},[1589,23723,1170],{"stretchy":1591},[1746,23725,23726,23728],{},[1585,23727,1158],{},[1585,23729,1776],{},[1589,23731,1177],{"separator":1121},[1746,23733,23734,23736],{},[1585,23735,3376],{},[1582,23737,23738,23740,23742,23744],{},[1585,23739,1600],{},[1585,23741,23198],{},[1589,23743,1177],{"separator":1121},[1585,23745,1776],{},[1589,23747,1603],{"stretchy":1591},[1605,23749,23207],{"encoding":1607},". Výsledkem jsou vždy dva diagramy.",[1550,23752,23754,23755],{"id":23753},"diagram-xˉrbarx-r","Diagram ",[1115,23756,23758],{"className":23757},[1573],[1575,23759,23760],{"xmlns":1577},[1579,23761,23762,23778],{},[1582,23763,23764,23766,23772,23774,23776],{},[1589,23765,1170],{"stretchy":1591},[3005,23767,23768,23770],{"accent":1121},[1585,23769,1158],{},[1589,23771,3408],{},[1589,23773,1177],{"separator":1121},[1585,23775,3376],{},[1589,23777,1603],{"stretchy":1591},[1605,23779,23142],{"encoding":1607},[1110,23781,23782,23783,23805,23806,23824],{},"Regulované veličiny jsou výběrové průměry ",[1115,23784,23786],{"className":23785},[1573],[1575,23787,23788],{"xmlns":1577},[1579,23789,23790,23802],{},[1582,23791,23792],{},[1746,23793,23794,23800],{},[3005,23795,23796,23798],{"accent":1121},[1585,23797,1158],{},[1589,23799,3408],{},[1585,23801,1776],{},[1605,23803,23804],{"encoding":1607},"\\bar{x}_i"," a výběrová rozpětí ",[1115,23807,23809],{"className":23808},[1573],[1575,23810,23811],{"xmlns":1577},[1579,23812,23813,23821],{},[1582,23814,23815],{},[1746,23816,23817,23819],{},[1585,23818,3376],{},[1585,23820,1776],{},[1605,23822,23823],{"encoding":1607},"R_i"," v logických podskupinách:",[1115,23826,23828],{"className":23827},[1573],[1575,23829,23830],{"xmlns":1577,"display":4601},[1579,23831,23832,23933],{},[1582,23833,23834,23844,23846,23852,23866,23876,23878,23880,23886,23888,23899,23909,23911,23921,23931],{},[1746,23835,23836,23842],{},[3005,23837,23838,23840],{"accent":1121},[1585,23839,1158],{},[1589,23841,3408],{},[1585,23843,1776],{},[1589,23845,1597],{},[5373,23847,23848,23850],{},[1716,23849,1718],{},[1585,23851,1781],{},[4620,23853,23854,23856,23864],{},[1589,23855,4624],{},[1582,23857,23858,23860,23862],{},[1585,23859,4521],{},[1589,23861,1597],{},[1716,23863,1718],{},[1585,23865,1781],{},[1746,23867,23868,23870],{},[1585,23869,1158],{},[1582,23871,23872,23874],{},[1585,23873,1776],{},[1585,23875,4521],{},[1589,23877,1177],{"separator":1121},[4648,23879],{"width":4650},[1746,23881,23882,23884],{},[1585,23883,3376],{},[1585,23885,1776],{},[1589,23887,1597],{},[23889,23890,23891,23897],"munder",{},[1582,23892,23893,23895],{},[1585,23894,14245],{},[1589,23896,7105],{},[1585,23898,4521],{},[1746,23900,23901,23903],{},[1585,23902,1158],{},[1582,23904,23905,23907],{},[1585,23906,1776],{},[1585,23908,4521],{},[1589,23910,1721],{},[23889,23912,23913,23919],{},[1582,23914,23915,23917],{},[1585,23916,7102],{},[1589,23918,7105],{},[1585,23920,4521],{},[1746,23922,23923,23925],{},[1585,23924,1158],{},[1582,23926,23927,23929],{},[1585,23928,1776],{},[1585,23930,4521],{},[1585,23932,2264],{"mathvariant":4022},[1605,23934,23935],{"encoding":1607},"\\bar{x}_i = \\frac{1}{n}\\sum_{j=1}^n x_{ij}, \\qquad R_i = \\max_j x_{ij} - \\min_j x_{ij}.",[1110,23937,23938],{},"Podmínky použití: regulovaná veličina je měřitelná a má normální rozdělení, jednotlivá měření jsou nezávislá, každá logická podskupina má stejný rozsah aspoň dvou měření. Má-li každá podskupina aspoň 4 měření, lze diagram pro výběrový průměr použít i pro data, která nepocházejí z normálního rozdělení.",[1110,23940,23941,23942,23968,23969,23982,23983,1260,24004,24021,24022,24035,24036,24054,24055,2264],{},"Data se zapisují do tabulky: řádek ",[1115,23943,23945],{"className":23944},[1573],[1575,23946,23947],{"xmlns":1577},[1579,23948,23949,23965],{},[1582,23950,23951,23953,23955,23957,23959,23961,23963],{},[1585,23952,1776],{},[1589,23954,1597],{},[1716,23956,1718],{},[1589,23958,1177],{"separator":1121},[1589,23960,2979],{},[1589,23962,1177],{"separator":1121},[1585,23964,1600],{},[1605,23966,23967],{"encoding":1607},"i = 1, \\dots, k"," je logická podskupina v pořadí, v jakém byla získána, sloupce obsahují ",[1115,23970,23972],{"className":23971},[1573],[1575,23973,23974],{"xmlns":1577},[1579,23975,23976,23980],{},[1582,23977,23978],{},[1585,23979,1781],{},[1605,23981,1781],{"encoding":1607}," naměřených hodnot a poslední dva sloupce ",[1115,23984,23986],{"className":23985},[1573],[1575,23987,23988],{"xmlns":1577},[1579,23989,23990,24002],{},[1582,23991,23992],{},[1746,23993,23994,24000],{},[3005,23995,23996,23998],{"accent":1121},[1585,23997,1158],{},[1589,23999,3408],{},[1585,24001,1776],{},[1605,24003,23804],{"encoding":1607},[1115,24005,24007],{"className":24006},[1573],[1575,24008,24009],{"xmlns":1577},[1579,24010,24011,24019],{},[1582,24012,24013],{},[1746,24014,24015,24017],{},[1585,24016,3376],{},[1585,24018,1776],{},[1605,24020,23823],{"encoding":1607},". Pro sestrojení diagramu je potřeba aspoň 20 podskupin. Nejprve se určí diagram ",[1115,24023,24025],{"className":24024},[1573],[1575,24026,24027],{"xmlns":1577},[1579,24028,24029,24033],{},[1582,24030,24031],{},[1585,24032,3376],{},[1605,24034,3376],{"encoding":1607},", potom diagram ",[1115,24037,24039],{"className":24038},[1573],[1575,24040,24041],{"xmlns":1577},[1579,24042,24043,24051],{},[1582,24044,24045],{},[3005,24046,24047,24049],{"accent":1121},[1585,24048,1158],{},[1589,24050,3408],{},[1605,24052,24053],{"encoding":1607},"\\bar{x}"," — u obou střední přímka a akční meze. V R se diagramy konstruují funkcí ",[1150,24056,3942],{},[1103,24058,24060,24067],{"className":24059,"dataCallout":6105},[1106,6104],[1110,24061,24063,24066],{"className":24062},[1113],[1115,24064],{"className":24065,"ariaHidden":1121},[1118,6112,1120],"Příklad: kontrola rozměru dílu ve 20 logických podskupinách",[1110,24068,24069,24070,24083,24084,1279,24102,24120,24121,2264],{},"Naměřená data znaku jakosti ",[1115,24071,24073],{"className":24072},[1573],[1575,24074,24075],{"xmlns":1577},[1579,24076,24077,24081],{},[1582,24078,24079],{},[1585,24080,1594],{},[1605,24082,1594],{"encoding":1607}," byla získána ve 20 logických podskupinách po 4 měřeních (",[1115,24085,24087],{"className":24086},[1573],[1575,24088,24089],{"xmlns":1577},[1579,24090,24091,24099],{},[1582,24092,24093,24095,24097],{},[1585,24094,1600],{},[1589,24096,1597],{},[1716,24098,6662],{},[1605,24100,24101],{"encoding":1607},"k=20",[1115,24103,24105],{"className":24104},[1573],[1575,24106,24107],{"xmlns":1577},[1579,24108,24109,24117],{},[1582,24110,24111,24113,24115],{},[1585,24112,1781],{},[1589,24114,1597],{},[1716,24116,6170],{},[1605,24118,24119],{"encoding":1607},"n=4","); znak je měřitelný a má normální rozdělení. Sestrojte regulační diagram ",[1115,24122,24124],{"className":24123},[1573],[1575,24125,24126],{"xmlns":1577},[1579,24127,24128,24144],{},[1582,24129,24130,24132,24138,24140,24142],{},[1589,24131,1170],{"stretchy":1591},[3005,24133,24134,24136],{"accent":1121},[1585,24135,1158],{},[1589,24137,3408],{},[1589,24139,1177],{"separator":1121},[1585,24141,3376],{},[1589,24143,1603],{"stretchy":1591},[1605,24145,23142],{"encoding":1607},[1310,24147,24148,24263],{},[1313,24149,24150],{},[1316,24151,24152,24167,24191,24215,24239],{},[1319,24153,24154],{},[1115,24155,24157],{"className":24156},[1573],[1575,24158,24159],{"xmlns":1577},[1579,24160,24161,24165],{},[1582,24162,24163],{},[1585,24164,1776],{},[1605,24166,1776],{"encoding":1607},[1319,24168,24169],{},[1115,24170,24172],{"className":24171},[1573],[1575,24173,24174],{"xmlns":1577},[1579,24175,24176,24188],{},[1582,24177,24178],{},[1746,24179,24180,24182],{},[1585,24181,1158],{},[1582,24183,24184,24186],{},[1585,24185,1776],{},[1716,24187,1718],{},[1605,24189,24190],{"encoding":1607},"x_{i1}",[1319,24192,24193],{},[1115,24194,24196],{"className":24195},[1573],[1575,24197,24198],{"xmlns":1577},[1579,24199,24200,24212],{},[1582,24201,24202],{},[1746,24203,24204,24206],{},[1585,24205,1158],{},[1582,24207,24208,24210],{},[1585,24209,1776],{},[1716,24211,1993],{},[1605,24213,24214],{"encoding":1607},"x_{i2}",[1319,24216,24217],{},[1115,24218,24220],{"className":24219},[1573],[1575,24221,24222],{"xmlns":1577},[1579,24223,24224,24236],{},[1582,24225,24226],{},[1746,24227,24228,24230],{},[1585,24229,1158],{},[1582,24231,24232,24234],{},[1585,24233,1776],{},[1716,24235,6220],{},[1605,24237,24238],{"encoding":1607},"x_{i3}",[1319,24240,24241],{},[1115,24242,24244],{"className":24243},[1573],[1575,24245,24246],{"xmlns":1577},[1579,24247,24248,24260],{},[1582,24249,24250],{},[1746,24251,24252,24254],{},[1585,24253,1158],{},[1582,24255,24256,24258],{},[1585,24257,1776],{},[1716,24259,6170],{},[1605,24261,24262],{"encoding":1607},"x_{i4}",[1332,24264,24265,24279,24294,24310,24325,24337,24351,24363,24376],{},[1316,24266,24267,24269,24272,24275,24277],{},[1337,24268,1718],{},[1337,24270,24271],{},"106",[1337,24273,24274],{},"98",[1337,24276,16591],{},[1337,24278,16591],{},[1316,24280,24281,24283,24286,24289,24292],{},[1337,24282,1993],{},[1337,24284,24285],{},"95",[1337,24287,24288],{},"94",[1337,24290,24291],{},"108",[1337,24293,8730],{},[1316,24295,24296,24298,24301,24304,24307],{},[1337,24297,6220],{},[1337,24299,24300],{},"122",[1337,24302,24303],{},"105",[1337,24305,24306],{},"103",[1337,24308,24309],{},"133",[1316,24311,24312,24314,24317,24319,24322],{},[1337,24313,6170],{},[1337,24315,24316],{},"113",[1337,24318,6192],{},[1337,24320,24321],{},"128",[1337,24323,24324],{},"135",[1316,24326,24327,24329,24331,24333,24335],{},[1337,24328,12470],{},[1337,24330,16591],{},[1337,24332,8730],{},[1337,24334,24306],{},[1337,24336,8730],{},[1316,24338,24339,24341,24343,24345,24348],{},[1337,24340,6581],{},[1337,24342,24274],{},[1337,24344,24306],{},[1337,24346,24347],{},"97",[1337,24349,24350],{},"99",[1316,24352,24353,24355,24357,24359,24361],{},[1337,24354,2979],{},[1337,24356,2979],{},[1337,24358,2979],{},[1337,24360,2979],{},[1337,24362,2979],{},[1316,24364,24365,24367,24369,24371,24374],{},[1337,24366,17225],{},[1337,24368,24321],{},[1337,24370,24309],{},[1337,24372,24373],{},"120",[1337,24375,17253],{},[1316,24377,24378,24380,24382,24384,24386],{},[1337,24379,6662],{},[1337,24381,24274],{},[1337,24383,24306],{},[1337,24385,24347],{},[1337,24387,24350],{},[1110,24389,24390,24391,24412,24413,4595],{},"Pro každou podskupinu se dopočítá výběrový průměr ",[1115,24392,24394],{"className":24393},[1573],[1575,24395,24396],{"xmlns":1577},[1579,24397,24398,24410],{},[1582,24399,24400],{},[1746,24401,24402,24408],{},[3005,24403,24404,24406],{"accent":1121},[1585,24405,1158],{},[1589,24407,3408],{},[1585,24409,1776],{},[1605,24411,23804],{"encoding":1607}," a rozpětí ",[1115,24414,24416],{"className":24415},[1573],[1575,24417,24418],{"xmlns":1577},[1579,24419,24420,24428],{},[1582,24421,24422],{},[1746,24423,24424,24426],{},[1585,24425,3376],{},[1585,24427,1776],{},[1605,24429,23823],{"encoding":1607},[1310,24431,24432,24493],{},[1313,24433,24434],{},[1316,24435,24436,24451,24474],{},[1319,24437,24438],{},[1115,24439,24441],{"className":24440},[1573],[1575,24442,24443],{"xmlns":1577},[1579,24444,24445,24449],{},[1582,24446,24447],{},[1585,24448,1776],{},[1605,24450,1776],{"encoding":1607},[1319,24452,24453],{},[1115,24454,24456],{"className":24455},[1573],[1575,24457,24458],{"xmlns":1577},[1579,24459,24460,24472],{},[1582,24461,24462],{},[1746,24463,24464,24470],{},[3005,24465,24466,24468],{"accent":1121},[1585,24467,1158],{},[1589,24469,3408],{},[1585,24471,1776],{},[1605,24473,23804],{"encoding":1607},[1319,24475,24476],{},[1115,24477,24479],{"className":24478},[1573],[1575,24480,24481],{"xmlns":1577},[1579,24482,24483,24491],{},[1582,24484,24485],{},[1746,24486,24487,24489],{},[1585,24488,3376],{},[1585,24490,1776],{},[1605,24492,23823],{"encoding":1607},[1332,24494,24495,24504,24514,24524,24534,24543,24552,24560,24569],{},[1316,24496,24497,24499,24502],{},[1337,24498,1718],{},[1337,24500,24501],{},"101,50",[1337,24503,17320],{},[1316,24505,24506,24508,24511],{},[1337,24507,1993],{},[1337,24509,24510],{},"97,25",[1337,24512,24513],{},"16",[1316,24515,24516,24518,24521],{},[1337,24517,6220],{},[1337,24519,24520],{},"115,75",[1337,24522,24523],{},"30",[1316,24525,24526,24528,24531],{},[1337,24527,6170],{},[1337,24529,24530],{},"111,75",[1337,24532,24533],{},"64",[1316,24535,24536,24538,24541],{},[1337,24537,12470],{},[1337,24539,24540],{},"97,00",[1337,24542,4890],{},[1316,24544,24545,24547,24550],{},[1337,24546,6581],{},[1337,24548,24549],{},"99,25",[1337,24551,6581],{},[1316,24553,24554,24556,24558],{},[1337,24555,2979],{},[1337,24557,2979],{},[1337,24559,2979],{},[1316,24561,24562,24564,24567],{},[1337,24563,17225],{},[1337,24565,24566],{},"126,50",[1337,24568,6173],{},[1316,24570,24571,24573,24575],{},[1337,24572,6662],{},[1337,24574,24549],{},[1337,24576,6581],{},[1110,24578,24579,24580,24593,24594,1279,24621,1279,24650,24678,24679,24701,24702,1279,24729,1279,24758,24785,24786,2264],{},"Nejprve se posoudí diagram ",[1115,24581,24583],{"className":24582},[1573],[1575,24584,24585],{"xmlns":1577},[1579,24586,24587,24591],{},[1582,24588,24589],{},[1585,24590,3376],{},[1605,24592,3376],{"encoding":1607}," na všech 20 podskupinách: ",[1115,24595,24597],{"className":24596},[1573],[1575,24598,24599],{"xmlns":1577},[1579,24600,24601,24618],{},[1582,24602,24603,24605,24607,24609,24611,24613,24615],{},[1585,24604,3627],{},[1585,24606,4002],{},[1589,24608,1170],{"stretchy":1591},[1585,24610,3376],{},[1589,24612,1603],{"stretchy":1591},[1589,24614,1597],{},[1716,24616,24617],{},"15,8",[1605,24619,24620],{"encoding":1607},"CL(R)=15{,}8",[1115,24622,24624],{"className":24623},[1573],[1575,24625,24626],{"xmlns":1577},[1579,24627,24628,24647],{},[1582,24629,24630,24632,24634,24636,24638,24640,24642,24644],{},[1585,24631,4013],{},[1585,24633,3627],{},[1585,24635,4002],{},[1589,24637,1170],{"stretchy":1591},[1585,24639,3376],{},[1589,24641,1603],{"stretchy":1591},[1589,24643,1597],{},[1716,24645,24646],{},"36,06",[1605,24648,24649],{"encoding":1607},"UCL(R)=36{,}06",[1115,24651,24653],{"className":24652},[1573],[1575,24654,24655],{"xmlns":1577},[1579,24656,24657,24675],{},[1582,24658,24659,24661,24663,24665,24667,24669,24671,24673],{},[1585,24660,4002],{},[1585,24662,3627],{},[1585,24664,4002],{},[1589,24666,1170],{"stretchy":1591},[1585,24668,3376],{},[1589,24670,1603],{"stretchy":1591},[1589,24672,1597],{},[1716,24674,2398],{},[1605,24676,24677],{"encoding":1607},"LCL(R)=0",". Rozpětí čtvrté podskupiny (",[1115,24680,24682],{"className":24681},[1573],[1575,24683,24684],{"xmlns":1577},[1579,24685,24686,24698],{},[1582,24687,24688,24694,24696],{},[1746,24689,24690,24692],{},[1585,24691,3376],{},[1716,24693,6170],{},[1589,24695,1597],{},[1716,24697,24533],{},[1605,24699,24700],{"encoding":1607},"R_4=64",") mez překračuje; po potvrzení vymezitelné příčiny se podskupina 4 z výpočtu vyřadí a meze se přepočítají — ",[1115,24703,24705],{"className":24704},[1573],[1575,24706,24707],{"xmlns":1577},[1579,24708,24709,24726],{},[1582,24710,24711,24713,24715,24717,24719,24721,24723],{},[1585,24712,3627],{},[1585,24714,4002],{},[1589,24716,1170],{"stretchy":1591},[1585,24718,3376],{},[1589,24720,1603],{"stretchy":1591},[1589,24722,1597],{},[1716,24724,24725],{},"13,26",[1605,24727,24728],{"encoding":1607},"CL(R)=13{,}26",[1115,24730,24732],{"className":24731},[1573],[1575,24733,24734],{"xmlns":1577},[1579,24735,24736,24755],{},[1582,24737,24738,24740,24742,24744,24746,24748,24750,24752],{},[1585,24739,4013],{},[1585,24741,3627],{},[1585,24743,4002],{},[1589,24745,1170],{"stretchy":1591},[1585,24747,3376],{},[1589,24749,1603],{"stretchy":1591},[1589,24751,1597],{},[1716,24753,24754],{},"30,27",[1605,24756,24757],{"encoding":1607},"UCL(R)=30{,}27",[1115,24759,24761],{"className":24760},[1573],[1575,24762,24763],{"xmlns":1577},[1579,24764,24765,24783],{},[1582,24766,24767,24769,24771,24773,24775,24777,24779,24781],{},[1585,24768,4002],{},[1585,24770,3627],{},[1585,24772,4002],{},[1589,24774,1170],{"stretchy":1591},[1585,24776,3376],{},[1589,24778,1603],{"stretchy":1591},[1589,24780,1597],{},[1716,24782,2398],{},[1605,24784,24677],{"encoding":1607},". Diagram rozpětí je teď zvládnutý, lze tedy posoudit diagram ",[1115,24787,24789],{"className":24788},[1573],[1575,24790,24791],{"xmlns":1577},[1579,24792,24793,24801],{},[1582,24794,24795],{},[3005,24796,24797,24799],{"accent":1121},[1585,24798,1158],{},[1589,24800,3408],{},[1605,24802,24053],{"encoding":1607},[1110,24804,23754,24805,24822,24823,1279,24854,1279,24887,24920,24921,24934,24935,1279,24962,1279,24991,25018],{},[1115,24806,24808],{"className":24807},[1573],[1575,24809,24810],{"xmlns":1577},[1579,24811,24812,24820],{},[1582,24813,24814],{},[3005,24815,24816,24818],{"accent":1121},[1585,24817,1158],{},[1589,24819,3408],{},[1605,24821,24053],{"encoding":1607}," bez čtvrté podskupiny dává ",[1115,24824,24826],{"className":24825},[1573],[1575,24827,24828],{"xmlns":1577},[1579,24829,24830,24851],{},[1582,24831,24832,24834,24836,24838,24844,24846,24848],{},[1585,24833,3627],{},[1585,24835,4002],{},[1589,24837,1170],{"stretchy":1591},[3005,24839,24840,24842],{"accent":1121},[1585,24841,1158],{},[1589,24843,3408],{},[1589,24845,1603],{"stretchy":1591},[1589,24847,1597],{},[1716,24849,24850],{},"102,01",[1605,24852,24853],{"encoding":1607},"CL(\\bar{x})=102{,}01",[1115,24855,24857],{"className":24856},[1573],[1575,24858,24859],{"xmlns":1577},[1579,24860,24861,24884],{},[1582,24862,24863,24865,24867,24869,24871,24877,24879,24881],{},[1585,24864,4013],{},[1585,24866,3627],{},[1585,24868,4002],{},[1589,24870,1170],{"stretchy":1591},[3005,24872,24873,24875],{"accent":1121},[1585,24874,1158],{},[1589,24876,3408],{},[1589,24878,1603],{"stretchy":1591},[1589,24880,1597],{},[1716,24882,24883],{},"111,68",[1605,24885,24886],{"encoding":1607},"UCL(\\bar{x})=111{,}68",[1115,24888,24890],{"className":24889},[1573],[1575,24891,24892],{"xmlns":1577},[1579,24893,24894,24917],{},[1582,24895,24896,24898,24900,24902,24904,24910,24912,24914],{},[1585,24897,4002],{},[1585,24899,3627],{},[1585,24901,4002],{},[1589,24903,1170],{"stretchy":1591},[3005,24905,24906,24908],{"accent":1121},[1585,24907,1158],{},[1589,24909,3408],{},[1589,24911,1603],{"stretchy":1591},[1589,24913,1597],{},[1716,24915,24916],{},"92,34",[1605,24918,24919],{"encoding":1607},"LCL(\\bar{x})=92{,}34",". Mez teď překračují průměry podskupin 3 a 19. Po potvrzení vymezitelné příčiny se vyřadí obě najednou a meze diagramu ",[1115,24922,24924],{"className":24923},[1573],[1575,24925,24926],{"xmlns":1577},[1579,24927,24928,24932],{},[1582,24929,24930],{},[1585,24931,3376],{},[1605,24933,3376],{"encoding":1607}," se přepočítají bez podskupin 3, 4 a 19: ",[1115,24936,24938],{"className":24937},[1573],[1575,24939,24940],{"xmlns":1577},[1579,24941,24942,24959],{},[1582,24943,24944,24946,24948,24950,24952,24954,24956],{},[1585,24945,3627],{},[1585,24947,4002],{},[1589,24949,1170],{"stretchy":1591},[1585,24951,3376],{},[1589,24953,1603],{"stretchy":1591},[1589,24955,1597],{},[1716,24957,24958],{},"12,29",[1605,24960,24961],{"encoding":1607},"CL(R)=12{,}29",[1115,24963,24965],{"className":24964},[1573],[1575,24966,24967],{"xmlns":1577},[1579,24968,24969,24988],{},[1582,24970,24971,24973,24975,24977,24979,24981,24983,24985],{},[1585,24972,4013],{},[1585,24974,3627],{},[1585,24976,4002],{},[1589,24978,1170],{"stretchy":1591},[1585,24980,3376],{},[1589,24982,1603],{"stretchy":1591},[1589,24984,1597],{},[1716,24986,24987],{},"28,06",[1605,24989,24990],{"encoding":1607},"UCL(R)=28{,}06",[1115,24992,24994],{"className":24993},[1573],[1575,24995,24996],{"xmlns":1577},[1579,24997,24998,25016],{},[1582,24999,25000,25002,25004,25006,25008,25010,25012,25014],{},[1585,25001,4002],{},[1585,25003,3627],{},[1585,25005,4002],{},[1589,25007,1170],{"stretchy":1591},[1585,25009,3376],{},[1589,25011,1603],{"stretchy":1591},[1589,25013,1597],{},[1716,25015,2398],{},[1605,25017,24677],{"encoding":1607}," — žádná z 17 zbývajících podskupin mez nepřekračuje.",[1110,25020,25021,25022,25039,25040,1279,25071,1279,25104,25137],{},"Konečný diagram ",[1115,25023,25025],{"className":25024},[1573],[1575,25026,25027],{"xmlns":1577},[1579,25028,25029,25037],{},[1582,25030,25031],{},[3005,25032,25033,25035],{"accent":1121},[1585,25034,1158],{},[1589,25036,3408],{},[1605,25038,24053],{"encoding":1607}," na stejných 17 podskupinách má ",[1115,25041,25043],{"className":25042},[1573],[1575,25044,25045],{"xmlns":1577},[1579,25046,25047,25068],{},[1582,25048,25049,25051,25053,25055,25061,25063,25065],{},[1585,25050,3627],{},[1585,25052,4002],{},[1589,25054,1170],{"stretchy":1591},[3005,25056,25057,25059],{"accent":1121},[1585,25058,1158],{},[1589,25060,3408],{},[1589,25062,1603],{"stretchy":1591},[1589,25064,1597],{},[1716,25066,25067],{},"99,76",[1605,25069,25070],{"encoding":1607},"CL(\\bar{x})=99{,}76",[1115,25072,25074],{"className":25073},[1573],[1575,25075,25076],{"xmlns":1577},[1579,25077,25078,25101],{},[1582,25079,25080,25082,25084,25086,25088,25094,25096,25098],{},[1585,25081,4013],{},[1585,25083,3627],{},[1585,25085,4002],{},[1589,25087,1170],{"stretchy":1591},[3005,25089,25090,25092],{"accent":1121},[1585,25091,1158],{},[1589,25093,3408],{},[1589,25095,1603],{"stretchy":1591},[1589,25097,1597],{},[1716,25099,25100],{},"108,73",[1605,25102,25103],{"encoding":1607},"UCL(\\bar{x})=108{,}73",[1115,25105,25107],{"className":25106},[1573],[1575,25108,25109],{"xmlns":1577},[1579,25110,25111,25134],{},[1582,25112,25113,25115,25117,25119,25121,25127,25129,25131],{},[1585,25114,4002],{},[1585,25116,3627],{},[1585,25118,4002],{},[1589,25120,1170],{"stretchy":1591},[3005,25122,25123,25125],{"accent":1121},[1585,25124,1158],{},[1589,25126,3408],{},[1589,25128,1603],{"stretchy":1591},[1589,25130,1597],{},[1716,25132,25133],{},"90,80",[1605,25135,25136],{"encoding":1607},"LCL(\\bar{x})=90{,}80"," — všechny výběrové průměry leží uvnitř mezí, proces je zvládnutý. Protože bylo vyřazeno několik podskupin, je vhodné měření doplnit tak, aby se pracovalo s počtem podskupin mezi 20 a 25.",[1110,25139,25140],{},[1303,25141],{"alt":25142,"className":25143,"src":25144},"mask-rd-priklad1-meze",[1130,1307],"\u002Fwiki-assets\u002Fmask-rd-priklad1-meze.png",[1110,25146,25147,25148,25150,25151,25153],{},"V R se diagramy sestrojí funkcí ",[1150,25149,3942],{}," z balíčku ",[1150,25152,360],{},". Data jsou tabulka, v níž řádek odpovídá logické podskupině a sloupce jednotlivým měřením:",[1144,25155,25157],{"className":1146,"code":25156,"language":71,"meta":1148,"style":1148},"library(qcc)\ndata \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"R\")      # diagram R\nqcc(data, type = \"xbar\")   # diagram x̄\n",[1150,25158,25159,25169,25192,25215],{"__ignoreMap":1148},[1115,25160,25161,25163,25165,25167],{"class":1154,"line":10},[1115,25162,19892],{"class":1161},[1115,25164,1170],{"class":1169},[1115,25166,360],{"class":1157},[1115,25168,6519],{"class":1169},[1115,25170,25171,25173,25175,25177,25179,25182,25184,25186,25188,25190],{"class":1154,"line":27},[1115,25172,3381],{"class":1157},[1115,25174,1162],{"class":1161},[1115,25176,22606],{"class":1165},[1115,25178,1170],{"class":1169},[1115,25180,25181],{"class":6458},"\"3_2.txt\"",[1115,25183,1177],{"class":1161},[1115,25185,22616],{"class":1157},[1115,25187,6416],{"class":1161},[1115,25189,6429],{"class":1173},[1115,25191,6519],{"class":1169},[1115,25193,25194,25196,25198,25200,25202,25204,25206,25209,25212],{"class":1154,"line":148},[1115,25195,360],{"class":1165},[1115,25197,1170],{"class":1169},[1115,25199,3381],{"class":1157},[1115,25201,1177],{"class":1161},[1115,25203,14734],{"class":1157},[1115,25205,6416],{"class":1161},[1115,25207,25208],{"class":6458}," \"R\"",[1115,25210,25211],{"class":1169},")      ",[1115,25213,25214],{"class":1222},"# diagram R\n",[1115,25216,25217,25219,25221,25223,25225,25227,25229,25232,25234],{"class":1154,"line":111},[1115,25218,360],{"class":1165},[1115,25220,1170],{"class":1169},[1115,25222,3381],{"class":1157},[1115,25224,1177],{"class":1161},[1115,25226,14734],{"class":1157},[1115,25228,6416],{"class":1161},[1115,25230,25231],{"class":6458}," \"xbar\"",[1115,25233,1219],{"class":1169},[1115,25235,25236],{"class":1222},"# diagram x̄\n",[1110,25238,25239,25240,25243],{},"Funkce vykreslí diagram se střední přímkou a akčními mezemi a body mimo meze zvýrazní. Podskupina s potvrzenou vymezitelnou příčinou se vyřadí z dat (například ",[1150,25241,25242],{},"data[-4, ]",") a diagram se sestrojí znovu.",[1550,25245,23754,25247],{"id":25246},"diagram-xˉsbarx-s",[1115,25248,25250],{"className":25249},[1573],[1575,25251,25252],{"xmlns":1577},[1579,25253,25254,25270],{},[1582,25255,25256,25258,25264,25266,25268],{},[1589,25257,1170],{"stretchy":1591},[3005,25259,25260,25262],{"accent":1121},[1585,25261,1158],{},[1589,25263,3408],{},[1589,25265,1177],{"separator":1121},[1585,25267,3433],{},[1589,25269,1603],{"stretchy":1591},[1605,25271,23168],{"encoding":1607},[1110,25273,23782,25274,25295,25296,25314,25315,25340],{},[1115,25275,25277],{"className":25276},[1573],[1575,25278,25279],{"xmlns":1577},[1579,25280,25281,25293],{},[1582,25282,25283],{},[1746,25284,25285,25291],{},[3005,25286,25287,25289],{"accent":1121},[1585,25288,1158],{},[1589,25290,3408],{},[1585,25292,1776],{},[1605,25294,23804],{"encoding":1607}," a výběrové směrodatné odchylky ",[1115,25297,25299],{"className":25298},[1573],[1575,25300,25301],{"xmlns":1577},[1579,25302,25303,25311],{},[1582,25304,25305],{},[1746,25306,25307,25309],{},[1585,25308,3433],{},[1585,25310,1776],{},[1605,25312,25313],{"encoding":1607},"s_i"," v logických podskupinách. Podmínky použití jsou stejné jako u ",[1115,25316,25318],{"className":25317},[1573],[1575,25319,25320],{"xmlns":1577},[1579,25321,25322,25338],{},[1582,25323,25324,25326,25332,25334,25336],{},[1589,25325,1170],{"stretchy":1591},[3005,25327,25328,25330],{"accent":1121},[1585,25329,1158],{},[1589,25331,3408],{},[1589,25333,1177],{"separator":1121},[1585,25335,3376],{},[1589,25337,1603],{"stretchy":1591},[1605,25339,23142],{"encoding":1607},", logické podskupiny ale sestávají z většího počtu měření. Data se zapisují do obdobné tabulky.",[1144,25342,25344],{"className":1146,"code":25343,"language":71,"meta":1148,"style":1148},"data \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"S\")      # diagram s\nqcc(data, type = \"xbar\")   # diagram x̄\n",[1150,25345,25346,25368,25390],{"__ignoreMap":1148},[1115,25347,25348,25350,25352,25354,25356,25358,25360,25362,25364,25366],{"class":1154,"line":10},[1115,25349,3381],{"class":1157},[1115,25351,1162],{"class":1161},[1115,25353,22606],{"class":1165},[1115,25355,1170],{"class":1169},[1115,25357,25181],{"class":6458},[1115,25359,1177],{"class":1161},[1115,25361,22616],{"class":1157},[1115,25363,6416],{"class":1161},[1115,25365,6429],{"class":1173},[1115,25367,6519],{"class":1169},[1115,25369,25370,25372,25374,25376,25378,25380,25382,25385,25387],{"class":1154,"line":27},[1115,25371,360],{"class":1165},[1115,25373,1170],{"class":1169},[1115,25375,3381],{"class":1157},[1115,25377,1177],{"class":1161},[1115,25379,14734],{"class":1157},[1115,25381,6416],{"class":1161},[1115,25383,25384],{"class":6458}," \"S\"",[1115,25386,25211],{"class":1169},[1115,25388,25389],{"class":1222},"# diagram s\n",[1115,25391,25392,25394,25396,25398,25400,25402,25404,25406,25408],{"class":1154,"line":148},[1115,25393,360],{"class":1165},[1115,25395,1170],{"class":1169},[1115,25397,3381],{"class":1157},[1115,25399,1177],{"class":1161},[1115,25401,14734],{"class":1157},[1115,25403,6416],{"class":1161},[1115,25405,25231],{"class":6458},[1115,25407,1219],{"class":1169},[1115,25409,25236],{"class":1222},[1550,25411,23754,25413],{"id":25412},"diagram-xirklix_i-r_kli",[1115,25414,25416],{"className":25415},[1573],[1575,25417,25418],{"xmlns":1577},[1579,25419,25420,25448],{},[1582,25421,25422,25424,25430,25432,25446],{},[1589,25423,1170],{"stretchy":1591},[1746,25425,25426,25428],{},[1585,25427,1158],{},[1585,25429,1776],{},[1589,25431,1177],{"separator":1121},[1746,25433,25434,25436],{},[1585,25435,3376],{},[1582,25437,25438,25440,25442,25444],{},[1585,25439,1600],{},[1585,25441,23198],{},[1589,25443,1177],{"separator":1121},[1585,25445,1776],{},[1589,25447,1603],{"stretchy":1591},[1605,25449,23207],{"encoding":1607},[1110,25451,25452,25453,25478,25479,4595],{},"Používá se za stejných podmínek jako ",[1115,25454,25456],{"className":25455},[1573],[1575,25457,25458],{"xmlns":1577},[1579,25459,25460,25476],{},[1582,25461,25462,25464,25470,25472,25474],{},[1589,25463,1170],{"stretchy":1591},[3005,25465,25466,25468],{"accent":1121},[1585,25467,1158],{},[1589,25469,3408],{},[1589,25471,1177],{"separator":1121},[1585,25473,3376],{},[1589,25475,1603],{"stretchy":1591},[1605,25477,23142],{"encoding":1607},", ale v každé logické podskupině se provede jen jedno měření — například proto, že náklady na kontrolu jsou vysoké nebo kontrola trvá dlouho. Charakteristikou rozptylu je pak ",[2227,25480,25481],{},"klouzavé rozpětí",[1115,25483,25485],{"className":25484},[1573],[1575,25486,25487],{"xmlns":1577,"display":4601},[1579,25488,25489,25616],{},[1582,25490,25491,25505,25507,25510,25516,25518,25530,25532,25534,25536,25538,25540,25542,25544,25546,25548,25550,25552,25554,25556,25558,25572,25574,25586,25600,25614],{},[1746,25492,25493,25495],{},[1585,25494,3376],{},[1582,25496,25497,25499,25501,25503],{},[1585,25498,1600],{},[1585,25500,23198],{},[1589,25502,1177],{"separator":1121},[1585,25504,1776],{},[1589,25506,1597],{},[1585,25508,25509],{"mathvariant":4022},"∣",[1746,25511,25512,25514],{},[1585,25513,1158],{},[1585,25515,1776],{},[1589,25517,1721],{},[1746,25519,25520,25522],{},[1585,25521,1158],{},[1582,25523,25524,25526,25528],{},[1585,25525,1776],{},[1589,25527,1721],{},[1716,25529,1718],{},[1585,25531,25509],{"mathvariant":4022},[1589,25533,1177],{"separator":1121},[4648,25535],{"width":20513},[1585,25537,1776],{},[1589,25539,1597],{},[1716,25541,1993],{},[1589,25543,1177],{"separator":1121},[1716,25545,6220],{},[1589,25547,1177],{"separator":1121},[1589,25549,2979],{},[1589,25551,1177],{"separator":1121},[1585,25553,1600],{},[1589,25555,1177],{"separator":1121},[4648,25557],{"width":4650},[1746,25559,25560,25566],{},[3005,25561,25562,25564],{"accent":1121},[1585,25563,3376],{},[1589,25565,3408],{},[1582,25567,25568,25570],{},[1585,25569,1600],{},[1585,25571,23198],{},[1589,25573,1597],{},[5373,25575,25576,25578],{},[1716,25577,1718],{},[1582,25579,25580,25582,25584],{},[1585,25581,1600],{},[1589,25583,1721],{},[1716,25585,1718],{},[4620,25587,25588,25590,25598],{},[1589,25589,4624],{},[1582,25591,25592,25594,25596],{},[1585,25593,1776],{},[1589,25595,1597],{},[1716,25597,1993],{},[1585,25599,1600],{},[1746,25601,25602,25604],{},[1585,25603,3376],{},[1582,25605,25606,25608,25610,25612],{},[1585,25607,1600],{},[1585,25609,23198],{},[1589,25611,1177],{"separator":1121},[1585,25613,1776],{},[1585,25615,2264],{"mathvariant":4022},[1605,25617,25618],{"encoding":1607},"R_{kl,i} = |x_i - x_{i-1}|, \\quad i = 2, 3, \\dots, k, \\qquad \\bar{R}_{kl} = \\frac{1}{k-1}\\sum_{i=2}^k R_{kl,i}.",[1110,25620,25621,25622,1260,25639,25665,25666,25691,25692,25709],{},"Regulované veličiny jsou hodnoty ",[1115,25623,25625],{"className":25624},[1573],[1575,25626,25627],{"xmlns":1577},[1579,25628,25629,25637],{},[1582,25630,25631],{},[1746,25632,25633,25635],{},[1585,25634,1158],{},[1585,25636,1776],{},[1605,25638,3035],{"encoding":1607},[1115,25640,25642],{"className":25641},[1573],[1575,25643,25644],{"xmlns":1577},[1579,25645,25646,25662],{},[1582,25647,25648],{},[1746,25649,25650,25652],{},[1585,25651,3376],{},[1582,25653,25654,25656,25658,25660],{},[1585,25655,1600],{},[1585,25657,23198],{},[1589,25659,1177],{"separator":1121},[1585,25661,1776],{},[1605,25663,25664],{"encoding":1607},"R_{kl,i}","; nejdříve se určí střední přímka a meze diagramu ",[1115,25667,25669],{"className":25668},[1573],[1575,25670,25671],{"xmlns":1577},[1579,25672,25673,25689],{},[1582,25674,25675],{},[1746,25676,25677,25679],{},[1585,25678,3376],{},[1582,25680,25681,25683,25685,25687],{},[1585,25682,1600],{},[1585,25684,23198],{},[1589,25686,1177],{"separator":1121},[1585,25688,1776],{},[1605,25690,25664],{"encoding":1607},", potom diagramu ",[1115,25693,25695],{"className":25694},[1573],[1575,25696,25697],{"xmlns":1577},[1579,25698,25699,25707],{},[1582,25700,25701],{},[1746,25702,25703,25705],{},[1585,25704,1158],{},[1585,25706,1776],{},[1605,25708,3035],{"encoding":1607},". Data jsou jeden vektor naměřených hodnot:",[1144,25711,25713],{"className":1146,"code":25712,"language":71,"meta":1148,"style":1148},"data \u003C- read.table(\"3_3.txt\", header = TRUE)\nqcc(data[, 1], type = \"xbar.one\")\n",[1150,25714,25715,25738],{"__ignoreMap":1148},[1115,25716,25717,25719,25721,25723,25725,25728,25730,25732,25734,25736],{"class":1154,"line":10},[1115,25718,3381],{"class":1157},[1115,25720,1162],{"class":1161},[1115,25722,22606],{"class":1165},[1115,25724,1170],{"class":1169},[1115,25726,25727],{"class":6458},"\"3_3.txt\"",[1115,25729,1177],{"class":1161},[1115,25731,22616],{"class":1157},[1115,25733,6416],{"class":1161},[1115,25735,6429],{"class":1173},[1115,25737,6519],{"class":1169},[1115,25739,25740,25742,25744,25746,25748,25750,25752,25754,25756,25758,25760,25763],{"class":1154,"line":27},[1115,25741,360],{"class":1165},[1115,25743,1170],{"class":1169},[1115,25745,3381],{"class":1157},[1115,25747,10756],{"class":1169},[1115,25749,1177],{"class":1161},[1115,25751,7253],{"class":1173},[1115,25753,10773],{"class":1169},[1115,25755,1177],{"class":1161},[1115,25757,14734],{"class":1157},[1115,25759,6416],{"class":1161},[1115,25761,25762],{"class":6458}," \"xbar.one\"",[1115,25764,6519],{"class":1169},[1136,25766,25768],{"id":25767},"regulace-srovnáváním","Regulace srovnáváním",[1110,25770,25771],{},"Diagramy pro regulaci srovnáváním se používají, sledují-li se počty neshodných produktů nebo počty neshod na produktech — regulovaná veličina je diskrétní náhodná veličina.",[1310,25773,25774,25787],{},[1313,25775,25776],{},[1316,25777,25778,25781,25784],{},[1319,25779,25780],{},"Sleduje se",[1319,25782,25783],{},"Konstantní rozsah podskupin",[1319,25785,25786],{},"Nekonstantní rozsah podskupin",[1332,25788,25789,25824],{},[1316,25790,25791,25794,25809],{},[1337,25792,25793],{},"počet neshod na produktech (např. vady na stejných tabulích skla)",[1337,25795,25796],{},[1115,25797,25799],{"className":25798},[1573],[1575,25800,25801],{"xmlns":1577},[1579,25802,25803,25807],{},[1582,25804,25805],{},[1585,25806,3499],{},[1605,25808,3499],{"encoding":1607},[1337,25810,25811],{},[1115,25812,25814],{"className":25813},[1573],[1575,25815,25816],{"xmlns":1577},[1579,25817,25818,25822],{},[1582,25819,25820],{},[1585,25821,3523],{},[1605,25823,3523],{"encoding":1607},[1316,25825,25826,25829,25846],{},[1337,25827,25828],{},"počet neshodných produktů ve výběru (např. neshodné kusy ze série na výrobní lince)",[1337,25830,25831],{},[1115,25832,25834],{"className":25833},[1573],[1575,25835,25836],{"xmlns":1577},[1579,25837,25838,25844],{},[1582,25839,25840,25842],{},[1585,25841,1781],{},[1585,25843,1110],{},[1605,25845,3555],{"encoding":1607},[1337,25847,25848],{},[1115,25849,25851],{"className":25850},[1573],[1575,25852,25853],{"xmlns":1577},[1579,25854,25855,25859],{},[1582,25856,25857],{},[1585,25858,1110],{},[1605,25860,1110],{"encoding":1607},[1550,25862,23754,25864],{"id":25863},"diagram-cc",[1115,25865,25867],{"className":25866},[1573],[1575,25868,25869],{"xmlns":1577},[1579,25870,25871,25875],{},[1582,25872,25873],{},[1585,25874,3499],{},[1605,25876,3499],{"encoding":1607},[1110,25878,25879,25880,25898,25899,25912,25913,25938,25939,25952],{},"Regulovanou veličinou ",[1115,25881,25883],{"className":25882},[1573],[1575,25884,25885],{"xmlns":1577},[1579,25886,25887,25895],{},[1582,25888,25889],{},[1746,25890,25891,25893],{},[1585,25892,3499],{},[1585,25894,1776],{},[1605,25896,25897],{"encoding":1607},"c_i"," je počet neshod na produktech v ",[1115,25900,25902],{"className":25901},[1573],[1575,25903,25904],{"xmlns":1577},[1579,25905,25906,25910],{},[1582,25907,25908],{},[1585,25909,1776],{},[1605,25911,1776],{"encoding":1607},"-té logické podskupině, ",[1115,25914,25916],{"className":25915},[1573],[1575,25917,25918],{"xmlns":1577},[1579,25919,25920,25936],{},[1582,25921,25922,25924,25926,25928,25930,25932,25934],{},[1585,25923,1776],{},[1589,25925,1597],{},[1716,25927,1718],{},[1589,25929,1177],{"separator":1121},[1589,25931,2979],{},[1589,25933,1177],{"separator":1121},[1585,25935,1600],{},[1605,25937,23967],{"encoding":1607},"; v každé podskupině je stejný počet ",[1115,25940,25942],{"className":25941},[1573],[1575,25943,25944],{"xmlns":1577},[1579,25945,25946,25950],{},[1582,25947,25948],{},[1585,25949,1781],{},[1605,25951,1781],{"encoding":1607}," produktů. Počet neshod má Poissonovo rozdělení, pokud může být počet neshod na produktu teoreticky neohraničený a pravděpodobnost více než jedné neshody v určitém místě produktu je zanedbatelná.",[1103,25954,25956,25963],{"className":25955,"dataCallout":6105},[1106,6104],[1110,25957,25959,25962],{"className":25958},[1113],[1115,25960],{"className":25961,"ariaHidden":1121},[1118,6112,1120],"Příklad: bodové vady na pásech látky",[1110,25964,25965,25966,25983,25984,2264],{},"Při tkaní látek se zjišťuje počet bodových vad na pásech dlouhých 100 metrů. Pro 20 pásů v pořadí, v jakém byly vybrány, jsou dány počty vad ",[1115,25967,25969],{"className":25968},[1573],[1575,25970,25971],{"xmlns":1577},[1579,25972,25973,25981],{},[1582,25974,25975],{},[1746,25976,25977,25979],{},[1585,25978,3499],{},[1585,25980,1776],{},[1605,25982,25897],{"encoding":1607},". Sestrojte regulační diagram ",[1115,25985,25987],{"className":25986},[1573],[1575,25988,25989],{"xmlns":1577},[1579,25990,25991,25995],{},[1582,25992,25993],{},[1585,25994,3499],{},[1605,25996,3499],{"encoding":1607},[1144,25998,26000],{"className":1146,"code":25999,"language":71,"meta":1148,"style":1148},"c_i \u003C- c(7, 1, 2, 5, 0, 6, 2, 0, 4, 4, 6, 3, 3, 3, 1, 6, 3, 1, 5, 6)\n\nq_c \u003C- qcc(c_i, type = \"c\")\nsummary(q_c)\n",[1150,26001,26002,26092,26096,26121],{"__ignoreMap":1148},[1115,26003,26004,26006,26008,26010,26012,26014,26016,26018,26020,26022,26024,26026,26028,26030,26032,26034,26036,26038,26040,26042,26044,26046,26048,26050,26052,26054,26056,26058,26060,26062,26064,26066,26068,26070,26072,26074,26076,26078,26080,26082,26084,26086,26088,26090],{"class":1154,"line":10},[1115,26005,25897],{"class":1157},[1115,26007,1162],{"class":1161},[1115,26009,1166],{"class":1165},[1115,26011,1170],{"class":1169},[1115,26013,3905],{"class":1173},[1115,26015,1177],{"class":1161},[1115,26017,7253],{"class":1173},[1115,26019,1177],{"class":1161},[1115,26021,6797],{"class":1173},[1115,26023,1177],{"class":1161},[1115,26025,12538],{"class":1173},[1115,26027,1177],{"class":1161},[1115,26029,12514],{"class":1173},[1115,26031,1177],{"class":1161},[1115,26033,14739],{"class":1173},[1115,26035,1177],{"class":1161},[1115,26037,6797],{"class":1173},[1115,26039,1177],{"class":1161},[1115,26041,12514],{"class":1173},[1115,26043,1177],{"class":1161},[1115,26045,6419],{"class":1173},[1115,26047,1177],{"class":1161},[1115,26049,6419],{"class":1173},[1115,26051,1177],{"class":1161},[1115,26053,14739],{"class":1173},[1115,26055,1177],{"class":1161},[1115,26057,13386],{"class":1173},[1115,26059,1177],{"class":1161},[1115,26061,13386],{"class":1173},[1115,26063,1177],{"class":1161},[1115,26065,13386],{"class":1173},[1115,26067,1177],{"class":1161},[1115,26069,7253],{"class":1173},[1115,26071,1177],{"class":1161},[1115,26073,14739],{"class":1173},[1115,26075,1177],{"class":1161},[1115,26077,13386],{"class":1173},[1115,26079,1177],{"class":1161},[1115,26081,7253],{"class":1173},[1115,26083,1177],{"class":1161},[1115,26085,12538],{"class":1173},[1115,26087,1177],{"class":1161},[1115,26089,14739],{"class":1173},[1115,26091,6519],{"class":1169},[1115,26093,26094],{"class":1154,"line":27},[1115,26095,12585],{"emptyLinePlaceholder":4157},[1115,26097,26098,26101,26103,26106,26108,26110,26112,26114,26116,26119],{"class":1154,"line":148},[1115,26099,26100],{"class":1157},"q_c",[1115,26102,1162],{"class":1161},[1115,26104,26105],{"class":1165}," qcc",[1115,26107,1170],{"class":1169},[1115,26109,25897],{"class":1157},[1115,26111,1177],{"class":1161},[1115,26113,14734],{"class":1157},[1115,26115,6416],{"class":1161},[1115,26117,26118],{"class":6458}," \"c\"",[1115,26120,6519],{"class":1169},[1115,26122,26123,26125,26127,26129],{"class":1154,"line":111},[1115,26124,19366],{"class":1165},[1115,26126,1170],{"class":1169},[1115,26128,26100],{"class":1157},[1115,26130,6519],{"class":1169},[1144,26132,26135],{"className":26133,"code":26134,"language":6540,"meta":1148},[6538],"Call:\nqcc(data = c_i, type = \"c\")\n\nc chart for c_i \n\nSummary of group statistics:\n   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n   0.00    1.75    3.00    3.40    5.25    7.00 \n\nGroup sample size:  1\nNumber of groups:  20\nCenter of group statistics:  3.4\nStandard deviation:  1.843909 \n\nControl limits:\n LCL      UCL\n   0 8.931727\n",[1150,26136,26134],{"__ignoreMap":1148},[1110,26138,26139,26140,26169,26170,26193,26194,26216],{},"Průměrný počet vad na pás je ",[1115,26141,26143],{"className":26142},[1573],[1575,26144,26145],{"xmlns":1577},[1579,26146,26147,26166],{},[1582,26148,26149,26151,26153,26155,26161,26163],{},[1585,26150,3627],{},[1585,26152,4002],{},[1589,26154,1597],{},[3005,26156,26157,26159],{"accent":1121},[1585,26158,3499],{},[1589,26160,3408],{},[1589,26162,1597],{},[1716,26164,26165],{},"3,4",[1605,26167,26168],{"encoding":1607},"CL = \\bar{c} = 3{,}4",", horní mez ",[1115,26171,26173],{"className":26172},[1573],[1575,26174,26175],{"xmlns":1577},[1579,26176,26177,26190],{},[1582,26178,26179,26181,26183,26185,26187],{},[1585,26180,4013],{},[1585,26182,3627],{},[1585,26184,4002],{},[1589,26186,1597],{},[1716,26188,26189],{},"8,93",[1605,26191,26192],{"encoding":1607},"UCL = 8{,}93"," a dolní mez ",[1115,26195,26197],{"className":26196},[1573],[1575,26198,26199],{"xmlns":1577},[1579,26200,26201,26213],{},[1582,26202,26203,26205,26207,26209,26211],{},[1585,26204,4002],{},[1585,26206,3627],{},[1585,26208,4002],{},[1589,26210,1597],{},[1716,26212,2398],{},[1605,26214,26215],{"encoding":1607},"LCL = 0",". Žádný pás meze nepřekračuje — proces je zvládnutý.",[1110,26218,26219],{},[1303,26220],{"alt":26221,"className":26222,"src":26223},"mask-rd-priklad2-c",[1130,1307],"\u002Fwiki-assets\u002Fmask-rd-priklad2-c.png",[1550,26225,23754,26227],{"id":26226},"diagram-uu",[1115,26228,26230],{"className":26229},[1573],[1575,26231,26232],{"xmlns":1577},[1579,26233,26234,26238],{},[1582,26235,26236],{},[1585,26237,3523],{},[1605,26239,3523],{"encoding":1607},[1110,26241,25879,26242,26276,26277,26295],{},[1115,26243,26245],{"className":26244},[1573],[1575,26246,26247],{"xmlns":1577},[1579,26248,26249,26273],{},[1582,26250,26251,26257,26259,26265,26267],{},[1746,26252,26253,26255],{},[1585,26254,3523],{},[1585,26256,1776],{},[1589,26258,1597],{},[1746,26260,26261,26263],{},[1585,26262,3499],{},[1585,26264,1776],{},[1585,26266,4023],{"mathvariant":4022},[1746,26268,26269,26271],{},[1585,26270,1781],{},[1585,26272,1776],{},[1605,26274,26275],{"encoding":1607},"u_i = c_i\u002Fn_i"," je průměrný počet neshod přepočítaný na jeden produkt z logické podskupiny; rozsah podskupin ",[1115,26278,26280],{"className":26279},[1573],[1575,26281,26282],{"xmlns":1577},[1579,26283,26284,26292],{},[1582,26285,26286],{},[1746,26287,26288,26290],{},[1585,26289,1781],{},[1585,26291,1776],{},[1605,26293,26294],{"encoding":1607},"n_i"," není konstantní, a proto se bod od bodu mění i meze.",[1110,26297,26298,26299,26301],{},"Za ",[1150,26300,3528],{}," se dosadí vektor rozsahů jednotlivých logických podskupin, resp. rozměr jejich jednotek:",[1144,26303,26305],{"className":1146,"code":26304,"language":71,"meta":1148,"style":1148},"data \u003C- read.table(\"3_4.txt\", header = TRUE)   # počty suků a rozměry prken\nqcc(data[, 1], type = \"u\", sizes = data[, 2])\n",[1150,26306,26307,26333],{"__ignoreMap":1148},[1115,26308,26309,26311,26313,26315,26317,26320,26322,26324,26326,26328,26330],{"class":1154,"line":10},[1115,26310,3381],{"class":1157},[1115,26312,1162],{"class":1161},[1115,26314,22606],{"class":1165},[1115,26316,1170],{"class":1169},[1115,26318,26319],{"class":6458},"\"3_4.txt\"",[1115,26321,1177],{"class":1161},[1115,26323,22616],{"class":1157},[1115,26325,6416],{"class":1161},[1115,26327,6429],{"class":1173},[1115,26329,1219],{"class":1169},[1115,26331,26332],{"class":1222},"# počty suků a rozměry prken\n",[1115,26334,26335,26337,26339,26341,26343,26345,26347,26349,26351,26353,26355,26358,26360,26363,26365,26367,26369,26371,26373],{"class":1154,"line":27},[1115,26336,360],{"class":1165},[1115,26338,1170],{"class":1169},[1115,26340,3381],{"class":1157},[1115,26342,10756],{"class":1169},[1115,26344,1177],{"class":1161},[1115,26346,7253],{"class":1173},[1115,26348,10773],{"class":1169},[1115,26350,1177],{"class":1161},[1115,26352,14734],{"class":1157},[1115,26354,6416],{"class":1161},[1115,26356,26357],{"class":6458}," \"u\"",[1115,26359,1177],{"class":1161},[1115,26361,26362],{"class":1157}," sizes",[1115,26364,6416],{"class":1161},[1115,26366,22660],{"class":1157},[1115,26368,10756],{"class":1169},[1115,26370,1177],{"class":1161},[1115,26372,6797],{"class":1173},[1115,26374,26375],{"class":1169},"])\n",[1550,26377,23754,26379],{"id":26378},"diagram-npnp",[1115,26380,26382],{"className":26381},[1573],[1575,26383,26384],{"xmlns":1577},[1579,26385,26386,26392],{},[1582,26387,26388,26390],{},[1585,26389,1781],{},[1585,26391,1110],{},[1605,26393,3555],{"encoding":1607},[1110,26395,26396,26397,2271,26412,26425],{},"Regulovanou veličinou je počet neshodných produktů (ne neshod) v logické podskupině. Podmínky použití: rozsahy podskupin jsou stejně velké a velké (alespoň 50 produktů). Počet neshodných produktů má pak přibližně binomické rozdělení se střední hodnotou ",[1115,26398,26400],{"className":26399},[1573],[1575,26401,26402],{"xmlns":1577},[1579,26403,26404,26410],{},[1582,26405,26406,26408],{},[1585,26407,1781],{},[1585,26409,1110],{},[1605,26411,3555],{"encoding":1607},[1115,26413,26415],{"className":26414},[1573],[1575,26416,26417],{"xmlns":1577},[1579,26418,26419,26423],{},[1582,26420,26421],{},[1585,26422,1110],{},[1605,26424,1110],{"encoding":1607}," je pravděpodobnost, že vyrobený produkt je neshodný.",[1110,26427,26428,26429,4595],{},"Pro konstantní rozsah ",[1115,26430,26432],{"className":26431},[1573],[1575,26433,26434],{"xmlns":1577},[1579,26435,26436,26440],{},[1582,26437,26438],{},[1585,26439,1781],{},[1605,26441,1781],{"encoding":1607},[1144,26443,26445],{"className":1146,"code":26444,"language":71,"meta":1148,"style":1148},"data \u003C- read.table(\"3_7.txt\", header = TRUE)   # počty vadných tabletů v sériích po 100 kusech\nqcc(data[, 1], type = \"np\", sizes = 100)\n",[1150,26446,26447,26473],{"__ignoreMap":1148},[1115,26448,26449,26451,26453,26455,26457,26460,26462,26464,26466,26468,26470],{"class":1154,"line":10},[1115,26450,3381],{"class":1157},[1115,26452,1162],{"class":1161},[1115,26454,22606],{"class":1165},[1115,26456,1170],{"class":1169},[1115,26458,26459],{"class":6458},"\"3_7.txt\"",[1115,26461,1177],{"class":1161},[1115,26463,22616],{"class":1157},[1115,26465,6416],{"class":1161},[1115,26467,6429],{"class":1173},[1115,26469,1219],{"class":1169},[1115,26471,26472],{"class":1222},"# počty vadných tabletů v sériích po 100 kusech\n",[1115,26474,26475,26477,26479,26481,26483,26485,26487,26489,26491,26493,26495,26498,26500,26502,26504,26506],{"class":1154,"line":27},[1115,26476,360],{"class":1165},[1115,26478,1170],{"class":1169},[1115,26480,3381],{"class":1157},[1115,26482,10756],{"class":1169},[1115,26484,1177],{"class":1161},[1115,26486,7253],{"class":1173},[1115,26488,10773],{"class":1169},[1115,26490,1177],{"class":1161},[1115,26492,14734],{"class":1157},[1115,26494,6416],{"class":1161},[1115,26496,26497],{"class":6458}," \"np\"",[1115,26499,1177],{"class":1161},[1115,26501,26362],{"class":1157},[1115,26503,6416],{"class":1161},[1115,26505,17845],{"class":1173},[1115,26507,6519],{"class":1169},[1550,26509,23754,26511],{"id":26510},"diagram-pp",[1115,26512,26514],{"className":26513},[1573],[1575,26515,26516],{"xmlns":1577},[1579,26517,26518,26522],{},[1582,26519,26520],{},[1585,26521,1110],{},[1605,26523,1110],{"encoding":1607},[1110,26525,26526,26527,26563],{},"Regulovanou veličinou je počet neshodných produktů v logické podskupině přepočtený na jednotku, ",[1115,26528,26530],{"className":26529},[1573],[1575,26531,26532],{"xmlns":1577},[1579,26533,26534,26560],{},[1582,26535,26536,26542,26544,26546,26552,26554],{},[1746,26537,26538,26540],{},[1585,26539,1110],{},[1585,26541,1776],{},[1589,26543,1597],{},[1585,26545,1781],{},[1746,26547,26548,26550],{},[1585,26549,1110],{},[1585,26551,1776],{},[1585,26553,4023],{"mathvariant":4022},[1746,26555,26556,26558],{},[1585,26557,1781],{},[1585,26559,1776],{},[1605,26561,26562],{"encoding":1607},"p_i = np_i\u002Fn_i","; rozsahy podskupin nemusí být konstantní.",[1110,26565,26298,26566,26568],{},[1150,26567,3528],{}," se dosadí vektor rozsahů logických podskupin:",[1144,26570,26572],{"className":1146,"code":26571,"language":71,"meta":1148,"style":1148},"data \u003C- read.table(\"3_6.txt\", header = TRUE)   # počty vadných tabletů a rozsahy sérií\nqcc(data[, 1], type = \"p\", sizes = data[, 2])\n",[1150,26573,26574,26600],{"__ignoreMap":1148},[1115,26575,26576,26578,26580,26582,26584,26587,26589,26591,26593,26595,26597],{"class":1154,"line":10},[1115,26577,3381],{"class":1157},[1115,26579,1162],{"class":1161},[1115,26581,22606],{"class":1165},[1115,26583,1170],{"class":1169},[1115,26585,26586],{"class":6458},"\"3_6.txt\"",[1115,26588,1177],{"class":1161},[1115,26590,22616],{"class":1157},[1115,26592,6416],{"class":1161},[1115,26594,6429],{"class":1173},[1115,26596,1219],{"class":1169},[1115,26598,26599],{"class":1222},"# počty vadných tabletů a rozsahy sérií\n",[1115,26601,26602,26604,26606,26608,26610,26612,26614,26616,26618,26620,26622,26625,26627,26629,26631,26633,26635,26637,26639],{"class":1154,"line":27},[1115,26603,360],{"class":1165},[1115,26605,1170],{"class":1169},[1115,26607,3381],{"class":1157},[1115,26609,10756],{"class":1169},[1115,26611,1177],{"class":1161},[1115,26613,7253],{"class":1173},[1115,26615,10773],{"class":1169},[1115,26617,1177],{"class":1161},[1115,26619,14734],{"class":1157},[1115,26621,6416],{"class":1161},[1115,26623,26624],{"class":6458}," \"p\"",[1115,26626,1177],{"class":1161},[1115,26628,26362],{"class":1157},[1115,26630,6416],{"class":1161},[1115,26632,22660],{"class":1157},[1115,26634,10756],{"class":1169},[1115,26636,1177],{"class":1161},[1115,26638,6797],{"class":1173},[1115,26640,26375],{"class":1169},[1136,26642,26644],{"id":26643},"indexy-způsobilosti","Indexy způsobilosti",[1110,26646,26647,26648,26666,26667,26685],{},"Zatímco regulační diagram posuzuje stabilitu procesu v čase, index způsobilosti posuzuje, zda se zvládnutý proces svou přirozenou variabilitou vejde do tolerančních mezí zadaných specifikací — dolní meze ",[1115,26649,26651],{"className":26650},[1573],[1575,26652,26653],{"xmlns":1577},[1579,26654,26655,26663],{},[1582,26656,26657,26659,26661],{},[1585,26658,4002],{},[1585,26660,4005],{},[1585,26662,4002],{},[1605,26664,26665],{"encoding":1607},"LSL"," a horní meze ",[1115,26668,26670],{"className":26669},[1573],[1575,26671,26672],{"xmlns":1577},[1579,26673,26674,26682],{},[1582,26675,26676,26678,26680],{},[1585,26677,4013],{},[1585,26679,4005],{},[1585,26681,4002],{},[1605,26683,26684],{"encoding":1607},"USL",". Způsobilost se zkoumá až pro proces, který je podle regulačních diagramů statisticky zvládnutý (třetí fáze regulace).",[1550,26687,26689,26706],{"id":26688},"cpc_p-index-způsobilosti",[1115,26690,26692],{"className":26691},[1573],[1575,26693,26694],{"xmlns":1577},[1579,26695,26696,26704],{},[1582,26697,26698],{},[1746,26699,26700,26702],{},[1585,26701,3627],{},[1585,26703,1110],{},[1605,26705,3632],{"encoding":1607}," — index způsobilosti",[1110,26708,26709,26710,4595],{},"Podíl mezi délkou tolerančního intervalu a délkou intervalu, ve kterém by za normálního rozdělení mělo ležet skoro všech 99,73 % hodnot znaku, tedy ",[1115,26711,26713],{"className":26712},[1573],[1575,26714,26715],{"xmlns":1577},[1579,26716,26717,26723],{},[1582,26718,26719,26721],{},[1716,26720,6581],{},[1585,26722,1990],{},[1605,26724,26725],{"encoding":1607},"6\\sigma",[1115,26727,26729],{"className":26728},[1573],[1575,26730,26731],{"xmlns":1577,"display":4601},[1579,26732,26733,26769],{},[1582,26734,26735,26741,26743,26767],{},[1746,26736,26737,26739],{},[1585,26738,3627],{},[1585,26740,1110],{},[1589,26742,1597],{},[5373,26744,26745,26761],{},[1582,26746,26747,26749,26751,26753,26755,26757,26759],{},[1585,26748,4013],{},[1585,26750,4005],{},[1585,26752,4002],{},[1589,26754,1721],{},[1585,26756,4002],{},[1585,26758,4005],{},[1585,26760,4002],{},[1582,26762,26763,26765],{},[1716,26764,6581],{},[1585,26766,1990],{},[1585,26768,2264],{"mathvariant":4022},[1605,26770,26771],{"encoding":1607},"C_p = \\frac{USL - LSL}{6\\sigma}.",[1110,26773,26774,26791,26792,26805,26806,2264],{},[1115,26775,26777],{"className":26776},[1573],[1575,26778,26779],{"xmlns":1577},[1579,26780,26781,26789],{},[1582,26782,26783],{},[1746,26784,26785,26787],{},[1585,26786,3627],{},[1585,26788,1110],{},[1605,26790,3632],{"encoding":1607}," srovnává jen délky, nevšímá si, kde uprostřed tolerance proces leží — centrovaný i silně vychýlený proces se stejným ",[1115,26793,26795],{"className":26794},[1573],[1575,26796,26797],{"xmlns":1577},[1579,26798,26799,26803],{},[1582,26800,26801],{},[1585,26802,1990],{},[1605,26804,2244],{"encoding":1607}," mají stejné ",[1115,26807,26809],{"className":26808},[1573],[1575,26810,26811],{"xmlns":1577},[1579,26812,26813,26821],{},[1582,26814,26815],{},[1746,26816,26817,26819],{},[1585,26818,3627],{},[1585,26820,1110],{},[1605,26822,3632],{"encoding":1607},[1110,26824,26825],{},"Doplňkové charakteristiky využití tolerančního intervalu:",[2220,26827,26828,26862,26950],{},[2223,26829,26830,6605,26833,26861],{},[2227,26831,26832],{},"míra využití tolerančního intervalu",[1115,26834,26836],{"className":26835},[1573],[1575,26837,26838],{"xmlns":1577},[1579,26839,26840,26858],{},[1582,26841,26842,26854,26856],{},[5873,26843,26844],{"scriptlevel":2398,"displaystyle":1121},[5373,26845,26846,26848],{},[1716,26847,14343],{},[1746,26849,26850,26852],{},[1585,26851,3627],{},[1585,26853,1110],{},[5543,26855,5545],{},[1585,26857,14350],{"mathvariant":4022},[1605,26859,26860],{"encoding":1607},"\\dfrac{100}{C_p}\\,\\%"," — na kolik procent je toleranční interval využíván sledovaným znakem,",[2223,26863,26864,26867,26868,26885,26886,1260,26918,1177],{},[2227,26865,26866],{},"robustnost procesu",": rezerva, kterou máme v tolerančních mezích, než index ",[1115,26869,26871],{"className":26870},[1573],[1575,26872,26873],{"xmlns":1577},[1579,26874,26875,26883],{},[1582,26876,26877],{},[1746,26878,26879,26881],{},[1585,26880,3627],{},[1585,26882,1110],{},[1605,26884,3632],{"encoding":1607}," nabyde hodnotu 1 — rovná se menší hodnotě z výrazů ",[1115,26887,26889],{"className":26888},[1573],[1575,26890,26891],{"xmlns":1577},[1579,26892,26893,26915],{},[1582,26894,26895,26897,26899,26901,26903,26905,26907,26909,26911,26913],{},[1585,26896,4013],{},[1585,26898,4005],{},[1585,26900,4002],{},[1589,26902,1721],{},[1589,26904,1170],{"stretchy":1591},[1585,26906,1982],{},[1589,26908,4010],{},[1716,26910,6220],{},[1585,26912,1990],{},[1589,26914,1603],{"stretchy":1591},[1605,26916,26917],{"encoding":1607},"USL-(\\mu+3\\sigma)",[1115,26919,26921],{"className":26920},[1573],[1575,26922,26923],{"xmlns":1577},[1579,26924,26925,26947],{},[1582,26926,26927,26929,26931,26933,26935,26937,26939,26941,26943,26945],{},[1589,26928,1170],{"stretchy":1591},[1585,26930,1982],{},[1589,26932,1721],{},[1716,26934,6220],{},[1585,26936,1990],{},[1589,26938,1603],{"stretchy":1591},[1589,26940,1721],{},[1585,26942,4002],{},[1585,26944,4005],{},[1585,26946,4002],{},[1605,26948,26949],{"encoding":1607},"(\\mu-3\\sigma)-LSL",[2223,26951,26952,6605,26955,2271,26995,27009],{},[2227,26953,26954],{},"podíl zmetků",[1115,26956,26958],{"className":26957},[1573],[1575,26959,26960],{"xmlns":1577},[1579,26961,26962,26992],{},[1582,26963,26964,26971,26973,26975,26978,26980,26982,26984,26990],{},[1746,26965,26966,26968],{},[1585,26967,1587],{},[1585,26969,26970],{},"z",[1589,26972,1597],{},[1716,26974,1993],{},[1585,26976,26977],{"mathvariant":4022},"Φ",[1589,26979,1170],{"stretchy":1591},[1589,26981,1721],{},[1716,26983,6220],{},[1746,26985,26986,26988],{},[1585,26987,3627],{},[1585,26989,1110],{},[1589,26991,1603],{"stretchy":1591},[1605,26993,26994],{"encoding":1607},"P_z = 2\\Phi(-3C_p)",[1115,26996,26998],{"className":26997},[1573],[1575,26999,27000],{"xmlns":1577},[1579,27001,27002,27006],{},[1582,27003,27004],{},[1585,27005,26977],{"mathvariant":4022},[1605,27007,27008],{"encoding":1607},"\\Phi"," je distribuční funkce normovaného normálního rozdělení.",[1550,27011,27013,27034],{"id":27012},"cpkc_pk-index-způsobilosti-s-ohledem-na-vychýlení",[1115,27014,27016],{"className":27015},[1573],[1575,27017,27018],{"xmlns":1577},[1579,27019,27020,27032],{},[1582,27021,27022],{},[1746,27023,27024,27026],{},[1585,27025,3627],{},[1582,27027,27028,27030],{},[1585,27029,1110],{},[1585,27031,1600],{},[1605,27033,3654],{"encoding":1607}," — index způsobilosti s ohledem na vychýlení",[1110,27036,27037],{},"Bere v úvahu, že proces nemusí být centrovaný na střed tolerance; počítá se samostatně vzdálenost k horní a dolní mezi a horší z obou se stane indexem:",[1115,27039,27041],{"className":27040},[1573],[1575,27042,27043],{"xmlns":1577,"display":4601},[1579,27044,27045,27115],{},[1582,27046,27047,27057,27059,27061,27063,27113],{},[1746,27048,27049,27051],{},[1585,27050,3627],{},[1582,27052,27053,27055],{},[1585,27054,1110],{},[1585,27056,1600],{},[1589,27058,1597],{},[1585,27060,7102],{},[1589,27062,7105],{},[1582,27064,27065,27067,27087,27089,27091,27111],{},[1589,27066,1170],{"fence":1121},[5373,27068,27069,27081],{},[1582,27070,27071,27073,27075,27077,27079],{},[1585,27072,4013],{},[1585,27074,4005],{},[1585,27076,4002],{},[1589,27078,1721],{},[1585,27080,1982],{},[1582,27082,27083,27085],{},[1716,27084,6220],{},[1585,27086,1990],{},[1589,27088,1177],{"separator":1121},[5543,27090,13843],{},[5373,27092,27093,27105],{},[1582,27094,27095,27097,27099,27101,27103],{},[1585,27096,1982],{},[1589,27098,1721],{},[1585,27100,4002],{},[1585,27102,4005],{},[1585,27104,4002],{},[1582,27106,27107,27109],{},[1716,27108,6220],{},[1585,27110,1990],{},[1589,27112,1603],{"fence":1121},[1585,27114,2264],{"mathvariant":4022},[1605,27116,27117],{"encoding":1607},"C_{pk} = \\min\\left(\\frac{USL-\\mu}{3\\sigma},\\ \\frac{\\mu-LSL}{3\\sigma}\\right).",[1110,27119,27120,27121,27134,27135,27165,27166,27187,27188,2264],{},"Vyjde-li některý z obou podílů záporný, položí se roven nule; to nastane, když střední hodnota ",[1115,27122,27124],{"className":27123},[1573],[1575,27125,27126],{"xmlns":1577},[1579,27127,27128,27132],{},[1582,27129,27130],{},[1585,27131,1982],{},[1605,27133,11376],{"encoding":1607}," leží mimo toleranční interval, a proces pak není pod statistickou kontrolou. U centrovaného procesu jsou oba podíly stejné a ",[1115,27136,27138],{"className":27137},[1573],[1575,27139,27140],{"xmlns":1577},[1579,27141,27142,27162],{},[1582,27143,27144,27154,27156],{},[1746,27145,27146,27148],{},[1585,27147,3627],{},[1582,27149,27150,27152],{},[1585,27151,1110],{},[1585,27153,1600],{},[1589,27155,1597],{},[1746,27157,27158,27160],{},[1585,27159,3627],{},[1585,27161,1110],{},[1605,27163,27164],{"encoding":1607},"C_{pk} = C_p","; čím víc je proces vychýlený, tím víc je ",[1115,27167,27169],{"className":27168},[1573],[1575,27170,27171],{"xmlns":1577},[1579,27172,27173,27185],{},[1582,27174,27175],{},[1746,27176,27177,27179],{},[1585,27178,3627],{},[1582,27180,27181,27183],{},[1585,27182,1110],{},[1585,27184,1600],{},[1605,27186,3654],{"encoding":1607}," menší než ",[1115,27189,27191],{"className":27190},[1573],[1575,27192,27193],{"xmlns":1577},[1579,27194,27195,27203],{},[1582,27196,27197],{},[1746,27198,27199,27201],{},[1585,27200,3627],{},[1585,27202,1110],{},[1605,27204,3632],{"encoding":1607},[1550,27206,27208,1260,27229,27252],{"id":27207},"cpmc_pm-a-cpmkc_pmk-indexy-vztažené-k-cíli",[1115,27209,27211],{"className":27210},[1573],[1575,27212,27213],{"xmlns":1577},[1579,27214,27215,27227],{},[1582,27216,27217],{},[1746,27218,27219,27221],{},[1585,27220,3627],{},[1582,27222,27223,27225],{},[1585,27224,1110],{},[1585,27226,3674],{},[1605,27228,3677],{"encoding":1607},[1115,27230,27232],{"className":27231},[1573],[1575,27233,27234],{"xmlns":1577},[1579,27235,27236,27250],{},[1582,27237,27238],{},[1746,27239,27240,27242],{},[1585,27241,3627],{},[1582,27243,27244,27246,27248],{},[1585,27245,1110],{},[1585,27247,3674],{},[1585,27249,1600],{},[1605,27251,23357],{"encoding":1607}," — indexy vztažené k cíli",[1110,27254,27255,27256,27269,27270,27283,27284,27327,27328,4595],{},"Pokud má proces zadaný cílový střed ",[1115,27257,27259],{"className":27258},[1573],[1575,27260,27261],{"xmlns":1577},[1579,27262,27263,27267],{},[1582,27264,27265],{},[1585,27266,4043],{},[1605,27268,4043],{"encoding":1607}," (ne nutně střed tolerance), nahradí se ",[1115,27271,27273],{"className":27272},[1573],[1575,27274,27275],{"xmlns":1577},[1579,27276,27277,27281],{},[1582,27278,27279],{},[1585,27280,1990],{},[1605,27282,2244],{"encoding":1607}," odmocninou ze střední čtvercové odchylky od cíle ",[1115,27285,27287],{"className":27286},[1573],[1575,27288,27289],{"xmlns":1577},[1579,27290,27291,27324],{},[1582,27292,27293,27296,27298],{},[1585,27294,27295],{},"τ",[1589,27297,1597],{},[7068,27299,27300],{},[1582,27301,27302,27308,27310,27312,27314,27316,27318],{},[1986,27303,27304,27306],{},[1585,27305,1990],{},[1716,27307,1993],{},[1589,27309,4010],{},[1589,27311,1170],{"stretchy":1591},[1585,27313,1982],{},[1589,27315,1721],{},[1585,27317,4043],{},[1986,27319,27320,27322],{},[1589,27321,1603],{"stretchy":1591},[1716,27323,1993],{},[1605,27325,27326],{"encoding":1607},"\\tau = \\sqrt{\\sigma^2+(\\mu-T)^2}",", která trestá i vychýlení od ",[1115,27329,27331],{"className":27330},[1573],[1575,27332,27333],{"xmlns":1577},[1579,27334,27335,27339],{},[1582,27336,27337],{},[1585,27338,4043],{},[1605,27340,4043],{"encoding":1607},[1115,27342,27344],{"className":27343},[1573],[1575,27345,27346],{"xmlns":1577,"display":4601},[1579,27347,27348,27460],{},[1582,27349,27350,27360,27362,27386,27388,27390,27402,27404,27406,27408,27458],{},[1746,27351,27352,27354],{},[1585,27353,3627],{},[1582,27355,27356,27358],{},[1585,27357,1110],{},[1585,27359,3674],{},[1589,27361,1597],{},[5373,27363,27364,27380],{},[1582,27365,27366,27368,27370,27372,27374,27376,27378],{},[1585,27367,4013],{},[1585,27369,4005],{},[1585,27371,4002],{},[1589,27373,1721],{},[1585,27375,4002],{},[1585,27377,4005],{},[1585,27379,4002],{},[1582,27381,27382,27384],{},[1716,27383,6581],{},[1585,27385,27295],{},[1589,27387,1177],{"separator":1121},[4648,27389],{"width":4650},[1746,27391,27392,27394],{},[1585,27393,3627],{},[1582,27395,27396,27398,27400],{},[1585,27397,1110],{},[1585,27399,3674],{},[1585,27401,1600],{},[1589,27403,1597],{},[1585,27405,7102],{},[1589,27407,7105],{},[1582,27409,27410,27412,27432,27434,27436,27456],{},[1589,27411,1170],{"fence":1121},[5373,27413,27414,27426],{},[1582,27415,27416,27418,27420,27422,27424],{},[1585,27417,4013],{},[1585,27419,4005],{},[1585,27421,4002],{},[1589,27423,1721],{},[1585,27425,1982],{},[1582,27427,27428,27430],{},[1716,27429,6220],{},[1585,27431,27295],{},[1589,27433,1177],{"separator":1121},[5543,27435,13843],{},[5373,27437,27438,27450],{},[1582,27439,27440,27442,27444,27446,27448],{},[1585,27441,1982],{},[1589,27443,1721],{},[1585,27445,4002],{},[1585,27447,4005],{},[1585,27449,4002],{},[1582,27451,27452,27454],{},[1716,27453,6220],{},[1585,27455,27295],{},[1589,27457,1603],{"fence":1121},[1585,27459,2264],{"mathvariant":4022},[1605,27461,27462],{"encoding":1607},"C_{pm} = \\frac{USL-LSL}{6\\tau}, \\qquad C_{pmk} = \\min\\left(\\frac{USL-\\mu}{3\\tau},\\ \\frac{\\mu-LSL}{3\\tau}\\right).",[1550,27464,27466],{"id":27465},"interpretace","Interpretace",[1310,27468,27469,27496],{},[1313,27470,27471],{},[1316,27472,27473,27493],{},[1319,27474,27475,27476],{},"Hodnota ",[1115,27477,27479],{"className":27478},[1573],[1575,27480,27481],{"xmlns":1577},[1579,27482,27483,27491],{},[1582,27484,27485],{},[1746,27486,27487,27489],{},[1585,27488,3627],{},[1585,27490,1110],{},[1605,27492,3632],{"encoding":1607},[1319,27494,27495],{},"Způsobilost procesu",[1332,27497,27498,27527,27570],{},[1316,27499,27500,27524],{},[1337,27501,27502],{},[1115,27503,27505],{"className":27504},[1573],[1575,27506,27507],{"xmlns":1577},[1579,27508,27509,27521],{},[1582,27510,27511,27517,27519],{},[1746,27512,27513,27515],{},[1585,27514,3627],{},[1585,27516,1110],{},[1589,27518,6949],{},[1716,27520,1718],{},[1605,27522,27523],{"encoding":1607},"C_p \u003C 1",[1337,27525,27526],{},"dosahovaná přesnost je menší než předepsaná — proces je nezpůsobilý",[1316,27528,27529,27553],{},[1337,27530,27531],{},[1115,27532,27534],{"className":27533},[1573],[1575,27535,27536],{"xmlns":1577},[1579,27537,27538,27550],{},[1582,27539,27540,27546,27548],{},[1746,27541,27542,27544],{},[1585,27543,3627],{},[1585,27545,1110],{},[1589,27547,1597],{},[1716,27549,1718],{},[1605,27551,27552],{"encoding":1607},"C_p = 1",[1337,27554,27555,27556,27569],{},"dosahovaná přesnost je rovna předepsané — proces je způsobilý, ale sebemenší zvětšení ",[1115,27557,27559],{"className":27558},[1573],[1575,27560,27561],{"xmlns":1577},[1579,27562,27563,27567],{},[1582,27564,27565],{},[1585,27566,1990],{},[1605,27568,2244],{"encoding":1607}," jej posune na nezpůsobilý",[1316,27571,27572,27596],{},[1337,27573,27574],{},[1115,27575,27577],{"className":27576},[1573],[1575,27578,27579],{"xmlns":1577},[1579,27580,27581,27593],{},[1582,27582,27583,27589,27591],{},[1746,27584,27585,27587],{},[1585,27586,3627],{},[1585,27588,1110],{},[1589,27590,1698],{},[1716,27592,1718],{},[1605,27594,27595],{"encoding":1607},"C_p > 1",[1337,27597,27598],{},"dosahovaná přesnost je větší než předepsaná — proces je způsobilý",[1110,27600,27601,27602,27623,27624,2264],{},"U indexu ",[1115,27603,27605],{"className":27604},[1573],[1575,27606,27607],{"xmlns":1577},[1579,27608,27609,27621],{},[1582,27610,27611],{},[1746,27612,27613,27615],{},[1585,27614,3627],{},[1582,27616,27617,27619],{},[1585,27618,1110],{},[1585,27620,1600],{},[1605,27622,3654],{"encoding":1607}," se v praxi požaduje víc než jen hodnota nad 1: s rozvojem technologií roste nárok na rezervu, a běžně se dnes vyžaduje hodnota alespoň ",[1115,27625,27627],{"className":27626},[1573],[1575,27628,27629],{"xmlns":1577},[1579,27630,27631,27636],{},[1582,27632,27633],{},[1716,27634,27635],{},"1,5",[1605,27637,27638],{"encoding":1607},"1{,}5",[1110,27640,27641],{},[1303,27642],{"alt":27643,"className":27644,"src":27645},"mask-rd-cp-panely",[1130,1307],"\u002Fwiki-assets\u002Fmask-rd-cp-panely.png",[1110,27647,27648],{},[1303,27649],{"alt":27650,"className":27651,"src":27652},"mask-rd-cpk-off-centre",[1130,1307],"\u002Fwiki-assets\u002Fmask-rd-cpk-off-centre.png",[1550,27654,27656],{"id":27655},"výpočet-v-r","Výpočet v R",[1110,27658,27659,27660,27662,27663,2402,27665,27668,27669,1260,27686,1279,27703,27705,27706,27719],{},"Indexy způsobilosti počítá ",[1150,27661,3963],{}," z výstupu regulačního diagramu ",[1150,27664,3969],{},[1150,27666,27667],{},"spec.limits"," jsou toleranční meze ",[1115,27670,27672],{"className":27671},[1573],[1575,27673,27674],{"xmlns":1577},[1579,27675,27676,27684],{},[1582,27677,27678,27680,27682],{},[1585,27679,4002],{},[1585,27681,4005],{},[1585,27683,4002],{},[1605,27685,26665],{"encoding":1607},[1115,27687,27689],{"className":27688},[1573],[1575,27690,27691],{"xmlns":1577},[1579,27692,27693,27701],{},[1582,27694,27695,27697,27699],{},[1585,27696,4013],{},[1585,27698,4005],{},[1585,27700,4002],{},[1605,27702,26684],{"encoding":1607},[1150,27704,3983],{}," cílová hodnota ",[1115,27707,27709],{"className":27708},[1573],[1575,27710,27711],{"xmlns":1577},[1579,27712,27713,27717],{},[1582,27714,27715],{},[1585,27716,4043],{},[1605,27718,4043],{"encoding":1607},". Pro velikost výrobku v mm s tolerančními mezemi 100 a 110 mm a cílovou hodnotou 105 mm:",[1144,27721,27723],{"className":1146,"code":27722,"language":71,"meta":1148,"style":1148},"library(qcc)\ndata \u003C- read.table(\"3_8.txt\", header = TRUE)\nx \u003C- as.matrix(data)\nq \u003C- qcc(x, type = \"xbar\")\nprocess.capability(q, spec.limits = c(100, 110), target = 105, std.dev = sd(x))\n",[1150,27724,27725,27735,27758,27773,27795],{"__ignoreMap":1148},[1115,27726,27727,27729,27731,27733],{"class":1154,"line":10},[1115,27728,19892],{"class":1161},[1115,27730,1170],{"class":1169},[1115,27732,360],{"class":1157},[1115,27734,6519],{"class":1169},[1115,27736,27737,27739,27741,27743,27745,27748,27750,27752,27754,27756],{"class":1154,"line":27},[1115,27738,3381],{"class":1157},[1115,27740,1162],{"class":1161},[1115,27742,22606],{"class":1165},[1115,27744,1170],{"class":1169},[1115,27746,27747],{"class":6458},"\"3_8.txt\"",[1115,27749,1177],{"class":1161},[1115,27751,22616],{"class":1157},[1115,27753,6416],{"class":1161},[1115,27755,6429],{"class":1173},[1115,27757,6519],{"class":1169},[1115,27759,27760,27762,27764,27767,27769,27771],{"class":1154,"line":148},[1115,27761,1158],{"class":1157},[1115,27763,1162],{"class":1161},[1115,27765,27766],{"class":1165}," as.matrix",[1115,27768,1170],{"class":1169},[1115,27770,3381],{"class":1157},[1115,27772,6519],{"class":1169},[1115,27774,27775,27777,27779,27781,27783,27785,27787,27789,27791,27793],{"class":1154,"line":111},[1115,27776,3969],{"class":1157},[1115,27778,1162],{"class":1161},[1115,27780,26105],{"class":1165},[1115,27782,1170],{"class":1169},[1115,27784,1158],{"class":1157},[1115,27786,1177],{"class":1161},[1115,27788,14734],{"class":1157},[1115,27790,6416],{"class":1161},[1115,27792,25231],{"class":6458},[1115,27794,6519],{"class":1169},[1115,27796,27797,27800,27802,27804,27806,27809,27811,27813,27815,27817,27819,27821,27823,27825,27828,27830,27833,27835,27838,27840,27842,27844,27846],{"class":1154,"line":96},[1115,27798,27799],{"class":1165},"process.capability",[1115,27801,1170],{"class":1169},[1115,27803,3969],{"class":1157},[1115,27805,1177],{"class":1161},[1115,27807,27808],{"class":1157}," spec.limits",[1115,27810,6416],{"class":1161},[1115,27812,1166],{"class":1165},[1115,27814,1170],{"class":1169},[1115,27816,14343],{"class":1173},[1115,27818,1177],{"class":1161},[1115,27820,16774],{"class":1173},[1115,27822,1603],{"class":1169},[1115,27824,1177],{"class":1161},[1115,27826,27827],{"class":1157}," target",[1115,27829,6416],{"class":1161},[1115,27831,27832],{"class":1173}," 105",[1115,27834,1177],{"class":1161},[1115,27836,27837],{"class":1157}," std.dev",[1115,27839,6416],{"class":1161},[1115,27841,11821],{"class":1165},[1115,27843,1170],{"class":1169},[1115,27845,1158],{"class":1157},[1115,27847,12073],{"class":1169},[1110,27849,27850,27851,1279,27854,1279,27857,1279,27860,1260,27863,27866,27867,1260,27869,27871,27872,27893,27894,27917],{},"Výpis obsahuje řádky ",[1150,27852,27853],{},"Cp",[1150,27855,27856],{},"Cp_l",[1150,27858,27859],{},"Cp_u",[1150,27861,27862],{},"Cp_k",[1150,27864,27865],{},"Cpm"," s hodnotou indexu a 95% intervalem spolehlivosti. ",[1150,27868,27856],{},[1150,27870,27859],{}," jsou dílčí poměry k dolní a horní mezi, jejich minimum je ",[1115,27873,27875],{"className":27874},[1573],[1575,27876,27877],{"xmlns":1577},[1579,27878,27879,27891],{},[1582,27880,27881],{},[1746,27882,27883,27885],{},[1585,27884,3627],{},[1582,27886,27887,27889],{},[1585,27888,1110],{},[1585,27890,1600],{},[1605,27892,3654],{"encoding":1607},". Index ",[1115,27895,27897],{"className":27896},[1573],[1575,27898,27899],{"xmlns":1577},[1579,27900,27901,27915],{},[1582,27902,27903],{},[1746,27904,27905,27907],{},[1585,27906,3627],{},[1582,27908,27909,27911,27913],{},[1585,27910,1110],{},[1585,27912,3674],{},[1585,27914,1600],{},[1605,27916,23357],{"encoding":1607}," a doplňkové charakteristiky se dopočítají ze vzorců výše:",[1144,27919,27921],{"className":1146,"code":27920,"language":71,"meta":1148,"style":1148},"mu \u003C- mean(x); sigma \u003C- sd(x)\nLSL \u003C- 100; USL \u003C- 110; T \u003C- 105\ntau \u003C- sqrt(sigma^2 + (mu - T)^2)\nCp \u003C- (USL - LSL) \u002F (6 * sigma)\nCpmk \u003C- min((USL - mu) \u002F (3 * tau), (mu - LSL) \u002F (3 * tau))\nmiravyuziti \u003C- 100 \u002F Cp\nrobustnost \u003C- min(USL - (mu + 3 * sigma), (mu - 3 * sigma) - LSL)\nPz \u003C- 2 * pnorm(-3 * Cp)\n",[1150,27922,27923,27950,27975,28012,28042,28100,28114,28165],{"__ignoreMap":1148},[1115,27924,27925,27928,27930,27932,27934,27936,27938,27940,27942,27944,27946,27948],{"class":1154,"line":10},[1115,27926,27927],{"class":1157},"mu",[1115,27929,1162],{"class":1161},[1115,27931,11811],{"class":1165},[1115,27933,1170],{"class":1169},[1115,27935,1158],{"class":1157},[1115,27937,14688],{"class":1169},[1115,27939,380],{"class":1157},[1115,27941,1162],{"class":1161},[1115,27943,11821],{"class":1165},[1115,27945,1170],{"class":1169},[1115,27947,1158],{"class":1157},[1115,27949,6519],{"class":1169},[1115,27951,27952,27954,27956,27958,27960,27962,27964,27966,27968,27970,27972],{"class":1154,"line":27},[1115,27953,26665],{"class":1157},[1115,27955,1162],{"class":1161},[1115,27957,17845],{"class":1173},[1115,27959,2402],{"class":1169},[1115,27961,26684],{"class":1157},[1115,27963,1162],{"class":1161},[1115,27965,16774],{"class":1173},[1115,27967,2402],{"class":1169},[1115,27969,4043],{"class":1157},[1115,27971,1162],{"class":1161},[1115,27973,27974],{"class":1173}," 105\n",[1115,27976,27977,27980,27982,27984,27986,27988,27990,27992,27994,27996,27998,28001,28004,28006,28008,28010],{"class":1154,"line":148},[1115,27978,27979],{"class":1157},"tau",[1115,27981,1162],{"class":1161},[1115,27983,7191],{"class":1165},[1115,27985,1170],{"class":1169},[1115,27987,380],{"class":1157},[1115,27989,3011],{"class":1161},[1115,27991,1993],{"class":1173},[1115,27993,21011],{"class":1161},[1115,27995,7219],{"class":1169},[1115,27997,27927],{"class":1157},[1115,27999,28000],{"class":1161}," -",[1115,28002,28003],{"class":1157}," T",[1115,28005,1603],{"class":1169},[1115,28007,3011],{"class":1161},[1115,28009,1993],{"class":1173},[1115,28011,6519],{"class":1169},[1115,28013,28014,28016,28018,28020,28022,28024,28027,28029,28031,28033,28035,28037,28040],{"class":1154,"line":111},[1115,28015,27853],{"class":1157},[1115,28017,1162],{"class":1161},[1115,28019,7219],{"class":1169},[1115,28021,26684],{"class":1157},[1115,28023,28000],{"class":1161},[1115,28025,28026],{"class":1157}," LSL",[1115,28028,7214],{"class":1169},[1115,28030,4023],{"class":1161},[1115,28032,7219],{"class":1169},[1115,28034,6581],{"class":1173},[1115,28036,21136],{"class":1161},[1115,28038,28039],{"class":1157}," sigma",[1115,28041,6519],{"class":1169},[1115,28043,28044,28047,28049,28051,28054,28056,28058,28061,28063,28065,28067,28069,28071,28074,28076,28078,28080,28082,28084,28086,28088,28090,28092,28094,28096,28098],{"class":1154,"line":96},[1115,28045,28046],{"class":1157},"Cpmk",[1115,28048,1162],{"class":1161},[1115,28050,14709],{"class":1165},[1115,28052,28053],{"class":1169},"((",[1115,28055,26684],{"class":1157},[1115,28057,28000],{"class":1161},[1115,28059,28060],{"class":1157}," mu",[1115,28062,7214],{"class":1169},[1115,28064,4023],{"class":1161},[1115,28066,7219],{"class":1169},[1115,28068,6220],{"class":1173},[1115,28070,21136],{"class":1161},[1115,28072,28073],{"class":1157}," tau",[1115,28075,1603],{"class":1169},[1115,28077,1177],{"class":1161},[1115,28079,7219],{"class":1169},[1115,28081,27927],{"class":1157},[1115,28083,28000],{"class":1161},[1115,28085,28026],{"class":1157},[1115,28087,7214],{"class":1169},[1115,28089,4023],{"class":1161},[1115,28091,7219],{"class":1169},[1115,28093,6220],{"class":1173},[1115,28095,21136],{"class":1161},[1115,28097,28073],{"class":1157},[1115,28099,12073],{"class":1169},[1115,28101,28102,28105,28107,28109,28111],{"class":1154,"line":89},[1115,28103,28104],{"class":1157},"miravyuziti",[1115,28106,1162],{"class":1161},[1115,28108,17845],{"class":1173},[1115,28110,12619],{"class":1161},[1115,28112,28113],{"class":1157}," Cp\n",[1115,28115,28116,28119,28121,28123,28125,28127,28129,28131,28133,28135,28137,28139,28141,28143,28145,28147,28149,28151,28153,28155,28157,28159,28161,28163],{"class":1154,"line":82},[1115,28117,28118],{"class":1157},"robustnost",[1115,28120,1162],{"class":1161},[1115,28122,14709],{"class":1165},[1115,28124,1170],{"class":1169},[1115,28126,26684],{"class":1157},[1115,28128,28000],{"class":1161},[1115,28130,7219],{"class":1169},[1115,28132,27927],{"class":1157},[1115,28134,21011],{"class":1161},[1115,28136,13386],{"class":1173},[1115,28138,21136],{"class":1161},[1115,28140,28039],{"class":1157},[1115,28142,1603],{"class":1169},[1115,28144,1177],{"class":1161},[1115,28146,7219],{"class":1169},[1115,28148,27927],{"class":1157},[1115,28150,28000],{"class":1161},[1115,28152,13386],{"class":1173},[1115,28154,21136],{"class":1161},[1115,28156,28039],{"class":1157},[1115,28158,7214],{"class":1169},[1115,28160,7250],{"class":1161},[1115,28162,28026],{"class":1157},[1115,28164,6519],{"class":1169},[1115,28166,28167,28170,28172,28174,28176,28178,28180,28182,28184,28186,28189],{"class":1154,"line":75},[1115,28168,28169],{"class":1157},"Pz",[1115,28171,1162],{"class":1161},[1115,28173,6797],{"class":1173},[1115,28175,21136],{"class":1161},[1115,28177,11931],{"class":1165},[1115,28179,1170],{"class":1169},[1115,28181,7250],{"class":1161},[1115,28183,6220],{"class":1173},[1115,28185,21136],{"class":1161},[1115,28187,28188],{"class":1157}," Cp",[1115,28190,6519],{"class":1169},[1136,28192,9014],{"id":9013},[2220,28194,28195,28198,28258,28349,28415],{},[2223,28196,28197],{},"Počítat indexy způsobilosti pro proces, který není statisticky zvládnutý — způsobilost se zkoumá až ve třetí fázi regulace.",[2223,28199,28200,28201,28218,28219,28236,28237,2264],{},"Posuzovat jen ",[1115,28202,28204],{"className":28203},[1573],[1575,28205,28206],{"xmlns":1577},[1579,28207,28208,28216],{},[1582,28209,28210],{},[1746,28211,28212,28214],{},[1585,28213,3627],{},[1585,28215,1110],{},[1605,28217,3632],{"encoding":1607}," u vychýleného procesu — ",[1115,28220,28222],{"className":28221},[1573],[1575,28223,28224],{"xmlns":1577},[1579,28225,28226,28234],{},[1582,28227,28228],{},[1746,28229,28230,28232],{},[1585,28231,3627],{},[1585,28233,1110],{},[1605,28235,3632],{"encoding":1607}," polohu střední hodnoty nezohledňuje, vychýlení zachytí až ",[1115,28238,28240],{"className":28239},[1573],[1575,28241,28242],{"xmlns":1577},[1579,28243,28244,28256],{},[1582,28245,28246],{},[1746,28247,28248,28250],{},[1585,28249,3627],{},[1582,28251,28252,28254],{},[1585,28253,1110],{},[1585,28255,1600],{},[1605,28257,3654],{"encoding":1607},[2223,28259,28260,28261,28274,28275,28288,28289,28274,28304,28317,28318,28331,28332,28345,28346,28348],{},"Zaměnit diagram ",[1115,28262,28264],{"className":28263},[1573],[1575,28265,28266],{"xmlns":1577},[1579,28267,28268,28272],{},[1582,28269,28270],{},[1585,28271,3499],{},[1605,28273,3499],{"encoding":1607}," s diagramem ",[1115,28276,28278],{"className":28277},[1573],[1575,28279,28280],{"xmlns":1577},[1579,28281,28282,28286],{},[1582,28283,28284],{},[1585,28285,3523],{},[1605,28287,3523],{"encoding":1607}," nebo diagram ",[1115,28290,28292],{"className":28291},[1573],[1575,28293,28294],{"xmlns":1577},[1579,28295,28296,28302],{},[1582,28297,28298,28300],{},[1585,28299,1781],{},[1585,28301,1110],{},[1605,28303,3555],{"encoding":1607},[1115,28305,28307],{"className":28306},[1573],[1575,28308,28309],{"xmlns":1577},[1579,28310,28311,28315],{},[1582,28312,28313],{},[1585,28314,1110],{},[1605,28316,1110],{"encoding":1607}," — při nekonstantním rozsahu podskupin se volí ",[1115,28319,28321],{"className":28320},[1573],[1575,28322,28323],{"xmlns":1577},[1579,28324,28325,28329],{},[1582,28326,28327],{},[1585,28328,3523],{},[1605,28330,3523],{"encoding":1607},", resp. ",[1115,28333,28335],{"className":28334},[1573],[1575,28336,28337],{"xmlns":1577},[1579,28338,28339,28343],{},[1582,28340,28341],{},[1585,28342,1110],{},[1605,28344,1110],{"encoding":1607},", a do ",[1150,28347,3528],{}," se zadává vektor rozsahů.",[2223,28350,28351,28352,28369,28370,28383,28384,28397,28398,2264],{},"Posuzovat diagram ",[1115,28353,28355],{"className":28354},[1573],[1575,28356,28357],{"xmlns":1577},[1579,28358,28359,28367],{},[1582,28360,28361],{},[3005,28362,28363,28365],{"accent":1121},[1585,28364,1158],{},[1589,28366,3408],{},[1605,28368,24053],{"encoding":1607}," dřív než diagram rozpětí — nejprve se určí a stabilizuje diagram ",[1115,28371,28373],{"className":28372},[1573],[1575,28374,28375],{"xmlns":1577},[1579,28376,28377,28381],{},[1582,28378,28379],{},[1585,28380,3376],{},[1605,28382,3376],{"encoding":1607}," (resp. ",[1115,28385,28387],{"className":28386},[1573],[1575,28388,28389],{"xmlns":1577},[1579,28390,28391,28395],{},[1582,28392,28393],{},[1585,28394,3433],{},[1605,28396,3433],{"encoding":1607},"), potom diagram ",[1115,28399,28401],{"className":28400},[1573],[1575,28402,28403],{"xmlns":1577},[1579,28404,28405,28413],{},[1582,28406,28407],{},[3005,28408,28409,28411],{"accent":1121},[1585,28410,1158],{},[1589,28412,3408],{},[1605,28414,24053],{"encoding":1607},[2223,28416,28417],{},"Vyřadit podskupinu jen podle polohy bodu — vyřazuje se až po zjištění a odstranění vymezitelné příčiny.",[1136,28419,4071],{"id":4070},[2220,28421,28422,28427,28432,28438,28443,28448,28453],{},[2223,28423,28424],{},[1127,28425,1133],{"className":28426,"dataFsResolvedFilePath":1131,"href":1132},[1130],[2223,28428,28429],{},[1127,28430,886],{"className":28431,"dataFsResolvedFilePath":2413,"href":2414},[1130],[2223,28433,28434],{},[1127,28435,28437],{"className":28436,"dataFsResolvedFilePath":1556,"href":1557},[1130],"nahodne-veliciny-a-rozdeleni",[2223,28439,28440],{},[1127,28441,141],{"className":28442,"dataFsResolvedFilePath":2658,"href":2659},[1130],[2223,28444,28445],{},[1127,28446,13616],{"className":28447,"dataFsResolvedFilePath":2796,"href":2797},[1130],[2223,28449,28450],{},[1127,28451,716],{"className":28452,"dataFsResolvedFilePath":3235,"href":3236},[1130],[2223,28454,28455],{},[1127,28456,9239],{"className":28457,"dataFsResolvedFilePath":9237,"href":9238},[1130],[1136,28459,4111],{"id":934},[1110,28461,4114,28462,4119],{},[4116,28463,4118],{},[1110,28465,4122,28466,28468],{},[4116,28467,4125],{},". 6. vyd. John Wiley & Sons, 2005.",[1110,28470,28471,28472,28475],{},"ČSN ISO 8258. ",[4116,28473,28474],{},"Shewhartovy regulační diagramy",". Praha: Český normalizační institut, 1994.",[1110,28477,4129,28478,4133],{},[4116,28479,4132],{},[4135,28481,28482],{},"html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sP4rz, html code.shiki .sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sCsY4, html code.shiki .sCsY4{--shiki-light:#6A737D;--shiki-default:#6A737D;--shiki-dark:#6A737D}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: 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uu",{"id":26378,"depth":148,"text":28502},"Diagram npnp",{"id":26510,"depth":148,"text":28504},"Diagram pp",{"id":26643,"depth":27,"text":26644,"children":28506},[28507,28509,28511,28513,28514],{"id":26688,"depth":148,"text":28508},"CpC_p — index způsobilosti",{"id":27012,"depth":148,"text":28510},"CpkC_{pk} — index způsobilosti s ohledem na vychýlení",{"id":27207,"depth":148,"text":28512},"CpmC_{pm} a CpmkC_{pmk} — indexy vztažené k cíli",{"id":27465,"depth":148,"text":27466},{"id":27655,"depth":148,"text":27656},{"id":9013,"depth":27,"text":9014},{"id":4070,"depth":27,"text":4071},{"id":934,"depth":27,"text":4111},{},"\u002Ftopics\u002Fregulacni-diagramy-a-indexy-zpusobilosti",{"title":3322,"description":1148},[28522,28523,4167,28524],"raw\u002Fmask\u002F06 regulační diagramy.pdf","raw\u002Fmask\u002F07 indexy způsobilosti.pdf","raw\u002Fmask\u002Fpříklady 06 a 07.pdf","topics\u002Fregulacni-diagramy-a-indexy-zpusobilosti",[23,137,274,360,67,71],"bwtPTtx6g53SO_ovQdrK_C3d6vq9rKG9Vb8jM13_yag",{"id":28529,"title":2660,"body":28530,"course":23,"courses":4153,"created":4154,"description":1148,"extension":4155,"meta":38307,"navigation":4157,"path":38308,"seo":38309,"sources":38310,"stem":38314,"tags":38315,"type":9267,"updated":4154,"__hash__":38316},"topics\u002Ftopics\u002Ftestovani-hypotez.md",{"type":1096,"value":28531,"toc":38280},[28532,28534,28733,28777,28781,28791,28794,28860,28910,29063,29067,29070,29164,29314,29333,29340,29429,29433,29468,29505,29543,29578,29582,29589,29807,29926,29930,30062,30116,30138,30480,30486,30574,30580,30619,30904,30913,31028,31034,31041,31046,31052,31146,31152,31178,31184,31276,31282,31332,31336,31532,31592,31954,32293,32392,32398,32626,32630,32895,32899,32902,32968,33015,33471,33475,33478,33665,33698,33920,34239,34278,34285,34942,35081,35087,35243,35249,35256,35307,35313,35486,35492,35556,35561,35746,35752,35797,35801,35804,35807,35854,36082,36098,36187,36193,36219,36222,36225,36297,36390,36459,36465,36488,36935,36942,36946,36976,36980,37230,37249,37310,37319,37475,37481,37507,37682,37685,37706,37737,37741,37765,37795,37798,37858,37916,37920,37925,38078,38080,38232,38234,38271,38273,38277],[1099,28533,2660],{"id":2654},[1103,28535,28537,28543],{"className":28536,"dataCallout":4184},[1106,4183],[1110,28538,28540,4192],{"className":28539},[1113],[1115,28541],{"className":28542,"ariaHidden":1121},[1118,4191,1120],[2220,28544,28545,28615,28697,28700,28703],{},[2223,28546,28547,28548,28565,28566,28583,28584,1279,28597,28614],{},"Test porovnává tvrzení ",[1115,28549,28551],{"className":28550},[1573],[1575,28552,28553],{"xmlns":1577},[1579,28554,28555,28563],{},[1582,28556,28557],{},[1746,28558,28559,28561],{},[1585,28560,1922],{},[1716,28562,2398],{},[1605,28564,4225],{"encoding":1607}," s alternativou ",[1115,28567,28569],{"className":28568},[1573],[1575,28570,28571],{"xmlns":1577},[1579,28572,28573,28581],{},[1582,28574,28575],{},[1746,28576,28577,28579],{},[1585,28578,1922],{},[1716,28580,1718],{},[1605,28582,3807],{"encoding":1607}," pomocí testového kritéria spočteného z výběru; padne-li kritérium do kritického oboru ",[1115,28585,28587],{"className":28586},[1573],[1575,28588,28589],{"xmlns":1577},[1579,28590,28591,28595],{},[1582,28592,28593],{},[1585,28594,4256],{},[1605,28596,4256],{"encoding":1607},[1115,28598,28600],{"className":28599},[1573],[1575,28601,28602],{"xmlns":1577},[1579,28603,28604,28612],{},[1582,28605,28606],{},[1746,28607,28608,28610],{},[1585,28609,1922],{},[1716,28611,2398],{},[1605,28613,4225],{"encoding":1607}," zamítáme.",[2223,28616,28617,28618,28631,28632,28649,28650,28664,28665,28682,28683,28696],{},"Rozhodnutí nese dva typy chyb: chybu I. druhu (",[1115,28619,28621],{"className":28620},[1573],[1575,28622,28623],{"xmlns":1577},[1579,28624,28625,28629],{},[1582,28626,28627],{},[1585,28628,3862],{},[1605,28630,6058],{"encoding":1607},", zamítnutí platné ",[1115,28633,28635],{"className":28634},[1573],[1575,28636,28637],{"xmlns":1577},[1579,28638,28639,28647],{},[1582,28640,28641],{},[1746,28642,28643,28645],{},[1585,28644,1922],{},[1716,28646,2398],{},[1605,28648,4225],{"encoding":1607},") a chybu II. druhu (",[1115,28651,28653],{"className":28652},[1573],[1575,28654,28655],{"xmlns":1577},[1579,28656,28657,28661],{},[1582,28658,28659],{},[1585,28660,18838],{},[1605,28662,28663],{"encoding":1607},"\\beta",", přijetí neplatné ",[1115,28666,28668],{"className":28667},[1573],[1575,28669,28670],{"xmlns":1577},[1579,28671,28672,28680],{},[1582,28673,28674],{},[1746,28675,28676,28678],{},[1585,28677,1922],{},[1716,28679,2398],{},[1605,28681,4225],{"encoding":1607},"). Hladina významnosti ",[1115,28684,28686],{"className":28685},[1573],[1575,28687,28688],{"xmlns":1577},[1579,28689,28690,28694],{},[1582,28691,28692],{},[1585,28693,3862],{},[1605,28695,6058],{"encoding":1607}," se volí předem, obvykle 0,05.",[2223,28698,28699],{},"Pro střední hodnotu normálního rozdělení slouží jednovýběrový a párový t-test; pro srovnání dvou souborů F-test (rozptyly) a dvouvýběrový t-test (střední hodnoty).",[2223,28701,28702],{},"Normalitu ověřuje Shapiro-Wilkův test, shodu s libovolným rozdělením Kolmogorov-Smirnovův test; při porušené normalitě nastupují neparametrické testy (Wilcoxonovy, Kruskalův-Wallisův, mediánový, Friedmanův).",[2223,28704,28705,28706,28719,28720,2264],{},"Rozhodnutí lze číst dvěma rovnocennými způsoby — podle polohy kritéria vůči ",[1115,28707,28709],{"className":28708},[1573],[1575,28710,28711],{"xmlns":1577},[1579,28712,28713,28717],{},[1582,28714,28715],{},[1585,28716,4256],{},[1605,28718,4256],{"encoding":1607},", nebo podle p-hodnoty vůči ",[1115,28721,28723],{"className":28722},[1573],[1575,28724,28725],{"xmlns":1577},[1579,28726,28727,28731],{},[1582,28728,28729],{},[1585,28730,3862],{},[1605,28732,6058],{"encoding":1607},[1110,28734,28735,28736,28740,28741,28745,28746,28750,28751,1279,28764,1295],{},"Testy statistických hypotéz jsou nástroj ",[1127,28737,28739],{"className":28738,"dataFsResolvedFilePath":1131,"href":1132},[1130],"Metod aplikované statistiky"," pro rozhodování o parametrech nebo tvaru rozdělení na základě náhodného výběru, nikoli vyčerpávajícího šetření celého základního souboru. Vycházejí z charakteristik, které lze předem spočítat jako ",[1127,28742,28744],{"className":28743,"dataFsResolvedFilePath":2413,"href":2414},[1130],"popisnou statistiku"," výběru, a z rozdělení uvedených u ",[1127,28747,28749],{"className":28748,"dataFsResolvedFilePath":1556,"href":1557},[1130],"náhodných veličin"," (normální, ",[1115,28752,28754],{"className":28753},[1573],[1575,28755,28756],{"xmlns":1577},[1579,28757,28758,28762],{},[1582,28759,28760],{},[1585,28761,2082],{},[1605,28763,2082],{"encoding":1607},[1115,28765,28767],{"className":28766},[1573],[1575,28768,28769],{"xmlns":1577},[1579,28770,28771,28775],{},[1582,28772,28773],{},[1585,28774,1669],{},[1605,28776,1669],{"encoding":1607},[1136,28778,28780],{"id":28779},"statistická-hypotéza-a-její-test","Statistická hypotéza a její test",[1110,28782,28783,28786,28787,28790],{},[2227,28784,28785],{},"Statistická hypotéza"," je předpoklad o parametru nebo tvaru rozdělení zkoumaného znaku — například že určitý typ auta má průměrnou spotřebu 7 l\u002F100 km. Ověřit ji na celém základním souboru je obvykle neekonomické nebo technicky neproveditelné, a tak se posuzuje na výběru. ",[2227,28788,28789],{},"Testování hypotéz"," je proces ověření správnosti nebo nesprávnosti hypotézy pomocí výsledků získaných náhodným výběrem.",[1110,28792,28793],{},"Proti sobě stojí dvě hypotézy:",[2220,28795,28796,28819],{},[2223,28797,28798,28818],{},[2227,28799,28800,28801],{},"Nulová hypotéza ",[1115,28802,28804],{"className":28803},[1573],[1575,28805,28806],{"xmlns":1577},[1579,28807,28808,28816],{},[1582,28809,28810],{},[1746,28811,28812,28814],{},[1585,28813,1922],{},[1716,28815,2398],{},[1605,28817,4225],{"encoding":1607}," — tvrzení o parametru nebo rozdělení, které chceme ověřit.",[2223,28820,28821,28841,28842,28859],{},[2227,28822,28823,28824],{},"Alternativní hypotéza ",[1115,28825,28827],{"className":28826},[1573],[1575,28828,28829],{"xmlns":1577},[1579,28830,28831,28839],{},[1582,28832,28833],{},[1746,28834,28835,28837],{},[1585,28836,1922],{},[1716,28838,1718],{},[1605,28840,3807],{"encoding":1607}," — staví se proti ",[1115,28843,28845],{"className":28844},[1573],[1575,28846,28847],{"xmlns":1577},[1579,28848,28849,28857],{},[1582,28850,28851],{},[1746,28852,28853,28855],{},[1585,28854,1922],{},[1716,28856,2398],{},[1605,28858,4225],{"encoding":1607}," a určitým způsobem popírá její tvrzení.",[1110,28861,4345,28862,28892,28893,4595],{},[1115,28863,28865],{"className":28864},[1573],[1575,28866,28867],{"xmlns":1577},[1579,28868,28869,28889],{},[1582,28870,28871,28877,28879,28881,28883],{},[1746,28872,28873,28875],{},[1585,28874,1922],{},[1716,28876,2398],{},[1589,28878,4595],{},[1585,28880,1982],{},[1589,28882,1597],{},[1746,28884,28885,28887],{},[1585,28886,1982],{},[1716,28888,2398],{},[1605,28890,28891],{"encoding":1607},"H_0: \\mu = \\mu_0"," existují tři varianty ",[1115,28894,28896],{"className":28895},[1573],[1575,28897,28898],{"xmlns":1577},[1579,28899,28900,28908],{},[1582,28901,28902],{},[1746,28903,28904,28906],{},[1585,28905,1922],{},[1716,28907,1718],{},[1605,28909,3807],{"encoding":1607},[1310,28911,28912,28942],{},[1313,28913,28914],{},[1316,28915,28916,28936,28939],{},[1319,28917,28918,28919],{},"Tvar ",[1115,28920,28922],{"className":28921},[1573],[1575,28923,28924],{"xmlns":1577},[1579,28925,28926,28934],{},[1582,28927,28928],{},[1746,28929,28930,28932],{},[1585,28931,1922],{},[1716,28933,1718],{},[1605,28935,3807],{"encoding":1607},[1319,28937,28938],{},"Zápis",[1319,28940,28941],{},"Typ",[1332,28943,28944,28984,29024],{},[1316,28945,28946,28949,28981],{},[1337,28947,28948],{},"nerovnost",[1337,28950,28951],{},[1115,28952,28954],{"className":28953},[1573],[1575,28955,28956],{"xmlns":1577},[1579,28957,28958,28978],{},[1582,28959,28960,28966,28968,28970,28972],{},[1746,28961,28962,28964],{},[1585,28963,1922],{},[1716,28965,1718],{},[1589,28967,4595],{},[1585,28969,1982],{},[1589,28971,13487],{"mathvariant":4022},[1746,28973,28974,28976],{},[1585,28975,1982],{},[1716,28977,2398],{},[1605,28979,28980],{"encoding":1607},"H_1: \\mu \\neq \\mu_0",[1337,28982,28983],{},"dvoustranná",[1316,28985,28986,28989,29021],{},[1337,28987,28988],{},"větší",[1337,28990,28991],{},[1115,28992,28994],{"className":28993},[1573],[1575,28995,28996],{"xmlns":1577},[1579,28997,28998,29018],{},[1582,28999,29000,29006,29008,29010,29012],{},[1746,29001,29002,29004],{},[1585,29003,1922],{},[1716,29005,1718],{},[1589,29007,4595],{},[1585,29009,1982],{},[1589,29011,1698],{},[1746,29013,29014,29016],{},[1585,29015,1982],{},[1716,29017,2398],{},[1605,29019,29020],{"encoding":1607},"H_1: \\mu > \\mu_0",[1337,29022,29023],{},"jednostranná",[1316,29025,29026,29029,29061],{},[1337,29027,29028],{},"menší",[1337,29030,29031],{},[1115,29032,29034],{"className":29033},[1573],[1575,29035,29036],{"xmlns":1577},[1579,29037,29038,29058],{},[1582,29039,29040,29046,29048,29050,29052],{},[1746,29041,29042,29044],{},[1585,29043,1922],{},[1716,29045,1718],{},[1589,29047,4595],{},[1585,29049,1982],{},[1589,29051,6949],{},[1746,29053,29054,29056],{},[1585,29055,1982],{},[1716,29057,2398],{},[1605,29059,29060],{"encoding":1607},"H_1: \\mu \u003C \\mu_0",[1337,29062,29023],{},[1550,29064,29066],{"id":29065},"chyba-i-a-ii-druhu","Chyba I. a II. druhu",[1110,29068,29069],{},"Protože je úsudek odvozen z náhodného výběru, může vést ke dvěma typům chybného rozhodnutí:",[2220,29071,29072,29109],{},[2223,29073,29074,29077,29078,29095,29096,2264],{},[2227,29075,29076],{},"Chyba I. druhu"," — zamítnutí ",[1115,29079,29081],{"className":29080},[1573],[1575,29082,29083],{"xmlns":1577},[1579,29084,29085,29093],{},[1582,29086,29087],{},[1746,29088,29089,29091],{},[1585,29090,1922],{},[1716,29092,2398],{},[1605,29094,4225],{"encoding":1607},", ačkoliv ve skutečnosti platí. Pravděpodobnost ",[1115,29097,29099],{"className":29098},[1573],[1575,29100,29101],{"xmlns":1577},[1579,29102,29103,29107],{},[1582,29104,29105],{},[1585,29106,3862],{},[1605,29108,6058],{"encoding":1607},[2223,29110,29111,29114,29115,29132,29133,29150,29151,2264],{},[2227,29112,29113],{},"Chyba II. druhu"," — přijetí ",[1115,29116,29118],{"className":29117},[1573],[1575,29119,29120],{"xmlns":1577},[1579,29121,29122,29130],{},[1582,29123,29124],{},[1746,29125,29126,29128],{},[1585,29127,1922],{},[1716,29129,2398],{},[1605,29131,4225],{"encoding":1607},", ačkoliv platí ",[1115,29134,29136],{"className":29135},[1573],[1575,29137,29138],{"xmlns":1577},[1579,29139,29140,29148],{},[1582,29141,29142],{},[1746,29143,29144,29146],{},[1585,29145,1922],{},[1716,29147,1718],{},[1605,29149,3807],{"encoding":1607},". Pravděpodobnost ",[1115,29152,29154],{"className":29153},[1573],[1575,29155,29156],{"xmlns":1577},[1579,29157,29158,29162],{},[1582,29159,29160],{},[1585,29161,18838],{},[1605,29163,28663],{"encoding":1607},[1310,29165,29166,29229],{},[1313,29167,29168],{},[1316,29169,29170,29190,29209],{},[1319,29171,29172,29173],{},"Úsudek o ",[1115,29174,29176],{"className":29175},[1573],[1575,29177,29178],{"xmlns":1577},[1579,29179,29180,29188],{},[1582,29181,29182],{},[1746,29183,29184,29186],{},[1585,29185,1922],{},[1716,29187,2398],{},[1605,29189,4225],{"encoding":1607},[1319,29191,29192,10932],{},[1115,29193,29195],{"className":29194},[1573],[1575,29196,29197],{"xmlns":1577},[1579,29198,29199,29207],{},[1582,29200,29201],{},[1746,29202,29203,29205],{},[1585,29204,1922],{},[1716,29206,2398],{},[1605,29208,4225],{"encoding":1607},[1319,29210,29211,29228],{},[1115,29212,29214],{"className":29213},[1573],[1575,29215,29216],{"xmlns":1577},[1579,29217,29218,29226],{},[1582,29219,29220],{},[1746,29221,29222,29224],{},[1585,29223,1922],{},[1716,29225,2398],{},[1605,29227,4225],{"encoding":1607}," neplatí",[1332,29230,29231,29273],{},[1316,29232,29233,29236,29257],{},[1337,29234,29235],{},"Nezamítá se",[1337,29237,29238,29239],{},"správné rozhodnutí, ",[1115,29240,29242],{"className":29241},[1573],[1575,29243,29244],{"xmlns":1577},[1579,29245,29246,29254],{},[1582,29247,29248,29250,29252],{},[1716,29249,1718],{},[1589,29251,1721],{},[1585,29253,3862],{},[1605,29255,29256],{"encoding":1607},"1-\\alpha",[1337,29258,29259,29260],{},"chyba II. druhu, ",[1115,29261,29263],{"className":29262},[1573],[1575,29264,29265],{"xmlns":1577},[1579,29266,29267,29271],{},[1582,29268,29269],{},[1585,29270,18838],{},[1605,29272,28663],{"encoding":1607},[1316,29274,29275,29278,29294],{},[1337,29276,29277],{},"Zamítá se",[1337,29279,29280,29281],{},"chyba I. druhu, ",[1115,29282,29284],{"className":29283},[1573],[1575,29285,29286],{"xmlns":1577},[1579,29287,29288,29292],{},[1582,29289,29290],{},[1585,29291,3862],{},[1605,29293,6058],{"encoding":1607},[1337,29295,29238,29296],{},[1115,29297,29299],{"className":29298},[1573],[1575,29300,29301],{"xmlns":1577},[1579,29302,29303,29311],{},[1582,29304,29305,29307,29309],{},[1716,29306,1718],{},[1589,29308,1721],{},[1585,29310,18838],{},[1605,29312,29313],{"encoding":1607},"1-\\beta",[1110,29315,29316,2230,29319,29332],{},[2227,29317,29318],{},"Hladina významnosti",[1115,29320,29322],{"className":29321},[1573],[1575,29323,29324],{"xmlns":1577},[1579,29325,29326,29330],{},[1582,29327,29328],{},[1585,29329,3862],{},[1605,29331,6058],{"encoding":1607}," je předem pevně zvolená pravděpodobnost chyby I. druhu (klasicky 5 %). Testovací postup je odvozen tak, aby při dané hladině významnosti zajišťoval minimální pravděpodobnost chyby II. druhu.",[1110,29334,29335],{},[1303,29336],{"alt":29337,"className":29338,"src":29339},"mask-th-chyba-i-ii",[1130,1307],"\u002Fwiki-assets\u002Fmask-th-chyba-i-ii.png",[1110,29341,29342,29343,29356,29357,29370,29371,29384,29385,4527,29398,29411,29412,2264],{},"Obrázek ukazuje, proč jde o kompromis: posunutí kritické hodnoty ",[1115,29344,29346],{"className":29345},[1573],[1575,29347,29348],{"xmlns":1577},[1579,29349,29350,29354],{},[1582,29351,29352],{},[1585,29353,3499],{},[1605,29355,3499],{"encoding":1607}," doleva zmenší ",[1115,29358,29360],{"className":29359},[1573],[1575,29361,29362],{"xmlns":1577},[1579,29363,29364,29368],{},[1582,29365,29366],{},[1585,29367,18838],{},[1605,29369,28663],{"encoding":1607},", ale zvětší ",[1115,29372,29374],{"className":29373},[1573],[1575,29375,29376],{"xmlns":1577},[1579,29377,29378,29382],{},[1582,29379,29380],{},[1585,29381,3862],{},[1605,29383,6058],{"encoding":1607},", a naopak. Pro danou hladinu ",[1115,29386,29388],{"className":29387},[1573],[1575,29389,29390],{"xmlns":1577},[1579,29391,29392,29396],{},[1582,29393,29394],{},[1585,29395,3862],{},[1605,29397,6058],{"encoding":1607},[1115,29399,29401],{"className":29400},[1573],[1575,29402,29403],{"xmlns":1577},[1579,29404,29405,29409],{},[1582,29406,29407],{},[1585,29408,3499],{},[1605,29410,3499],{"encoding":1607}," jednoznačně určena rozdělením kritéria za platnosti ",[1115,29413,29415],{"className":29414},[1573],[1575,29416,29417],{"xmlns":1577},[1579,29418,29419,29427],{},[1582,29420,29421],{},[1746,29422,29423,29425],{},[1585,29424,1922],{},[1716,29426,2398],{},[1605,29428,4225],{"encoding":1607},[1550,29430,29432],{"id":29431},"testové-kritérium-a-kritický-obor","Testové kritérium a kritický obor",[1110,29434,29435,2230,29437,29450,29451,2264],{},[2227,29436,5633],{},[1115,29438,29440],{"className":29439},[1573],[1575,29441,29442],{"xmlns":1577},[1579,29443,29444,29448],{},[1582,29445,29446],{},[1585,29447,4043],{},[1605,29449,4043],{"encoding":1607}," je statistika spočtená z výběru; aby bylo možné test provést, musí být známo jeho rozdělení za platnosti ",[1115,29452,29454],{"className":29453},[1573],[1575,29455,29456],{"xmlns":1577},[1579,29457,29458,29466],{},[1582,29459,29460],{},[1746,29461,29462,29464],{},[1585,29463,1922],{},[1716,29465,2398],{},[1605,29467,4225],{"encoding":1607},[1110,29469,29470,2230,29473,29486,29487,29504],{},[2227,29471,29472],{},"Kritický obor",[1115,29474,29476],{"className":29475},[1573],[1575,29477,29478],{"xmlns":1577},[1579,29479,29480,29484],{},[1582,29481,29482],{},[1585,29483,4256],{},[1605,29485,4256],{"encoding":1607}," je množina hodnot svědčících pro ",[1115,29488,29490],{"className":29489},[1573],[1575,29491,29492],{"xmlns":1577},[1579,29493,29494,29502],{},[1582,29495,29496],{},[1746,29497,29498,29500],{},[1585,29499,1922],{},[1716,29501,1718],{},[1605,29503,3807],{"encoding":1607},". Je zkonstruován tak, aby",[1115,29506,29508],{"className":29507},[1573],[1575,29509,29510],{"xmlns":1577,"display":4601},[1579,29511,29512,29540],{},[1582,29513,29514,29516,29518,29520,29522,29524,29526,29532,29534,29536,29538],{},[1585,29515,1587],{},[1589,29517,1170],{"stretchy":1591},[1585,29519,4043],{},[1589,29521,9605],{},[1585,29523,4256],{},[1589,29525,25509],{},[1746,29527,29528,29530],{},[1585,29529,1922],{},[1716,29531,2398],{},[1589,29533,1603],{"stretchy":1591},[1589,29535,1597],{},[1585,29537,3862],{},[1589,29539,1177],{"separator":1121},[1605,29541,29542],{"encoding":1607},"P(T \\in W \\mid H_0) = \\alpha,",[1110,29544,29545,29546,29559,29560,29577],{},"tedy aby pravděpodobnost, že výběr dá hodnotu kritéria v ",[1115,29547,29549],{"className":29548},[1573],[1575,29550,29551],{"xmlns":1577},[1579,29552,29553,29557],{},[1582,29554,29555],{},[1585,29556,4256],{},[1605,29558,4256],{"encoding":1607}," i při platné ",[1115,29561,29563],{"className":29562},[1573],[1575,29564,29565],{"xmlns":1577},[1579,29566,29567,29575],{},[1582,29568,29569],{},[1746,29570,29571,29573],{},[1585,29572,1922],{},[1716,29574,2398],{},[1605,29576,4225],{"encoding":1607},", byla rovna zvolené hladině významnosti.",[1550,29579,29581],{"id":29580},"postup-testování-hypotézy","Postup testování hypotézy",[1110,29583,29584],{},[1303,29585],{"alt":29586,"className":29587,"src":29588},"mask-ilu-postup-testovani",[1130,1307],"\u002Fwiki-assets\u002Fmask-ilu-postup-testovani.png",[5499,29590,29591,29628,29631,29647],{},[2223,29592,29593,29594,1260,29611,2264],{},"Formulace hypotéz ",[1115,29595,29597],{"className":29596},[1573],[1575,29598,29599],{"xmlns":1577},[1579,29600,29601,29609],{},[1582,29602,29603],{},[1746,29604,29605,29607],{},[1585,29606,1922],{},[1716,29608,2398],{},[1605,29610,4225],{"encoding":1607},[1115,29612,29614],{"className":29613},[1573],[1575,29615,29616],{"xmlns":1577},[1579,29617,29618,29626],{},[1582,29619,29620],{},[1746,29621,29622,29624],{},[1585,29623,1922],{},[1716,29625,1718],{},[1605,29627,3807],{"encoding":1607},[2223,29629,29630],{},"Volba testového kritéria a výpočet jeho hodnoty.",[2223,29632,29633,29634,2264],{},"Volba hladiny významnosti a sestrojení příslušného kritického oboru ",[1115,29635,29637],{"className":29636},[1573],[1575,29638,29639],{"xmlns":1577},[1579,29640,29641,29645],{},[1582,29642,29643],{},[1585,29644,4256],{},[1605,29646,4256],{"encoding":1607},[2223,29648,29649,29650],{},"Formulace závěru:\n",[2220,29651,29652,29730],{},[2223,29653,29654,29655,6605,29673,29690,29691,29711,29712,29729],{},"pokud ",[1115,29656,29658],{"className":29657},[1573],[1575,29659,29660],{"xmlns":1577},[1579,29661,29662,29670],{},[1582,29663,29664,29666,29668],{},[1585,29665,4043],{},[1589,29667,9605],{},[1585,29669,4256],{},[1605,29671,29672],{"encoding":1607},"T \\in W",[1115,29674,29676],{"className":29675},[1573],[1575,29677,29678],{"xmlns":1577},[1579,29679,29680,29688],{},[1582,29681,29682],{},[1746,29683,29684,29686],{},[1585,29685,1922],{},[1716,29687,1718],{},[1605,29689,3807],{"encoding":1607}," je testem prokázána na hladině významnosti ",[1115,29692,29694],{"className":29693},[1573],[1575,29695,29696],{"xmlns":1577},[1579,29697,29698,29708],{},[1582,29699,29700,29702,29704,29706],{},[1716,29701,14343],{},[1585,29703,3862],{},[5543,29705,5545],{},[1585,29707,14350],{"mathvariant":4022},[1605,29709,29710],{"encoding":1607},"100\\alpha\\,\\%"," (zamítáme ",[1115,29713,29715],{"className":29714},[1573],[1575,29716,29717],{"xmlns":1577},[1579,29718,29719,29727],{},[1582,29720,29721],{},[1746,29722,29723,29725],{},[1585,29724,1922],{},[1716,29726,2398],{},[1605,29728,4225],{"encoding":1607},");",[2223,29731,29654,29732,6605,29751,29768,29769,29788,29789,29806],{},[1115,29733,29735],{"className":29734},[1573],[1575,29736,29737],{"xmlns":1577},[1579,29738,29739,29748],{},[1582,29740,29741,29743,29746],{},[1585,29742,4043],{},[1589,29744,29745],{"mathvariant":4022},"∉",[1585,29747,4256],{},[1605,29749,29750],{"encoding":1607},"T \\notin W",[1115,29752,29754],{"className":29753},[1573],[1575,29755,29756],{"xmlns":1577},[1579,29757,29758,29766],{},[1582,29759,29760],{},[1746,29761,29762,29764],{},[1585,29763,1922],{},[1716,29765,1718],{},[1605,29767,3807],{"encoding":1607}," není testem prokázána na hladině významnosti ",[1115,29770,29772],{"className":29771},[1573],[1575,29773,29774],{"xmlns":1577},[1579,29775,29776,29786],{},[1582,29777,29778,29780,29782,29784],{},[1716,29779,14343],{},[1585,29781,3862],{},[5543,29783,5545],{},[1585,29785,14350],{"mathvariant":4022},[1605,29787,29710],{"encoding":1607}," ; ",[1115,29790,29792],{"className":29791},[1573],[1575,29793,29794],{"xmlns":1577},[1579,29795,29796,29804],{},[1582,29797,29798],{},[1746,29799,29800,29802],{},[1585,29801,1922],{},[1716,29803,2398],{},[1605,29805,4225],{"encoding":1607}," nezamítáme.",[1110,29808,29809,29810,29813,29814,29831,29832,29849,29850,29870,29871,2402,29888,2230,29908,29925],{},"Rovnocennou alternativou je ",[2227,29811,29812],{},"p-hodnota",": udává, nakolik jsou data slučitelná s ",[1115,29815,29817],{"className":29816},[1573],[1575,29818,29819],{"xmlns":1577},[1579,29820,29821,29829],{},[1582,29822,29823],{},[1746,29824,29825,29827],{},[1585,29826,1922],{},[1716,29828,2398],{},[1605,29830,4225],{"encoding":1607},". Čím menší p-hodnota, tím více data svědčí proti ",[1115,29833,29835],{"className":29834},[1573],[1575,29836,29837],{"xmlns":1577},[1579,29838,29839,29847],{},[1582,29840,29841],{},[1746,29842,29843,29845],{},[1585,29844,1922],{},[1716,29846,2398],{},[1605,29848,4225],{"encoding":1607},". Rozhodovací pravidlo: ",[1115,29851,29853],{"className":29852},[1573],[1575,29854,29855],{"xmlns":1577},[1579,29856,29857,29867],{},[1582,29858,29859,29861,29863,29865],{},[1585,29860,1110],{},[1589,29862,1650],{},[1585,29864,3862],{},[1589,29866,10131],{},[1605,29868,29869],{"encoding":1607},"p \\le \\alpha \\Rightarrow"," zamítáme ",[1115,29872,29874],{"className":29873},[1573],[1575,29875,29876],{"xmlns":1577},[1579,29877,29878,29886],{},[1582,29879,29880],{},[1746,29881,29882,29884],{},[1585,29883,1922],{},[1716,29885,2398],{},[1605,29887,4225],{"encoding":1607},[1115,29889,29891],{"className":29890},[1573],[1575,29892,29893],{"xmlns":1577},[1579,29894,29895,29905],{},[1582,29896,29897,29899,29901,29903],{},[1585,29898,1110],{},[1589,29900,1698],{},[1585,29902,3862],{},[1589,29904,10131],{},[1605,29906,29907],{"encoding":1607},"p > \\alpha \\Rightarrow",[1115,29909,29911],{"className":29910},[1573],[1575,29912,29913],{"xmlns":1577},[1579,29914,29915,29923],{},[1582,29916,29917],{},[1746,29918,29919,29921],{},[1585,29920,1922],{},[1716,29922,2398],{},[1605,29924,4225],{"encoding":1607}," nezamítáme. Obě cesty — kritický obor i p-hodnota — vedou vždy ke stejnému závěru; R u všech testů vrací p-hodnotu přímo.",[1136,29927,29929],{"id":29928},"jednovýběrový-t-test","Jednovýběrový t-test",[1110,29931,29932,29933,29946,29947,29979,29980,29993,29994,1260,30011,30028,30029,30047,30048,30061],{},"Test o střední hodnotě ",[1115,29934,29936],{"className":29935},[1573],[1575,29937,29938],{"xmlns":1577},[1579,29939,29940,29944],{},[1582,29941,29942],{},[1585,29943,1982],{},[1605,29945,11376],{"encoding":1607}," rozdělení ",[1115,29948,29950],{"className":29949},[1573],[1575,29951,29952],{"xmlns":1577},[1579,29953,29954,29976],{},[1582,29955,29956,29958,29960,29962,29964,29966,29968,29974],{},[1585,29957,1594],{},[1589,29959,11763],{},[1585,29961,1927],{},[1589,29963,1170],{"stretchy":1591},[1585,29965,1982],{},[1589,29967,1177],{"separator":1121},[1986,29969,29970,29972],{},[1585,29971,1990],{},[1716,29973,1993],{},[1589,29975,1603],{"stretchy":1591},[1605,29977,29978],{"encoding":1607},"X \\sim N(\\mu, \\sigma^2)",". Z výběru o rozsahu ",[1115,29981,29983],{"className":29982},[1573],[1575,29984,29985],{"xmlns":1577},[1579,29986,29987,29991],{},[1582,29988,29989],{},[1585,29990,1781],{},[1605,29992,1781],{"encoding":1607}," se určí charakteristiky ",[1115,29995,29997],{"className":29996},[1573],[1575,29998,29999],{"xmlns":1577},[1579,30000,30001,30009],{},[1582,30002,30003],{},[3005,30004,30005,30007],{"accent":1121},[1585,30006,1158],{},[1589,30008,3408],{},[1605,30010,24053],{"encoding":1607},[1115,30012,30014],{"className":30013},[1573],[1575,30015,30016],{"xmlns":1577},[1579,30017,30018,30026],{},[1582,30019,30020],{},[1986,30021,30022,30024],{},[1585,30023,3433],{},[1716,30025,1993],{},[1605,30027,18281],{"encoding":1607},"; testem se posuzuje vztah mezi zvoleným číslem ",[1115,30030,30032],{"className":30031},[1573],[1575,30033,30034],{"xmlns":1577},[1579,30035,30036,30044],{},[1582,30037,30038],{},[1746,30039,30040,30042],{},[1585,30041,1982],{},[1716,30043,2398],{},[1605,30045,30046],{"encoding":1607},"\\mu_0"," a neznámou hodnotou ",[1115,30049,30051],{"className":30050},[1573],[1575,30052,30053],{"xmlns":1577},[1579,30054,30055,30059],{},[1582,30056,30057],{},[1585,30058,1982],{},[1605,30060,11376],{"encoding":1607},". Testové kritérium",[1115,30063,30065],{"className":30064},[1573],[1575,30066,30067],{"xmlns":1577,"display":4601},[1579,30068,30069,30113],{},[1582,30070,30071,30073,30075,30095,30099,30101],{},[1585,30072,4043],{},[1589,30074,1597],{},[5373,30076,30077,30093],{},[1582,30078,30079,30085,30087],{},[3005,30080,30081,30083],{"accent":1121},[1585,30082,1158],{},[1589,30084,3408],{},[1589,30086,1721],{},[1746,30088,30089,30091],{},[1585,30090,1982],{},[1716,30092,2398],{},[1585,30094,3433],{},[7068,30096,30097],{},[1585,30098,1781],{},[1589,30100,11763],{},[1746,30102,30103,30105],{},[1585,30104,2082],{},[1582,30106,30107,30109,30111],{},[1585,30108,1781],{},[1589,30110,1721],{},[1716,30112,1718],{},[1605,30114,30115],{"encoding":1607},"T = \\frac{\\bar{x} - \\mu_0}{s}\\sqrt{n} \\sim t_{n-1}",[1110,30117,30118,30119,30137],{},"má Studentovo rozdělení o ",[1115,30120,30122],{"className":30121},[1573],[1575,30123,30124],{"xmlns":1577},[1579,30125,30126,30134],{},[1582,30127,30128,30130,30132],{},[1585,30129,1781],{},[1589,30131,1721],{},[1716,30133,1718],{},[1605,30135,30136],{"encoding":1607},"n-1"," stupních volnosti.",[1310,30139,30140,30198],{},[1313,30141,30142],{},[1316,30143,30144,30163,30182],{},[1319,30145,30146],{},[1115,30147,30149],{"className":30148},[1573],[1575,30150,30151],{"xmlns":1577},[1579,30152,30153,30161],{},[1582,30154,30155],{},[1746,30156,30157,30159],{},[1585,30158,1922],{},[1716,30160,2398],{},[1605,30162,4225],{"encoding":1607},[1319,30164,30165],{},[1115,30166,30168],{"className":30167},[1573],[1575,30169,30170],{"xmlns":1577},[1579,30171,30172,30180],{},[1582,30173,30174],{},[1746,30175,30176,30178],{},[1585,30177,1922],{},[1716,30179,1718],{},[1605,30181,3807],{"encoding":1607},[1319,30183,30184,30185],{},"Kritický obor ",[1115,30186,30188],{"className":30187},[1573],[1575,30189,30190],{"xmlns":1577},[1579,30191,30192,30196],{},[1582,30193,30194],{},[1585,30195,4256],{},[1605,30197,4256],{"encoding":1607},[1332,30199,30200,30290,30388],{},[1316,30201,30202,30226,30250],{},[1337,30203,30204],{},[1115,30205,30207],{"className":30206},[1573],[1575,30208,30209],{"xmlns":1577},[1579,30210,30211,30223],{},[1582,30212,30213,30215,30217],{},[1585,30214,1982],{},[1589,30216,1650],{},[1746,30218,30219,30221],{},[1585,30220,1982],{},[1716,30222,2398],{},[1605,30224,30225],{"encoding":1607},"\\mu \\le \\mu_0",[1337,30227,30228],{},[1115,30229,30231],{"className":30230},[1573],[1575,30232,30233],{"xmlns":1577},[1579,30234,30235,30247],{},[1582,30236,30237,30239,30241],{},[1585,30238,1982],{},[1589,30240,1698],{},[1746,30242,30243,30245],{},[1585,30244,1982],{},[1716,30246,2398],{},[1605,30248,30249],{"encoding":1607},"\\mu > \\mu_0",[1337,30251,30252],{},[1115,30253,30255],{"className":30254},[1573],[1575,30256,30257],{"xmlns":1577},[1579,30258,30259,30287],{},[1582,30260,30261,30263,30265,30277,30279,30281,30283,30285],{},[1585,30262,2082],{},[1589,30264,5983],{},[1746,30266,30267,30269],{},[1585,30268,2082],{},[1582,30270,30271,30273,30275],{},[1716,30272,1718],{},[1589,30274,1721],{},[1585,30276,3862],{},[1589,30278,1170],{"stretchy":1591},[1585,30280,1781],{},[1589,30282,1721],{},[1716,30284,1718],{},[1589,30286,1603],{"stretchy":1591},[1605,30288,30289],{"encoding":1607},"t \\ge t_{1-\\alpha}(n-1)",[1316,30291,30292,30316,30340],{},[1337,30293,30294],{},[1115,30295,30297],{"className":30296},[1573],[1575,30298,30299],{"xmlns":1577},[1579,30300,30301,30313],{},[1582,30302,30303,30305,30307],{},[1585,30304,1982],{},[1589,30306,1597],{},[1746,30308,30309,30311],{},[1585,30310,1982],{},[1716,30312,2398],{},[1605,30314,30315],{"encoding":1607},"\\mu = \\mu_0",[1337,30317,30318],{},[1115,30319,30321],{"className":30320},[1573],[1575,30322,30323],{"xmlns":1577},[1579,30324,30325,30337],{},[1582,30326,30327,30329,30331],{},[1585,30328,1982],{},[1589,30330,13487],{"mathvariant":4022},[1746,30332,30333,30335],{},[1585,30334,1982],{},[1716,30336,2398],{},[1605,30338,30339],{"encoding":1607},"\\mu \\neq \\mu_0",[1337,30341,30342],{},[1115,30343,30345],{"className":30344},[1573],[1575,30346,30347],{"xmlns":1577},[1579,30348,30349,30385],{},[1582,30350,30351,30353,30355,30357,30359,30375,30377,30379,30381,30383],{},[1589,30352,25509],{"stretchy":1591},[1585,30354,2082],{},[1589,30356,25509],{"stretchy":1591},[1589,30358,5983],{},[1746,30360,30361,30363],{},[1585,30362,2082],{},[1582,30364,30365,30367,30369,30371,30373],{},[1716,30366,1718],{},[1589,30368,1721],{},[1585,30370,3862],{},[1585,30372,4023],{"mathvariant":4022},[1716,30374,1993],{},[1589,30376,1170],{"stretchy":1591},[1585,30378,1781],{},[1589,30380,1721],{},[1716,30382,1718],{},[1589,30384,1603],{"stretchy":1591},[1605,30386,30387],{"encoding":1607},"\\lvert t \\rvert \\ge t_{1-\\alpha\u002F2}(n-1)",[1316,30389,30390,30414,30438],{},[1337,30391,30392],{},[1115,30393,30395],{"className":30394},[1573],[1575,30396,30397],{"xmlns":1577},[1579,30398,30399,30411],{},[1582,30400,30401,30403,30405],{},[1585,30402,1982],{},[1589,30404,5983],{},[1746,30406,30407,30409],{},[1585,30408,1982],{},[1716,30410,2398],{},[1605,30412,30413],{"encoding":1607},"\\mu \\ge \\mu_0",[1337,30415,30416],{},[1115,30417,30419],{"className":30418},[1573],[1575,30420,30421],{"xmlns":1577},[1579,30422,30423,30435],{},[1582,30424,30425,30427,30429],{},[1585,30426,1982],{},[1589,30428,6949],{},[1746,30430,30431,30433],{},[1585,30432,1982],{},[1716,30434,2398],{},[1605,30436,30437],{"encoding":1607},"\\mu \u003C \\mu_0",[1337,30439,30440],{},[1115,30441,30443],{"className":30442},[1573],[1575,30444,30445],{"xmlns":1577},[1579,30446,30447,30477],{},[1582,30448,30449,30451,30453,30455,30467,30469,30471,30473,30475],{},[1585,30450,2082],{},[1589,30452,1650],{},[1589,30454,1721],{},[1746,30456,30457,30459],{},[1585,30458,2082],{},[1582,30460,30461,30463,30465],{},[1716,30462,1718],{},[1589,30464,1721],{},[1585,30466,3862],{},[1589,30468,1170],{"stretchy":1591},[1585,30470,1781],{},[1589,30472,1721],{},[1716,30474,1718],{},[1589,30476,1603],{"stretchy":1591},[1605,30478,30479],{"encoding":1607},"t \\le -t_{1-\\alpha}(n-1)",[1110,30481,30482,30483,30485],{},"V R test provádí ",[1150,30484,3750],{},". Autobusová linka měla na trase průměrnou dobu jízdy 12 minut; po úpravě trasy se při devíti jízdách naměřily časy v minutách. Ovlivnila úprava trasy dobu jízdy?",[1144,30487,30489],{"className":1146,"code":30488,"language":71,"meta":1148,"style":1148},"x \u003C- c(12.5, 13.5, 11.9, 12.2, 13.0, 14.3, 12.2, 11.8, 14.0)\nt.test(x, mu = 12, alternative = \"two.sided\")\n",[1150,30490,30491,30545],{"__ignoreMap":1148},[1115,30492,30493,30495,30497,30499,30501,30504,30506,30509,30511,30514,30516,30519,30521,30524,30526,30529,30531,30533,30535,30538,30540,30543],{"class":1154,"line":10},[1115,30494,1158],{"class":1157},[1115,30496,1162],{"class":1161},[1115,30498,1166],{"class":1165},[1115,30500,1170],{"class":1169},[1115,30502,30503],{"class":1173},"12.5",[1115,30505,1177],{"class":1161},[1115,30507,30508],{"class":1173}," 13.5",[1115,30510,1177],{"class":1161},[1115,30512,30513],{"class":1173}," 11.9",[1115,30515,1177],{"class":1161},[1115,30517,30518],{"class":1173}," 12.2",[1115,30520,1177],{"class":1161},[1115,30522,30523],{"class":1173}," 13.0",[1115,30525,1177],{"class":1161},[1115,30527,30528],{"class":1173}," 14.3",[1115,30530,1177],{"class":1161},[1115,30532,30518],{"class":1173},[1115,30534,1177],{"class":1161},[1115,30536,30537],{"class":1173}," 11.8",[1115,30539,1177],{"class":1161},[1115,30541,30542],{"class":1173}," 14.0",[1115,30544,6519],{"class":1169},[1115,30546,30547,30550,30552,30554,30556,30558,30560,30562,30564,30567,30569,30572],{"class":1154,"line":27},[1115,30548,30549],{"class":1165},"t.test",[1115,30551,1170],{"class":1169},[1115,30553,1158],{"class":1157},[1115,30555,1177],{"class":1161},[1115,30557,28060],{"class":1157},[1115,30559,6416],{"class":1161},[1115,30561,6353],{"class":1173},[1115,30563,1177],{"class":1161},[1115,30565,30566],{"class":1157}," alternative",[1115,30568,6416],{"class":1161},[1115,30570,30571],{"class":6458}," \"two.sided\"",[1115,30573,6519],{"class":1169},[1144,30575,30578],{"className":30576,"code":30577,"language":6540,"meta":1148},[6538],"    One Sample t-test\n\ndata:  x\nt = 2.6685, df = 8, p-value = 0.02843\nalternative hypothesis: true mean is not equal to 12\n95 percent confidence interval:\n 12.11169 13.53275\nsample estimates:\nmean of x \n 12.82222 \n",[1150,30579,30577],{"__ignoreMap":1148},[1110,30581,30582,30584,30585,30588,30589,30591,30592,30594,30595,30618],{},[1150,30583,2082],{}," je testové kritérium, ",[1150,30586,30587],{},"df"," stupně volnosti, ",[1150,30590,1352],{}," p-hodnota pro zvolenou alternativu a ",[1150,30593,1356],{}," výběrový průměr. Zde ",[1115,30596,30598],{"className":30597},[1573],[1575,30599,30600],{"xmlns":1577},[1579,30601,30602,30615],{},[1582,30603,30604,30606,30608,30611,30613],{},[1585,30605,1110],{},[1589,30607,1597],{},[1716,30609,30610],{},"0,02843",[1589,30612,6949],{},[1716,30614,6601],{},[1605,30616,30617],{"encoding":1607},"p = 0{,}02843 \u003C 0{,}05",": úprava trasy průměrnou dobu jízdy (původně 12 minut) statisticky významně změnila.",[1103,30620,30622,30629,30717,30773,30865],{"className":30621,"dataCallout":6105},[1106,6104],[1110,30623,30625,30628],{"className":30624},[1113],[1115,30626],{"className":30627,"ariaHidden":1121},[1118,6112,1120],"Příklad: Kontrola objemu lahví",[1110,30630,30631,30632,30654,30655,30673,30674,30697,30698,30716],{},"Pivovar plní lahve, deklarovaný objem je ",[1115,30633,30635],{"className":30634},[1573],[1575,30636,30637],{"xmlns":1577},[1579,30638,30639,30651],{},[1582,30640,30641,30647,30649],{},[1746,30642,30643,30645],{},[1585,30644,1982],{},[1716,30646,2398],{},[1589,30648,1597],{},[1716,30650,11038],{},[1605,30652,30653],{"encoding":1607},"\\mu_0 = 0{,}5"," l. Náhodný výběr ",[1115,30656,30658],{"className":30657},[1573],[1575,30659,30660],{"xmlns":1577},[1579,30661,30662,30670],{},[1582,30663,30664,30666,30668],{},[1585,30665,1781],{},[1589,30667,1597],{},[1716,30669,6662],{},[1605,30671,30672],{"encoding":1607},"n = 20"," lahví dal ",[1115,30675,30677],{"className":30676},[1573],[1575,30678,30679],{"xmlns":1577},[1579,30680,30681,30694],{},[1582,30682,30683,30689,30691],{},[3005,30684,30685,30687],{"accent":1121},[1585,30686,1158],{},[1589,30688,3408],{},[1589,30690,1597],{},[1716,30692,30693],{},"0,492",[1605,30695,30696],{"encoding":1607},"\\bar{x} = 0{,}492"," l, ",[1115,30699,30701],{"className":30700},[1573],[1575,30702,30703],{"xmlns":1577},[1579,30704,30705,30713],{},[1582,30706,30707,30709,30711],{},[1585,30708,3433],{},[1589,30710,1597],{},[1716,30712,17301],{},[1605,30714,30715],{"encoding":1607},"s = 0{,}015"," l. Na hladině významnosti 5 % ověřte podezření, že pivovar lahve nedoplňuje.",[1110,30718,30719,30745,30746,30772],{},[1115,30720,30722],{"className":30721},[1573],[1575,30723,30724],{"xmlns":1577},[1579,30725,30726,30742],{},[1582,30727,30728,30734,30736,30738,30740],{},[1746,30729,30730,30732],{},[1585,30731,1922],{},[1716,30733,2398],{},[1589,30735,4595],{},[1585,30737,1982],{},[1589,30739,5983],{},[1716,30741,11038],{},[1605,30743,30744],{"encoding":1607},"H_0: \\mu \\ge 0{,}5"," l (objem je v pořádku nebo větší), ",[1115,30747,30749],{"className":30748},[1573],[1575,30750,30751],{"xmlns":1577},[1579,30752,30753,30769],{},[1582,30754,30755,30761,30763,30765,30767],{},[1746,30756,30757,30759],{},[1585,30758,1922],{},[1716,30760,1718],{},[1589,30762,4595],{},[1585,30764,1982],{},[1589,30766,6949],{},[1716,30768,11038],{},[1605,30770,30771],{"encoding":1607},"H_1: \\mu \u003C 0{,}5"," l (lahve jsou nedoplněné).",[1110,30774,30775],{},[1115,30776,30778],{"className":30777},[1573],[1575,30779,30780],{"xmlns":1577},[1579,30781,30782,30862],{},[1582,30783,30784,30786,30788,30800,30804,30806,30808,30811,30813,30815,30817,30819,30821,30823,30825,30827,30839,30841,30843,30845,30847,30849,30851,30853,30855,30857,30860],{},[1585,30785,2082],{},[1589,30787,1597],{},[5373,30789,30790,30798],{},[1582,30791,30792,30794,30796],{},[1716,30793,30693],{},[1589,30795,1721],{},[1716,30797,11038],{},[1716,30799,17301],{},[7068,30801,30802],{},[1716,30803,6662],{},[1589,30805,1597],{},[1589,30807,1721],{},[1716,30809,30810],{},"2,385",[1589,30812,1177],{"separator":1121},[4648,30814],{"width":4650},[1585,30816,4256],{},[1589,30818,1597],{},[1589,30820,5966],{"stretchy":1591},[1585,30822,2082],{},[1589,30824,1650],{},[1589,30826,1721],{},[1746,30828,30829,30831],{},[1585,30830,2082],{},[1582,30832,30833,30835,30837],{},[1716,30834,2398],{},[1589,30836,1177],{"separator":1121},[1716,30838,24285],{},[1589,30840,1170],{"stretchy":1591},[1716,30842,17225],{},[1589,30844,1603],{"stretchy":1591},[1589,30846,6024],{"stretchy":1591},[1589,30848,1597],{},[1589,30850,5966],{"stretchy":1591},[1585,30852,2082],{},[1589,30854,1650],{},[1589,30856,1721],{},[1716,30858,30859],{},"1,729",[1589,30861,6024],{"stretchy":1591},[1605,30863,30864],{"encoding":1607},"t = \\frac{0{,}492 - 0{,}5}{0{,}015}\\sqrt{20} = -2{,}385, \\qquad W = \\{t \\le -t_{0,95}(19)\\} = \\{t \\le -1{,}729\\}",[1110,30866,30867,30868,8614,30886,30903],{},"Protože ",[1115,30869,30871],{"className":30870},[1573],[1575,30872,30873],{"xmlns":1577},[1579,30874,30875,30883],{},[1582,30876,30877,30879,30881],{},[1585,30878,2082],{},[1589,30880,9605],{},[1585,30882,4256],{},[1605,30884,30885],{"encoding":1607},"t \\in W",[1115,30887,30889],{"className":30888},[1573],[1575,30890,30891],{"xmlns":1577},[1579,30892,30893,30901],{},[1582,30894,30895],{},[1746,30896,30897,30899],{},[1585,30898,1922],{},[1716,30900,2398],{},[1605,30902,4225],{"encoding":1607},": na hladině významnosti 5 % se potvrdilo, že pivovar plní lahve pod deklarovaný objem.",[1110,30905,30906,30907,30909,30910,4595],{},"Ze souhrnných charakteristik bez surových dat ",[1150,30908,3750],{}," spustit nelze — kritérium a kritická hodnota se dopočítají přímo z definice pomocí ",[1150,30911,30912],{},"qt()",[1144,30914,30916],{"className":1146,"code":30915,"language":71,"meta":1148,"style":1148},"xbar \u003C- 0.492; s \u003C- 0.015; n \u003C- 20; mu0 \u003C- 0.5\nt \u003C- (xbar - mu0) \u002F s * sqrt(n)\nt_krit \u003C- qt(0.05, df = n - 1)\nt\nt_krit\n",[1150,30917,30918,30956,30988,31018,31023],{"__ignoreMap":1148},[1115,30919,30920,30923,30925,30928,30930,30932,30934,30937,30939,30941,30943,30946,30948,30951,30953],{"class":1154,"line":10},[1115,30921,30922],{"class":1157},"xbar",[1115,30924,1162],{"class":1161},[1115,30926,30927],{"class":1173}," 0.492",[1115,30929,2402],{"class":1169},[1115,30931,3433],{"class":1157},[1115,30933,1162],{"class":1161},[1115,30935,30936],{"class":1173}," 0.015",[1115,30938,2402],{"class":1169},[1115,30940,1781],{"class":1157},[1115,30942,1162],{"class":1161},[1115,30944,30945],{"class":1173}," 20",[1115,30947,2402],{"class":1169},[1115,30949,30950],{"class":1157},"mu0",[1115,30952,1162],{"class":1161},[1115,30954,30955],{"class":1173}," 0.5\n",[1115,30957,30958,30960,30962,30964,30966,30968,30971,30973,30975,30978,30980,30982,30984,30986],{"class":1154,"line":27},[1115,30959,2082],{"class":1157},[1115,30961,1162],{"class":1161},[1115,30963,7219],{"class":1169},[1115,30965,30922],{"class":1157},[1115,30967,28000],{"class":1161},[1115,30969,30970],{"class":1157}," mu0",[1115,30972,7214],{"class":1169},[1115,30974,4023],{"class":1161},[1115,30976,30977],{"class":1157}," s",[1115,30979,21136],{"class":1161},[1115,30981,7191],{"class":1165},[1115,30983,1170],{"class":1169},[1115,30985,1781],{"class":1157},[1115,30987,6519],{"class":1169},[1115,30989,30990,30993,30995,30998,31000,31003,31005,31007,31009,31012,31014,31016],{"class":1154,"line":148},[1115,30991,30992],{"class":1157},"t_krit",[1115,30994,1162],{"class":1161},[1115,30996,30997],{"class":1165}," qt",[1115,30999,1170],{"class":1169},[1115,31001,31002],{"class":1173},"0.05",[1115,31004,1177],{"class":1161},[1115,31006,13341],{"class":1157},[1115,31008,6416],{"class":1161},[1115,31010,31011],{"class":1157}," n",[1115,31013,28000],{"class":1161},[1115,31015,7253],{"class":1173},[1115,31017,6519],{"class":1169},[1115,31019,31020],{"class":1154,"line":111},[1115,31021,31022],{"class":1157},"t\n",[1115,31024,31025],{"class":1154,"line":96},[1115,31026,31027],{"class":1157},"t_krit\n",[1144,31029,31032],{"className":31030,"code":31031,"language":6540,"meta":1148},[6538],"[1] -2.385139\n[1] -1.729133\n",[1150,31033,31031],{"__ignoreMap":1148},[1110,31035,31036],{},[1303,31037],{"alt":31038,"className":31039,"src":31040},"mask-th-t-jednostranny",[1130,1307],"\u002Fwiki-assets\u002Fmask-th-t-jednostranny.png",[1110,31042,31043,31044,4595],{},"Další dva příklady mají k dispozici surová data, takže je lze otestovat přímo ",[1150,31045,3750],{},[1110,31047,31048,31051],{},[2227,31049,31050],{},"Životnost baterií."," Výrobce udává průměrnou životnost 10 hodin, na 11 bateriích byly naměřeny hodnoty v hodinách.",[1144,31053,31055],{"className":1146,"code":31054,"language":71,"meta":1148,"style":1148},"x2 \u003C- c(9.5, 10.5, 8.9, 9.2, 10.0, 8.5, 9.2, 8.8, 10.0, 9.5, 9.2)\nt.test(x2, mu = 10, alternative = \"two.sided\")\n",[1150,31056,31057,31120],{"__ignoreMap":1148},[1115,31058,31059,31062,31064,31066,31068,31071,31073,31076,31078,31081,31083,31086,31088,31091,31093,31096,31098,31100,31102,31105,31107,31109,31111,31114,31116,31118],{"class":1154,"line":10},[1115,31060,31061],{"class":1157},"x2",[1115,31063,1162],{"class":1161},[1115,31065,1166],{"class":1165},[1115,31067,1170],{"class":1169},[1115,31069,31070],{"class":1173},"9.5",[1115,31072,1177],{"class":1161},[1115,31074,31075],{"class":1173}," 10.5",[1115,31077,1177],{"class":1161},[1115,31079,31080],{"class":1173}," 8.9",[1115,31082,1177],{"class":1161},[1115,31084,31085],{"class":1173}," 9.2",[1115,31087,1177],{"class":1161},[1115,31089,31090],{"class":1173}," 10.0",[1115,31092,1177],{"class":1161},[1115,31094,31095],{"class":1173}," 8.5",[1115,31097,1177],{"class":1161},[1115,31099,31085],{"class":1173},[1115,31101,1177],{"class":1161},[1115,31103,31104],{"class":1173}," 8.8",[1115,31106,1177],{"class":1161},[1115,31108,31090],{"class":1173},[1115,31110,1177],{"class":1161},[1115,31112,31113],{"class":1173}," 9.5",[1115,31115,1177],{"class":1161},[1115,31117,31085],{"class":1173},[1115,31119,6519],{"class":1169},[1115,31121,31122,31124,31126,31128,31130,31132,31134,31136,31138,31140,31142,31144],{"class":1154,"line":27},[1115,31123,30549],{"class":1165},[1115,31125,1170],{"class":1169},[1115,31127,31061],{"class":1157},[1115,31129,1177],{"class":1161},[1115,31131,28060],{"class":1157},[1115,31133,6416],{"class":1161},[1115,31135,12057],{"class":1173},[1115,31137,1177],{"class":1161},[1115,31139,30566],{"class":1157},[1115,31141,6416],{"class":1161},[1115,31143,30571],{"class":6458},[1115,31145,6519],{"class":1169},[1144,31147,31150],{"className":31148,"code":31149,"language":6540,"meta":1148},[6538],"    One Sample t-test\n\ndata:  x2\nt = -3.42, df = 10, p-value = 0.006548\nalternative hypothesis: true mean is not equal to 10\n95 percent confidence interval:\n 8.994081 9.787737\nsample estimates:\nmean of x \n 9.390909 \n",[1150,31151,31149],{"__ignoreMap":1148},[1110,31153,31154,31177],{},[1115,31155,31157],{"className":31156},[1573],[1575,31158,31159],{"xmlns":1577},[1579,31160,31161,31174],{},[1582,31162,31163,31165,31167,31170,31172],{},[1585,31164,1110],{},[1589,31166,1597],{},[1716,31168,31169],{},"0,006548",[1589,31171,6949],{},[1716,31173,6601],{},[1605,31175,31176],{"encoding":1607},"p = 0{,}006548 \u003C 0{,}05",": skutečná životnost se od deklarovaných 10 hodin statisticky významně liší (baterie vydrží méně).",[1110,31179,31180,31183],{},[2227,31181,31182],{},"Odpad materiálu."," Na deseti obráběných kusech byl naměřen odpad materiálu v procentech; testuje se rozdíl proti 4 % a zároveň normalita dat.",[1144,31185,31187],{"className":1146,"code":31186,"language":71,"meta":1148,"style":1148},"x3 \u003C- c(4.1, 4.0, 3.8, 3.9, 3.8, 3.8, 3.5, 3.7, 4.0, 4.0)\nt.test(x3, mu = 4, alternative = \"two.sided\")\nshapiro.test(x3)\n",[1150,31188,31189,31240,31266],{"__ignoreMap":1148},[1115,31190,31191,31194,31196,31198,31200,31202,31204,31206,31208,31210,31212,31214,31216,31218,31220,31222,31224,31226,31228,31230,31232,31234,31236,31238],{"class":1154,"line":10},[1115,31192,31193],{"class":1157},"x3",[1115,31195,1162],{"class":1161},[1115,31197,1166],{"class":1165},[1115,31199,1170],{"class":1169},[1115,31201,1174],{"class":1173},[1115,31203,1177],{"class":1161},[1115,31205,1180],{"class":1173},[1115,31207,1177],{"class":1161},[1115,31209,1185],{"class":1173},[1115,31211,1177],{"class":1161},[1115,31213,1190],{"class":1173},[1115,31215,1177],{"class":1161},[1115,31217,1185],{"class":1173},[1115,31219,1177],{"class":1161},[1115,31221,1185],{"class":1173},[1115,31223,1177],{"class":1161},[1115,31225,1203],{"class":1173},[1115,31227,1177],{"class":1161},[1115,31229,1208],{"class":1173},[1115,31231,1177],{"class":1161},[1115,31233,1180],{"class":1173},[1115,31235,1177],{"class":1161},[1115,31237,1180],{"class":1173},[1115,31239,6519],{"class":1169},[1115,31241,31242,31244,31246,31248,31250,31252,31254,31256,31258,31260,31262,31264],{"class":1154,"line":27},[1115,31243,30549],{"class":1165},[1115,31245,1170],{"class":1169},[1115,31247,31193],{"class":1157},[1115,31249,1177],{"class":1161},[1115,31251,28060],{"class":1157},[1115,31253,6416],{"class":1161},[1115,31255,6419],{"class":1173},[1115,31257,1177],{"class":1161},[1115,31259,30566],{"class":1157},[1115,31261,6416],{"class":1161},[1115,31263,30571],{"class":6458},[1115,31265,6519],{"class":1169},[1115,31267,31268,31270,31272,31274],{"class":1154,"line":148},[1115,31269,20072],{"class":1165},[1115,31271,1170],{"class":1169},[1115,31273,31193],{"class":1157},[1115,31275,6519],{"class":1169},[1144,31277,31280],{"className":31278,"code":31279,"language":6540,"meta":1148},[6538],"    One Sample t-test\n\ndata:  x3\nt = -2.4922, df = 9, p-value = 0.0343\nalternative hypothesis: true mean is not equal to 4\n95 percent confidence interval:\n 3.732925 3.987075\nsample estimates:\nmean of x \n     3.86 \n\n    Shapiro-Wilk normality test\n\ndata:  x3\nW = 0.93156, p-value = 0.4634\n",[1150,31281,31279],{"__ignoreMap":1148},[1110,31283,31284,31307,31308,31331],{},[1115,31285,31287],{"className":31286},[1573],[1575,31288,31289],{"xmlns":1577},[1579,31290,31291,31304],{},[1582,31292,31293,31295,31297,31300,31302],{},[1585,31294,1110],{},[1589,31296,1597],{},[1716,31298,31299],{},"0,0343",[1589,31301,6949],{},[1716,31303,6601],{},[1605,31305,31306],{"encoding":1607},"p = 0{,}0343 \u003C 0{,}05",": průměrný odpad se od 4 % statisticky významně liší (výběrový průměr 3,86 %). Shapiro-Wilkův test dává ",[1115,31309,31311],{"className":31310},[1573],[1575,31312,31313],{"xmlns":1577},[1579,31314,31315,31328],{},[1582,31316,31317,31319,31321,31324,31326],{},[1585,31318,1110],{},[1589,31320,1597],{},[1716,31322,31323],{},"0,4634",[1589,31325,1698],{},[1716,31327,6601],{},[1605,31329,31330],{"encoding":1607},"p = 0{,}4634 > 0{,}05",", předpoklad normality pro t-test je v pořádku.",[1136,31333,31335],{"id":31334},"párový-t-test","Párový t-test",[1110,31337,31338,31339,31369,31370,2271,31404,31442,31443,31456,31457,1260,31475,31495,31496,31513,31514,30061],{},"Používá se, když jsou měření závislá — na stejných objektech se měří dvě hodnoty ",[1115,31340,31342],{"className":31341},[1573],[1575,31343,31344],{"xmlns":1577},[1579,31345,31346,31366],{},[1582,31347,31348,31350,31356,31358,31364],{},[1589,31349,1170],{"stretchy":1591},[1746,31351,31352,31354],{},[1585,31353,1594],{},[1585,31355,1776],{},[1589,31357,1177],{"separator":1121},[1746,31359,31360,31362],{},[1585,31361,9674],{},[1585,31363,1776],{},[1589,31365,1603],{"stretchy":1591},[1605,31367,31368],{"encoding":1607},"(X_i, Y_i)"," a vyhodnocují se jejich diference ",[1115,31371,31373],{"className":31372},[1573],[1575,31374,31375],{"xmlns":1577},[1579,31376,31377,31401],{},[1582,31378,31379,31385,31387,31393,31395],{},[1746,31380,31381,31383],{},[1585,31382,10733],{},[1585,31384,1776],{},[1589,31386,1597],{},[1746,31388,31389,31391],{},[1585,31390,1594],{},[1585,31392,1776],{},[1589,31394,1721],{},[1746,31396,31397,31399],{},[1585,31398,9674],{},[1585,31400,1776],{},[1605,31402,31403],{"encoding":1607},"D_i = X_i - Y_i",[1115,31405,31407],{"className":31406},[1573],[1575,31408,31409],{"xmlns":1577},[1579,31410,31411,31439],{},[1582,31412,31413,31415,31417,31419,31421,31427,31429,31437],{},[1585,31414,10733],{},[1589,31416,11763],{},[1585,31418,1927],{},[1589,31420,1170],{"stretchy":1591},[1746,31422,31423,31425],{},[1585,31424,1982],{},[1585,31426,10733],{},[1589,31428,1177],{"separator":1121},[2920,31430,31431,31433,31435],{},[1585,31432,1990],{},[1585,31434,10733],{},[1716,31436,1993],{},[1589,31438,1603],{"stretchy":1591},[1605,31440,31441],{"encoding":1607},"D \\sim N(\\mu_D, \\sigma_D^2)",". Z ",[1115,31444,31446],{"className":31445},[1573],[1575,31447,31448],{"xmlns":1577},[1579,31449,31450,31454],{},[1582,31451,31452],{},[1585,31453,1781],{},[1605,31455,1781],{"encoding":1607}," dvojic se určí ",[1115,31458,31460],{"className":31459},[1573],[1575,31461,31462],{"xmlns":1577},[1579,31463,31464,31472],{},[1582,31465,31466],{},[3005,31467,31468,31470],{"accent":1121},[1585,31469,10377],{},[1589,31471,3408],{},[1605,31473,31474],{"encoding":1607},"\\bar{d}",[1115,31476,31478],{"className":31477},[1573],[1575,31479,31480],{"xmlns":1577},[1579,31481,31482,31492],{},[1582,31483,31484],{},[2920,31485,31486,31488,31490],{},[1585,31487,3433],{},[1585,31489,10377],{},[1716,31491,1993],{},[1605,31493,31494],{"encoding":1607},"s_d^2","; testuje se vztah mezi zvoleným číslem ",[1115,31497,31499],{"className":31498},[1573],[1575,31500,31501],{"xmlns":1577},[1579,31502,31503,31511],{},[1582,31504,31505],{},[1746,31506,31507,31509],{},[1585,31508,1982],{},[1716,31510,2398],{},[1605,31512,30046],{"encoding":1607}," (obvykle 0) a ",[1115,31515,31517],{"className":31516},[1573],[1575,31518,31519],{"xmlns":1577},[1579,31520,31521,31529],{},[1582,31522,31523],{},[1746,31524,31525,31527],{},[1585,31526,1982],{},[1585,31528,10733],{},[1605,31530,31531],{"encoding":1607},"\\mu_D",[1115,31533,31535],{"className":31534},[1573],[1575,31536,31537],{"xmlns":1577,"display":4601},[1579,31538,31539,31589],{},[1582,31540,31541,31543,31545,31569,31573,31575,31587],{},[1585,31542,4043],{},[1589,31544,1597],{},[5373,31546,31547,31563],{},[1582,31548,31549,31555,31557],{},[3005,31550,31551,31553],{"accent":1121},[1585,31552,10377],{},[1589,31554,3408],{},[1589,31556,1721],{},[1746,31558,31559,31561],{},[1585,31560,1982],{},[1716,31562,2398],{},[1746,31564,31565,31567],{},[1585,31566,3433],{},[1585,31568,10377],{},[7068,31570,31571],{},[1585,31572,1781],{},[1589,31574,11763],{},[1746,31576,31577,31579],{},[1585,31578,2082],{},[1582,31580,31581,31583,31585],{},[1585,31582,1781],{},[1589,31584,1721],{},[1716,31586,1718],{},[1585,31588,2264],{"mathvariant":4022},[1605,31590,31591],{"encoding":1607},"T = \\frac{\\bar{d} - \\mu_0}{s_d}\\sqrt{n} \\sim t_{n-1}.",[1310,31593,31594,31651],{},[1313,31595,31596],{},[1316,31597,31598,31617,31636],{},[1319,31599,31600],{},[1115,31601,31603],{"className":31602},[1573],[1575,31604,31605],{"xmlns":1577},[1579,31606,31607,31615],{},[1582,31608,31609],{},[1746,31610,31611,31613],{},[1585,31612,1922],{},[1716,31614,2398],{},[1605,31616,4225],{"encoding":1607},[1319,31618,31619],{},[1115,31620,31622],{"className":31621},[1573],[1575,31623,31624],{"xmlns":1577},[1579,31625,31626,31634],{},[1582,31627,31628],{},[1746,31629,31630,31632],{},[1585,31631,1922],{},[1716,31633,1718],{},[1605,31635,3807],{"encoding":1607},[1319,31637,30184,31638],{},[1115,31639,31641],{"className":31640},[1573],[1575,31642,31643],{"xmlns":1577},[1579,31644,31645,31649],{},[1582,31646,31647],{},[1585,31648,4256],{},[1605,31650,4256],{"encoding":1607},[1332,31652,31653,31750,31855],{},[1316,31654,31655,31683,31711],{},[1337,31656,31657],{},[1115,31658,31660],{"className":31659},[1573],[1575,31661,31662],{"xmlns":1577},[1579,31663,31664,31680],{},[1582,31665,31666,31672,31674],{},[1746,31667,31668,31670],{},[1585,31669,1982],{},[1585,31671,10733],{},[1589,31673,1650],{},[1746,31675,31676,31678],{},[1585,31677,1982],{},[1716,31679,2398],{},[1605,31681,31682],{"encoding":1607},"\\mu_D \\le \\mu_0",[1337,31684,31685],{},[1115,31686,31688],{"className":31687},[1573],[1575,31689,31690],{"xmlns":1577},[1579,31691,31692,31708],{},[1582,31693,31694,31700,31702],{},[1746,31695,31696,31698],{},[1585,31697,1982],{},[1585,31699,10733],{},[1589,31701,1698],{},[1746,31703,31704,31706],{},[1585,31705,1982],{},[1716,31707,2398],{},[1605,31709,31710],{"encoding":1607},"\\mu_D > \\mu_0",[1337,31712,31713],{},[1115,31714,31716],{"className":31715},[1573],[1575,31717,31718],{"xmlns":1577},[1579,31719,31720,31748],{},[1582,31721,31722,31724,31726,31738,31740,31742,31744,31746],{},[1585,31723,2082],{},[1589,31725,5983],{},[1746,31727,31728,31730],{},[1585,31729,2082],{},[1582,31731,31732,31734,31736],{},[1716,31733,1718],{},[1589,31735,1721],{},[1585,31737,3862],{},[1589,31739,1170],{"stretchy":1591},[1585,31741,1781],{},[1589,31743,1721],{},[1716,31745,1718],{},[1589,31747,1603],{"stretchy":1591},[1605,31749,30289],{"encoding":1607},[1316,31751,31752,31780,31808],{},[1337,31753,31754],{},[1115,31755,31757],{"className":31756},[1573],[1575,31758,31759],{"xmlns":1577},[1579,31760,31761,31777],{},[1582,31762,31763,31769,31771],{},[1746,31764,31765,31767],{},[1585,31766,1982],{},[1585,31768,10733],{},[1589,31770,1597],{},[1746,31772,31773,31775],{},[1585,31774,1982],{},[1716,31776,2398],{},[1605,31778,31779],{"encoding":1607},"\\mu_D = \\mu_0",[1337,31781,31782],{},[1115,31783,31785],{"className":31784},[1573],[1575,31786,31787],{"xmlns":1577},[1579,31788,31789,31805],{},[1582,31790,31791,31797,31799],{},[1746,31792,31793,31795],{},[1585,31794,1982],{},[1585,31796,10733],{},[1589,31798,13487],{"mathvariant":4022},[1746,31800,31801,31803],{},[1585,31802,1982],{},[1716,31804,2398],{},[1605,31806,31807],{"encoding":1607},"\\mu_D \\neq \\mu_0",[1337,31809,31810],{},[1115,31811,31813],{"className":31812},[1573],[1575,31814,31815],{"xmlns":1577},[1579,31816,31817,31853],{},[1582,31818,31819,31821,31823,31825,31827,31843,31845,31847,31849,31851],{},[1589,31820,25509],{"stretchy":1591},[1585,31822,2082],{},[1589,31824,25509],{"stretchy":1591},[1589,31826,5983],{},[1746,31828,31829,31831],{},[1585,31830,2082],{},[1582,31832,31833,31835,31837,31839,31841],{},[1716,31834,1718],{},[1589,31836,1721],{},[1585,31838,3862],{},[1585,31840,4023],{"mathvariant":4022},[1716,31842,1993],{},[1589,31844,1170],{"stretchy":1591},[1585,31846,1781],{},[1589,31848,1721],{},[1716,31850,1718],{},[1589,31852,1603],{"stretchy":1591},[1605,31854,30387],{"encoding":1607},[1316,31856,31857,31885,31913],{},[1337,31858,31859],{},[1115,31860,31862],{"className":31861},[1573],[1575,31863,31864],{"xmlns":1577},[1579,31865,31866,31882],{},[1582,31867,31868,31874,31876],{},[1746,31869,31870,31872],{},[1585,31871,1982],{},[1585,31873,10733],{},[1589,31875,5983],{},[1746,31877,31878,31880],{},[1585,31879,1982],{},[1716,31881,2398],{},[1605,31883,31884],{"encoding":1607},"\\mu_D \\ge \\mu_0",[1337,31886,31887],{},[1115,31888,31890],{"className":31889},[1573],[1575,31891,31892],{"xmlns":1577},[1579,31893,31894,31910],{},[1582,31895,31896,31902,31904],{},[1746,31897,31898,31900],{},[1585,31899,1982],{},[1585,31901,10733],{},[1589,31903,6949],{},[1746,31905,31906,31908],{},[1585,31907,1982],{},[1716,31909,2398],{},[1605,31911,31912],{"encoding":1607},"\\mu_D \u003C \\mu_0",[1337,31914,31915],{},[1115,31916,31918],{"className":31917},[1573],[1575,31919,31920],{"xmlns":1577},[1579,31921,31922,31952],{},[1582,31923,31924,31926,31928,31930,31942,31944,31946,31948,31950],{},[1585,31925,2082],{},[1589,31927,1650],{},[1589,31929,1721],{},[1746,31931,31932,31934],{},[1585,31933,2082],{},[1582,31935,31936,31938,31940],{},[1716,31937,1718],{},[1589,31939,1721],{},[1585,31941,3862],{},[1589,31943,1170],{"stretchy":1591},[1585,31945,1781],{},[1589,31947,1721],{},[1716,31949,1718],{},[1589,31951,1603],{"stretchy":1591},[1605,31953,30479],{"encoding":1607},[1103,31955,31957,31964,32106,32170,32256],{"className":31956,"dataCallout":6105},[1106,6104],[1110,31958,31960,31963],{"className":31959},[1113],[1115,31961],{"className":31962,"ariaHidden":1121},[1118,6112,1120],"Příklad: Snížení spotřeby paliva aditivem",[1110,31965,31966,31967,31985,31986,32004,32005,32023,32024,32057,32058,32081,32082,32105],{},"U ",[1115,31968,31970],{"className":31969},[1573],[1575,31971,31972],{"xmlns":1577},[1579,31973,31974,31982],{},[1582,31975,31976,31978,31980],{},[1585,31977,1781],{},[1589,31979,1597],{},[1716,31981,11613],{},[1605,31983,31984],{"encoding":1607},"n = 10"," vozů se změřila spotřeba před přidáním aditiva (",[1115,31987,31989],{"className":31988},[1573],[1575,31990,31991],{"xmlns":1577},[1579,31992,31993,32001],{},[1582,31994,31995],{},[1746,31996,31997,31999],{},[1585,31998,1594],{},[1585,32000,1776],{},[1605,32002,32003],{"encoding":1607},"X_i",") a po něm (",[1115,32006,32008],{"className":32007},[1573],[1575,32009,32010],{"xmlns":1577},[1579,32011,32012,32020],{},[1582,32013,32014],{},[1746,32015,32016,32018],{},[1585,32017,9674],{},[1585,32019,1776],{},[1605,32021,32022],{"encoding":1607},"Y_i","), diference ",[1115,32025,32027],{"className":32026},[1573],[1575,32028,32029],{"xmlns":1577},[1579,32030,32031,32055],{},[1582,32032,32033,32039,32041,32047,32049],{},[1746,32034,32035,32037],{},[1585,32036,10733],{},[1585,32038,1776],{},[1589,32040,1597],{},[1746,32042,32043,32045],{},[1585,32044,1594],{},[1585,32046,1776],{},[1589,32048,1721],{},[1746,32050,32051,32053],{},[1585,32052,9674],{},[1585,32054,1776],{},[1605,32056,31403],{"encoding":1607}," představují úsporu paliva. Z dat vyšla průměrná úspora ",[1115,32059,32061],{"className":32060},[1573],[1575,32062,32063],{"xmlns":1577},[1579,32064,32065,32078],{},[1582,32066,32067,32073,32075],{},[3005,32068,32069,32071],{"accent":1121},[1585,32070,10377],{},[1589,32072,3408],{},[1589,32074,1597],{},[1716,32076,32077],{},"0,4",[1605,32079,32080],{"encoding":1607},"\\bar{d} = 0{,}4"," l\u002F100 km, ",[1115,32083,32085],{"className":32084},[1573],[1575,32086,32087],{"xmlns":1577},[1579,32088,32089,32102],{},[1582,32090,32091,32097,32099],{},[1746,32092,32093,32095],{},[1585,32094,3433],{},[1585,32096,10377],{},[1589,32098,1597],{},[1716,32100,32101],{},"0,35",[1605,32103,32104],{"encoding":1607},"s_d = 0{,}35"," l\u002F100 km. Ověřte, že aditivum spotřebu statisticky významně snižuje.",[1110,32107,32108,32138,32139,32169],{},[1115,32109,32111],{"className":32110},[1573],[1575,32112,32113],{"xmlns":1577},[1579,32114,32115,32135],{},[1582,32116,32117,32123,32125,32131,32133],{},[1746,32118,32119,32121],{},[1585,32120,1922],{},[1716,32122,2398],{},[1589,32124,4595],{},[1746,32126,32127,32129],{},[1585,32128,1982],{},[1585,32130,10733],{},[1589,32132,1650],{},[1716,32134,2398],{},[1605,32136,32137],{"encoding":1607},"H_0: \\mu_D \\le 0"," (aditivum nemá vliv nebo spotřebu zvyšuje), ",[1115,32140,32142],{"className":32141},[1573],[1575,32143,32144],{"xmlns":1577},[1579,32145,32146,32166],{},[1582,32147,32148,32154,32156,32162,32164],{},[1746,32149,32150,32152],{},[1585,32151,1922],{},[1716,32153,1718],{},[1589,32155,4595],{},[1746,32157,32158,32160],{},[1585,32159,1982],{},[1585,32161,10733],{},[1589,32163,1698],{},[1716,32165,2398],{},[1605,32167,32168],{"encoding":1607},"H_1: \\mu_D > 0"," (aditivum spotřebu snižuje).",[1110,32171,32172],{},[1115,32173,32175],{"className":32174},[1573],[1575,32176,32177],{"xmlns":1577},[1579,32178,32179,32253],{},[1582,32180,32181,32183,32185,32197,32201,32203,32206,32208,32210,32212,32214,32216,32218,32220,32232,32234,32236,32238,32240,32242,32244,32246,32248,32251],{},[1585,32182,2082],{},[1589,32184,1597],{},[5373,32186,32187,32195],{},[1582,32188,32189,32191,32193],{},[1716,32190,32077],{},[1589,32192,1721],{},[1716,32194,2398],{},[1716,32196,32101],{},[7068,32198,32199],{},[1716,32200,11613],{},[1589,32202,1597],{},[1716,32204,32205],{},"3,614",[1589,32207,1177],{"separator":1121},[4648,32209],{"width":4650},[1585,32211,4256],{},[1589,32213,1597],{},[1589,32215,5966],{"stretchy":1591},[1585,32217,2082],{},[1589,32219,5983],{},[1746,32221,32222,32224],{},[1585,32223,2082],{},[1582,32225,32226,32228,32230],{},[1716,32227,2398],{},[1589,32229,1177],{"separator":1121},[1716,32231,24285],{},[1589,32233,1170],{"stretchy":1591},[1716,32235,6223],{},[1589,32237,1603],{"stretchy":1591},[1589,32239,6024],{"stretchy":1591},[1589,32241,1597],{},[1589,32243,5966],{"stretchy":1591},[1585,32245,2082],{},[1589,32247,5983],{},[1716,32249,32250],{},"1,833",[1589,32252,6024],{"stretchy":1591},[1605,32254,32255],{"encoding":1607},"t = \\frac{0{,}4 - 0}{0{,}35}\\sqrt{10} = 3{,}614, \\qquad W = \\{t \\ge t_{0,95}(9)\\} = \\{t \\ge 1{,}833\\}",[1110,32257,30867,32258,8614,32275,32292],{},[1115,32259,32261],{"className":32260},[1573],[1575,32262,32263],{"xmlns":1577},[1579,32264,32265,32273],{},[1582,32266,32267,32269,32271],{},[1585,32268,2082],{},[1589,32270,9605],{},[1585,32272,4256],{},[1605,32274,30885],{"encoding":1607},[1115,32276,32278],{"className":32277},[1573],[1575,32279,32280],{"xmlns":1577},[1579,32281,32282,32290],{},[1582,32283,32284],{},[1746,32285,32286,32288],{},[1585,32287,1922],{},[1716,32289,2398],{},[1605,32291,4225],{"encoding":1607},": aditivum prokazatelně snižuje průměrnou spotřebu paliva.",[1144,32294,32296],{"className":1146,"code":32295,"language":71,"meta":1148,"style":1148},"dbar \u003C- 0.4; sd_d \u003C- 0.35; n \u003C- 10\nt \u003C- (dbar - 0) \u002F sd_d * sqrt(n)\nt_krit \u003C- qt(0.95, df = n - 1)\nt\nt_krit\n",[1150,32297,32298,32327,32358,32384,32388],{"__ignoreMap":1148},[1115,32299,32300,32303,32305,32308,32310,32313,32315,32318,32320,32322,32324],{"class":1154,"line":10},[1115,32301,32302],{"class":1157},"dbar",[1115,32304,1162],{"class":1161},[1115,32306,32307],{"class":1173}," 0.4",[1115,32309,2402],{"class":1169},[1115,32311,32312],{"class":1157},"sd_d",[1115,32314,1162],{"class":1161},[1115,32316,32317],{"class":1173}," 0.35",[1115,32319,2402],{"class":1169},[1115,32321,1781],{"class":1157},[1115,32323,1162],{"class":1161},[1115,32325,32326],{"class":1173}," 10\n",[1115,32328,32329,32331,32333,32335,32337,32339,32341,32343,32345,32348,32350,32352,32354,32356],{"class":1154,"line":27},[1115,32330,2082],{"class":1157},[1115,32332,1162],{"class":1161},[1115,32334,7219],{"class":1169},[1115,32336,32302],{"class":1157},[1115,32338,28000],{"class":1161},[1115,32340,12514],{"class":1173},[1115,32342,7214],{"class":1169},[1115,32344,4023],{"class":1161},[1115,32346,32347],{"class":1157}," sd_d",[1115,32349,21136],{"class":1161},[1115,32351,7191],{"class":1165},[1115,32353,1170],{"class":1169},[1115,32355,1781],{"class":1157},[1115,32357,6519],{"class":1169},[1115,32359,32360,32362,32364,32366,32368,32370,32372,32374,32376,32378,32380,32382],{"class":1154,"line":148},[1115,32361,30992],{"class":1157},[1115,32363,1162],{"class":1161},[1115,32365,30997],{"class":1165},[1115,32367,1170],{"class":1169},[1115,32369,3843],{"class":1173},[1115,32371,1177],{"class":1161},[1115,32373,13341],{"class":1157},[1115,32375,6416],{"class":1161},[1115,32377,31011],{"class":1157},[1115,32379,28000],{"class":1161},[1115,32381,7253],{"class":1173},[1115,32383,6519],{"class":1169},[1115,32385,32386],{"class":1154,"line":111},[1115,32387,31022],{"class":1157},[1115,32389,32390],{"class":1154,"line":96},[1115,32391,31027],{"class":1157},[1144,32393,32396],{"className":32394,"code":32395,"language":6540,"meta":1148},[6538],"[1] 3.614032\n[1] 1.833113\n",[1150,32397,32395],{"__ignoreMap":1148},[1103,32399,32401,32408,32411,32556,32562],{"className":32400,"dataCallout":9019},[1106,9018],[1110,32402,32404,32407],{"className":32403},[1113],[1115,32405],{"className":32406,"ariaHidden":1121},[1118,9026,1120],"Ověřte normalitu diferencí, ne jen výsledek testu",[1110,32409,32410],{},"Realitní kancelář nechala dva odhadce ocenit osm nemovitostí (tisíce Kč):",[1144,32412,32414],{"className":1146,"code":32413,"language":71,"meta":1148,"style":1148},"estA \u003C- c(3282, 2506, 2812, 5453, 3263, 4571, 3121, 2963)\nestB \u003C- c(3271, 2531, 2799, 5471, 3285, 4557, 3139, 2976)\nt.test(estA, estB, paired = TRUE)\nshapiro.test(estA - estB)\n",[1150,32415,32416,32467,32518,32542],{"__ignoreMap":1148},[1115,32417,32418,32421,32423,32425,32427,32430,32432,32435,32437,32440,32442,32445,32447,32450,32452,32455,32457,32460,32462,32465],{"class":1154,"line":10},[1115,32419,32420],{"class":1157},"estA",[1115,32422,1162],{"class":1161},[1115,32424,1166],{"class":1165},[1115,32426,1170],{"class":1169},[1115,32428,32429],{"class":1173},"3282",[1115,32431,1177],{"class":1161},[1115,32433,32434],{"class":1173}," 2506",[1115,32436,1177],{"class":1161},[1115,32438,32439],{"class":1173}," 2812",[1115,32441,1177],{"class":1161},[1115,32443,32444],{"class":1173}," 5453",[1115,32446,1177],{"class":1161},[1115,32448,32449],{"class":1173}," 3263",[1115,32451,1177],{"class":1161},[1115,32453,32454],{"class":1173}," 4571",[1115,32456,1177],{"class":1161},[1115,32458,32459],{"class":1173}," 3121",[1115,32461,1177],{"class":1161},[1115,32463,32464],{"class":1173}," 2963",[1115,32466,6519],{"class":1169},[1115,32468,32469,32472,32474,32476,32478,32481,32483,32486,32488,32491,32493,32496,32498,32501,32503,32506,32508,32511,32513,32516],{"class":1154,"line":27},[1115,32470,32471],{"class":1157},"estB",[1115,32473,1162],{"class":1161},[1115,32475,1166],{"class":1165},[1115,32477,1170],{"class":1169},[1115,32479,32480],{"class":1173},"3271",[1115,32482,1177],{"class":1161},[1115,32484,32485],{"class":1173}," 2531",[1115,32487,1177],{"class":1161},[1115,32489,32490],{"class":1173}," 2799",[1115,32492,1177],{"class":1161},[1115,32494,32495],{"class":1173}," 5471",[1115,32497,1177],{"class":1161},[1115,32499,32500],{"class":1173}," 3285",[1115,32502,1177],{"class":1161},[1115,32504,32505],{"class":1173}," 4557",[1115,32507,1177],{"class":1161},[1115,32509,32510],{"class":1173}," 3139",[1115,32512,1177],{"class":1161},[1115,32514,32515],{"class":1173}," 2976",[1115,32517,6519],{"class":1169},[1115,32519,32520,32522,32524,32526,32528,32531,32533,32536,32538,32540],{"class":1154,"line":148},[1115,32521,30549],{"class":1165},[1115,32523,1170],{"class":1169},[1115,32525,32420],{"class":1157},[1115,32527,1177],{"class":1161},[1115,32529,32530],{"class":1157}," estB",[1115,32532,1177],{"class":1161},[1115,32534,32535],{"class":1157}," paired",[1115,32537,6416],{"class":1161},[1115,32539,6429],{"class":1173},[1115,32541,6519],{"class":1169},[1115,32543,32544,32546,32548,32550,32552,32554],{"class":1154,"line":111},[1115,32545,20072],{"class":1165},[1115,32547,1170],{"class":1169},[1115,32549,32420],{"class":1157},[1115,32551,28000],{"class":1161},[1115,32553,32530],{"class":1157},[1115,32555,6519],{"class":1169},[1144,32557,32560],{"className":32558,"code":32559,"language":6540,"meta":1148},[6538],"    Paired t-test\n\ndata:  estA and estB\nt = -1.2157, df = 7, p-value = 0.2635\nalternative hypothesis: true mean difference is not equal to 0\n95 percent confidence interval:\n -21.351272   6.851272\nsample estimates:\nmean difference \n          -7.25 \n\n    Shapiro-Wilk normality test\n\ndata:  estA - estB\nW = 0.80456, p-value = 0.03203\n",[1150,32561,32559],{"__ignoreMap":1148},[1110,32563,32564,32565,7219,32582,32601,32602,32625],{},"Párový t-test sám nezamítá ",[1115,32566,32568],{"className":32567},[1573],[1575,32569,32570],{"xmlns":1577},[1579,32571,32572,32580],{},[1582,32573,32574],{},[1746,32575,32576,32578],{},[1585,32577,1922],{},[1716,32579,2398],{},[1605,32581,4225],{"encoding":1607},[1115,32583,32585],{"className":32584},[1573],[1575,32586,32587],{"xmlns":1577},[1579,32588,32589,32598],{},[1582,32590,32591,32593,32595],{},[1585,32592,1110],{},[1589,32594,1597],{},[1716,32596,32597],{},"0,2635",[1605,32599,32600],{"encoding":1607},"p = 0{,}2635","): odhadci se podle něj neliší. Shapiro-Wilkův test na diferencích ale dává ",[1115,32603,32605],{"className":32604},[1573],[1575,32606,32607],{"xmlns":1577},[1579,32608,32609,32622],{},[1582,32610,32611,32613,32615,32618,32620],{},[1585,32612,1110],{},[1589,32614,1597],{},[1716,32616,32617],{},"0,03203",[1589,32619,6949],{},[1716,32621,6601],{},[1605,32623,32624],{"encoding":1607},"p = 0{,}03203 \u003C 0{,}05"," — předpoklad normality diferencí je porušen a výsledek t-testu proto není spolehlivý. Správný postup je ověřit normalitu diferencí dříve, než se párový t-test interpretuje, a při jejím porušení použít párový Wilcoxonův test (viz oddíl Neparametrické testy níže).",[1136,32627,32629],{"id":32628},"testy-o-dvou-základních-souborech","Testy o dvou základních souborech",[1110,32631,32632,32633,32659,32660,3707,32698,1260,32716,3707,32754,32772,32773,1260,32805,32837,32838,32864,32865,2264],{},"Uvažují se dva nezávislé základní soubory ",[1115,32634,32636],{"className":32635},[1573],[1575,32637,32638],{"xmlns":1577},[1579,32639,32640,32656],{},[1582,32641,32642,32648,32650],{},[1746,32643,32644,32646],{},[1585,32645,11505],{},[1716,32647,1718],{},[1589,32649,1177],{"separator":1121},[1746,32651,32652,32654],{},[1585,32653,11505],{},[1716,32655,1993],{},[1605,32657,32658],{"encoding":1607},"Z_1, Z_2"," se znakem ",[1115,32661,32663],{"className":32662},[1573],[1575,32664,32665],{"xmlns":1577},[1579,32666,32667,32695],{},[1582,32668,32669,32671,32673,32675,32677,32683,32685,32693],{},[1585,32670,1594],{},[1589,32672,11763],{},[1585,32674,1927],{},[1589,32676,1170],{"stretchy":1591},[1746,32678,32679,32681],{},[1585,32680,1982],{},[1716,32682,1718],{},[1589,32684,1177],{"separator":1121},[2920,32686,32687,32689,32691],{},[1585,32688,1990],{},[1716,32690,1718],{},[1716,32692,1993],{},[1589,32694,1603],{"stretchy":1591},[1605,32696,32697],{"encoding":1607},"X \\sim N(\\mu_1, \\sigma_1^2)",[1115,32699,32701],{"className":32700},[1573],[1575,32702,32703],{"xmlns":1577},[1579,32704,32705,32713],{},[1582,32706,32707],{},[1746,32708,32709,32711],{},[1585,32710,11505],{},[1716,32712,1718],{},[1605,32714,32715],{"encoding":1607},"Z_1",[1115,32717,32719],{"className":32718},[1573],[1575,32720,32721],{"xmlns":1577},[1579,32722,32723,32751],{},[1582,32724,32725,32727,32729,32731,32733,32739,32741,32749],{},[1585,32726,1594],{},[1589,32728,11763],{},[1585,32730,1927],{},[1589,32732,1170],{"stretchy":1591},[1746,32734,32735,32737],{},[1585,32736,1982],{},[1716,32738,1993],{},[1589,32740,1177],{"separator":1121},[2920,32742,32743,32745,32747],{},[1585,32744,1990],{},[1716,32746,1993],{},[1716,32748,1993],{},[1589,32750,1603],{"stretchy":1591},[1605,32752,32753],{"encoding":1607},"X \\sim N(\\mu_2, \\sigma_2^2)",[1115,32755,32757],{"className":32756},[1573],[1575,32758,32759],{"xmlns":1577},[1579,32760,32761,32769],{},[1582,32762,32763],{},[1746,32764,32765,32767],{},[1585,32766,11505],{},[1716,32768,1993],{},[1605,32770,32771],{"encoding":1607},"Z_2",". Z výběrů se určí ",[1115,32774,32776],{"className":32775},[1573],[1575,32777,32778],{"xmlns":1577},[1579,32779,32780,32802],{},[1582,32781,32782,32792,32794],{},[1746,32783,32784,32790],{},[3005,32785,32786,32788],{"accent":1121},[1585,32787,1158],{},[1589,32789,3408],{},[1716,32791,1718],{},[1589,32793,1177],{"separator":1121},[2920,32795,32796,32798,32800],{},[1585,32797,3433],{},[1716,32799,1718],{},[1716,32801,1993],{},[1605,32803,32804],{"encoding":1607},"\\bar{x}_1, s_1^2",[1115,32806,32808],{"className":32807},[1573],[1575,32809,32810],{"xmlns":1577},[1579,32811,32812,32834],{},[1582,32813,32814,32824,32826],{},[1746,32815,32816,32822],{},[3005,32817,32818,32820],{"accent":1121},[1585,32819,1158],{},[1589,32821,3408],{},[1716,32823,1993],{},[1589,32825,1177],{"separator":1121},[2920,32827,32828,32830,32832],{},[1585,32829,3433],{},[1716,32831,1993],{},[1716,32833,1993],{},[1605,32835,32836],{"encoding":1607},"\\bar{x}_2, s_2^2",". Testují se varianty vztahů mezi ",[1115,32839,32841],{"className":32840},[1573],[1575,32842,32843],{"xmlns":1577},[1579,32844,32845,32861],{},[1582,32846,32847,32853,32855],{},[1746,32848,32849,32851],{},[1585,32850,1982],{},[1716,32852,1718],{},[1589,32854,1177],{"separator":1121},[1746,32856,32857,32859],{},[1585,32858,1982],{},[1716,32860,1993],{},[1605,32862,32863],{"encoding":1607},"\\mu_1, \\mu_2",", resp. mezi ",[1115,32866,32868],{"className":32867},[1573],[1575,32869,32870],{"xmlns":1577},[1579,32871,32872,32892],{},[1582,32873,32874,32882,32884],{},[2920,32875,32876,32878,32880],{},[1585,32877,1990],{},[1716,32879,1718],{},[1716,32881,1993],{},[1589,32883,1177],{"separator":1121},[2920,32885,32886,32888,32890],{},[1585,32887,1990],{},[1716,32889,1993],{},[1716,32891,1993],{},[1605,32893,32894],{"encoding":1607},"\\sigma_1^2, \\sigma_2^2",[1550,32896,32898],{"id":32897},"f-test-o-rozptylech","F-test o rozptylech",[1110,32900,32901],{},"Statistika",[1115,32903,32905],{"className":32904},[1573],[1575,32906,32907],{"xmlns":1577,"display":4601},[1579,32908,32909,32965],{},[1582,32910,32911,32913,32915,32933,32935],{},[1585,32912,1669],{},[1589,32914,1597],{},[5373,32916,32917,32925],{},[2920,32918,32919,32921,32923],{},[1585,32920,3433],{},[1716,32922,1718],{},[1716,32924,1993],{},[2920,32926,32927,32929,32931],{},[1585,32928,3433],{},[1716,32930,1993],{},[1716,32932,1993],{},[1589,32934,11763],{},[1746,32936,32937,32939],{},[1585,32938,1669],{},[1582,32940,32941,32947,32949,32951,32953,32955,32961,32963],{},[1746,32942,32943,32945],{},[1585,32944,1781],{},[1716,32946,1718],{},[1589,32948,1721],{},[1716,32950,1718],{},[1589,32952,1177],{"separator":1121},[5543,32954,5545],{},[1746,32956,32957,32959],{},[1585,32958,1781],{},[1716,32960,1993],{},[1589,32962,1721],{},[1716,32964,1718],{},[1605,32966,32967],{"encoding":1607},"F = \\frac{s_1^2}{s_2^2} \\sim F_{n_1-1,\\,n_2-1}",[1110,32969,32970,32971,1260,32993,30137],{},"má Fisherovo-Snedecorovo rozdělení o ",[1115,32972,32974],{"className":32973},[1573],[1575,32975,32976],{"xmlns":1577},[1579,32977,32978,32990],{},[1582,32979,32980,32986,32988],{},[1746,32981,32982,32984],{},[1585,32983,1781],{},[1716,32985,1718],{},[1589,32987,1721],{},[1716,32989,1718],{},[1605,32991,32992],{"encoding":1607},"n_1-1",[1115,32994,32996],{"className":32995},[1573],[1575,32997,32998],{"xmlns":1577},[1579,32999,33000,33012],{},[1582,33001,33002,33008,33010],{},[1746,33003,33004,33006],{},[1585,33005,1781],{},[1716,33007,1993],{},[1589,33009,1721],{},[1716,33011,1718],{},[1605,33013,33014],{"encoding":1607},"n_2-1",[1310,33016,33017,33074],{},[1313,33018,33019],{},[1316,33020,33021,33040,33059],{},[1319,33022,33023],{},[1115,33024,33026],{"className":33025},[1573],[1575,33027,33028],{"xmlns":1577},[1579,33029,33030,33038],{},[1582,33031,33032],{},[1746,33033,33034,33036],{},[1585,33035,1922],{},[1716,33037,2398],{},[1605,33039,4225],{"encoding":1607},[1319,33041,33042],{},[1115,33043,33045],{"className":33044},[1573],[1575,33046,33047],{"xmlns":1577},[1579,33048,33049,33057],{},[1582,33050,33051],{},[1746,33052,33053,33055],{},[1585,33054,1922],{},[1716,33056,1718],{},[1605,33058,3807],{"encoding":1607},[1319,33060,30184,33061],{},[1115,33062,33064],{"className":33063},[1573],[1575,33065,33066],{"xmlns":1577},[1579,33067,33068,33072],{},[1582,33069,33070],{},[1585,33071,4256],{},[1605,33073,4256],{"encoding":1607},[1332,33075,33076,33190,33363],{},[1316,33077,33078,33106,33134],{},[1337,33079,33080],{},[1115,33081,33083],{"className":33082},[1573],[1575,33084,33085],{"xmlns":1577},[1579,33086,33087,33103],{},[1582,33088,33089,33095,33097],{},[1746,33090,33091,33093],{},[1585,33092,1990],{},[1716,33094,1718],{},[1589,33096,1650],{},[1746,33098,33099,33101],{},[1585,33100,1990],{},[1716,33102,1993],{},[1605,33104,33105],{"encoding":1607},"\\sigma_1 \\le \\sigma_2",[1337,33107,33108],{},[1115,33109,33111],{"className":33110},[1573],[1575,33112,33113],{"xmlns":1577},[1579,33114,33115,33131],{},[1582,33116,33117,33123,33125],{},[1746,33118,33119,33121],{},[1585,33120,1990],{},[1716,33122,1718],{},[1589,33124,1698],{},[1746,33126,33127,33129],{},[1585,33128,1990],{},[1716,33130,1993],{},[1605,33132,33133],{"encoding":1607},"\\sigma_1 > \\sigma_2",[1337,33135,33136],{},[1115,33137,33139],{"className":33138},[1573],[1575,33140,33141],{"xmlns":1577},[1579,33142,33143,33187],{},[1582,33144,33145,33147,33149,33161,33163,33169,33171,33173,33175,33181,33183,33185],{},[1585,33146,1669],{},[1589,33148,5983],{},[1746,33150,33151,33153],{},[1585,33152,1669],{},[1582,33154,33155,33157,33159],{},[1716,33156,1718],{},[1589,33158,1721],{},[1585,33160,3862],{},[1589,33162,1170],{"stretchy":1591},[1746,33164,33165,33167],{},[1585,33166,1781],{},[1716,33168,1718],{},[1589,33170,1721],{},[1716,33172,1718],{},[1589,33174,1177],{"separator":1121},[1746,33176,33177,33179],{},[1585,33178,1781],{},[1716,33180,1993],{},[1589,33182,1721],{},[1716,33184,1718],{},[1589,33186,1603],{"stretchy":1591},[1605,33188,33189],{"encoding":1607},"F \\ge F_{1-\\alpha}(n_1-1, n_2-1)",[1316,33191,33192,33220,33248],{},[1337,33193,33194],{},[1115,33195,33197],{"className":33196},[1573],[1575,33198,33199],{"xmlns":1577},[1579,33200,33201,33217],{},[1582,33202,33203,33209,33211],{},[1746,33204,33205,33207],{},[1585,33206,1990],{},[1716,33208,1718],{},[1589,33210,1597],{},[1746,33212,33213,33215],{},[1585,33214,1990],{},[1716,33216,1993],{},[1605,33218,33219],{"encoding":1607},"\\sigma_1 = \\sigma_2",[1337,33221,33222],{},[1115,33223,33225],{"className":33224},[1573],[1575,33226,33227],{"xmlns":1577},[1579,33228,33229,33245],{},[1582,33230,33231,33237,33239],{},[1746,33232,33233,33235],{},[1585,33234,1990],{},[1716,33236,1718],{},[1589,33238,13487],{"mathvariant":4022},[1746,33240,33241,33243],{},[1585,33242,1990],{},[1716,33244,1993],{},[1605,33246,33247],{"encoding":1607},"\\sigma_1 \\neq \\sigma_2",[1337,33249,33250,33304,33305],{},[1115,33251,33253],{"className":33252},[1573],[1575,33254,33255],{"xmlns":1577},[1579,33256,33257,33301],{},[1582,33258,33259,33261,33263,33275,33277,33283,33285,33287,33289,33295,33297,33299],{},[1585,33260,1669],{},[1589,33262,1650],{},[1746,33264,33265,33267],{},[1585,33266,1669],{},[1582,33268,33269,33271,33273],{},[1585,33270,3862],{},[1585,33272,4023],{"mathvariant":4022},[1716,33274,1993],{},[1589,33276,1170],{"stretchy":1591},[1746,33278,33279,33281],{},[1585,33280,1781],{},[1716,33282,1718],{},[1589,33284,1721],{},[1716,33286,1718],{},[1589,33288,1177],{"separator":1121},[1746,33290,33291,33293],{},[1585,33292,1781],{},[1716,33294,1993],{},[1589,33296,1721],{},[1716,33298,1718],{},[1589,33300,1603],{"stretchy":1591},[1605,33302,33303],{"encoding":1607},"F \\le F_{\\alpha\u002F2}(n_1-1, n_2-1)"," nebo ",[1115,33306,33308],{"className":33307},[1573],[1575,33309,33310],{"xmlns":1577},[1579,33311,33312,33360],{},[1582,33313,33314,33316,33318,33334,33336,33342,33344,33346,33348,33354,33356,33358],{},[1585,33315,1669],{},[1589,33317,5983],{},[1746,33319,33320,33322],{},[1585,33321,1669],{},[1582,33323,33324,33326,33328,33330,33332],{},[1716,33325,1718],{},[1589,33327,1721],{},[1585,33329,3862],{},[1585,33331,4023],{"mathvariant":4022},[1716,33333,1993],{},[1589,33335,1170],{"stretchy":1591},[1746,33337,33338,33340],{},[1585,33339,1781],{},[1716,33341,1718],{},[1589,33343,1721],{},[1716,33345,1718],{},[1589,33347,1177],{"separator":1121},[1746,33349,33350,33352],{},[1585,33351,1781],{},[1716,33353,1993],{},[1589,33355,1721],{},[1716,33357,1718],{},[1589,33359,1603],{"stretchy":1591},[1605,33361,33362],{"encoding":1607},"F \\ge F_{1-\\alpha\u002F2}(n_1-1, n_2-1)",[1316,33364,33365,33393,33421],{},[1337,33366,33367],{},[1115,33368,33370],{"className":33369},[1573],[1575,33371,33372],{"xmlns":1577},[1579,33373,33374,33390],{},[1582,33375,33376,33382,33384],{},[1746,33377,33378,33380],{},[1585,33379,1990],{},[1716,33381,1718],{},[1589,33383,5983],{},[1746,33385,33386,33388],{},[1585,33387,1990],{},[1716,33389,1993],{},[1605,33391,33392],{"encoding":1607},"\\sigma_1 \\ge \\sigma_2",[1337,33394,33395],{},[1115,33396,33398],{"className":33397},[1573],[1575,33399,33400],{"xmlns":1577},[1579,33401,33402,33418],{},[1582,33403,33404,33410,33412],{},[1746,33405,33406,33408],{},[1585,33407,1990],{},[1716,33409,1718],{},[1589,33411,6949],{},[1746,33413,33414,33416],{},[1585,33415,1990],{},[1716,33417,1993],{},[1605,33419,33420],{"encoding":1607},"\\sigma_1 \u003C \\sigma_2",[1337,33422,33423],{},[1115,33424,33426],{"className":33425},[1573],[1575,33427,33428],{"xmlns":1577},[1579,33429,33430,33468],{},[1582,33431,33432,33434,33436,33442,33444,33450,33452,33454,33456,33462,33464,33466],{},[1585,33433,1669],{},[1589,33435,1650],{},[1746,33437,33438,33440],{},[1585,33439,1669],{},[1585,33441,3862],{},[1589,33443,1170],{"stretchy":1591},[1746,33445,33446,33448],{},[1585,33447,1781],{},[1716,33449,1718],{},[1589,33451,1721],{},[1716,33453,1718],{},[1589,33455,1177],{"separator":1121},[1746,33457,33458,33460],{},[1585,33459,1781],{},[1716,33461,1993],{},[1589,33463,1721],{},[1716,33465,1718],{},[1589,33467,1603],{"stretchy":1591},[1605,33469,33470],{"encoding":1607},"F \\le F_{\\alpha}(n_1-1, n_2-1)",[1550,33472,33474],{"id":33473},"dvouvýběrový-t-test-o-středních-hodnotách","Dvouvýběrový t-test o středních hodnotách",[1110,33476,33477],{},"Volba statistiky závisí na tom, zda jsou rozptyly považovány za shodné:",[1115,33479,33481],{"className":33480},[1573],[1575,33482,33483],{"xmlns":1577,"display":4601},[1579,33484,33485,33662],{},[1582,33486,33487,33493,33495,33571,33619,33621,33623,33632,33634,33640,33642,33648,33650,33656,33658,33660],{},[1746,33488,33489,33491],{},[1585,33490,4043],{},[1716,33492,1718],{},[1589,33494,1597],{},[5373,33496,33497,33521],{},[1582,33498,33499,33509,33511],{},[1746,33500,33501,33507],{},[3005,33502,33503,33505],{"accent":1121},[1585,33504,1158],{},[1589,33506,3408],{},[1716,33508,1718],{},[1589,33510,1721],{},[1746,33512,33513,33519],{},[3005,33514,33515,33517],{"accent":1121},[1585,33516,1158],{},[1589,33518,3408],{},[1716,33520,1993],{},[7068,33522,33523],{},[1582,33524,33525,33527,33533,33535,33537,33539,33547,33549,33551,33557,33559,33561,33563],{},[1589,33526,1170],{"stretchy":1591},[1746,33528,33529,33531],{},[1585,33530,1781],{},[1716,33532,1718],{},[1589,33534,1721],{},[1716,33536,1718],{},[1589,33538,1603],{"stretchy":1591},[2920,33540,33541,33543,33545],{},[1585,33542,3433],{},[1716,33544,1718],{},[1716,33546,1993],{},[1589,33548,4010],{},[1589,33550,1170],{"stretchy":1591},[1746,33552,33553,33555],{},[1585,33554,1781],{},[1716,33556,1993],{},[1589,33558,1721],{},[1716,33560,1718],{},[1589,33562,1603],{"stretchy":1591},[2920,33564,33565,33567,33569],{},[1585,33566,3433],{},[1716,33568,1993],{},[1716,33570,1993],{},[7068,33572,33573],{},[5373,33574,33575,33595],{},[1582,33576,33577,33583,33585,33591,33593],{},[1746,33578,33579,33581],{},[1585,33580,1781],{},[1716,33582,1718],{},[1589,33584,4010],{},[1746,33586,33587,33589],{},[1585,33588,1781],{},[1716,33590,1993],{},[1589,33592,1721],{},[1716,33594,1993],{},[1582,33596,33597,33607,33609],{},[5373,33598,33599,33601],{},[1716,33600,1718],{},[1746,33602,33603,33605],{},[1585,33604,1781],{},[1716,33606,1718],{},[1589,33608,4010],{},[5373,33610,33611,33613],{},[1716,33612,1718],{},[1746,33614,33615,33617],{},[1585,33616,1781],{},[1716,33618,1993],{},[1589,33620,1177],{"separator":1121},[4648,33622],{"width":4650},[2920,33624,33625,33627,33629],{},[1585,33626,2082],{},[1585,33628,1110],{},[1589,33630,33631],{},"∗",[1589,33633,1597],{},[1746,33635,33636,33638],{},[1585,33637,2082],{},[1585,33639,1110],{},[1589,33641,1170],{"stretchy":1591},[1746,33643,33644,33646],{},[1585,33645,1781],{},[1716,33647,1718],{},[1589,33649,4010],{},[1746,33651,33652,33654],{},[1585,33653,1781],{},[1716,33655,1993],{},[1589,33657,1721],{},[1716,33659,1993],{},[1589,33661,1603],{"stretchy":1591},[1605,33663,33664],{"encoding":1607},"T_1 = \\frac{\\bar{x}_1 - \\bar{x}_2}{\\sqrt{(n_1-1)s_1^2 + (n_2-1)s_2^2}}\\sqrt{\\frac{n_1+n_2-2}{\\frac1{n_1}+\\frac1{n_2}}}, \\qquad t_p^* = t_p(n_1+n_2-2)",[1110,33666,33667,33668,33697],{},"se použije, pokud jsou rozptyly ",[1115,33669,33671],{"className":33670},[1573],[1575,33672,33673],{"xmlns":1577},[1579,33674,33675,33695],{},[1582,33676,33677,33685,33687],{},[2920,33678,33679,33681,33683],{},[1585,33680,1990],{},[1716,33682,1718],{},[1716,33684,1993],{},[1589,33686,1177],{"separator":1121},[2920,33688,33689,33691,33693],{},[1585,33690,1990],{},[1716,33692,1993],{},[1716,33694,1993],{},[1605,33696,32894],{"encoding":1607}," alespoň přibližně shodné; při rozdílných rozptylech",[1115,33699,33701],{"className":33700},[1573],[1575,33702,33703],{"xmlns":1577,"display":4601},[1579,33704,33705,33917],{},[1582,33706,33707,33713,33715,33779,33781,33783,33791,33793,33915],{},[1746,33708,33709,33711],{},[1585,33710,4043],{},[1716,33712,1993],{},[1589,33714,1597],{},[5373,33716,33717,33741],{},[1582,33718,33719,33729,33731],{},[1746,33720,33721,33727],{},[3005,33722,33723,33725],{"accent":1121},[1585,33724,1158],{},[1589,33726,3408],{},[1716,33728,1718],{},[1589,33730,1721],{},[1746,33732,33733,33739],{},[3005,33734,33735,33737],{"accent":1121},[1585,33736,1158],{},[1589,33738,3408],{},[1716,33740,1993],{},[7068,33742,33743],{},[1582,33744,33745,33753,33755,33761,33763,33771,33773],{},[2920,33746,33747,33749,33751],{},[1585,33748,3433],{},[1716,33750,1718],{},[1716,33752,1993],{},[1585,33754,4023],{"mathvariant":4022},[1746,33756,33757,33759],{},[1585,33758,1781],{},[1716,33760,1718],{},[1589,33762,4010],{},[2920,33764,33765,33767,33769],{},[1585,33766,3433],{},[1716,33768,1993],{},[1716,33770,1993],{},[1585,33772,4023],{"mathvariant":4022},[1746,33774,33775,33777],{},[1585,33776,1781],{},[1716,33778,1993],{},[1589,33780,1177],{"separator":1121},[4648,33782],{"width":4650},[2920,33784,33785,33787,33789],{},[1585,33786,2082],{},[1585,33788,1110],{},[1589,33790,33631],{},[1589,33792,1597],{},[5373,33794,33795,33875],{},[1582,33796,33797,33815,33821,33823,33829,33831,33833,33835,33837,33855,33861,33863,33869,33871,33873],{},[5873,33798,33799],{"scriptlevel":2398,"displaystyle":1121},[5373,33800,33801,33809],{},[2920,33802,33803,33805,33807],{},[1585,33804,3433],{},[1716,33806,1718],{},[1716,33808,1993],{},[1746,33810,33811,33813],{},[1585,33812,1781],{},[1716,33814,1718],{},[1746,33816,33817,33819],{},[1585,33818,2082],{},[1585,33820,1110],{},[1589,33822,1170],{"stretchy":1591},[1746,33824,33825,33827],{},[1585,33826,1781],{},[1716,33828,1718],{},[1589,33830,1721],{},[1716,33832,1718],{},[1589,33834,1603],{"stretchy":1591},[1589,33836,4010],{},[5873,33838,33839],{"scriptlevel":2398,"displaystyle":1121},[5373,33840,33841,33849],{},[2920,33842,33843,33845,33847],{},[1585,33844,3433],{},[1716,33846,1993],{},[1716,33848,1993],{},[1746,33850,33851,33853],{},[1585,33852,1781],{},[1716,33854,1993],{},[1746,33856,33857,33859],{},[1585,33858,2082],{},[1585,33860,1110],{},[1589,33862,1170],{"stretchy":1591},[1746,33864,33865,33867],{},[1585,33866,1781],{},[1716,33868,1993],{},[1589,33870,1721],{},[1716,33872,1718],{},[1589,33874,1603],{"stretchy":1591},[1582,33876,33877,33895,33897],{},[5873,33878,33879],{"scriptlevel":2398,"displaystyle":1121},[5373,33880,33881,33889],{},[2920,33882,33883,33885,33887],{},[1585,33884,3433],{},[1716,33886,1718],{},[1716,33888,1993],{},[1746,33890,33891,33893],{},[1585,33892,1781],{},[1716,33894,1718],{},[1589,33896,4010],{},[5873,33898,33899],{"scriptlevel":2398,"displaystyle":1121},[5373,33900,33901,33909],{},[2920,33902,33903,33905,33907],{},[1585,33904,3433],{},[1716,33906,1993],{},[1716,33908,1993],{},[1746,33910,33911,33913],{},[1585,33912,1781],{},[1716,33914,1993],{},[1585,33916,2264],{"mathvariant":4022},[1605,33918,33919],{"encoding":1607},"T_2 = \\frac{\\bar{x}_1-\\bar{x}_2}{\\sqrt{s_1^2\u002Fn_1 + s_2^2\u002Fn_2}}, \\qquad t_p^* = \\frac{\\dfrac{s_1^2}{n_1}t_p(n_1-1) + \\dfrac{s_2^2}{n_2}t_p(n_2-1)}{\\dfrac{s_1^2}{n_1}+\\dfrac{s_2^2}{n_2}}.",[1310,33921,33922,33979],{},[1313,33923,33924],{},[1316,33925,33926,33945,33964],{},[1319,33927,33928],{},[1115,33929,33931],{"className":33930},[1573],[1575,33932,33933],{"xmlns":1577},[1579,33934,33935,33943],{},[1582,33936,33937],{},[1746,33938,33939,33941],{},[1585,33940,1922],{},[1716,33942,2398],{},[1605,33944,4225],{"encoding":1607},[1319,33946,33947],{},[1115,33948,33950],{"className":33949},[1573],[1575,33951,33952],{"xmlns":1577},[1579,33953,33954,33962],{},[1582,33955,33956],{},[1746,33957,33958,33960],{},[1585,33959,1922],{},[1716,33961,1718],{},[1605,33963,3807],{"encoding":1607},[1319,33965,30184,33966],{},[1115,33967,33969],{"className":33968},[1573],[1575,33970,33971],{"xmlns":1577},[1579,33972,33973,33977],{},[1582,33974,33975],{},[1585,33976,4256],{},[1605,33978,4256],{"encoding":1607},[1332,33980,33981,34065,34153],{},[1316,33982,33983,34011,34039],{},[1337,33984,33985],{},[1115,33986,33988],{"className":33987},[1573],[1575,33989,33990],{"xmlns":1577},[1579,33991,33992,34008],{},[1582,33993,33994,34000,34002],{},[1746,33995,33996,33998],{},[1585,33997,1982],{},[1716,33999,1718],{},[1589,34001,1650],{},[1746,34003,34004,34006],{},[1585,34005,1982],{},[1716,34007,1993],{},[1605,34009,34010],{"encoding":1607},"\\mu_1 \\le \\mu_2",[1337,34012,34013],{},[1115,34014,34016],{"className":34015},[1573],[1575,34017,34018],{"xmlns":1577},[1579,34019,34020,34036],{},[1582,34021,34022,34028,34030],{},[1746,34023,34024,34026],{},[1585,34025,1982],{},[1716,34027,1718],{},[1589,34029,1698],{},[1746,34031,34032,34034],{},[1585,34033,1982],{},[1716,34035,1993],{},[1605,34037,34038],{"encoding":1607},"\\mu_1 > \\mu_2",[1337,34040,34041],{},[1115,34042,34044],{"className":34043},[1573],[1575,34045,34046],{"xmlns":1577},[1579,34047,34048,34062],{},[1582,34049,34050,34052,34054],{},[1585,34051,2082],{},[1589,34053,5983],{},[2920,34055,34056,34058,34060],{},[1585,34057,2082],{},[1585,34059,1110],{},[1589,34061,33631],{},[1605,34063,34064],{"encoding":1607},"t \\ge t_p^*",[1316,34066,34067,34095,34123],{},[1337,34068,34069],{},[1115,34070,34072],{"className":34071},[1573],[1575,34073,34074],{"xmlns":1577},[1579,34075,34076,34092],{},[1582,34077,34078,34084,34086],{},[1746,34079,34080,34082],{},[1585,34081,1982],{},[1716,34083,1718],{},[1589,34085,1597],{},[1746,34087,34088,34090],{},[1585,34089,1982],{},[1716,34091,1993],{},[1605,34093,34094],{"encoding":1607},"\\mu_1 = \\mu_2",[1337,34096,34097],{},[1115,34098,34100],{"className":34099},[1573],[1575,34101,34102],{"xmlns":1577},[1579,34103,34104,34120],{},[1582,34105,34106,34112,34114],{},[1746,34107,34108,34110],{},[1585,34109,1982],{},[1716,34111,1718],{},[1589,34113,13487],{"mathvariant":4022},[1746,34115,34116,34118],{},[1585,34117,1982],{},[1716,34119,1993],{},[1605,34121,34122],{"encoding":1607},"\\mu_1 \\neq \\mu_2",[1337,34124,34125],{},[1115,34126,34128],{"className":34127},[1573],[1575,34129,34130],{"xmlns":1577},[1579,34131,34132,34150],{},[1582,34133,34134,34136,34138,34140,34142],{},[1589,34135,25509],{"stretchy":1591},[1585,34137,2082],{},[1589,34139,25509],{"stretchy":1591},[1589,34141,5983],{},[2920,34143,34144,34146,34148],{},[1585,34145,2082],{},[1585,34147,1110],{},[1589,34149,33631],{},[1605,34151,34152],{"encoding":1607},"\\lvert t \\rvert \\ge t_p^*",[1316,34154,34155,34183,34211],{},[1337,34156,34157],{},[1115,34158,34160],{"className":34159},[1573],[1575,34161,34162],{"xmlns":1577},[1579,34163,34164,34180],{},[1582,34165,34166,34172,34174],{},[1746,34167,34168,34170],{},[1585,34169,1982],{},[1716,34171,1718],{},[1589,34173,5983],{},[1746,34175,34176,34178],{},[1585,34177,1982],{},[1716,34179,1993],{},[1605,34181,34182],{"encoding":1607},"\\mu_1 \\ge \\mu_2",[1337,34184,34185],{},[1115,34186,34188],{"className":34187},[1573],[1575,34189,34190],{"xmlns":1577},[1579,34191,34192,34208],{},[1582,34193,34194,34200,34202],{},[1746,34195,34196,34198],{},[1585,34197,1982],{},[1716,34199,1718],{},[1589,34201,6949],{},[1746,34203,34204,34206],{},[1585,34205,1982],{},[1716,34207,1993],{},[1605,34209,34210],{"encoding":1607},"\\mu_1 \u003C \\mu_2",[1337,34212,34213],{},[1115,34214,34216],{"className":34215},[1573],[1575,34217,34218],{"xmlns":1577},[1579,34219,34220,34236],{},[1582,34221,34222,34224,34226,34228],{},[1585,34223,2082],{},[1589,34225,1650],{},[1589,34227,1721],{},[2920,34229,34230,34232,34234],{},[1585,34231,2082],{},[1585,34233,1110],{},[1589,34235,33631],{},[1605,34237,34238],{"encoding":1607},"t \\le -t_p^*",[1110,34240,34241,34242,33304,34260,2264],{},"Postup je dvoukrokový: nejprve F-test rozhodne o shodě rozptylů, pak se podle výsledku zvolí ",[1115,34243,34245],{"className":34244},[1573],[1575,34246,34247],{"xmlns":1577},[1579,34248,34249,34257],{},[1582,34250,34251],{},[1746,34252,34253,34255],{},[1585,34254,4043],{},[1716,34256,1718],{},[1605,34258,34259],{"encoding":1607},"T_1",[1115,34261,34263],{"className":34262},[1573],[1575,34264,34265],{"xmlns":1577},[1579,34266,34267,34275],{},[1582,34268,34269],{},[1746,34270,34271,34273],{},[1585,34272,4043],{},[1716,34274,1993],{},[1605,34276,34277],{"encoding":1607},"T_2",[1110,34279,34280],{},[1303,34281],{"alt":34282,"className":34283,"src":34284},"mask-th-f-kriticky-obor",[1130,1307],"\u002Fwiki-assets\u002Fmask-th-f-kriticky-obor.png",[1103,34286,34288,34295,34445,34526,34655,34693,34766,34905],{"className":34287,"dataCallout":6105},[1106,6104],[1110,34289,34291,34294],{"className":34290},[1113],[1115,34292],{"className":34293,"ariaHidden":1121},[1118,6112,1120],"Příklad: Porovnání dvou dodavatelů součástek",[1110,34296,34297,34298,1279,34320,34346,34347,34371,34372,1279,34394,34346,34420,34444],{},"Pevnost plastových dílů: dodavatel A (",[1115,34299,34301],{"className":34300},[1573],[1575,34302,34303],{"xmlns":1577},[1579,34304,34305,34317],{},[1582,34306,34307,34313,34315],{},[1746,34308,34309,34311],{},[1585,34310,1781],{},[1716,34312,1718],{},[1589,34314,1597],{},[1716,34316,11613],{},[1605,34318,34319],{"encoding":1607},"n_1 = 10",[1115,34321,34323],{"className":34322},[1573],[1575,34324,34325],{"xmlns":1577},[1579,34326,34327,34343],{},[1582,34328,34329,34339,34341],{},[1746,34330,34331,34337],{},[3005,34332,34333,34335],{"accent":1121},[1585,34334,1158],{},[1589,34336,3408],{},[1716,34338,1718],{},[1589,34340,1597],{},[1716,34342,6256],{},[1605,34344,34345],{"encoding":1607},"\\bar{x}_1 = 82"," MPa, ",[1115,34348,34350],{"className":34349},[1573],[1575,34351,34352],{"xmlns":1577},[1579,34353,34354,34368],{},[1582,34355,34356,34364,34366],{},[2920,34357,34358,34360,34362],{},[1585,34359,3433],{},[1716,34361,1718],{},[1716,34363,1993],{},[1589,34365,1597],{},[1716,34367,6675],{},[1605,34369,34370],{"encoding":1607},"s_1^2 = 25","), dodavatel B (",[1115,34373,34375],{"className":34374},[1573],[1575,34376,34377],{"xmlns":1577},[1579,34378,34379,34391],{},[1582,34380,34381,34387,34389],{},[1746,34382,34383,34385],{},[1585,34384,1781],{},[1716,34386,1993],{},[1589,34388,1597],{},[1716,34390,4911],{},[1605,34392,34393],{"encoding":1607},"n_2 = 12",[1115,34395,34397],{"className":34396},[1573],[1575,34398,34399],{"xmlns":1577},[1579,34400,34401,34417],{},[1582,34402,34403,34413,34415],{},[1746,34404,34405,34411],{},[3005,34406,34407,34409],{"accent":1121},[1585,34408,1158],{},[1589,34410,3408],{},[1716,34412,1993],{},[1589,34414,1597],{},[1716,34416,17238],{},[1605,34418,34419],{"encoding":1607},"\\bar{x}_2 = 75",[1115,34421,34423],{"className":34422},[1573],[1575,34424,34425],{"xmlns":1577},[1579,34426,34427,34441],{},[1582,34428,34429,34437,34439],{},[2920,34430,34431,34433,34435],{},[1585,34432,3433],{},[1716,34434,1993],{},[1716,34436,1993],{},[1589,34438,1597],{},[1716,34440,24513],{},[1605,34442,34443],{"encoding":1607},"s_2^2 = 16","). Předpokládá se normalita obou rozdělení.",[1110,34446,34447,2230,34450,1279,34488,2264],{},[2227,34448,34449],{},"Krok 1 — F-test rozptylů.",[1115,34451,34453],{"className":34452},[1573],[1575,34454,34455],{"xmlns":1577},[1579,34456,34457,34485],{},[1582,34458,34459,34465,34467,34475,34477],{},[1746,34460,34461,34463],{},[1585,34462,1922],{},[1716,34464,2398],{},[1589,34466,4595],{},[2920,34468,34469,34471,34473],{},[1585,34470,1990],{},[1716,34472,1718],{},[1716,34474,1993],{},[1589,34476,1597],{},[2920,34478,34479,34481,34483],{},[1585,34480,1990],{},[1716,34482,1993],{},[1716,34484,1993],{},[1605,34486,34487],{"encoding":1607},"H_0: \\sigma_1^2 = \\sigma_2^2",[1115,34489,34491],{"className":34490},[1573],[1575,34492,34493],{"xmlns":1577},[1579,34494,34495,34523],{},[1582,34496,34497,34503,34505,34513,34515],{},[1746,34498,34499,34501],{},[1585,34500,1922],{},[1716,34502,1718],{},[1589,34504,4595],{},[2920,34506,34507,34509,34511],{},[1585,34508,1990],{},[1716,34510,1718],{},[1716,34512,1993],{},[1589,34514,13487],{"mathvariant":4022},[2920,34516,34517,34519,34521],{},[1585,34518,1990],{},[1716,34520,1993],{},[1716,34522,1993],{},[1605,34524,34525],{"encoding":1607},"H_1: \\sigma_1^2 \\neq \\sigma_2^2",[1110,34527,34528],{},[1115,34529,34531],{"className":34530},[1573],[1575,34532,34533],{"xmlns":1577},[1579,34534,34535,34652],{},[1582,34536,34537,34539,34541,34547,34549,34552,34554,34556,34558,34560,34562,34564,34566,34579,34581,34583,34585,34587,34589,34592,34595,34597,34599,34601,34614,34616,34618,34620,34622,34624,34626,34628,34630,34632,34634,34637,34639,34641,34643,34645,34647,34650],{},[1585,34538,1669],{},[1589,34540,1597],{},[5373,34542,34543,34545],{},[1716,34544,6675],{},[1716,34546,24513],{},[1589,34548,1597],{},[1716,34550,34551],{},"1,5625",[1589,34553,1177],{"separator":1121},[4648,34555],{"width":4650},[1585,34557,4256],{},[1589,34559,1597],{},[1589,34561,5966],{"stretchy":1591},[1585,34563,1669],{},[1589,34565,1650],{},[1746,34567,34568,34570],{},[1585,34569,1669],{},[1582,34571,34572,34574,34576],{},[1716,34573,2398],{},[1589,34575,1177],{"separator":1121},[1716,34577,34578],{},"025",[1589,34580,1170],{"stretchy":1591},[1716,34582,6223],{},[1589,34584,1177],{"separator":1121},[1716,34586,4890],{},[1589,34588,1603],{"stretchy":1591},[5543,34590,34591],{},"  ",[5543,34593,34594],{},"nebo",[5543,34596,34591],{},[1585,34598,1669],{},[1589,34600,5983],{},[1746,34602,34603,34605],{},[1585,34604,1669],{},[1582,34606,34607,34609,34611],{},[1716,34608,2398],{},[1589,34610,1177],{"separator":1121},[1716,34612,34613],{},"975",[1589,34615,1170],{"stretchy":1591},[1716,34617,6223],{},[1589,34619,1177],{"separator":1121},[1716,34621,4890],{},[1589,34623,1603],{"stretchy":1591},[1589,34625,6024],{"stretchy":1591},[1589,34627,1597],{},[1589,34629,5966],{"stretchy":1591},[1585,34631,1669],{},[1589,34633,1650],{},[1716,34635,34636],{},"0,256",[5543,34638,34591],{},[5543,34640,34594],{},[5543,34642,34591],{},[1585,34644,1669],{},[1589,34646,5983],{},[1716,34648,34649],{},"3,588",[1589,34651,6024],{"stretchy":1591},[1605,34653,34654],{"encoding":1607},"F = \\frac{25}{16} = 1{,}5625, \\qquad W = \\{F \\le F_{0,025}(9,11) \\;\\text{nebo}\\; F \\ge F_{0,975}(9,11)\\} = \\{F \\le 0{,}256 \\;\\text{nebo}\\; F \\ge 3{,}588\\}",[1110,34656,34657,34675,34676,2264],{},[1115,34658,34660],{"className":34659},[1573],[1575,34661,34662],{"xmlns":1577},[1579,34663,34664,34672],{},[1582,34665,34666,34668,34670],{},[1585,34667,1669],{},[1589,34669,29745],{"mathvariant":4022},[1585,34671,4256],{},[1605,34673,34674],{"encoding":1607},"F \\notin W",", rozptyly nezamítáme jako shodné — pro t-test se použije ",[1115,34677,34679],{"className":34678},[1573],[1575,34680,34681],{"xmlns":1577},[1579,34682,34683,34691],{},[1582,34684,34685],{},[1746,34686,34687,34689],{},[1585,34688,4043],{},[1716,34690,1718],{},[1605,34692,34259],{"encoding":1607},[1110,34694,34695,2230,34698,1279,34732,2264],{},[2227,34696,34697],{},"Krok 2 — dvouvýběrový t-test středních hodnot.",[1115,34699,34701],{"className":34700},[1573],[1575,34702,34703],{"xmlns":1577},[1579,34704,34705,34729],{},[1582,34706,34707,34713,34715,34721,34723],{},[1746,34708,34709,34711],{},[1585,34710,1922],{},[1716,34712,2398],{},[1589,34714,4595],{},[1746,34716,34717,34719],{},[1585,34718,1982],{},[1716,34720,1718],{},[1589,34722,1597],{},[1746,34724,34725,34727],{},[1585,34726,1982],{},[1716,34728,1993],{},[1605,34730,34731],{"encoding":1607},"H_0: \\mu_1 = \\mu_2",[1115,34733,34735],{"className":34734},[1573],[1575,34736,34737],{"xmlns":1577},[1579,34738,34739,34763],{},[1582,34740,34741,34747,34749,34755,34757],{},[1746,34742,34743,34745],{},[1585,34744,1922],{},[1716,34746,1718],{},[1589,34748,4595],{},[1746,34750,34751,34753],{},[1585,34752,1982],{},[1716,34754,1718],{},[1589,34756,13487],{"mathvariant":4022},[1746,34758,34759,34761],{},[1585,34760,1982],{},[1716,34762,1993],{},[1605,34764,34765],{"encoding":1607},"H_1: \\mu_1 \\neq \\mu_2",[1110,34767,34768],{},[1115,34769,34771],{"className":34770},[1573],[1575,34772,34773],{"xmlns":1577},[1579,34774,34775,34902],{},[1582,34776,34777,34785,34787,34807,34809,34812,34814,34816,34818,34820,34834,34842,34844,34847,34849,34851,34853,34855,34857,34859,34861,34863,34865,34877,34879,34881,34883,34885,34887,34889,34891,34893,34895,34897,34900],{},[2920,34778,34779,34781,34783],{},[1585,34780,3433],{},[1585,34782,1110],{},[1716,34784,1993],{},[1589,34786,1597],{},[5373,34788,34789,34805],{},[1582,34790,34791,34793,34795,34797,34799,34801,34803],{},[1716,34792,6223],{},[1589,34794,10691],{},[1716,34796,6675],{},[1589,34798,4010],{},[1716,34800,4890],{},[1589,34802,10691],{},[1716,34804,24513],{},[1716,34806,6662],{},[1589,34808,1597],{},[1716,34810,34811],{},"20,05",[1589,34813,1177],{"separator":1121},[4648,34815],{"width":4650},[1585,34817,2082],{},[1589,34819,1597],{},[5373,34821,34822,34830],{},[1582,34823,34824,34826,34828],{},[1716,34825,6256],{},[1589,34827,1721],{},[1716,34829,17238],{},[7068,34831,34832],{},[1716,34833,34811],{},[7068,34835,34836],{},[5373,34837,34838,34840],{},[1716,34839,24373],{},[1716,34841,5025],{},[1589,34843,12020],{},[1716,34845,34846],{},"3,651",[1589,34848,1177],{"separator":1121},[4648,34850],{"width":4650},[1585,34852,4256],{},[1589,34854,1597],{},[1589,34856,5966],{"stretchy":1591},[1589,34858,25509],{"stretchy":1591},[1585,34860,2082],{},[1589,34862,25509],{"stretchy":1591},[1589,34864,5983],{},[1746,34866,34867,34869],{},[1585,34868,2082],{},[1582,34870,34871,34873,34875],{},[1716,34872,2398],{},[1589,34874,1177],{"separator":1121},[1716,34876,34613],{},[1589,34878,1170],{"stretchy":1591},[1716,34880,6662],{},[1589,34882,1603],{"stretchy":1591},[1589,34884,6024],{"stretchy":1591},[1589,34886,1597],{},[1589,34888,5966],{"stretchy":1591},[1589,34890,25509],{"stretchy":1591},[1585,34892,2082],{},[1589,34894,25509],{"stretchy":1591},[1589,34896,5983],{},[1716,34898,34899],{},"2,086",[1589,34901,6024],{"stretchy":1591},[1605,34903,34904],{"encoding":1607},"s_p^2 = \\frac{9\\cdot 25 + 11\\cdot 16}{20} = 20{,}05, \\qquad t = \\frac{82-75}{\\sqrt{20{,}05}}\\sqrt{\\frac{120}{22}} \\approx 3{,}651, \\qquad W = \\{\\lvert t\\rvert \\ge t_{0,975}(20)\\} = \\{\\lvert t\\rvert \\ge 2{,}086\\}",[1110,34906,34907,8614,34924,34941],{},[1115,34908,34910],{"className":34909},[1573],[1575,34911,34912],{"xmlns":1577},[1579,34913,34914,34922],{},[1582,34915,34916,34918,34920],{},[1585,34917,2082],{},[1589,34919,9605],{},[1585,34921,4256],{},[1605,34923,30885],{"encoding":1607},[1115,34925,34927],{"className":34926},[1573],[1575,34928,34929],{"xmlns":1577},[1579,34930,34931,34939],{},[1582,34932,34933],{},[1746,34934,34935,34937],{},[1585,34936,1922],{},[1716,34938,2398],{},[1605,34940,4225],{"encoding":1607},": pevnost součástek od obou dodavatelů se statisticky významně liší.",[1144,34943,34945],{"className":1146,"code":34944,"language":71,"meta":1148,"style":1148},"s1 \u003C- 25; n1 \u003C- 10\ns2 \u003C- 16; n2 \u003C- 12\nFstat \u003C- s1 \u002F s2\nF_dolni \u003C- qf(0.025, n1 - 1, n2 - 1)\nF_horni \u003C- qf(0.975, n1 - 1, n2 - 1)\nFstat\nF_dolni\nF_horni\n",[1150,34946,34947,34965,34985,35000,35035,35066,35071,35076],{"__ignoreMap":1148},[1115,34948,34949,34952,34954,34956,34958,34961,34963],{"class":1154,"line":10},[1115,34950,34951],{"class":1157},"s1",[1115,34953,1162],{"class":1161},[1115,34955,16908],{"class":1173},[1115,34957,2402],{"class":1169},[1115,34959,34960],{"class":1157},"n1",[1115,34962,1162],{"class":1161},[1115,34964,32326],{"class":1173},[1115,34966,34967,34970,34972,34975,34977,34980,34982],{"class":1154,"line":27},[1115,34968,34969],{"class":1157},"s2",[1115,34971,1162],{"class":1161},[1115,34973,34974],{"class":1173}," 16",[1115,34976,2402],{"class":1169},[1115,34978,34979],{"class":1157},"n2",[1115,34981,1162],{"class":1161},[1115,34983,34984],{"class":1173}," 12\n",[1115,34986,34987,34990,34992,34995,34997],{"class":1154,"line":148},[1115,34988,34989],{"class":1157},"Fstat",[1115,34991,1162],{"class":1161},[1115,34993,34994],{"class":1157}," s1",[1115,34996,12619],{"class":1161},[1115,34998,34999],{"class":1157}," s2\n",[1115,35001,35002,35005,35007,35010,35012,35015,35017,35020,35022,35024,35026,35029,35031,35033],{"class":1154,"line":111},[1115,35003,35004],{"class":1157},"F_dolni",[1115,35006,1162],{"class":1161},[1115,35008,35009],{"class":1165}," qf",[1115,35011,1170],{"class":1169},[1115,35013,35014],{"class":1173},"0.025",[1115,35016,1177],{"class":1161},[1115,35018,35019],{"class":1157}," n1",[1115,35021,28000],{"class":1161},[1115,35023,7253],{"class":1173},[1115,35025,1177],{"class":1161},[1115,35027,35028],{"class":1157}," n2",[1115,35030,28000],{"class":1161},[1115,35032,7253],{"class":1173},[1115,35034,6519],{"class":1169},[1115,35036,35037,35040,35042,35044,35046,35048,35050,35052,35054,35056,35058,35060,35062,35064],{"class":1154,"line":96},[1115,35038,35039],{"class":1157},"F_horni",[1115,35041,1162],{"class":1161},[1115,35043,35009],{"class":1165},[1115,35045,1170],{"class":1169},[1115,35047,11669],{"class":1173},[1115,35049,1177],{"class":1161},[1115,35051,35019],{"class":1157},[1115,35053,28000],{"class":1161},[1115,35055,7253],{"class":1173},[1115,35057,1177],{"class":1161},[1115,35059,35028],{"class":1157},[1115,35061,28000],{"class":1161},[1115,35063,7253],{"class":1173},[1115,35065,6519],{"class":1169},[1115,35067,35068],{"class":1154,"line":89},[1115,35069,35070],{"class":1157},"Fstat\n",[1115,35072,35073],{"class":1154,"line":82},[1115,35074,35075],{"class":1157},"F_dolni\n",[1115,35077,35078],{"class":1154,"line":75},[1115,35079,35080],{"class":1157},"F_horni\n",[1144,35082,35085],{"className":35083,"code":35084,"language":6540,"meta":1148},[6538],"[1] 1.5625\n[1] 0.2556189\n[1] 3.587899\n",[1150,35086,35084],{"__ignoreMap":1148},[1144,35088,35090],{"className":1146,"code":35089,"language":71,"meta":1148,"style":1148},"sp2 \u003C- ((n1 - 1) * s1 + (n2 - 1) * s2) \u002F (n1 + n2 - 2)\nt \u003C- (82 - 75) \u002F sqrt(sp2) * sqrt(n1 * n2 \u002F (n1 + n2))\nt_krit \u003C- qt(0.975, df = n1 + n2 - 2)\nsp2\nt\nt_krit\n",[1150,35091,35092,35149,35200,35230,35235,35239],{"__ignoreMap":1148},[1115,35093,35094,35097,35099,35102,35104,35106,35108,35110,35112,35114,35116,35118,35120,35122,35124,35126,35128,35131,35133,35135,35137,35139,35141,35143,35145,35147],{"class":1154,"line":10},[1115,35095,35096],{"class":1157},"sp2",[1115,35098,1162],{"class":1161},[1115,35100,35101],{"class":1169}," ((",[1115,35103,34960],{"class":1157},[1115,35105,28000],{"class":1161},[1115,35107,7253],{"class":1173},[1115,35109,7214],{"class":1169},[1115,35111,7231],{"class":1161},[1115,35113,34994],{"class":1157},[1115,35115,21011],{"class":1161},[1115,35117,7219],{"class":1169},[1115,35119,34979],{"class":1157},[1115,35121,28000],{"class":1161},[1115,35123,7253],{"class":1173},[1115,35125,7214],{"class":1169},[1115,35127,7231],{"class":1161},[1115,35129,35130],{"class":1157}," s2",[1115,35132,7214],{"class":1169},[1115,35134,4023],{"class":1161},[1115,35136,7219],{"class":1169},[1115,35138,34960],{"class":1157},[1115,35140,21011],{"class":1161},[1115,35142,35028],{"class":1157},[1115,35144,28000],{"class":1161},[1115,35146,6797],{"class":1173},[1115,35148,6519],{"class":1169},[1115,35150,35151,35153,35155,35157,35159,35161,35164,35166,35168,35170,35172,35174,35176,35178,35180,35182,35184,35186,35188,35190,35192,35194,35196,35198],{"class":1154,"line":27},[1115,35152,2082],{"class":1157},[1115,35154,1162],{"class":1161},[1115,35156,7219],{"class":1169},[1115,35158,6256],{"class":1173},[1115,35160,28000],{"class":1161},[1115,35162,35163],{"class":1173}," 75",[1115,35165,7214],{"class":1169},[1115,35167,4023],{"class":1161},[1115,35169,7191],{"class":1165},[1115,35171,1170],{"class":1169},[1115,35173,35096],{"class":1157},[1115,35175,7214],{"class":1169},[1115,35177,7231],{"class":1161},[1115,35179,7191],{"class":1165},[1115,35181,1170],{"class":1169},[1115,35183,34960],{"class":1157},[1115,35185,21136],{"class":1161},[1115,35187,35028],{"class":1157},[1115,35189,12619],{"class":1161},[1115,35191,7219],{"class":1169},[1115,35193,34960],{"class":1157},[1115,35195,21011],{"class":1161},[1115,35197,35028],{"class":1157},[1115,35199,12073],{"class":1169},[1115,35201,35202,35204,35206,35208,35210,35212,35214,35216,35218,35220,35222,35224,35226,35228],{"class":1154,"line":148},[1115,35203,30992],{"class":1157},[1115,35205,1162],{"class":1161},[1115,35207,30997],{"class":1165},[1115,35209,1170],{"class":1169},[1115,35211,11669],{"class":1173},[1115,35213,1177],{"class":1161},[1115,35215,13341],{"class":1157},[1115,35217,6416],{"class":1161},[1115,35219,35019],{"class":1157},[1115,35221,21011],{"class":1161},[1115,35223,35028],{"class":1157},[1115,35225,28000],{"class":1161},[1115,35227,6797],{"class":1173},[1115,35229,6519],{"class":1169},[1115,35231,35232],{"class":1154,"line":111},[1115,35233,35234],{"class":1157},"sp2\n",[1115,35236,35237],{"class":1154,"line":96},[1115,35238,31022],{"class":1157},[1115,35240,35241],{"class":1154,"line":89},[1115,35242,31027],{"class":1157},[1144,35244,35247],{"className":35245,"code":35246,"language":6540,"meta":1148},[6538],"[1] 20.05\n[1] 3.65107\n[1] 2.085963\n",[1150,35248,35246],{"__ignoreMap":1148},[1110,35250,35251],{},[1303,35252],{"alt":35253,"className":35254,"src":35255},"mask-th-t-dvoustranny",[1130,1307],"\u002Fwiki-assets\u002Fmask-th-t-dvoustranny.png",[1110,35257,35258,35259,1260,35261,35263,35264,35266,35267,1260,35284,6605,35301,35303,35304,35306],{},"V R provede obě kroky ",[1150,35260,3775],{},[1150,35262,3750],{},". Parametr ",[1150,35265,1431],{}," nastavuje volbu mezi ",[1115,35268,35270],{"className":35269},[1573],[1575,35271,35272],{"xmlns":1577},[1579,35273,35274,35282],{},[1582,35275,35276],{},[1746,35277,35278,35280],{},[1585,35279,4043],{},[1716,35281,1718],{},[1605,35283,34259],{"encoding":1607},[1115,35285,35287],{"className":35286},[1573],[1575,35288,35289],{"xmlns":1577},[1579,35290,35291,35299],{},[1582,35292,35293],{},[1746,35294,35295,35297],{},[1585,35296,4043],{},[1716,35298,1993],{},[1605,35300,34277],{"encoding":1607},[1150,35302,3715],{}," znamená předpoklad shodných rozptylů (podle výsledku F-testu), ",[1150,35305,2315],{}," předpoklad rozdílných rozptylů.",[1110,35308,35309,35312],{},[2227,35310,35311],{},"Kabely A\u002FB."," Pevnost v tahu dvou výrobců (MPa, 12 kabelů od každého):",[1144,35314,35316],{"className":1146,"code":35315,"language":71,"meta":1148,"style":1148},"A \u003C- c(313, 299, 315, 312, 310, 308, 314, 313, 305, 310, 309, 314)\nB \u003C- c(307, 322, 313, 313, 311, 316, 315, 314, 308, 319, 313, 312)\nvar.test(A, B)\nt.test(A, B, var.equal = TRUE)\n",[1150,35317,35318,35384,35447,35463],{"__ignoreMap":1148},[1115,35319,35320,35322,35324,35326,35328,35331,35333,35336,35338,35341,35343,35346,35348,35350,35352,35355,35357,35360,35362,35364,35366,35369,35371,35373,35375,35378,35380,35382],{"class":1154,"line":10},[1115,35321,4420],{"class":1157},[1115,35323,1162],{"class":1161},[1115,35325,1166],{"class":1165},[1115,35327,1170],{"class":1169},[1115,35329,35330],{"class":1173},"313",[1115,35332,1177],{"class":1161},[1115,35334,35335],{"class":1173}," 299",[1115,35337,1177],{"class":1161},[1115,35339,35340],{"class":1173}," 315",[1115,35342,1177],{"class":1161},[1115,35344,35345],{"class":1173}," 312",[1115,35347,1177],{"class":1161},[1115,35349,17876],{"class":1173},[1115,35351,1177],{"class":1161},[1115,35353,35354],{"class":1173}," 308",[1115,35356,1177],{"class":1161},[1115,35358,35359],{"class":1173}," 314",[1115,35361,1177],{"class":1161},[1115,35363,16668],{"class":1173},[1115,35365,1177],{"class":1161},[1115,35367,35368],{"class":1173}," 305",[1115,35370,1177],{"class":1161},[1115,35372,17876],{"class":1173},[1115,35374,1177],{"class":1161},[1115,35376,35377],{"class":1173}," 309",[1115,35379,1177],{"class":1161},[1115,35381,35359],{"class":1173},[1115,35383,6519],{"class":1169},[1115,35385,35386,35388,35390,35392,35394,35397,35399,35402,35404,35406,35408,35410,35412,35415,35417,35420,35422,35424,35426,35428,35430,35432,35434,35437,35439,35441,35443,35445],{"class":1154,"line":27},[1115,35387,1773],{"class":1157},[1115,35389,1162],{"class":1161},[1115,35391,1166],{"class":1165},[1115,35393,1170],{"class":1169},[1115,35395,35396],{"class":1173},"307",[1115,35398,1177],{"class":1161},[1115,35400,35401],{"class":1173}," 322",[1115,35403,1177],{"class":1161},[1115,35405,16668],{"class":1173},[1115,35407,1177],{"class":1161},[1115,35409,16668],{"class":1173},[1115,35411,1177],{"class":1161},[1115,35413,35414],{"class":1173}," 311",[1115,35416,1177],{"class":1161},[1115,35418,35419],{"class":1173}," 316",[1115,35421,1177],{"class":1161},[1115,35423,35340],{"class":1173},[1115,35425,1177],{"class":1161},[1115,35427,35359],{"class":1173},[1115,35429,1177],{"class":1161},[1115,35431,35354],{"class":1173},[1115,35433,1177],{"class":1161},[1115,35435,35436],{"class":1173}," 319",[1115,35438,1177],{"class":1161},[1115,35440,16668],{"class":1173},[1115,35442,1177],{"class":1161},[1115,35444,35345],{"class":1173},[1115,35446,6519],{"class":1169},[1115,35448,35449,35452,35454,35456,35458,35461],{"class":1154,"line":148},[1115,35450,35451],{"class":1165},"var.test",[1115,35453,1170],{"class":1169},[1115,35455,4420],{"class":1157},[1115,35457,1177],{"class":1161},[1115,35459,35460],{"class":1157}," B",[1115,35462,6519],{"class":1169},[1115,35464,35465,35467,35469,35471,35473,35475,35477,35480,35482,35484],{"class":1154,"line":111},[1115,35466,30549],{"class":1165},[1115,35468,1170],{"class":1169},[1115,35470,4420],{"class":1157},[1115,35472,1177],{"class":1161},[1115,35474,35460],{"class":1157},[1115,35476,1177],{"class":1161},[1115,35478,35479],{"class":1157}," var.equal",[1115,35481,6416],{"class":1161},[1115,35483,6429],{"class":1173},[1115,35485,6519],{"class":1169},[1144,35487,35490],{"className":35488,"code":35489,"language":6540,"meta":1148},[6538],"    F test to compare two variances\n\ndata:  A and B\nF = 1.1905, num df = 11, denom df = 11, p-value = 0.7776\nalternative hypothesis: true ratio of variances is not equal to 1\n95 percent confidence interval:\n 0.3427173 4.1354275\nsample estimates:\nratio of variances \n          1.190497 \n\n    Two Sample t-test\n\ndata:  A and B\nt = -1.9096, df = 22, p-value = 0.06932\nalternative hypothesis: true difference in means is not equal to 0\n95 percent confidence interval:\n -7.1273286  0.2939953\nsample estimates:\nmean of x mean of y \n 310.1667  313.5833 \n",[1150,35491,35489],{"__ignoreMap":1148},[1110,35493,35494,35495,14566,35514,35517,35518,35537,35538,35555],{},"F-test shodu rozptylů nezamítá (",[1115,35496,35498],{"className":35497},[1573],[1575,35499,35500],{"xmlns":1577},[1579,35501,35502,35511],{},[1582,35503,35504,35506,35508],{},[1585,35505,1110],{},[1589,35507,1597],{},[1716,35509,35510],{},"0,7776",[1605,35512,35513],{"encoding":1607},"p = 0{,}7776",[1150,35515,35516],{},"var.equal = TRUE",". Výsledný t-test dává ",[1115,35519,35521],{"className":35520},[1573],[1575,35522,35523],{"xmlns":1577},[1579,35524,35525,35534],{},[1582,35526,35527,35529,35531],{},[1585,35528,1110],{},[1589,35530,1597],{},[1716,35532,35533],{},"0,06932",[1605,35535,35536],{"encoding":1607},"p = 0{,}06932"," — na hladině 5 % se ",[1115,35539,35541],{"className":35540},[1573],[1575,35542,35543],{"xmlns":1577},[1579,35544,35545,35553],{},[1582,35546,35547],{},[1746,35548,35549,35551],{},[1585,35550,1922],{},[1716,35552,2398],{},[1605,35554,4225],{"encoding":1607}," nezamítá, ale hodnota je těsně nad hranicí.",[1110,35557,35558],{},[2227,35559,35560],{},"Výšky chlapců a dívek v páté třídě:",[1144,35562,35564],{"className":1146,"code":35563,"language":71,"meta":1148,"style":1148},"boys \u003C- c(130, 140, 136, 141, 139, 133, 149, 151, 139, 136, 138, 142, 127, 139, 147)\ngirls \u003C- c(135, 141, 143, 132, 146, 146, 151, 141, 141, 131, 142, 141)\nvar.test(boys, girls)\nt.test(boys, girls, var.equal = TRUE)\n",[1150,35565,35566,35646,35709,35724],{"__ignoreMap":1148},[1115,35567,35568,35571,35573,35575,35577,35580,35582,35584,35586,35589,35591,35594,35596,35599,35601,35604,35606,35608,35610,35612,35614,35616,35618,35620,35622,35625,35627,35630,35632,35635,35637,35639,35641,35644],{"class":1154,"line":10},[1115,35569,35570],{"class":1157},"boys",[1115,35572,1162],{"class":1161},[1115,35574,1166],{"class":1165},[1115,35576,1170],{"class":1169},[1115,35578,35579],{"class":1173},"130",[1115,35581,1177],{"class":1161},[1115,35583,17825],{"class":1173},[1115,35585,1177],{"class":1161},[1115,35587,35588],{"class":1173}," 136",[1115,35590,1177],{"class":1161},[1115,35592,35593],{"class":1173}," 141",[1115,35595,1177],{"class":1161},[1115,35597,35598],{"class":1173}," 139",[1115,35600,1177],{"class":1161},[1115,35602,35603],{"class":1173}," 133",[1115,35605,1177],{"class":1161},[1115,35607,20968],{"class":1173},[1115,35609,1177],{"class":1161},[1115,35611,16683],{"class":1173},[1115,35613,1177],{"class":1161},[1115,35615,35598],{"class":1173},[1115,35617,1177],{"class":1161},[1115,35619,35588],{"class":1173},[1115,35621,1177],{"class":1161},[1115,35623,35624],{"class":1173}," 138",[1115,35626,1177],{"class":1161},[1115,35628,35629],{"class":1173}," 142",[1115,35631,1177],{"class":1161},[1115,35633,35634],{"class":1173}," 127",[1115,35636,1177],{"class":1161},[1115,35638,35598],{"class":1173},[1115,35640,1177],{"class":1161},[1115,35642,35643],{"class":1173}," 147",[1115,35645,6519],{"class":1169},[1115,35647,35648,35651,35653,35655,35657,35659,35661,35663,35665,35668,35670,35673,35675,35678,35680,35682,35684,35686,35688,35690,35692,35694,35696,35699,35701,35703,35705,35707],{"class":1154,"line":27},[1115,35649,35650],{"class":1157},"girls",[1115,35652,1162],{"class":1161},[1115,35654,1166],{"class":1165},[1115,35656,1170],{"class":1169},[1115,35658,24324],{"class":1173},[1115,35660,1177],{"class":1161},[1115,35662,35593],{"class":1173},[1115,35664,1177],{"class":1161},[1115,35666,35667],{"class":1173}," 143",[1115,35669,1177],{"class":1161},[1115,35671,35672],{"class":1173}," 132",[1115,35674,1177],{"class":1161},[1115,35676,35677],{"class":1173}," 146",[1115,35679,1177],{"class":1161},[1115,35681,35677],{"class":1173},[1115,35683,1177],{"class":1161},[1115,35685,16683],{"class":1173},[1115,35687,1177],{"class":1161},[1115,35689,35593],{"class":1173},[1115,35691,1177],{"class":1161},[1115,35693,35593],{"class":1173},[1115,35695,1177],{"class":1161},[1115,35697,35698],{"class":1173}," 131",[1115,35700,1177],{"class":1161},[1115,35702,35629],{"class":1173},[1115,35704,1177],{"class":1161},[1115,35706,35593],{"class":1173},[1115,35708,6519],{"class":1169},[1115,35710,35711,35713,35715,35717,35719,35722],{"class":1154,"line":148},[1115,35712,35451],{"class":1165},[1115,35714,1170],{"class":1169},[1115,35716,35570],{"class":1157},[1115,35718,1177],{"class":1161},[1115,35720,35721],{"class":1157}," girls",[1115,35723,6519],{"class":1169},[1115,35725,35726,35728,35730,35732,35734,35736,35738,35740,35742,35744],{"class":1154,"line":111},[1115,35727,30549],{"class":1165},[1115,35729,1170],{"class":1169},[1115,35731,35570],{"class":1157},[1115,35733,1177],{"class":1161},[1115,35735,35721],{"class":1157},[1115,35737,1177],{"class":1161},[1115,35739,35479],{"class":1157},[1115,35741,6416],{"class":1161},[1115,35743,6429],{"class":1173},[1115,35745,6519],{"class":1169},[1144,35747,35750],{"className":35748,"code":35749,"language":6540,"meta":1148},[6538],"    F test to compare two variances\n\ndata:  boys and girls\nF = 1.2721, num df = 14, denom df = 11, p-value = 0.6977\nalternative hypothesis: true ratio of variances is not equal to 1\n95 percent confidence interval:\n 0.3787299 3.9365720\nsample estimates:\nratio of variances \n          1.272082 \n\n    Two Sample t-test\n\ndata:  boys and girls\nt = -0.70344, df = 25, p-value = 0.4883\nalternative hypothesis: true difference in means is not equal to 0\n95 percent confidence interval:\n -6.67727  3.27727\nsample estimates:\nmean of x mean of y \n 139.1333  140.8333 \n",[1150,35751,35749],{"__ignoreMap":1148},[1110,35753,35494,35754,35773,35774,35776,35777,35796],{},[1115,35755,35757],{"className":35756},[1573],[1575,35758,35759],{"xmlns":1577},[1579,35760,35761,35770],{},[1582,35762,35763,35765,35767],{},[1585,35764,1110],{},[1589,35766,1597],{},[1716,35768,35769],{},"0,6977",[1605,35771,35772],{"encoding":1607},"p = 0{,}6977","), t-test s ",[1150,35775,35516],{}," dává ",[1115,35778,35780],{"className":35779},[1573],[1575,35781,35782],{"xmlns":1577},[1579,35783,35784,35793],{},[1582,35785,35786,35788,35790],{},[1585,35787,1110],{},[1589,35789,1597],{},[1716,35791,35792],{},"0,4883",[1605,35794,35795],{"encoding":1607},"p = 0{,}4883",": na hladině 5 % se rozdíl průměrných výšek chlapců a dívek neprokázal.",[1136,35798,35800],{"id":35799},"testy-dobré-shody-a-normalita","Testy dobré shody a normalita",[1110,35802,35803],{},"Testy dobré shody ověřují, zda datový soubor pochází ze základního souboru s určitým typem rozdělení (normální, exponenciální apod.).",[1550,35805,1529],{"id":35806},"kolmogorovův-smirnovův-test",[1110,35808,35809,35810,35833,35834,35853],{},"Univerzální test pro spojitá rozdělení. Porovnává empirickou distribuční funkci ",[1115,35811,35813],{"className":35812},[1573],[1575,35814,35815],{"xmlns":1577},[1579,35816,35817,35831],{},[1582,35818,35819,35825,35827,35829],{},[1746,35820,35821,35823],{},[1585,35822,1669],{},[1585,35824,1781],{},[1589,35826,1170],{"stretchy":1591},[1585,35828,1158],{},[1589,35830,1603],{"stretchy":1591},[1605,35832,13712],{"encoding":1607}," s teoretickou distribuční funkcí ",[1115,35835,35837],{"className":35836},[1573],[1575,35838,35839],{"xmlns":1577},[1579,35840,35841,35851],{},[1582,35842,35843,35845,35847,35849],{},[1585,35844,1669],{},[1589,35846,1170],{"stretchy":1591},[1585,35848,1158],{},[1589,35850,1603],{"stretchy":1591},[1605,35852,1678],{"encoding":1607}," testovaného rozdělení.",[2220,35855,35856,35919,35939,35995],{},[2223,35857,35858,35875,35876,1260,35899,35918],{},[1115,35859,35861],{"className":35860},[1573],[1575,35862,35863],{"xmlns":1577},[1579,35864,35865,35873],{},[1582,35866,35867],{},[1746,35868,35869,35871],{},[1585,35870,1922],{},[1716,35872,2398],{},[1605,35874,4225],{"encoding":1607},": odchylky mezi ",[1115,35877,35879],{"className":35878},[1573],[1575,35880,35881],{"xmlns":1577},[1579,35882,35883,35897],{},[1582,35884,35885,35891,35893,35895],{},[1746,35886,35887,35889],{},[1585,35888,1669],{},[1585,35890,1781],{},[1589,35892,1170],{"stretchy":1591},[1585,35894,1158],{},[1589,35896,1603],{"stretchy":1591},[1605,35898,13712],{"encoding":1607},[1115,35900,35902],{"className":35901},[1573],[1575,35903,35904],{"xmlns":1577},[1579,35905,35906,35916],{},[1582,35907,35908,35910,35912,35914],{},[1585,35909,1669],{},[1589,35911,1170],{"stretchy":1591},[1585,35913,1158],{},[1589,35915,1603],{"stretchy":1591},[1605,35917,1678],{"encoding":1607}," jsou náhodné (data mají dané rozdělení).",[2223,35920,35921,35938],{},[1115,35922,35924],{"className":35923},[1573],[1575,35925,35926],{"xmlns":1577},[1579,35927,35928,35936],{},[1582,35929,35930],{},[1746,35931,35932,35934],{},[1585,35933,1922],{},[1716,35935,1718],{},[1605,35937,3807],{"encoding":1607},": data nemají dané rozdělení.",[2223,35940,35941,35942,2264],{},"Testové kritérium: ",[1115,35943,35945],{"className":35944},[1573],[1575,35946,35947],{"xmlns":1577},[1579,35948,35949,35992],{},[1582,35950,35951,35953,35955,35966,35968,35974,35976,35978,35980,35982,35984,35986,35988,35990],{},[1585,35952,10733],{},[1589,35954,1597],{},[1746,35956,35957,35964],{},[1582,35958,35959,35962],{},[1585,35960,35961],{},"sup",[1589,35963,7105],{},[1585,35965,1158],{},[1589,35967,25509],{"stretchy":1591},[1746,35969,35970,35972],{},[1585,35971,1669],{},[1585,35973,1781],{},[1589,35975,1170],{"stretchy":1591},[1585,35977,1158],{},[1589,35979,1603],{"stretchy":1591},[1589,35981,1721],{},[1585,35983,1669],{},[1589,35985,1170],{"stretchy":1591},[1585,35987,1158],{},[1589,35989,1603],{"stretchy":1591},[1589,35991,25509],{"stretchy":1591},[1605,35993,35994],{"encoding":1607},"D = \\sup_x \\lvert F_n(x) - F(x) \\rvert",[2223,35996,5950,35997,36041,36042,36060,36061,2264],{},[1115,35998,36000],{"className":35999},[1573],[1575,36001,36002],{"xmlns":1577},[1579,36003,36004,36038],{},[1582,36005,36006,36012,36014,36016,36018,36020,36022,36024,36030,36032,36034,36036],{},[1746,36007,36008,36010],{},[1585,36009,4256],{},[1585,36011,3862],{},[1589,36013,1597],{},[1589,36015,5966],{"stretchy":1591},[1585,36017,10377],{},[1589,36019,4595],{},[1585,36021,10377],{},[1589,36023,1698],{},[1746,36025,36026,36028],{},[1585,36027,10733],{},[1585,36029,3862],{},[1589,36031,1170],{"stretchy":1591},[1585,36033,1781],{},[1589,36035,1603],{"stretchy":1591},[1589,36037,6024],{"stretchy":1591},[1605,36039,36040],{"encoding":1607},"W_\\alpha = \\{d : d > D_\\alpha(n)\\}","; pro ",[1115,36043,36045],{"className":36044},[1573],[1575,36046,36047],{"xmlns":1577},[1579,36048,36049,36057],{},[1582,36050,36051,36053,36055],{},[1585,36052,1781],{},[1589,36054,1698],{},[1716,36056,24523],{},[1605,36058,36059],{"encoding":1607},"n>30"," se kritická hodnota aproximuje zlomkem ",[1115,36062,36064],{"className":36063},[1573],[1575,36065,36066],{"xmlns":1577},[1579,36067,36068,36079],{},[1582,36069,36070,36073,36075],{},[1716,36071,36072],{},"1,36",[1585,36074,4023],{"mathvariant":4022},[7068,36076,36077],{},[1585,36078,1781],{},[1605,36080,36081],{"encoding":1607},"1{,}36\u002F\\sqrt{n}",[1110,36083,30482,36084,36087,36088,36090,36091,1279,36094,36097],{},[1150,36085,36086],{},"ks.test()",", kde se za ",[1150,36089,1678],{}," dosadí příslušná distribuční funkce (",[1150,36092,36093],{},"\"pnorm\"",[1150,36095,36096],{},"\"pexp\"",", …) s jejími parametry:",[1144,36099,36101],{"className":1146,"code":36100,"language":71,"meta":1148,"style":1148},"x3 \u003C- c(4.1, 4.0, 3.8, 3.9, 3.8, 3.8, 3.5, 3.7, 4.0, 4.0)\nks.test(x3, \"pnorm\", mean(x3), sd(x3))\n",[1150,36102,36103,36153],{"__ignoreMap":1148},[1115,36104,36105,36107,36109,36111,36113,36115,36117,36119,36121,36123,36125,36127,36129,36131,36133,36135,36137,36139,36141,36143,36145,36147,36149,36151],{"class":1154,"line":10},[1115,36106,31193],{"class":1157},[1115,36108,1162],{"class":1161},[1115,36110,1166],{"class":1165},[1115,36112,1170],{"class":1169},[1115,36114,1174],{"class":1173},[1115,36116,1177],{"class":1161},[1115,36118,1180],{"class":1173},[1115,36120,1177],{"class":1161},[1115,36122,1185],{"class":1173},[1115,36124,1177],{"class":1161},[1115,36126,1190],{"class":1173},[1115,36128,1177],{"class":1161},[1115,36130,1185],{"class":1173},[1115,36132,1177],{"class":1161},[1115,36134,1185],{"class":1173},[1115,36136,1177],{"class":1161},[1115,36138,1203],{"class":1173},[1115,36140,1177],{"class":1161},[1115,36142,1208],{"class":1173},[1115,36144,1177],{"class":1161},[1115,36146,1180],{"class":1173},[1115,36148,1177],{"class":1161},[1115,36150,1180],{"class":1173},[1115,36152,6519],{"class":1169},[1115,36154,36155,36158,36160,36162,36164,36167,36169,36171,36173,36175,36177,36179,36181,36183,36185],{"class":1154,"line":27},[1115,36156,36157],{"class":1165},"ks.test",[1115,36159,1170],{"class":1169},[1115,36161,31193],{"class":1157},[1115,36163,1177],{"class":1161},[1115,36165,36166],{"class":6458}," \"pnorm\"",[1115,36168,1177],{"class":1161},[1115,36170,11811],{"class":1165},[1115,36172,1170],{"class":1169},[1115,36174,31193],{"class":1157},[1115,36176,1603],{"class":1169},[1115,36178,1177],{"class":1161},[1115,36180,11821],{"class":1165},[1115,36182,1170],{"class":1169},[1115,36184,31193],{"class":1157},[1115,36186,12073],{"class":1169},[1144,36188,36191],{"className":36189,"code":36190,"language":6540,"meta":1148},[6538],"    Asymptotic one-sample Kolmogorov-Smirnov test\n\ndata:  x3\nD = 0.18469, p-value = 0.8847\nalternative hypothesis: two-sided\n",[1150,36192,36190],{"__ignoreMap":1148},[1110,36194,36195,36218],{},[1115,36196,36198],{"className":36197},[1573],[1575,36199,36200],{"xmlns":1577},[1579,36201,36202,36215],{},[1582,36203,36204,36206,36208,36211,36213],{},[1585,36205,1110],{},[1589,36207,1597],{},[1716,36209,36210],{},"0,8847",[1589,36212,1698],{},[1716,36214,6601],{},[1605,36216,36217],{"encoding":1607},"p = 0{,}8847 > 0{,}05",": odpad materiálu je slučitelný s normálním rozdělením se stejným průměrem a směrodatnou odchylkou.",[1550,36220,1513],{"id":36221},"shapiro-wilkův-test",[1110,36223,36224],{},"Nejpoužívanější a nejsilnější obecný test normality, citlivý na odchylky v šikmosti i špičatosti. Využívá korelaci mezi uspořádanými hodnotami výběru a jejich očekávanými hodnotami v normálním rozdělení.",[2220,36226,36227,36247,36267],{},[2223,36228,36229,36246],{},[1115,36230,36232],{"className":36231},[1573],[1575,36233,36234],{"xmlns":1577},[1579,36235,36236,36244],{},[1582,36237,36238],{},[1746,36239,36240,36242],{},[1585,36241,1922],{},[1716,36243,2398],{},[1605,36245,4225],{"encoding":1607},": data mají normální rozdělení.",[2223,36248,36249,36266],{},[1115,36250,36252],{"className":36251},[1573],[1575,36253,36254],{"xmlns":1577},[1579,36255,36256,36264],{},[1582,36257,36258],{},[1746,36259,36260,36262],{},[1585,36261,1922],{},[1716,36263,1718],{},[1605,36265,3807],{"encoding":1607},": data nemají normální rozdělení.",[2223,36268,36269,36270,36296],{},"Testová statistika ",[1115,36271,36273],{"className":36272},[1573],[1575,36274,36275],{"xmlns":1577},[1579,36276,36277,36293],{},[1582,36278,36279,36281,36283,36285,36287,36289,36291],{},[1585,36280,4256],{},[1589,36282,9605],{},[1589,36284,11006],{"stretchy":1591},[1716,36286,2398],{},[1589,36288,1177],{"separator":1121},[1716,36290,1718],{},[1589,36292,10025],{"stretchy":1591},[1605,36294,36295],{"encoding":1607},"W \\in \\langle 0,1 \\rangle","; hodnoty blízké 1 indikují shodu s normalitou.",[1110,36298,36299,36300,36313,36314,2230,36334,36351,36352,2230,36372,36389],{},"Na rozdíl od ostatních testů v této kapitole se Shapiro-Wilkův test v praxi vyhodnocuje pouze přes p-hodnotu (tabulka kritických hodnot pro ",[1115,36301,36303],{"className":36302},[1573],[1575,36304,36305],{"xmlns":1577},[1579,36306,36307,36311],{},[1582,36308,36309],{},[1585,36310,4256],{},[1605,36312,4256],{"encoding":1607}," se běžně neudává): ",[1115,36315,36317],{"className":36316},[1573],[1575,36318,36319],{"xmlns":1577},[1579,36320,36321,36331],{},[1582,36322,36323,36325,36327,36329],{},[1585,36324,1110],{},[1589,36326,5983],{},[1585,36328,3862],{},[1589,36330,10131],{},[1605,36332,36333],{"encoding":1607},"p \\ge \\alpha \\Rightarrow",[1115,36335,36337],{"className":36336},[1573],[1575,36338,36339],{"xmlns":1577},[1579,36340,36341,36349],{},[1582,36342,36343],{},[1746,36344,36345,36347],{},[1585,36346,1922],{},[1716,36348,2398],{},[1605,36350,4225],{"encoding":1607}," nezamítáme (normalitu lze předpokládat); ",[1115,36353,36355],{"className":36354},[1573],[1575,36356,36357],{"xmlns":1577},[1579,36358,36359,36369],{},[1582,36360,36361,36363,36365,36367],{},[1585,36362,1110],{},[1589,36364,6949],{},[1585,36366,3862],{},[1589,36368,10131],{},[1605,36370,36371],{"encoding":1607},"p \u003C \\alpha \\Rightarrow",[1115,36373,36375],{"className":36374},[1573],[1575,36376,36377],{"xmlns":1577},[1579,36378,36379,36387],{},[1582,36380,36381],{},[1746,36382,36383,36385],{},[1585,36384,1922],{},[1716,36386,2398],{},[1605,36388,4225],{"encoding":1607}," zamítáme (předpoklad normality je porušen).",[1144,36391,36393],{"className":1146,"code":36392,"language":71,"meta":1148,"style":1148},"x2 \u003C- c(9.5, 10.5, 8.9, 9.2, 10.0, 8.5, 9.2, 8.8, 10.0, 9.5, 9.2)\nshapiro.test(x2)\n",[1150,36394,36395,36449],{"__ignoreMap":1148},[1115,36396,36397,36399,36401,36403,36405,36407,36409,36411,36413,36415,36417,36419,36421,36423,36425,36427,36429,36431,36433,36435,36437,36439,36441,36443,36445,36447],{"class":1154,"line":10},[1115,36398,31061],{"class":1157},[1115,36400,1162],{"class":1161},[1115,36402,1166],{"class":1165},[1115,36404,1170],{"class":1169},[1115,36406,31070],{"class":1173},[1115,36408,1177],{"class":1161},[1115,36410,31075],{"class":1173},[1115,36412,1177],{"class":1161},[1115,36414,31080],{"class":1173},[1115,36416,1177],{"class":1161},[1115,36418,31085],{"class":1173},[1115,36420,1177],{"class":1161},[1115,36422,31090],{"class":1173},[1115,36424,1177],{"class":1161},[1115,36426,31095],{"class":1173},[1115,36428,1177],{"class":1161},[1115,36430,31085],{"class":1173},[1115,36432,1177],{"class":1161},[1115,36434,31104],{"class":1173},[1115,36436,1177],{"class":1161},[1115,36438,31090],{"class":1173},[1115,36440,1177],{"class":1161},[1115,36442,31113],{"class":1173},[1115,36444,1177],{"class":1161},[1115,36446,31085],{"class":1173},[1115,36448,6519],{"class":1169},[1115,36450,36451,36453,36455,36457],{"class":1154,"line":27},[1115,36452,20072],{"class":1165},[1115,36454,1170],{"class":1169},[1115,36456,31061],{"class":1157},[1115,36458,6519],{"class":1169},[1144,36460,36463],{"className":36461,"code":36462,"language":6540,"meta":1148},[6538],"    Shapiro-Wilk normality test\n\ndata:  x2\nW = 0.96022, p-value = 0.7744\n",[1150,36464,36462],{"__ignoreMap":1148},[1110,36466,36467,36468,36487],{},"U dat o životnosti baterií se normalita nezamítá (",[1115,36469,36471],{"className":36470},[1573],[1575,36472,36473],{"xmlns":1577},[1579,36474,36475,36484],{},[1582,36476,36477,36479,36481],{},[1585,36478,1110],{},[1589,36480,1597],{},[1716,36482,36483],{},"0,7744",[1605,36485,36486],{"encoding":1607},"p = 0{,}7744","), předpoklad t-testu je tedy splněn.",[1103,36489,36491,36498,36501,36868,36874],{"className":36490,"dataCallout":6105},[1106,6104],[1110,36492,36494,36497],{"className":36493},[1113],[1115,36495],{"className":36496,"ariaHidden":1121},[1118,6112,1120],"Příklad: Doba do poruchy výrobku",[1110,36499,36500],{},"Zkoušky životnosti nového výrobku daly soubor 68 hodnot doby do poruchy (v minutách). Odhadněte charakteristiky a zákon rozdělení.",[1144,36502,36504],{"className":1146,"code":36503,"language":71,"meta":1148,"style":1148},"x9 \u003C- c(101, 338, 150, 47, 10, 2, 12, 392, 5, 73, 367, 54, 114, 213, 71, 341, 313, 112, 343, 151,\n        9, 160, 18, 113, 77, 71, 159, 12, 119, 130, 140, 161, 379, 54, 373, 168, 365, 110, 145,\n        88, 74, 46, 246, 259, 19, 119, 48, 3, 163, 179, 194, 33, 49, 501, 193, 19, 5, 2, 221, 300,\n        88, 13, 428, 249, 25, 209, 54, 91)\nmean(x9)\nsd(x9)\nmedian(x9)\nshapiro.test(x9)\nks.test(x9, \"pexp\", rate = 1 \u002F mean(x9))\n",[1150,36505,36506,36597,36675,36763,36797,36807,36817,36827,36837],{"__ignoreMap":1148},[1115,36507,36508,36510,36512,36514,36516,36518,36520,36522,36524,36526,36528,36530,36532,36534,36536,36538,36540,36542,36544,36546,36548,36550,36552,36554,36556,36559,36561,36563,36565,36567,36569,36571,36573,36575,36577,36579,36581,36583,36585,36587,36589,36591,36593,36595],{"class":1154,"line":10},[1115,36509,16582],{"class":1157},[1115,36511,1162],{"class":1161},[1115,36513,1166],{"class":1165},[1115,36515,1170],{"class":1169},[1115,36517,16591],{"class":1173},[1115,36519,1177],{"class":1161},[1115,36521,16596],{"class":1173},[1115,36523,1177],{"class":1161},[1115,36525,16601],{"class":1173},[1115,36527,1177],{"class":1161},[1115,36529,16606],{"class":1173},[1115,36531,1177],{"class":1161},[1115,36533,12057],{"class":1173},[1115,36535,1177],{"class":1161},[1115,36537,6797],{"class":1173},[1115,36539,1177],{"class":1161},[1115,36541,6353],{"class":1173},[1115,36543,1177],{"class":1161},[1115,36545,16623],{"class":1173},[1115,36547,1177],{"class":1161},[1115,36549,12538],{"class":1173},[1115,36551,1177],{"class":1161},[1115,36553,16632],{"class":1173},[1115,36555,1177],{"class":1161},[1115,36557,36558],{"class":1173}," 367",[1115,36560,1177],{"class":1161},[1115,36562,16644],{"class":1173},[1115,36564,1177],{"class":1161},[1115,36566,16649],{"class":1173},[1115,36568,1177],{"class":1161},[1115,36570,16654],{"class":1173},[1115,36572,1177],{"class":1161},[1115,36574,6371],{"class":1173},[1115,36576,1177],{"class":1161},[1115,36578,16663],{"class":1173},[1115,36580,1177],{"class":1161},[1115,36582,16668],{"class":1173},[1115,36584,1177],{"class":1161},[1115,36586,16673],{"class":1173},[1115,36588,1177],{"class":1161},[1115,36590,16678],{"class":1173},[1115,36592,1177],{"class":1161},[1115,36594,16683],{"class":1173},[1115,36596,6356],{"class":1161},[1115,36598,36599,36601,36603,36605,36607,36609,36611,36613,36615,36617,36619,36621,36623,36625,36627,36629,36631,36633,36635,36637,36639,36641,36643,36645,36647,36649,36651,36653,36655,36657,36659,36661,36663,36665,36667,36669,36671,36673],{"class":1154,"line":27},[1115,36600,16690],{"class":1173},[1115,36602,1177],{"class":1161},[1115,36604,16695],{"class":1173},[1115,36606,1177],{"class":1161},[1115,36608,16700],{"class":1173},[1115,36610,1177],{"class":1161},[1115,36612,16705],{"class":1173},[1115,36614,1177],{"class":1161},[1115,36616,16710],{"class":1173},[1115,36618,1177],{"class":1161},[1115,36620,6371],{"class":1173},[1115,36622,1177],{"class":1161},[1115,36624,16719],{"class":1173},[1115,36626,1177],{"class":1161},[1115,36628,6353],{"class":1173},[1115,36630,1177],{"class":1161},[1115,36632,16728],{"class":1173},[1115,36634,1177],{"class":1161},[1115,36636,16733],{"class":1173},[1115,36638,1177],{"class":1161},[1115,36640,17825],{"class":1173},[1115,36642,1177],{"class":1161},[1115,36644,16745],{"class":1173},[1115,36646,1177],{"class":1161},[1115,36648,16750],{"class":1173},[1115,36650,1177],{"class":1161},[1115,36652,16644],{"class":1173},[1115,36654,1177],{"class":1161},[1115,36656,16759],{"class":1173},[1115,36658,1177],{"class":1161},[1115,36660,16764],{"class":1173},[1115,36662,1177],{"class":1161},[1115,36664,16769],{"class":1173},[1115,36666,1177],{"class":1161},[1115,36668,16774],{"class":1173},[1115,36670,1177],{"class":1161},[1115,36672,16779],{"class":1173},[1115,36674,6356],{"class":1161},[1115,36676,36677,36679,36681,36684,36686,36688,36690,36692,36694,36696,36698,36700,36702,36704,36706,36708,36710,36712,36714,36716,36718,36720,36722,36725,36727,36729,36731,36733,36735,36737,36739,36741,36743,36745,36747,36749,36751,36753,36755,36757,36759,36761],{"class":1154,"line":148},[1115,36678,16889],{"class":1173},[1115,36680,1177],{"class":1161},[1115,36682,36683],{"class":1173}," 74",[1115,36685,1177],{"class":1161},[1115,36687,16796],{"class":1173},[1115,36689,1177],{"class":1161},[1115,36691,16801],{"class":1173},[1115,36693,1177],{"class":1161},[1115,36695,16806],{"class":1173},[1115,36697,1177],{"class":1161},[1115,36699,16811],{"class":1173},[1115,36701,1177],{"class":1161},[1115,36703,16728],{"class":1173},[1115,36705,1177],{"class":1161},[1115,36707,16820],{"class":1173},[1115,36709,1177],{"class":1161},[1115,36711,13386],{"class":1173},[1115,36713,1177],{"class":1161},[1115,36715,16829],{"class":1173},[1115,36717,1177],{"class":1161},[1115,36719,16834],{"class":1173},[1115,36721,1177],{"class":1161},[1115,36723,36724],{"class":1173}," 194",[1115,36726,1177],{"class":1161},[1115,36728,6762],{"class":1173},[1115,36730,1177],{"class":1161},[1115,36732,16850],{"class":1173},[1115,36734,1177],{"class":1161},[1115,36736,16855],{"class":1173},[1115,36738,1177],{"class":1161},[1115,36740,16860],{"class":1173},[1115,36742,1177],{"class":1161},[1115,36744,16811],{"class":1173},[1115,36746,1177],{"class":1161},[1115,36748,12538],{"class":1173},[1115,36750,1177],{"class":1161},[1115,36752,6797],{"class":1173},[1115,36754,1177],{"class":1161},[1115,36756,16877],{"class":1173},[1115,36758,1177],{"class":1161},[1115,36760,16882],{"class":1173},[1115,36762,6356],{"class":1161},[1115,36764,36765,36767,36769,36771,36773,36775,36777,36779,36781,36783,36785,36787,36789,36791,36793,36795],{"class":1154,"line":111},[1115,36766,16889],{"class":1173},[1115,36768,1177],{"class":1161},[1115,36770,6348],{"class":1173},[1115,36772,1177],{"class":1161},[1115,36774,16898],{"class":1173},[1115,36776,1177],{"class":1161},[1115,36778,16903],{"class":1173},[1115,36780,1177],{"class":1161},[1115,36782,16908],{"class":1173},[1115,36784,1177],{"class":1161},[1115,36786,16913],{"class":1173},[1115,36788,1177],{"class":1161},[1115,36790,16644],{"class":1173},[1115,36792,1177],{"class":1161},[1115,36794,16922],{"class":1173},[1115,36796,6519],{"class":1169},[1115,36798,36799,36801,36803,36805],{"class":1154,"line":96},[1115,36800,14649],{"class":1165},[1115,36802,1170],{"class":1169},[1115,36804,16582],{"class":1157},[1115,36806,6519],{"class":1169},[1115,36808,36809,36811,36813,36815],{"class":1154,"line":89},[1115,36810,14671],{"class":1165},[1115,36812,1170],{"class":1169},[1115,36814,16582],{"class":1157},[1115,36816,6519],{"class":1169},[1115,36818,36819,36821,36823,36825],{"class":1154,"line":82},[1115,36820,15370],{"class":1165},[1115,36822,1170],{"class":1169},[1115,36824,16582],{"class":1157},[1115,36826,6519],{"class":1169},[1115,36828,36829,36831,36833,36835],{"class":1154,"line":75},[1115,36830,20072],{"class":1165},[1115,36832,1170],{"class":1169},[1115,36834,16582],{"class":1157},[1115,36836,6519],{"class":1169},[1115,36838,36839,36841,36843,36845,36847,36850,36852,36854,36856,36858,36860,36862,36864,36866],{"class":1154,"line":6509},[1115,36840,36157],{"class":1165},[1115,36842,1170],{"class":1169},[1115,36844,16582],{"class":1157},[1115,36846,1177],{"class":1161},[1115,36848,36849],{"class":6458}," \"pexp\"",[1115,36851,1177],{"class":1161},[1115,36853,12612],{"class":1157},[1115,36855,6416],{"class":1161},[1115,36857,7253],{"class":1173},[1115,36859,12619],{"class":1161},[1115,36861,11811],{"class":1165},[1115,36863,1170],{"class":1169},[1115,36865,16582],{"class":1157},[1115,36867,12073],{"class":1169},[1144,36869,36872],{"className":36870,"code":36871,"language":6540,"meta":1148},[6538],"[1] 145.4412\n[1] 126.1283\n[1] 113.5\n\n    Shapiro-Wilk normality test\n\ndata:  x9\nW = 0.89872, p-value = 4.389e-05\n\n    Asymptotic one-sample Kolmogorov-Smirnov test\n\ndata:  x9\nD = 0.074727, p-value = 0.8421\nalternative hypothesis: two-sided\n",[1150,36873,36871],{"__ignoreMap":1148},[1110,36875,36876,36877,36896,36897,36914,36915,36934],{},"Výběrový průměr (145,44 min) je blízký směrodatné odchylce (126,13 min) a medián (113,5 min) je výrazně nižší než průměr — typický tvar doby do poruchy. Shapiro-Wilkův test normalitu jasně zamítá (",[1115,36878,36880],{"className":36879},[1573],[1575,36881,36882],{"xmlns":1577},[1579,36883,36884,36893],{},[1582,36885,36886,36888,36890],{},[1585,36887,1110],{},[1589,36889,6949],{},[1716,36891,36892],{},"0,0001",[1605,36894,36895],{"encoding":1607},"p \u003C 0{,}0001","), zatímco Kolmogorov-Smirnovův test proti exponenciálnímu rozdělení se střední hodnotou ",[1115,36898,36900],{"className":36899},[1573],[1575,36901,36902],{"xmlns":1577},[1579,36903,36904,36912],{},[1582,36905,36906],{},[3005,36907,36908,36910],{"accent":1121},[1585,36909,1158],{},[1589,36911,3408],{},[1605,36913,24053],{"encoding":1607}," shodu nezamítá (",[1115,36916,36918],{"className":36917},[1573],[1575,36919,36920],{"xmlns":1577},[1579,36921,36922,36931],{},[1582,36923,36924,36926,36928],{},[1585,36925,1110],{},[1589,36927,1597],{},[1716,36929,36930],{},"0,8421",[1605,36932,36933],{"encoding":1607},"p = 0{,}8421","): data odpovídají spíše exponenciálnímu rozdělení než normálnímu.",[1110,36936,36937],{},[1303,36938],{"alt":36939,"className":36940,"src":36941},"mask-th-exponencialni-shoda",[1130,1307],"\u002Fwiki-assets\u002Fmask-th-exponencialni-shoda.png",[1136,36943,36945],{"id":36944},"neparametrické-testy","Neparametrické testy",[1110,36947,36948,36949,7219,36951,36975],{},"Když předpoklad normality neplatí, nahrazují t-testy jejich neparametrické obdoby — Wilcoxonovy testy posuzují ",[2227,36950,14077],{},[1115,36952,36954],{"className":36953},[1573],[1575,36955,36956],{"xmlns":1577},[1579,36957,36958,36972],{},[1582,36959,36960],{},[1746,36961,36962,36964],{},[1585,36963,1158],{},[1582,36965,36966,36968,36970],{},[1716,36967,2398],{},[1589,36969,1177],{"separator":1121},[1716,36971,12470],{},[1605,36973,36974],{"encoding":1607},"x_{0,5}",") místo střední hodnoty a nevyžadují normalitu dat.",[1550,36977,36979],{"id":36978},"wilcoxonovy-testy","Wilcoxonovy testy",[1310,36981,36982,37027],{},[1313,36983,36984],{},[1316,36985,36986,37005,37024],{},[1319,36987,36988],{},[1115,36989,36991],{"className":36990},[1573],[1575,36992,36993],{"xmlns":1577},[1579,36994,36995,37003],{},[1582,36996,36997],{},[1746,36998,36999,37001],{},[1585,37000,1922],{},[1716,37002,2398],{},[1605,37004,4225],{"encoding":1607},[1319,37006,37007],{},[1115,37008,37010],{"className":37009},[1573],[1575,37011,37012],{"xmlns":1577},[1579,37013,37014,37022],{},[1582,37015,37016],{},[1746,37017,37018,37020],{},[1585,37019,1922],{},[1716,37021,1718],{},[1605,37023,3807],{"encoding":1607},[1319,37025,37026],{},"Příkaz v R",[1332,37028,37029,37096,37163],{},[1316,37030,37031,37061,37091],{},[1337,37032,37033],{},[1115,37034,37036],{"className":37035},[1573],[1575,37037,37038],{"xmlns":1577},[1579,37039,37040,37058],{},[1582,37041,37042,37054,37056],{},[1746,37043,37044,37046],{},[1585,37045,1158],{},[1582,37047,37048,37050,37052],{},[1716,37049,2398],{},[1589,37051,1177],{"separator":1121},[1716,37053,12470],{},[1589,37055,1650],{},[1585,37057,3499],{},[1605,37059,37060],{"encoding":1607},"x_{0,5} \\le c",[1337,37062,37063],{},[1115,37064,37066],{"className":37065},[1573],[1575,37067,37068],{"xmlns":1577},[1579,37069,37070,37088],{},[1582,37071,37072,37084,37086],{},[1746,37073,37074,37076],{},[1585,37075,1158],{},[1582,37077,37078,37080,37082],{},[1716,37079,2398],{},[1589,37081,1177],{"separator":1121},[1716,37083,12470],{},[1589,37085,1698],{},[1585,37087,3499],{},[1605,37089,37090],{"encoding":1607},"x_{0,5} > c",[1337,37092,37093],{},[1150,37094,37095],{},"wilcox.test(x, alternative = \"greater\", mu = c)",[1316,37097,37098,37128,37158],{},[1337,37099,37100],{},[1115,37101,37103],{"className":37102},[1573],[1575,37104,37105],{"xmlns":1577},[1579,37106,37107,37125],{},[1582,37108,37109,37121,37123],{},[1746,37110,37111,37113],{},[1585,37112,1158],{},[1582,37114,37115,37117,37119],{},[1716,37116,2398],{},[1589,37118,1177],{"separator":1121},[1716,37120,12470],{},[1589,37122,1597],{},[1585,37124,3499],{},[1605,37126,37127],{"encoding":1607},"x_{0,5} = c",[1337,37129,37130],{},[1115,37131,37133],{"className":37132},[1573],[1575,37134,37135],{"xmlns":1577},[1579,37136,37137,37155],{},[1582,37138,37139,37151,37153],{},[1746,37140,37141,37143],{},[1585,37142,1158],{},[1582,37144,37145,37147,37149],{},[1716,37146,2398],{},[1589,37148,1177],{"separator":1121},[1716,37150,12470],{},[1589,37152,13487],{"mathvariant":4022},[1585,37154,3499],{},[1605,37156,37157],{"encoding":1607},"x_{0,5} \\neq c",[1337,37159,37160],{},[1150,37161,37162],{},"wilcox.test(x, alternative = \"two.sided\", mu = c)",[1316,37164,37165,37195,37225],{},[1337,37166,37167],{},[1115,37168,37170],{"className":37169},[1573],[1575,37171,37172],{"xmlns":1577},[1579,37173,37174,37192],{},[1582,37175,37176,37188,37190],{},[1746,37177,37178,37180],{},[1585,37179,1158],{},[1582,37181,37182,37184,37186],{},[1716,37183,2398],{},[1589,37185,1177],{"separator":1121},[1716,37187,12470],{},[1589,37189,5983],{},[1585,37191,3499],{},[1605,37193,37194],{"encoding":1607},"x_{0,5} \\ge c",[1337,37196,37197],{},[1115,37198,37200],{"className":37199},[1573],[1575,37201,37202],{"xmlns":1577},[1579,37203,37204,37222],{},[1582,37205,37206,37218,37220],{},[1746,37207,37208,37210],{},[1585,37209,1158],{},[1582,37211,37212,37214,37216],{},[1716,37213,2398],{},[1589,37215,1177],{"separator":1121},[1716,37217,12470],{},[1589,37219,6949],{},[1585,37221,3499],{},[1605,37223,37224],{"encoding":1607},"x_{0,5} \u003C c",[1337,37226,37227],{},[1150,37228,37229],{},"wilcox.test(x, alternative = \"less\", mu = c)",[1110,37231,37232,37235,37236,2264],{},[4116,37233,37234],{},"Jednovýběrový Wilcoxonův test"," (obdoba t-testu) posuzuje odchylku mediánu od konstanty ",[1115,37237,37239],{"className":37238},[1573],[1575,37240,37241],{"xmlns":1577},[1579,37242,37243,37247],{},[1582,37244,37245],{},[1585,37246,3499],{},[1605,37248,3499],{"encoding":1607},[1110,37250,37251,37254,37255,11414,37293,37306,37307,2264],{},[4116,37252,37253],{},"Jednovýběrový Wilcoxonův test na diferencích"," (obdoba párového t-testu) posuzuje odchylku mediánu rozdílu ",[1115,37256,37258],{"className":37257},[1573],[1575,37259,37260],{"xmlns":1577},[1579,37261,37262,37290],{},[1582,37263,37264,37276,37278],{},[1746,37265,37266,37268],{},[1585,37267,1158],{},[1582,37269,37270,37272,37274],{},[1716,37271,2398],{},[1589,37273,1177],{"separator":1121},[1716,37275,12470],{},[1589,37277,1721],{},[1746,37279,37280,37282],{},[1585,37281,2862],{},[1582,37283,37284,37286,37288],{},[1716,37285,2398],{},[1589,37287,1177],{"separator":1121},[1716,37289,12470],{},[1605,37291,37292],{"encoding":1607},"x_{0,5}-y_{0,5}",[1115,37294,37296],{"className":37295},[1573],[1575,37297,37298],{"xmlns":1577},[1579,37299,37300,37304],{},[1582,37301,37302],{},[1585,37303,3499],{},[1605,37305,3499],{"encoding":1607},"; v R se volá se stejnými argumenty jako výše a navíc ",[1150,37308,37309],{},"paired = TRUE",[1110,37311,37312,37315,37316,37318],{},[4116,37313,37314],{},"Dvouvýběrový Wilcoxonův test"," (obdoba dvouvýběrového t-testu) posuzuje odchylku mediánů dvou nezávislých výběrů; argument ",[1150,37317,27927],{}," odpadá. Pro výšky chlapců a dívek z příkladu výše:",[1144,37320,37322],{"className":1146,"code":37321,"language":71,"meta":1148,"style":1148},"boys \u003C- c(130, 140, 136, 141, 139, 133, 149, 151, 139, 136, 138, 142, 127, 139, 147)\ngirls \u003C- c(135, 141, 143, 132, 146, 146, 151, 141, 141, 131, 142, 141)\nwilcox.test(boys, girls, alternative = \"two.sided\")\n",[1150,37323,37324,37394,37452],{"__ignoreMap":1148},[1115,37325,37326,37328,37330,37332,37334,37336,37338,37340,37342,37344,37346,37348,37350,37352,37354,37356,37358,37360,37362,37364,37366,37368,37370,37372,37374,37376,37378,37380,37382,37384,37386,37388,37390,37392],{"class":1154,"line":10},[1115,37327,35570],{"class":1157},[1115,37329,1162],{"class":1161},[1115,37331,1166],{"class":1165},[1115,37333,1170],{"class":1169},[1115,37335,35579],{"class":1173},[1115,37337,1177],{"class":1161},[1115,37339,17825],{"class":1173},[1115,37341,1177],{"class":1161},[1115,37343,35588],{"class":1173},[1115,37345,1177],{"class":1161},[1115,37347,35593],{"class":1173},[1115,37349,1177],{"class":1161},[1115,37351,35598],{"class":1173},[1115,37353,1177],{"class":1161},[1115,37355,35603],{"class":1173},[1115,37357,1177],{"class":1161},[1115,37359,20968],{"class":1173},[1115,37361,1177],{"class":1161},[1115,37363,16683],{"class":1173},[1115,37365,1177],{"class":1161},[1115,37367,35598],{"class":1173},[1115,37369,1177],{"class":1161},[1115,37371,35588],{"class":1173},[1115,37373,1177],{"class":1161},[1115,37375,35624],{"class":1173},[1115,37377,1177],{"class":1161},[1115,37379,35629],{"class":1173},[1115,37381,1177],{"class":1161},[1115,37383,35634],{"class":1173},[1115,37385,1177],{"class":1161},[1115,37387,35598],{"class":1173},[1115,37389,1177],{"class":1161},[1115,37391,35643],{"class":1173},[1115,37393,6519],{"class":1169},[1115,37395,37396,37398,37400,37402,37404,37406,37408,37410,37412,37414,37416,37418,37420,37422,37424,37426,37428,37430,37432,37434,37436,37438,37440,37442,37444,37446,37448,37450],{"class":1154,"line":27},[1115,37397,35650],{"class":1157},[1115,37399,1162],{"class":1161},[1115,37401,1166],{"class":1165},[1115,37403,1170],{"class":1169},[1115,37405,24324],{"class":1173},[1115,37407,1177],{"class":1161},[1115,37409,35593],{"class":1173},[1115,37411,1177],{"class":1161},[1115,37413,35667],{"class":1173},[1115,37415,1177],{"class":1161},[1115,37417,35672],{"class":1173},[1115,37419,1177],{"class":1161},[1115,37421,35677],{"class":1173},[1115,37423,1177],{"class":1161},[1115,37425,35677],{"class":1173},[1115,37427,1177],{"class":1161},[1115,37429,16683],{"class":1173},[1115,37431,1177],{"class":1161},[1115,37433,35593],{"class":1173},[1115,37435,1177],{"class":1161},[1115,37437,35593],{"class":1173},[1115,37439,1177],{"class":1161},[1115,37441,35698],{"class":1173},[1115,37443,1177],{"class":1161},[1115,37445,35629],{"class":1173},[1115,37447,1177],{"class":1161},[1115,37449,35593],{"class":1173},[1115,37451,6519],{"class":1169},[1115,37453,37454,37457,37459,37461,37463,37465,37467,37469,37471,37473],{"class":1154,"line":148},[1115,37455,37456],{"class":1165},"wilcox.test",[1115,37458,1170],{"class":1169},[1115,37460,35570],{"class":1157},[1115,37462,1177],{"class":1161},[1115,37464,35721],{"class":1157},[1115,37466,1177],{"class":1161},[1115,37468,30566],{"class":1157},[1115,37470,6416],{"class":1161},[1115,37472,30571],{"class":6458},[1115,37474,6519],{"class":1169},[1144,37476,37479],{"className":37477,"code":37478,"language":6540,"meta":1148},[6538],"    Wilcoxon rank sum exact test\n\ndata:  boys and girls\nW = 69, p-value = 0.315\nalternative hypothesis: true location shift is not equal to 0\n",[1150,37480,37478],{"__ignoreMap":1148},[1110,37482,37483,37506],{},[1115,37484,37486],{"className":37485},[1573],[1575,37487,37488],{"xmlns":1577},[1579,37489,37490,37503],{},[1582,37491,37492,37494,37496,37499,37501],{},[1585,37493,1110],{},[1589,37495,1597],{},[1716,37497,37498],{},"0,315",[1589,37500,1698],{},[1716,37502,6601],{},[1605,37504,37505],{"encoding":1607},"p = 0{,}315 > 0{,}05",": mediány výšek chlapců a dívek se statisticky významně neliší — stejný závěr jako u dvouvýběrového t-testu.",[1103,37508,37510,37517,37539,37650,37656],{"className":37509,"dataCallout":6105},[1106,6104],[1110,37511,37513,37516],{"className":37512},[1113],[1115,37514],{"className":37515,"ariaHidden":1121},[1118,6112,1120],"Příklad: Realitní odhadci — neparametrická alternativa",[1110,37518,37519,37520,37538],{},"U odhadů cen z párového t-testu výše normalita diferencí neplatí (",[1115,37521,37523],{"className":37522},[1573],[1575,37524,37525],{"xmlns":1577},[1579,37526,37527,37535],{},[1582,37528,37529,37531,37533],{},[1585,37530,1110],{},[1589,37532,1597],{},[1716,37534,32617],{},[1605,37536,37537],{"encoding":1607},"p = 0{,}03203","). Správnou volbou je párový Wilcoxonův test:",[1144,37540,37542],{"className":1146,"code":37541,"language":71,"meta":1148,"style":1148},"estA \u003C- c(3282, 2506, 2812, 5453, 3263, 4571, 3121, 2963)\nestB \u003C- c(3271, 2531, 2799, 5471, 3285, 4557, 3139, 2976)\nwilcox.test(estA, estB, paired = TRUE)\n",[1150,37543,37544,37586,37628],{"__ignoreMap":1148},[1115,37545,37546,37548,37550,37552,37554,37556,37558,37560,37562,37564,37566,37568,37570,37572,37574,37576,37578,37580,37582,37584],{"class":1154,"line":10},[1115,37547,32420],{"class":1157},[1115,37549,1162],{"class":1161},[1115,37551,1166],{"class":1165},[1115,37553,1170],{"class":1169},[1115,37555,32429],{"class":1173},[1115,37557,1177],{"class":1161},[1115,37559,32434],{"class":1173},[1115,37561,1177],{"class":1161},[1115,37563,32439],{"class":1173},[1115,37565,1177],{"class":1161},[1115,37567,32444],{"class":1173},[1115,37569,1177],{"class":1161},[1115,37571,32449],{"class":1173},[1115,37573,1177],{"class":1161},[1115,37575,32454],{"class":1173},[1115,37577,1177],{"class":1161},[1115,37579,32459],{"class":1173},[1115,37581,1177],{"class":1161},[1115,37583,32464],{"class":1173},[1115,37585,6519],{"class":1169},[1115,37587,37588,37590,37592,37594,37596,37598,37600,37602,37604,37606,37608,37610,37612,37614,37616,37618,37620,37622,37624,37626],{"class":1154,"line":27},[1115,37589,32471],{"class":1157},[1115,37591,1162],{"class":1161},[1115,37593,1166],{"class":1165},[1115,37595,1170],{"class":1169},[1115,37597,32480],{"class":1173},[1115,37599,1177],{"class":1161},[1115,37601,32485],{"class":1173},[1115,37603,1177],{"class":1161},[1115,37605,32490],{"class":1173},[1115,37607,1177],{"class":1161},[1115,37609,32495],{"class":1173},[1115,37611,1177],{"class":1161},[1115,37613,32500],{"class":1173},[1115,37615,1177],{"class":1161},[1115,37617,32505],{"class":1173},[1115,37619,1177],{"class":1161},[1115,37621,32510],{"class":1173},[1115,37623,1177],{"class":1161},[1115,37625,32515],{"class":1173},[1115,37627,6519],{"class":1169},[1115,37629,37630,37632,37634,37636,37638,37640,37642,37644,37646,37648],{"class":1154,"line":148},[1115,37631,37456],{"class":1165},[1115,37633,1170],{"class":1169},[1115,37635,32420],{"class":1157},[1115,37637,1177],{"class":1161},[1115,37639,32530],{"class":1157},[1115,37641,1177],{"class":1161},[1115,37643,32535],{"class":1157},[1115,37645,6416],{"class":1161},[1115,37647,6429],{"class":1173},[1115,37649,6519],{"class":1169},[1144,37651,37654],{"className":37652,"code":37653,"language":6540,"meta":1148},[6538],"    Wilcoxon signed rank exact test\n\ndata:  estA and estB\nV = 7.5, p-value = 0.1484\nalternative hypothesis: true location shift is not equal to 0\n",[1150,37655,37653],{"__ignoreMap":1148},[1110,37657,37658,37681],{},[1115,37659,37661],{"className":37660},[1573],[1575,37662,37663],{"xmlns":1577},[1579,37664,37665,37678],{},[1582,37666,37667,37669,37671,37674,37676],{},[1585,37668,1110],{},[1589,37670,1597],{},[1716,37672,37673],{},"0,1484",[1589,37675,1698],{},[1716,37677,6601],{},[1605,37679,37680],{"encoding":1607},"p = 0{,}1484 > 0{,}05",": medián diferencí se od nuly statisticky významně neliší, odhadci se neliší. Závěr je stejný jako u (nespolehlivého) párového t-testu, ale tady je podložený testem, jehož předpoklady data splňují.",[1550,37683,1479],{"id":37684},"kruskalův-wallisův-test",[1110,37686,37687,37688,37705],{},"Zobecnění dvouvýběrového Wilcoxonova testu, neparametrická obdoba analýzy rozptylu jednoduchého třídění. ",[1115,37689,37691],{"className":37690},[1573],[1575,37692,37693],{"xmlns":1577},[1579,37694,37695,37703],{},[1582,37696,37697],{},[1746,37698,37699,37701],{},[1585,37700,1922],{},[1716,37702,2398],{},[1605,37704,4225],{"encoding":1607},": všechny výběry pocházejí ze stejného rozdělení.",[1144,37707,37709],{"className":1146,"code":37708,"language":71,"meta":1148,"style":1148},"kruskal.test(kvantitativní_proměnná ~ faktor, data = soubor)\n",[1150,37710,37711],{"__ignoreMap":1148},[1115,37712,37713,37716,37718,37721,37723,37726,37728,37730,37732,37735],{"class":1154,"line":10},[1115,37714,37715],{"class":1165},"kruskal.test",[1115,37717,1170],{"class":1169},[1115,37719,37720],{"class":1157},"kvantitativní_proměnná",[1115,37722,19356],{"class":1161},[1115,37724,37725],{"class":1157}," faktor",[1115,37727,1177],{"class":1161},[1115,37729,22660],{"class":1157},[1115,37731,6416],{"class":1161},[1115,37733,37734],{"class":1157}," soubor",[1115,37736,6519],{"class":1169},[1550,37738,37740],{"id":37739},"mediánový-test","Mediánový test",[1110,37742,37743,37744,37761,37762,4595],{},"Má stejný účel jako Kruskalův-Wallisův test (obdoba analýzy rozptylu jednoduchého třídění, ",[1115,37745,37747],{"className":37746},[1573],[1575,37748,37749],{"xmlns":1577},[1579,37750,37751,37759],{},[1582,37752,37753],{},[1746,37754,37755,37757],{},[1585,37756,1922],{},[1716,37758,2398],{},[1605,37760,4225],{"encoding":1607},": všechny výběry pocházejí ze stejného rozdělení) a je součástí balíčku ",[1150,37763,37764],{},"agricolae",[1144,37766,37768],{"className":1146,"code":37767,"language":71,"meta":1148,"style":1148},"library(agricolae)\nMedian.test(kvantitativní_proměnná, faktor)\n",[1150,37769,37770,37780],{"__ignoreMap":1148},[1115,37771,37772,37774,37776,37778],{"class":1154,"line":10},[1115,37773,19892],{"class":1161},[1115,37775,1170],{"class":1169},[1115,37777,37764],{"class":1157},[1115,37779,6519],{"class":1169},[1115,37781,37782,37785,37787,37789,37791,37793],{"class":1154,"line":27},[1115,37783,37784],{"class":1165},"Median.test",[1115,37786,1170],{"class":1169},[1115,37788,37720],{"class":1157},[1115,37790,1177],{"class":1161},[1115,37792,37725],{"class":1157},[1115,37794,6519],{"class":1169},[1550,37796,1496],{"id":37797},"friedmanův-test",[1110,37799,37800,37801,37818,37819,37857],{},"Neparametrická obdoba analýzy rozptylu dvojného třídění s jedním pozorováním v každé podtřídě. ",[1115,37802,37804],{"className":37803},[1573],[1575,37805,37806],{"xmlns":1577},[1579,37807,37808,37816],{},[1582,37809,37810],{},[1746,37811,37812,37814],{},[1585,37813,1922],{},[1716,37815,2398],{},[1605,37817,4225],{"encoding":1607},": distribuční funkce veličin ",[1115,37820,37822],{"className":37821},[1573],[1575,37823,37824],{"xmlns":1577},[1579,37825,37826,37854],{},[1582,37827,37828,37838,37840,37842,37844],{},[1746,37829,37830,37832],{},[1585,37831,1594],{},[1582,37833,37834,37836],{},[1585,37835,1776],{},[1716,37837,1718],{},[1589,37839,1177],{"separator":1121},[1589,37841,2979],{},[1589,37843,1177],{"separator":1121},[1746,37845,37846,37848],{},[1585,37847,1594],{},[1582,37849,37850,37852],{},[1585,37851,1776],{},[1585,37853,1600],{},[1605,37855,37856],{"encoding":1607},"X_{i1}, \\dots, X_{ik}"," jsou totožné.",[1144,37859,37861],{"className":1146,"code":37860,"language":71,"meta":1148,"style":1148},"friedman.test(kvantitativní_proměnná ~ faktor_A | faktor_B, data = soubor)\n# jsou-li proměnné samostatné vektory (bez argumentu data):\nfriedman.test(kvantitativní_proměnná, faktor_A, faktor_B)\n",[1150,37862,37863,37893,37898],{"__ignoreMap":1148},[1115,37864,37865,37868,37870,37872,37874,37877,37880,37883,37885,37887,37889,37891],{"class":1154,"line":10},[1115,37866,37867],{"class":1165},"friedman.test",[1115,37869,1170],{"class":1169},[1115,37871,37720],{"class":1157},[1115,37873,19356],{"class":1161},[1115,37875,37876],{"class":1157}," faktor_A",[1115,37878,37879],{"class":1161}," |",[1115,37881,37882],{"class":1157}," faktor_B",[1115,37884,1177],{"class":1161},[1115,37886,22660],{"class":1157},[1115,37888,6416],{"class":1161},[1115,37890,37734],{"class":1157},[1115,37892,6519],{"class":1169},[1115,37894,37895],{"class":1154,"line":27},[1115,37896,37897],{"class":1222},"# jsou-li proměnné samostatné vektory (bez argumentu data):\n",[1115,37899,37900,37902,37904,37906,37908,37910,37912,37914],{"class":1154,"line":148},[1115,37901,37867],{"class":1165},[1115,37903,1170],{"class":1169},[1115,37905,37720],{"class":1157},[1115,37907,1177],{"class":1161},[1115,37909,37876],{"class":1157},[1115,37911,1177],{"class":1161},[1115,37913,37882],{"class":1157},[1115,37915,6519],{"class":1169},[1136,37917,37919],{"id":37918},"přehled-testů","Přehled testů",[1110,37921,37922],{},[1303,37923],{"alt":1305,"className":37924,"src":1308},[1130,1307],[1310,37926,37927,37938],{},[1313,37928,37929],{},[1316,37930,37931,37933,37935],{},[1319,37932,1321],{},[1319,37934,1324],{},[1319,37936,37937],{},"R funkce",[1332,37939,37940,37951,37962,37973,37984,37997,38008,38019,38030,38041,38052,38067],{},[1316,37941,37942,37945,37947],{},[1337,37943,37944],{},"Jedna střední hodnota vs. zadané číslo, normální data",[1337,37946,1342],{},[1337,37948,37949],{},[1150,37950,1347],{},[1316,37952,37953,37956,37958],{},[1337,37954,37955],{},"Rozdíl dvou závislých měření, diference normální",[1337,37957,1381],{},[1337,37959,37960],{},[1150,37961,1386],{},[1316,37963,37964,37967,37969],{},[1337,37965,37966],{},"Shoda rozptylů dvou nezávislých normálních výběrů",[1337,37968,1418],{},[1337,37970,37971],{},[1150,37972,1423],{},[1316,37974,37975,37978,37980],{},[1337,37976,37977],{},"Shoda středních hodnot dvou nezávislých normálních výběrů",[1337,37979,1440],{},[1337,37981,37982],{},[1150,37983,1445],{},[1316,37985,37986,37989,37991],{},[1337,37987,37988],{},"Shoda dat se zadaným typem rozdělení (normální, exponenciální, …)",[1337,37990,1529],{},[1337,37992,37993,1279,37995],{},[1150,37994,1534],{},[1150,37996,2731],{},[1316,37998,37999,38002,38004],{},[1337,38000,38001],{},"Normalita dat",[1337,38003,1513],{},[1337,38005,38006],{},[1150,38007,1263],{},[1316,38009,38010,38013,38015],{},[1337,38011,38012],{},"Medián jednoho výběru vs. konstanta, data nejsou normální",[1337,38014,1364],{},[1337,38016,38017],{},[1150,38018,1369],{},[1316,38020,38021,38024,38026],{},[1337,38022,38023],{},"Medián diferencí dvou závislých měření, data nejsou normální",[1337,38025,1401],{},[1337,38027,38028],{},[1150,38029,1406],{},[1316,38031,38032,38035,38037],{},[1337,38033,38034],{},"Mediány dvou nezávislých výběrů, data nejsou normální",[1337,38036,1462],{},[1337,38038,38039],{},[1150,38040,1467],{},[1316,38042,38043,38046,38048],{},[1337,38044,38045],{},"Více než dva nezávislé výběry, data nejsou normální",[1337,38047,1479],{},[1337,38049,38050],{},[1150,38051,1484],{},[1316,38053,38054,38057,38060],{},[1337,38055,38056],{},"Více než dva nezávislé výběry, data nejsou normální (alternativa)",[1337,38058,38059],{},"mediánový test",[1337,38061,38062,25150,38065],{},[1150,38063,38064],{},"Median.test(y, faktor)",[1150,38066,37764],{},[1316,38068,38069,38072,38074],{},[1337,38070,38071],{},"Více než dva závislé výběry (dvojné třídění, jedno pozorování na podtřídu)",[1337,38073,1496],{},[1337,38075,38076],{},[1150,38077,1501],{},[1136,38079,9014],{"id":9013},[2220,38081,38082,38159,38165,38182,38212],{},[2223,38083,38084,38123,38124,35537,38141,38158],{},[2227,38085,38086,38087,38104,38105,38122],{},"Nezamítnutí ",[1115,38088,38090],{"className":38089},[1573],[1575,38091,38092],{"xmlns":1577},[1579,38093,38094,38102],{},[1582,38095,38096],{},[1746,38097,38098,38100],{},[1585,38099,1922],{},[1716,38101,2398],{},[1605,38103,4225],{"encoding":1607}," není důkaz, že ",[1115,38106,38108],{"className":38107},[1573],[1575,38109,38110],{"xmlns":1577},[1579,38111,38112,38120],{},[1582,38113,38114],{},[1746,38115,38116,38118],{},[1585,38117,1922],{},[1716,38119,2398],{},[1605,38121,4225],{"encoding":1607}," platí."," U kabelů A\u002FB vyšlo ",[1115,38125,38127],{"className":38126},[1573],[1575,38128,38129],{"xmlns":1577},[1579,38130,38131,38139],{},[1582,38132,38133,38135,38137],{},[1585,38134,1110],{},[1589,38136,1597],{},[1716,38138,35533],{},[1605,38140,35536],{"encoding":1607},[1115,38142,38144],{"className":38143},[1573],[1575,38145,38146],{"xmlns":1577},[1579,38147,38148,38156],{},[1582,38149,38150],{},[1746,38151,38152,38154],{},[1585,38153,1922],{},[1716,38155,2398],{},[1605,38157,4225],{"encoding":1607}," nezamítá, ale hodnota je blízko hranice; správná interpretace je „data rovnost průměrů nevyvracejí“, ne „rovnost je prokázána“.",[2223,38160,38161,38164],{},[2227,38162,38163],{},"Před párovým nebo dvouvýběrovým t-testem ověřte normalitu."," U realitních odhadců vycházel párový t-test bez varování, ale Shapiro-Wilkův test na diferencích normalitu zamítl — správným testem byl párový Wilcoxonův test.",[2223,38166,38167,38174,38175,38178,38179,38181],{},[2227,38168,38169,3707,38171,38173],{},[1150,38170,1431],{},[1150,38172,3750],{}," se volí podle F-testu, ne podle výchozí hodnoty."," Výchozí nastavení R je ",[1150,38176,38177],{},"var.equal = FALSE"," (Welchova varianta); pokud F-test potvrdí shodné rozptyly, je třeba explicitně napsat ",[1150,38180,35516],{},", jinak se použije jiná statistika a jiné stupně volnosti.",[2223,38183,38184,38187,38188,38191,38192,38209,38210,2264],{},[2227,38185,38186],{},"Jednostranná vs. dvoustranná alternativa mění kritický obor i závěr."," Volba ",[1150,38189,38190],{},"alternative = \"greater\"\u002F\"less\"\u002F\"two.sided\""," musí odpovídat formulaci ",[1115,38193,38195],{"className":38194},[1573],[1575,38196,38197],{"xmlns":1577},[1579,38198,38199,38207],{},[1582,38200,38201],{},[1746,38202,38203,38205],{},[1585,38204,1922],{},[1716,38206,1718],{},[1605,38208,3807],{"encoding":1607}," v zadání, ne být ponechána na výchozí hodnotě ",[1150,38211,3780],{},[2223,38213,38214,38217,38218,38231],{},[2227,38215,38216],{},"Shapiro-Wilkův test se vyhodnocuje jen přes p-hodnotu",", ne porovnáním ",[1115,38219,38221],{"className":38220},[1573],[1575,38222,38223],{"xmlns":1577},[1579,38224,38225,38229],{},[1582,38226,38227],{},[1585,38228,4256],{},[1605,38230,4256],{"encoding":1607}," s tabulkovou kritickou hodnotou jako u ostatních testů v této kapitole.",[1136,38233,4071],{"id":4070},[2220,38235,38236,38241,38246,38251,38256,38261,38266],{},[2223,38237,38238],{},[1127,38239,1133],{"className":38240,"dataFsResolvedFilePath":1131,"href":1132},[1130],[2223,38242,38243],{},[1127,38244,1558],{"className":38245,"dataFsResolvedFilePath":1556,"href":1557},[1130],[2223,38247,38248],{},[1127,38249,2415],{"className":38250,"dataFsResolvedFilePath":2413,"href":2414},[1130],[2223,38252,38253],{},[1127,38254,2798],{"className":38255,"dataFsResolvedFilePath":2796,"href":2797},[1130],[2223,38257,38258],{},[1127,38259,3237],{"className":38260,"dataFsResolvedFilePath":3235,"href":3236},[1130],[2223,38262,38263],{},[1127,38264,3322],{"className":38265,"dataFsResolvedFilePath":3320,"href":3321},[1130],[2223,38267,38268],{},[1127,38269,9239],{"className":38270,"dataFsResolvedFilePath":9237,"href":9238},[1130],[1136,38272,4111],{"id":934},[1110,38274,4114,38275,4119],{},[4116,38276,4118],{},[4135,38278,38279],{},"html pre.shiki code .sP4rz, html 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