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— minimalizací součtu čtverců reziduí ",[1115,1184,1186],{"className":1185},[1137],[1139,1187,1188],{"xmlns":1141},[1143,1189,1190,1233],{},[1146,1191,1192,1196,1200,1208,1211,1223],{},[1193,1194,1195],"mo",{},"∑",[1193,1197,1199],{"stretchy":1198},"false","(",[1201,1202,1203,1205],"msub",{},[1149,1204,1151],{},[1149,1206,1207],{},"i",[1193,1209,1210],{},"−",[1201,1212,1213,1221],{},[1214,1215,1216,1218],"mover",{"accent":1121},[1149,1217,1151],{},[1193,1219,1220],{},"^",[1149,1222,1207],{},[1224,1225,1226,1229],"msup",{},[1193,1227,1228],{"stretchy":1198},")",[1230,1231,1232],"mn",{},"2",[1153,1234,1235],{"encoding":1155},"\\sum(y_i-\\hat y_i)^2",".",[1127,1238,1239,1240,1243,1244,1263,1264,1243,1267,1294,1295,1243,1298,1236],{},"Kvalitu fitu měří ",[1130,1241,1242],{},"index determinace"," ",[1115,1245,1247],{"className":1246},[1137],[1139,1248,1249],{"xmlns":1141},[1143,1250,1251,1260],{},[1146,1252,1253],{},[1224,1254,1255,1258],{},[1149,1256,1257],{},"R",[1230,1259,1232],{},[1153,1261,1262],{"encoding":1155},"R^2","; obecnou těsnost závislosti ",[1130,1265,1266],{},"index korelace",[1115,1268,1270],{"className":1269},[1137],[1139,1271,1272],{"xmlns":1141},[1143,1273,1274,1291],{},[1146,1275,1276,1279,1282],{},[1149,1277,1278],{},"I",[1193,1280,1281],{},"=",[1283,1284,1285],"msqrt",{},[1224,1286,1287,1289],{},[1149,1288,1257],{},[1230,1290,1232],{},[1153,1292,1293],{"encoding":1155},"I=\\sqrt{R^2}",", který je pro regresní přímku roven ",[1130,1296,1297],{},"koeficientu korelace",[1115,1299,1301],{"className":1300},[1137],[1139,1302,1303],{"xmlns":1141},[1143,1304,1305,1317],{},[1146,1306,1307],{},[1201,1308,1309,1311],{},[1149,1310,71],{},[1146,1312,1313,1315],{},[1149,1314,1168],{},[1149,1316,1151],{},[1153,1318,1319],{"encoding":1155},"r_{xy}",[1127,1321,1322,1323,1326,1327,1330,1331,1335],{},"Když přímka nestačí, volí se ",[1130,1324,1325],{},"parabolická, polynomická, hyperbolická nebo logaritmická"," regrese (stále lineární v parametrech, odhad metodou nejmenších čtverců) nebo ",[1130,1328,1329],{},"exponenciální"," regrese (nelineární v parametrech, odhad přes ",[1332,1333,1334],"code",{},"nls2",").",[1127,1337,1338,1341],{},[1130,1339,1340],{},"Vícenásobná regrese"," rozšiřuje model o více regresorů; vyžaduje výběr proměnných (ENTER\u002Fstepwise), ověření šesti předpokladů modelu a kontrolu multikolinearity přes VIF.",[1127,1343,1344,1345,1348,1349,1348,1352,1348,1355,1348,1358,1348,1361,1348,1364,1348,1367,1348,1370,1348,1373,1236],{},"V R: ",[1332,1346,1347],{},"lm()",", ",[1332,1350,1351],{},"nls2()",[1332,1353,1354],{},"summary()",[1332,1356,1357],{},"confint()",[1332,1359,1360],{},"predict()",[1332,1362,1363],{},"step()",[1332,1365,1366],{},"car::vif()",[1332,1368,1369],{},"lmtest::dwtest()",[1332,1371,1372],{},"whitestrap::white_test()",[1332,1374,1375],{},"shapiro.test()",[1377,1378,1380],"h2",{"id":1379},"základní-pojmy","Základní pojmy",[1110,1382,1383,1391,1392,1405,1406,1419,1420,1422,1423,1436,1437,1450,1451,1454],{},[1384,1385,1390],"a",{"className":1386,"dataFsResolvedFilePath":1388,"href":1389},[1387],"wikilink","courses\u002Fmask.md","\u002Fwiki\u002Fmask","Metody aplikované statistiky"," pracuje se dvěma znaky ",[1115,1393,1395],{"className":1394},[1137],[1139,1396,1397],{"xmlns":1141},[1143,1398,1399,1403],{},[1146,1400,1401],{},[1149,1402,1168],{},[1153,1404,1168],{"encoding":1155}," a ",[1115,1407,1409],{"className":1408},[1137],[1139,1410,1411],{"xmlns":1141},[1143,1412,1413,1417],{},[1146,1414,1415],{},[1149,1416,1151],{},[1153,1418,1151],{"encoding":1155}," zjištěnými na stejných jednotkách. ",[1130,1421,1132],{}," se zabývá jednostrannými závislostmi, kdy proti sobě stojí vysvětlující (nezávisle) proměnná ",[1115,1424,1426],{"className":1425},[1137],[1139,1427,1428],{"xmlns":1141},[1143,1429,1430,1434],{},[1146,1431,1432],{},[1149,1433,1168],{},[1153,1435,1168],{"encoding":1155}," v úloze příčiny a vysvětlovaná (závisle) proměnná ",[1115,1438,1440],{"className":1439},[1137],[1139,1441,1442],{"xmlns":1141},[1143,1443,1444,1448],{},[1146,1445,1446],{},[1149,1447,1151],{},[1153,1449,1151],{"encoding":1155}," v úloze následku. ",[1130,1452,1453],{},"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.",[1110,1456,1457,1458,1335],{},"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 (",[1130,1459,1460],{},"regresní funkce",[1110,1462,1463],{},"Druh regresní analýzy určuje struktura datového souboru:",[1124,1465,1466,1504],{},[1127,1467,1468,1471,1472,1485,1486,1499,1500,1503],{},[1130,1469,1470],{},"dvourozměrný datový soubor"," (jedna ",[1115,1473,1475],{"className":1474},[1137],[1139,1476,1477],{"xmlns":1141},[1143,1478,1479,1483],{},[1146,1480,1481],{},[1149,1482,1168],{},[1153,1484,1168],{"encoding":1155},", jedna ",[1115,1487,1489],{"className":1488},[1137],[1139,1490,1491],{"xmlns":1141},[1143,1492,1493,1497],{},[1146,1494,1495],{},[1149,1496,1151],{},[1153,1498,1151],{"encoding":1155},") → ",[1130,1501,1502],{},"regresní analýza dvou proměnných",",",[1127,1505,1506,1509,1510,1499,1542,1236],{},[1130,1507,1508],{},"vícerozměrný datový soubor"," (více ",[1115,1511,1513],{"className":1512},[1137],[1139,1514,1515],{"xmlns":1141},[1143,1516,1517,1539],{},[1146,1518,1519,1526,1528,1531,1533],{},[1201,1520,1521,1523],{},[1149,1522,1168],{},[1230,1524,1525],{},"1",[1193,1527,1503],{"separator":1121},[1193,1529,1530],{},"…",[1193,1532,1503],{"separator":1121},[1201,1534,1535,1537],{},[1149,1536,1168],{},[1149,1538,1110],{},[1153,1540,1541],{"encoding":1155},"x_1,\\dots,x_p",[1130,1543,1544],{},"vícenásobná regresní analýza",[1110,1546,1547,1548,1551,1552,1555],{},"Volba konkrétní regresní funkce by měla vycházet jak z ",[1130,1549,1550],{},"ekonomické teorie"," (ta napovídá, zda závislost roste, nebo klesá, zda je přímková, nebo zakřivená), tak z ",[1130,1553,1554],{},"grafické a matematicko-statistické analýzy"," dat — oba přístupy je vhodné kombinovat.",[1377,1557,1559],{"id":1558},"metoda-nejmenších-čtverců","Metoda nejmenších čtverců",[1110,1561,1562,1563,1243,1566,1623,1624,1642,1643,1243,1646,1703,1704,1722,1723,1740,1741,1780,1781,1236],{},"Rozlišují se ",[1130,1564,1565],{},"teoretická regresní funkce",[1115,1567,1569],{"className":1568},[1137],[1139,1570,1571],{"xmlns":1141},[1143,1572,1573,1620],{},[1146,1574,1575,1578,1580,1583,1585,1587,1590,1598,1600,1606,1608,1610,1612,1618],{},[1149,1576,1577],{},"η",[1193,1579,1281],{},[1149,1581,1582],{},"f",[1193,1584,1199],{"stretchy":1198},[1149,1586,1168],{},[1193,1588,1589],{"separator":1121},";",[1201,1591,1592,1595],{},[1149,1593,1594],{},"β",[1230,1596,1597],{},"0",[1193,1599,1503],{"separator":1121},[1201,1601,1602,1604],{},[1149,1603,1594],{},[1230,1605,1525],{},[1193,1607,1503],{"separator":1121},[1193,1609,1530],{},[1193,1611,1503],{"separator":1121},[1201,1613,1614,1616],{},[1149,1615,1594],{},[1149,1617,1110],{},[1193,1619,1228],{"stretchy":1198},[1153,1621,1622],{"encoding":1155},"\\eta = f(x;\\beta_0,\\beta_1,\\dots,\\beta_p)"," — neznámá, populační, daná neznámými parametry ",[1115,1625,1627],{"className":1626},[1137],[1139,1628,1629],{"xmlns":1141},[1143,1630,1631,1639],{},[1146,1632,1633],{},[1201,1634,1635,1637],{},[1149,1636,1594],{},[1149,1638,1207],{},[1153,1640,1641],{"encoding":1155},"\\beta_i"," — a ",[1130,1644,1645],{},"empirická regresní funkce",[1115,1647,1649],{"className":1648},[1137],[1139,1650,1651],{"xmlns":1141},[1143,1652,1653,1700],{},[1146,1654,1655,1661,1663,1665,1667,1669,1671,1678,1680,1686,1688,1690,1692,1698],{},[1214,1656,1657,1659],{"accent":1121},[1149,1658,1151],{},[1193,1660,1220],{},[1193,1662,1281],{},[1149,1664,1582],{},[1193,1666,1199],{"stretchy":1198},[1149,1668,1168],{},[1193,1670,1589],{"separator":1121},[1201,1672,1673,1676],{},[1149,1674,1675],{},"b",[1230,1677,1597],{},[1193,1679,1503],{"separator":1121},[1201,1681,1682,1684],{},[1149,1683,1675],{},[1230,1685,1525],{},[1193,1687,1503],{"separator":1121},[1193,1689,1530],{},[1193,1691,1503],{"separator":1121},[1201,1693,1694,1696],{},[1149,1695,1675],{},[1149,1697,1110],{},[1193,1699,1228],{"stretchy":1198},[1153,1701,1702],{"encoding":1155},"\\hat y = f(x; b_0,b_1,\\dots,b_p)",", jejíž odhadnuté parametry ",[1115,1705,1707],{"className":1706},[1137],[1139,1708,1709],{"xmlns":1141},[1143,1710,1711,1719],{},[1146,1712,1713],{},[1201,1714,1715,1717],{},[1149,1716,1675],{},[1149,1718,1207],{},[1153,1720,1721],{"encoding":1155},"b_i"," jsou odhadem ",[1115,1724,1726],{"className":1725},[1137],[1139,1727,1728],{"xmlns":1141},[1143,1729,1730,1738],{},[1146,1731,1732],{},[1201,1733,1734,1736],{},[1149,1735,1594],{},[1149,1737,1207],{},[1153,1739,1641],{"encoding":1155}," vypočteným z konkrétních dat. Odchylky skutečných hodnot od empirické funkce, ",[1115,1742,1744],{"className":1743},[1137],[1139,1745,1746],{"xmlns":1141},[1143,1747,1748,1777],{},[1146,1749,1750,1757,1759,1765,1767],{},[1201,1751,1752,1755],{},[1149,1753,1754],{},"e",[1149,1756,1207],{},[1193,1758,1281],{},[1201,1760,1761,1763],{},[1149,1762,1151],{},[1149,1764,1207],{},[1193,1766,1210],{},[1201,1768,1769,1775],{},[1214,1770,1771,1773],{"accent":1121},[1149,1772,1151],{},[1193,1774,1220],{},[1149,1776,1207],{},[1153,1778,1779],{"encoding":1155},"e_i=y_i-\\hat y_i",", se nazývají ",[1130,1782,1783],{},"rezidua",[1110,1785,1786,1787,1790],{},"Nejpoužívanější metodou odhadu parametrů je ",[1130,1788,1789],{},"metoda nejmenších čtverců (OLS)",": hledají se takové parametry, pro které je součet čtverců reziduí minimální,",[1115,1792,1794],{"className":1793},[1137],[1139,1795,1797],{"xmlns":1141,"display":1796},"block",[1143,1798,1799,1855],{},[1146,1800,1801,1817,1819,1825,1827,1837,1843,1846,1849,1852],{},[1802,1803,1804,1806,1814],"munderover",{},[1193,1805,1195],{},[1146,1807,1808,1810,1812],{},[1149,1809,1207],{},[1193,1811,1281],{},[1230,1813,1525],{},[1149,1815,1816],{},"n",[1193,1818,1199],{"stretchy":1198},[1201,1820,1821,1823],{},[1149,1822,1151],{},[1149,1824,1207],{},[1193,1826,1210],{},[1201,1828,1829,1835],{},[1214,1830,1831,1833],{"accent":1121},[1149,1832,1151],{},[1193,1834,1220],{},[1149,1836,1207],{},[1224,1838,1839,1841],{},[1193,1840,1228],{"stretchy":1198},[1230,1842,1232],{},[1193,1844,1845],{},"→",[1149,1847,1848],{},"min",[1193,1850,1851],{},"⁡",[1149,1853,1236],{"mathvariant":1854},"normal",[1153,1856,1857],{"encoding":1155},"\\sum_{i=1}^n (y_i - \\hat y_i)^2 \\to \\min.",[1110,1859,1860],{},"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.",[1110,1862,1863],{},[1864,1865],"img",{"alt":1866,"className":1867,"src":1869},"mask-ra-primka-rezidua",[1387,1868],"wikilink-broken","\u002Fwiki-assets\u002Fmask-ra-primka-rezidua.png",[1110,1871,1872,1873,1891],{},"Obrázek ukazuje přesně to, co metoda minimalizuje: délky červených úseček jsou rezidua ",[1115,1874,1876],{"className":1875},[1137],[1139,1877,1878],{"xmlns":1141},[1143,1879,1880,1888],{},[1146,1881,1882],{},[1201,1883,1884,1886],{},[1149,1885,1754],{},[1149,1887,1207],{},[1153,1889,1890],{"encoding":1155},"e_i",", metoda nejmenších čtverců volí přímku tak, aby součet jejich čtverců byl nejmenší možný.",[1377,1893,1895],{"id":1894},"regresní-přímka","Regresní přímka",[1110,1897,1898,1899,1902],{},"Nejjednodušší regresní funkcí je ",[1130,1900,1901],{},"regresní přímka",":",[1115,1904,1906],{"className":1905},[1137],[1139,1907,1908],{"xmlns":1141,"display":1796},[1143,1909,1910,1965],{},[1146,1911,1912,1914,1916,1922,1925,1931,1933,1935,1939,1945,1947,1953,1955,1961,1963],{},[1149,1913,1577],{},[1193,1915,1281],{},[1201,1917,1918,1920],{},[1149,1919,1594],{},[1230,1921,1597],{},[1193,1923,1924],{},"+",[1201,1926,1927,1929],{},[1149,1928,1594],{},[1230,1930,1525],{},[1149,1932,1168],{},[1193,1934,1503],{"separator":1121},[1936,1937],"mspace",{"width":1938},"2em",[1214,1940,1941,1943],{"accent":1121},[1149,1942,1151],{},[1193,1944,1220],{},[1193,1946,1281],{},[1201,1948,1949,1951],{},[1149,1950,1675],{},[1230,1952,1597],{},[1193,1954,1924],{},[1201,1956,1957,1959],{},[1149,1958,1675],{},[1230,1960,1525],{},[1149,1962,1168],{},[1149,1964,1236],{"mathvariant":1854},[1153,1966,1967],{"encoding":1155},"\\eta = \\beta_0 + \\beta_1 x, \\qquad \\hat y = b_0 + b_1 x.",[1110,1969,1970,1971,1989,1990,2003,2004,2017],{},"Koeficient ",[1115,1972,1974],{"className":1973},[1137],[1139,1975,1976],{"xmlns":1141},[1143,1977,1978,1986],{},[1146,1979,1980],{},[1201,1981,1982,1984],{},[1149,1983,1675],{},[1230,1985,1525],{},[1153,1987,1988],{"encoding":1155},"b_1"," udává změnu průměru ",[1115,1991,1993],{"className":1992},[1137],[1139,1994,1995],{"xmlns":1141},[1143,1996,1997,2001],{},[1146,1998,1999],{},[1149,2000,1151],{},[1153,2002,1151],{"encoding":1155}," při jednotkové změně ",[1115,2005,2007],{"className":2006},[1137],[1139,2008,2009],{"xmlns":1141},[1143,2010,2011,2015],{},[1146,2012,2013],{},[1149,2014,1168],{},[1153,2016,1168],{"encoding":1155},"; jeho znaménko určuje, zda je závislost přímá, nebo nepřímá.",[2019,2020,2022],"h3",{"id":2021},"v-r","V R",[1110,2024,2025,2026,2029,2030,2033],{},"Vstupní data se nahrají buď ze souboru (",[1332,2027,2028],{},"d \u003C- read.table(\"data.txt\")",", případně ",[1332,2031,2032],{},"d \u003C- read.table(file.choose())","), nebo zapíší přímo jako vektory. Na šesti domácnostech sledujeme počet členů domácnosti a jejich týdenní výdaje:",[2035,2036,2040],"pre",{"className":2037,"code":2038,"language":71,"meta":2039,"style":2039},"language-r shiki shiki-themes github-light github-light github-dark","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","",[1332,2041,2042,2091,2132,2153],{"__ignoreMap":2039},[1115,2043,2045,2049,2053,2057,2060,2063,2065,2068,2070,2073,2075,2078,2080,2083,2085,2088],{"class":2044,"line":10},"line",[1115,2046,2048],{"class":2047},"sP4rz","pocet_clenu",[1115,2050,2052],{"class":2051},"s8jYJ"," \u003C-",[1115,2054,2056],{"class":2055},"snPdu"," c",[1115,2058,1199],{"class":2059},"sxrX7",[1115,2061,1525],{"class":2062},"sBjJW",[1115,2064,1503],{"class":2051},[1115,2066,2067],{"class":2062}," 2",[1115,2069,1503],{"class":2051},[1115,2071,2072],{"class":2062}," 3",[1115,2074,1503],{"class":2051},[1115,2076,2077],{"class":2062}," 4",[1115,2079,1503],{"class":2051},[1115,2081,2082],{"class":2062}," 5",[1115,2084,1503],{"class":2051},[1115,2086,2087],{"class":2062}," 6",[1115,2089,2090],{"class":2059},")\n",[1115,2092,2093,2096,2098,2100,2102,2105,2107,2110,2112,2115,2117,2120,2122,2125,2127,2130],{"class":2044,"line":27},[1115,2094,2095],{"class":2047},"tydenni_vydaje",[1115,2097,2052],{"class":2051},[1115,2099,2056],{"class":2055},[1115,2101,1199],{"class":2059},[1115,2103,2104],{"class":2062},"490",[1115,2106,1503],{"class":2051},[1115,2108,2109],{"class":2062}," 820",[1115,2111,1503],{"class":2051},[1115,2113,2114],{"class":2062}," 1230",[1115,2116,1503],{"class":2051},[1115,2118,2119],{"class":2062}," 1570",[1115,2121,1503],{"class":2051},[1115,2123,2124],{"class":2062}," 1950",[1115,2126,1503],{"class":2051},[1115,2128,2129],{"class":2062}," 2320",[1115,2131,2090],{"class":2059},[1115,2133,2134,2136,2138,2141,2143,2145,2148,2151],{"class":2044,"line":148},[1115,2135,786],{"class":2047},[1115,2137,2052],{"class":2051},[1115,2139,2140],{"class":2055}," lm",[1115,2142,1199],{"class":2059},[1115,2144,2095],{"class":2047},[1115,2146,2147],{"class":2051}," ~",[1115,2149,2150],{"class":2047}," pocet_clenu",[1115,2152,2090],{"class":2059},[1115,2154,2155,2158,2160,2162],{"class":2044,"line":111},[1115,2156,2157],{"class":2055},"summary",[1115,2159,1199],{"class":2059},[1115,2161,786],{"class":2047},[1115,2163,2090],{"class":2059},[2035,2165,2170],{"className":2166,"code":2168,"language":2169,"meta":2039},[2167],"language-text","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","text",[1332,2171,2168],{"__ignoreMap":2039},[1110,2173,2174,2175,2209,2210,2213,2214,2245,2246,2277,2278,2281,2282,2305],{},"Odhadnutý model je ",[1115,2176,2178],{"className":2177},[1137],[1139,2179,2180],{"xmlns":1141},[1143,2181,2182,2206],{},[1146,2183,2184,2190,2192,2195,2197,2200,2204],{},[1214,2185,2186,2188],{"accent":1121},[1149,2187,1151],{},[1193,2189,1220],{},[1193,2191,1281],{},[1230,2193,2194],{},"108,7",[1193,2196,1924],{},[1230,2198,2199],{},"368,0",[2201,2202,2203],"mtext",{}," ",[1149,2205,1168],{},[1153,2207,2208],{"encoding":1155},"\\hat y = 108{,}7 + 368{,}0\\,x",". Sloupec ",[1332,2211,2212],{},"Pr(>|t|)"," je p-hodnota t-testu ",[1115,2215,2217],{"className":2216},[1137],[1139,2218,2219],{"xmlns":1141},[1143,2220,2221,2242],{},[1146,2222,2223,2230,2232,2238,2240],{},[1201,2224,2225,2228],{},[1149,2226,2227],{},"H",[1230,2229,1597],{},[1193,2231,1902],{},[1201,2233,2234,2236],{},[1149,2235,1594],{},[1149,2237,1207],{},[1193,2239,1281],{},[1230,2241,1597],{},[1153,2243,2244],{"encoding":1155},"H_0:\\beta_i=0"," proti ",[1115,2247,2249],{"className":2248},[1137],[1139,2250,2251],{"xmlns":1141},[1143,2252,2253,2274],{},[1146,2254,2255,2261,2263,2269,2272],{},[1201,2256,2257,2259],{},[1149,2258,2227],{},[1230,2260,1525],{},[1193,2262,1902],{},[1201,2264,2265,2267],{},[1149,2266,1594],{},[1149,2268,1207],{},[1193,2270,2271],{"mathvariant":1854},"≠",[1230,2273,1597],{},[1153,2275,2276],{"encoding":1155},"H_1:\\beta_i\\neq0"," pro každý parametr — obě p-hodnoty jsou hluboko pod 0,05, oba parametry jsou tedy statisticky významné. ",[1332,2279,2280],{},"Multiple R-squared"," je index determinace ",[1115,2283,2285],{"className":2284},[1137],[1139,2286,2287],{"xmlns":1141},[1143,2288,2289,2302],{},[1146,2290,2291,2297,2299],{},[1224,2292,2293,2295],{},[1149,2294,1257],{},[1230,2296,1232],{},[1193,2298,1281],{},[1230,2300,2301],{},"0,9995",[1153,2303,2304],{"encoding":1155},"R^2=0{,}9995",": model vysvětluje 99,95 % rozptylu výdajů.",[1110,2307,2308],{},"Pro doplňkový přehled slouží přímé přístupové funkce:",[2035,2310,2312],{"className":2037,"code":2311,"language":71,"meta":2039,"style":2039},"coef(model)\nfitted(model)\nresiduals(model)\n",[1332,2313,2314,2325,2336],{"__ignoreMap":2039},[1115,2315,2316,2319,2321,2323],{"class":2044,"line":10},[1115,2317,2318],{"class":2055},"coef",[1115,2320,1199],{"class":2059},[1115,2322,786],{"class":2047},[1115,2324,2090],{"class":2059},[1115,2326,2327,2330,2332,2334],{"class":2044,"line":27},[1115,2328,2329],{"class":2055},"fitted",[1115,2331,1199],{"class":2059},[1115,2333,786],{"class":2047},[1115,2335,2090],{"class":2059},[1115,2337,2338,2341,2343,2345],{"class":2044,"line":148},[1115,2339,2340],{"class":2055},"residuals",[1115,2342,1199],{"class":2059},[1115,2344,786],{"class":2047},[1115,2346,2090],{"class":2059},[2035,2348,2351],{"className":2349,"code":2350,"language":2169,"meta":2039},[2167],"(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",[1332,2352,2350],{"__ignoreMap":2039},[1110,2354,2355,2358,2359,1348,2385,2388,2389,2411,2412,1348,2430,2433,2434,2471],{},[1332,2356,2357],{},"coef()"," vrací odhadnuté parametry ",[1115,2360,2362],{"className":2361},[1137],[1139,2363,2364],{"xmlns":1141},[1143,2365,2366,2382],{},[1146,2367,2368,2374,2376],{},[1201,2369,2370,2372],{},[1149,2371,1675],{},[1230,2373,1597],{},[1193,2375,1503],{"separator":1121},[1201,2377,2378,2380],{},[1149,2379,1675],{},[1230,2381,1525],{},[1153,2383,2384],{"encoding":1155},"b_0,b_1",[1332,2386,2387],{},"fitted()"," predikce ",[1115,2390,2392],{"className":2391},[1137],[1139,2393,2394],{"xmlns":1141},[1143,2395,2396,2408],{},[1146,2397,2398],{},[1201,2399,2400,2406],{},[1214,2401,2402,2404],{"accent":1121},[1149,2403,1151],{},[1193,2405,1220],{},[1149,2407,1207],{},[1153,2409,2410],{"encoding":1155},"\\hat y_i"," pro pozorované ",[1115,2413,2415],{"className":2414},[1137],[1139,2416,2417],{"xmlns":1141},[1143,2418,2419,2427],{},[1146,2420,2421],{},[1201,2422,2423,2425],{},[1149,2424,1168],{},[1149,2426,1207],{},[1153,2428,2429],{"encoding":1155},"x_i",[1332,2431,2432],{},"residuals()"," rezidua ",[1115,2435,2437],{"className":2436},[1137],[1139,2438,2439],{"xmlns":1141},[1143,2440,2441,2469],{},[1146,2442,2443,2449,2451,2457,2459],{},[1201,2444,2445,2447],{},[1149,2446,1754],{},[1149,2448,1207],{},[1193,2450,1281],{},[1201,2452,2453,2455],{},[1149,2454,1151],{},[1149,2456,1207],{},[1193,2458,1210],{},[1201,2460,2461,2467],{},[1214,2462,2463,2465],{"accent":1121},[1149,2464,1151],{},[1193,2466,1220],{},[1149,2468,1207],{},[1153,2470,1779],{"encoding":1155}," — stejná čísla, která na obrázku výše tvoří délky červených úseček.",[1110,2473,2474,2475,2488],{},"Intervaly spolehlivosti pro parametry a pro predikci v nových bodech ",[1115,2476,2478],{"className":2477},[1137],[1139,2479,2480],{"xmlns":1141},[1143,2481,2482,2486],{},[1146,2483,2484],{},[1149,2485,1168],{},[1153,2487,1168],{"encoding":1155}," (zde 7 a 8 členů domácnosti):",[2035,2490,2492],{"className":2037,"code":2491,"language":71,"meta":2039,"style":2039},"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",[1332,2493,2494,2516,2547,2587],{"__ignoreMap":2039},[1115,2495,2496,2499,2501,2503,2505,2508,2511,2514],{"class":2044,"line":10},[1115,2497,2498],{"class":2055},"confint",[1115,2500,1199],{"class":2059},[1115,2502,786],{"class":2047},[1115,2504,1503],{"class":2051},[1115,2506,2507],{"class":2047}," level",[1115,2509,2510],{"class":2051}," =",[1115,2512,2513],{"class":2062}," 0.95",[1115,2515,2090],{"class":2059},[1115,2517,2518,2521,2523,2526,2528,2530,2532,2534,2536,2539,2541,2544],{"class":2044,"line":27},[1115,2519,2520],{"class":2047},"nove",[1115,2522,2052],{"class":2051},[1115,2524,2525],{"class":2055}," data.frame",[1115,2527,1199],{"class":2059},[1115,2529,2048],{"class":2047},[1115,2531,2510],{"class":2051},[1115,2533,2056],{"class":2055},[1115,2535,1199],{"class":2059},[1115,2537,2538],{"class":2062},"7",[1115,2540,1503],{"class":2051},[1115,2542,2543],{"class":2062}," 8",[1115,2545,2546],{"class":2059},"))\n",[1115,2548,2549,2552,2554,2556,2558,2561,2563,2566,2568,2571,2573,2577,2579,2581,2583,2585],{"class":2044,"line":148},[1115,2550,2551],{"class":2055},"predict",[1115,2553,1199],{"class":2059},[1115,2555,786],{"class":2047},[1115,2557,1503],{"class":2051},[1115,2559,2560],{"class":2047}," newdata",[1115,2562,2510],{"class":2051},[1115,2564,2565],{"class":2047}," nove",[1115,2567,1503],{"class":2051},[1115,2569,2570],{"class":2047}," interval",[1115,2572,2510],{"class":2051},[1115,2574,2576],{"class":2575},"sIIMD"," \"confidence\"",[1115,2578,1503],{"class":2051},[1115,2580,2507],{"class":2047},[1115,2582,2510],{"class":2051},[1115,2584,2513],{"class":2062},[1115,2586,2090],{"class":2059},[1115,2588,2589,2591,2593,2595,2597,2599,2601,2603,2605,2607,2609,2612,2614,2616,2618,2620],{"class":2044,"line":111},[1115,2590,2551],{"class":2055},[1115,2592,1199],{"class":2059},[1115,2594,786],{"class":2047},[1115,2596,1503],{"class":2051},[1115,2598,2560],{"class":2047},[1115,2600,2510],{"class":2051},[1115,2602,2565],{"class":2047},[1115,2604,1503],{"class":2051},[1115,2606,2570],{"class":2047},[1115,2608,2510],{"class":2051},[1115,2610,2611],{"class":2575}," \"prediction\"",[1115,2613,1503],{"class":2051},[1115,2615,2507],{"class":2047},[1115,2617,2510],{"class":2051},[1115,2619,2513],{"class":2062},[1115,2621,2090],{"class":2059},[2035,2623,2626],{"className":2624,"code":2625,"language":2169,"meta":2039},[2167]," 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",[1332,2627,2625],{"__ignoreMap":2039},[1110,2629,2630,2633,2634,1243,2637,2650,2651,1348,2664,2667,2668,2671],{},[1332,2631,2632],{},"interval = \"confidence\""," dává interval spolehlivosti pro ",[1130,2635,2636],{},"střední hodnotu",[1115,2638,2640],{"className":2639},[1137],[1139,2641,2642],{"xmlns":1141},[1143,2643,2644,2648],{},[1146,2645,2646],{},[1149,2647,1151],{},[1153,2649,1151],{"encoding":1155}," při daném ",[1115,2652,2654],{"className":2653},[1137],[1139,2655,2656],{"xmlns":1141},[1143,2657,2658,2662],{},[1146,2659,2660],{},[1149,2661,1168],{},[1153,2663,1168],{"encoding":1155},[1332,2665,2666],{},"interval = \"prediction\""," širší interval pro ",[1130,2669,2670],{},"jednotlivé budoucí pozorování"," — ten musí zahrnout i rozptyl kolem regresní přímky, proto je vždy širší.",[2019,2673,2675],{"id":2674},"diagnostika-modelu","Diagnostika modelu",[1110,2677,2678,2679,1348,2682,1405,2685,2688],{},"Platnost závěrů z regresní přímky stojí na předpokladech o reziduích: ",[1130,2680,2681],{},"absenci autokorelace",[1130,2683,2684],{},"stálosti rozptylu (homoskedasticitě)",[1130,2686,2687],{},"normalitě",". V R se ověřují takto:",[2035,2690,2692],{"className":2037,"code":2691,"language":71,"meta":2039,"style":2039},"library(lmtest)\ndwtest(model)\n",[1332,2693,2694,2706],{"__ignoreMap":2039},[1115,2695,2696,2699,2701,2704],{"class":2044,"line":10},[1115,2697,2698],{"class":2051},"library",[1115,2700,1199],{"class":2059},[1115,2702,2703],{"class":2047},"lmtest",[1115,2705,2090],{"class":2059},[1115,2707,2708,2711,2713,2715],{"class":2044,"line":27},[1115,2709,2710],{"class":2055},"dwtest",[1115,2712,1199],{"class":2059},[1115,2714,786],{"class":2047},[1115,2716,2090],{"class":2059},[2035,2718,2721],{"className":2719,"code":2720,"language":2169,"meta":2039},[2167]," Durbin-Watson test\n\ndata: model\nDW = 3.4121, p-value = 0.9555\nalternative hypothesis: true autocorrelation is greater than 0\n",[1332,2722,2720],{"__ignoreMap":2039},[1110,2724,2725,2726,2744,2745,2763,2764,2781],{},"Durbinův–Watsonův test má ",[1115,2727,2729],{"className":2728},[1137],[1139,2730,2731],{"xmlns":1141},[1143,2732,2733,2741],{},[1146,2734,2735],{},[1201,2736,2737,2739],{},[1149,2738,2227],{},[1230,2740,1597],{},[1153,2742,2743],{"encoding":1155},"H_0",": v modelu není problém s autokorelací, proti ",[1115,2746,2748],{"className":2747},[1137],[1139,2749,2750],{"xmlns":1141},[1143,2751,2752,2760],{},[1146,2753,2754],{},[1201,2755,2756,2758],{},[1149,2757,2227],{},[1230,2759,1525],{},[1153,2761,2762],{"encoding":1155},"H_1",": 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, ",[1115,2765,2767],{"className":2766},[1137],[1139,2768,2769],{"xmlns":1141},[1143,2770,2771,2779],{},[1146,2772,2773],{},[1201,2774,2775,2777],{},[1149,2776,2227],{},[1230,2778,1597],{},[1153,2780,2743],{"encoding":1155}," se nezamítá.",[2035,2783,2785],{"className":2037,"code":2784,"language":71,"meta":2039,"style":2039},"library(whitestrap)\nwhite_test(model)\n",[1332,2786,2787,2798],{"__ignoreMap":2039},[1115,2788,2789,2791,2793,2796],{"class":2044,"line":10},[1115,2790,2698],{"class":2051},[1115,2792,1199],{"class":2059},[1115,2794,2795],{"class":2047},"whitestrap",[1115,2797,2090],{"class":2059},[1115,2799,2800,2803,2805,2807],{"class":2044,"line":27},[1115,2801,2802],{"class":2055},"white_test",[1115,2804,1199],{"class":2059},[1115,2806,786],{"class":2047},[1115,2808,2090],{"class":2059},[2035,2810,2813],{"className":2811,"code":2812,"language":2169,"meta":2039},[2167],"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",[1332,2814,2812],{"__ignoreMap":2039},[1110,2816,2817,2818,2835,2836,2853,2854,2781],{},"Whiteův test má ",[1115,2819,2821],{"className":2820},[1137],[1139,2822,2823],{"xmlns":1141},[1143,2824,2825,2833],{},[1146,2826,2827],{},[1201,2828,2829,2831],{},[1149,2830,2227],{},[1230,2832,1597],{},[1153,2834,2743],{"encoding":1155},": rozptyl reziduí je stálý (homoskedasticita), proti ",[1115,2837,2839],{"className":2838},[1137],[1139,2840,2841],{"xmlns":1141},[1143,2842,2843,2851],{},[1146,2844,2845],{},[1201,2846,2847,2849],{},[1149,2848,2227],{},[1230,2850,1525],{},[1153,2852,2762],{"encoding":1155},": rozptyl není stálý (heteroskedasticita). P-hodnota 0,21 je nad 0,05, ",[1115,2855,2857],{"className":2856},[1137],[1139,2858,2859],{"xmlns":1141},[1143,2860,2861,2869],{},[1146,2862,2863],{},[1201,2864,2865,2867],{},[1149,2866,2227],{},[1230,2868,1597],{},[1153,2870,2743],{"encoding":1155},[2035,2872,2874],{"className":2037,"code":2873,"language":71,"meta":2039,"style":2039},"shapiro.test(residuals(model))\n",[1332,2875,2876],{"__ignoreMap":2039},[1115,2877,2878,2881,2883,2885,2887,2889],{"class":2044,"line":10},[1115,2879,2880],{"class":2055},"shapiro.test",[1115,2882,1199],{"class":2059},[1115,2884,2340],{"class":2055},[1115,2886,1199],{"class":2059},[1115,2888,786],{"class":2047},[1115,2890,2546],{"class":2059},[2035,2892,2895],{"className":2893,"code":2894,"language":2169,"meta":2039},[2167]," Shapiro-Wilk normality test\n\ndata: residuals(model)\nW = 0.94818, p-value = 0.7255\n",[1332,2896,2894],{"__ignoreMap":2039},[1110,2898,2899,2900,2917],{},"Shapiro–Wilkův test má ",[1115,2901,2903],{"className":2902},[1137],[1139,2904,2905],{"xmlns":1141},[1143,2906,2907,2915],{},[1146,2908,2909],{},[1201,2910,2911,2913],{},[1149,2912,2227],{},[1230,2914,1597],{},[1153,2916,2743],{"encoding":1155},": rezidua pocházejí z normálního rozdělení. P-hodnota 0,73 opět nevede k zamítnutí — všechny tři předpoklady model splňuje.",[1110,2919,2920],{},[1864,2921],{"alt":2922,"className":2923,"src":2924},"mask-ra-diagnostika-rezidui",[1387,1868],"\u002Fwiki-assets\u002Fmask-ra-diagnostika-rezidui.png",[1110,2926,2927],{},"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.",[1103,2929,2933,2941,2972,3007,3074],{"className":2930,"dataCallout":2932},[1106,2931],"callout-example","example",[1110,2934,2936,2940],{"className":2935},[1113],[1115,2937],{"className":2938,"ariaHidden":1121},[1118,2939,1120],"i-lucide:flask-conical","Příklad: Regresní přímka",[1110,2942,2943,2944,2957,2958,2971],{},"V souboru s údaji o hodnotě produkce (v milionech Kč, proměnná ",[1115,2945,2947],{"className":2946},[1137],[1139,2948,2949],{"xmlns":1141},[1143,2950,2951,2955],{},[1146,2952,2953],{},[1149,2954,1151],{},[1153,2956,1151],{"encoding":1155},") a výši investic (ve stovkách tisíc Kč, proměnná ",[1115,2959,2961],{"className":2960},[1137],[1139,2962,2963],{"xmlns":1141},[1143,2964,2965,2969],{},[1146,2966,2967],{},[1149,2968,1168],{},[1153,2970,1168],{"encoding":1155},") 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.",[1110,2973,2974,2975,1236],{},"Výsledek: ",[1115,2976,2978],{"className":2977},[1137],[1139,2979,2980],{"xmlns":1141},[1143,2981,2982,3004],{},[1146,2983,2984,2990,2992,2995,2997,3000,3002],{},[1214,2985,2986,2988],{"accent":1121},[1149,2987,1151],{},[1193,2989,1220],{},[1193,2991,1281],{},[1230,2993,2994],{},"32,74",[1193,2996,1924],{},[1230,2998,2999],{},"2,15",[2201,3001,2203],{},[1149,3003,1168],{},[1153,3005,3006],{"encoding":1155},"\\hat y = 32{,}74 + 2{,}15\\,x",[1110,3008,1970,3009,3031,3032,3073],{},[1115,3010,3012],{"className":3011},[1137],[1139,3013,3014],{"xmlns":1141},[1143,3015,3016,3028],{},[1146,3017,3018,3024,3026],{},[1201,3019,3020,3022],{},[1149,3021,1675],{},[1230,3023,1525],{},[1193,3025,1281],{},[1230,3027,2999],{},[1153,3029,3030],{"encoding":1155},"b_1=2{,}15"," říká, že se zvýšením investic o 100 000 Kč vzroste produkce v průměru o ",[1115,3033,3035],{"className":3034},[1137],[1139,3036,3037],{"xmlns":1141},[1143,3038,3039,3070],{},[1146,3040,3041,3043,3046,3048,3050,3053,3055,3057,3059,3061,3063,3066,3068],{},[1230,3042,2999],{},[1193,3044,3045],{},"⋅",[1230,3047,1525],{},[2201,3049,2203],{},[1230,3051,3052],{},"000",[2201,3054,2203],{},[1230,3056,3052],{},[1193,3058,1281],{},[1230,3060,1232],{},[2201,3062,2203],{},[1230,3064,3065],{},"150",[2201,3067,2203],{},[1230,3069,3052],{},[1153,3071,3072],{"encoding":1155},"2{,}15\\cdot 1\\,000\\,000=2\\,150\\,000"," Kč.",[1110,3075,3076,3077,3096,3097,3146,3147,1335],{},"Dosazením libovolné hodnoty investic do empirické regresní funkce dostaneme predikci produkce, například pro třináctou firmu s investicemi ",[1115,3078,3080],{"className":3079},[1137],[1139,3081,3082],{"xmlns":1141},[1143,3083,3084,3093],{},[1146,3085,3086,3088,3090],{},[1149,3087,1168],{},[1193,3089,1281],{},[1230,3091,3092],{},"34",[1153,3094,3095],{"encoding":1155},"x=34",": ",[1115,3098,3100],{"className":3099},[1137],[1139,3101,3102],{"xmlns":1141},[1143,3103,3104,3143],{},[1146,3105,3106,3117,3119,3125,3127,3133,3135,3137,3140],{},[1201,3107,3108,3114],{},[1214,3109,3110,3112],{"accent":1121},[1149,3111,1151],{},[1193,3113,1220],{},[1230,3115,3116],{},"13",[1193,3118,1281],{},[1201,3120,3121,3123],{},[1149,3122,1675],{},[1230,3124,1597],{},[1193,3126,1924],{},[1201,3128,3129,3131],{},[1149,3130,1675],{},[1230,3132,1525],{},[1193,3134,3045],{},[1230,3136,3092],{},[1193,3138,3139],{},"≐",[1230,3141,3142],{},"105,81",[1153,3144,3145],{"encoding":1155},"\\hat y_{13} = b_0 + b_1\\cdot 34 \\doteq 105{,}81"," milionu Kč (se zaokrouhlenými koeficienty ",[1115,3148,3150],{"className":3149},[1137],[1139,3151,3152],{"xmlns":1141},[1143,3153,3154,3171],{},[1146,3155,3156,3158,3160,3162,3164,3166,3168],{},[1230,3157,2994],{},[1193,3159,1924],{},[1230,3161,2999],{},[1193,3163,3045],{},[1230,3165,3092],{},[1193,3167,3139],{},[1230,3169,3170],{},"105,8",[1153,3172,3173],{"encoding":1155},"32{,}74 + 2{,}15\\cdot 34 \\doteq 105{,}8",[1377,3175,3177],{"id":3176},"nelineární-a-vyšší-řády-regresních-funkcí","Nelineární a vyšší řády regresních funkcí",[1110,3179,3180,3181,3184,3185,3252,3253,3271,3272,3289],{},"Když přímka závislost nevystihuje, nabízí se další ",[1130,3182,3183],{},"lineární funkce"," — tedy funkce lineární ve svých parametrech, zapsatelné ve tvaru ",[1115,3186,3188],{"className":3187},[1137],[1139,3189,3190],{"xmlns":1141},[1143,3191,3192,3249],{},[1146,3193,3194,3196,3198,3204,3206,3212,3218,3220,3222,3224,3226,3229,3231,3237,3243,3245,3247],{},[1149,3195,1577],{},[1193,3197,1281],{},[1201,3199,3200,3202],{},[1149,3201,1594],{},[1230,3203,1597],{},[1193,3205,1924],{},[1201,3207,3208,3210],{},[1149,3209,1594],{},[1230,3211,1525],{},[1201,3213,3214,3216],{},[1149,3215,1582],{},[1230,3217,1525],{},[1193,3219,1199],{"stretchy":1198},[1149,3221,1168],{},[1193,3223,1228],{"stretchy":1198},[1193,3225,1924],{},[1193,3227,3228],{},"⋯",[1193,3230,1924],{},[1201,3232,3233,3235],{},[1149,3234,1594],{},[1149,3236,1110],{},[1201,3238,3239,3241],{},[1149,3240,1582],{},[1149,3242,1110],{},[1193,3244,1199],{"stretchy":1198},[1149,3246,1168],{},[1193,3248,1228],{"stretchy":1198},[1153,3250,3251],{"encoding":1155},"\\eta=\\beta_0+\\beta_1 f_1(x)+\\dots+\\beta_p f_p(x)"," se známými funkcemi ",[1115,3254,3256],{"className":3255},[1137],[1139,3257,3258],{"xmlns":1141},[1143,3259,3260,3268],{},[1146,3261,3262],{},[1201,3263,3264,3266],{},[1149,3265,1582],{},[1149,3267,1207],{},[1153,3269,3270],{"encoding":1155},"f_i"," a neznámými parametry ",[1115,3273,3275],{"className":3274},[1137],[1139,3276,3277],{"xmlns":1141},[1143,3278,3279,3287],{},[1146,3280,3281],{},[1201,3282,3283,3285],{},[1149,3284,1594],{},[1149,3286,1207],{},[1153,3288,1641],{"encoding":1155},". I tyto parametry se odhadují metodou nejmenších čtverců, stejně jako u přímky:",[1115,3291,3293],{"className":3292},[1137],[1139,3294,3295],{"xmlns":1141,"display":1796},[1143,3296,3297,3612],{},[3298,3299,3303,3378,3492,3552],"mtable",{"rowspacing":3300,"columnalign":3301,"columnspacing":3302},"0.25em","right left","0em",[3304,3305,3306,3332],"mtr",{},[3307,3308,3309],"mtd",{},[3310,3311,3312],"mstyle",{"scriptlevel":1597,"displaystyle":1121},[1146,3313,3314,3329],{},[1146,3315,3316,3319,3326],{},[2201,3317,3318],{},"parabolick",[1214,3320,3321,3323],{"accent":1121},[2201,3322,1384],{},[1193,3324,3325],{},"ˊ",[2201,3327,3328],{}," regrese: ",[1936,3330],{"width":3331},"1em",[3307,3333,3334],{},[3310,3335,3336],{"scriptlevel":1597,"displaystyle":1121},[1146,3337,3338,3340,3346,3348,3354,3356,3362,3364,3366,3372],{},[1146,3339],{},[1214,3341,3342,3344],{"accent":1121},[1149,3343,1151],{},[1193,3345,1220],{},[1193,3347,1281],{},[1201,3349,3350,3352],{},[1149,3351,1675],{},[1230,3353,1597],{},[1193,3355,1924],{},[1201,3357,3358,3360],{},[1149,3359,1675],{},[1230,3361,1525],{},[1149,3363,1168],{},[1193,3365,1924],{},[1201,3367,3368,3370],{},[1149,3369,1675],{},[1230,3371,1232],{},[1224,3373,3374,3376],{},[1149,3375,1168],{},[1230,3377,1232],{},[3304,3379,3380,3428],{},[3307,3381,3382],{},[3310,3383,3384],{"scriptlevel":1597,"displaystyle":1121},[1146,3385,3386,3426],{},[1146,3387,3388,3391,3397,3400,3404,3407,3413,3416,3423],{},[2201,3389,3390],{},"polynomick",[1214,3392,3393,3395],{"accent":1121},[2201,3394,1384],{},[1193,3396,3325],{},[2201,3398,3399],{}," regrese ",[3310,3401,3402],{"scriptlevel":1597,"displaystyle":1198},[1149,3403,1110],{},[2201,3405,3406],{},"-t",[1214,3408,3409,3411],{"accent":1121},[2201,3410,1754],{},[1193,3412,3325],{},[2201,3414,3415],{},"ho stupn",[1214,3417,3418,3420],{"accent":1121},[2201,3419,1754],{},[1193,3421,3422],{},"ˇ",[2201,3424,3425],{},": ",[1936,3427],{"width":3331},[3307,3429,3430],{},[3310,3431,3432],{"scriptlevel":1597,"displaystyle":1121},[1146,3433,3434,3436,3442,3444,3450,3452,3458,3460,3462,3468,3474,3476,3478,3480,3486],{},[1146,3435],{},[1214,3437,3438,3440],{"accent":1121},[1149,3439,1151],{},[1193,3441,1220],{},[1193,3443,1281],{},[1201,3445,3446,3448],{},[1149,3447,1675],{},[1230,3449,1597],{},[1193,3451,1924],{},[1201,3453,3454,3456],{},[1149,3455,1675],{},[1230,3457,1525],{},[1149,3459,1168],{},[1193,3461,1924],{},[1201,3463,3464,3466],{},[1149,3465,1675],{},[1230,3467,1232],{},[1224,3469,3470,3472],{},[1149,3471,1168],{},[1230,3473,1232],{},[1193,3475,1924],{},[1193,3477,3228],{},[1193,3479,1924],{},[1201,3481,3482,3484],{},[1149,3483,1675],{},[1149,3485,1110],{},[1224,3487,3488,3490],{},[1149,3489,1168],{},[1149,3491,1110],{},[3304,3493,3494,3515],{},[3307,3495,3496],{},[3310,3497,3498],{"scriptlevel":1597,"displaystyle":1121},[1146,3499,3500,3513],{},[1146,3501,3502,3505,3511],{},[2201,3503,3504],{},"hyperbolick",[1214,3506,3507,3509],{"accent":1121},[2201,3508,1384],{},[1193,3510,3325],{},[2201,3512,3328],{},[1936,3514],{"width":3331},[3307,3516,3517],{},[3310,3518,3519],{"scriptlevel":1597,"displaystyle":1121},[1146,3520,3521,3523,3529,3531,3537,3539,3545],{},[1146,3522],{},[1214,3524,3525,3527],{"accent":1121},[1149,3526,1151],{},[1193,3528,1220],{},[1193,3530,1281],{},[1201,3532,3533,3535],{},[1149,3534,1675],{},[1230,3536,1597],{},[1193,3538,1924],{},[1201,3540,3541,3543],{},[1149,3542,1675],{},[1230,3544,1525],{},[3546,3547,3548,3550],"mfrac",{},[1230,3549,1525],{},[1149,3551,1168],{},[3304,3553,3554,3575],{},[3307,3555,3556],{},[3310,3557,3558],{"scriptlevel":1597,"displaystyle":1121},[1146,3559,3560,3573],{},[1146,3561,3562,3565,3571],{},[2201,3563,3564],{},"logaritmick",[1214,3566,3567,3569],{"accent":1121},[2201,3568,1384],{},[1193,3570,3325],{},[2201,3572,3328],{},[1936,3574],{"width":3331},[3307,3576,3577],{},[3310,3578,3579],{"scriptlevel":1597,"displaystyle":1121},[1146,3580,3581,3583,3589,3591,3597,3599,3605,3608,3610],{},[1146,3582],{},[1214,3584,3585,3587],{"accent":1121},[1149,3586,1151],{},[1193,3588,1220],{},[1193,3590,1281],{},[1201,3592,3593,3595],{},[1149,3594,1675],{},[1230,3596,1597],{},[1193,3598,1924],{},[1201,3600,3601,3603],{},[1149,3602,1675],{},[1230,3604,1525],{},[1149,3606,3607],{},"ln",[1193,3609,1851],{},[1149,3611,1168],{},[1153,3613,3614],{"encoding":1155},"\\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}",[1110,3616,3617,3618,3621,3622,3668,3669,1902],{},"Naproti tomu ",[1130,3619,3620],{},"nelineární funkce"," nelze do tvaru ",[1115,3623,3625],{"className":3624},[1137],[1139,3626,3627],{"xmlns":1141},[1143,3628,3629,3665],{},[1146,3630,3631,3633,3635,3641,3643,3649,3655,3657,3659,3661,3663],{},[1149,3632,1577],{},[1193,3634,1281],{},[1201,3636,3637,3639],{},[1149,3638,1594],{},[1230,3640,1597],{},[1193,3642,1924],{},[1201,3644,3645,3647],{},[1149,3646,1594],{},[1230,3648,1525],{},[1201,3650,3651,3653],{},[1149,3652,1582],{},[1230,3654,1525],{},[1193,3656,1199],{"stretchy":1198},[1149,3658,1168],{},[1193,3660,1228],{"stretchy":1198},[1193,3662,1924],{},[1193,3664,1530],{},[1153,3666,3667],{"encoding":1155},"\\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 ",[1130,3670,3671],{},"exponenciální regrese",[1115,3673,3675],{"className":3674},[1137],[1139,3676,3677],{"xmlns":1141,"display":1796},[1143,3678,3679,3712],{},[1146,3680,3681,3687,3689,3695,3697,3710],{},[1214,3682,3683,3685],{"accent":1121},[1149,3684,1151],{},[1193,3686,1220],{},[1193,3688,1281],{},[1201,3690,3691,3693],{},[1149,3692,1675],{},[1230,3694,1597],{},[1193,3696,3045],{},[3698,3699,3700,3702,3704],"msubsup",{},[1149,3701,1675],{},[1230,3703,1525],{},[1146,3705,3706,3708],{},[2201,3707,2203],{},[1149,3709,1168],{},[1149,3711,1236],{"mathvariant":1854},[1153,3713,3714],{"encoding":1155},"\\hat y = b_0 \\cdot b_1^{\\,x}.",[1110,3716,3717],{},[1864,3718],{"alt":3719,"className":3720,"src":3721},"mask-ra-nelinearni-krivky",[1387,1868],"\u002Fwiki-assets\u002Fmask-ra-nelinearni-krivky.png",[2019,3723,3725],{"id":3724},"v-r-parabolická-regrese","V R — parabolická regrese",[1110,3727,3728,3729,1902],{},"Na ročních ziscích firmy (šest let) se parabolická regrese odhadne přidáním kvadratického členu ",[1332,3730,3731],{},"I(x^2)",[2035,3733,3735],{"className":2037,"code":3734,"language":71,"meta":2039,"style":2039},"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",[1332,3736,3737,3772,3812,3846],{"__ignoreMap":2039},[1115,3738,3739,3742,3744,3746,3748,3750,3752,3754,3756,3758,3760,3762,3764,3766,3768,3770],{"class":2044,"line":10},[1115,3740,3741],{"class":2047},"rok",[1115,3743,2052],{"class":2051},[1115,3745,2056],{"class":2055},[1115,3747,1199],{"class":2059},[1115,3749,1525],{"class":2062},[1115,3751,1503],{"class":2051},[1115,3753,2067],{"class":2062},[1115,3755,1503],{"class":2051},[1115,3757,2072],{"class":2062},[1115,3759,1503],{"class":2051},[1115,3761,2077],{"class":2062},[1115,3763,1503],{"class":2051},[1115,3765,2082],{"class":2062},[1115,3767,1503],{"class":2051},[1115,3769,2087],{"class":2062},[1115,3771,2090],{"class":2059},[1115,3773,3774,3776,3778,3780,3782,3785,3787,3790,3792,3795,3797,3800,3802,3805,3807,3810],{"class":2044,"line":27},[1115,3775,1088],{"class":2047},[1115,3777,2052],{"class":2051},[1115,3779,2056],{"class":2055},[1115,3781,1199],{"class":2059},[1115,3783,3784],{"class":2062},"112",[1115,3786,1503],{"class":2051},[1115,3788,3789],{"class":2062}," 149",[1115,3791,1503],{"class":2051},[1115,3793,3794],{"class":2062}," 238",[1115,3796,1503],{"class":2051},[1115,3798,3799],{"class":2062}," 354",[1115,3801,1503],{"class":2051},[1115,3803,3804],{"class":2062}," 580",[1115,3806,1503],{"class":2051},[1115,3808,3809],{"class":2062}," 867",[1115,3811,2090],{"class":2059},[1115,3813,3814,3817,3819,3821,3823,3825,3827,3830,3833,3836,3838,3840,3842,3844],{"class":2044,"line":148},[1115,3815,3816],{"class":2047},"model_parabola",[1115,3818,2052],{"class":2051},[1115,3820,2140],{"class":2055},[1115,3822,1199],{"class":2059},[1115,3824,1088],{"class":2047},[1115,3826,2147],{"class":2051},[1115,3828,3829],{"class":2047}," rok",[1115,3831,3832],{"class":2051}," +",[1115,3834,3835],{"class":2055}," I",[1115,3837,1199],{"class":2059},[1115,3839,3741],{"class":2047},[1115,3841,1220],{"class":2051},[1115,3843,1232],{"class":2062},[1115,3845,2546],{"class":2059},[1115,3847,3848,3850,3852,3854],{"class":2044,"line":111},[1115,3849,2157],{"class":2055},[1115,3851,1199],{"class":2059},[1115,3853,3816],{"class":2047},[1115,3855,2090],{"class":2059},[2035,3857,3860],{"className":3858,"code":3859,"language":2169,"meta":2039},[2167],"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",[1332,3861,3859],{"__ignoreMap":2039},[1110,3863,3864,3865,3910],{},"Odhadnutá parabola ",[1115,3866,3868],{"className":3867},[1137],[1139,3869,3870],{"xmlns":1141},[1143,3871,3872,3907],{},[1146,3873,3874,3880,3882,3885,3887,3890,3892,3894,3896,3899,3901],{},[1214,3875,3876,3878],{"accent":1121},[1149,3877,1151],{},[1193,3879,1220],{},[1193,3881,1281],{},[1230,3883,3884],{},"164,6",[1193,3886,1210],{},[1230,3888,3889],{},"76,6",[2201,3891,2203],{},[1149,3893,1168],{},[1193,3895,1924],{},[1230,3897,3898],{},"32,1",[2201,3900,2203],{},[1224,3902,3903,3905],{},[1149,3904,1168],{},[1230,3906,1232],{},[1153,3908,3909],{"encoding":1155},"\\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.",[2019,3912,3914],{"id":3913},"v-r-exponenciální-regrese","V R — exponenciální regrese",[1110,3916,3917,3918,3920],{},"Nelineární funkce se v R odhadují funkcí ",[1332,3919,1351],{}," ze stejnojmenného balíčku. Bez zadaných počátečních hodnot R upozorní, že parametry nastavil na 1, a odhad dopočítá iteračně:",[2035,3922,3924],{"className":2037,"code":3923,"language":71,"meta":2039,"style":2039},"library(nls2)\nmodel_exp \u003C- nls2(zisk ~ b1 * exp(b2 * rok))\nsummary(model_exp)\n",[1332,3925,3926,3936,3972],{"__ignoreMap":2039},[1115,3927,3928,3930,3932,3934],{"class":2044,"line":10},[1115,3929,2698],{"class":2051},[1115,3931,1199],{"class":2059},[1115,3933,1334],{"class":2047},[1115,3935,2090],{"class":2059},[1115,3937,3938,3941,3943,3946,3948,3950,3952,3955,3958,3961,3963,3966,3968,3970],{"class":2044,"line":27},[1115,3939,3940],{"class":2047},"model_exp",[1115,3942,2052],{"class":2051},[1115,3944,3945],{"class":2055}," nls2",[1115,3947,1199],{"class":2059},[1115,3949,1088],{"class":2047},[1115,3951,2147],{"class":2051},[1115,3953,3954],{"class":2047}," b1",[1115,3956,3957],{"class":2051}," *",[1115,3959,3960],{"class":2055}," exp",[1115,3962,1199],{"class":2059},[1115,3964,3965],{"class":2047},"b2",[1115,3967,3957],{"class":2051},[1115,3969,3829],{"class":2047},[1115,3971,2546],{"class":2059},[1115,3973,3974,3976,3978,3980],{"class":2044,"line":148},[1115,3975,2157],{"class":2055},[1115,3977,1199],{"class":2059},[1115,3979,3940],{"class":2047},[1115,3981,2090],{"class":2059},[2035,3983,3986],{"className":3984,"code":3985,"language":2169,"meta":2039},[2167],"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",[1332,3987,3985],{"__ignoreMap":2039},[1110,3989,3990,3991,1902],{},"Stejnou křivku lze zapsat i v mocninném tvaru ",[1115,3992,3994],{"className":3993},[1137],[1139,3995,3996],{"xmlns":1141},[1143,3997,3998,4024],{},[1146,3999,4000,4006,4008,4014,4016],{},[1214,4001,4002,4004],{"accent":1121},[1149,4003,1151],{},[1193,4005,1220],{},[1193,4007,1281],{},[1201,4009,4010,4012],{},[1149,4011,1675],{},[1230,4013,1525],{},[1193,4015,3045],{},[3698,4017,4018,4020,4022],{},[1149,4019,1675],{},[1230,4021,1232],{},[1149,4023,1168],{},[1153,4025,4026],{"encoding":1155},"\\hat y=b_1\\cdot b_2^{x}",[2035,4028,4030],{"className":2037,"code":4029,"language":71,"meta":2039,"style":2039},"model_pow \u003C- nls2(zisk ~ b1 * (b2^rok))\nsummary(model_pow)\n",[1332,4031,4032,4062],{"__ignoreMap":2039},[1115,4033,4034,4037,4039,4041,4043,4045,4047,4049,4051,4054,4056,4058,4060],{"class":2044,"line":10},[1115,4035,4036],{"class":2047},"model_pow",[1115,4038,2052],{"class":2051},[1115,4040,3945],{"class":2055},[1115,4042,1199],{"class":2059},[1115,4044,1088],{"class":2047},[1115,4046,2147],{"class":2051},[1115,4048,3954],{"class":2047},[1115,4050,3957],{"class":2051},[1115,4052,4053],{"class":2059}," (",[1115,4055,3965],{"class":2047},[1115,4057,1220],{"class":2051},[1115,4059,3741],{"class":2047},[1115,4061,2546],{"class":2059},[1115,4063,4064,4066,4068,4070],{"class":2044,"line":27},[1115,4065,2157],{"class":2055},[1115,4067,1199],{"class":2059},[1115,4069,4036],{"class":2047},[1115,4071,2090],{"class":2059},[2035,4073,4076],{"className":4074,"code":4075,"language":2169,"meta":2039},[2167],"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",[1332,4077,4075],{"__ignoreMap":2039},[1110,4079,4080,4081,4146,4147,4172],{},"Obě varianty popisují stejnou křivku (",[1115,4082,4084],{"className":4083},[1137],[1139,4085,4086],{"xmlns":1141},[1143,4087,4088,4143],{},[1146,4089,4090,4107,4109],{},[3698,4091,4092,4094,4096],{},[1149,4093,1675],{},[1230,4095,1232],{},[1146,4097,4098,4101],{},[2201,4099,4100],{},"mocninn",[1214,4102,4103,4105],{"accent":1121},[2201,4104,1151],{},[1193,4106,3325],{},[1193,4108,1281],{},[1224,4110,4111,4113],{},[1149,4112,1754],{},[1146,4114,4115,4117],{},[2201,4116,2203],{},[3698,4118,4119,4121,4123],{},[1149,4120,1675],{},[1230,4122,1232],{},[1146,4124,4125,4128,4134,4136],{},[2201,4126,4127],{},"exponenci",[1214,4129,4130,4132],{"accent":1121},[2201,4131,1384],{},[1193,4133,3325],{},[2201,4135,3607],{},[1214,4137,4138,4141],{"accent":1121},[2201,4139,4140],{},"ı",[1193,4142,3325],{},[1153,4144,4145],{"encoding":1155},"b_2^{\\text{mocninný}} = e^{\\,b_2^{\\text{exponenciální}}}",", zde ",[1115,4148,4150],{"className":4149},[1137],[1139,4151,4152],{"xmlns":1141},[1143,4153,4154,4169],{},[1146,4155,4156,4163,4166],{},[1224,4157,4158,4160],{},[1149,4159,1754],{},[1230,4161,4162],{},"0,4316",[1193,4164,4165],{},"≈",[1230,4167,4168],{},"1,540",[1153,4170,4171],{"encoding":1155},"e^{0{,}4316}\\approx 1{,}540",") a mají totožnou reziduální chybu — je to jen otázka parametrizace.",[2019,4174,4176],{"id":4175},"v-r-hyperbolická-regrese","V R — hyperbolická regrese",[1110,4178,4179,4180,1902],{},"Hyperbolická regrese se odhadne jako obyčejná lineární regrese na transformované proměnné ",[1332,4181,4182],{},"I(1\u002Fx)",[2035,4184,4186],{"className":2037,"code":4185,"language":71,"meta":2039,"style":2039},"model_hyperbola \u003C- lm(tydenni_vydaje ~ I(1 \u002F pocet_clenu))\nsummary(model_hyperbola)\n",[1332,4187,4188,4216],{"__ignoreMap":2039},[1115,4189,4190,4193,4195,4197,4199,4201,4203,4205,4207,4209,4212,4214],{"class":2044,"line":10},[1115,4191,4192],{"class":2047},"model_hyperbola",[1115,4194,2052],{"class":2051},[1115,4196,2140],{"class":2055},[1115,4198,1199],{"class":2059},[1115,4200,2095],{"class":2047},[1115,4202,2147],{"class":2051},[1115,4204,3835],{"class":2055},[1115,4206,1199],{"class":2059},[1115,4208,1525],{"class":2062},[1115,4210,4211],{"class":2051}," \u002F",[1115,4213,2150],{"class":2047},[1115,4215,2546],{"class":2059},[1115,4217,4218,4220,4222,4224],{"class":2044,"line":27},[1115,4219,2157],{"class":2055},[1115,4221,1199],{"class":2059},[1115,4223,4192],{"class":2047},[1115,4225,2090],{"class":2059},[2035,4227,4230],{"className":4228,"code":4229,"language":2169,"meta":2039},[2167],"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",[1332,4231,4229],{"__ignoreMap":2039},[1110,4233,4234,4235,4269,4270,4291],{},"Model ",[1115,4236,4238],{"className":4237},[1137],[1139,4239,4240],{"xmlns":1141},[1143,4241,4242,4266],{},[1146,4243,4244,4250,4252,4255,4257],{},[1214,4245,4246,4248],{"accent":1121},[1149,4247,1151],{},[1193,4249,1220],{},[1193,4251,1281],{},[1230,4253,4254],{},"2180,7",[1193,4256,1210],{},[3310,4258,4259],{"scriptlevel":1597,"displaystyle":1121},[3546,4260,4261,4264],{},[1230,4262,4263],{},"1920,0",[1149,4265,1168],{},[1153,4267,4268],{"encoding":1155},"\\hat y = 2180{,}7 - \\dfrac{1920{,}0}{x}"," vysvětluje jen 76,3 % rozptylu — u těchto dat je hyperbola podstatně horší volbou než přímka (",[1115,4271,4273],{"className":4272},[1137],[1139,4274,4275],{"xmlns":1141},[1143,4276,4277,4289],{},[1146,4278,4279,4285,4287],{},[1224,4280,4281,4283],{},[1149,4282,1257],{},[1230,4284,1232],{},[1193,4286,1281],{},[1230,4288,2301],{},[1153,4290,2304],{"encoding":1155},"). Právě k takovému porovnání slouží index determinace: nízká hodnota signalizuje, že zvolený typ funkce k datům nesedí.",[1103,4293,4295,4302,4333,4382],{"className":4294,"dataCallout":2932},[1106,2931],[1110,4296,4298,4301],{"className":4297},[1113],[1115,4299],{"className":4300,"ariaHidden":1121},[1118,2939,1120],"Příklad: Parabolická regrese",[1110,4303,4304,4305,4318,4319,4332],{},"Prodejna počítačových her nechala prodavače absolvovat kurz prodejních dovedností. Při dvaceti měřeních sledovala, kolik zákazníků navštíví prodejnu během prodejní doby (proměnná ",[1115,4306,4308],{"className":4307},[1137],[1139,4309,4310],{"xmlns":1141},[1143,4311,4312,4316],{},[1146,4313,4314],{},[1149,4315,1168],{},[1153,4317,1168],{"encoding":1155},") a jaká je toho dne tržba v tisících Kč (proměnná ",[1115,4320,4322],{"className":4321},[1137],[1139,4323,4324],{"xmlns":1141},[1143,4325,4326,4330],{},[1146,4327,4328],{},[1149,4329,1151],{},[1153,4331,1151],{"encoding":1155},"). Zároveň chtěla zjistit, zda při rostoucím počtu zákazníků stačí stávající počet prodavačů.",[1110,4334,2974,4335,1236],{},[1115,4336,4338],{"className":4337},[1137],[1139,4339,4340],{"xmlns":1141},[1143,4341,4342,4379],{},[1146,4343,4344,4350,4352,4354,4357,4359,4362,4364,4366,4368,4371,4373],{},[1214,4345,4346,4348],{"accent":1121},[1149,4347,1151],{},[1193,4349,1220],{},[1193,4351,1281],{},[1193,4353,1210],{},[1230,4355,4356],{},"60,3",[1193,4358,1924],{},[1230,4360,4361],{},"4,55",[2201,4363,2203],{},[1149,4365,1168],{},[1193,4367,1210],{},[1230,4369,4370],{},"0,05",[2201,4372,2203],{},[1224,4374,4375,4377],{},[1149,4376,1168],{},[1230,4378,1232],{},[1153,4380,4381],{"encoding":1155},"\\hat y = -60{,}3 + 4{,}55\\,x - 0{,}05\\,x^2",[1110,4383,4384,4385,4403],{},"Záporný koeficient ",[1115,4386,4388],{"className":4387},[1137],[1139,4389,4390],{"xmlns":1141},[1143,4391,4392,4400],{},[1146,4393,4394],{},[1201,4395,4396,4398],{},[1149,4397,1675],{},[1230,4399,1232],{},[1153,4401,4402],{"encoding":1155},"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.",[1103,4405,4407,4414,4444,4489],{"className":4406,"dataCallout":2932},[1106,2931],[1110,4408,4410,4413],{"className":4409},[1113],[1115,4411],{"className":4412,"ariaHidden":1121},[1118,2939,1120],"Příklad: Hyperbolická regrese",[1110,4415,4416,4417,4430,4431,1335],{},"V podniku se podle interního účetnictví sledovala závislost vlastních nákladů na jednotku produkce v Kč (proměnná ",[1115,4418,4420],{"className":4419},[1137],[1139,4421,4422],{"xmlns":1141},[1143,4423,4424,4428],{},[1146,4425,4426],{},[1149,4427,1151],{},[1153,4429,1151],{"encoding":1155},") na objemu produkce v tisících kusů (proměnná ",[1115,4432,4434],{"className":4433},[1137],[1139,4435,4436],{"xmlns":1141},[1143,4437,4438,4442],{},[1146,4439,4440],{},[1149,4441,1168],{},[1153,4443,1168],{"encoding":1155},[1110,4445,2974,4446,1236],{},[1115,4447,4449],{"className":4448},[1137],[1139,4450,4451],{"xmlns":1141},[1143,4452,4453,4486],{},[1146,4454,4455,4461,4463,4465,4468,4470],{},[1214,4456,4457,4459],{"accent":1121},[1149,4458,1151],{},[1193,4460,1220],{},[1193,4462,1281],{},[1193,4464,1210],{},[1230,4466,4467],{},"96,78",[1193,4469,1924],{},[3310,4471,4472],{"scriptlevel":1597,"displaystyle":1121},[3546,4473,4474,4484],{},[1146,4475,4476,4479,4481],{},[1230,4477,4478],{},"250",[2201,4480,2203],{},[1230,4482,4483],{},"528,88",[1149,4485,1168],{},[1153,4487,4488],{"encoding":1155},"\\hat y = -96{,}78 + \\dfrac{250\\,528{,}88}{x}",[1110,4490,4491,4492,4509],{},"Záporná hodnota ",[1115,4493,4495],{"className":4494},[1137],[1139,4496,4497],{"xmlns":1141},[1143,4498,4499,4507],{},[1146,4500,4501],{},[1201,4502,4503,4505],{},[1149,4504,1675],{},[1230,4506,1525],{},[1153,4508,1988],{"encoding":1155}," v čitateli ukazuje klesající náklady na jednotku s rostoucím objemem produkce — typický projev úspor z rozsahu, který hyperbola dobře zachycuje.",[1377,4511,4513],{"id":4512},"kvalita-regresní-funkce-a-korelační-analýza","Kvalita regresní funkce a korelační analýza",[1110,4515,4516,4517,1902],{},"Kvalitu odhadnuté regresní funkce vyjadřuje ",[1130,4518,1242],{},[1115,4520,4522],{"className":4521},[1137],[1139,4523,4524],{"xmlns":1141,"display":1796},[1143,4525,4526,4595],{},[1146,4527,4528,4534,4536,4559,4561,4563,4565,4593],{},[1224,4529,4530,4532],{},[1149,4531,1257],{},[1230,4533,1232],{},[1193,4535,1281],{},[3546,4537,4538,4551],{},[3698,4539,4540,4543,4549],{},[1149,4541,4542],{},"s",[1214,4544,4545,4547],{"accent":1121},[1149,4546,1151],{},[1193,4548,1220],{},[1230,4550,1232],{},[3698,4552,4553,4555,4557],{},[1149,4554,4542],{},[1149,4556,1151],{},[1230,4558,1232],{},[1193,4560,1281],{},[1230,4562,1525],{},[1193,4564,1210],{},[3546,4566,4567,4585],{},[3698,4568,4569,4571,4583],{},[1149,4570,4542],{},[1146,4572,4573,4575,4577],{},[1149,4574,1151],{},[1193,4576,1210],{},[1214,4578,4579,4581],{"accent":1121},[1149,4580,1151],{},[1193,4582,1220],{},[1230,4584,1232],{},[3698,4586,4587,4589,4591],{},[1149,4588,4542],{},[1149,4590,1151],{},[1230,4592,1232],{},[1149,4594,1236],{"mathvariant":1854},[1153,4596,4597],{"encoding":1155},"R^2 = \\frac{s^2_{\\hat y}}{s^2_y} = 1 - \\frac{s^2_{y-\\hat y}}{s^2_y}.",[1110,4599,4600,4601,4618,4619,4632],{},"Čím blíž je ",[1115,4602,4604],{"className":4603},[1137],[1139,4605,4606],{"xmlns":1141},[1143,4607,4608,4616],{},[1146,4609,4610],{},[1224,4611,4612,4614],{},[1149,4613,1257],{},[1230,4615,1232],{},[1153,4617,1262],{"encoding":1155}," k 1, tím silnější je závislost; v procentech udává, jakou část rozptylu závisle proměnné ",[1115,4620,4622],{"className":4621},[1137],[1139,4623,4624],{"xmlns":1141},[1143,4625,4626,4630],{},[1146,4627,4628],{},[1149,4629,1151],{},[1153,4631,1151],{"encoding":1155}," se podařilo vysvětlit zvolenou regresní funkcí. Nízký index determinace může signalizovat špatně zvolený typ regresní funkce, ne nutně absenci závislosti.",[1110,4634,4635,4636,1243,4638,4661,4662,1902],{},"Obecnou mírou těsnosti závislosti — platnou pro libovolný typ regresní funkce — je ",[1130,4637,1266],{},[1115,4639,4641],{"className":4640},[1137],[1139,4642,4643],{"xmlns":1141},[1143,4644,4645,4659],{},[1146,4646,4647,4649,4651],{},[1149,4648,1278],{},[1193,4650,1281],{},[1283,4652,4653],{},[1224,4654,4655,4657],{},[1149,4656,1257],{},[1230,4658,1232],{},[1153,4660,1293],{"encoding":1155},". Je-li zvolenou funkcí regresní přímka, index korelace je roven (až na znaménko) ",[1130,4663,1297],{},[1115,4665,4667],{"className":4666},[1137],[1139,4668,4669],{"xmlns":1141,"display":1796},[1143,4670,4671,4721],{},[1146,4672,4673,4683,4685,4719],{},[1201,4674,4675,4677],{},[1149,4676,71],{},[1146,4678,4679,4681],{},[1149,4680,1168],{},[1149,4682,1151],{},[1193,4684,1281],{},[3546,4686,4687,4697],{},[1201,4688,4689,4691],{},[1149,4690,4542],{},[1146,4692,4693,4695],{},[1149,4694,1168],{},[1149,4696,1151],{},[1283,4698,4699],{},[1146,4700,4701,4709,4711],{},[3698,4702,4703,4705,4707],{},[1149,4704,4542],{},[1149,4706,1168],{},[1230,4708,1232],{},[1193,4710,3045],{},[3698,4712,4713,4715,4717],{},[1149,4714,4542],{},[1149,4716,1151],{},[1230,4718,1232],{},[1149,4720,1236],{"mathvariant":1854},[1153,4722,4723],{"encoding":1155},"r_{xy} = \\frac{s_{xy}}{\\sqrt{s^2_x\\cdot s^2_y}}.",[1110,4725,4726,4727,4743,4744,4760],{},"Koeficient korelace nabývá hodnot od ",[1115,4728,4730],{"className":4729},[1137],[1139,4731,4732],{"xmlns":1141},[1143,4733,4734,4740],{},[1146,4735,4736,4738],{},[1193,4737,1210],{},[1230,4739,1525],{},[1153,4741,4742],{"encoding":1155},"-1"," do ",[1115,4745,4747],{"className":4746},[1137],[1139,4748,4749],{"xmlns":1141},[1143,4750,4751,4757],{},[1146,4752,4753,4755],{},[1193,4754,1924],{},[1230,4756,1525],{},[1153,4758,4759],{"encoding":1155},"+1",": znaménko určuje typ závislosti (pozitivní, nebo negativní), absolutní hodnota její sílu — čím blíž k 0, tím je závislost slabší.",[1110,4762,4763],{},[1864,4764],{"alt":4765,"className":4766,"src":4767},"mask-ra-korelace-sila",[1387,1868],"\u002Fwiki-assets\u002Fmask-ra-korelace-sila.png",[1110,4769,4770,4771,4784,4785,4803,4804,1405,4817,4830],{},"S rostoucí absolutní hodnotou ",[1115,4772,4774],{"className":4773},[1137],[1139,4775,4776],{"xmlns":1141},[1143,4777,4778,4782],{},[1146,4779,4780],{},[1149,4781,71],{},[1153,4783,71],{"encoding":1155}," se body v rozptylovém grafu víc blíží přímce; kolem ",[1115,4786,4788],{"className":4787},[1137],[1139,4789,4790],{"xmlns":1141},[1143,4791,4792,4800],{},[1146,4793,4794,4796,4798],{},[1149,4795,71],{},[1193,4797,4165],{},[1230,4799,1597],{},[1153,4801,4802],{"encoding":1155},"r\\approx 0"," je mezi ",[1115,4805,4807],{"className":4806},[1137],[1139,4808,4809],{"xmlns":1141},[1143,4810,4811,4815],{},[1146,4812,4813],{},[1149,4814,1168],{},[1153,4816,1168],{"encoding":1155},[1115,4818,4820],{"className":4819},[1137],[1139,4821,4822],{"xmlns":1141},[1143,4823,4824,4828],{},[1146,4825,4826],{},[1149,4827,1151],{},[1153,4829,1151],{"encoding":1155}," patrná jen náhodná rozptýlenost bez lineárního trendu.",[2019,4832,2022],{"id":4833},"v-r-1",[2035,4835,4837],{"className":2037,"code":4836,"language":71,"meta":2039,"style":2039},"cor(pocet_clenu, tydenni_vydaje)\n",[1332,4838,4839],{"__ignoreMap":2039},[1115,4840,4841,4844,4846,4848,4850,4853],{"class":2044,"line":10},[1115,4842,4843],{"class":2055},"cor",[1115,4845,1199],{"class":2059},[1115,4847,2048],{"class":2047},[1115,4849,1503],{"class":2051},[1115,4851,4852],{"class":2047}," tydenni_vydaje",[1115,4854,2090],{"class":2059},[2035,4856,4859],{"className":4857,"code":4858,"language":2169,"meta":2039},[2167],"[1] 0.9997441\n",[1332,4860,4858],{"__ignoreMap":2039},[1110,4862,4863,4864,4890],{},"Hodnota 0,9997 odpovídá ",[1115,4865,4867],{"className":4866},[1137],[1139,4868,4869],{"xmlns":1141},[1143,4870,4871,4887],{},[1146,4872,4873,4881,4883],{},[1283,4874,4875],{},[1224,4876,4877,4879],{},[1149,4878,1257],{},[1230,4880,1232],{},[1193,4882,1281],{},[1283,4884,4885],{},[1230,4886,2301],{},[1153,4888,4889],{"encoding":1155},"\\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.",[1103,4892,4894,4901,4904],{"className":4893,"dataCallout":2932},[1106,2931],[1110,4895,4897,4900],{"className":4896},[1113],[1115,4898],{"className":4899,"ariaHidden":1121},[1118,2939,1120],"Příklad: Koeficient korelace",[1110,4902,4903],{},"Pro stejná data o hodnotě produkce a výši investic dvanácti firem jako u regresní přímky byl spočten koeficient korelace mezi oběma proměnnými.",[1110,4905,2974,4906,4933],{},[1115,4907,4909],{"className":4908},[1137],[1139,4910,4911],{"xmlns":1141},[1143,4912,4913,4930],{},[1146,4914,4915,4925,4927],{},[1201,4916,4917,4919],{},[1149,4918,71],{},[1146,4920,4921,4923],{},[1149,4922,1168],{},[1149,4924,1151],{},[1193,4926,1281],{},[1230,4928,4929],{},"0,739",[1153,4931,4932],{"encoding":1155},"r_{xy} = 0{,}739"," — silná kladná závislost hodnoty produkce na výši investic.",[1377,4935,4937],{"id":4936},"vícenásobná-regrese-a-korelace","Vícenásobná regrese a korelace",[1110,4939,4940,4941,4954],{},"Pokud na závisle proměnnou ",[1115,4942,4944],{"className":4943},[1137],[1139,4945,4946],{"xmlns":1141},[1143,4947,4948,4952],{},[1146,4949,4950],{},[1149,4951,1151],{},[1153,4953,1151],{"encoding":1155}," působí víc vysvětlujících proměnných současně, analyzuje se zvlášť vliv každé z nich a výsledná regresní funkce se konstruuje jako součet jednoduchých regresních funkcí:",[1115,4956,4958],{"className":4957},[1137],[1139,4959,4960],{"xmlns":1141,"display":1796},[1143,4961,4962,5072],{},[1146,4963,4964,4966,4968,4974,4976,4982,4988,4990,4996,5002,5004,5006,5008,5014,5020,5022,5024,5030,5032,5038,5040,5046,5052,5054,5056,5058,5064,5070],{},[1149,4965,1577],{},[1193,4967,1281],{},[1201,4969,4970,4972],{},[1149,4971,1594],{},[1230,4973,1597],{},[1193,4975,1924],{},[1201,4977,4978,4980],{},[1149,4979,1594],{},[1230,4981,1525],{},[1201,4983,4984,4986],{},[1149,4985,1168],{},[1230,4987,1525],{},[1193,4989,1924],{},[1201,4991,4992,4994],{},[1149,4993,1594],{},[1230,4995,1232],{},[1201,4997,4998,5000],{},[1149,4999,1168],{},[1230,5001,1232],{},[1193,5003,1924],{},[1193,5005,3228],{},[1193,5007,1924],{},[1201,5009,5010,5012],{},[1149,5011,1594],{},[1149,5013,1110],{},[1201,5015,5016,5018],{},[1149,5017,1168],{},[1149,5019,1110],{},[1193,5021,1503],{"separator":1121},[1936,5023],{"width":1938},[1214,5025,5026,5028],{"accent":1121},[1149,5027,1151],{},[1193,5029,1220],{},[1193,5031,1281],{},[1201,5033,5034,5036],{},[1149,5035,1675],{},[1230,5037,1597],{},[1193,5039,1924],{},[1201,5041,5042,5044],{},[1149,5043,1675],{},[1230,5045,1525],{},[1201,5047,5048,5050],{},[1149,5049,1168],{},[1230,5051,1525],{},[1193,5053,1924],{},[1193,5055,3228],{},[1193,5057,1924],{},[1201,5059,5060,5062],{},[1149,5061,1675],{},[1149,5063,1110],{},[1201,5065,5066,5068],{},[1149,5067,1168],{},[1149,5069,1110],{},[1149,5071,1236],{"mathvariant":1854},[1153,5073,5074],{"encoding":1155},"\\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.",[2019,5076,5078],{"id":5077},"výběr-proměnných","Výběr proměnných",[1124,5080,5081,5087],{},[1127,5082,5083,5086],{},[1130,5084,5085],{},"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.",[1127,5088,5089,5092,5093,5096,5097,5100],{},[1130,5090,5091],{},"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 ",[1130,5094,5095],{},"forward"," proměnné postupně přidává, varianta ",[1130,5098,5099],{},"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.",[2019,5102,5104],{"id":5103},"postup-odhadu","Postup odhadu",[5106,5107,5108,5111,5114],"ol",{},[1127,5109,5110],{},"ověření předpokladů regresního modelu,",[1127,5112,5113],{},"samotný odhad parametrů,",[1127,5115,5116],{},"reziduální analýza výsledného modelu.",[1110,5118,5119,5120,5137,5138,3096,5140,5169,5170,5199,5200,5217],{},"Důležitost každého parametru ",[1115,5121,5123],{"className":5122},[1137],[1139,5124,5125],{"xmlns":1141},[1143,5126,5127,5135],{},[1146,5128,5129],{},[1201,5130,5131,5133],{},[1149,5132,1675],{},[1149,5134,1207],{},[1153,5136,1721],{"encoding":1155}," v modelu ověřuje ",[1130,5139,992],{},[1115,5141,5143],{"className":5142},[1137],[1139,5144,5145],{"xmlns":1141},[1143,5146,5147,5167],{},[1146,5148,5149,5155,5157,5163,5165],{},[1201,5150,5151,5153],{},[1149,5152,2227],{},[1230,5154,1597],{},[1193,5156,1902],{},[1201,5158,5159,5161],{},[1149,5160,1594],{},[1149,5162,1207],{},[1193,5164,1281],{},[1230,5166,1597],{},[1153,5168,2244],{"encoding":1155}," (proměnná je v modelu nevýznamná) proti ",[1115,5171,5173],{"className":5172},[1137],[1139,5174,5175],{"xmlns":1141},[1143,5176,5177,5197],{},[1146,5178,5179,5185,5187,5193,5195],{},[1201,5180,5181,5183],{},[1149,5182,2227],{},[1230,5184,1525],{},[1193,5186,1902],{},[1201,5188,5189,5191],{},[1149,5190,1594],{},[1149,5192,1207],{},[1193,5194,2271],{"mathvariant":1854},[1230,5196,1597],{},[1153,5198,2276],{"encoding":1155}," (proměnná je významná). Při nezamítnutí ",[1115,5201,5203],{"className":5202},[1137],[1139,5204,5205],{"xmlns":1141},[1143,5206,5207,5215],{},[1146,5208,5209],{},[1201,5210,5211,5213],{},[1149,5212,2227],{},[1230,5214,1597],{},[1153,5216,2743],{"encoding":1155}," by proměnná — a s ní spojený regresor — v modelu neměla zůstat.",[2019,5219,5221],{"id":5220},"předpoklady-modelu","Předpoklady modelu",[5106,5223,5224,5241,5274,5280,5283,5286],{},[1127,5225,5226,5227,5240],{},"Závisle proměnná ",[1115,5228,5230],{"className":5229},[1137],[1139,5231,5232],{"xmlns":1141},[1143,5233,5234,5238],{},[1146,5235,5236],{},[1149,5237,1151],{},[1153,5239,1151],{"encoding":1155}," musí být aspoň intervalového typu (ne binární, diskrétní s málo hodnotami apod.) — jinak je na místě logistická regrese.",[1127,5242,5243,5244,5273],{},"Nezávislé proměnné ",[1115,5245,5247],{"className":5246},[1137],[1139,5248,5249],{"xmlns":1141},[1143,5250,5251,5271],{},[1146,5252,5253,5259,5261,5263,5265],{},[1201,5254,5255,5257],{},[1149,5256,1168],{},[1230,5258,1525],{},[1193,5260,1503],{"separator":1121},[1193,5262,1530],{},[1193,5264,1503],{"separator":1121},[1201,5266,5267,5269],{},[1149,5268,1168],{},[1149,5270,1110],{},[1153,5272,1541],{"encoding":1155}," jsou rovněž aspoň intervalového typu, mohou být i alternativní.",[1127,5275,5276,5277,1236],{},"Nezávislé proměnné by mezi sebou neměly být příliš vysoce korelované — ",[1130,5278,5279],{},"multikolinearita",[1127,5281,5282],{},"V datech nesmí být odlehlé či extrémní hodnoty; regresní analýza je na ně citlivá a mohou vážně narušit kvalitu odhadů.",[1127,5284,5285],{},"Proměnné musí být ve vzájemně lineárním vztahu — vícenásobná lineární regrese je založená na Pearsonově koeficientu korelace, takže nelineární vztahy mezi proměnnými zůstanou neodhalené.",[1127,5287,5288,5289,5295],{},"Proměnné mají mít ",[1384,5290,5294],{"className":5291,"dataFsResolvedFilePath":5292,"href":5293},[1387],"topics\u002Fnahodne-veliciny-a-rozdeleni.md","\u002Fwiki\u002Fnahodne-veliciny-a-rozdeleni","normální rozložení","; význam tohoto předpokladu ustupuje do pozadí u dostatečně velkého datového souboru díky centrální limitní větě.",[1110,5297,5298,5299,5305],{},"Normalita se u menšího počtu pozorování ověřuje stejnými testy jako u jiných znaků (viz ",[1384,5300,5304],{"className":5301,"dataFsResolvedFilePath":5302,"href":5303},[1387],"topics\u002Ftestovani-hypotez.md","\u002Fwiki\u002Ftestovani-hypotez","testování statistických hypotéz",") — 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.",[2019,5307,5308],{"id":5279},"Multikolinearita",[1110,5310,5311],{},"Multikolinearita vzniká, když vysvětlující proměnné silně závisejí jedna na druhé. Je nežádoucí, protože:",[1124,5313,5314,5317,5320],{},[1127,5315,5316],{},"výsledky regrese jsou pak nespolehlivé,",[1127,5318,5319],{},"zvyšuje pravděpodobnost, že se důležitá proměnná jeví jako statisticky nevýznamná a bude z modelu vyřazena,",[1127,5321,5322],{},"směrodatné odchylky odhadnutých parametrů jsou vysoké, testová kritéria t-testů nízká, p-hodnoty vysoké.",[1110,5324,5325,5326,5329,5330,5355,5356,5375,5376,5393],{},"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 ",[1130,5327,5328],{},"VIF (Variance Inflation Factor)",": hodnoty ",[1115,5331,5333],{"className":5332},[1137],[1139,5334,5335],{"xmlns":1141},[1143,5336,5337,5352],{},[1146,5338,5339,5341,5344,5347,5349],{},[1230,5340,1525],{},[1193,5342,5343],{},"\u003C",[2201,5345,5346],{},"VIF",[1193,5348,5343],{},[1230,5350,5351],{},"5",[1153,5353,5354],{"encoding":1155},"1\u003C\\text{VIF}\u003C5"," jsou varující, ",[1115,5357,5359],{"className":5358},[1137],[1139,5360,5361],{"xmlns":1141},[1143,5362,5363,5372],{},[1146,5364,5365,5367,5370],{},[2201,5366,5346],{},[1193,5368,5369],{},">",[1230,5371,5351],{},[1153,5373,5374],{"encoding":1155},"\\text{VIF}>5"," (přísněji ",[1115,5377,5379],{"className":5378},[1137],[1139,5380,5381],{"xmlns":1141},[1143,5382,5383,5390],{},[1146,5384,5385,5387],{},[1193,5386,5369],{},[1230,5388,5389],{},"10",[1153,5391,5392],{"encoding":1155},">10",") značí vysokou multikolinearitu.",[1110,5395,5396],{},"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.",[2019,5398,5400],{"id":5399},"další-ukazatele-kvality-modelu","Další ukazatele kvality modelu",[1124,5402,5403,5409,5415],{},[1127,5404,5405,5408],{},[1130,5406,5407],{},"F-test"," — testuje hypotézu, že všechny regresní koeficienty jsou rovny nule, proti alternativě, že aspoň jeden v modelu být má (celková významnost modelu).",[1127,5410,5411,5414],{},[1130,5412,5413],{},"RMSE"," (odmocnina z reziduálního rozptylu) — absolutní měřítko vhodnosti funkce (na rozdíl od indexu determinace, který je relativní); nižší hodnota znamená lepší fit.",[1127,5416,5417,5420,5421,5424],{},[1130,5418,5419],{},"AIC"," (Akaikeho informační kritérium) a ",[1130,5422,5423],{},"BIC"," (Bayesovo informační kritérium) — čím nižší hodnoty obou kritérií, tím lepší model; používají se hlavně při stepwise výběru proměnných.",[2019,5426,2022],{"id":5427},"v-r-2",[1110,5429,5430],{},"Pro vícenásobnou regresi je postup v R rozšířením postupu pro regresní přímku — přibývá výběr proměnných a kontrola multikolinearity:",[2035,5432,5434],{"className":2037,"code":5433,"language":71,"meta":2039,"style":2039},"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",[1332,5435,5436,5463,5507,5533,5543,5549,5560,5571,5575,5586,5596,5600,5610,5620,5625],{"__ignoreMap":2039},[1115,5437,5438,5441,5443,5446,5448,5451,5453,5456,5458,5461],{"class":2044,"line":10},[1115,5439,5440],{"class":2047},"data",[1115,5442,2052],{"class":2051},[1115,5444,5445],{"class":2055}," read.table",[1115,5447,1199],{"class":2059},[1115,5449,5450],{"class":2575},"\"4_4.txt\"",[1115,5452,1503],{"class":2051},[1115,5454,5455],{"class":2047}," header",[1115,5457,2510],{"class":2051},[1115,5459,5460],{"class":2062}," TRUE",[1115,5462,2090],{"class":2059},[1115,5464,5465,5468,5470,5472,5474,5476,5478,5481,5483,5486,5488,5491,5493,5496,5498,5501,5503,5505],{"class":2044,"line":27},[1115,5466,5467],{"class":2047},"model_plny",[1115,5469,2052],{"class":2051},[1115,5471,2140],{"class":2055},[1115,5473,1199],{"class":2059},[1115,5475,1151],{"class":2047},[1115,5477,2147],{"class":2051},[1115,5479,5480],{"class":2047}," x1",[1115,5482,3832],{"class":2051},[1115,5484,5485],{"class":2047}," x2",[1115,5487,3832],{"class":2051},[1115,5489,5490],{"class":2047}," x3",[1115,5492,3832],{"class":2051},[1115,5494,5495],{"class":2047}," x4",[1115,5497,1503],{"class":2051},[1115,5499,5500],{"class":2047}," data",[1115,5502,2510],{"class":2051},[1115,5504,5500],{"class":2047},[1115,5506,2090],{"class":2059},[1115,5508,5509,5512,5514,5517,5519,5521,5523,5526,5528,5531],{"class":2044,"line":148},[1115,5510,5511],{"class":2047},"model_krok",[1115,5513,2052],{"class":2051},[1115,5515,5516],{"class":2055}," step",[1115,5518,1199],{"class":2059},[1115,5520,5467],{"class":2047},[1115,5522,1503],{"class":2051},[1115,5524,5525],{"class":2047}," direction",[1115,5527,2510],{"class":2051},[1115,5529,5530],{"class":2575}," \"both\"",[1115,5532,2090],{"class":2059},[1115,5534,5535,5537,5539,5541],{"class":2044,"line":111},[1115,5536,2157],{"class":2055},[1115,5538,1199],{"class":2059},[1115,5540,5511],{"class":2047},[1115,5542,2090],{"class":2059},[1115,5544,5545],{"class":2044,"line":96},[1115,5546,5548],{"emptyLinePlaceholder":5547},true,"\n",[1115,5550,5551,5553,5555,5558],{"class":2044,"line":89},[1115,5552,2698],{"class":2051},[1115,5554,1199],{"class":2059},[1115,5556,5557],{"class":2047},"car",[1115,5559,2090],{"class":2059},[1115,5561,5562,5565,5567,5569],{"class":2044,"line":82},[1115,5563,5564],{"class":2055},"vif",[1115,5566,1199],{"class":2059},[1115,5568,5511],{"class":2047},[1115,5570,2090],{"class":2059},[1115,5572,5573],{"class":2044,"line":75},[1115,5574,5548],{"emptyLinePlaceholder":5547},[1115,5576,5578,5580,5582,5584],{"class":2044,"line":5577},9,[1115,5579,2698],{"class":2051},[1115,5581,1199],{"class":2059},[1115,5583,2703],{"class":2047},[1115,5585,2090],{"class":2059},[1115,5587,5588,5590,5592,5594],{"class":2044,"line":72},[1115,5589,2710],{"class":2055},[1115,5591,1199],{"class":2059},[1115,5593,5511],{"class":2047},[1115,5595,2090],{"class":2059},[1115,5597,5598],{"class":2044,"line":25},[1115,5599,5548],{"emptyLinePlaceholder":5547},[1115,5601,5602,5604,5606,5608],{"class":2044,"line":65},[1115,5603,2698],{"class":2051},[1115,5605,1199],{"class":2059},[1115,5607,2795],{"class":2047},[1115,5609,2090],{"class":2059},[1115,5611,5612,5614,5616,5618],{"class":2044,"line":63},[1115,5613,2802],{"class":2055},[1115,5615,1199],{"class":2059},[1115,5617,5511],{"class":2047},[1115,5619,2090],{"class":2059},[1115,5621,5623],{"class":2044,"line":5622},14,[1115,5624,5548],{"emptyLinePlaceholder":5547},[1115,5626,5627,5629,5631,5633,5635,5637],{"class":2044,"line":60},[1115,5628,2880],{"class":2055},[1115,5630,1199],{"class":2059},[1115,5632,2340],{"class":2055},[1115,5634,1199],{"class":2059},[1115,5636,5511],{"class":2047},[1115,5638,2546],{"class":2059},[1110,5640,5641,5643,5644,5647],{},[1332,5642,1363],{}," provádí stepwise výběr podle AIC, ",[1332,5645,5646],{},"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.",[1103,5649,5651,5658,5661,5664],{"className":5650,"dataCallout":2932},[1106,2931],[1110,5652,5654,5657],{"className":5653},[1113],[1115,5655],{"className":5656,"ariaHidden":1121},[1118,2939,1120],"Příklad: Vícenásobná regrese",[1110,5659,5660],{},"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.",[1110,5662,5663],{},"Postup: odhad plného modelu → stepwise analýza podle AIC → ověření předpokladů.",[1110,5665,5666,5667,5670,5671,5673,5674,5677],{},"Diagnostika odhaleného modelu ukázala tři problémy: (1) ",[1130,5668,5669],{},"nelinearita"," — mezi některými vysvětlujícími proměnnými a cenou je zjevně jiný než lineární vztah, řešením je zkusit u nich druhou mocninu; (2) ",[1130,5672,5279],{}," mezi dvojicí proměnných popisujících vzdálenost (k silnici a ke spalovně) — doporučeno jednu z nich vynechat; (3) ",[1130,5675,5676],{},"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.",[1377,5679,5681],{"id":5680},"časté-chyby","Časté chyby",[1103,5683,5687,5695],{"className":5684,"dataCallout":5686},[1106,5685],"callout-warning","warning",[1110,5688,5690,5694],{"className":5689},[1113],[1115,5691],{"className":5692,"ariaHidden":1121},[1118,5693,1120],"i-lucide:triangle-alert","Koeficient korelace jen pro přímku",[1110,5696,5697,5698,5755,5756,5773,5774,5794,5795,1405,5808,1236],{},"Vzorec ",[1115,5699,5701],{"className":5700},[1137],[1139,5702,5703],{"xmlns":1141},[1143,5704,5705,5752],{},[1146,5706,5707,5717,5719,5729,5732],{},[1201,5708,5709,5711],{},[1149,5710,71],{},[1146,5712,5713,5715],{},[1149,5714,1168],{},[1149,5716,1151],{},[1193,5718,1281],{},[1201,5720,5721,5723],{},[1149,5722,4542],{},[1146,5724,5725,5727],{},[1149,5726,1168],{},[1149,5728,1151],{},[1149,5730,5731],{"mathvariant":1854},"\u002F",[1283,5733,5734],{},[1146,5735,5736,5744],{},[3698,5737,5738,5740,5742],{},[1149,5739,4542],{},[1149,5741,1168],{},[1230,5743,1232],{},[3698,5745,5746,5748,5750],{},[1149,5747,4542],{},[1149,5749,1151],{},[1230,5751,1232],{},[1153,5753,5754],{"encoding":1155},"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 ",[1115,5757,5759],{"className":5758},[1137],[1139,5760,5761],{"xmlns":1141},[1143,5762,5763,5771],{},[1146,5764,5765],{},[1224,5766,5767,5769],{},[1149,5768,1257],{},[1230,5770,1232],{},[1153,5772,1262],{"encoding":1155},", případně obecným indexem korelace ",[1115,5775,5777],{"className":5776},[1137],[1139,5778,5779],{"xmlns":1141},[1143,5780,5781,5791],{},[1146,5782,5783],{},[1283,5784,5785],{},[1224,5786,5787,5789],{},[1149,5788,1257],{},[1230,5790,1232],{},[1153,5792,5793],{"encoding":1155},"\\sqrt{R^2}"," — ne koeficientem korelace mezi ",[1115,5796,5798],{"className":5797},[1137],[1139,5799,5800],{"xmlns":1141},[1143,5801,5802,5806],{},[1146,5803,5804],{},[1149,5805,1168],{},[1153,5807,1168],{"encoding":1155},[1115,5809,5811],{"className":5810},[1137],[1139,5812,5813],{"xmlns":1141},[1143,5814,5815,5819],{},[1146,5816,5817],{},[1149,5818,1151],{},[1153,5820,1151],{"encoding":1155},[1103,5822,5824,5831],{"className":5823,"dataCallout":5686},[1106,5685],[1110,5825,5827,5830],{"className":5826},[1113],[1115,5828],{"className":5829,"ariaHidden":1121},[1118,5693,1120],"Významný F-test, nevýznamné t-testy",[1110,5832,5833],{},"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.",[1103,5835,5837,5844],{"className":5836,"dataCallout":5686},[1106,5685],[1110,5838,5840,5843],{"className":5839},[1113],[1115,5841],{"className":5842,"ariaHidden":1121},[1118,5693,1120],"Durbin-Watsonova statistika mimo okolí 2",[1110,5845,5846],{},"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.",[1103,5848,5850,5857],{"className":5849,"dataCallout":5686},[1106,5685],[1110,5851,5853,5856],{"className":5852},[1113],[1115,5854],{"className":5855,"ariaHidden":1121},[1118,5693,1120],"Nízký počet pozorování při stepwise výběru",[1110,5858,5859],{},"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.",[1377,5861,5863],{"id":5862},"související-stránky","Související stránky",[1124,5865,5866,5871,5877,5885,5891,5899,5907],{},[1127,5867,5868],{},[1384,5869,1390],{"className":5870,"dataFsResolvedFilePath":1388,"href":1389},[1387],[1127,5872,5873],{},[1384,5874,5876],{"className":5875,"dataFsResolvedFilePath":5292,"href":5293},[1387],"Náhodné veličiny a rozdělení pravděpodobnosti",[1127,5878,5879],{},[1384,5880,5884],{"className":5881,"dataFsResolvedFilePath":5882,"href":5883},[1387],"topics\u002Fpopisna-statistika.md","\u002Fwiki\u002Fpopisna-statistika","Popisná statistika a datové soubory",[1127,5886,5887],{},[1384,5888,5890],{"className":5889,"dataFsResolvedFilePath":5302,"href":5303},[1387],"Testování statistických hypotéz",[1127,5892,5893],{},[1384,5894,5898],{"className":5895,"dataFsResolvedFilePath":5896,"href":5897},[1387],"topics\u002Fkontingencni-tabulky.md","\u002Fwiki\u002Fkontingencni-tabulky","Kontingenční tabulky",[1127,5900,5901],{},[1384,5902,5906],{"className":5903,"dataFsResolvedFilePath":5904,"href":5905},[1387],"topics\u002Fregulacni-diagramy-a-indexy-zpusobilosti.md","\u002Fwiki\u002Fregulacni-diagramy-a-indexy-zpusobilosti","Regulační diagramy a indexy způsobilosti",[1127,5908,5909],{},[1384,5910,5914],{"className":5911,"dataFsResolvedFilePath":5912,"href":5913},[1387],"outputs\u002Fmask-r-tahak.md","\u002Fwiki\u002Fmask-r-tahak","Tahák pro R",[1377,5916,5917],{"id":934},"Reference",[1110,5919,5920,5921,5925],{},"KROPÁČ, J. ",[5922,5923,5924],"em",{},"Statistika A",". 4. vyd. Brno: Fakulta podnikatelská VUT, 2011.",[5927,5928,5929],"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 .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);}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}",{"title":2039,"searchDepth":27,"depth":27,"links":5931},[5932,5933,5934,5938,5943,5946,5954,5955,5956],{"id":1379,"depth":27,"text":1380},{"id":1558,"depth":27,"text":1559},{"id":1894,"depth":27,"text":1895,"children":5935},[5936,5937],{"id":2021,"depth":148,"text":2022},{"id":2674,"depth":148,"text":2675},{"id":3176,"depth":27,"text":3177,"children":5939},[5940,5941,5942],{"id":3724,"depth":148,"text":3725},{"id":3913,"depth":148,"text":3914},{"id":4175,"depth":148,"text":4176},{"id":4512,"depth":27,"text":4513,"children":5944},[5945],{"id":4833,"depth":148,"text":2022},{"id":4936,"depth":27,"text":4937,"children":5947},[5948,5949,5950,5951,5952,5953],{"id":5077,"depth":148,"text":5078},{"id":5103,"depth":148,"text":5104},{"id":5220,"depth":148,"text":5221},{"id":5279,"depth":148,"text":5308},{"id":5399,"depth":148,"text":5400},{"id":5427,"depth":148,"text":2022},{"id":5680,"depth":27,"text":5681},{"id":5862,"depth":27,"text":5863},{"id":934,"depth":27,"text":5917},null,"2026-10-02","md",{},"\u002Ftopics\u002Fregresni-a-korelacni-analyza",{"title":1094,"description":2039},[5964,5965],"raw\u002Fmask\u002F04 regresní analýza.pdf","raw\u002Fmask\u002F04 regresní analýza - návod R.pdf","topics\u002Fregresni-a-korelacni-analyza",[23,67,135,294,71],"topic","qS8RwxtzOoJHO1BXdLvvzGC9r7PL779FUTYQspgRw5k","topics",[5972,11045,15492,20247,24446,29901],{"id":5973,"title":5898,"body":5974,"course":23,"courses":5957,"created":5958,"description":2039,"extension":5959,"meta":11036,"navigation":5547,"path":11037,"seo":11038,"sources":11039,"stem":11042,"tags":11043,"type":5968,"updated":5958,"__hash__":11044},"topics\u002Ftopics\u002Fkontingencni-tabulky.md",{"type":1096,"value":5975,"toc":11026},[5976,5979,6151,6155,6170,6188,6392,6527,7127,7144,7254,7258,7289,7294,7889,7895,8111,8321,8327,8406,8518,8670,8676,8756,8777,8784,8818,8825,8828,8834,8897,8956,9107,9113,9120,9198,9201,9257,9595,9616,9720,9829,9832,9853,9856,10110,10191,10198,10202,10432,10446,10595,10729,10735,10793,10795,10811,10826,10832,10877,10896,10911,10917,10976,10978,11017,11019,11023],[1099,5977,5898],{"id":5978},"kontingenční-tabulky",[1103,5980,5982,5988],{"className":5981,"dataCallout":1108},[1106,1107],[1110,5983,5985,1122],{"className":5984},[1113],[1115,5986],{"className":5987,"ariaHidden":1121},[1118,1119,1120],[1124,5989,5990,5997,6056,6077,6115,6140],{},[1127,5991,5992,5993,5996],{},"Kontingenční tabulka zaznamenává ",[1130,5994,5995],{},"simultánní četnosti"," dvou kvalitativních znaků naměřených na stejném souboru.",[1127,5998,5999,6002,6003,6020,6021,6040,6041,6055],{},[1130,6000,6001],{},"Test nezávislosti"," srovnává pozorované četnosti s očekávanými za platnosti ",[1115,6004,6006],{"className":6005},[1137],[1139,6007,6008],{"xmlns":1141},[1143,6009,6010,6018],{},[1146,6011,6012],{},[1201,6013,6014,6016],{},[1149,6015,2227],{},[1230,6017,1597],{},[1153,6019,2743],{"encoding":1155}," pomocí statistiky ",[1115,6022,6024],{"className":6023},[1137],[1139,6025,6026],{"xmlns":1141},[1143,6027,6028,6037],{},[1146,6029,6030],{},[1224,6031,6032,6035],{},[1149,6033,6034],{},"χ",[1230,6036,1232],{},[1153,6038,6039],{"encoding":1155},"\\chi^2","; rozhoduje kritický obor ",[1115,6042,6044],{"className":6043},[1137],[1139,6045,6046],{"xmlns":1141},[1143,6047,6048,6053],{},[1146,6049,6050],{},[1149,6051,6052],{},"W",[1153,6054,6052],{"encoding":1155},", prakticky p-hodnota.",[1127,6057,6058,6059,6076],{},"Aproximace ",[1115,6060,6062],{"className":6061},[1137],[1139,6063,6064],{"xmlns":1141},[1143,6065,6066,6074],{},[1146,6067,6068],{},[1224,6069,6070,6072],{},[1149,6071,6034],{},[1230,6073,1232],{},[1153,6075,6039],{"encoding":1155}," rozdělením platí jen tehdy, když jsou očekávané četnosti dostatečně velké — proto se vždy kontrolují.",[1127,6078,6079,6080,6097,6098,1243,6101,1236],{},"Zamítnutí ",[1115,6081,6083],{"className":6082},[1137],[1139,6084,6085],{"xmlns":1141},[1143,6086,6087,6095],{},[1146,6088,6089],{},[1201,6090,6091,6093],{},[1149,6092,2227],{},[1230,6094,1597],{},[1153,6096,2743],{"encoding":1155}," samo o sobě neříká, jak silná závislost je — na to slouží ",[1130,6099,6100],{},"Cramérův koeficient kontingence",[1115,6102,6104],{"className":6103},[1137],[1139,6105,6106],{"xmlns":1141},[1143,6107,6108,6113],{},[1146,6109,6110],{},[1149,6111,6112],{},"V",[1153,6114,6112],{"encoding":1155},[1127,6116,6117,6120,6121,1236],{},[1130,6118,6119],{},"Čtyřpolní tabulka"," (2×2) je speciální případ s vlastním zjednodušeným vzorcem pro ",[1115,6122,6124],{"className":6123},[1137],[1139,6125,6126],{"xmlns":1141},[1143,6127,6128,6137],{},[1146,6129,6130,6132,6134],{},[1149,6131,1816],{},[1193,6133,5369],{},[1230,6135,6136],{},"40",[1153,6138,6139],{"encoding":1155},"n>40",[1127,6141,6142,6143,6146,6147,6150],{},"Pro ",[1130,6144,6145],{},"párová data"," (stejné prvky měřené dvakrát, např. před\u002Fpo zásahu) se používá ",[1130,6148,6149],{},"McNemarův test",", ne obyčejný test nezávislosti.",[1377,6152,6154],{"id":6153},"kontingenční-tabulka","Kontingenční tabulka",[1110,6156,6157,6158,6161,6162,6165,6166,6169],{},"V rámci ",[1384,6159,1390],{"className":6160,"dataFsResolvedFilePath":1388,"href":1389},[1387]," navazují kontingenční tabulky na\n",[1384,6163,5304],{"className":6164,"dataFsResolvedFilePath":5302,"href":5303},[1387],": místo jedné náhodné veličiny teď sledujeme dva\n",[1130,6167,6168],{},"kvalitativní"," (kategoriální) znaky současně a ptáme se, zda spolu souvisí.",[1110,6171,6172,6173,6176,6177,6179,6180,6183,6184,6187],{},"Znak je ",[1130,6174,6175],{},"kvantitativní",", pokud nabývá číselných hodnot (stáří, stav tachometru), a ",[1130,6178,6168],{},"\n(kategoriální), pokud nabývá slovních variant (vzdělání, kuřák\u002Fnekuřák). Kvalitativní znaky dále dělíme na\n",[1130,6181,6182],{},"alternativní"," (dvě varianty, např. vada ano\u002Fne) a ",[1130,6185,6186],{},"množné"," (více než dvě varianty, např. svobodný\u002Frozvedený\u002Fženatý).",[1110,6189,6190,6191,6204,6205,6219,6220,6250,6251,6265,6266,6296,6297,6300,6301,6324,6325,1243,6328,6350,6351,6369,6370,6388,6389,1902],{},"Mějme ",[1115,6192,6194],{"className":6193},[1137],[1139,6195,6196],{"xmlns":1141},[1143,6197,6198,6202],{},[1146,6199,6200],{},[1149,6201,1816],{},[1153,6203,1816],{"encoding":1155}," opakování pokusu, při nichž sledujeme dva kvalitativní znaky ",[1115,6206,6208],{"className":6207},[1137],[1139,6209,6210],{"xmlns":1141},[1143,6211,6212,6217],{},[1146,6213,6214],{},[1149,6215,6216],{},"A",[1153,6218,6216],{"encoding":1155}," (varianty ",[1115,6221,6223],{"className":6222},[1137],[1139,6224,6225],{"xmlns":1141},[1143,6226,6227,6247],{},[1146,6228,6229,6235,6237,6239,6241],{},[1201,6230,6231,6233],{},[1149,6232,6216],{},[1230,6234,1525],{},[1193,6236,1503],{"separator":1121},[1193,6238,1530],{},[1193,6240,1503],{"separator":1121},[1201,6242,6243,6245],{},[1149,6244,6216],{},[1149,6246,71],{},[1153,6248,6249],{"encoding":1155},"A_1,\\dots,A_r",") a ",[1115,6252,6254],{"className":6253},[1137],[1139,6255,6256],{"xmlns":1141},[1143,6257,6258,6263],{},[1146,6259,6260],{},[1149,6261,6262],{},"B",[1153,6264,6262],{"encoding":1155},"\n(varianty ",[1115,6267,6269],{"className":6268},[1137],[1139,6270,6271],{"xmlns":1141},[1143,6272,6273,6293],{},[1146,6274,6275,6281,6283,6285,6287],{},[1201,6276,6277,6279],{},[1149,6278,6262],{},[1230,6280,1525],{},[1193,6282,1503],{"separator":1121},[1193,6284,1530],{},[1193,6286,1503],{"separator":1121},[1201,6288,6289,6291],{},[1149,6290,6262],{},[1149,6292,4542],{},[1153,6294,6295],{"encoding":1155},"B_1,\\dots,B_s","). Výsledky zapíšeme do ",[1130,6298,6299],{},"kontingenční tabulky",": v políčku ",[1115,6302,6304],{"className":6303},[1137],[1139,6305,6306],{"xmlns":1141},[1143,6307,6308,6321],{},[1146,6309,6310,6312,6314,6316,6319],{},[1193,6311,1199],{"stretchy":1198},[1149,6313,1207],{},[1193,6315,1503],{"separator":1121},[1149,6317,6318],{},"j",[1193,6320,1228],{"stretchy":1198},[1153,6322,6323],{"encoding":1155},"(i,j)"," je ",[1130,6326,6327],{},"simultánní\nčetnost",[1115,6329,6331],{"className":6330},[1137],[1139,6332,6333],{"xmlns":1141},[1143,6334,6335,6347],{},[1146,6336,6337],{},[1201,6338,6339,6341],{},[1149,6340,1816],{},[1146,6342,6343,6345],{},[1149,6344,1207],{},[1149,6346,6318],{},[1153,6348,6349],{"encoding":1155},"n_{ij}",", tedy počet pokusů s variantou ",[1115,6352,6354],{"className":6353},[1137],[1139,6355,6356],{"xmlns":1141},[1143,6357,6358,6366],{},[1146,6359,6360],{},[1201,6361,6362,6364],{},[1149,6363,6216],{},[1149,6365,1207],{},[1153,6367,6368],{"encoding":1155},"A_i"," zároveň s variantou ",[1115,6371,6373],{"className":6372},[1137],[1139,6374,6375],{"xmlns":1141},[1143,6376,6377,6385],{},[1146,6378,6379],{},[1201,6380,6381,6383],{},[1149,6382,6262],{},[1149,6384,6318],{},[1153,6386,6387],{"encoding":1155},"B_j",". Řádkové a sloupcové součty\njsou ",[1130,6390,6391],{},"marginální četnosti",[1115,6393,6395],{"className":6394},[1137],[1139,6396,6397],{"xmlns":1141,"display":1796},[1143,6398,6399,6524],{},[1146,6400,6401,6412,6414,6428,6438,6440,6442,6452,6454,6468,6478,6480,6482,6484,6486,6500,6514],{},[1201,6402,6403,6405],{},[1149,6404,1816],{},[1146,6406,6407,6409],{},[1149,6408,1207],{},[1193,6410,6411],{},"∙",[1193,6413,1281],{},[1802,6415,6416,6418,6426],{},[1193,6417,1195],{},[1146,6419,6420,6422,6424],{},[1149,6421,6318],{},[1193,6423,1281],{},[1230,6425,1525],{},[1149,6427,4542],{},[1201,6429,6430,6432],{},[1149,6431,1816],{},[1146,6433,6434,6436],{},[1149,6435,1207],{},[1149,6437,6318],{},[1193,6439,1503],{"separator":1121},[1936,6441],{"width":1938},[1201,6443,6444,6446],{},[1149,6445,1816],{},[1146,6447,6448,6450],{},[1193,6449,6411],{},[1149,6451,6318],{},[1193,6453,1281],{},[1802,6455,6456,6458,6466],{},[1193,6457,1195],{},[1146,6459,6460,6462,6464],{},[1149,6461,1207],{},[1193,6463,1281],{},[1230,6465,1525],{},[1149,6467,71],{},[1201,6469,6470,6472],{},[1149,6471,1816],{},[1146,6473,6474,6476],{},[1149,6475,1207],{},[1149,6477,6318],{},[1193,6479,1503],{"separator":1121},[1936,6481],{"width":1938},[1149,6483,1816],{},[1193,6485,1281],{},[1802,6487,6488,6490,6498],{},[1193,6489,1195],{},[1146,6491,6492,6494,6496],{},[1149,6493,1207],{},[1193,6495,1281],{},[1230,6497,1525],{},[1149,6499,71],{},[1802,6501,6502,6504,6512],{},[1193,6503,1195],{},[1146,6505,6506,6508,6510],{},[1149,6507,6318],{},[1193,6509,1281],{},[1230,6511,1525],{},[1149,6513,4542],{},[1201,6515,6516,6518],{},[1149,6517,1816],{},[1146,6519,6520,6522],{},[1149,6521,1207],{},[1149,6523,6318],{},[1153,6525,6526],{"encoding":1155},"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}",[6528,6529,6530,6644],"table",{},[6531,6532,6533],"thead",{},[6534,6535,6536,6558,6578,6598,6600,6620],"tr",{},[6537,6538,6539],"th",{},[1115,6540,6542],{"className":6541},[1137],[1139,6543,6544],{"xmlns":1141},[1143,6545,6546,6555],{},[1146,6547,6548,6550,6553],{},[1149,6549,6216],{},[1149,6551,6552],{"mathvariant":1854},"\\",[1149,6554,6262],{},[1153,6556,6557],{"encoding":1155},"A \\backslash B",[6537,6559,6560],{},[1115,6561,6563],{"className":6562},[1137],[1139,6564,6565],{"xmlns":1141},[1143,6566,6567,6575],{},[1146,6568,6569],{},[1201,6570,6571,6573],{},[1149,6572,6262],{},[1230,6574,1525],{},[1153,6576,6577],{"encoding":1155},"B_1",[6537,6579,6580],{},[1115,6581,6583],{"className":6582},[1137],[1139,6584,6585],{"xmlns":1141},[1143,6586,6587,6595],{},[1146,6588,6589],{},[1201,6590,6591,6593],{},[1149,6592,6262],{},[1230,6594,1232],{},[1153,6596,6597],{"encoding":1155},"B_2",[6537,6599,1530],{},[6537,6601,6602],{},[1115,6603,6605],{"className":6604},[1137],[1139,6606,6607],{"xmlns":1141},[1143,6608,6609,6617],{},[1146,6610,6611],{},[1201,6612,6613,6615],{},[1149,6614,6262],{},[1149,6616,4542],{},[1153,6618,6619],{"encoding":1155},"B_s",[6537,6621,6622],{},[1115,6623,6625],{"className":6624},[1137],[1139,6626,6627],{"xmlns":1141},[1143,6628,6629,6641],{},[1146,6630,6631],{},[1201,6632,6633,6635],{},[1149,6634,1816],{},[1146,6636,6637,6639],{},[1149,6638,1207],{},[1193,6640,6411],{},[1153,6642,6643],{"encoding":1155},"n_{i\\bullet}",[6645,6646,6647,6762,6876,6892,7012],"tbody",{},[6534,6648,6649,6670,6691,6712,6714,6738],{},[6650,6651,6652],"td",{},[1115,6653,6655],{"className":6654},[1137],[1139,6656,6657],{"xmlns":1141},[1143,6658,6659,6667],{},[1146,6660,6661],{},[1201,6662,6663,6665],{},[1149,6664,6216],{},[1230,6666,1525],{},[1153,6668,6669],{"encoding":1155},"A_1",[6650,6671,6672],{},[1115,6673,6675],{"className":6674},[1137],[1139,6676,6677],{"xmlns":1141},[1143,6678,6679,6688],{},[1146,6680,6681],{},[1201,6682,6683,6685],{},[1149,6684,1816],{},[1230,6686,6687],{},"11",[1153,6689,6690],{"encoding":1155},"n_{11}",[6650,6692,6693],{},[1115,6694,6696],{"className":6695},[1137],[1139,6697,6698],{"xmlns":1141},[1143,6699,6700,6709],{},[1146,6701,6702],{},[1201,6703,6704,6706],{},[1149,6705,1816],{},[1230,6707,6708],{},"12",[1153,6710,6711],{"encoding":1155},"n_{12}",[6650,6713,1530],{},[6650,6715,6716],{},[1115,6717,6719],{"className":6718},[1137],[1139,6720,6721],{"xmlns":1141},[1143,6722,6723,6735],{},[1146,6724,6725],{},[1201,6726,6727,6729],{},[1149,6728,1816],{},[1146,6730,6731,6733],{},[1230,6732,1525],{},[1149,6734,4542],{},[1153,6736,6737],{"encoding":1155},"n_{1s}",[6650,6739,6740],{},[1115,6741,6743],{"className":6742},[1137],[1139,6744,6745],{"xmlns":1141},[1143,6746,6747,6759],{},[1146,6748,6749],{},[1201,6750,6751,6753],{},[1149,6752,1816],{},[1146,6754,6755,6757],{},[1230,6756,1525],{},[1193,6758,6411],{},[1153,6760,6761],{"encoding":1155},"n_{1\\bullet}",[6534,6763,6764,6784,6805,6826,6828,6852],{},[6650,6765,6766],{},[1115,6767,6769],{"className":6768},[1137],[1139,6770,6771],{"xmlns":1141},[1143,6772,6773,6781],{},[1146,6774,6775],{},[1201,6776,6777,6779],{},[1149,6778,6216],{},[1230,6780,1232],{},[1153,6782,6783],{"encoding":1155},"A_2",[6650,6785,6786],{},[1115,6787,6789],{"className":6788},[1137],[1139,6790,6791],{"xmlns":1141},[1143,6792,6793,6802],{},[1146,6794,6795],{},[1201,6796,6797,6799],{},[1149,6798,1816],{},[1230,6800,6801],{},"21",[1153,6803,6804],{"encoding":1155},"n_{21}",[6650,6806,6807],{},[1115,6808,6810],{"className":6809},[1137],[1139,6811,6812],{"xmlns":1141},[1143,6813,6814,6823],{},[1146,6815,6816],{},[1201,6817,6818,6820],{},[1149,6819,1816],{},[1230,6821,6822],{},"22",[1153,6824,6825],{"encoding":1155},"n_{22}",[6650,6827,1530],{},[6650,6829,6830],{},[1115,6831,6833],{"className":6832},[1137],[1139,6834,6835],{"xmlns":1141},[1143,6836,6837,6849],{},[1146,6838,6839],{},[1201,6840,6841,6843],{},[1149,6842,1816],{},[1146,6844,6845,6847],{},[1230,6846,1232],{},[1149,6848,4542],{},[1153,6850,6851],{"encoding":1155},"n_{2s}",[6650,6853,6854],{},[1115,6855,6857],{"className":6856},[1137],[1139,6858,6859],{"xmlns":1141},[1143,6860,6861,6873],{},[1146,6862,6863],{},[1201,6864,6865,6867],{},[1149,6866,1816],{},[1146,6868,6869,6871],{},[1230,6870,1232],{},[1193,6872,6411],{},[1153,6874,6875],{"encoding":1155},"n_{2\\bullet}",[6534,6877,6878,6881,6883,6885,6888,6890],{},[6650,6879,6880],{},"⋮",[6650,6882,6880],{},[6650,6884,6880],{},[6650,6886,6887],{},"⋱",[6650,6889,6880],{},[6650,6891,6880],{},[6534,6893,6894,6914,6938,6962,6964,6988],{},[6650,6895,6896],{},[1115,6897,6899],{"className":6898},[1137],[1139,6900,6901],{"xmlns":1141},[1143,6902,6903,6911],{},[1146,6904,6905],{},[1201,6906,6907,6909],{},[1149,6908,6216],{},[1149,6910,71],{},[1153,6912,6913],{"encoding":1155},"A_r",[6650,6915,6916],{},[1115,6917,6919],{"className":6918},[1137],[1139,6920,6921],{"xmlns":1141},[1143,6922,6923,6935],{},[1146,6924,6925],{},[1201,6926,6927,6929],{},[1149,6928,1816],{},[1146,6930,6931,6933],{},[1149,6932,71],{},[1230,6934,1525],{},[1153,6936,6937],{"encoding":1155},"n_{r1}",[6650,6939,6940],{},[1115,6941,6943],{"className":6942},[1137],[1139,6944,6945],{"xmlns":1141},[1143,6946,6947,6959],{},[1146,6948,6949],{},[1201,6950,6951,6953],{},[1149,6952,1816],{},[1146,6954,6955,6957],{},[1149,6956,71],{},[1230,6958,1232],{},[1153,6960,6961],{"encoding":1155},"n_{r2}",[6650,6963,1530],{},[6650,6965,6966],{},[1115,6967,6969],{"className":6968},[1137],[1139,6970,6971],{"xmlns":1141},[1143,6972,6973,6985],{},[1146,6974,6975],{},[1201,6976,6977,6979],{},[1149,6978,1816],{},[1146,6980,6981,6983],{},[1149,6982,71],{},[1149,6984,4542],{},[1153,6986,6987],{"encoding":1155},"n_{rs}",[6650,6989,6990],{},[1115,6991,6993],{"className":6992},[1137],[1139,6994,6995],{"xmlns":1141},[1143,6996,6997,7009],{},[1146,6998,6999],{},[1201,7000,7001,7003],{},[1149,7002,1816],{},[1146,7004,7005,7007],{},[1149,7006,71],{},[1193,7008,6411],{},[1153,7010,7011],{"encoding":1155},"n_{r\\bullet}",[6534,7013,7014,7038,7062,7086,7088,7112],{},[6650,7015,7016],{},[1115,7017,7019],{"className":7018},[1137],[1139,7020,7021],{"xmlns":1141},[1143,7022,7023,7035],{},[1146,7024,7025],{},[1201,7026,7027,7029],{},[1149,7028,1816],{},[1146,7030,7031,7033],{},[1193,7032,6411],{},[1149,7034,6318],{},[1153,7036,7037],{"encoding":1155},"n_{\\bullet j}",[6650,7039,7040],{},[1115,7041,7043],{"className":7042},[1137],[1139,7044,7045],{"xmlns":1141},[1143,7046,7047,7059],{},[1146,7048,7049],{},[1201,7050,7051,7053],{},[1149,7052,1816],{},[1146,7054,7055,7057],{},[1193,7056,6411],{},[1230,7058,1525],{},[1153,7060,7061],{"encoding":1155},"n_{\\bullet 1}",[6650,7063,7064],{},[1115,7065,7067],{"className":7066},[1137],[1139,7068,7069],{"xmlns":1141},[1143,7070,7071,7083],{},[1146,7072,7073],{},[1201,7074,7075,7077],{},[1149,7076,1816],{},[1146,7078,7079,7081],{},[1193,7080,6411],{},[1230,7082,1232],{},[1153,7084,7085],{"encoding":1155},"n_{\\bullet 2}",[6650,7087,1530],{},[6650,7089,7090],{},[1115,7091,7093],{"className":7092},[1137],[1139,7094,7095],{"xmlns":1141},[1143,7096,7097,7109],{},[1146,7098,7099],{},[1201,7100,7101,7103],{},[1149,7102,1816],{},[1146,7104,7105,7107],{},[1193,7106,6411],{},[1149,7108,4542],{},[1153,7110,7111],{"encoding":1155},"n_{\\bullet s}",[6650,7113,7114],{},[1115,7115,7117],{"className":7116},[1137],[1139,7118,7119],{"xmlns":1141},[1143,7120,7121,7125],{},[1146,7122,7123],{},[1149,7124,1816],{},[1153,7126,1816],{"encoding":1155},[1110,7128,7129,7130,7143],{},"Vydělením četností počtem opakování ",[1115,7131,7133],{"className":7132},[1137],[1139,7134,7135],{"xmlns":1141},[1143,7136,7137,7141],{},[1146,7138,7139],{},[1149,7140,1816],{},[1153,7142,1816],{"encoding":1155}," dostaneme odhady pravděpodobností:",[1115,7145,7147],{"className":7146},[1137],[1139,7148,7149],{"xmlns":1141,"display":1796},[1143,7150,7151,7251],{},[1146,7152,7153,7167,7169,7183,7185,7187,7201,7203,7217,7219,7221,7235,7237],{},[1201,7154,7155,7161],{},[1214,7156,7157,7159],{"accent":1121},[1149,7158,1110],{},[1193,7160,1220],{},[1146,7162,7163,7165],{},[1149,7164,1207],{},[1149,7166,6318],{},[1193,7168,1281],{},[3546,7170,7171,7181],{},[1201,7172,7173,7175],{},[1149,7174,1816],{},[1146,7176,7177,7179],{},[1149,7178,1207],{},[1149,7180,6318],{},[1149,7182,1816],{},[1193,7184,1503],{"separator":1121},[1936,7186],{"width":1938},[1201,7188,7189,7195],{},[1214,7190,7191,7193],{"accent":1121},[1149,7192,1110],{},[1193,7194,1220],{},[1146,7196,7197,7199],{},[1149,7198,1207],{},[1193,7200,6411],{},[1193,7202,1281],{},[3546,7204,7205,7215],{},[1201,7206,7207,7209],{},[1149,7208,1816],{},[1146,7210,7211,7213],{},[1149,7212,1207],{},[1193,7214,6411],{},[1149,7216,1816],{},[1193,7218,1503],{"separator":1121},[1936,7220],{"width":1938},[1201,7222,7223,7229],{},[1214,7224,7225,7227],{"accent":1121},[1149,7226,1110],{},[1193,7228,1220],{},[1146,7230,7231,7233],{},[1193,7232,6411],{},[1149,7234,6318],{},[1193,7236,1281],{},[3546,7238,7239,7249],{},[1201,7240,7241,7243],{},[1149,7242,1816],{},[1146,7244,7245,7247],{},[1193,7246,6411],{},[1149,7248,6318],{},[1149,7250,1816],{},[1153,7252,7253],{"encoding":1155},"\\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}",[1377,7255,7257],{"id":7256},"test-nezávislosti-dvou-kvalitativních-znaků","Test nezávislosti dvou kvalitativních znaků",[1110,7259,7260,7261,7274,7275,7288],{},"Test ověřuje, zda varianty znaku ",[1115,7262,7264],{"className":7263},[1137],[1139,7265,7266],{"xmlns":1141},[1143,7267,7268,7272],{},[1146,7269,7270],{},[1149,7271,6216],{},[1153,7273,6216],{"encoding":1155}," a varianty znaku ",[1115,7276,7278],{"className":7277},[1137],[1139,7279,7280],{"xmlns":1141},[1143,7281,7282,7286],{},[1146,7283,7284],{},[1149,7285,6262],{},[1153,7287,6262],{"encoding":1155}," jsou na sobě nezávislé, tedy zda simultánní\npravděpodobnost je součinem marginálních pravděpodobností.",[1110,7290,7291],{},[1130,7292,7293],{},"Postup testu:",[5106,7295,7296,7424,7740,7821],{},[1127,7297,7298,7352,7353,1348,7379,7405,7406,7423],{},[1115,7299,7301],{"className":7300},[1137],[1139,7302,7303],{"xmlns":1141},[1143,7304,7305,7349],{},[1146,7306,7307,7313,7315,7325,7327,7337,7339],{},[1201,7308,7309,7311],{},[1149,7310,2227],{},[1230,7312,1597],{},[1193,7314,1902],{},[1201,7316,7317,7319],{},[1149,7318,1110],{},[1146,7320,7321,7323],{},[1149,7322,1207],{},[1149,7324,6318],{},[1193,7326,1281],{},[1201,7328,7329,7331],{},[1149,7330,1110],{},[1146,7332,7333,7335],{},[1149,7334,1207],{},[1193,7336,6411],{},[2201,7338,2203],{},[1201,7340,7341,7343],{},[1149,7342,1110],{},[1146,7344,7345,7347],{},[1193,7346,6411],{},[1149,7348,6318],{},[1153,7350,7351],{"encoding":1155},"H_0: p_{ij} = p_{i\\bullet}\\,p_{\\bullet j}"," pro všechna ",[1115,7354,7356],{"className":7355},[1137],[1139,7357,7358],{"xmlns":1141},[1143,7359,7360,7376],{},[1146,7361,7362,7364,7366,7368,7370,7372,7374],{},[1149,7363,1207],{},[1193,7365,1281],{},[1230,7367,1525],{},[1193,7369,1503],{"separator":1121},[1193,7371,1530],{},[1193,7373,1503],{"separator":1121},[1149,7375,71],{},[1153,7377,7378],{"encoding":1155},"i = 1,\\dots,r",[1115,7380,7382],{"className":7381},[1137],[1139,7383,7384],{"xmlns":1141},[1143,7385,7386,7402],{},[1146,7387,7388,7390,7392,7394,7396,7398,7400],{},[1149,7389,6318],{},[1193,7391,1281],{},[1230,7393,1525],{},[1193,7395,1503],{"separator":1121},[1193,7397,1530],{},[1193,7399,1503],{"separator":1121},[1149,7401,4542],{},[1153,7403,7404],{"encoding":1155},"j = 1,\\dots,s"," (znaky jsou na sobě\nnezávislé) proti ",[1115,7407,7409],{"className":7408},[1137],[1139,7410,7411],{"xmlns":1141},[1143,7412,7413,7421],{},[1146,7414,7415],{},[1201,7416,7417,7419],{},[1149,7418,2227],{},[1230,7420,1525],{},[1153,7422,2762],{"encoding":1155},": znaky jsou závislé.",[1127,7425,7426,7427,7583,7586,7587,7604,7605,7637,7638,6324,7696,7699,7700,7721,7722,7739],{},"Testové kritérium",[1115,7428,7430],{"className":7429},[1137],[1139,7431,7432],{"xmlns":1141,"display":1796},[1143,7433,7434,7580],{},[1146,7435,7436,7442,7444,7458,7472,7530,7532,7534,7548,7550,7564,7566],{},[1224,7437,7438,7440],{},[1149,7439,6034],{},[1230,7441,1232],{},[1193,7443,1281],{},[1802,7445,7446,7448,7456],{},[1193,7447,1195],{},[1146,7449,7450,7452,7454],{},[1149,7451,1207],{},[1193,7453,1281],{},[1230,7455,1525],{},[1149,7457,71],{},[1802,7459,7460,7462,7470],{},[1193,7461,1195],{},[1146,7463,7464,7466,7468],{},[1149,7465,6318],{},[1193,7467,1281],{},[1230,7469,1525],{},[1149,7471,4542],{},[3546,7473,7474,7512],{},[1146,7475,7476,7478,7488,7490,7492,7506],{},[1193,7477,1199],{"stretchy":1198},[1201,7479,7480,7482],{},[1149,7481,1816],{},[1146,7483,7484,7486],{},[1149,7485,1207],{},[1149,7487,6318],{},[1193,7489,1210],{},[1149,7491,1816],{},[1201,7493,7494,7500],{},[1214,7495,7496,7498],{"accent":1121},[1149,7497,1110],{},[1193,7499,1220],{},[1146,7501,7502,7504],{},[1149,7503,1207],{},[1149,7505,6318],{},[1224,7507,7508,7510],{},[1193,7509,1228],{"stretchy":1198},[1230,7511,1232],{},[1146,7513,7514,7516],{},[1149,7515,1816],{},[1201,7517,7518,7524],{},[1214,7519,7520,7522],{"accent":1121},[1149,7521,1110],{},[1193,7523,1220],{},[1146,7525,7526,7528],{},[1149,7527,1207],{},[1149,7529,6318],{},[1193,7531,1503],{"separator":1121},[1936,7533],{"width":1938},[1201,7535,7536,7542],{},[1214,7537,7538,7540],{"accent":1121},[1149,7539,1110],{},[1193,7541,1220],{},[1146,7543,7544,7546],{},[1149,7545,1207],{},[1149,7547,6318],{},[1193,7549,1281],{},[1201,7551,7552,7558],{},[1214,7553,7554,7556],{"accent":1121},[1149,7555,1110],{},[1193,7557,1220],{},[1146,7559,7560,7562],{},[1149,7561,1207],{},[1193,7563,6411],{},[2201,7565,2203],{},[1201,7567,7568,7574],{},[1214,7569,7570,7572],{"accent":1121},[1149,7571,1110],{},[1193,7573,1220],{},[1146,7575,7576,7578],{},[1193,7577,6411],{},[1149,7579,6318],{},[1153,7581,7582],{"encoding":1155},"\\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}",[7584,7585],"br",{},"má asymptoticky Pearsonovo (",[1115,7588,7590],{"className":7589},[1137],[1139,7591,7592],{"xmlns":1141},[1143,7593,7594,7602],{},[1146,7595,7596],{},[1224,7597,7598,7600],{},[1149,7599,6034],{},[1230,7601,1232],{},[1153,7603,6039],{"encoding":1155},") rozdělení o ",[1115,7606,7608],{"className":7607},[1137],[1139,7609,7610],{"xmlns":1141},[1143,7611,7612,7634],{},[1146,7613,7614,7616,7618,7620,7622,7624,7626,7628,7630,7632],{},[1193,7615,1199],{"stretchy":1198},[1149,7617,71],{},[1193,7619,1210],{},[1230,7621,1525],{},[1193,7623,1228],{"stretchy":1198},[1193,7625,1199],{"stretchy":1198},[1149,7627,4542],{},[1193,7629,1210],{},[1230,7631,1525],{},[1193,7633,1228],{"stretchy":1198},[1153,7635,7636],{"encoding":1155},"(r-1)(s-1)"," stupních volnosti. Hodnota ",[1115,7639,7641],{"className":7640},[1137],[1139,7642,7643],{"xmlns":1141},[1143,7644,7645,7693],{},[1146,7646,7647,7649,7663,7665],{},[1149,7648,1816],{},[1201,7650,7651,7657],{},[1214,7652,7653,7655],{"accent":1121},[1149,7654,1110],{},[1193,7656,1220],{},[1146,7658,7659,7661],{},[1149,7660,1207],{},[1149,7662,6318],{},[1193,7664,1281],{},[3310,7666,7667],{"scriptlevel":1597,"displaystyle":1121},[3546,7668,7669,7691],{},[1146,7670,7671,7681],{},[1201,7672,7673,7675],{},[1149,7674,1816],{},[1146,7676,7677,7679],{},[1149,7678,1207],{},[1193,7680,6411],{},[1201,7682,7683,7685],{},[1149,7684,1816],{},[1146,7686,7687,7689],{},[1193,7688,6411],{},[1149,7690,6318],{},[1149,7692,1816],{},[1153,7694,7695],{"encoding":1155},"n\\hat p_{ij} = \\dfrac{n_{i\\bullet}n_{\\bullet j}}{n}",[1130,7697,7698],{},"očekávaná četnost"," políčka ",[1115,7701,7703],{"className":7702},[1137],[1139,7704,7705],{"xmlns":1141},[1143,7706,7707,7719],{},[1146,7708,7709,7711,7713,7715,7717],{},[1193,7710,1199],{"stretchy":1198},[1149,7712,1207],{},[1193,7714,1503],{"separator":1121},[1149,7716,6318],{},[1193,7718,1228],{"stretchy":1198},[1153,7720,6323],{"encoding":1155}," — četnost, kterou bychom čekali, kdyby ",[1115,7723,7725],{"className":7724},[1137],[1139,7726,7727],{"xmlns":1141},[1143,7728,7729,7737],{},[1146,7730,7731],{},[1201,7732,7733,7735],{},[1149,7734,2227],{},[1230,7736,1597],{},[1153,7738,2743],{"encoding":1155}," platila.",[1127,7741,7742,7743,1236],{},"Kritický obor: ",[1115,7744,7746],{"className":7745},[1137],[1139,7747,7748],{"xmlns":1141},[1143,7749,7750,7818],{},[1146,7751,7752,7754,7756,7759,7765,7767,7773,7776,7791,7793,7795,7797,7799,7801,7803,7805,7807,7809,7811,7813,7815],{},[1149,7753,6052],{},[1193,7755,1281],{},[1193,7757,7758],{"stretchy":1198},"{",[1224,7760,7761,7763],{},[1149,7762,6034],{},[1230,7764,1232],{},[1193,7766,1902],{},[1224,7768,7769,7771],{},[1149,7770,6034],{},[1230,7772,1232],{},[1193,7774,7775],{},"≥",[3698,7777,7778,7780,7789],{},[1149,7779,6034],{},[1146,7781,7782,7784,7786],{},[1230,7783,1525],{},[1193,7785,1210],{},[1149,7787,7788],{},"α",[1230,7790,1232],{},[1193,7792,1199],{"stretchy":1198},[1193,7794,1199],{"stretchy":1198},[1149,7796,71],{},[1193,7798,1210],{},[1230,7800,1525],{},[1193,7802,1228],{"stretchy":1198},[1193,7804,1199],{"stretchy":1198},[1149,7806,4542],{},[1193,7808,1210],{},[1230,7810,1525],{},[1193,7812,1228],{"stretchy":1198},[1193,7814,1228],{"stretchy":1198},[1193,7816,7817],{"stretchy":1198},"}",[1153,7819,7820],{"encoding":1155},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}((r-1)(s-1))\\}",[1127,7822,7823,7824,7837,7838,7852,7853,7870,7871,7888],{},"Padne-li testové kritérium do ",[1115,7825,7827],{"className":7826},[1137],[1139,7828,7829],{"xmlns":1141},[1143,7830,7831,7835],{},[1146,7832,7833],{},[1149,7834,6052],{},[1153,7836,6052],{"encoding":1155},", zamítáme na hladině ",[1115,7839,7841],{"className":7840},[1137],[1139,7842,7843],{"xmlns":1141},[1143,7844,7845,7849],{},[1146,7846,7847],{},[1149,7848,7788],{},[1153,7850,7851],{"encoding":1155},"\\alpha"," nulovou hypotézu o nezávislosti a přijímáme\n",[1115,7854,7856],{"className":7855},[1137],[1139,7857,7858],{"xmlns":1141},[1143,7859,7860,7868],{},[1146,7861,7862],{},[1201,7863,7864,7866],{},[1149,7865,2227],{},[1230,7867,1525],{},[1153,7869,2762],{"encoding":1155},"; jinak nemáme důvod ",[1115,7872,7874],{"className":7873},[1137],[1139,7875,7876],{"xmlns":1141},[1143,7877,7878,7886],{},[1146,7879,7880],{},[1201,7881,7882,7884],{},[1149,7883,2227],{},[1230,7885,1597],{},[1153,7887,2743],{"encoding":1155}," zamítnout.",[1110,7890,7891,7892,1236],{},"V R počítá test i očekávané četnosti funkce ",[1332,7893,7894],{},"chisq.test()",[1103,7896,7898,7905,7908,7911,8056],{"className":7897,"dataCallout":2932},[1106,2931],[1110,7899,7901,7904],{"className":7900},[1113],[1115,7902],{"className":7903,"ariaHidden":1121},[1118,2939,1120],"Příklad: nákup potravin na internetu a vzdělání",[1110,7906,7907],{},"Testujte hypotézu, zda se vzájemně ovlivňuje zkušenost s nákupem potravin na internetu a vzdělání respondenta\n(n = 385 respondentů).",[1110,7909,7910],{},"Základní soubor: respondenti; výběrový soubor: respondenti, kteří odpověděli; měřený znak A: vzdělání, měřený\nznak B: způsob nákupu.",[6528,7912,7913,7952],{},[6531,7914,7915],{},[6534,7916,7917,7920,7923,7926,7929],{},[6537,7918,7919],{},"vzdělání \\ nákup",[6537,7921,7922],{},"ano",[6537,7924,7925],{},"ne, ale plánuji",[6537,7927,7928],{},"ne, neplánuji",[6537,7930,7931],{},[1115,7932,7934],{"className":7933},[1137],[1139,7935,7936],{"xmlns":1141},[1143,7937,7938,7950],{},[1146,7939,7940],{},[1201,7941,7942,7944],{},[1149,7943,1816],{},[1146,7945,7946,7948],{},[1149,7947,1207],{},[1193,7949,6411],{},[1153,7951,6643],{"encoding":1155},[6645,7953,7954,7969,7986,8003,8019],{},[6534,7955,7956,7959,7962,7964,7966],{},[6650,7957,7958],{},"SŠ bez maturity",[6650,7960,7961],{},"4",[6650,7963,3116],{},[6650,7965,6708],{},[6650,7967,7968],{},"29",[6534,7970,7971,7974,7977,7980,7983],{},[6650,7972,7973],{},"SŠ s maturitou, VOŠ",[6650,7975,7976],{},"31",[6650,7978,7979],{},"62",[6650,7981,7982],{},"71",[6650,7984,7985],{},"164",[6534,7987,7988,7991,7994,7997,8000],{},[6650,7989,7990],{},"VŠ",[6650,7992,7993],{},"44",[6650,7995,7996],{},"58",[6650,7998,7999],{},"66",[6650,8001,8002],{},"168",[6534,8004,8005,8008,8011,8014,8016],{},[6650,8006,8007],{},"ZŠ",[6650,8009,8010],{},"3",[6650,8012,8013],{},"9",[6650,8015,6708],{},[6650,8017,8018],{},"24",[6534,8020,8021,8044,8047,8050,8053],{},[6650,8022,8023],{},[1115,8024,8026],{"className":8025},[1137],[1139,8027,8028],{"xmlns":1141},[1143,8029,8030,8042],{},[1146,8031,8032],{},[1201,8033,8034,8036],{},[1149,8035,1816],{},[1146,8037,8038,8040],{},[1193,8039,6411],{},[1149,8041,6318],{},[1153,8043,7037],{"encoding":1155},[6650,8045,8046],{},"82",[6650,8048,8049],{},"142",[6650,8051,8052],{},"161",[6650,8054,8055],{},"385",[1110,8057,8058,8110],{},[1115,8059,8061],{"className":8060},[1137],[1139,8062,8063],{"xmlns":1141},[1143,8064,8065,8107],{},[1146,8066,8067,8073,8075,8085,8087,8097],{},[1201,8068,8069,8071],{},[1149,8070,2227],{},[1230,8072,1597],{},[1193,8074,1902],{},[1201,8076,8077,8079],{},[1149,8078,1110],{},[1146,8080,8081,8083],{},[1149,8082,1207],{},[1149,8084,6318],{},[1193,8086,1281],{},[1201,8088,8089,8091],{},[1149,8090,1110],{},[1146,8092,8093,8095],{},[1149,8094,1207],{},[1193,8096,6411],{},[1201,8098,8099,8101],{},[1149,8100,1110],{},[1146,8102,8103,8105],{},[1193,8104,6411],{},[1149,8106,6318],{},[1153,8108,8109],{"encoding":1155},"H_0: p_{ij} = p_{i\\bullet}p_{\\bullet j}"," — vzdělání a způsob nákupu jsou na sobě nezávislé.",[2035,8112,8114],{"className":2037,"code":8113,"language":71,"meta":2039,"style":2039},"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",[1332,8115,8116,8148,8165,8182,8200,8220,8233,8266,8294,8305],{"__ignoreMap":2039},[1115,8117,8118,8121,8123,8126,8128,8131,8133,8135,8137,8140,8142,8145],{"class":2044,"line":10},[1115,8119,8120],{"class":2047},"tab1",[1115,8122,2052],{"class":2051},[1115,8124,8125],{"class":2055}," matrix",[1115,8127,1199],{"class":2059},[1115,8129,8130],{"class":2055},"c",[1115,8132,1199],{"class":2059},[1115,8134,7961],{"class":2062},[1115,8136,1503],{"class":2051},[1115,8138,8139],{"class":2062}," 13",[1115,8141,1503],{"class":2051},[1115,8143,8144],{"class":2062}," 12",[1115,8146,8147],{"class":2051},",\n",[1115,8149,8150,8153,8155,8158,8160,8163],{"class":2044,"line":27},[1115,8151,8152],{"class":2062}," 31",[1115,8154,1503],{"class":2051},[1115,8156,8157],{"class":2062}," 62",[1115,8159,1503],{"class":2051},[1115,8161,8162],{"class":2062}," 71",[1115,8164,8147],{"class":2051},[1115,8166,8167,8170,8172,8175,8177,8180],{"class":2044,"line":148},[1115,8168,8169],{"class":2062}," 44",[1115,8171,1503],{"class":2051},[1115,8173,8174],{"class":2062}," 58",[1115,8176,1503],{"class":2051},[1115,8178,8179],{"class":2062}," 66",[1115,8181,8147],{"class":2051},[1115,8183,8184,8187,8189,8192,8194,8196,8198],{"class":2044,"line":111},[1115,8185,8186],{"class":2062}," 3",[1115,8188,1503],{"class":2051},[1115,8190,8191],{"class":2062}," 9",[1115,8193,1503],{"class":2051},[1115,8195,8144],{"class":2062},[1115,8197,1228],{"class":2059},[1115,8199,8147],{"class":2051},[1115,8201,8202,8205,8207,8209,8211,8214,8216,8218],{"class":2044,"line":96},[1115,8203,8204],{"class":2047}," nrow",[1115,8206,2510],{"class":2051},[1115,8208,2077],{"class":2062},[1115,8210,1503],{"class":2051},[1115,8212,8213],{"class":2047}," byrow",[1115,8215,2510],{"class":2051},[1115,8217,5460],{"class":2062},[1115,8219,8147],{"class":2051},[1115,8221,8222,8225,8227,8230],{"class":2044,"line":89},[1115,8223,8224],{"class":2047}," dimnames",[1115,8226,2510],{"class":2051},[1115,8228,8229],{"class":2055}," list",[1115,8231,8232],{"class":2059},"(\n",[1115,8234,8235,8238,8240,8242,8244,8247,8249,8252,8254,8257,8259,8262,8264],{"class":2044,"line":82},[1115,8236,8237],{"class":2047}," vzdelani",[1115,8239,2510],{"class":2051},[1115,8241,2056],{"class":2055},[1115,8243,1199],{"class":2059},[1115,8245,8246],{"class":2575},"\"SS bez maturity\"",[1115,8248,1503],{"class":2051},[1115,8250,8251],{"class":2575}," \"SS s maturitou nebo VOS\"",[1115,8253,1503],{"class":2051},[1115,8255,8256],{"class":2575}," \"VS\"",[1115,8258,1503],{"class":2051},[1115,8260,8261],{"class":2575}," \"ZS\"",[1115,8263,1228],{"class":2059},[1115,8265,8147],{"class":2051},[1115,8267,8268,8271,8274,8276,8278,8281,8283,8286,8288,8291],{"class":2044,"line":75},[1115,8269,8270],{"class":2047}," nakup",[1115,8272,8273],{"class":2051}," =",[1115,8275,2056],{"class":2055},[1115,8277,1199],{"class":2059},[1115,8279,8280],{"class":2575},"\"ano\"",[1115,8282,1503],{"class":2051},[1115,8284,8285],{"class":2575}," \"ne, ale planuji\"",[1115,8287,1503],{"class":2051},[1115,8289,8290],{"class":2575}," \"ne, neplanuji\"",[1115,8292,8293],{"class":2059},")))\n",[1115,8295,8296,8299,8301,8303],{"class":2044,"line":5577},[1115,8297,8298],{"class":2055},"chisq.test",[1115,8300,1199],{"class":2059},[1115,8302,8120],{"class":2047},[1115,8304,2090],{"class":2059},[1115,8306,8307,8309,8311,8313,8315,8318],{"class":2044,"line":72},[1115,8308,8298],{"class":2055},[1115,8310,1199],{"class":2059},[1115,8312,8120],{"class":2047},[1115,8314,1228],{"class":2059},[1115,8316,8317],{"class":2051},"$",[1115,8319,8320],{"class":2047},"expected\n",[2035,8322,8325],{"className":8323,"code":8324,"language":2169,"meta":2039},[2167]," 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",[1332,8326,8324],{"__ignoreMap":2039},[1110,8328,8329,8330,8353,8354,8368,8369,3096,8388,8405],{},"Všechny očekávané četnosti jsou nad 5, aproximace je v pořádku. Testové kritérium ",[1115,8331,8333],{"className":8332},[1137],[1139,8334,8335],{"xmlns":1141},[1143,8336,8337,8350],{},[1146,8338,8339,8345,8347],{},[1224,8340,8341,8343],{},[1149,8342,6034],{},[1230,8344,1232],{},[1193,8346,1281],{},[1230,8348,8349],{},"5,49",[1153,8351,8352],{"encoding":1155},"\\chi^2 = 5{,}49"," s ",[1115,8355,8357],{"className":8356},[1137],[1139,8358,8359],{"xmlns":1141},[1143,8360,8361,8366],{},[1146,8362,8363],{},[1230,8364,8365],{},"6",[1153,8367,8365],{"encoding":1155}," stupni\nvolnosti dává p-hodnotu ",[1115,8370,8372],{"className":8371},[1137],[1139,8373,8374],{"xmlns":1141},[1143,8375,8376,8385],{},[1146,8377,8378,8381,8383],{},[1230,8379,8380],{},"0,483",[1193,8382,5369],{},[1230,8384,4370],{},[1153,8386,8387],{"encoding":1155},"0{,}483 > 0{,}05",[1115,8389,8391],{"className":8390},[1137],[1139,8392,8393],{"xmlns":1141},[1143,8394,8395,8403],{},[1146,8396,8397],{},[1201,8398,8399,8401],{},[1149,8400,2227],{},[1230,8402,1597],{},[1153,8404,2743],{"encoding":1155}," nezamítáme, závislost mezi zkušeností s nákupem potravin na\ninternetu a vzděláním respondenta se neprokázala.",[1103,8407,8409,8416,8419,8464],{"className":8408,"dataCallout":2932},[1106,2931],[1110,8410,8412,8415],{"className":8411},[1113],[1115,8413],{"className":8414,"ariaHidden":1121},[1118,2939,1120],"Příklad: vzdělání a zveřejňování citlivých údajů na Facebooku",[1110,8417,8418],{},"Mezi 221 osobami bylo zaznamenáno vzdělání a zda zveřejňují na Facebooku citlivé údaje. Proveďte test\nnezávislosti.",[6528,8420,8421,8435],{},[6531,8422,8423],{},[6534,8424,8425,8428,8431,8433],{},[6537,8426,8427],{},"zveřejňuje \\ vzdělání",[6537,8429,8430],{},"SŠ",[6537,8432,7990],{},[6537,8434,8007],{},[6645,8436,8437,8451],{},[6534,8438,8439,8442,8445,8448],{},[6650,8440,8441],{},"ne",[6650,8443,8444],{},"20",[6650,8446,8447],{},"33",[6650,8449,8450],{},"39",[6534,8452,8453,8455,8458,8461],{},[6650,8454,7922],{},[6650,8456,8457],{},"25",[6650,8459,8460],{},"28",[6650,8462,8463],{},"76",[1110,8465,8466,8517],{},[1115,8467,8469],{"className":8468},[1137],[1139,8470,8471],{"xmlns":1141},[1143,8472,8473,8515],{},[1146,8474,8475,8481,8483,8493,8495,8505],{},[1201,8476,8477,8479],{},[1149,8478,2227],{},[1230,8480,1597],{},[1193,8482,1902],{},[1201,8484,8485,8487],{},[1149,8486,1110],{},[1146,8488,8489,8491],{},[1149,8490,1207],{},[1149,8492,6318],{},[1193,8494,1281],{},[1201,8496,8497,8499],{},[1149,8498,1110],{},[1146,8500,8501,8503],{},[1149,8502,1207],{},[1193,8504,6411],{},[1201,8506,8507,8509],{},[1149,8508,1110],{},[1146,8510,8511,8513],{},[1193,8512,6411],{},[1149,8514,6318],{},[1153,8516,8109],{"encoding":1155}," — vzdělání a zveřejňování citlivých údajů jsou na sobě nezávislé.",[2035,8519,8521],{"className":2037,"code":8520,"language":71,"meta":2039,"style":2039},"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",[1332,8522,8523,8552,8571,8589,8599,8622,8646,8656],{"__ignoreMap":2039},[1115,8524,8525,8528,8530,8532,8534,8536,8538,8540,8542,8545,8547,8550],{"class":2044,"line":10},[1115,8526,8527],{"class":2047},"tab2",[1115,8529,2052],{"class":2051},[1115,8531,8125],{"class":2055},[1115,8533,1199],{"class":2059},[1115,8535,8130],{"class":2055},[1115,8537,1199],{"class":2059},[1115,8539,8444],{"class":2062},[1115,8541,1503],{"class":2051},[1115,8543,8544],{"class":2062}," 33",[1115,8546,1503],{"class":2051},[1115,8548,8549],{"class":2062}," 39",[1115,8551,8147],{"class":2051},[1115,8553,8554,8557,8559,8562,8564,8567,8569],{"class":2044,"line":27},[1115,8555,8556],{"class":2062}," 25",[1115,8558,1503],{"class":2051},[1115,8560,8561],{"class":2062}," 28",[1115,8563,1503],{"class":2051},[1115,8565,8566],{"class":2062}," 76",[1115,8568,1228],{"class":2059},[1115,8570,8147],{"class":2051},[1115,8572,8573,8575,8577,8579,8581,8583,8585,8587],{"class":2044,"line":148},[1115,8574,8204],{"class":2047},[1115,8576,2510],{"class":2051},[1115,8578,2067],{"class":2062},[1115,8580,1503],{"class":2051},[1115,8582,8213],{"class":2047},[1115,8584,2510],{"class":2051},[1115,8586,5460],{"class":2062},[1115,8588,8147],{"class":2051},[1115,8590,8591,8593,8595,8597],{"class":2044,"line":111},[1115,8592,8224],{"class":2047},[1115,8594,2510],{"class":2051},[1115,8596,8229],{"class":2055},[1115,8598,8232],{"class":2059},[1115,8600,8601,8604,8606,8608,8610,8613,8615,8618,8620],{"class":2044,"line":96},[1115,8602,8603],{"class":2047}," zverejnuje",[1115,8605,2510],{"class":2051},[1115,8607,2056],{"class":2055},[1115,8609,1199],{"class":2059},[1115,8611,8612],{"class":2575},"\"ne\"",[1115,8614,1503],{"class":2051},[1115,8616,8617],{"class":2575}," \"ano\"",[1115,8619,1228],{"class":2059},[1115,8621,8147],{"class":2051},[1115,8623,8624,8626,8629,8631,8633,8636,8638,8640,8642,8644],{"class":2044,"line":89},[1115,8625,8237],{"class":2047},[1115,8627,8628],{"class":2051}," =",[1115,8630,2056],{"class":2055},[1115,8632,1199],{"class":2059},[1115,8634,8635],{"class":2575},"\"SS\"",[1115,8637,1503],{"class":2051},[1115,8639,8256],{"class":2575},[1115,8641,1503],{"class":2051},[1115,8643,8261],{"class":2575},[1115,8645,8293],{"class":2059},[1115,8647,8648,8650,8652,8654],{"class":2044,"line":82},[1115,8649,8298],{"class":2055},[1115,8651,1199],{"class":2059},[1115,8653,8527],{"class":2047},[1115,8655,2090],{"class":2059},[1115,8657,8658,8660,8662,8664,8666,8668],{"class":2044,"line":75},[1115,8659,8298],{"class":2055},[1115,8661,1199],{"class":2059},[1115,8663,8527],{"class":2047},[1115,8665,1228],{"class":2059},[1115,8667,8317],{"class":2051},[1115,8669,8320],{"class":2047},[2035,8671,8674],{"className":8672,"code":8673,"language":2169,"meta":2039},[2167]," 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",[1332,8675,8673],{"__ignoreMap":2039},[1110,8677,8678,8679,8353,8702,8715,8716,3096,8735,8752,8753,1236],{},"I zde jsou všechny očekávané četnosti nad 5. Testové kritérium ",[1115,8680,8682],{"className":8681},[1137],[1139,8683,8684],{"xmlns":1141},[1143,8685,8686,8699],{},[1146,8687,8688,8694,8696],{},[1224,8689,8690,8692],{},[1149,8691,6034],{},[1230,8693,1232],{},[1193,8695,1281],{},[1230,8697,8698],{},"6,87",[1153,8700,8701],{"encoding":1155},"\\chi^2 = 6{,}87",[1115,8703,8705],{"className":8704},[1137],[1139,8706,8707],{"xmlns":1141},[1143,8708,8709,8713],{},[1146,8710,8711],{},[1230,8712,1232],{},[1153,8714,1232],{"encoding":1155}," stupni volnosti dává\np-hodnotu ",[1115,8717,8719],{"className":8718},[1137],[1139,8720,8721],{"xmlns":1141},[1143,8722,8723,8732],{},[1146,8724,8725,8728,8730],{},[1230,8726,8727],{},"0,032",[1193,8729,5343],{},[1230,8731,4370],{},[1153,8733,8734],{"encoding":1155},"0{,}032 \u003C 0{,}05",[1115,8736,8738],{"className":8737},[1137],[1139,8739,8740],{"xmlns":1141},[1143,8741,8742,8750],{},[1146,8743,8744],{},[1201,8745,8746,8748],{},[1149,8747,2227],{},[1230,8749,1597],{},[1153,8751,2743],{"encoding":1155}," zamítáme — na rozdíl od předchozího příkladu tady vzdělání a zveřejňování\ncitlivých údajů na Facebooku na sobě ",[1130,8754,8755],{},"závisí",[1110,8757,8758,8759,8776],{},"Srovnání pozorovaných a očekávaných četností ukazuje, proč jeden příklad ",[1115,8760,8762],{"className":8761},[1137],[1139,8763,8764],{"xmlns":1141},[1143,8765,8766,8774],{},[1146,8767,8768],{},[1201,8769,8770,8772],{},[1149,8771,2227],{},[1230,8773,1597],{},[1153,8775,2743],{"encoding":1155}," nezamítá a druhý ano — ve druhém\nse pozorované sloupce (zejména u ZŠ) systematicky odchylují od očekávaných, v prvním kolísají jen náhodně kolem nich:",[1110,8778,8779],{},[1864,8780],{"alt":8781,"className":8782,"src":8783},"mask-kt-observed-expected",[1387,1868],"\u002Fwiki-assets\u002Fmask-kt-observed-expected.png",[1110,8785,8786,8787,8804,8805,1902],{},"Totéž je vidět na rozdělení testového kritéria: u prvního příkladu leží ",[1115,8788,8790],{"className":8789},[1137],[1139,8791,8792],{"xmlns":1141},[1143,8793,8794,8802],{},[1146,8795,8796],{},[1224,8797,8798,8800],{},[1149,8799,6034],{},[1230,8801,1232],{},[1153,8803,6039],{"encoding":1155}," hluboko pod kritickou hodnotou,\nu druhého uvnitř kritického oboru ",[1115,8806,8808],{"className":8807},[1137],[1139,8809,8810],{"xmlns":1141},[1143,8811,8812,8816],{},[1146,8813,8814],{},[1149,8815,6052],{},[1153,8817,6052],{"encoding":1155},[1110,8819,8820],{},[1864,8821],{"alt":8822,"className":8823,"src":8824},"mask-kt-chi2-kriticky-obor",[1387,1868],"\u002Fwiki-assets\u002Fmask-kt-chi2-kriticky-obor.png",[1377,8826,6100],{"id":8827},"cramérův-koeficient-kontingence",[1110,8829,8830,8831,1902],{},"Test nezávislosti pouze rozhodne, zda jsou znaky závislé, nebo ne. Sílu závislosti měří ",[1130,8832,8833],{},"Cramérův koeficient\nkontingence",[1115,8835,8837],{"className":8836},[1137],[1139,8838,8839],{"xmlns":1141,"display":1796},[1143,8840,8841,8894],{},[1146,8842,8843,8845,8847,8872,8874,8876,8878,8880,8882,8884,8886,8888,8890,8892],{},[1149,8844,6112],{},[1193,8846,1281],{},[1283,8848,8849],{},[3546,8850,8851,8857],{},[1224,8852,8853,8855],{},[1149,8854,6034],{},[1230,8856,1232],{},[1146,8858,8859,8861,8863,8866,8868,8870],{},[1149,8860,1816],{},[1193,8862,1199],{"stretchy":1198},[1149,8864,8865],{},"m",[1193,8867,1210],{},[1230,8869,1525],{},[1193,8871,1228],{"stretchy":1198},[1193,8873,1503],{"separator":1121},[1936,8875],{"width":1938},[1149,8877,8865],{},[1193,8879,1281],{},[1149,8881,1848],{},[1193,8883,1851],{},[1193,8885,1199],{"stretchy":1198},[1149,8887,71],{},[1193,8889,1503],{"separator":1121},[1149,8891,4542],{},[1193,8893,1228],{"stretchy":1198},[1153,8895,8896],{"encoding":1155},"V = \\sqrt{\\frac{\\chi^2}{n(m-1)}}, \\qquad m = \\min(r, s)",[1110,8898,8899,8900,8917,8918,8936,8937,8955],{},"kde ",[1115,8901,8903],{"className":8902},[1137],[1139,8904,8905],{"xmlns":1141},[1143,8906,8907,8915],{},[1146,8908,8909],{},[1224,8910,8911,8913],{},[1149,8912,6034],{},[1230,8914,1232],{},[1153,8916,6039],{"encoding":1155}," je hodnota testového kritéria z testu nezávislosti. ",[1115,8919,8921],{"className":8920},[1137],[1139,8922,8923],{"xmlns":1141},[1143,8924,8925,8933],{},[1146,8926,8927,8929,8931],{},[1149,8928,6112],{},[1193,8930,1281],{},[1230,8932,1597],{},[1153,8934,8935],{"encoding":1155},"V = 0"," odpovídá úplné nezávislosti znaků,\n",[1115,8938,8940],{"className":8939},[1137],[1139,8941,8942],{"xmlns":1141},[1143,8943,8944,8952],{},[1146,8945,8946,8948,8950],{},[1149,8947,6112],{},[1193,8949,1281],{},[1230,8951,1525],{},[1153,8953,8954],{"encoding":1155},"V = 1"," jejich úplné závislosti.",[2035,8957,8959],{"className":2037,"code":8958,"language":71,"meta":2039,"style":2039},"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",[1332,8960,8961,9034,9097,9102],{"__ignoreMap":2039},[1115,8962,8963,8966,8968,8971,8973,8976,8978,8980,8982,8984,8986,8988,8991,8994,8996,8998,9001,9003,9005,9007,9010,9012,9014,9016,9019,9021,9023,9026,9029,9032],{"class":2044,"line":10},[1115,8964,8965],{"class":2047},"V1",[1115,8967,2052],{"class":2051},[1115,8969,8970],{"class":2055}," sqrt",[1115,8972,1199],{"class":2059},[1115,8974,8975],{"class":2055},"as.numeric",[1115,8977,1199],{"class":2059},[1115,8979,8298],{"class":2055},[1115,8981,1199],{"class":2059},[1115,8983,8120],{"class":2047},[1115,8985,1228],{"class":2059},[1115,8987,8317],{"class":2051},[1115,8989,8990],{"class":2047},"statistic",[1115,8992,8993],{"class":2059},") ",[1115,8995,5731],{"class":2051},[1115,8997,4053],{"class":2059},[1115,8999,9000],{"class":2055},"sum",[1115,9002,1199],{"class":2059},[1115,9004,8120],{"class":2047},[1115,9006,8993],{"class":2059},[1115,9008,9009],{"class":2051},"*",[1115,9011,4053],{"class":2059},[1115,9013,1848],{"class":2055},[1115,9015,1199],{"class":2059},[1115,9017,9018],{"class":2055},"dim",[1115,9020,1199],{"class":2059},[1115,9022,8120],{"class":2047},[1115,9024,9025],{"class":2059},")) ",[1115,9027,9028],{"class":2051},"-",[1115,9030,9031],{"class":2062}," 1",[1115,9033,8293],{"class":2059},[1115,9035,9036,9039,9041,9043,9045,9047,9049,9051,9053,9055,9057,9059,9061,9063,9065,9067,9069,9071,9073,9075,9077,9079,9081,9083,9085,9087,9089,9091,9093,9095],{"class":2044,"line":27},[1115,9037,9038],{"class":2047},"V2",[1115,9040,2052],{"class":2051},[1115,9042,8970],{"class":2055},[1115,9044,1199],{"class":2059},[1115,9046,8975],{"class":2055},[1115,9048,1199],{"class":2059},[1115,9050,8298],{"class":2055},[1115,9052,1199],{"class":2059},[1115,9054,8527],{"class":2047},[1115,9056,1228],{"class":2059},[1115,9058,8317],{"class":2051},[1115,9060,8990],{"class":2047},[1115,9062,8993],{"class":2059},[1115,9064,5731],{"class":2051},[1115,9066,4053],{"class":2059},[1115,9068,9000],{"class":2055},[1115,9070,1199],{"class":2059},[1115,9072,8527],{"class":2047},[1115,9074,8993],{"class":2059},[1115,9076,9009],{"class":2051},[1115,9078,4053],{"class":2059},[1115,9080,1848],{"class":2055},[1115,9082,1199],{"class":2059},[1115,9084,9018],{"class":2055},[1115,9086,1199],{"class":2059},[1115,9088,8527],{"class":2047},[1115,9090,9025],{"class":2059},[1115,9092,9028],{"class":2051},[1115,9094,9031],{"class":2062},[1115,9096,8293],{"class":2059},[1115,9098,9099],{"class":2044,"line":148},[1115,9100,9101],{"class":2047},"V1\n",[1115,9103,9104],{"class":2044,"line":111},[1115,9105,9106],{"class":2047},"V2\n",[2035,9108,9111],{"className":9109,"code":9110,"language":2169,"meta":2039},[2167],"[1] 0.08441958\n[1] 0.1762822\n",[1332,9112,9110],{"__ignoreMap":2039},[1110,9114,9115],{},[1864,9116],{"alt":9117,"className":9118,"src":9119},"mask-kt-cramerovo-v",[1387,1868],"\u002Fwiki-assets\u002Fmask-kt-cramerovo-v.png",[1110,9121,9122,9123,9142,9143,9160,9161,3096,9180,9197],{},"U nákupu potravin je ",[1115,9124,9126],{"className":9125},[1137],[1139,9127,9128],{"xmlns":1141},[1143,9129,9130,9139],{},[1146,9131,9132,9134,9136],{},[1149,9133,6112],{},[1193,9135,1281],{},[1230,9137,9138],{},"0,084",[1153,9140,9141],{"encoding":1155},"V = 0{,}084"," zanedbatelné — ostatně ",[1115,9144,9146],{"className":9145},[1137],[1139,9147,9148],{"xmlns":1141},[1143,9149,9150,9158],{},[1146,9151,9152],{},[1201,9153,9154,9156],{},[1149,9155,2227],{},[1230,9157,1597],{},[1153,9159,2743],{"encoding":1155}," jsme ani nezamítli. U zveřejňování údajů je ",[1115,9162,9164],{"className":9163},[1137],[1139,9165,9166],{"xmlns":1141},[1143,9167,9168,9177],{},[1146,9169,9170,9172,9174],{},[1149,9171,6112],{},[1193,9173,1281],{},[1230,9175,9176],{},"0,176",[1153,9178,9179],{"encoding":1155},"V = 0{,}176",[1115,9181,9183],{"className":9182},[1137],[1139,9184,9185],{"xmlns":1141},[1143,9186,9187,9195],{},[1146,9188,9189],{},[1201,9190,9191,9193],{},[1149,9192,2227],{},[1230,9194,1597],{},[1153,9196,2743],{"encoding":1155},"\njsme zamítli, ale samotná závislost je stále slabá.",[1377,9199,6119],{"id":9200},"čtyřpolní-tabulka",[1110,9202,9203,9205,9206,9219,9220,9233,9234,9256],{},[1130,9204,6119],{}," je speciální případ kontingenční tabulky, kdy oba znaky ",[1115,9207,9209],{"className":9208},[1137],[1139,9210,9211],{"xmlns":1141},[1143,9212,9213,9217],{},[1146,9214,9215],{},[1149,9216,6216],{},[1153,9218,6216],{"encoding":1155}," i ",[1115,9221,9223],{"className":9222},[1137],[1139,9224,9225],{"xmlns":1141},[1143,9226,9227,9231],{},[1146,9228,9229],{},[1149,9230,6262],{},[1153,9232,6262],{"encoding":1155}," mají jen dvě varianty\n(",[1115,9235,9237],{"className":9236},[1137],[1139,9238,9239],{"xmlns":1141},[1143,9240,9241,9253],{},[1146,9242,9243,9245,9247,9249,9251],{},[1149,9244,71],{},[1193,9246,1281],{},[1149,9248,4542],{},[1193,9250,1281],{},[1230,9252,1232],{},[1153,9254,9255],{"encoding":1155},"r = s = 2","):",[6528,9258,9259,9343],{},[6531,9260,9261],{},[6534,9262,9263,9282,9301,9320],{},[6537,9264,9265],{},[1115,9266,9268],{"className":9267},[1137],[1139,9269,9270],{"xmlns":1141},[1143,9271,9272,9280],{},[1146,9273,9274,9276,9278],{},[1149,9275,6216],{},[1149,9277,6552],{"mathvariant":1854},[1149,9279,6262],{},[1153,9281,6557],{"encoding":1155},[6537,9283,9284],{},[1115,9285,9287],{"className":9286},[1137],[1139,9288,9289],{"xmlns":1141},[1143,9290,9291,9299],{},[1146,9292,9293],{},[1201,9294,9295,9297],{},[1149,9296,6262],{},[1230,9298,1525],{},[1153,9300,6577],{"encoding":1155},[6537,9302,9303],{},[1115,9304,9306],{"className":9305},[1137],[1139,9307,9308],{"xmlns":1141},[1143,9309,9310,9318],{},[1146,9311,9312],{},[1201,9313,9314,9316],{},[1149,9315,6262],{},[1230,9317,1232],{},[1153,9319,6597],{"encoding":1155},[6537,9321,9322],{},[1115,9323,9325],{"className":9324},[1137],[1139,9326,9327],{"xmlns":1141},[1143,9328,9329,9341],{},[1146,9330,9331],{},[1201,9332,9333,9335],{},[1149,9334,1816],{},[1146,9336,9337,9339],{},[1149,9338,1207],{},[1193,9340,6411],{},[1153,9342,6643],{"encoding":1155},[6645,9344,9345,9427,9509],{},[6534,9346,9347,9366,9385,9404],{},[6650,9348,9349],{},[1115,9350,9352],{"className":9351},[1137],[1139,9353,9354],{"xmlns":1141},[1143,9355,9356,9364],{},[1146,9357,9358],{},[1201,9359,9360,9362],{},[1149,9361,6216],{},[1230,9363,1525],{},[1153,9365,6669],{"encoding":1155},[6650,9367,9368],{},[1115,9369,9371],{"className":9370},[1137],[1139,9372,9373],{"xmlns":1141},[1143,9374,9375,9383],{},[1146,9376,9377],{},[1201,9378,9379,9381],{},[1149,9380,1816],{},[1230,9382,6687],{},[1153,9384,6690],{"encoding":1155},[6650,9386,9387],{},[1115,9388,9390],{"className":9389},[1137],[1139,9391,9392],{"xmlns":1141},[1143,9393,9394,9402],{},[1146,9395,9396],{},[1201,9397,9398,9400],{},[1149,9399,1816],{},[1230,9401,6708],{},[1153,9403,6711],{"encoding":1155},[6650,9405,9406],{},[1115,9407,9409],{"className":9408},[1137],[1139,9410,9411],{"xmlns":1141},[1143,9412,9413,9425],{},[1146,9414,9415],{},[1201,9416,9417,9419],{},[1149,9418,1816],{},[1146,9420,9421,9423],{},[1230,9422,1525],{},[1193,9424,6411],{},[1153,9426,6761],{"encoding":1155},[6534,9428,9429,9448,9467,9486],{},[6650,9430,9431],{},[1115,9432,9434],{"className":9433},[1137],[1139,9435,9436],{"xmlns":1141},[1143,9437,9438,9446],{},[1146,9439,9440],{},[1201,9441,9442,9444],{},[1149,9443,6216],{},[1230,9445,1232],{},[1153,9447,6783],{"encoding":1155},[6650,9449,9450],{},[1115,9451,9453],{"className":9452},[1137],[1139,9454,9455],{"xmlns":1141},[1143,9456,9457,9465],{},[1146,9458,9459],{},[1201,9460,9461,9463],{},[1149,9462,1816],{},[1230,9464,6801],{},[1153,9466,6804],{"encoding":1155},[6650,9468,9469],{},[1115,9470,9472],{"className":9471},[1137],[1139,9473,9474],{"xmlns":1141},[1143,9475,9476,9484],{},[1146,9477,9478],{},[1201,9479,9480,9482],{},[1149,9481,1816],{},[1230,9483,6822],{},[1153,9485,6825],{"encoding":1155},[6650,9487,9488],{},[1115,9489,9491],{"className":9490},[1137],[1139,9492,9493],{"xmlns":1141},[1143,9494,9495,9507],{},[1146,9496,9497],{},[1201,9498,9499,9501],{},[1149,9500,1816],{},[1146,9502,9503,9505],{},[1230,9504,1232],{},[1193,9506,6411],{},[1153,9508,6875],{"encoding":1155},[6534,9510,9511,9534,9557,9580],{},[6650,9512,9513],{},[1115,9514,9516],{"className":9515},[1137],[1139,9517,9518],{"xmlns":1141},[1143,9519,9520,9532],{},[1146,9521,9522],{},[1201,9523,9524,9526],{},[1149,9525,1816],{},[1146,9527,9528,9530],{},[1193,9529,6411],{},[1149,9531,6318],{},[1153,9533,7037],{"encoding":1155},[6650,9535,9536],{},[1115,9537,9539],{"className":9538},[1137],[1139,9540,9541],{"xmlns":1141},[1143,9542,9543,9555],{},[1146,9544,9545],{},[1201,9546,9547,9549],{},[1149,9548,1816],{},[1146,9550,9551,9553],{},[1193,9552,6411],{},[1230,9554,1525],{},[1153,9556,7061],{"encoding":1155},[6650,9558,9559],{},[1115,9560,9562],{"className":9561},[1137],[1139,9563,9564],{"xmlns":1141},[1143,9565,9566,9578],{},[1146,9567,9568],{},[1201,9569,9570,9572],{},[1149,9571,1816],{},[1146,9573,9574,9576],{},[1193,9575,6411],{},[1230,9577,1232],{},[1153,9579,7085],{"encoding":1155},[6650,9581,9582],{},[1115,9583,9585],{"className":9584},[1137],[1139,9586,9587],{"xmlns":1141},[1143,9588,9589,9593],{},[1146,9590,9591],{},[1149,9592,1816],{},[1153,9594,1816],{"encoding":1155},[1110,9596,6142,9597,9615],{},[1115,9598,9600],{"className":9599},[1137],[1139,9601,9602],{"xmlns":1141},[1143,9603,9604,9612],{},[1146,9605,9606,9608,9610],{},[1149,9607,1816],{},[1193,9609,5369],{},[1230,9611,6136],{},[1153,9613,9614],{"encoding":1155},"n > 40"," se místo obecného vzorce používá zjednodušená varianta testového kritéria:",[1115,9617,9619],{"className":9618},[1137],[1139,9620,9621],{"xmlns":1141,"display":1796},[1143,9622,9623,9717],{},[1146,9624,9625,9631,9633,9635,9637],{},[1224,9626,9627,9629],{},[1149,9628,6034],{},[1230,9630,1232],{},[1193,9632,1281],{},[1149,9634,1816],{},[2201,9636,2203],{},[3546,9638,9639,9675],{},[1146,9640,9641,9643,9649,9655,9657,9663,9669],{},[1193,9642,1199],{"stretchy":1198},[1201,9644,9645,9647],{},[1149,9646,1816],{},[1230,9648,6687],{},[1201,9650,9651,9653],{},[1149,9652,1816],{},[1230,9654,6822],{},[1193,9656,1210],{},[1201,9658,9659,9661],{},[1149,9660,1816],{},[1230,9662,6708],{},[1201,9664,9665,9667],{},[1149,9666,1816],{},[1230,9668,6801],{},[1224,9670,9671,9673],{},[1193,9672,1228],{"stretchy":1198},[1230,9674,1232],{},[1146,9676,9677,9687,9697,9707],{},[1201,9678,9679,9681],{},[1149,9680,1816],{},[1146,9682,9683,9685],{},[1230,9684,1525],{},[1193,9686,6411],{},[1201,9688,9689,9691],{},[1149,9690,1816],{},[1146,9692,9693,9695],{},[1230,9694,1232],{},[1193,9696,6411],{},[1201,9698,9699,9701],{},[1149,9700,1816],{},[1146,9702,9703,9705],{},[1193,9704,6411],{},[1230,9706,1525],{},[1201,9708,9709,9711],{},[1149,9710,1816],{},[1146,9712,9713,9715],{},[1193,9714,6411],{},[1230,9716,1232],{},[1153,9718,9719],{"encoding":1155},"\\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}}",[1110,9721,9722,9723,9783,9784,9820,9821,9824,9825,9828],{},"s kritickým oborem ",[1115,9724,9726],{"className":9725},[1137],[1139,9727,9728],{"xmlns":1141},[1143,9729,9730,9780],{},[1146,9731,9732,9738,9740,9742,9748,9750,9756,9758,9772,9774,9776,9778],{},[1201,9733,9734,9736],{},[1149,9735,6052],{},[1149,9737,7788],{},[1193,9739,1281],{},[1193,9741,7758],{"stretchy":1198},[1224,9743,9744,9746],{},[1149,9745,6034],{},[1230,9747,1232],{},[1193,9749,1902],{},[1224,9751,9752,9754],{},[1149,9753,6034],{},[1230,9755,1232],{},[1193,9757,7775],{},[3698,9759,9760,9762,9770],{},[1149,9761,6034],{},[1146,9763,9764,9766,9768],{},[1230,9765,1525],{},[1193,9767,1210],{},[1149,9769,7788],{},[1230,9771,1232],{},[1193,9773,1199],{"stretchy":1198},[1230,9775,1525],{},[1193,9777,1228],{"stretchy":1198},[1193,9779,7817],{"stretchy":1198},[1153,9781,9782],{"encoding":1155},"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 ",[1115,9785,9787],{"className":9786},[1137],[1139,9788,9789],{"xmlns":1141},[1143,9790,9791,9817],{},[1146,9792,9793,9795,9797,9799,9801,9803,9805,9807,9809,9811,9813,9815],{},[1193,9794,1199],{"stretchy":1198},[1149,9796,71],{},[1193,9798,1210],{},[1230,9800,1525],{},[1193,9802,1228],{"stretchy":1198},[1193,9804,1199],{"stretchy":1198},[1149,9806,4542],{},[1193,9808,1210],{},[1230,9810,1525],{},[1193,9812,1228],{"stretchy":1198},[1193,9814,1281],{},[1230,9816,1525],{},[1153,9818,9819],{"encoding":1155},"(r-1)(s-1) = 1"," stupeň volnosti. V R dává tuto hodnotu ",[1332,9822,9823],{},"chisq.test(tab, correct = FALSE)",". Bez ",[1332,9826,9827],{},"correct = FALSE"," R u tabulky 2 × 2 použije Yatesovu korekci na kontinuitu a testové kritérium vyjde menší.",[1377,9830,6149],{"id":9831},"mcnemarův-test",[1110,9833,9834,9835,9838,9839,9841,9842,9845,9846,9849,9850,9852],{},"Čtyřpolní tabulka z předchozí sekce porovnává dva ",[1130,9836,9837],{},"různé"," znaky na stejném souboru. ",[1130,9840,6149],{}," řeší\njinou situaci: na prvcích základního souboru se měří ",[1130,9843,9844],{},"jeden"," alternativní znak, a to ",[1130,9847,9848],{},"dvakrát"," — před a po\nnějakém zásahu. Cílem je zjistit, zda zásah změnil pravděpodobnostní rozdělení variant tohoto znaku. Jde tedy o\n",[1130,9851,6145],{}," (stejné prvky měřené opakovaně), ne o dva nezávisle naměřené znaky.",[1110,9854,9855],{},"Kontingenční tabulka před\u002Fpo má tvar:",[6528,9857,9858,9892],{},[6531,9859,9860],{},[6534,9861,9862,9865,9867,9869],{},[6537,9863,9864],{},"před \\ po",[6537,9866,1924],{},[6537,9868,1210],{},[6537,9870,9871],{},[1115,9872,9874],{"className":9873},[1137],[1139,9875,9876],{"xmlns":1141},[1143,9877,9878,9890],{},[1146,9879,9880],{},[1201,9881,9882,9884],{},[1149,9883,1816],{},[1146,9885,9886,9888],{},[1149,9887,1207],{},[1193,9889,6411],{},[1153,9891,6643],{"encoding":1155},[6645,9893,9894,9959,10024],{},[6534,9895,9896,9898,9917,9936],{},[6650,9897,1924],{},[6650,9899,9900],{},[1115,9901,9903],{"className":9902},[1137],[1139,9904,9905],{"xmlns":1141},[1143,9906,9907,9915],{},[1146,9908,9909],{},[1201,9910,9911,9913],{},[1149,9912,1816],{},[1230,9914,6687],{},[1153,9916,6690],{"encoding":1155},[6650,9918,9919],{},[1115,9920,9922],{"className":9921},[1137],[1139,9923,9924],{"xmlns":1141},[1143,9925,9926,9934],{},[1146,9927,9928],{},[1201,9929,9930,9932],{},[1149,9931,1816],{},[1230,9933,6708],{},[1153,9935,6711],{"encoding":1155},[6650,9937,9938],{},[1115,9939,9941],{"className":9940},[1137],[1139,9942,9943],{"xmlns":1141},[1143,9944,9945,9957],{},[1146,9946,9947],{},[1201,9948,9949,9951],{},[1149,9950,1816],{},[1146,9952,9953,9955],{},[1230,9954,1525],{},[1193,9956,6411],{},[1153,9958,6761],{"encoding":1155},[6534,9960,9961,9963,9982,10001],{},[6650,9962,1210],{},[6650,9964,9965],{},[1115,9966,9968],{"className":9967},[1137],[1139,9969,9970],{"xmlns":1141},[1143,9971,9972,9980],{},[1146,9973,9974],{},[1201,9975,9976,9978],{},[1149,9977,1816],{},[1230,9979,6801],{},[1153,9981,6804],{"encoding":1155},[6650,9983,9984],{},[1115,9985,9987],{"className":9986},[1137],[1139,9988,9989],{"xmlns":1141},[1143,9990,9991,9999],{},[1146,9992,9993],{},[1201,9994,9995,9997],{},[1149,9996,1816],{},[1230,9998,6822],{},[1153,10000,6825],{"encoding":1155},[6650,10002,10003],{},[1115,10004,10006],{"className":10005},[1137],[1139,10007,10008],{"xmlns":1141},[1143,10009,10010,10022],{},[1146,10011,10012],{},[1201,10013,10014,10016],{},[1149,10015,1816],{},[1146,10017,10018,10020],{},[1230,10019,1232],{},[1193,10021,6411],{},[1153,10023,6875],{"encoding":1155},[6534,10025,10026,10049,10072,10095],{},[6650,10027,10028],{},[1115,10029,10031],{"className":10030},[1137],[1139,10032,10033],{"xmlns":1141},[1143,10034,10035,10047],{},[1146,10036,10037],{},[1201,10038,10039,10041],{},[1149,10040,1816],{},[1146,10042,10043,10045],{},[1193,10044,6411],{},[1149,10046,6318],{},[1153,10048,7037],{"encoding":1155},[6650,10050,10051],{},[1115,10052,10054],{"className":10053},[1137],[1139,10055,10056],{"xmlns":1141},[1143,10057,10058,10070],{},[1146,10059,10060],{},[1201,10061,10062,10064],{},[1149,10063,1816],{},[1146,10065,10066,10068],{},[1193,10067,6411],{},[1230,10069,1525],{},[1153,10071,7061],{"encoding":1155},[6650,10073,10074],{},[1115,10075,10077],{"className":10076},[1137],[1139,10078,10079],{"xmlns":1141},[1143,10080,10081,10093],{},[1146,10082,10083],{},[1201,10084,10085,10087],{},[1149,10086,1816],{},[1146,10088,10089,10091],{},[1193,10090,6411],{},[1230,10092,1232],{},[1153,10094,7085],{"encoding":1155},[6650,10096,10097],{},[1115,10098,10100],{"className":10099},[1137],[1139,10101,10102],{"xmlns":1141},[1143,10103,10104,10108],{},[1146,10105,10106],{},[1149,10107,1816],{},[1153,10109,1816],{"encoding":1155},[1110,10111,10112,10113,1405,10130,10147,10148,10151,10152,1405,10169,10186,10187,10190],{},"Pole ",[1115,10114,10116],{"className":10115},[1137],[1139,10117,10118],{"xmlns":1141},[1143,10119,10120,10128],{},[1146,10121,10122],{},[1201,10123,10124,10126],{},[1149,10125,1816],{},[1230,10127,6687],{},[1153,10129,6690],{"encoding":1155},[1115,10131,10133],{"className":10132},[1137],[1139,10134,10135],{"xmlns":1141},[1143,10136,10137,10145],{},[1146,10138,10139],{},[1201,10140,10141,10143],{},[1149,10142,1816],{},[1230,10144,6822],{},[1153,10146,6825],{"encoding":1155}," jsou ",[1130,10149,10150],{},"shodná"," (prvek zůstal ve stejné variantě), pole ",[1115,10153,10155],{"className":10154},[1137],[1139,10156,10157],{"xmlns":1141},[1143,10158,10159,10167],{},[1146,10160,10161],{},[1201,10162,10163,10165],{},[1149,10164,1816],{},[1230,10166,6708],{},[1153,10168,6711],{"encoding":1155},[1115,10170,10172],{"className":10171},[1137],[1139,10173,10174],{"xmlns":1141},[1143,10175,10176,10184],{},[1146,10177,10178],{},[1201,10179,10180,10182],{},[1149,10181,1816],{},[1230,10183,6801],{},[1153,10185,6804],{"encoding":1155}," jsou\n",[1130,10188,10189],{},"diskordantní"," (prvek mezi měřeními variantu změnil) — jen ta rozhodují o výsledku testu:",[1110,10192,10193],{},[1864,10194],{"alt":10195,"className":10196,"src":10197},"mask-kt-mcnemar-tabulka",[1387,1868],"\u002Fwiki-assets\u002Fmask-kt-mcnemar-tabulka.png",[1110,10199,10200],{},[1130,10201,7293],{},[5106,10203,10204,10241,10322,10380],{},[1127,10205,10206,10240],{},[1115,10207,10209],{"className":10208},[1137],[1139,10210,10211],{"xmlns":1141},[1143,10212,10213,10237],{},[1146,10214,10215,10221,10223,10229,10231],{},[1201,10216,10217,10219],{},[1149,10218,2227],{},[1230,10220,1597],{},[1193,10222,1902],{},[1201,10224,10225,10227],{},[1149,10226,1110],{},[1230,10228,6708],{},[1193,10230,1281],{},[1201,10232,10233,10235],{},[1149,10234,1110],{},[1230,10236,6801],{},[1153,10238,10239],{"encoding":1155},"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.",[1127,10242,7426,10243,10305,10307,10308,10321],{},[1115,10244,10246],{"className":10245},[1137],[1139,10247,10248],{"xmlns":1141,"display":1796},[1143,10249,10250,10302],{},[1146,10251,10252,10258,10260],{},[1224,10253,10254,10256],{},[1149,10255,6034],{},[1230,10257,1232],{},[1193,10259,1281],{},[3546,10261,10262,10286],{},[1146,10263,10264,10266,10272,10274,10280],{},[1193,10265,1199],{"stretchy":1198},[1201,10267,10268,10270],{},[1149,10269,1816],{},[1230,10271,6708],{},[1193,10273,1210],{},[1201,10275,10276,10278],{},[1149,10277,1816],{},[1230,10279,6801],{},[1224,10281,10282,10284],{},[1193,10283,1228],{"stretchy":1198},[1230,10285,1232],{},[1146,10287,10288,10294,10296],{},[1201,10289,10290,10292],{},[1149,10291,1816],{},[1230,10293,6708],{},[1193,10295,1924],{},[1201,10297,10298,10300],{},[1149,10299,1816],{},[1230,10301,6801],{},[1153,10303,10304],{"encoding":1155},"\\chi^2 = \\frac{(n_{12} - n_{21})^2}{n_{12} + n_{21}}",[7584,10306],{},"má asymptoticky Pearsonovo rozdělení o ",[1115,10309,10311],{"className":10310},[1137],[1139,10312,10313],{"xmlns":1141},[1143,10314,10315,10319],{},[1146,10316,10317],{},[1230,10318,1525],{},[1153,10320,1525],{"encoding":1155}," stupni volnosti.",[1127,10323,7742,10324,1236],{},[1115,10325,10327],{"className":10326},[1137],[1139,10328,10329],{"xmlns":1141},[1143,10330,10331,10377],{},[1146,10332,10333,10335,10337,10339,10345,10347,10353,10355,10369,10371,10373,10375],{},[1149,10334,6052],{},[1193,10336,1281],{},[1193,10338,7758],{"stretchy":1198},[1224,10340,10341,10343],{},[1149,10342,6034],{},[1230,10344,1232],{},[1193,10346,1902],{},[1224,10348,10349,10351],{},[1149,10350,6034],{},[1230,10352,1232],{},[1193,10354,7775],{},[3698,10356,10357,10359,10367],{},[1149,10358,6034],{},[1146,10360,10361,10363,10365],{},[1230,10362,1525],{},[1193,10364,1210],{},[1149,10366,7788],{},[1230,10368,1232],{},[1193,10370,1199],{"stretchy":1198},[1230,10372,1525],{},[1193,10374,1228],{"stretchy":1198},[1193,10376,7817],{"stretchy":1198},[1153,10378,10379],{"encoding":1155},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}(1)\\}",[1127,10381,7823,10382,10395,10396,10413,10414,10431],{},[1115,10383,10385],{"className":10384},[1137],[1139,10386,10387],{"xmlns":1141},[1143,10388,10389,10393],{},[1146,10390,10391],{},[1149,10392,6052],{},[1153,10394,6052],{"encoding":1155},", zamítáme ",[1115,10397,10399],{"className":10398},[1137],[1139,10400,10401],{"xmlns":1141},[1143,10402,10403,10411],{},[1146,10404,10405],{},[1201,10406,10407,10409],{},[1149,10408,2227],{},[1230,10410,1597],{},[1153,10412,2743],{"encoding":1155}," a přijímáme ",[1115,10415,10417],{"className":10416},[1137],[1139,10418,10419],{"xmlns":1141},[1143,10420,10421,10429],{},[1146,10422,10423],{},[1201,10424,10425,10427],{},[1149,10426,2227],{},[1230,10428,1525],{},[1153,10430,2762],{"encoding":1155},": zásah rozdělení variant změnil.",[1110,10433,10434,10435,10438,10439,10442,10443,10445],{},"V R počítá tento test funkce ",[1332,10436,10437],{},"mcnemar.test()",". Vzorec výše ",[1130,10440,10441],{},"neobsahuje korekci na kontinuitu"," — aby R vrátilo\npřesně tuto hodnotu, musí se volat s ",[1332,10444,9827],{}," (viz Časté chyby níže).",[1103,10447,10449,10456,10459,10462,10559],{"className":10448,"dataCallout":2932},[1106,2931],[1110,10450,10452,10455],{"className":10451},[1113],[1115,10453],{"className":10454,"ariaHidden":1121},[1118,2939,1120],"Příklad: informační kampaň a zveřejňování na Facebooku",[1110,10457,10458],{},"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.",[1110,10460,10461],{},"Základní soubor: všichni studenti; výběrový soubor: vybraní studenti; měřený znak: zveřejňování (ano \u002F ne).",[6528,10463,10464,10499],{},[6531,10465,10466],{},[6534,10467,10468,10470,10473,10476],{},[6537,10469,9864],{},[6537,10471,10472],{},"nezveřejňuje",[6537,10474,10475],{},"zveřejňuje",[6537,10477,10478],{},[1115,10479,10481],{"className":10480},[1137],[1139,10482,10483],{"xmlns":1141},[1143,10484,10485,10497],{},[1146,10486,10487],{},[1201,10488,10489,10491],{},[1149,10490,1816],{},[1146,10492,10493,10495],{},[1149,10494,1207],{},[1193,10496,6411],{},[1153,10498,6643],{"encoding":1155},[6645,10500,10501,10513,10525],{},[6534,10502,10503,10505,10507,10510],{},[6650,10504,10472],{},[6650,10506,8018],{},[6650,10508,10509],{},"68",[6650,10511,10512],{},"92",[6534,10514,10515,10517,10519,10522],{},[6650,10516,10475],{},[6650,10518,8460],{},[6650,10520,10521],{},"50",[6650,10523,10524],{},"78",[6534,10526,10527,10550,10553,10556],{},[6650,10528,10529],{},[1115,10530,10532],{"className":10531},[1137],[1139,10533,10534],{"xmlns":1141},[1143,10535,10536,10548],{},[1146,10537,10538],{},[1201,10539,10540,10542],{},[1149,10541,1816],{},[1146,10543,10544,10546],{},[1193,10545,6411],{},[1149,10547,6318],{},[1153,10549,7037],{"encoding":1155},[6650,10551,10552],{},"52",[6650,10554,10555],{},"118",[6650,10557,10558],{},"170",[1110,10560,10561,10594],{},[1115,10562,10564],{"className":10563},[1137],[1139,10565,10566],{"xmlns":1141},[1143,10567,10568,10592],{},[1146,10569,10570,10576,10578,10584,10586],{},[1201,10571,10572,10574],{},[1149,10573,2227],{},[1230,10575,1597],{},[1193,10577,1902],{},[1201,10579,10580,10582],{},[1149,10581,1110],{},[1230,10583,6708],{},[1193,10585,1281],{},[1201,10587,10588,10590],{},[1149,10589,1110],{},[1230,10591,6801],{},[1153,10593,10239],{"encoding":1155}," — informační kampaň nemá na chování vliv.",[2035,10596,10598],{"className":2037,"code":10597,"language":71,"meta":2039,"style":2039},"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",[1332,10599,10600,10624,10638,10656,10666,10689,10708],{"__ignoreMap":2039},[1115,10601,10602,10605,10607,10609,10611,10613,10615,10617,10619,10622],{"class":2044,"line":10},[1115,10603,10604],{"class":2047},"tab3",[1115,10606,2052],{"class":2051},[1115,10608,8125],{"class":2055},[1115,10610,1199],{"class":2059},[1115,10612,8130],{"class":2055},[1115,10614,1199],{"class":2059},[1115,10616,8018],{"class":2062},[1115,10618,1503],{"class":2051},[1115,10620,10621],{"class":2062}," 68",[1115,10623,8147],{"class":2051},[1115,10625,10626,10629,10631,10634,10636],{"class":2044,"line":27},[1115,10627,10628],{"class":2062}," 28",[1115,10630,1503],{"class":2051},[1115,10632,10633],{"class":2062}," 50",[1115,10635,1228],{"class":2059},[1115,10637,8147],{"class":2051},[1115,10639,10640,10642,10644,10646,10648,10650,10652,10654],{"class":2044,"line":148},[1115,10641,8204],{"class":2047},[1115,10643,2510],{"class":2051},[1115,10645,2067],{"class":2062},[1115,10647,1503],{"class":2051},[1115,10649,8213],{"class":2047},[1115,10651,2510],{"class":2051},[1115,10653,5460],{"class":2062},[1115,10655,8147],{"class":2051},[1115,10657,10658,10660,10662,10664],{"class":2044,"line":111},[1115,10659,8224],{"class":2047},[1115,10661,2510],{"class":2051},[1115,10663,8229],{"class":2055},[1115,10665,8232],{"class":2059},[1115,10667,10668,10671,10673,10675,10677,10680,10682,10685,10687],{"class":2044,"line":96},[1115,10669,10670],{"class":2047}," pred",[1115,10672,2510],{"class":2051},[1115,10674,2056],{"class":2055},[1115,10676,1199],{"class":2059},[1115,10678,10679],{"class":2575},"\"nezverejnuje\"",[1115,10681,1503],{"class":2051},[1115,10683,10684],{"class":2575}," \"zverejnuje\"",[1115,10686,1228],{"class":2059},[1115,10688,8147],{"class":2051},[1115,10690,10691,10694,10696,10698,10700,10702,10704,10706],{"class":2044,"line":89},[1115,10692,10693],{"class":2047}," po",[1115,10695,8628],{"class":2051},[1115,10697,2056],{"class":2055},[1115,10699,1199],{"class":2059},[1115,10701,10679],{"class":2575},[1115,10703,1503],{"class":2051},[1115,10705,10684],{"class":2575},[1115,10707,8293],{"class":2059},[1115,10709,10710,10713,10715,10717,10719,10722,10724,10727],{"class":2044,"line":82},[1115,10711,10712],{"class":2055},"mcnemar.test",[1115,10714,1199],{"class":2059},[1115,10716,10604],{"class":2047},[1115,10718,1503],{"class":2051},[1115,10720,10721],{"class":2047}," correct",[1115,10723,2510],{"class":2051},[1115,10725,10726],{"class":2062}," FALSE",[1115,10728,2090],{"class":2059},[2035,10730,10733],{"className":10731,"code":10732,"language":2169,"meta":2039},[2167]," McNemar's Chi-squared test\n\ndata: tab3\nMcNemar's chi-squared = 16.667, df = 1, p-value = 4.456e-05\n",[1332,10734,10732],{"__ignoreMap":2039},[1110,10736,10737,10738,3096,10757,10774,10775,10792],{},"P-hodnota ",[1115,10739,10741],{"className":10740},[1137],[1139,10742,10743],{"xmlns":1141},[1143,10744,10745,10754],{},[1146,10746,10747,10750,10752],{},[1230,10748,10749],{},"0,00004456",[1193,10751,5343],{},[1230,10753,4370],{},[1153,10755,10756],{"encoding":1155},"0{,}00004456 \u003C 0{,}05",[1115,10758,10760],{"className":10759},[1137],[1139,10761,10762],{"xmlns":1141},[1143,10763,10764,10772],{},[1146,10765,10766],{},[1201,10767,10768,10770],{},[1149,10769,2227],{},[1230,10771,1597],{},[1153,10773,2743],{"encoding":1155}," zamítáme, přijímáme ",[1115,10776,10778],{"className":10777},[1137],[1139,10779,10780],{"xmlns":1141},[1143,10781,10782,10790],{},[1146,10783,10784],{},[1201,10785,10786,10788],{},[1149,10787,2227],{},[1230,10789,1525],{},[1153,10791,2762],{"encoding":1155}," — informační kampaň měla vliv na změnu\nchování studentů ve zveřejňování údajů na Facebooku.",[1377,10794,5681],{"id":5680},[1103,10796,10798,10805],{"className":10797,"dataCallout":5686},[1106,5685],[1110,10799,10801,10804],{"className":10800},[1113],[1115,10802],{"className":10803,"ariaHidden":1121},[1118,5693,1120],"Test nezávislosti na párovaných datech",[1110,10806,10807,10808,10810],{},"Tabulka před\u002Fpo vypadá jako obyčejná kontingenční tabulka, ale ",[1332,10809,7894],{}," 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.",[2035,10812,10814],{"className":2037,"code":10813,"language":71,"meta":2039,"style":2039},"chisq.test(tab3)\n",[1332,10815,10816],{"__ignoreMap":2039},[1115,10817,10818,10820,10822,10824],{"class":2044,"line":10},[1115,10819,8298],{"class":2055},[1115,10821,1199],{"class":2059},[1115,10823,10604],{"class":2047},[1115,10825,2090],{"class":2059},[2035,10827,10830],{"className":10828,"code":10829,"language":2169,"meta":2039},[2167]," Pearson's Chi-squared test with Yates' continuity correction\n\ndata: tab3\nX-squared = 1.4793, df = 1, p-value = 0.2239\n",[1332,10831,10829],{"__ignoreMap":2039},[1110,10833,10737,10834,10853,10854,10871,10872,10874,10875,1236],{},[1115,10835,10837],{"className":10836},[1137],[1139,10838,10839],{"xmlns":1141},[1143,10840,10841,10850],{},[1146,10842,10843,10846,10848],{},[1230,10844,10845],{},"0,224",[1193,10847,5369],{},[1230,10849,4370],{},[1153,10851,10852],{"encoding":1155},"0{,}224 > 0{,}05"," by vedla k nezamítnutí ",[1115,10855,10857],{"className":10856},[1137],[1139,10858,10859],{"xmlns":1141},[1143,10860,10861,10869],{},[1146,10862,10863],{},[1201,10864,10865,10867],{},[1149,10866,2227],{},[1230,10868,1597],{},[1153,10870,2743],{"encoding":1155}," — opačný závěr než správný McNemarův test. Na\npárovaná data (stejné prvky měřené dvakrát) vždy patří ",[1332,10873,10437],{},", nikdy ",[1332,10876,7894],{},[1103,10878,10880,10889],{"className":10879,"dataCallout":5686},[1106,5685],[1110,10881,10883,10886,10887],{"className":10882},[1113],[1115,10884],{"className":10885,"ariaHidden":1121},[1118,5693,1120],"Výchozí korekce na kontinuitu v ",[1332,10888,10437],{},[1110,10890,10891,10892,10895],{},"Bez argumentu ",[1332,10893,10894],{},"correct"," R ve výchozím nastavení použije Yatesovu korekci na kontinuitu, která dá jinou\np-hodnotu než nekorigovaný vzorec uvedený výše.",[2035,10897,10899],{"className":2037,"code":10898,"language":71,"meta":2039,"style":2039},"mcnemar.test(tab3)\n",[1332,10900,10901],{"__ignoreMap":2039},[1115,10902,10903,10905,10907,10909],{"class":2044,"line":10},[1115,10904,10712],{"class":2055},[1115,10906,1199],{"class":2059},[1115,10908,10604],{"class":2047},[1115,10910,2090],{"class":2059},[2035,10912,10915],{"className":10913,"code":10914,"language":2169,"meta":2039},[2167]," 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",[1332,10916,10914],{"__ignoreMap":2039},[1110,10918,10919,10920,10938,10939,10958,10959,10972,10973,1236],{},"Oproti nekorigované hodnotě ",[1115,10921,10923],{"className":10922},[1137],[1139,10924,10925],{"xmlns":1141},[1143,10926,10927,10935],{},[1146,10928,10929,10931,10933],{},[1149,10930,1110],{},[1193,10932,1281],{},[1230,10934,10749],{},[1153,10936,10937],{"encoding":1155},"p = 0{,}00004456"," vyjde ",[1115,10940,10942],{"className":10941},[1137],[1139,10943,10944],{"xmlns":1141},[1143,10945,10946,10955],{},[1146,10947,10948,10950,10952],{},[1149,10949,1110],{},[1193,10951,1281],{},[1230,10953,10954],{},"0,00006879",[1153,10956,10957],{"encoding":1155},"p = 0{,}00006879"," — v tomto příkladu obě vedou ke\nstejnému rozhodnutí, ale u hodnot blíž hranici ",[1115,10960,10962],{"className":10961},[1137],[1139,10963,10964],{"xmlns":1141},[1143,10965,10966,10970],{},[1146,10967,10968],{},[1149,10969,7788],{},[1153,10971,7851],{"encoding":1155}," by korekce mohla rozhodnutí změnit. Aby R reprodukovalo\nnekorigovaný vzorec, je třeba vždy volat ",[1332,10974,10975],{},"mcnemar.test(x, correct = FALSE)",[1377,10977,5863],{"id":5862},[1124,10979,10980,10985,10990,10995,11000,11007,11012],{},[1127,10981,10982],{},[1384,10983,1390],{"className":10984,"dataFsResolvedFilePath":1388,"href":1389},[1387],[1127,10986,10987],{},[1384,10988,5890],{"className":10989,"dataFsResolvedFilePath":5302,"href":5303},[1387],[1127,10991,10992],{},[1384,10993,5884],{"className":10994,"dataFsResolvedFilePath":5882,"href":5883},[1387],[1127,10996,10997],{},[1384,10998,5876],{"className":10999,"dataFsResolvedFilePath":5292,"href":5293},[1387],[1127,11001,11002],{},[1384,11003,1094],{"className":11004,"dataFsResolvedFilePath":11005,"href":11006},[1387],"topics\u002Fregresni-a-korelacni-analyza.md","\u002Fwiki\u002Fregresni-a-korelacni-analyza",[1127,11008,11009],{},[1384,11010,5906],{"className":11011,"dataFsResolvedFilePath":5904,"href":5905},[1387],[1127,11013,11014],{},[1384,11015,5914],{"className":11016,"dataFsResolvedFilePath":5912,"href":5913},[1387],[1377,11018,5917],{"id":934},[1110,11020,5920,11021,5925],{},[5922,11022,5924],{},[5927,11024,11025],{},"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: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: 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var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":2039,"searchDepth":27,"depth":27,"links":11027},[11028,11029,11030,11031,11032,11033,11034,11035],{"id":6153,"depth":27,"text":6154},{"id":7256,"depth":27,"text":7257},{"id":8827,"depth":27,"text":6100},{"id":9200,"depth":27,"text":6119},{"id":9831,"depth":27,"text":6149},{"id":5680,"depth":27,"text":5681},{"id":5862,"depth":27,"text":5863},{"id":934,"depth":27,"text":5917},{},"\u002Ftopics\u002Fkontingencni-tabulky",{"title":5898,"description":2039},[11040,11041],"raw\u002Fmask\u002F05 kontingenční tabulky.pdf","raw\u002Fmask\u002Fpříklady 04 a 05.docx","topics\u002Fkontingencni-tabulky",[23,67,714,486,768,71],"E-gDO0c3LOdVy6YB6I-h8KKMQKlrqjomMSQWFmOANZE",{"id":11046,"title":5876,"body":11047,"course":23,"courses":5957,"created":5958,"description":2039,"extension":5959,"meta":15482,"navigation":5547,"path":15483,"seo":15484,"sources":15485,"stem":15489,"tags":15490,"type":5968,"updated":5958,"__hash__":15491},"topics\u002Ftopics\u002Fnahodne-veliciny-a-rozdeleni.md",{"type":1096,"value":11048,"toc":15470},[11049,11052,11335,11339,11571,11574,11642,11646,11653,11660,11819,11858,11861,12094,12097,12175,12229,12327,12331,12433,12436,12440,12446,12501,12504,12512,12663,12670,12723,12753,12872,12875,12923,13084,13139,13146,13253,13315,13319,13421,13424,13461,13467,13526,13575,13582,13618,13624,13627,13675,13682,13744,13750,13753,13816,13823,13861,13867,13870,13874,13900,14231,14269,14323,14449,14455,14459,14466,14485,14590,14634,14653,14748,14765,14807,14982,14989,14992,14995,15149,15152,15227,15233,15235,15420,15422,15461,15463,15467],[1099,11050,5876],{"id":11051},"náhodné-veličiny-a-rozdělení-pravděpodobnosti",[1103,11053,11055,11061],{"className":11054,"dataCallout":1108},[1106,1107],[1110,11056,11058,1122],{"className":11057},[1113],[1115,11059],{"className":11060,"ariaHidden":1121},[1118,1119,1120],[1124,11062,11063,11074,11176,11243,11323],{},[1127,11064,11065,11066,11069,11070,11073],{},"Náhodná veličina je funkce, která výsledkům pokusu přiřazuje reálná čísla; rozlišujeme ",[1130,11067,11068],{},"diskrétní"," (izolované hodnoty s nenulovou pravděpodobností) a ",[1130,11071,11072],{},"spojité"," (hodnoty z intervalu, každý bod má nulovou pravděpodobnost).",[1127,11075,11076,11077,1243,11080,11118,11119,11154,11155,11175],{},"Každou náhodnou veličinu popisuje ",[1130,11078,11079],{},"distribuční funkce",[1115,11081,11083],{"className":11082},[1137],[1139,11084,11085],{"xmlns":1141},[1143,11086,11087,11115],{},[1146,11088,11089,11092,11094,11096,11098,11100,11103,11105,11108,11111,11113],{},[1149,11090,11091],{},"F",[1193,11093,1199],{"stretchy":1198},[1149,11095,1168],{},[1193,11097,1228],{"stretchy":1198},[1193,11099,1281],{},[1149,11101,11102],{},"P",[1193,11104,1199],{"stretchy":1198},[1149,11106,11107],{},"X",[1193,11109,11110],{},"≤",[1149,11112,1168],{},[1193,11114,1228],{"stretchy":1198},[1153,11116,11117],{"encoding":1155},"F(x) = P(X \\le x)","; u spojité veličiny platí ",[1115,11120,11122],{"className":11121},[1137],[1139,11123,11124],{"xmlns":1141},[1143,11125,11126,11151],{},[1146,11127,11128,11135,11137,11139,11141,11143,11145,11147,11149],{},[1224,11129,11130,11132],{},[1149,11131,11091],{},[1193,11133,11134],{"mathvariant":1854,"lspace":3302,"rspace":3302},"′",[1193,11136,1199],{"stretchy":1198},[1149,11138,1168],{},[1193,11140,1228],{"stretchy":1198},[1193,11142,1281],{},[1149,11144,1582],{},[1193,11146,1199],{"stretchy":1198},[1149,11148,1168],{},[1193,11150,1228],{"stretchy":1198},[1153,11152,11153],{"encoding":1155},"F'(x) = f(x)",", kde ",[1115,11156,11158],{"className":11157},[1137],[1139,11159,11160],{"xmlns":1141},[1143,11161,11162,11172],{},[1146,11163,11164,11166,11168,11170],{},[1149,11165,1582],{},[1193,11167,1199],{"stretchy":1198},[1149,11169,1168],{},[1193,11171,1228],{"stretchy":1198},[1153,11173,11174],{"encoding":1155},"f(x)"," je hustota pravděpodobnosti.",[1127,11177,11178,11179,1236],{},"Pravděpodobnost na intervalu se počítá jako ",[1115,11180,11182],{"className":11181},[1137],[1139,11183,11184],{"xmlns":1141},[1143,11185,11186,11240],{},[1146,11187,11188,11190,11192,11198,11200,11202,11204,11210,11212,11214,11216,11218,11224,11226,11228,11230,11232,11238],{},[1149,11189,11102],{},[1193,11191,1199],{"stretchy":1198},[1201,11193,11194,11196],{},[1149,11195,1168],{},[1230,11197,1525],{},[1193,11199,5343],{},[1149,11201,11107],{},[1193,11203,5343],{},[1201,11205,11206,11208],{},[1149,11207,1168],{},[1230,11209,1232],{},[1193,11211,1228],{"stretchy":1198},[1193,11213,1281],{},[1149,11215,11091],{},[1193,11217,1199],{"stretchy":1198},[1201,11219,11220,11222],{},[1149,11221,1168],{},[1230,11223,1232],{},[1193,11225,1228],{"stretchy":1198},[1193,11227,1210],{},[1149,11229,11091],{},[1193,11231,1199],{"stretchy":1198},[1201,11233,11234,11236],{},[1149,11235,1168],{},[1230,11237,1525],{},[1193,11239,1228],{"stretchy":1198},[1153,11241,11242],{"encoding":1155},"P(x_1 \u003C X \u003C x_2) = F(x_2) - F(x_1)",[1127,11244,11245,1243,11248,11279,11280,1348,11283,1348,11286,11289,11290,11304,11305,1236],{},[1130,11246,11247],{},"Normální rozdělení",[1115,11249,11251],{"className":11250},[1137],[1139,11252,11253],{"xmlns":1141},[1143,11254,11255,11276],{},[1146,11256,11257,11260,11262,11265,11267,11274],{},[1149,11258,11259],{},"N",[1193,11261,1199],{"stretchy":1198},[1149,11263,11264],{},"μ",[1193,11266,1589],{"separator":1121},[1224,11268,11269,11272],{},[1149,11270,11271],{},"σ",[1230,11273,1232],{},[1193,11275,1228],{"stretchy":1198},[1153,11277,11278],{"encoding":1155},"N(\\mu; \\sigma^2)"," je nejdůležitější spojité rozdělení; v R ho počítáme funkcemi ",[1332,11281,11282],{},"dnorm",[1332,11284,11285],{},"pnorm",[1332,11287,11288],{},"qnorm"," — R jako parametr očekává směrodatnou odchylku ",[1115,11291,11293],{"className":11292},[1137],[1139,11294,11295],{"xmlns":1141},[1143,11296,11297,11301],{},[1146,11298,11299],{},[1149,11300,11271],{},[1153,11302,11303],{"encoding":1155},"\\sigma",", ne rozptyl ",[1115,11306,11308],{"className":11307},[1137],[1139,11309,11310],{"xmlns":1141},[1143,11311,11312,11320],{},[1146,11313,11314],{},[1224,11315,11316,11318],{},[1149,11317,11271],{},[1230,11319,1232],{},[1153,11321,11322],{"encoding":1155},"\\sigma^2",[1127,11324,11325,1348,11328,1405,11331,11334],{},[1130,11326,11327],{},"Studentovo",[1130,11329,11330],{},"Pearsonovo (χ²)",[1130,11332,11333],{},"Fisherovo-Snedecorovo"," rozdělení slouží jako nástroj pro pozdější konstrukci intervalů spolehlivosti a testování hypotéz.",[1377,11336,11338],{"id":11337},"náhodná-veličina","Náhodná veličina",[1110,11340,11341,11344,11345,11360,11361,1243,11363,11376,11377,11397,11398,11154,11411,11435,11436,1348,11449,1348,11463,11477,11478,1348,11491,1348,11504,11518,11519,11532,11533,11546,11547,1236],{},[1384,11342,1390],{"className":11343,"dataFsResolvedFilePath":1388,"href":1389},[1387]," pracuje s veličinami, jejichž hodnota závisí na náhodě. Formálně: uvažujeme základní prostor ",[1115,11346,11348],{"className":11347},[1137],[1139,11349,11350],{"xmlns":1141},[1143,11351,11352,11357],{},[1146,11353,11354],{},[1149,11355,11356],{"mathvariant":1854},"Ω",[1153,11358,11359],{"encoding":1155},"\\Omega"," přiřazený výsledkům pokusu. ",[1130,11362,11338],{},[1115,11364,11366],{"className":11365},[1137],[1139,11367,11368],{"xmlns":1141},[1143,11369,11370,11374],{},[1146,11371,11372],{},[1149,11373,11107],{},[1153,11375,11107],{"encoding":1155}," je funkce, která prvkům ",[1115,11378,11380],{"className":11379},[1137],[1139,11381,11382],{"xmlns":1141},[1143,11383,11384,11394],{},[1146,11385,11386,11389,11392],{},[1149,11387,11388],{},"ω",[1193,11390,11391],{},"∈",[1149,11393,11356],{"mathvariant":1854},[1153,11395,11396],{"encoding":1155},"\\omega \\in \\Omega"," přiřazuje reálná čísla ",[1115,11399,11401],{"className":11400},[1137],[1139,11402,11403],{"xmlns":1141},[1143,11404,11405,11409],{},[1146,11406,11407],{},[1149,11408,1168],{},[1153,11410,1168],{"encoding":1155},[1115,11412,11414],{"className":11413},[1137],[1139,11415,11416],{"xmlns":1141},[1143,11417,11418,11432],{},[1146,11419,11420,11422,11424,11426,11428,11430],{},[1149,11421,1168],{},[1193,11423,1281],{},[1149,11425,11107],{},[1193,11427,1199],{"stretchy":1198},[1149,11429,11388],{},[1193,11431,1228],{"stretchy":1198},[1153,11433,11434],{"encoding":1155},"x = X(\\omega)",". Náhodné veličiny značíme velkými písmeny (",[1115,11437,11439],{"className":11438},[1137],[1139,11440,11441],{"xmlns":1141},[1143,11442,11443,11447],{},[1146,11444,11445],{},[1149,11446,11107],{},[1153,11448,11107],{"encoding":1155},[1115,11450,11452],{"className":11451},[1137],[1139,11453,11454],{"xmlns":1141},[1143,11455,11456,11461],{},[1146,11457,11458],{},[1149,11459,11460],{},"Y",[1153,11462,11460],{"encoding":1155},[1115,11464,11466],{"className":11465},[1137],[1139,11467,11468],{"xmlns":1141},[1143,11469,11470,11475],{},[1146,11471,11472],{},[1149,11473,11474],{},"T",[1153,11476,11474],{"encoding":1155},"), jejich konkrétní hodnoty odpovídajícími malými písmeny (",[1115,11479,11481],{"className":11480},[1137],[1139,11482,11483],{"xmlns":1141},[1143,11484,11485,11489],{},[1146,11486,11487],{},[1149,11488,1168],{},[1153,11490,1168],{"encoding":1155},[1115,11492,11494],{"className":11493},[1137],[1139,11495,11496],{"xmlns":1141},[1143,11497,11498,11502],{},[1146,11499,11500],{},[1149,11501,1151],{},[1153,11503,1151],{"encoding":1155},[1115,11505,11507],{"className":11506},[1137],[1139,11508,11509],{"xmlns":1141},[1143,11510,11511,11516],{},[1146,11512,11513],{},[1149,11514,11515],{},"t",[1153,11517,11515],{"encoding":1155},"); pravděpodobnost, že ",[1115,11520,11522],{"className":11521},[1137],[1139,11523,11524],{"xmlns":1141},[1143,11525,11526,11530],{},[1146,11527,11528],{},[1149,11529,11107],{},[1153,11531,11107],{"encoding":1155}," nabyla hodnoty ",[1115,11534,11536],{"className":11535},[1137],[1139,11537,11538],{"xmlns":1141},[1143,11539,11540,11544],{},[1146,11541,11542],{},[1149,11543,1168],{},[1153,11545,1168],{"encoding":1155},", zapisujeme ",[1115,11548,11550],{"className":11549},[1137],[1139,11551,11552],{"xmlns":1141},[1143,11553,11554,11568],{},[1146,11555,11556,11558,11560,11562,11564,11566],{},[1149,11557,11102],{},[1193,11559,1199],{"stretchy":1198},[1149,11561,11107],{},[1193,11563,1281],{},[1149,11565,1168],{},[1193,11567,1228],{"stretchy":1198},[1153,11569,11570],{"encoding":1155},"P(X = x)",[1110,11572,11573],{},"Podle typu hodnot, kterých náhodná veličina nabývá, rozlišujeme dva typy:",[1124,11575,11576,11636],{},[1127,11577,11578,11581,11582,11595,11596,11635],{},[1130,11579,11580],{},"Diskrétní náhodná veličina"," — prvky ",[1115,11583,11585],{"className":11584},[1137],[1139,11586,11587],{"xmlns":1141},[1143,11588,11589,11593],{},[1146,11590,11591],{},[1149,11592,11356],{"mathvariant":1854},[1153,11594,11359],{"encoding":1155}," se zobrazí na osu reálných čísel jako izolované body ",[1115,11597,11599],{"className":11598},[1137],[1139,11600,11601],{"xmlns":1141},[1143,11602,11603,11632],{},[1146,11604,11605,11611,11613,11619,11621,11623,11625],{},[1201,11606,11607,11609],{},[1149,11608,1168],{},[1230,11610,1525],{},[1193,11612,1503],{"separator":1121},[1201,11614,11615,11617],{},[1149,11616,1168],{},[1230,11618,1232],{},[1193,11620,1503],{"separator":1121},[1193,11622,1530],{},[1193,11624,1503],{"separator":1121},[1201,11626,11627,11629],{},[1149,11628,1168],{},[1149,11630,11631],{},"k",[1153,11633,11634],{"encoding":1155},"x_1, x_2, \\dots, x_k",", přičemž každý z nich má nenulovou pravděpodobnost. Příklad: počet bodů při hodu kostkou, počet studentů na cvičení.",[1127,11637,11638,11641],{},[1130,11639,11640],{},"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.",[1377,11643,11645],{"id":11644},"distribuční-funkce","Distribuční funkce",[1110,11647,11648,11649,11652],{},"Náhodná veličina nabývá při pokusu určité hodnoty, aniž bychom předem věděli, které. Při opakování pokusu se ale projevují zákonitosti, které popisují ",[1130,11650,11651],{},"zákony rozdělení",". Nejobecnějším z nich je distribuční funkce.",[1110,11654,11655],{},[1864,11656],{"alt":11657,"className":11658,"src":11659},"mask-nv-distribucni-funkce",[1387,1868],"\u002Fwiki-assets\u002Fmask-nv-distribucni-funkce.png",[1103,11661,11664,11671],{"className":11662,"dataCallout":654},[1106,11663],"callout-info",[1110,11665,11667,11670],{"className":11666},[1113],[1115,11668],{"className":11669,"ariaHidden":1121},[1118,1119,1120],"Definice",[1110,11672,11673,11674,11687,11688,11708,11709,11722,11723,11759,11778,11779,11792,11793,1236],{},"Distribuční funkcí náhodné veličiny ",[1115,11675,11677],{"className":11676},[1137],[1139,11678,11679],{"xmlns":1141},[1143,11680,11681,11685],{},[1146,11682,11683],{},[1149,11684,11107],{},[1153,11686,11107],{"encoding":1155}," nazýváme reálnou funkci ",[1115,11689,11691],{"className":11690},[1137],[1139,11692,11693],{"xmlns":1141},[1143,11694,11695,11705],{},[1146,11696,11697,11699,11701,11703],{},[1149,11698,11091],{},[1193,11700,1199],{"stretchy":1198},[1149,11702,1168],{},[1193,11704,1228],{"stretchy":1198},[1153,11706,11707],{"encoding":1155},"F(x)"," definovanou pro každé reálné číslo ",[1115,11710,11712],{"className":11711},[1137],[1139,11713,11714],{"xmlns":1141},[1143,11715,11716,11720],{},[1146,11717,11718],{},[1149,11719,1168],{},[1153,11721,1168],{"encoding":1155}," jako\n",[1115,11724,11726],{"className":11725},[1137],[1139,11727,11728],{"xmlns":1141},[1143,11729,11730,11756],{},[1146,11731,11732,11734,11736,11738,11740,11742,11744,11746,11748,11750,11752,11754],{},[1149,11733,11091],{},[1193,11735,1199],{"stretchy":1198},[1149,11737,1168],{},[1193,11739,1228],{"stretchy":1198},[1193,11741,1281],{},[1149,11743,11102],{},[1193,11745,1199],{"stretchy":1198},[1149,11747,11107],{},[1193,11749,11110],{},[1149,11751,1168],{},[1193,11753,1228],{"stretchy":1198},[1149,11755,1236],{"mathvariant":1854},[1153,11757,11758],{"encoding":1155},"F(x) = P(X \\le x).",[1115,11760,11762],{"className":11761},[1137],[1139,11763,11764],{"xmlns":1141},[1143,11765,11766,11776],{},[1146,11767,11768,11770,11772,11774],{},[1149,11769,11091],{},[1193,11771,1199],{"stretchy":1198},[1149,11773,1168],{},[1193,11775,1228],{"stretchy":1198},[1153,11777,11707],{"encoding":1155}," tedy vyjadřuje pravděpodobnost, s jakou ",[1115,11780,11782],{"className":11781},[1137],[1139,11783,11784],{"xmlns":1141},[1143,11785,11786,11790],{},[1146,11787,11788],{},[1149,11789,11107],{},[1153,11791,11107],{"encoding":1155}," nabude hodnoty z intervalu ",[1115,11794,11796],{"className":11795},[1137],[1139,11797,11798],{"xmlns":1141},[1143,11799,11800,11816],{},[1146,11801,11802,11804,11806,11809,11811,11813],{},[1193,11803,1199],{"stretchy":1198},[1193,11805,1210],{},[1149,11807,11808],{"mathvariant":1854},"∞",[1193,11810,1503],{"separator":1121},[1149,11812,1168],{},[1193,11814,11815],{"stretchy":1198},"⟩",[1153,11817,11818],{"encoding":1155},"(-\\infty, x\\rangle",[1110,11820,11821,11822,11835,11836,11857],{},"Značí-li například ",[1115,11823,11825],{"className":11824},[1137],[1139,11826,11827],{"xmlns":1141},[1143,11828,11829,11833],{},[1146,11830,11831],{},[1149,11832,11107],{},[1153,11834,11107],{"encoding":1155}," výšku mužů v populaci, pak ",[1115,11837,11839],{"className":11838},[1137],[1139,11840,11841],{"xmlns":1141},[1143,11842,11843,11854],{},[1146,11844,11845,11847,11849,11852],{},[1149,11846,11091],{},[1193,11848,1199],{"stretchy":1198},[1230,11850,11851],{},"175",[1193,11853,1228],{"stretchy":1198},[1153,11855,11856],{"encoding":1155},"F(175)"," je pravděpodobnost, že muž měří nejvýše 175 cm.",[1110,11859,11860],{},"Pro distribuční funkci vždy platí:",[1124,11862,11863,11893,11951,12010],{},[1127,11864,11865,1503],{},[1115,11866,11868],{"className":11867},[1137],[1139,11869,11870],{"xmlns":1141},[1143,11871,11872,11890],{},[1146,11873,11874,11876,11878,11880,11882,11884,11886,11888],{},[1230,11875,1597],{},[1193,11877,11110],{},[1149,11879,11091],{},[1193,11881,1199],{"stretchy":1198},[1149,11883,1168],{},[1193,11885,1228],{"stretchy":1198},[1193,11887,11110],{},[1230,11889,1525],{},[1153,11891,11892],{"encoding":1155},"0 \\le F(x) \\le 1",[1127,11894,11895,11896,1503],{},"je neklesající: ",[1115,11897,11899],{"className":11898},[1137],[1139,11900,11901],{"xmlns":1141},[1143,11902,11903,11948],{},[1146,11904,11905,11911,11913,11919,11922,11924,11926,11932,11934,11936,11938,11940,11946],{},[1201,11906,11907,11909],{},[1149,11908,1168],{},[1230,11910,1525],{},[1193,11912,11110],{},[1201,11914,11915,11917],{},[1149,11916,1168],{},[1230,11918,1232],{},[1193,11920,11921],{},"⇒",[1149,11923,11091],{},[1193,11925,1199],{"stretchy":1198},[1201,11927,11928,11930],{},[1149,11929,1168],{},[1230,11931,1525],{},[1193,11933,1228],{"stretchy":1198},[1193,11935,11110],{},[1149,11937,11091],{},[1193,11939,1199],{"stretchy":1198},[1201,11941,11942,11944],{},[1149,11943,1168],{},[1230,11945,1232],{},[1193,11947,1228],{"stretchy":1198},[1153,11949,11950],{"encoding":1155},"x_1 \\le x_2 \\Rightarrow F(x_1) \\le F(x_2)",[1127,11952,11953,11954,1503],{},"je spojitá zprava: ",[1115,11955,11957],{"className":11956},[1137],[1139,11958,11959],{"xmlns":1141},[1143,11960,11961,12007],{},[1146,11962,11963,11985,11987,11989,11991,11993,11995,11997,11999,12001,12003,12005],{},[1201,11964,11965,11972],{},[1146,11966,11967,11970],{},[1149,11968,11969],{},"lim",[1193,11971,1851],{},[1146,11973,11974,11977,11979],{},[1149,11975,11976],{},"h",[1193,11978,1845],{},[1224,11980,11981,11983],{},[1230,11982,1597],{},[1193,11984,1924],{},[1149,11986,11091],{},[1193,11988,1199],{"stretchy":1198},[1149,11990,1168],{},[1193,11992,1924],{},[1149,11994,11976],{},[1193,11996,1228],{"stretchy":1198},[1193,11998,1281],{},[1149,12000,11091],{},[1193,12002,1199],{"stretchy":1198},[1149,12004,1168],{},[1193,12006,1228],{"stretchy":1198},[1153,12008,12009],{"encoding":1155},"\\lim_{h \\to 0^+} F(x+h) = F(x)",[1127,12011,12012,1348,12054,1236],{},[1115,12013,12015],{"className":12014},[1137],[1139,12016,12017],{"xmlns":1141},[1143,12018,12019,12051],{},[1146,12020,12021,12039,12041,12043,12045,12047,12049],{},[1201,12022,12023,12029],{},[1146,12024,12025,12027],{},[1149,12026,11969],{},[1193,12028,1851],{},[1146,12030,12031,12033,12035,12037],{},[1149,12032,1168],{},[1193,12034,1845],{},[1193,12036,1210],{},[1149,12038,11808],{"mathvariant":1854},[1149,12040,11091],{},[1193,12042,1199],{"stretchy":1198},[1149,12044,1168],{},[1193,12046,1228],{"stretchy":1198},[1193,12048,1281],{},[1230,12050,1597],{},[1153,12052,12053],{"encoding":1155},"\\lim_{x \\to -\\infty} F(x) = 0",[1115,12055,12057],{"className":12056},[1137],[1139,12058,12059],{"xmlns":1141},[1143,12060,12061,12091],{},[1146,12062,12063,12079,12081,12083,12085,12087,12089],{},[1201,12064,12065,12071],{},[1146,12066,12067,12069],{},[1149,12068,11969],{},[1193,12070,1851],{},[1146,12072,12073,12075,12077],{},[1149,12074,1168],{},[1193,12076,1845],{},[1149,12078,11808],{"mathvariant":1854},[1149,12080,11091],{},[1193,12082,1199],{"stretchy":1198},[1149,12084,1168],{},[1193,12086,1228],{"stretchy":1198},[1193,12088,1281],{},[1230,12090,1525],{},[1153,12092,12093],{"encoding":1155},"\\lim_{x \\to \\infty} F(x) = 1",[1110,12095,12096],{},"U spojité náhodné veličiny je distribuční funkce svázaná s hustotou pravděpodobnosti vztahem",[1115,12098,12100],{"className":12099},[1137],[1139,12101,12102],{"xmlns":1141,"display":1796},[1143,12103,12104,12172],{},[1146,12105,12106,12112,12114,12116,12118,12120,12122,12124,12126,12128,12130,12132,12134,12136,12138,12140,12142,12155,12157,12159,12161,12163,12165,12168,12170],{},[1224,12107,12108,12110],{},[1149,12109,11091],{},[1193,12111,11134],{"mathvariant":1854,"lspace":3302,"rspace":3302},[1193,12113,1199],{"stretchy":1198},[1149,12115,1168],{},[1193,12117,1228],{"stretchy":1198},[1193,12119,1281],{},[1149,12121,1582],{},[1193,12123,1199],{"stretchy":1198},[1149,12125,1168],{},[1193,12127,1228],{"stretchy":1198},[1193,12129,1503],{"separator":1121},[1936,12131],{"width":1938},[1149,12133,11091],{},[1193,12135,1199],{"stretchy":1198},[1149,12137,1168],{},[1193,12139,1228],{"stretchy":1198},[1193,12141,1281],{},[3698,12143,12144,12147,12153],{},[1193,12145,12146],{},"∫",[1146,12148,12149,12151],{},[1193,12150,1210],{},[1149,12152,11808],{"mathvariant":1854},[1149,12154,1168],{},[1149,12156,1582],{},[1193,12158,1199],{"stretchy":1198},[1149,12160,11515],{},[1193,12162,1228],{"stretchy":1198},[2201,12164,2203],{},[1149,12166,12167],{},"d",[1149,12169,11515],{},[1149,12171,1236],{"mathvariant":1854},[1153,12173,12174],{"encoding":1155},"F'(x) = f(x), \\qquad F(x) = \\int_{-\\infty}^{x} f(t)\\,dt.",[1110,12176,12177,12178,12191,12192,1405,12210,12228],{},"Pravděpodobnost, že ",[1115,12179,12181],{"className":12180},[1137],[1139,12182,12183],{"xmlns":1141},[1143,12184,12185,12189],{},[1146,12186,12187],{},[1149,12188,11107],{},[1153,12190,11107],{"encoding":1155}," padne mezi body ",[1115,12193,12195],{"className":12194},[1137],[1139,12196,12197],{"xmlns":1141},[1143,12198,12199,12207],{},[1146,12200,12201],{},[1201,12202,12203,12205],{},[1149,12204,1168],{},[1230,12206,1525],{},[1153,12208,12209],{"encoding":1155},"x_1",[1115,12211,12213],{"className":12212},[1137],[1139,12214,12215],{"xmlns":1141},[1143,12216,12217,12225],{},[1146,12218,12219],{},[1201,12220,12221,12223],{},[1149,12222,1168],{},[1230,12224,1232],{},[1153,12226,12227],{"encoding":1155},"x_2",", se pak počítá jako",[1115,12230,12232],{"className":12231},[1137],[1139,12233,12234],{"xmlns":1141,"display":1796},[1143,12235,12236,12324],{},[1146,12237,12238,12240,12242,12248,12250,12252,12254,12260,12262,12264,12280,12282,12284,12286,12288,12290,12292,12294,12296,12298,12300,12306,12308,12310,12312,12314,12320,12322],{},[1149,12239,11102],{},[1193,12241,1199],{"stretchy":1198},[1201,12243,12244,12246],{},[1149,12245,1168],{},[1230,12247,1525],{},[1193,12249,5343],{},[1149,12251,11107],{},[1193,12253,5343],{},[1201,12255,12256,12258],{},[1149,12257,1168],{},[1230,12259,1232],{},[1193,12261,1228],{"stretchy":1198},[1193,12263,1281],{},[3698,12265,12266,12268,12274],{},[1193,12267,12146],{},[1201,12269,12270,12272],{},[1149,12271,1168],{},[1230,12273,1525],{},[1201,12275,12276,12278],{},[1149,12277,1168],{},[1230,12279,1232],{},[1149,12281,1582],{},[1193,12283,1199],{"stretchy":1198},[1149,12285,11515],{},[1193,12287,1228],{"stretchy":1198},[2201,12289,2203],{},[1149,12291,12167],{},[1149,12293,11515],{},[1193,12295,1281],{},[1149,12297,11091],{},[1193,12299,1199],{"stretchy":1198},[1201,12301,12302,12304],{},[1149,12303,1168],{},[1230,12305,1232],{},[1193,12307,1228],{"stretchy":1198},[1193,12309,1210],{},[1149,12311,11091],{},[1193,12313,1199],{"stretchy":1198},[1201,12315,12316,12318],{},[1149,12317,1168],{},[1230,12319,1525],{},[1193,12321,1228],{"stretchy":1198},[1149,12323,1236],{"mathvariant":1854},[1153,12325,12326],{"encoding":1155},"P(x_1 \u003C X \u003C x_2) = \\int_{x_1}^{x_2} f(t)\\,dt = F(x_2) - F(x_1).",[1377,12328,12330],{"id":12329},"hustota-pravděpodobnosti","Hustota pravděpodobnosti",[1103,12332,12334,12340],{"className":12333,"dataCallout":654},[1106,11663],[1110,12335,12337,11670],{"className":12336},[1113],[1115,12338],{"className":12339,"ariaHidden":1121},[1118,1119,1120],[1110,12341,12342,12343,12362,12363,12376,12377,12390,12391,1236],{},"Hustota pravděpodobnosti ",[1115,12344,12346],{"className":12345},[1137],[1139,12347,12348],{"xmlns":1141},[1143,12349,12350,12360],{},[1146,12351,12352,12354,12356,12358],{},[1149,12353,1582],{},[1193,12355,1199],{"stretchy":1198},[1149,12357,1168],{},[1193,12359,1228],{"stretchy":1198},[1153,12361,11174],{"encoding":1155}," určuje, jak jsou hodnoty spojité náhodné veličiny ",[1115,12364,12366],{"className":12365},[1137],[1139,12367,12368],{"xmlns":1141},[1143,12369,12370,12374],{},[1146,12371,12372],{},[1149,12373,11107],{},[1153,12375,11107],{"encoding":1155}," nahuštěny v okolí bodu ",[1115,12378,12380],{"className":12379},[1137],[1139,12381,12382],{"xmlns":1141},[1143,12383,12384,12388],{},[1146,12385,12386],{},[1149,12387,1168],{},[1153,12389,1168],{"encoding":1155},". Je vždy nezáporná a platí pro ni ",[1115,12392,12394],{"className":12393},[1137],[1139,12395,12396],{"xmlns":1141},[1143,12397,12398,12430],{},[1146,12399,12400,12412,12414,12416,12418,12420,12422,12424,12426,12428],{},[3698,12401,12402,12404,12410],{},[1193,12403,12146],{},[1146,12405,12406,12408],{},[1193,12407,1210],{},[1149,12409,11808],{"mathvariant":1854},[1149,12411,11808],{"mathvariant":1854},[1149,12413,1582],{},[1193,12415,1199],{"stretchy":1198},[1149,12417,1168],{},[1193,12419,1228],{"stretchy":1198},[2201,12421,2203],{},[1149,12423,12167],{},[1149,12425,1168],{},[1193,12427,1281],{},[1230,12429,1525],{},[1153,12431,12432],{"encoding":1155},"\\int_{-\\infty}^{\\infty} f(x)\\,dx = 1",[1110,12434,12435],{},"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.",[1377,12437,12439],{"id":12438},"charakteristiky-spojité-náhodné-veličiny","Charakteristiky spojité náhodné veličiny",[1110,12441,12442,12445],{},[1130,12443,12444],{},"Střední hodnota"," je nejdůležitější charakteristika náhodné veličiny:",[1115,12447,12449],{"className":12448},[1137],[1139,12450,12451],{"xmlns":1141,"display":1796},[1143,12452,12453,12498],{},[1146,12454,12455,12458,12460,12462,12464,12466,12478,12480,12482,12484,12486,12488,12490,12492,12494,12496],{},[1149,12456,12457],{},"E",[1193,12459,1199],{"stretchy":1198},[1149,12461,11107],{},[1193,12463,1228],{"stretchy":1198},[1193,12465,1281],{},[3698,12467,12468,12470,12476],{},[1193,12469,12146],{},[1146,12471,12472,12474],{},[1193,12473,1210],{},[1149,12475,11808],{"mathvariant":1854},[1149,12477,11808],{"mathvariant":1854},[1149,12479,1168],{},[1193,12481,3045],{},[1149,12483,1582],{},[1193,12485,1199],{"stretchy":1198},[1149,12487,1168],{},[1193,12489,1228],{"stretchy":1198},[2201,12491,2203],{},[1149,12493,12167],{},[1149,12495,1168],{},[1149,12497,1236],{"mathvariant":1854},[1153,12499,12500],{"encoding":1155},"E(X) = \\int_{-\\infty}^{\\infty} x \\cdot f(x)\\,dx.",[1110,12502,12503],{},"Je to číslo, kolem něhož kolísají výběrové průměry vypočtené ze sérií pozorovaných hodnot náhodné veličiny.",[1110,12505,12506,1405,12509,1902],{},[1130,12507,12508],{},"Rozptyl",[1130,12510,12511],{},"směrodatná odchylka",[1115,12513,12515],{"className":12514},[1137],[1139,12516,12517],{"xmlns":1141,"display":1796},[1143,12518,12519,12660],{},[1146,12520,12521,12524,12526,12528,12530,12532,12544,12547,12549,12551,12553,12555,12557,12559,12566,12568,12570,12572,12574,12576,12578,12580,12582,12594,12600,12602,12604,12606,12608,12610,12612,12614,12616,12618,12620,12622,12624,12626,12632,12634,12636,12638,12640,12642,12644,12646,12658],{},[1149,12522,12523],{},"D",[1193,12525,1199],{"stretchy":1198},[1149,12527,11107],{},[1193,12529,1228],{"stretchy":1198},[1193,12531,1281],{},[3698,12533,12534,12536,12542],{},[1193,12535,12146],{},[1146,12537,12538,12540],{},[1193,12539,1210],{},[1149,12541,11808],{"mathvariant":1854},[1149,12543,11808],{"mathvariant":1854},[1193,12545,12546],{"stretchy":1198},"[",[1149,12548,1168],{},[1193,12550,1210],{},[1149,12552,12457],{},[1193,12554,1199],{"stretchy":1198},[1149,12556,11107],{},[1193,12558,1228],{"stretchy":1198},[1224,12560,12561,12564],{},[1193,12562,12563],{"stretchy":1198},"]",[1230,12565,1232],{},[1149,12567,1582],{},[1193,12569,1199],{"stretchy":1198},[1149,12571,1168],{},[1193,12573,1228],{"stretchy":1198},[2201,12575,2203],{},[1149,12577,12167],{},[1149,12579,1168],{},[1193,12581,1281],{},[3698,12583,12584,12586,12592],{},[1193,12585,12146],{},[1146,12587,12588,12590],{},[1193,12589,1210],{},[1149,12591,11808],{"mathvariant":1854},[1149,12593,11808],{"mathvariant":1854},[1224,12595,12596,12598],{},[1149,12597,1168],{},[1230,12599,1232],{},[1149,12601,1582],{},[1193,12603,1199],{"stretchy":1198},[1149,12605,1168],{},[1193,12607,1228],{"stretchy":1198},[2201,12609,2203],{},[1149,12611,12167],{},[1149,12613,1168],{},[1193,12615,1210],{},[1193,12617,12546],{"stretchy":1198},[1149,12619,12457],{},[1193,12621,1199],{"stretchy":1198},[1149,12623,11107],{},[1193,12625,1228],{"stretchy":1198},[1224,12627,12628,12630],{},[1193,12629,12563],{"stretchy":1198},[1230,12631,1232],{},[1193,12633,1503],{"separator":1121},[1936,12635],{"width":1938},[1149,12637,11271],{},[1193,12639,1199],{"stretchy":1198},[1149,12641,11107],{},[1193,12643,1228],{"stretchy":1198},[1193,12645,1281],{},[1283,12647,12648],{},[1146,12649,12650,12652,12654,12656],{},[1149,12651,12523],{},[1193,12653,1199],{"stretchy":1198},[1149,12655,11107],{},[1193,12657,1228],{"stretchy":1198},[1149,12659,1236],{"mathvariant":1854},[1153,12661,12662],{"encoding":1155},"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)}.",[1110,12664,12665,12666,12669],{},"Směrodatná odchylka udává, jak moc jsou hodnoty náhodné veličiny rozptýlené kolem střední hodnoty. (Pro odhad těchto charakteristik z naměřených dat viz empirické protějšky v ",[1384,12667,886],{"className":12668,"dataFsResolvedFilePath":5882,"href":5883},[1387],".)",[1110,12671,12672,12675,12676,12689,12690,12708,12709,12722],{},[1130,12673,12674],{},"Kvantily"," udávají, jak jsou hodnoty náhodné veličiny ",[1115,12677,12679],{"className":12678},[1137],[1139,12680,12681],{"xmlns":1141},[1143,12682,12683,12687],{},[1146,12684,12685],{},[1149,12686,11107],{},[1153,12688,11107],{"encoding":1155}," rozděleny na ose reálných čísel v určitém pravděpodobnostním poměru. 100p%-ní kvantil ",[1115,12691,12693],{"className":12692},[1137],[1139,12694,12695],{"xmlns":1141},[1143,12696,12697,12705],{},[1146,12698,12699],{},[1201,12700,12701,12703],{},[1149,12702,1168],{},[1149,12704,1110],{},[1153,12706,12707],{"encoding":1155},"x_p"," je číslo, pro které při zvolené pravděpodobnosti ",[1115,12710,12712],{"className":12711},[1137],[1139,12713,12714],{"xmlns":1141},[1143,12715,12716,12720],{},[1146,12717,12718],{},[1149,12719,1110],{},[1153,12721,1110],{"encoding":1155}," platí",[1115,12724,12726],{"className":12725},[1137],[1139,12727,12728],{"xmlns":1141,"display":1796},[1143,12729,12730,12750],{},[1146,12731,12732,12734,12736,12742,12744,12746,12748],{},[1149,12733,11091],{},[1193,12735,1199],{"stretchy":1198},[1201,12737,12738,12740],{},[1149,12739,1168],{},[1149,12741,1110],{},[1193,12743,1228],{"stretchy":1198},[1193,12745,1281],{},[1149,12747,1110],{},[1149,12749,1236],{"mathvariant":1854},[1153,12751,12752],{"encoding":1155},"F(x_p) = p.",[1110,12754,12755,12756,12784,12785,12812,12813,12832,12833,12852,12853,1236],{},"V intervalu ",[1115,12757,12759],{"className":12758},[1137],[1139,12760,12761],{"xmlns":1141},[1143,12762,12763,12781],{},[1146,12764,12765,12767,12769,12771,12773,12779],{},[1193,12766,1199],{"stretchy":1198},[1193,12768,1210],{},[1149,12770,11808],{"mathvariant":1854},[1193,12772,1589],{"separator":1121},[1201,12774,12775,12777],{},[1149,12776,1168],{},[1149,12778,1110],{},[1193,12780,1228],{"stretchy":1198},[1153,12782,12783],{"encoding":1155},"(-\\infty; x_p)"," leží 100p % hodnot, v intervalu ",[1115,12786,12788],{"className":12787},[1137],[1139,12789,12790],{"xmlns":1141},[1143,12791,12792,12809],{},[1146,12793,12794,12797,12803,12805,12807],{},[1193,12795,12796],{"stretchy":1198},"⟨",[1201,12798,12799,12801],{},[1149,12800,1168],{},[1149,12802,1110],{},[1193,12804,1589],{"separator":1121},[1149,12806,11808],{"mathvariant":1854},[1193,12808,1228],{"stretchy":1198},[1153,12810,12811],{"encoding":1155},"\\langle x_p; \\infty)"," leží 100(1-p) % hodnot. Nejdůležitější kvantily jsou medián ",[1115,12814,12816],{"className":12815},[1137],[1139,12817,12818],{"xmlns":1141},[1143,12819,12820,12829],{},[1146,12821,12822],{},[1201,12823,12824,12826],{},[1149,12825,1168],{},[1230,12827,12828],{},"0,5",[1153,12830,12831],{"encoding":1155},"x_{0{,}5}",", dolní kvartil ",[1115,12834,12836],{"className":12835},[1137],[1139,12837,12838],{"xmlns":1141},[1143,12839,12840,12849],{},[1146,12841,12842],{},[1201,12843,12844,12846],{},[1149,12845,1168],{},[1230,12847,12848],{},"0,25",[1153,12850,12851],{"encoding":1155},"x_{0{,}25}"," a horní kvartil ",[1115,12854,12856],{"className":12855},[1137],[1139,12857,12858],{"xmlns":1141},[1143,12859,12860,12869],{},[1146,12861,12862],{},[1201,12863,12864,12866],{},[1149,12865,1168],{},[1230,12867,12868],{},"0,75",[1153,12870,12871],{"encoding":1155},"x_{0{,}75}",[1377,12873,11247],{"id":12874},"normální-rozdělení",[1110,12876,12877,12878,12891,12892,1243,12895,12922],{},"Spojitá náhodná veličina ",[1115,12879,12881],{"className":12880},[1137],[1139,12882,12883],{"xmlns":1141},[1143,12884,12885,12889],{},[1146,12886,12887],{},[1149,12888,11107],{},[1153,12890,11107],{"encoding":1155}," má ",[1130,12893,12894],{},"normální rozdělení",[1115,12896,12898],{"className":12897},[1137],[1139,12899,12900],{"xmlns":1141},[1143,12901,12902,12920],{},[1146,12903,12904,12906,12908,12910,12912,12918],{},[1149,12905,11259],{},[1193,12907,1199],{"stretchy":1198},[1149,12909,11264],{},[1193,12911,1589],{"separator":1121},[1224,12913,12914,12916],{},[1149,12915,11271],{},[1230,12917,1232],{},[1193,12919,1228],{"stretchy":1198},[1153,12921,11278],{"encoding":1155},", jestliže její hustota pravděpodobnosti a distribuční funkce jsou dány předpisy",[1115,12924,12926],{"className":12925},[1137],[1139,12927,12928],{"xmlns":1141,"display":1796},[1143,12929,12930,13081],{},[1146,12931,12932,12934,12936,12938,12940,12942,12959,12995,12997,12999,13001,13003,13005,13007,13009,13025,13037,13073,13075,13077,13079],{},[1149,12933,1582],{},[1193,12935,1199],{"stretchy":1198},[1149,12937,1168],{},[1193,12939,1228],{"stretchy":1198},[1193,12941,1281],{},[3546,12943,12944,12946],{},[1230,12945,1525],{},[1146,12947,12948,12950],{},[1149,12949,11271],{},[1283,12951,12952],{},[1146,12953,12954,12956],{},[1230,12955,1232],{},[1149,12957,12958],{},"π",[1224,12960,12961,12963],{},[1149,12962,1754],{},[1146,12964,12965,12967],{},[1193,12966,1210],{},[3546,12968,12969,12985],{},[1146,12970,12971,12973,12975,12977,12979],{},[1193,12972,1199],{"stretchy":1198},[1149,12974,1168],{},[1193,12976,1210],{},[1149,12978,11264],{},[1224,12980,12981,12983],{},[1193,12982,1228],{"stretchy":1198},[1230,12984,1232],{},[1146,12986,12987,12989],{},[1230,12988,1232],{},[1224,12990,12991,12993],{},[1149,12992,11271],{},[1230,12994,1232],{},[1193,12996,1503],{"separator":1121},[1936,12998],{"width":1938},[1149,13000,11091],{},[1193,13002,1199],{"stretchy":1198},[1149,13004,1168],{},[1193,13006,1228],{"stretchy":1198},[1193,13008,1281],{},[3546,13010,13011,13013],{},[1230,13012,1525],{},[1146,13014,13015,13017],{},[1149,13016,11271],{},[1283,13018,13019],{},[1146,13020,13021,13023],{},[1230,13022,1232],{},[1149,13024,12958],{},[3698,13026,13027,13029,13035],{},[1193,13028,12146],{},[1146,13030,13031,13033],{},[1193,13032,1210],{},[1149,13034,11808],{"mathvariant":1854},[1149,13036,1168],{},[1224,13038,13039,13041],{},[1149,13040,1754],{},[1146,13042,13043,13045],{},[1193,13044,1210],{},[3546,13046,13047,13063],{},[1146,13048,13049,13051,13053,13055,13057],{},[1193,13050,1199],{"stretchy":1198},[1149,13052,11515],{},[1193,13054,1210],{},[1149,13056,11264],{},[1224,13058,13059,13061],{},[1193,13060,1228],{"stretchy":1198},[1230,13062,1232],{},[1146,13064,13065,13067],{},[1230,13066,1232],{},[1224,13068,13069,13071],{},[1149,13070,11271],{},[1230,13072,1232],{},[2201,13074,2203],{},[1149,13076,12167],{},[1149,13078,11515],{},[1193,13080,1503],{"separator":1121},[1153,13082,13083],{"encoding":1155},"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,",[1110,13085,13086,13087,1348,13111,1236],{},"přičemž ",[1115,13088,13090],{"className":13089},[1137],[1139,13091,13092],{"xmlns":1141},[1143,13093,13094,13108],{},[1146,13095,13096,13098,13100,13102,13104,13106],{},[1149,13097,12457],{},[1193,13099,1199],{"stretchy":1198},[1149,13101,11107],{},[1193,13103,1228],{"stretchy":1198},[1193,13105,1281],{},[1149,13107,11264],{},[1153,13109,13110],{"encoding":1155},"E(X) = \\mu",[1115,13112,13114],{"className":13113},[1137],[1139,13115,13116],{"xmlns":1141},[1143,13117,13118,13136],{},[1146,13119,13120,13122,13124,13126,13128,13130],{},[1149,13121,12523],{},[1193,13123,1199],{"stretchy":1198},[1149,13125,11107],{},[1193,13127,1228],{"stretchy":1198},[1193,13129,1281],{},[1224,13131,13132,13134],{},[1149,13133,11271],{},[1230,13135,1232],{},[1153,13137,13138],{"encoding":1155},"D(X) = \\sigma^2",[1110,13140,13141],{},[1864,13142],{"alt":13143,"className":13144,"src":13145},"mask-nv-normalni",[1387,1868],"\u002Fwiki-assets\u002Fmask-nv-normalni.png",[1110,13147,13148,13149,13152,13153,13167,13168,13187,13188,13204,13205,13218,13219,1236],{},"Křivka hustoty se nazývá ",[1130,13150,13151],{},"Gaussova křivka",": je symetrická kolem svislé přímky procházející ",[1115,13154,13156],{"className":13155},[1137],[1139,13157,13158],{"xmlns":1141},[1143,13159,13160,13164],{},[1146,13161,13162],{},[1149,13163,11264],{},[1153,13165,13166],{"encoding":1155},"\\mu",", kde má ",[1115,13169,13171],{"className":13170},[1137],[1139,13172,13173],{"xmlns":1141},[1143,13174,13175,13185],{},[1146,13176,13177,13179,13181,13183],{},[1149,13178,1582],{},[1193,13180,1199],{"stretchy":1198},[1149,13182,1168],{},[1193,13184,1228],{"stretchy":1198},[1153,13186,11174],{"encoding":1155}," globální maximum, a ve vzdálenosti ",[1115,13189,13191],{"className":13190},[1137],[1139,13192,13193],{"xmlns":1141},[1143,13194,13195,13201],{},[1146,13196,13197,13199],{},[1230,13198,8010],{},[1149,13200,11271],{},[1153,13202,13203],{"encoding":1155},"3\\sigma"," od ",[1115,13206,13208],{"className":13207},[1137],[1139,13209,13210],{"xmlns":1141},[1143,13211,13212,13216],{},[1146,13213,13214],{},[1149,13215,11264],{},[1153,13217,13166],{"encoding":1155}," se téměř dotýká osy x — zhruba 99,73 % hodnot leží v intervalu ",[1115,13220,13222],{"className":13221},[1137],[1139,13223,13224],{"xmlns":1141},[1143,13225,13226,13250],{},[1146,13227,13228,13230,13232,13234,13236,13238,13240,13242,13244,13246,13248],{},[1193,13229,1199],{"stretchy":1198},[1149,13231,11264],{},[1193,13233,1210],{},[1230,13235,8010],{},[1149,13237,11271],{},[1193,13239,1589],{"separator":1121},[1149,13241,11264],{},[1193,13243,1924],{},[1230,13245,8010],{},[1149,13247,11271],{},[1193,13249,1228],{"stretchy":1198},[1153,13251,13252],{"encoding":1155},"(\\mu - 3\\sigma; \\mu + 3\\sigma)",[1110,13254,13255,13256,1243,13259,13283,13284,1236],{},"Zvláštní postavení má ",[1130,13257,13258],{},"normované normální rozdělení",[1115,13260,13262],{"className":13261},[1137],[1139,13263,13264],{"xmlns":1141},[1143,13265,13266,13280],{},[1146,13267,13268,13270,13272,13274,13276,13278],{},[1149,13269,11259],{},[1193,13271,1199],{"stretchy":1198},[1230,13273,1597],{},[1193,13275,1589],{"separator":1121},[1230,13277,1525],{},[1193,13279,1228],{"stretchy":1198},[1153,13281,13282],{"encoding":1155},"N(0; 1)",", na které se dá libovolné normální rozdělení převést standardizací ",[1115,13285,13287],{"className":13286},[1137],[1139,13288,13289],{"xmlns":1141},[1143,13290,13291,13312],{},[1146,13292,13293,13296,13298,13300,13302,13304,13306,13308,13310],{},[1149,13294,13295],{},"Z",[1193,13297,1281],{},[1193,13299,1199],{"stretchy":1198},[1149,13301,11107],{},[1193,13303,1210],{},[1149,13305,11264],{},[1193,13307,1228],{"stretchy":1198},[1149,13309,5731],{"mathvariant":1854},[1149,13311,11271],{},[1153,13313,13314],{"encoding":1155},"Z = (X-\\mu)\u002F\\sigma",[13316,13317],"graph-mount",{"spec":13318},"{\"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\"}]}",[1103,13320,13322,13329],{"className":13321,"dataCallout":5686},[1106,5685],[1110,13323,13325,13328],{"className":13324},[1113],[1115,13326],{"className":13327,"ariaHidden":1121},[1118,5693,1120],"R očekává směrodatnou odchylku, ne rozptyl",[1110,13330,13331,13332,13359,13360,13363,13364,1348,13366,1405,13368,13370,13371,1243,13374,13387,13388,13413,13414,13417,13418,1236],{},"Zápis ",[1115,13333,13335],{"className":13334},[1137],[1139,13336,13337],{"xmlns":1141},[1143,13338,13339,13357],{},[1146,13340,13341,13343,13345,13347,13349,13355],{},[1149,13342,11259],{},[1193,13344,1199],{"stretchy":1198},[1149,13346,11264],{},[1193,13348,1589],{"separator":1121},[1224,13350,13351,13353],{},[1149,13352,11271],{},[1230,13354,1232],{},[1193,13356,1228],{"stretchy":1198},[1153,13358,11278],{"encoding":1155}," v definici používá ",[1130,13361,13362],{},"rozptyl",". Funkce ",[1332,13365,11282],{},[1332,13367,11285],{},[1332,13369,11288],{}," v R ale jako třetí argument berou ",[1130,13372,13373],{},"směrodatnou odchylku",[1115,13375,13377],{"className":13376},[1137],[1139,13378,13379],{"xmlns":1141},[1143,13380,13381,13385],{},[1146,13382,13383],{},[1149,13384,11271],{},[1153,13386,11303],{"encoding":1155},". Má-li náhodná veličina rozdělení ",[1115,13389,13391],{"className":13390},[1137],[1139,13392,13393],{"xmlns":1141},[1143,13394,13395,13410],{},[1146,13396,13397,13399,13401,13403,13405,13408],{},[1149,13398,11259],{},[1193,13400,1199],{"stretchy":1198},[1230,13402,5389],{},[1193,13404,1589],{"separator":1121},[1230,13406,13407],{},"0,12",[1193,13409,1228],{"stretchy":1198},[1153,13411,13412],{"encoding":1155},"N(10; 0{,}12)",", je ",[1332,13415,13416],{},"sd = sqrt(0.12)",", ne ",[1332,13419,13420],{},"sd = 0.12",[1110,13422,13423],{},"V R:",[2035,13425,13427],{"className":2037,"code":13426,"language":71,"meta":2039,"style":2039},"dnorm(0)\npnorm(1.96)\nqnorm(0.975)\n",[1332,13428,13429,13439,13450],{"__ignoreMap":2039},[1115,13430,13431,13433,13435,13437],{"class":2044,"line":10},[1115,13432,11282],{"class":2055},[1115,13434,1199],{"class":2059},[1115,13436,1597],{"class":2062},[1115,13438,2090],{"class":2059},[1115,13440,13441,13443,13445,13448],{"class":2044,"line":27},[1115,13442,11285],{"class":2055},[1115,13444,1199],{"class":2059},[1115,13446,13447],{"class":2062},"1.96",[1115,13449,2090],{"class":2059},[1115,13451,13452,13454,13456,13459],{"class":2044,"line":148},[1115,13453,11288],{"class":2055},[1115,13455,1199],{"class":2059},[1115,13457,13458],{"class":2062},"0.975",[1115,13460,2090],{"class":2059},[2035,13462,13465],{"className":13463,"code":13464,"language":2169,"meta":2039},[2167],"[1] 0.3989423\n[1] 0.9750021\n[1] 1.959964\n",[1332,13466,13464],{"__ignoreMap":2039},[1110,13468,13469,13472,13473,13497,13498,6324,13501,1405,13522,13525],{},[1332,13470,13471],{},"dnorm(0)"," je hodnota hustoty ",[1115,13474,13476],{"className":13475},[1137],[1139,13477,13478],{"xmlns":1141},[1143,13479,13480,13494],{},[1146,13481,13482,13484,13486,13488,13490,13492],{},[1149,13483,11259],{},[1193,13485,1199],{"stretchy":1198},[1230,13487,1597],{},[1193,13489,1589],{"separator":1121},[1230,13491,1525],{},[1193,13493,1228],{"stretchy":1198},[1153,13495,13496],{"encoding":1155},"N(0;1)"," v bodě 0, ",[1332,13499,13500],{},"pnorm(1.96)",[1115,13502,13504],{"className":13503},[1137],[1139,13505,13506],{"xmlns":1141},[1143,13507,13508,13519],{},[1146,13509,13510,13512,13514,13517],{},[1149,13511,11091],{},[1193,13513,1199],{"stretchy":1198},[1230,13515,13516],{},"1,96",[1193,13518,1228],{"stretchy":1198},[1153,13520,13521],{"encoding":1155},"F(1{,}96)",[1332,13523,13524],{},"qnorm(0.975)"," je 97,5%-ní kvantil — hodnota, pod kterou leží 97,5 % pravděpodobnosti.",[1103,13527,13529,13536],{"className":13528,"dataCallout":2932},[1106,2931],[1110,13530,13532,13535],{"className":13531},[1113],[1115,13533],{"className":13534,"ariaHidden":1121},[1118,2939,1120],"Příklad: Návštěvnost zábavního parku",[1110,13537,13538,13539,13574],{},"Denní návštěvnost zábavního parku je náhodná veličina s normálním rozdělením, průměrnou hodnotou 230 a směrodatnou odchylkou 27,5 návštěvníků: ",[1115,13540,13542],{"className":13541},[1137],[1139,13543,13544],{"xmlns":1141},[1143,13545,13546,13571],{},[1146,13547,13548,13550,13553,13555,13557,13560,13562,13569],{},[1149,13549,11107],{},[1193,13551,13552],{},"∼",[1149,13554,11259],{},[1193,13556,1199],{"stretchy":1198},[1230,13558,13559],{},"230",[1193,13561,1589],{"separator":1121},[1224,13563,13564,13567],{},[1230,13565,13566],{},"27,5",[1230,13568,1232],{},[1193,13570,1228],{"stretchy":1198},[1153,13572,13573],{"encoding":1155},"X \\sim N(230; 27{,}5^2)",". Přijde-li za den méně než 180 návštěvníků, je park ztrátový. Kolik procent dní je ztrátových?",[1110,13576,13577],{},[1864,13578],{"alt":13579,"className":13580,"src":13581},"mask-nv-priklad-park",[1387,1868],"\u002Fwiki-assets\u002Fmask-nv-priklad-park.png",[2035,13583,13585],{"className":2037,"code":13584,"language":71,"meta":2039,"style":2039},"pnorm(180, mean = 230, sd = 27.5)\n",[1332,13586,13587],{"__ignoreMap":2039},[1115,13588,13589,13591,13593,13596,13598,13601,13603,13606,13608,13611,13613,13616],{"class":2044,"line":10},[1115,13590,11285],{"class":2055},[1115,13592,1199],{"class":2059},[1115,13594,13595],{"class":2062},"180",[1115,13597,1503],{"class":2051},[1115,13599,13600],{"class":2047}," mean",[1115,13602,2510],{"class":2051},[1115,13604,13605],{"class":2062}," 230",[1115,13607,1503],{"class":2051},[1115,13609,13610],{"class":2047}," sd",[1115,13612,2510],{"class":2051},[1115,13614,13615],{"class":2062}," 27.5",[1115,13617,2090],{"class":2059},[2035,13619,13622],{"className":13620,"code":13621,"language":2169,"meta":2039},[2167],"[1] 0.03451817\n",[1332,13623,13621],{"__ignoreMap":2039},[1110,13625,13626],{},"Park je ztrátový přibližně v 3,45 % dní.",[1103,13628,13630,13637],{"className":13629,"dataCallout":2932},[1106,2931],[1110,13631,13633,13636],{"className":13632},[1113],[1115,13634],{"className":13635,"ariaHidden":1121},[1118,2939,1120],"Příklad: Délka výrobku",[1110,13638,13639,13640,13674],{},"Automat je seřízen tak, aby střední hodnota délky výrobku byla 42 mm, s přesností charakterizovanou směrodatnou odchylkou 1,2 mm: ",[1115,13641,13643],{"className":13642},[1137],[1139,13644,13645],{"xmlns":1141},[1143,13646,13647,13671],{},[1146,13648,13649,13651,13653,13655,13657,13660,13662,13669],{},[1149,13650,11107],{},[1193,13652,13552],{},[1149,13654,11259],{},[1193,13656,1199],{"stretchy":1198},[1230,13658,13659],{},"42",[1193,13661,1589],{"separator":1121},[1224,13663,13664,13667],{},[1230,13665,13666],{},"1,2",[1230,13668,1232],{},[1193,13670,1228],{"stretchy":1198},[1153,13672,13673],{"encoding":1155},"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?",[1110,13676,13677],{},[1864,13678],{"alt":13679,"className":13680,"src":13681},"mask-nv-priklad-delka",[1387,1868],"\u002Fwiki-assets\u002Fmask-nv-priklad-delka.png",[2035,13683,13685],{"className":2037,"code":13684,"language":71,"meta":2039,"style":2039},"pnorm(43, mean = 42, sd = 1.2) - pnorm(41, mean = 42, sd = 1.2)\n",[1332,13686,13687],{"__ignoreMap":2039},[1115,13688,13689,13691,13693,13696,13698,13700,13702,13705,13707,13709,13711,13714,13716,13718,13721,13723,13726,13728,13730,13732,13734,13736,13738,13740,13742],{"class":2044,"line":10},[1115,13690,11285],{"class":2055},[1115,13692,1199],{"class":2059},[1115,13694,13695],{"class":2062},"43",[1115,13697,1503],{"class":2051},[1115,13699,13600],{"class":2047},[1115,13701,2510],{"class":2051},[1115,13703,13704],{"class":2062}," 42",[1115,13706,1503],{"class":2051},[1115,13708,13610],{"class":2047},[1115,13710,2510],{"class":2051},[1115,13712,13713],{"class":2062}," 1.2",[1115,13715,8993],{"class":2059},[1115,13717,9028],{"class":2051},[1115,13719,13720],{"class":2055}," pnorm",[1115,13722,1199],{"class":2059},[1115,13724,13725],{"class":2062},"41",[1115,13727,1503],{"class":2051},[1115,13729,13600],{"class":2047},[1115,13731,2510],{"class":2051},[1115,13733,13704],{"class":2062},[1115,13735,1503],{"class":2051},[1115,13737,13610],{"class":2047},[1115,13739,2510],{"class":2051},[1115,13741,13713],{"class":2062},[1115,13743,2090],{"class":2059},[2035,13745,13748],{"className":13746,"code":13747,"language":2169,"meta":2039},[2167],"[1] 0.5953432\n",[1332,13749,13747],{"__ignoreMap":2039},[1110,13751,13752],{},"Do 1. jakostní třídy spadá přibližně 59,53 % výrobků.",[1103,13754,13756,13763],{"className":13755,"dataCallout":2932},[1106,2931],[1110,13757,13759,13762],{"className":13758},[1113],[1115,13760],{"className":13761,"ariaHidden":1121},[1118,2939,1120],"Příklad: Obsah ampulky",[1110,13764,13765,13766,13789,13790,13815],{},"Obsah ampulky s lékem (v cm³) má rozdělení ",[1115,13767,13769],{"className":13768},[1137],[1139,13770,13771],{"xmlns":1141},[1143,13772,13773,13787],{},[1146,13774,13775,13777,13779,13781,13783,13785],{},[1149,13776,11259],{},[1193,13778,1199],{"stretchy":1198},[1230,13780,5389],{},[1193,13782,1589],{"separator":1121},[1230,13784,13407],{},[1193,13786,1228],{"stretchy":1198},[1153,13788,13412],{"encoding":1155},", tedy střední hodnota 10 a rozptyl 0,12 (",[1115,13791,13793],{"className":13792},[1137],[1139,13794,13795],{"xmlns":1141},[1143,13796,13797,13812],{},[1146,13798,13799,13801,13803,13807,13809],{},[1149,13800,11271],{},[1193,13802,1281],{},[1283,13804,13805],{},[1230,13806,13407],{},[1193,13808,4165],{},[1230,13810,13811],{},"0,346",[1153,13813,13814],{"encoding":1155},"\\sigma = \\sqrt{0{,}12} \\approx 0{,}346","). Kolik procent ampulek má obsah menší než 9,8 cm³?",[1110,13817,13818],{},[1864,13819],{"alt":13820,"className":13821,"src":13822},"mask-nv-priklad-ampulka",[1387,1868],"\u002Fwiki-assets\u002Fmask-nv-priklad-ampulka.png",[2035,13824,13826],{"className":2037,"code":13825,"language":71,"meta":2039,"style":2039},"pnorm(9.8, mean = 10, sd = sqrt(0.12))\n",[1332,13827,13828],{"__ignoreMap":2039},[1115,13829,13830,13832,13834,13837,13839,13841,13843,13846,13848,13850,13852,13854,13856,13859],{"class":2044,"line":10},[1115,13831,11285],{"class":2055},[1115,13833,1199],{"class":2059},[1115,13835,13836],{"class":2062},"9.8",[1115,13838,1503],{"class":2051},[1115,13840,13600],{"class":2047},[1115,13842,2510],{"class":2051},[1115,13844,13845],{"class":2062}," 10",[1115,13847,1503],{"class":2051},[1115,13849,13610],{"class":2047},[1115,13851,2510],{"class":2051},[1115,13853,8970],{"class":2055},[1115,13855,1199],{"class":2059},[1115,13857,13858],{"class":2062},"0.12",[1115,13860,2546],{"class":2059},[2035,13862,13865],{"className":13863,"code":13864,"language":2169,"meta":2039},[2167],"[1] 0.2818514\n",[1332,13866,13864],{"__ignoreMap":2039},[1110,13868,13869],{},"Obsah menší než 9,8 cm³ má přibližně 28,19 % ampulek.",[1377,13871,13873],{"id":13872},"další-rozdělení-dostupná-v-r","Další rozdělení dostupná v R",[1110,13875,13876,13877,13880,13881,13884,13885,13888,13889,5731,13892,13895,13896,13899],{},"Vedle normálního rozdělení R přímo nabízí hustotu, distribuční funkci a kvantilovou funkci i pro další běžná rozdělení. Pojmenování funkcí je jednotné: ",[1332,13878,13879],{},"d*"," je hustota\u002Fpravděpodobnostní funkce, ",[1332,13882,13883],{},"p*"," distribuční funkce (s ",[1332,13886,13887],{},"lower.tail = FALSE",", případně čtvrtým argumentem ",[1332,13890,13891],{},"TRUE",[1332,13893,13894],{},"FALSE",", pro horní chvost) a ",[1332,13897,13898],{},"q*"," kvantilová funkce.",[6528,13901,13902,14008],{},[6531,13903,13904],{},[6534,13905,13906,13909,13955,13981],{},[6537,13907,13908],{},"Rozdělení",[6537,13910,13911,13935,13936],{},[1115,13912,13914],{"className":13913},[1137],[1139,13915,13916],{"xmlns":1141},[1143,13917,13918,13932],{},[1146,13919,13920,13922,13924,13926,13928,13930],{},[1149,13921,11102],{},[1193,13923,1199],{"stretchy":1198},[1149,13925,11107],{},[1193,13927,1281],{},[1149,13929,11631],{},[1193,13931,1228],{"stretchy":1198},[1153,13933,13934],{"encoding":1155},"P(X=k)"," \u002F ",[1115,13937,13939],{"className":13938},[1137],[1139,13940,13941],{"xmlns":1141},[1143,13942,13943,13953],{},[1146,13944,13945,13947,13949,13951],{},[1149,13946,1582],{},[1193,13948,1199],{"stretchy":1198},[1149,13950,1168],{},[1193,13952,1228],{"stretchy":1198},[1153,13954,11174],{"encoding":1155},[6537,13956,13957],{},[1115,13958,13960],{"className":13959},[1137],[1139,13961,13962],{"xmlns":1141},[1143,13963,13964,13978],{},[1146,13965,13966,13968,13970,13972,13974,13976],{},[1149,13967,11102],{},[1193,13969,1199],{"stretchy":1198},[1149,13971,11107],{},[1193,13973,11110],{},[1149,13975,11631],{},[1193,13977,1228],{"stretchy":1198},[1153,13979,13980],{"encoding":1155},"P(X \\le k)",[6537,13982,13983,13984],{},"horní chvost ",[1115,13985,13987],{"className":13986},[1137],[1139,13988,13989],{"xmlns":1141},[1143,13990,13991,14005],{},[1146,13992,13993,13995,13997,13999,14001,14003],{},[1149,13994,11102],{},[1193,13996,1199],{"stretchy":1198},[1149,13998,11107],{},[1193,14000,5369],{},[1149,14002,11631],{},[1193,14004,1228],{"stretchy":1198},[1153,14006,14007],{"encoding":1155},"P(X>k)",[6645,14009,14010,14056,14100,14141,14190],{},[6534,14011,14012,14041,14046,14051],{},[6650,14013,14014,14015],{},"Binomické ",[1115,14016,14018],{"className":14017},[1137],[1139,14019,14020],{"xmlns":1141},[1143,14021,14022,14038],{},[1146,14023,14024,14026,14028,14030,14032,14034,14036],{},[1149,14025,6262],{},[1149,14027,1207],{},[1193,14029,1199],{"stretchy":1198},[1149,14031,1816],{},[1193,14033,1503],{"separator":1121},[1149,14035,1110],{},[1193,14037,1228],{"stretchy":1198},[1153,14039,14040],{"encoding":1155},"Bi(n,p)",[6650,14042,14043],{},[1332,14044,14045],{},"dbinom(k, n, p)",[6650,14047,14048],{},[1332,14049,14050],{},"pbinom(k, n, p)",[6650,14052,14053],{},[1332,14054,14055],{},"pbinom(k, n, p, FALSE)",[6534,14057,14058,14085,14090,14095],{},[6650,14059,14060,14061],{},"Poissonovo ",[1115,14062,14064],{"className":14063},[1137],[1139,14065,14066],{"xmlns":1141},[1143,14067,14068,14082],{},[1146,14069,14070,14072,14075,14077,14080],{},[1149,14071,11102],{},[1149,14073,14074],{},"o",[1193,14076,1199],{"stretchy":1198},[1149,14078,14079],{},"λ",[1193,14081,1228],{"stretchy":1198},[1153,14083,14084],{"encoding":1155},"Po(\\lambda)",[6650,14086,14087],{},[1332,14088,14089],{},"dpois(k, lambda)",[6650,14091,14092],{},[1332,14093,14094],{},"ppois(k, lambda)",[6650,14096,14097],{},[1332,14098,14099],{},"ppois(k, lambda, FALSE)",[6534,14101,14102,14126,14131,14136],{},[6650,14103,14104,14105],{},"Geometrické ",[1115,14106,14108],{"className":14107},[1137],[1139,14109,14110],{"xmlns":1141},[1143,14111,14112,14123],{},[1146,14113,14114,14117,14119,14121],{},[1149,14115,14116],{},"G",[1193,14118,1199],{"stretchy":1198},[1149,14120,1110],{},[1193,14122,1228],{"stretchy":1198},[1153,14124,14125],{"encoding":1155},"G(p)",[6650,14127,14128],{},[1332,14129,14130],{},"dgeom(k, p)",[6650,14132,14133],{},[1332,14134,14135],{},"pgeom(k, p)",[6650,14137,14138],{},[1332,14139,14140],{},"pgeom(k, p, FALSE)",[6534,14142,14143,14175,14180,14185],{},[6650,14144,14145,14146],{},"Hypergeometrické ",[1115,14147,14149],{"className":14148},[1137],[1139,14150,14151],{"xmlns":1141},[1143,14152,14153,14172],{},[1146,14154,14155,14157,14159,14161,14163,14166,14168,14170],{},[1149,14156,2227],{},[1193,14158,1199],{"stretchy":1198},[1149,14160,11259],{},[1193,14162,1503],{"separator":1121},[1149,14164,14165],{},"M",[1193,14167,1503],{"separator":1121},[1149,14169,1816],{},[1193,14171,1228],{"stretchy":1198},[1153,14173,14174],{"encoding":1155},"H(N,M,n)",[6650,14176,14177],{},[1332,14178,14179],{},"dhyper(k, M, N-M, n)",[6650,14181,14182],{},[1332,14183,14184],{},"phyper(k, M, N-M, n)",[6650,14186,14187],{},[1332,14188,14189],{},"phyper(k, M, N-M, n, FALSE)",[6534,14191,14192,14216,14221,14226],{},[6650,14193,14194,14195],{},"Exponenciální ",[1115,14196,14198],{"className":14197},[1137],[1139,14199,14200],{"xmlns":1141},[1143,14201,14202,14213],{},[1146,14203,14204,14206,14208,14211],{},[1149,14205,12457],{},[1193,14207,1199],{"stretchy":1198},[1149,14209,14210],{},"δ",[1193,14212,1228],{"stretchy":1198},[1153,14214,14215],{"encoding":1155},"E(\\delta)",[6650,14217,14218],{},[1332,14219,14220],{},"dexp(k, 1\u002Fdelta)",[6650,14222,14223],{},[1332,14224,14225],{},"pexp(k, 1\u002Fdelta)",[6650,14227,14228],{},[1332,14229,14230],{},"pexp(k, 1\u002Fdelta, FALSE)",[1103,14232,14234,14241],{"className":14233,"dataCallout":5686},[1106,5685],[1110,14235,14237,14240],{"className":14236},[1113],[1115,14238],{"className":14239,"ariaHidden":1121},[1118,5693,1120],"Exponenciální rozdělení: R bere intenzitu, ne střední hodnotu",[1110,14242,14243,14244,14247,14248,14262,14263,13417,14266,1236],{},"R parametrizuje exponenciální rozdělení intenzitou (",[1332,14245,14246],{},"rate","). Je-li ",[1115,14249,14251],{"className":14250},[1137],[1139,14252,14253],{"xmlns":1141},[1143,14254,14255,14259],{},[1146,14256,14257],{},[1149,14258,14210],{},[1153,14260,14261],{"encoding":1155},"\\delta"," střední doba do události, do R se dosazuje ",[1332,14264,14265],{},"1\u002Fdelta",[1332,14267,14268],{},"delta",[1110,14270,14271,14272,14303,14304,14322],{},"V R (pravděpodobnostní a distribuční funkce diskrétní náhodné veličiny ",[1115,14273,14275],{"className":14274},[1137],[1139,14276,14277],{"xmlns":1141},[1143,14278,14279,14300],{},[1146,14280,14281,14283,14285,14287,14289,14291,14293,14295,14298],{},[1149,14282,11107],{},[1193,14284,13552],{},[1149,14286,6262],{},[1149,14288,1207],{},[1193,14290,1199],{"stretchy":1198},[1230,14292,5351],{},[1193,14294,1589],{"separator":1121},[1230,14296,14297],{},"0,95",[1193,14299,1228],{"stretchy":1198},[1153,14301,14302],{"encoding":1155},"X \\sim Bi(5; 0{,}95)",", a pravděpodobnost, že u exponenciálního rozdělení se střední hodnotou ",[1115,14305,14307],{"className":14306},[1137],[1139,14308,14309],{"xmlns":1141},[1143,14310,14311,14319],{},[1146,14312,14313,14315,14317],{},[1149,14314,14210],{},[1193,14316,1281],{},[1230,14318,5351],{},[1153,14320,14321],{"encoding":1155},"\\delta = 5"," nastane událost do 3 jednotek času):",[2035,14324,14326],{"className":2037,"code":14325,"language":71,"meta":2039,"style":2039},"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",[1332,14327,14328,14342,14372,14401,14405,14414],{"__ignoreMap":2039},[1115,14329,14330,14332,14334,14337,14339],{"class":2044,"line":10},[1115,14331,1168],{"class":2047},[1115,14333,2052],{"class":2051},[1115,14335,14336],{"class":2062}," 0",[1115,14338,1902],{"class":2051},[1115,14340,14341],{"class":2062},"5\n",[1115,14343,14344,14347,14349,14352,14354,14356,14358,14360,14362,14364,14366,14368,14370],{"class":2044,"line":27},[1115,14345,14346],{"class":2055},"round",[1115,14348,1199],{"class":2059},[1115,14350,14351],{"class":2055},"dbinom",[1115,14353,1199],{"class":2059},[1115,14355,1168],{"class":2047},[1115,14357,1503],{"class":2051},[1115,14359,2082],{"class":2062},[1115,14361,1503],{"class":2051},[1115,14363,2513],{"class":2062},[1115,14365,1228],{"class":2059},[1115,14367,1503],{"class":2051},[1115,14369,2077],{"class":2062},[1115,14371,2090],{"class":2059},[1115,14373,14374,14376,14378,14381,14383,14385,14387,14389,14391,14393,14395,14397,14399],{"class":2044,"line":148},[1115,14375,14346],{"class":2055},[1115,14377,1199],{"class":2059},[1115,14379,14380],{"class":2055},"pbinom",[1115,14382,1199],{"class":2059},[1115,14384,1168],{"class":2047},[1115,14386,1503],{"class":2051},[1115,14388,2082],{"class":2062},[1115,14390,1503],{"class":2051},[1115,14392,2513],{"class":2062},[1115,14394,1228],{"class":2059},[1115,14396,1503],{"class":2051},[1115,14398,2077],{"class":2062},[1115,14400,2090],{"class":2059},[1115,14402,14403],{"class":2044,"line":111},[1115,14404,5548],{"emptyLinePlaceholder":5547},[1115,14406,14407,14409,14411],{"class":2044,"line":96},[1115,14408,14268],{"class":2047},[1115,14410,2052],{"class":2051},[1115,14412,14413],{"class":2062}," 5\n",[1115,14415,14416,14418,14420,14423,14425,14427,14429,14432,14434,14436,14438,14441,14443,14445,14447],{"class":2044,"line":89},[1115,14417,14346],{"class":2055},[1115,14419,1199],{"class":2059},[1115,14421,14422],{"class":2055},"pexp",[1115,14424,1199],{"class":2059},[1115,14426,8010],{"class":2062},[1115,14428,1503],{"class":2051},[1115,14430,14431],{"class":2047}," rate",[1115,14433,2510],{"class":2051},[1115,14435,9031],{"class":2062},[1115,14437,4211],{"class":2051},[1115,14439,14440],{"class":2047}," delta",[1115,14442,1228],{"class":2059},[1115,14444,1503],{"class":2051},[1115,14446,2077],{"class":2062},[1115,14448,2090],{"class":2059},[2035,14450,14453],{"className":14451,"code":14452,"language":2169,"meta":2039},[2167],"[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",[1332,14454,14452],{"__ignoreMap":2039},[1377,14456,14458],{"id":14457},"studentovo-pearsonovo-a-fisherovo-snedecorovo-rozdělení","Studentovo, Pearsonovo a Fisherovo-Snedecorovo rozdělení",[1110,14460,14461,14462,14465],{},"Tato tři rozdělení mají statistiky, které se dále používají při konstrukci intervalů spolehlivosti a testování hypotéz (viz ",[1384,14463,141],{"className":14464,"dataFsResolvedFilePath":5302,"href":5303},[1387],") — na rozdíl od normálního rozdělení se v příkladech této kapitoly samostatně nepočítají, jsou to nástroje pro další kapitoly.",[1110,14467,14468,8353,14471,14484],{},[1130,14469,14470],{},"Studentovo rozdělení",[1115,14472,14474],{"className":14473},[1137],[1139,14475,14476],{"xmlns":1141},[1143,14477,14478,14482],{},[1146,14479,14480],{},[1149,14481,11631],{},[1153,14483,11631],{"encoding":1155}," stupni volnosti má hustotu pravděpodobnosti",[1115,14486,14488],{"className":14487},[1137],[1139,14489,14490],{"xmlns":1141,"display":1796},[1143,14491,14492,14587],{},[1146,14493,14494,14496,14498,14500,14502,14504,14536,14574,14576,14578,14580,14582,14585],{},[1149,14495,1582],{},[1193,14497,1199],{"stretchy":1198},[1149,14499,1168],{},[1193,14501,1228],{"stretchy":1198},[1193,14503,1281],{},[3546,14505,14506,14508],{},[1230,14507,1525],{},[1146,14509,14510,14512,14532],{},[1149,14511,6262],{},[1146,14513,14514,14516,14522,14524,14530],{},[1193,14515,1199],{"fence":1121},[3546,14517,14518,14520],{},[1230,14519,1525],{},[1230,14521,1232],{},[1193,14523,1503],{"separator":1121},[3546,14525,14526,14528],{},[1149,14527,11631],{},[1230,14529,1232],{},[1193,14531,1228],{"fence":1121},[1283,14533,14534],{},[1149,14535,11631],{},[1224,14537,14538,14558],{},[1146,14539,14540,14542,14544,14546,14556],{},[1193,14541,1199],{"fence":1121},[1230,14543,1525],{},[1193,14545,1924],{},[3546,14547,14548,14554],{},[1224,14549,14550,14552],{},[1149,14551,1168],{},[1230,14553,1232],{},[1149,14555,11631],{},[1193,14557,1228],{"fence":1121},[1146,14559,14560,14562],{},[1193,14561,1210],{},[3546,14563,14564,14572],{},[1146,14565,14566,14568,14570],{},[1149,14567,11631],{},[1193,14569,1924],{},[1230,14571,1525],{},[1230,14573,1232],{},[1193,14575,1503],{"separator":1121},[1936,14577],{"width":1938},[1149,14579,1168],{},[1193,14581,11391],{},[1149,14583,1257],{"mathvariant":14584},"double-struck",[1193,14586,1503],{"separator":1121},[1153,14588,14589],{"encoding":1155},"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},",[1110,14591,8899,14592,14605,14606,14619,14620,14633],{},[1115,14593,14595],{"className":14594},[1137],[1139,14596,14597],{"xmlns":1141},[1143,14598,14599,14603],{},[1146,14600,14601],{},[1149,14602,6262],{},[1153,14604,6262],{"encoding":1155}," je funkce beta. Je symetrické kolem nuly; číslo ",[1115,14607,14609],{"className":14608},[1137],[1139,14610,14611],{"xmlns":1141},[1143,14612,14613,14617],{},[1146,14614,14615],{},[1149,14616,11631],{},[1153,14618,11631],{"encoding":1155}," určuje tvar křivky — s rostoucím ",[1115,14621,14623],{"className":14622},[1137],[1139,14624,14625],{"xmlns":1141},[1143,14626,14627,14631],{},[1146,14628,14629],{},[1149,14630,11631],{},[1153,14632,11631],{"encoding":1155}," se rozdělení blíží normálnímu.",[1110,14635,14636,8353,14639,14652],{},[1130,14637,14638],{},"Pearsonovo (chí-kvadrát) rozdělení",[1115,14640,14642],{"className":14641},[1137],[1139,14643,14644],{"xmlns":1141},[1143,14645,14646,14650],{},[1146,14647,14648],{},[1149,14649,11631],{},[1153,14651,11631],{"encoding":1155}," stupni volnosti:",[1115,14654,14656],{"className":14655},[1137],[1139,14657,14658],{"xmlns":1141,"display":1796},[1143,14659,14660,14745],{},[1146,14661,14662,14664,14666,14668,14670,14672,14703,14719,14733,14735,14737,14739,14741,14743],{},[1149,14663,1582],{},[1193,14665,1199],{"stretchy":1198},[1149,14667,1168],{},[1193,14669,1228],{"stretchy":1198},[1193,14671,1281],{},[3546,14673,14674,14676],{},[1230,14675,1525],{},[1146,14677,14678,14690,14693,14695,14697,14699,14701],{},[1224,14679,14680,14682],{},[1230,14681,1232],{},[1146,14683,14684,14686,14688],{},[1149,14685,11631],{},[1149,14687,5731],{"mathvariant":1854},[1230,14689,1232],{},[1149,14691,14692],{"mathvariant":1854},"Γ",[1193,14694,1199],{"stretchy":1198},[1149,14696,11631],{},[1149,14698,5731],{"mathvariant":1854},[1230,14700,1232],{},[1193,14702,1228],{"stretchy":1198},[1224,14704,14705,14707],{},[1149,14706,1168],{},[1146,14708,14709,14711,14713,14715,14717],{},[1149,14710,11631],{},[1149,14712,5731],{"mathvariant":1854},[1230,14714,1232],{},[1193,14716,1210],{},[1230,14718,1525],{},[1224,14720,14721,14723],{},[1149,14722,1754],{},[1146,14724,14725,14727,14729,14731],{},[1193,14726,1210],{},[1149,14728,1168],{},[1149,14730,5731],{"mathvariant":1854},[1230,14732,1232],{},[1193,14734,1503],{"separator":1121},[1936,14736],{"width":1938},[1149,14738,1168],{},[1193,14740,5369],{},[1230,14742,1597],{},[1193,14744,1503],{"separator":1121},[1153,14746,14747],{"encoding":1155},"f(x) = \\frac{1}{2^{k\u002F2}\\Gamma(k\u002F2)} x^{k\u002F2-1} e^{-x\u002F2}, \\qquad x > 0,",[1110,14749,8899,14750,14764],{},[1115,14751,14753],{"className":14752},[1137],[1139,14754,14755],{"xmlns":1141},[1143,14756,14757,14761],{},[1146,14758,14759],{},[1149,14760,14692],{"mathvariant":1854},[1153,14762,14763],{"encoding":1155},"\\Gamma"," je funkce gama.",[1110,14766,14767,14770,14771,1405,14789,1902],{},[1130,14768,14769],{},"Fisherovo-Snedecorovo rozdělení"," se stupni volnosti ",[1115,14772,14774],{"className":14773},[1137],[1139,14775,14776],{"xmlns":1141},[1143,14777,14778,14786],{},[1146,14779,14780],{},[1201,14781,14782,14784],{},[1149,14783,11631],{},[1230,14785,1525],{},[1153,14787,14788],{"encoding":1155},"k_1",[1115,14790,14792],{"className":14791},[1137],[1139,14793,14794],{"xmlns":1141},[1143,14795,14796,14804],{},[1146,14797,14798],{},[1201,14799,14800,14802],{},[1149,14801,11631],{},[1230,14803,1232],{},[1153,14805,14806],{"encoding":1155},"k_2",[1115,14808,14810],{"className":14809},[1137],[1139,14811,14812],{"xmlns":1141,"display":1796},[1143,14813,14814,14979],{},[1146,14815,14816,14818,14820,14822,14824,14826,14862,14896,14916,14968,14970,14972,14974,14976],{},[1149,14817,1582],{},[1193,14819,1199],{"stretchy":1198},[1149,14821,1168],{},[1193,14823,1228],{"stretchy":1198},[1193,14825,1281],{},[3546,14827,14828,14830],{},[1230,14829,1525],{},[1146,14831,14832,14834],{},[1149,14833,6262],{},[1146,14835,14836,14838,14848,14850,14860],{},[1193,14837,1199],{"fence":1121},[3546,14839,14840,14846],{},[1201,14841,14842,14844],{},[1149,14843,11631],{},[1230,14845,1525],{},[1230,14847,1232],{},[1193,14849,1503],{"separator":1121},[3546,14851,14852,14858],{},[1201,14853,14854,14856],{},[1149,14855,11631],{},[1230,14857,1232],{},[1230,14859,1232],{},[1193,14861,1228],{"fence":1121},[1224,14863,14864,14884],{},[1146,14865,14866,14868,14882],{},[1193,14867,1199],{"fence":1121},[3546,14869,14870,14876],{},[1201,14871,14872,14874],{},[1149,14873,11631],{},[1230,14875,1525],{},[1201,14877,14878,14880],{},[1149,14879,11631],{},[1230,14881,1232],{},[1193,14883,1228],{"fence":1121},[1146,14885,14886,14892,14894],{},[1201,14887,14888,14890],{},[1149,14889,11631],{},[1230,14891,1525],{},[1149,14893,5731],{"mathvariant":1854},[1230,14895,1232],{},[1224,14897,14898,14900],{},[1149,14899,1168],{},[1146,14901,14902,14908,14910,14912,14914],{},[1201,14903,14904,14906],{},[1149,14905,11631],{},[1230,14907,1525],{},[1149,14909,5731],{"mathvariant":1854},[1230,14911,1232],{},[1193,14913,1210],{},[1230,14915,1525],{},[1224,14917,14918,14944],{},[1146,14919,14920,14922,14924,14926,14940,14942],{},[1193,14921,1199],{"fence":1121},[1230,14923,1525],{},[1193,14925,1924],{},[3546,14927,14928,14934],{},[1201,14929,14930,14932],{},[1149,14931,11631],{},[1230,14933,1525],{},[1201,14935,14936,14938],{},[1149,14937,11631],{},[1230,14939,1232],{},[1149,14941,1168],{},[1193,14943,1228],{"fence":1121},[1146,14945,14946,14948],{},[1193,14947,1210],{},[3546,14949,14950,14966],{},[1146,14951,14952,14958,14960],{},[1201,14953,14954,14956],{},[1149,14955,11631],{},[1230,14957,1525],{},[1193,14959,1924],{},[1201,14961,14962,14964],{},[1149,14963,11631],{},[1230,14965,1232],{},[1230,14967,1232],{},[1193,14969,1503],{"separator":1121},[1936,14971],{"width":1938},[1149,14973,1168],{},[1193,14975,5369],{},[1230,14977,14978],{},"0.",[1153,14980,14981],{"encoding":1155},"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.",[1110,14983,14984],{},[1864,14985],{"alt":14986,"className":14987,"src":14988},"mask-nv-specialni-rozdeleni",[1387,1868],"\u002Fwiki-assets\u002Fmask-nv-specialni-rozdeleni.png",[13316,14990],{"spec":14991},"{\"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\":[]}",[1110,14993,14994],{},"R funkce pro tato tři rozdělení:",[6528,14996,14997,15011],{},[6531,14998,14999],{},[6534,15000,15001,15003,15006,15008],{},[6537,15002,13908],{},[6537,15004,15005],{},"hustota",[6537,15007,11079],{},[6537,15009,15010],{},"kvantil",[6645,15012,15013,15053,15097],{},[6534,15014,15015,15038,15043,15048],{},[6650,15016,15017,15018],{},"Studentovo ",[1115,15019,15021],{"className":15020},[1137],[1139,15022,15023],{"xmlns":1141},[1143,15024,15025,15035],{},[1146,15026,15027,15029,15031,15033],{},[1149,15028,11515],{},[1193,15030,1199],{"stretchy":1198},[1149,15032,11631],{},[1193,15034,1228],{"stretchy":1198},[1153,15036,15037],{"encoding":1155},"t(k)",[6650,15039,15040],{},[1332,15041,15042],{},"dt(x, df = k)",[6650,15044,15045],{},[1332,15046,15047],{},"pt(x, df = k)",[6650,15049,15050],{},[1332,15051,15052],{},"qt(p, df = k)",[6534,15054,15055,15082,15087,15092],{},[6650,15056,15057,15058],{},"Pearsonovo ",[1115,15059,15061],{"className":15060},[1137],[1139,15062,15063],{"xmlns":1141},[1143,15064,15065,15079],{},[1146,15066,15067,15073,15075,15077],{},[1224,15068,15069,15071],{},[1149,15070,6034],{},[1230,15072,1232],{},[1193,15074,1199],{"stretchy":1198},[1149,15076,11631],{},[1193,15078,1228],{"stretchy":1198},[1153,15080,15081],{"encoding":1155},"\\chi^2(k)",[6650,15083,15084],{},[1332,15085,15086],{},"dchisq(x, df = k)",[6650,15088,15089],{},[1332,15090,15091],{},"pchisq(x, df = k)",[6650,15093,15094],{},[1332,15095,15096],{},"qchisq(p, df = k)",[6534,15098,15099,15134,15139,15144],{},[6650,15100,15101,15102],{},"Fisherovo-Snedecorovo ",[1115,15103,15105],{"className":15104},[1137],[1139,15106,15107],{"xmlns":1141},[1143,15108,15109,15131],{},[1146,15110,15111,15113,15115,15121,15123,15129],{},[1149,15112,11091],{},[1193,15114,1199],{"stretchy":1198},[1201,15116,15117,15119],{},[1149,15118,11631],{},[1230,15120,1525],{},[1193,15122,1503],{"separator":1121},[1201,15124,15125,15127],{},[1149,15126,11631],{},[1230,15128,1232],{},[1193,15130,1228],{"stretchy":1198},[1153,15132,15133],{"encoding":1155},"F(k_1, k_2)",[6650,15135,15136],{},[1332,15137,15138],{},"df(x, df1 = k1, df2 = k2)",[6650,15140,15141],{},[1332,15142,15143],{},"pf(x, df1 = k1, df2 = k2)",[6650,15145,15146],{},[1332,15147,15148],{},"qf(p, df1 = k1, df2 = k2)",[1110,15150,15151],{},"V R (97,5%-ní kvantil Studentova rozdělení s 9 stupni volnosti, 95%-ní kvantily Pearsonova a Fisherova-Snedecorova rozdělení):",[2035,15153,15155],{"className":2037,"code":15154,"language":71,"meta":2039,"style":2039},"qt(0.975, df = 9)\nqchisq(0.95, df = 9)\nqf(0.95, df1 = 3, df2 = 10)\n",[1332,15156,15157,15178,15198],{"__ignoreMap":2039},[1115,15158,15159,15162,15164,15166,15168,15171,15173,15176],{"class":2044,"line":10},[1115,15160,15161],{"class":2055},"qt",[1115,15163,1199],{"class":2059},[1115,15165,13458],{"class":2062},[1115,15167,1503],{"class":2051},[1115,15169,15170],{"class":2047}," df",[1115,15172,2510],{"class":2051},[1115,15174,15175],{"class":2062}," 9",[1115,15177,2090],{"class":2059},[1115,15179,15180,15183,15185,15188,15190,15192,15194,15196],{"class":2044,"line":27},[1115,15181,15182],{"class":2055},"qchisq",[1115,15184,1199],{"class":2059},[1115,15186,15187],{"class":2062},"0.95",[1115,15189,1503],{"class":2051},[1115,15191,15170],{"class":2047},[1115,15193,2510],{"class":2051},[1115,15195,15175],{"class":2062},[1115,15197,2090],{"class":2059},[1115,15199,15200,15203,15205,15207,15209,15212,15214,15216,15218,15221,15223,15225],{"class":2044,"line":148},[1115,15201,15202],{"class":2055},"qf",[1115,15204,1199],{"class":2059},[1115,15206,15187],{"class":2062},[1115,15208,1503],{"class":2051},[1115,15210,15211],{"class":2047}," df1",[1115,15213,2510],{"class":2051},[1115,15215,2072],{"class":2062},[1115,15217,1503],{"class":2051},[1115,15219,15220],{"class":2047}," df2",[1115,15222,2510],{"class":2051},[1115,15224,13845],{"class":2062},[1115,15226,2090],{"class":2059},[2035,15228,15231],{"className":15229,"code":15230,"language":2169,"meta":2039},[2167],"[1] 2.262157\n[1] 16.91898\n[1] 3.708265\n",[1332,15232,15230],{"__ignoreMap":2039},[1377,15234,5681],{"id":5680},[1124,15236,15237,15322,15372],{},[1127,15238,15239,15242,15243,15270,15271,5731,15273,5731,15275,15277,15278,15298,15299,15321],{},[1130,15240,15241],{},"Rozptyl vs. směrodatná odchylka v R."," Zápis ",[1115,15244,15246],{"className":15245},[1137],[1139,15247,15248],{"xmlns":1141},[1143,15249,15250,15268],{},[1146,15251,15252,15254,15256,15258,15260,15266],{},[1149,15253,11259],{},[1193,15255,1199],{"stretchy":1198},[1149,15257,11264],{},[1193,15259,1589],{"separator":1121},[1224,15261,15262,15264],{},[1149,15263,11271],{},[1230,15265,1232],{},[1193,15267,1228],{"stretchy":1198},[1153,15269,11278],{"encoding":1155}," používá rozptyl, ale ",[1332,15272,11282],{},[1332,15274,11285],{},[1332,15276,11288],{}," očekávají směrodatnou odchylku. Dosazení rozptylu místo ",[1115,15279,15281],{"className":15280},[1137],[1139,15282,15283],{"xmlns":1141},[1143,15284,15285,15295],{},[1146,15286,15287],{},[1283,15288,15289],{},[1224,15290,15291,15293],{},[1149,15292,11271],{},[1230,15294,1232],{},[1153,15296,15297],{"encoding":1155},"\\sqrt{\\sigma^2}"," dává jiný — a pro ",[1115,15300,15302],{"className":15301},[1137],[1139,15303,15304],{"xmlns":1141},[1143,15305,15306,15318],{},[1146,15307,15308,15314,15316],{},[1224,15309,15310,15312],{},[1149,15311,11271],{},[1230,15313,1232],{},[1193,15315,2271],{"mathvariant":1854},[1230,15317,1525],{},[1153,15319,15320],{"encoding":1155},"\\sigma^2 \\ne 1"," výrazně odlišný — výsledek (viz příklad s ampulkou).",[1127,15323,15324,15351,15352,15371],{},[1130,15325,15326,15350],{},[1115,15327,15329],{"className":15328},[1137],[1139,15330,15331],{"xmlns":1141},[1143,15332,15333,15347],{},[1146,15334,15335,15337,15339,15341,15343,15345],{},[1149,15336,11102],{},[1193,15338,1199],{"stretchy":1198},[1149,15340,11107],{},[1193,15342,1281],{},[1149,15344,1168],{},[1193,15346,1228],{"stretchy":1198},[1153,15348,15349],{"encoding":1155},"P(X=x)"," u spojité veličiny je vždy 0."," Hustota ",[1115,15353,15355],{"className":15354},[1137],[1139,15356,15357],{"xmlns":1141},[1143,15358,15359,15369],{},[1146,15360,15361,15363,15365,15367],{},[1149,15362,1582],{},[1193,15364,1199],{"stretchy":1198},[1149,15366,1168],{},[1193,15368,1228],{"stretchy":1198},[1153,15370,11174],{"encoding":1155}," sama o sobě pravděpodobnost neudává — pravděpodobnost dává až plocha pod křivkou na intervalu.",[1127,15373,15374,1243,15377,15394,15395,15412,15413,15416,15417,1236],{},[1130,15375,15376],{},"Záměna stupňů volnosti u Fisherova-Snedecorova rozdělení.",[1115,15378,15380],{"className":15379},[1137],[1139,15381,15382],{"xmlns":1141},[1143,15383,15384,15392],{},[1146,15385,15386],{},[1201,15387,15388,15390],{},[1149,15389,11631],{},[1230,15391,1525],{},[1153,15393,14788],{"encoding":1155}," (čitatel) a ",[1115,15396,15398],{"className":15397},[1137],[1139,15399,15400],{"xmlns":1141},[1143,15401,15402,15410],{},[1146,15403,15404],{},[1201,15405,15406,15408],{},[1149,15407,11631],{},[1230,15409,1232],{},[1153,15411,14806],{"encoding":1155}," (jmenovatel) nejsou zaměnitelné — ",[1332,15414,15415],{},"qf(p, df1, df2)"," dá jiný výsledek než ",[1332,15418,15419],{},"qf(p, df2, df1)",[1377,15421,5863],{"id":5862},[1124,15423,15424,15429,15434,15439,15445,15450,15456],{},[1127,15425,15426],{},[1384,15427,1390],{"className":15428,"dataFsResolvedFilePath":1388,"href":1389},[1387],[1127,15430,15431],{},[1384,15432,886],{"className":15433,"dataFsResolvedFilePath":5882,"href":5883},[1387],[1127,15435,15436],{},[1384,15437,141],{"className":15438,"dataFsResolvedFilePath":5302,"href":5303},[1387],[1127,15440,15441],{},[1384,15442,15444],{"className":15443,"dataFsResolvedFilePath":11005,"href":11006},[1387],"regresni-a-korelacni-analyza",[1127,15446,15447],{},[1384,15448,716],{"className":15449,"dataFsResolvedFilePath":5896,"href":5897},[1387],[1127,15451,15452],{},[1384,15453,15455],{"className":15454,"dataFsResolvedFilePath":5904,"href":5905},[1387],"regulacni-diagramy-a-indexy-zpusobilosti",[1127,15457,15458],{},[1384,15459,5914],{"className":15460,"dataFsResolvedFilePath":5912,"href":5913},[1387],[1377,15462,5917],{"id":934},[1110,15464,5920,15465,5925],{},[5922,15466,5924],{},[5927,15468,15469],{},"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":2039,"searchDepth":27,"depth":27,"links":15471},[15472,15473,15474,15475,15476,15477,15478,15479,15480,15481],{"id":11337,"depth":27,"text":11338},{"id":11644,"depth":27,"text":11645},{"id":12329,"depth":27,"text":12330},{"id":12438,"depth":27,"text":12439},{"id":12874,"depth":27,"text":11247},{"id":13872,"depth":27,"text":13873},{"id":14457,"depth":27,"text":14458},{"id":5680,"depth":27,"text":5681},{"id":5862,"depth":27,"text":5863},{"id":934,"depth":27,"text":5917},{},"\u002Ftopics\u002Fnahodne-veliciny-a-rozdeleni",{"title":5876,"description":2039},[15486,15487,15488],"raw\u002Fmask\u002F01 náhodné veličiny.pdf","raw\u002Fmask\u002F01 náhodné veličiny - návod R.pdf","raw\u002Fmask\u002Fpříklady 01 a 02.docx","topics\u002Fnahodne-veliciny-a-rozdeleni",[23,67,812,332,532,71],"y7MCWBwmskoGgsMoqVPhRRaL6YYTo3Cf-R4Yf-89eMs",{"id":15493,"title":5884,"body":15494,"course":23,"courses":5957,"created":5958,"description":2039,"extension":5959,"meta":20234,"navigation":5547,"path":20235,"seo":20236,"sources":20237,"stem":20244,"tags":20245,"type":5968,"updated":5958,"__hash__":20246},"topics\u002Ftopics\u002Fpopisna-statistika.md",{"type":1096,"value":15495,"toc":20225},[15496,15499,15592,15594,15604,15729,15736,15747,15751,15794,15799,15898,15908,15913,16052,16127,16131,16232,16313,16320,16391,16410,16412,16627,16633,16643,16650,16653,16707,16713,16723,16736,16882,16885,16898,17217,17223,17226,17230,17309,17343,17372,17374,17452,17458,17519,17526,17539,17616,17731,17781,17794,17949,17955,17982,17986,18011,18014,18227,18295,18396,18403,18416,18919,18925,18957,19217,19370,19481,19510,19516,19523,19529,19542,19971,19977,19980,19982,20177,20179,20216,20218,20222],[1099,15497,5884],{"id":15498},"popisná-statistika-a-datové-soubory",[1103,15500,15502,15508],{"className":15501,"dataCallout":1108},[1106,1107],[1110,15503,15505,1122],{"className":15504},[1113],[1115,15506],{"className":15507,"ariaHidden":1121},[1118,1119,1120],[1124,15509,15510,15513,15516,15543,15589],{},[1127,15511,15512],{},"Rozlišit základní a výběrový soubor, typ statistického znaku (kvantitativní\u002Fkvalitativní, diskrétní\u002Fspojitý) a požadavek reprezentativity a nezávislého výběru.",[1127,15514,15515],{},"Spočítat výběrový průměr, rozptyl, směrodatnou odchylku a variační rozpětí; interpretovat je jako bodové odhady charakteristik náhodné veličiny.",[1127,15517,15518,15519,1236],{},"Určit medián a kvartily a číst empirickou distribuční funkci ",[1115,15520,15522],{"className":15521},[1137],[1139,15523,15524],{"xmlns":1141},[1143,15525,15526,15540],{},[1146,15527,15528,15534,15536,15538],{},[1201,15529,15530,15532],{},[1149,15531,11091],{},[1149,15533,1816],{},[1193,15535,1199],{"stretchy":1198},[1149,15537,1168],{},[1193,15539,1228],{"stretchy":1198},[1153,15541,15542],{"encoding":1155},"F_n(x)",[1127,15544,15545,15546,15588],{},"Roztřídit velký datový soubor do tříd (intervalové rozdělení četností), sestavit tabulku ",[1115,15547,15549],{"className":15548},[1137],[1139,15550,15551],{"xmlns":1141},[1143,15552,15553,15585],{},[1146,15554,15555,15561,15563,15569,15571,15577,15579],{},[1201,15556,15557,15559],{},[1149,15558,1278],{},[1149,15560,6318],{},[1193,15562,1503],{"separator":1121},[1201,15564,15565,15567],{},[1149,15566,13295],{},[1149,15568,6318],{},[1193,15570,1503],{"separator":1121},[1201,15572,15573,15575],{},[1149,15574,1582],{},[1149,15576,6318],{},[1193,15578,1503],{"separator":1121},[1201,15580,15581,15583],{},[1149,15582,1110],{},[1149,15584,6318],{},[1153,15586,15587],{"encoding":1155},"I_j, Z_j, f_j, p_j"," a nakreslit histogram.",[1127,15590,15591],{},"Z histogramu odhadnout zákon rozdělení dat; formální test shody patří do testování hypotéz.",[1377,15593,1380],{"id":1379},[1110,15595,15596,15599,15600,15603],{},[1384,15597,1390],{"className":15598,"dataFsResolvedFilePath":1388,"href":1389},[1387]," pracuje s ",[1130,15601,15602],{},"datovými soubory"," — konkrétními hodnotami, které popisují vlastnost zkoumaných prvků.",[1124,15605,15606,15612,15636,15642,15716],{},[1127,15607,15608,15611],{},[1130,15609,15610],{},"Základní soubor"," — množina prvků, na nichž provádíme šetření (např. všichni výdělečně činní obyvatelé ČR).",[1127,15613,15614,15617,15618],{},[1130,15615,15616],{},"Statistický znak"," — funkce, která vyjadřuje určitou vlastnost prvku (např. velikost platu). Znaky dělíme na:\n",[1124,15619,15620,15631],{},[1127,15621,15622,15624,15625,15627,15628,15630],{},[1130,15623,6175],{}," (vyjádřitelné číslem) — dále ",[1130,15626,11068],{}," (spočetně mnoho hodnot) nebo ",[1130,15629,11072],{}," (libovolná hodnota v intervalu);",[1127,15632,15633,15635],{},[1130,15634,6168],{}," (vyjádřitelné slovně).",[1127,15637,15638,15641],{},[1130,15639,15640],{},"Výběrový soubor"," — podmnožina prvků základního souboru, na níž znak skutečně zjišťujeme (např. 5 náhodně vybraných obyvatel).",[1127,15643,15644,15647,15648,1236],{},[1130,15645,15646],{},"Datový soubor"," — n-tice naměřených hodnot zkoumaného znaku, např. ",[1115,15649,15651],{"className":15650},[1137],[1139,15652,15653],{"xmlns":1141},[1143,15654,15655,15713],{},[1146,15656,15657,15659,15661,15663,15666,15668,15671,15674,15676,15678,15680,15682,15685,15687,15690,15692,15694,15696,15698,15700,15702,15704,15706,15708,15711],{},[1193,15658,1199],{"stretchy":1198},[1230,15660,7968],{},[2201,15662,2203],{},[1230,15664,15665],{},"500",[1193,15667,1503],{"separator":1121},[2201,15669,15670],{}," ",[1230,15672,15673],{},"38",[2201,15675,2203],{},[1230,15677,3052],{},[1193,15679,1503],{"separator":1121},[2201,15681,15670],{},[1230,15683,15684],{},"37",[2201,15686,2203],{},[1230,15688,15689],{},"800",[1193,15691,1503],{"separator":1121},[2201,15693,15670],{},[1230,15695,13725],{},[2201,15697,2203],{},[1230,15699,3052],{},[1193,15701,1503],{"separator":1121},[2201,15703,15670],{},[1230,15705,7976],{},[2201,15707,2203],{},[1230,15709,15710],{},"200",[1193,15712,1228],{"stretchy":1198},[1153,15714,15715],{"encoding":1155},"(29\\,500,\\ 38\\,000,\\ 37\\,800,\\ 41\\,000,\\ 31\\,200)",[1127,15717,15718,15719,1348,15722,1405,15725,15728],{},"Podle počtu sledovaných znaků rozlišujeme ",[1130,15720,15721],{},"jednorozměrné",[1130,15723,15724],{},"dvourozměrné",[1130,15726,15727],{},"vícerozměrné"," datové soubory.",[1110,15730,15731],{},[1864,15732],{"alt":15733,"className":15734,"src":15735},"mask-ilu-zakladni-soubor-vyber",[1387,1868],"\u002Fwiki-assets\u002Fmask-ilu-zakladni-soubor-vyber.png",[1110,15737,15738,15739,15742,15743,15746],{},"Aby výběrový soubor dobře vypovídal o základním souboru, měl by být ",[1130,15740,15741],{},"reprezentativní"," (podobný základnímu souboru svým složením). Není-li to možné zajistit přímo, volí se prvky do výběru náhodně — ",[1130,15744,15745],{},"nezávislý výběr",". Bez náhodnosti výběru nelze vlastnosti základního souboru správně vystihnout.",[1377,15748,15750],{"id":15749},"empirické-charakteristiky","Empirické charakteristiky",[1110,15752,15753,15754,15757,15758,15761,15762,15775,15776,15779,15780,15793],{},"Zpracováním datového souboru získáme ",[1130,15755,15756],{},"empirické charakteristiky"," a odhad ",[1130,15759,15760],{},"zákona rozdělení"," zkoumané náhodné veličiny ",[1115,15763,15765],{"className":15764},[1137],[1139,15766,15767],{"xmlns":1141},[1143,15768,15769,15773],{},[1146,15770,15771],{},[1149,15772,11107],{},[1153,15774,11107],{"encoding":1155},". Jde o ",[1130,15777,15778],{},"bodové odhady"," charakteristik ",[1115,15781,15783],{"className":15782},[1137],[1139,15784,15785],{"xmlns":1141},[1143,15786,15787,15791],{},[1146,15788,15789],{},[1149,15790,11107],{},[1153,15792,11107],{"encoding":1155},"; ruční výpočet podle vzorců níže je potřeba jen bez dostupného softwaru.",[1110,15795,15796],{},[1130,15797,15798],{},"Míry polohy",[1115,15800,15802],{"className":15801},[1137],[1139,15803,15804],{"xmlns":1141,"display":1796},[1143,15805,15806,15895],{},[1146,15807,15808,15815,15817,15823,15837,15843,15845],{},[1214,15809,15810,15812],{"accent":1121},[1149,15811,1168],{},[1193,15813,15814],{},"ˉ",[1193,15816,1281],{},[3546,15818,15819,15821],{},[1230,15820,1525],{},[1149,15822,1816],{},[1802,15824,15825,15827,15835],{},[1193,15826,1195],{},[1146,15828,15829,15831,15833],{},[1149,15830,1207],{},[1193,15832,1281],{},[1230,15834,1525],{},[1149,15836,1816],{},[1201,15838,15839,15841],{},[1149,15840,1168],{},[1149,15842,1207],{},[1936,15844],{"width":1938},[1146,15846,15847,15850,15856,15858,15864,15867,15873,15876,15884,15886,15892],{},[2201,15848,15849],{},"(v",[1214,15851,15852,15854],{"accent":1121},[2201,15853,1151],{},[1193,15855,3325],{},[2201,15857,1675],{},[1214,15859,15860,15862],{"accent":1121},[2201,15861,1754],{},[1193,15863,3422],{},[2201,15865,15866],{},"rov",[1214,15868,15869,15871],{"accent":1121},[2201,15870,1151],{},[1193,15872,3325],{},[2201,15874,15875],{}," pr",[1214,15877,15878,15881],{"accent":1121},[2201,15879,15880],{},"u",[1193,15882,15883],{},"˚",[2201,15885,8865],{},[1214,15887,15888,15890],{"accent":1121},[2201,15889,1754],{},[1193,15891,3422],{},[2201,15893,15894],{},"r)",[1153,15896,15897],{"encoding":1155},"\\bar{x} = \\frac{1}{n}\\sum_{i=1}^{n} x_i \\qquad \\text{(výběrový průměr)}",[1110,15899,15900,15901,1405,15904,15907],{},"Dalšími mírami polohy jsou ",[1130,15902,15903],{},"medián",[1130,15905,15906],{},"modus"," (nejčetnější hodnota výběru).",[1110,15909,15910],{},[1130,15911,15912],{},"Míry variability",[1115,15914,15916],{"className":15915},[1137],[1139,15917,15918],{"xmlns":1141,"display":1796},[1143,15919,15920,16049],{},[1146,15921,15922,15928,15930,15942,15984,15986,15988,15990,15992,16000,16002],{},[1224,15923,15924,15926],{},[1149,15925,4542],{},[1230,15927,1232],{},[1193,15929,1281],{},[3546,15931,15932,15934],{},[1230,15933,1525],{},[1146,15935,15936,15938,15940],{},[1149,15937,1816],{},[1193,15939,1210],{},[1230,15941,1525],{},[1146,15943,15944,15946,15960,15968,15970,15972,15982],{},[1193,15945,1199],{"fence":1121},[1802,15947,15948,15950,15958],{},[1193,15949,1195],{},[1146,15951,15952,15954,15956],{},[1149,15953,1207],{},[1193,15955,1281],{},[1230,15957,1525],{},[1149,15959,1816],{},[3698,15961,15962,15964,15966],{},[1149,15963,1168],{},[1149,15965,1207],{},[1230,15967,1232],{},[1193,15969,1210],{},[1149,15971,1816],{},[1224,15973,15974,15980],{},[1214,15975,15976,15978],{"accent":1121},[1149,15977,1168],{},[1193,15979,15814],{},[1230,15981,1232],{},[1193,15983,1228],{"fence":1121},[1193,15985,1503],{"separator":1121},[1936,15987],{"width":1938},[1149,15989,4542],{},[1193,15991,1281],{},[1283,15993,15994],{},[1224,15995,15996,15998],{},[1149,15997,4542],{},[1230,15999,1232],{},[1936,16001],{"width":1938},[1146,16003,16004,16006,16012,16014,16020,16022,16028,16031,16037,16040,16046],{},[2201,16005,15849],{},[1214,16007,16008,16010],{"accent":1121},[2201,16009,1151],{},[1193,16011,3325],{},[2201,16013,1675],{},[1214,16015,16016,16018],{"accent":1121},[2201,16017,1754],{},[1193,16019,3422],{},[2201,16021,15866],{},[1214,16023,16024,16026],{"accent":1121},[2201,16025,1151],{},[1193,16027,3325],{},[2201,16029,16030],{}," rozptyl, sm",[1214,16032,16033,16035],{"accent":1121},[2201,16034,1754],{},[1193,16036,3422],{},[2201,16038,16039],{},"rodatn",[1214,16041,16042,16044],{"accent":1121},[2201,16043,1384],{},[1193,16045,3325],{},[2201,16047,16048],{}," odchylka)",[1153,16050,16051],{"encoding":1155},"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)}",[1115,16053,16055],{"className":16054},[1137],[1139,16056,16057],{"xmlns":1141,"display":1796},[1143,16058,16059,16124],{},[1146,16060,16061,16063,16065,16074,16076,16084,16086],{},[1149,16062,1257],{},[1193,16064,1281],{},[1201,16066,16067,16069,16072],{},[1149,16068,1168],{},[1149,16070,16071],{},"max",[1193,16073,1851],{},[1193,16075,1210],{},[1201,16077,16078,16080,16082],{},[1149,16079,1168],{},[1149,16081,1848],{},[1193,16083,1851],{},[1936,16085],{"width":1938},[1146,16087,16088,16091,16097,16099,16105,16108,16114,16116,16122],{},[2201,16089,16090],{},"(varia",[1214,16092,16093,16095],{"accent":1121},[2201,16094,8130],{},[1193,16096,3422],{},[2201,16098,1816],{},[1214,16100,16101,16103],{"accent":1121},[2201,16102,4140],{},[1193,16104,3325],{},[2201,16106,16107],{}," rozp",[1214,16109,16110,16112],{"accent":1121},[2201,16111,1754],{},[1193,16113,3422],{},[2201,16115,11515],{},[1214,16117,16118,16120],{"accent":1121},[2201,16119,4140],{},[1193,16121,3325],{},[2201,16123,1228],{},[1153,16125,16126],{"encoding":1155},"R = x_{\\max} - x_{\\min} \\qquad \\text{(variační rozpětí)}",[1110,16128,16129],{},[1130,16130,12674],{},[1110,16132,16133,16134,16157,16158,16180,16181,16202,16203,16231],{},"Kvantil ",[1115,16135,16137],{"className":16136},[1137],[1139,16138,16139],{"xmlns":1141},[1143,16140,16141,16154],{},[1146,16142,16143],{},[1201,16144,16145,16152],{},[1214,16146,16147,16149],{"accent":1121},[1149,16148,1168],{},[1193,16150,16151],{},"~",[1149,16153,1110],{},[1153,16155,16156],{"encoding":1155},"\\tilde{x}_p"," dělí hodnoty datového souboru na dvě části: ",[1115,16159,16161],{"className":16160},[1137],[1139,16162,16163],{"xmlns":1141},[1143,16164,16165,16177],{},[1146,16166,16167,16170,16172,16174],{},[1230,16168,16169],{},"100",[1149,16171,1110],{},[2201,16173,2203],{},[1149,16175,16176],{"mathvariant":1854},"%",[1153,16178,16179],{"encoding":1155},"100p\\,\\%"," hodnot je menších nebo rovných ",[1115,16182,16184],{"className":16183},[1137],[1139,16185,16186],{"xmlns":1141},[1143,16187,16188,16200],{},[1146,16189,16190],{},[1201,16191,16192,16198],{},[1214,16193,16194,16196],{"accent":1121},[1149,16195,1168],{},[1193,16197,16151],{},[1149,16199,1110],{},[1153,16201,16156],{"encoding":1155},", zbylých ",[1115,16204,16206],{"className":16205},[1137],[1139,16207,16208],{"xmlns":1141},[1143,16209,16210,16228],{},[1146,16211,16212,16214,16216,16218,16220,16222,16224,16226],{},[1230,16213,16169],{},[1193,16215,1199],{"stretchy":1198},[1230,16217,1525],{},[1193,16219,1210],{},[1149,16221,1110],{},[1193,16223,1228],{"stretchy":1198},[2201,16225,2203],{},[1149,16227,16176],{"mathvariant":1854},[1153,16229,16230],{"encoding":1155},"100(1-p)\\,\\%"," je větších. Nejdůležitější kvantily:",[1124,16233,16234,16261],{},[1127,16235,16236,1243,16238,16260],{},[1130,16237,15903],{},[1115,16239,16241],{"className":16240},[1137],[1139,16242,16243],{"xmlns":1141},[1143,16244,16245,16257],{},[1146,16246,16247],{},[1201,16248,16249,16255],{},[1214,16250,16251,16253],{"accent":1121},[1149,16252,1168],{},[1193,16254,16151],{},[1230,16256,12828],{},[1153,16258,16259],{"encoding":1155},"\\tilde{x}_{0{,}5}"," — pro lichý počet prvků uspořádaného souboru prostřední prvek, pro sudý počet průměr dvou prostředních prvků;",[1127,16262,16263,1243,16266,1405,16288,1243,16291,1236],{},[1130,16264,16265],{},"dolní kvartil",[1115,16267,16269],{"className":16268},[1137],[1139,16270,16271],{"xmlns":1141},[1143,16272,16273,16285],{},[1146,16274,16275],{},[1201,16276,16277,16283],{},[1214,16278,16279,16281],{"accent":1121},[1149,16280,1168],{},[1193,16282,16151],{},[1230,16284,12848],{},[1153,16286,16287],{"encoding":1155},"\\tilde{x}_{0{,}25}",[1130,16289,16290],{},"horní kvartil",[1115,16292,16294],{"className":16293},[1137],[1139,16295,16296],{"xmlns":1141},[1143,16297,16298,16310],{},[1146,16299,16300],{},[1201,16301,16302,16308],{},[1214,16303,16304,16306],{"accent":1121},[1149,16305,1168],{},[1193,16307,16151],{},[1230,16309,12868],{},[1153,16311,16312],{"encoding":1155},"\\tilde{x}_{0{,}75}",[1110,16314,16315,16316,16319],{},"Datový soubor se do R zadává buď přímo (",[1332,16317,16318],{},"x \u003C- c(...)","), nebo načtením ze souboru:",[2035,16321,16323],{"className":2037,"code":16322,"language":71,"meta":2039,"style":2039},"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",[1332,16324,16325,16386],{"__ignoreMap":2039},[1115,16326,16327,16329,16331,16333,16335,16338,16340,16343,16345,16348,16350,16353,16355,16357,16359,16361,16363,16366,16368,16371,16373,16375,16377,16379,16382],{"class":2044,"line":10},[1115,16328,1168],{"class":2047},[1115,16330,2052],{"class":2051},[1115,16332,2056],{"class":2055},[1115,16334,1199],{"class":2059},[1115,16336,16337],{"class":2062},"4.1",[1115,16339,1503],{"class":2051},[1115,16341,16342],{"class":2062}," 4.0",[1115,16344,1503],{"class":2051},[1115,16346,16347],{"class":2062}," 3.8",[1115,16349,1503],{"class":2051},[1115,16351,16352],{"class":2062}," 3.9",[1115,16354,1503],{"class":2051},[1115,16356,16347],{"class":2062},[1115,16358,1503],{"class":2051},[1115,16360,16347],{"class":2062},[1115,16362,1503],{"class":2051},[1115,16364,16365],{"class":2062}," 3.5",[1115,16367,1503],{"class":2051},[1115,16369,16370],{"class":2062}," 3.7",[1115,16372,1503],{"class":2051},[1115,16374,16342],{"class":2062},[1115,16376,1503],{"class":2051},[1115,16378,16342],{"class":2062},[1115,16380,16381],{"class":2059},") ",[1115,16383,16385],{"class":16384},"sCsY4","# přímé zadání hodnot\n",[1115,16387,16388],{"class":2044,"line":27},[1115,16389,16390],{"class":16384},"# x \u003C- read.table(\"data.txt\")[, 1] # načtení prvního sloupce ze souboru\n",[1110,16392,16393,16394,16397,16398,16401,16402,16405,16406,16409],{},"Řádek s načtením ze souboru je zakomentovaný znakem ",[1332,16395,16396],{},"#",": soubor musí ležet v pracovním adresáři R. ",[1332,16399,16400],{},"read.table()"," vrací datovou tabulku (",[1332,16403,16404],{},"data.frame","), proto ",[1332,16407,16408],{},"[, 1]"," vybere její první sloupec jako vektor.",[1110,16411,13423],{},[2035,16413,16415],{"className":2037,"code":16414,"language":71,"meta":2039,"style":2039},"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",[1332,16416,16417,16474,16485,16496,16507,16518,16556,16581,16604],{"__ignoreMap":2039},[1115,16418,16419,16421,16423,16425,16427,16430,16432,16435,16437,16440,16442,16445,16447,16449,16451,16454,16456,16458,16460,16463,16465,16468,16470,16472],{"class":2044,"line":10},[1115,16420,1168],{"class":2047},[1115,16422,2052],{"class":2051},[1115,16424,2056],{"class":2055},[1115,16426,1199],{"class":2059},[1115,16428,16429],{"class":2062},"11.1",[1115,16431,1503],{"class":2051},[1115,16433,16434],{"class":2062}," 12.7",[1115,16436,1503],{"class":2051},[1115,16438,16439],{"class":2062}," 10.8",[1115,16441,1503],{"class":2051},[1115,16443,16444],{"class":2062}," 13.2",[1115,16446,1503],{"class":2051},[1115,16448,16434],{"class":2062},[1115,16450,1503],{"class":2051},[1115,16452,16453],{"class":2062}," 13.4",[1115,16455,1503],{"class":2051},[1115,16457,16434],{"class":2062},[1115,16459,1503],{"class":2051},[1115,16461,16462],{"class":2062}," 14.4",[1115,16464,1503],{"class":2051},[1115,16466,16467],{"class":2062}," 14.7",[1115,16469,1503],{"class":2051},[1115,16471,16462],{"class":2062},[1115,16473,2090],{"class":2059},[1115,16475,16476,16479,16481,16483],{"class":2044,"line":27},[1115,16477,16478],{"class":2055},"length",[1115,16480,1199],{"class":2059},[1115,16482,1168],{"class":2047},[1115,16484,2090],{"class":2059},[1115,16486,16487,16490,16492,16494],{"class":2044,"line":148},[1115,16488,16489],{"class":2055},"mean",[1115,16491,1199],{"class":2059},[1115,16493,1168],{"class":2047},[1115,16495,2090],{"class":2059},[1115,16497,16498,16501,16503,16505],{"class":2044,"line":111},[1115,16499,16500],{"class":2055},"var",[1115,16502,1199],{"class":2059},[1115,16504,1168],{"class":2047},[1115,16506,2090],{"class":2059},[1115,16508,16509,16512,16514,16516],{"class":2044,"line":96},[1115,16510,16511],{"class":2055},"sd",[1115,16513,1199],{"class":2059},[1115,16515,1168],{"class":2047},[1115,16517,2090],{"class":2059},[1115,16519,16520,16522,16524,16526,16529,16531,16533,16535,16537,16539,16541,16543,16545,16547,16550,16552,16554],{"class":2044,"line":89},[1115,16521,1848],{"class":2055},[1115,16523,1199],{"class":2059},[1115,16525,1168],{"class":2047},[1115,16527,16528],{"class":2059},"); ",[1115,16530,16071],{"class":2055},[1115,16532,1199],{"class":2059},[1115,16534,1168],{"class":2047},[1115,16536,16528],{"class":2059},[1115,16538,16071],{"class":2055},[1115,16540,1199],{"class":2059},[1115,16542,1168],{"class":2047},[1115,16544,8993],{"class":2059},[1115,16546,9028],{"class":2051},[1115,16548,16549],{"class":2055}," min",[1115,16551,1199],{"class":2059},[1115,16553,1168],{"class":2047},[1115,16555,2090],{"class":2059},[1115,16557,16558,16561,16563,16565,16567,16570,16572,16575,16577,16579],{"class":2044,"line":82},[1115,16559,16560],{"class":2055},"quantile",[1115,16562,1199],{"class":2059},[1115,16564,1168],{"class":2047},[1115,16566,1503],{"class":2051},[1115,16568,16569],{"class":2062}," 0.5",[1115,16571,1503],{"class":2051},[1115,16573,16574],{"class":2047}," type",[1115,16576,2510],{"class":2051},[1115,16578,2087],{"class":2062},[1115,16580,2090],{"class":2059},[1115,16582,16583,16585,16587,16589,16591,16594,16596,16598,16600,16602],{"class":2044,"line":75},[1115,16584,16560],{"class":2055},[1115,16586,1199],{"class":2059},[1115,16588,1168],{"class":2047},[1115,16590,1503],{"class":2051},[1115,16592,16593],{"class":2062}," 0.25",[1115,16595,1503],{"class":2051},[1115,16597,16574],{"class":2047},[1115,16599,2510],{"class":2051},[1115,16601,2087],{"class":2062},[1115,16603,2090],{"class":2059},[1115,16605,16606,16608,16610,16612,16614,16617,16619,16621,16623,16625],{"class":2044,"line":5577},[1115,16607,16560],{"class":2055},[1115,16609,1199],{"class":2059},[1115,16611,1168],{"class":2047},[1115,16613,1503],{"class":2051},[1115,16615,16616],{"class":2062}," 0.75",[1115,16618,1503],{"class":2051},[1115,16620,16574],{"class":2047},[1115,16622,2510],{"class":2051},[1115,16624,2087],{"class":2062},[1115,16626,2090],{"class":2059},[2035,16628,16631],{"className":16629,"code":16630,"language":2169,"meta":2039},[2167],"[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",[1332,16632,16630],{"__ignoreMap":2039},[1110,16634,16635,16638,16639,16642],{},[1332,16636,16637],{},"quantile(x, p, type = 6)"," je potřeba zadat explicitně — výchozí typ v R (",[1332,16640,16641],{},"type = 7",") by u některých souborů dal mírně odlišné hodnoty kvantilů než ruční výpočet použitý v této kapitole.",[1110,16644,16645],{},[1864,16646],{"alt":16647,"className":16648,"src":16649},"mask-ps-kvantily",[1387,1868],"\u002Fwiki-assets\u002Fmask-ps-kvantily.png",[1110,16651,16652],{},"Seřazení souboru a krabicový graf:",[2035,16654,16656],{"className":2037,"code":16655,"language":71,"meta":2039,"style":2039},"sort(x) # vzestupně\nsort(x, decreasing = TRUE) # sestupně\nboxplot(x)\n",[1332,16657,16658,16673,16696],{"__ignoreMap":2039},[1115,16659,16660,16663,16665,16667,16670],{"class":2044,"line":10},[1115,16661,16662],{"class":2055},"sort",[1115,16664,1199],{"class":2059},[1115,16666,1168],{"class":2047},[1115,16668,16669],{"class":2059},") ",[1115,16671,16672],{"class":16384},"# vzestupně\n",[1115,16674,16675,16677,16679,16681,16683,16686,16688,16690,16693],{"class":2044,"line":27},[1115,16676,16662],{"class":2055},[1115,16678,1199],{"class":2059},[1115,16680,1168],{"class":2047},[1115,16682,1503],{"class":2051},[1115,16684,16685],{"class":2047}," decreasing",[1115,16687,2510],{"class":2051},[1115,16689,5460],{"class":2062},[1115,16691,16692],{"class":2059},") ",[1115,16694,16695],{"class":16384},"# sestupně\n",[1115,16697,16698,16701,16703,16705],{"class":2044,"line":148},[1115,16699,16700],{"class":2055},"boxplot",[1115,16702,1199],{"class":2059},[1115,16704,1168],{"class":2047},[1115,16706,2090],{"class":2059},[2035,16708,16711],{"className":16709,"code":16710,"language":2169,"meta":2039},[2167]," [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",[1332,16712,16710],{"__ignoreMap":2039},[1110,16714,16715,16718,16719,16722],{},[1332,16716,16717],{},"boxplot()"," kreslí krabici mezi hodnotami ",[1332,16720,16721],{},"fivenum(x)"," (zde 12,7 a 14,4), které se od kvartilů typu 6 mohou mírně lišit.",[1103,16724,16726,16733],{"className":16725,"dataCallout":2932},[1106,2931],[1110,16727,16729,16732],{"className":16728},[1113],[1115,16730],{"className":16731,"ariaHidden":1121},[1118,2939,1120],"Příklad: Empirické charakteristiky",[1110,16734,16735],{},"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.",[1110,16737,16738,16739,1348,16762,1348,16785,1348,16804,16823,16824,12832,16851,16866,16867,1236],{},"Výstup R kódu výše dává ",[1115,16740,16742],{"className":16741},[1137],[1139,16743,16744],{"xmlns":1141},[1143,16745,16746,16759],{},[1146,16747,16748,16754,16756],{},[1214,16749,16750,16752],{"accent":1121},[1149,16751,1168],{},[1193,16753,15814],{},[1193,16755,1281],{},[1230,16757,16758],{},"13,01",[1153,16760,16761],{"encoding":1155},"\\bar{x}=13{,}01",[1115,16763,16765],{"className":16764},[1137],[1139,16766,16767],{"xmlns":1141},[1143,16768,16769,16782],{},[1146,16770,16771,16777,16779],{},[1224,16772,16773,16775],{},[1149,16774,4542],{},[1230,16776,1232],{},[1193,16778,1281],{},[1230,16780,16781],{},"1,75",[1153,16783,16784],{"encoding":1155},"s^2=1{,}75",[1115,16786,16788],{"className":16787},[1137],[1139,16789,16790],{"xmlns":1141},[1143,16791,16792,16801],{},[1146,16793,16794,16796,16798],{},[1149,16795,4542],{},[1193,16797,1281],{},[1230,16799,16800],{},"1,32",[1153,16802,16803],{"encoding":1155},"s=1{,}32",[1115,16805,16807],{"className":16806},[1137],[1139,16808,16809],{"xmlns":1141},[1143,16810,16811,16820],{},[1146,16812,16813,16815,16817],{},[1149,16814,1257],{},[1193,16816,1281],{},[1230,16818,16819],{},"3,9",[1153,16821,16822],{"encoding":1155},"R=3{,}9",", medián ",[1115,16825,16827],{"className":16826},[1137],[1139,16828,16829],{"xmlns":1141},[1143,16830,16831,16848],{},[1146,16832,16833,16843,16845],{},[1201,16834,16835,16841],{},[1214,16836,16837,16839],{"accent":1121},[1149,16838,1168],{},[1193,16840,16151],{},[1230,16842,12828],{},[1193,16844,1281],{},[1230,16846,16847],{},"12,95",[1153,16849,16850],{"encoding":1155},"\\tilde{x}_{0{,}5}=12{,}95",[1115,16852,16854],{"className":16853},[1137],[1139,16855,16856],{"xmlns":1141},[1143,16857,16858,16863],{},[1146,16859,16860],{},[1230,16861,16862],{},"12,3",[1153,16864,16865],{"encoding":1155},"12{,}3",", horní kvartil ",[1115,16868,16870],{"className":16869},[1137],[1139,16871,16872],{"xmlns":1141},[1143,16873,16874,16879],{},[1146,16875,16876],{},[1230,16877,16878],{},"14,4",[1153,16880,16881],{"encoding":1155},"14{,}4",[1110,16883,16884],{},"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.",[1103,16886,16888,16895],{"className":16887,"dataCallout":2932},[1106,2931],[1110,16889,16891,16894],{"className":16890},[1113],[1115,16892],{"className":16893,"ariaHidden":1121},[1118,2939,1120],"Příklad: Doba oprav televizorů",[1110,16896,16897],{},"Při 50 opravách určité závady televizoru byly naměřeny časy (v minutách). Určete empirické charakteristiky.",[2035,16899,16901],{"className":2037,"code":16900,"language":71,"meta":2039,"style":2039},"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",[1332,16902,16903,16963,17014,17061,17108,17156,17166,17176,17186,17206],{"__ignoreMap":2039},[1115,16904,16905,16908,16910,16912,16914,16916,16918,16921,16923,16926,16928,16931,16933,16936,16938,16941,16943,16946,16948,16951,16953,16956,16958,16961],{"class":2044,"line":10},[1115,16906,16907],{"class":2047},"x6",[1115,16909,2052],{"class":2051},[1115,16911,2056],{"class":2055},[1115,16913,1199],{"class":2059},[1115,16915,7993],{"class":2062},[1115,16917,1503],{"class":2051},[1115,16919,16920],{"class":2062}," 40.2",[1115,16922,1503],{"class":2051},[1115,16924,16925],{"class":2062}," 41.9",[1115,16927,1503],{"class":2051},[1115,16929,16930],{"class":2062}," 43.4",[1115,16932,1503],{"class":2051},[1115,16934,16935],{"class":2062}," 42.8",[1115,16937,1503],{"class":2051},[1115,16939,16940],{"class":2062}," 42.3",[1115,16942,1503],{"class":2051},[1115,16944,16945],{"class":2062}," 43.2",[1115,16947,1503],{"class":2051},[1115,16949,16950],{"class":2062}," 45",[1115,16952,1503],{"class":2051},[1115,16954,16955],{"class":2062}," 41.5",[1115,16957,1503],{"class":2051},[1115,16959,16960],{"class":2062}," 42.7",[1115,16962,8147],{"class":2051},[1115,16964,16965,16968,16970,16973,16975,16978,16980,16983,16985,16988,16990,16993,16995,16998,17000,17003,17005,17007,17009,17012],{"class":2044,"line":27},[1115,16966,16967],{"class":2062}," 43.9",[1115,16969,1503],{"class":2051},[1115,16971,16972],{"class":2062}," 40.1",[1115,16974,1503],{"class":2051},[1115,16976,16977],{"class":2062}," 43.3",[1115,16979,1503],{"class":2051},[1115,16981,16982],{"class":2062}," 41.1",[1115,16984,1503],{"class":2051},[1115,16986,16987],{"class":2062}," 42.5",[1115,16989,1503],{"class":2051},[1115,16991,16992],{"class":2062}," 42.4",[1115,16994,1503],{"class":2051},[1115,16996,16997],{"class":2062}," 41.4",[1115,16999,1503],{"class":2051},[1115,17001,17002],{"class":2062}," 40.8",[1115,17004,1503],{"class":2051},[1115,17006,13704],{"class":2062},[1115,17008,1503],{"class":2051},[1115,17010,17011],{"class":2062}," 44.7",[1115,17013,8147],{"class":2051},[1115,17015,17016,17019,17021,17023,17025,17027,17029,17032,17034,17037,17039,17042,17044,17046,17048,17051,17053,17055,17057,17059],{"class":2044,"line":148},[1115,17017,17018],{"class":2062}," 41.2",[1115,17020,1503],{"class":2051},[1115,17022,16925],{"class":2062},[1115,17024,1503],{"class":2051},[1115,17026,16992],{"class":2062},[1115,17028,1503],{"class":2051},[1115,17030,17031],{"class":2062}," 44.4",[1115,17033,1503],{"class":2051},[1115,17035,17036],{"class":2062}," 40.5",[1115,17038,1503],{"class":2051},[1115,17040,17041],{"class":2062}," 39.7",[1115,17043,1503],{"class":2051},[1115,17045,16982],{"class":2062},[1115,17047,1503],{"class":2051},[1115,17049,17050],{"class":2062}," 41",[1115,17052,1503],{"class":2051},[1115,17054,16925],{"class":2062},[1115,17056,1503],{"class":2051},[1115,17058,17002],{"class":2062},[1115,17060,8147],{"class":2051},[1115,17062,17063,17066,17068,17070,17072,17075,17077,17079,17081,17083,17085,17088,17090,17093,17095,17097,17099,17102,17104,17106],{"class":2044,"line":111},[1115,17064,17065],{"class":2062}," 43",[1115,17067,1503],{"class":2051},[1115,17069,16935],{"class":2062},[1115,17071,1503],{"class":2051},[1115,17073,17074],{"class":2062}," 42.9",[1115,17076,1503],{"class":2051},[1115,17078,16960],{"class":2062},[1115,17080,1503],{"class":2051},[1115,17082,16977],{"class":2062},[1115,17084,1503],{"class":2051},[1115,17086,17087],{"class":2062}," 42.2",[1115,17089,1503],{"class":2051},[1115,17091,17092],{"class":2062}," 39.2",[1115,17094,1503],{"class":2051},[1115,17096,16955],{"class":2062},[1115,17098,1503],{"class":2051},[1115,17100,17101],{"class":2062}," 41.6",[1115,17103,1503],{"class":2051},[1115,17105,16960],{"class":2062},[1115,17107,8147],{"class":2051},[1115,17109,17110,17113,17115,17117,17119,17122,17124,17126,17128,17131,17133,17136,17138,17141,17143,17145,17147,17150,17152,17154],{"class":2044,"line":96},[1115,17111,17112],{"class":2062}," 45",[1115,17114,1503],{"class":2051},[1115,17116,16940],{"class":2062},[1115,17118,1503],{"class":2051},[1115,17120,17121],{"class":2062}," 43.6",[1115,17123,1503],{"class":2051},[1115,17125,16945],{"class":2062},[1115,17127,1503],{"class":2051},[1115,17129,17130],{"class":2062}," 38.8",[1115,17132,1503],{"class":2051},[1115,17134,17135],{"class":2062}," 43",[1115,17137,1503],{"class":2051},[1115,17139,17140],{"class":2062}," 44.2",[1115,17142,1503],{"class":2051},[1115,17144,17135],{"class":2062},[1115,17146,1503],{"class":2051},[1115,17148,17149],{"class":2062}," 40",[1115,17151,1503],{"class":2051},[1115,17153,17031],{"class":2062},[1115,17155,2090],{"class":2059},[1115,17157,17158,17160,17162,17164],{"class":2044,"line":89},[1115,17159,16478],{"class":2055},[1115,17161,1199],{"class":2059},[1115,17163,16907],{"class":2047},[1115,17165,2090],{"class":2059},[1115,17167,17168,17170,17172,17174],{"class":2044,"line":82},[1115,17169,16489],{"class":2055},[1115,17171,1199],{"class":2059},[1115,17173,16907],{"class":2047},[1115,17175,2090],{"class":2059},[1115,17177,17178,17180,17182,17184],{"class":2044,"line":75},[1115,17179,16511],{"class":2055},[1115,17181,1199],{"class":2059},[1115,17183,16907],{"class":2047},[1115,17185,2090],{"class":2059},[1115,17187,17188,17190,17192,17194,17196,17198,17200,17202,17204],{"class":2044,"line":5577},[1115,17189,16071],{"class":2055},[1115,17191,1199],{"class":2059},[1115,17193,16907],{"class":2047},[1115,17195,8993],{"class":2059},[1115,17197,9028],{"class":2051},[1115,17199,16549],{"class":2055},[1115,17201,1199],{"class":2059},[1115,17203,16907],{"class":2047},[1115,17205,2090],{"class":2059},[1115,17207,17208,17211,17213,17215],{"class":2044,"line":72},[1115,17209,17210],{"class":2055},"median",[1115,17212,1199],{"class":2059},[1115,17214,16907],{"class":2047},[1115,17216,2090],{"class":2059},[2035,17218,17221],{"className":17219,"code":17220,"language":2169,"meta":2039},[2167],"[1] 50\n[1] 42.27\n[1] 1.48052\n[1] 6.2\n[1] 42.4\n",[1332,17222,17220],{"__ignoreMap":2039},[1110,17224,17225],{},"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.",[1377,17227,17229],{"id":17228},"empirická-distribuční-funkce","Empirická distribuční funkce",[1110,17231,17232,17233,17246,17247,1243,17250,17273,17274,17308],{},"Pro libovolný rozsah datového souboru, diskrétní i spojitou náhodnou veličinu ",[1115,17234,17236],{"className":17235},[1137],[1139,17237,17238],{"xmlns":1141},[1143,17239,17240,17244],{},[1146,17241,17242],{},[1149,17243,11107],{},[1153,17245,11107],{"encoding":1155},", lze sestrojit ",[1130,17248,17249],{},"empirickou distribuční funkci",[1115,17251,17253],{"className":17252},[1137],[1139,17254,17255],{"xmlns":1141},[1143,17256,17257,17271],{},[1146,17258,17259,17265,17267,17269],{},[1201,17260,17261,17263],{},[1149,17262,11091],{},[1149,17264,1816],{},[1193,17266,1199],{"stretchy":1198},[1149,17268,1168],{},[1193,17270,1228],{"stretchy":1198},[1153,17272,15542],{"encoding":1155},". Pro datový soubor ",[1115,17275,17277],{"className":17276},[1137],[1139,17278,17279],{"xmlns":1141},[1143,17280,17281,17305],{},[1146,17282,17283,17285,17291,17293,17295,17297,17303],{},[1193,17284,1199],{"stretchy":1198},[1201,17286,17287,17289],{},[1149,17288,1168],{},[1230,17290,1525],{},[1193,17292,1503],{"separator":1121},[1193,17294,1530],{},[1193,17296,1503],{"separator":1121},[1201,17298,17299,17301],{},[1149,17300,1168],{},[1149,17302,1816],{},[1193,17304,1228],{"stretchy":1198},[1153,17306,17307],{"encoding":1155},"(x_1,\\dots,x_n)"," je",[1115,17310,17312],{"className":17311},[1137],[1139,17313,17314],{"xmlns":1141,"display":1796},[1143,17315,17316,17340],{},[1146,17317,17318,17324,17326,17328,17330,17332,17338],{},[1201,17319,17320,17322],{},[1149,17321,11091],{},[1149,17323,1816],{},[1193,17325,1199],{"stretchy":1198},[1149,17327,1168],{},[1193,17329,1228],{"stretchy":1198},[1193,17331,1281],{},[3546,17333,17334,17336],{},[1149,17335,11631],{},[1149,17337,1816],{},[1193,17339,1503],{"separator":1121},[1153,17341,17342],{"encoding":1155},"F_n(x) = \\frac{k}{n},",[1110,17344,8899,17345,17358,17359,1236],{},[1115,17346,17348],{"className":17347},[1137],[1139,17349,17350],{"xmlns":1141},[1143,17351,17352,17356],{},[1146,17353,17354],{},[1149,17355,11631],{},[1153,17357,11631],{"encoding":1155}," je počet prvků datového souboru menších nebo rovných číslu ",[1115,17360,17362],{"className":17361},[1137],[1139,17363,17364],{"xmlns":1141},[1143,17365,17366,17370],{},[1146,17367,17368],{},[1149,17369,1168],{},[1153,17371,1168],{"encoding":1155},[1110,17373,13423],{},[2035,17375,17377],{"className":2037,"code":17376,"language":71,"meta":2039,"style":2039},"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",[1332,17378,17379,17394,17409,17427,17441],{"__ignoreMap":2039},[1115,17380,17381,17383,17385,17388,17390,17392],{"class":2044,"line":10},[1115,17382,1582],{"class":2047},[1115,17384,2052],{"class":2051},[1115,17386,17387],{"class":2055}," ecdf",[1115,17389,1199],{"class":2059},[1115,17391,1168],{"class":2047},[1115,17393,2090],{"class":2059},[1115,17395,17396,17399,17401,17403,17406],{"class":2044,"line":27},[1115,17397,17398],{"class":2055},"knots",[1115,17400,1199],{"class":2059},[1115,17402,1582],{"class":2047},[1115,17404,17405],{"class":2059},") ",[1115,17407,17408],{"class":16384},"# vzestupně seřazené různé hodnoty datového souboru\n",[1115,17410,17411,17413,17415,17417,17419,17421,17424],{"class":2044,"line":148},[1115,17412,1582],{"class":2055},[1115,17414,1199],{"class":2059},[1115,17416,17398],{"class":2055},[1115,17418,1199],{"class":2059},[1115,17420,1582],{"class":2047},[1115,17422,17423],{"class":2059},")) ",[1115,17425,17426],{"class":16384},"# hodnoty Fn(x) v těchto bodech\n",[1115,17428,17429,17431,17433,17435,17438],{"class":2044,"line":111},[1115,17430,1582],{"class":2055},[1115,17432,1199],{"class":2059},[1115,17434,3116],{"class":2062},[1115,17436,17437],{"class":2059},") ",[1115,17439,17440],{"class":16384},"# Fn v libovolném bodě\n",[1115,17442,17443,17446,17448,17450],{"class":2044,"line":96},[1115,17444,17445],{"class":2055},"plot",[1115,17447,1199],{"class":2059},[1115,17449,1582],{"class":2047},[1115,17451,2090],{"class":2059},[2035,17453,17456],{"className":17454,"code":17455,"language":2169,"meta":2039},[2167],"[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",[1332,17457,17455],{"__ignoreMap":2039},[1110,17459,17460,17463,17464,17482,17483,17486,17487,17500,17501,1236],{},[1332,17461,17462],{},"knots()"," vrací jen různé hodnoty (opakující se hodnota 12,7 je ve výpočtu ",[1115,17465,17467],{"className":17466},[1137],[1139,17468,17469],{"xmlns":1141},[1143,17470,17471,17479],{},[1146,17472,17473],{},[1201,17474,17475,17477],{},[1149,17476,11091],{},[1149,17478,1816],{},[1153,17480,17481],{"encoding":1155},"F_n"," započtena třikrát, v seznamu uzlů je ale jen jednou); ",[1332,17484,17485],{},"plot(f)"," nakreslí schodovitý graf, který v každém uzlu skáče o ",[1115,17488,17490],{"className":17489},[1137],[1139,17491,17492],{"xmlns":1141},[1143,17493,17494,17498],{},[1146,17495,17496],{},[1149,17497,11631],{},[1153,17499,11631],{"encoding":1155},"-násobek ",[1115,17502,17504],{"className":17503},[1137],[1139,17505,17506],{"xmlns":1141},[1143,17507,17508,17516],{},[1146,17509,17510,17512,17514],{},[1230,17511,1525],{},[1149,17513,5731],{"mathvariant":1854},[1149,17515,1816],{},[1153,17517,17518],{"encoding":1155},"1\u002Fn",[1110,17520,17521],{},[1864,17522],{"alt":17523,"className":17524,"src":17525},"mask-ps-ecdf",[1387,1868],"\u002Fwiki-assets\u002Fmask-ps-ecdf.png",[1103,17527,17529,17536],{"className":17528,"dataCallout":2932},[1106,2931],[1110,17530,17532,17535],{"className":17531},[1113],[1115,17533],{"className":17534,"ariaHidden":1121},[1118,2939,1120],"Příklad: Empirická distribuční funkce",[1110,17537,17538],{},"Pro předchozí datový soubor (doba opravy součástky) určete empirickou distribuční funkci.",[1110,17540,17541,17542,1236],{},"Uspořádaný soubor je ",[1115,17543,17545],{"className":17544},[1137],[1139,17546,17547],{"xmlns":1141},[1143,17548,17549,17613],{},[1146,17550,17551,17554,17556,17558,17561,17563,17565,17568,17570,17572,17574,17576,17578,17580,17582,17584,17587,17589,17591,17594,17596,17598,17600,17602,17604,17606,17608,17610],{},[1230,17552,17553],{},"10,8",[1193,17555,1589],{"separator":1121},[2201,17557,15670],{},[1230,17559,17560],{},"11,1",[1193,17562,1589],{"separator":1121},[2201,17564,15670],{},[1230,17566,17567],{},"12,7",[1193,17569,1589],{"separator":1121},[2201,17571,15670],{},[1230,17573,17567],{},[1193,17575,1589],{"separator":1121},[2201,17577,15670],{},[1230,17579,17567],{},[1193,17581,1589],{"separator":1121},[2201,17583,15670],{},[1230,17585,17586],{},"13,2",[1193,17588,1589],{"separator":1121},[2201,17590,15670],{},[1230,17592,17593],{},"13,4",[1193,17595,1589],{"separator":1121},[2201,17597,15670],{},[1230,17599,16878],{},[1193,17601,1589],{"separator":1121},[2201,17603,15670],{},[1230,17605,16878],{},[1193,17607,1589],{"separator":1121},[2201,17609,15670],{},[1230,17611,17612],{},"14,7",[1153,17614,17615],{"encoding":1155},"10{,}8;\\ 11{,}1;\\ 12{,}7;\\ 12{,}7;\\ 12{,}7;\\ 13{,}2;\\ 13{,}4;\\ 14{,}4;\\ 14{,}4;\\ 14{,}7",[6528,17617,17618,17651],{},[6531,17619,17620],{},[6534,17621,17622,17637,17639,17641,17643,17645,17647,17649],{},[6537,17623,17624],{},[1115,17625,17627],{"className":17626},[1137],[1139,17628,17629],{"xmlns":1141},[1143,17630,17631,17635],{},[1146,17632,17633],{},[1149,17634,1168],{},[1153,17636,1168],{"encoding":1155},[6537,17638,17553],{},[6537,17640,17560],{},[6537,17642,17567],{},[6537,17644,17586],{},[6537,17646,17593],{},[6537,17648,16878],{},[6537,17650,17612],{},[6645,17652,17653,17684],{},[6534,17654,17655,17670,17672,17674,17676,17678,17680,17682],{},[6650,17656,17657],{},[1115,17658,17660],{"className":17659},[1137],[1139,17661,17662],{"xmlns":1141},[1143,17663,17664,17668],{},[1146,17665,17666],{},[1149,17667,11631],{},[1153,17669,11631],{"encoding":1155},[6650,17671,1525],{},[6650,17673,1232],{},[6650,17675,5351],{},[6650,17677,8365],{},[6650,17679,2538],{},[6650,17681,8013],{},[6650,17683,5389],{},[6534,17685,17686,17711,17714,17717,17719,17722,17725,17728],{},[6650,17687,17688],{},[1115,17689,17691],{"className":17690},[1137],[1139,17692,17693],{"xmlns":1141},[1143,17694,17695,17709],{},[1146,17696,17697,17703,17705,17707],{},[1201,17698,17699,17701],{},[1149,17700,11091],{},[1149,17702,1816],{},[1193,17704,1199],{"stretchy":1198},[1149,17706,1168],{},[1193,17708,1228],{"stretchy":1198},[1153,17710,15542],{"encoding":1155},[6650,17712,17713],{},"0,1",[6650,17715,17716],{},"0,2",[6650,17718,12828],{},[6650,17720,17721],{},"0,6",[6650,17723,17724],{},"0,7",[6650,17726,17727],{},"0,9",[6650,17729,17730],{},"1,0",[1110,17732,17733,17734,17756,17757,17780],{},"Graf (levý panel výše) odpovídá tabulce: funkce je nulová pod 10,8, skáče o ",[1115,17735,17737],{"className":17736},[1137],[1139,17738,17739],{"xmlns":1141},[1143,17740,17741,17753],{},[1146,17742,17743,17745,17747,17749,17751],{},[1230,17744,1525],{},[1149,17746,5731],{"mathvariant":1854},[1149,17748,1816],{},[1193,17750,1281],{},[1230,17752,17713],{},[1153,17754,17755],{"encoding":1155},"1\u002Fn = 0{,}1"," v každé jednoduché hodnotě a o ",[1115,17758,17760],{"className":17759},[1137],[1139,17761,17762],{"xmlns":1141},[1143,17763,17764,17777],{},[1146,17765,17766,17768,17770,17772,17774],{},[1230,17767,8010],{},[1149,17769,5731],{"mathvariant":1854},[1149,17771,1816],{},[1193,17773,1281],{},[1230,17775,17776],{},"0,3",[1153,17778,17779],{"encoding":1155},"3\u002Fn = 0{,}3"," v bodě 12,7, kde se hodnota opakuje třikrát.",[1103,17782,17784,17791],{"className":17783,"dataCallout":2932},[1106,2931],[1110,17785,17787,17790],{"className":17786},[1113],[1115,17788],{"className":17789,"ariaHidden":1121},[1118,2939,1120],"Příklad: Odpad materiálu",[1110,17792,17793],{},"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.",[2035,17795,17797],{"className":2037,"code":17796,"language":71,"meta":2039,"style":2039},"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",[1332,17798,17799,17850,17860,17870,17880,17900,17910,17925,17935],{"__ignoreMap":2039},[1115,17800,17801,17804,17806,17808,17810,17812,17814,17816,17818,17820,17822,17824,17826,17828,17830,17832,17834,17836,17838,17840,17842,17844,17846,17848],{"class":2044,"line":10},[1115,17802,17803],{"class":2047},"x4",[1115,17805,2052],{"class":2051},[1115,17807,2056],{"class":2055},[1115,17809,1199],{"class":2059},[1115,17811,16337],{"class":2062},[1115,17813,1503],{"class":2051},[1115,17815,16342],{"class":2062},[1115,17817,1503],{"class":2051},[1115,17819,16347],{"class":2062},[1115,17821,1503],{"class":2051},[1115,17823,16352],{"class":2062},[1115,17825,1503],{"class":2051},[1115,17827,16347],{"class":2062},[1115,17829,1503],{"class":2051},[1115,17831,16347],{"class":2062},[1115,17833,1503],{"class":2051},[1115,17835,16365],{"class":2062},[1115,17837,1503],{"class":2051},[1115,17839,16370],{"class":2062},[1115,17841,1503],{"class":2051},[1115,17843,16342],{"class":2062},[1115,17845,1503],{"class":2051},[1115,17847,16342],{"class":2062},[1115,17849,2090],{"class":2059},[1115,17851,17852,17854,17856,17858],{"class":2044,"line":27},[1115,17853,16478],{"class":2055},[1115,17855,1199],{"class":2059},[1115,17857,17803],{"class":2047},[1115,17859,2090],{"class":2059},[1115,17861,17862,17864,17866,17868],{"class":2044,"line":148},[1115,17863,16489],{"class":2055},[1115,17865,1199],{"class":2059},[1115,17867,17803],{"class":2047},[1115,17869,2090],{"class":2059},[1115,17871,17872,17874,17876,17878],{"class":2044,"line":111},[1115,17873,16511],{"class":2055},[1115,17875,1199],{"class":2059},[1115,17877,17803],{"class":2047},[1115,17879,2090],{"class":2059},[1115,17881,17882,17884,17886,17888,17890,17892,17894,17896,17898],{"class":2044,"line":96},[1115,17883,16071],{"class":2055},[1115,17885,1199],{"class":2059},[1115,17887,17803],{"class":2047},[1115,17889,8993],{"class":2059},[1115,17891,9028],{"class":2051},[1115,17893,16549],{"class":2055},[1115,17895,1199],{"class":2059},[1115,17897,17803],{"class":2047},[1115,17899,2090],{"class":2059},[1115,17901,17902,17904,17906,17908],{"class":2044,"line":89},[1115,17903,17210],{"class":2055},[1115,17905,1199],{"class":2059},[1115,17907,17803],{"class":2047},[1115,17909,2090],{"class":2059},[1115,17911,17912,17915,17917,17919,17921,17923],{"class":2044,"line":82},[1115,17913,17914],{"class":2047},"f4",[1115,17916,2052],{"class":2051},[1115,17918,17387],{"class":2055},[1115,17920,1199],{"class":2059},[1115,17922,17803],{"class":2047},[1115,17924,2090],{"class":2059},[1115,17926,17927,17929,17931,17933],{"class":2044,"line":75},[1115,17928,17398],{"class":2055},[1115,17930,1199],{"class":2059},[1115,17932,17914],{"class":2047},[1115,17934,2090],{"class":2059},[1115,17936,17937,17939,17941,17943,17945,17947],{"class":2044,"line":5577},[1115,17938,17914],{"class":2055},[1115,17940,1199],{"class":2059},[1115,17942,17398],{"class":2055},[1115,17944,1199],{"class":2059},[1115,17946,17914],{"class":2047},[1115,17948,2546],{"class":2059},[2035,17950,17953],{"className":17951,"code":17952,"language":2169,"meta":2039},[2167],"[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",[1332,17954,17952],{"__ignoreMap":2039},[1110,17956,17957,17958,17981],{},"Průměrný odpad je 3,86 % se směrodatnou odchylkou 0,18 % a mediánem 3,85 %. Pravý panel obrázku výše ukazuje tvar ",[1115,17959,17961],{"className":17960},[1137],[1139,17962,17963],{"xmlns":1141},[1143,17964,17965,17979],{},[1146,17966,17967,17973,17975,17977],{},[1201,17968,17969,17971],{},[1149,17970,11091],{},[1149,17972,1816],{},[1193,17974,1199],{"stretchy":1198},[1149,17976,1168],{},[1193,17978,1228],{"stretchy":1198},[1153,17980,15542],{"encoding":1155},": hodnota 3,8 se v souboru opakuje třikrát, proto zde funkce skáče o 0,3 najednou, stejně jako hodnota 4,0.",[1377,17983,17985],{"id":17984},"třídění-datového-souboru-do-tříd","Třídění datového souboru do tříd",[1110,17987,17988,17989,17992,17993,18006,18007,18010],{},"Je-li rozsah datového souboru velký (řádově přes 30 až 50 pozorování), hodnoty se před dalším zpracováním ",[1130,17990,17991],{},"roztřídí",": variační rozpětí ",[1115,17994,17996],{"className":17995},[1137],[1139,17997,17998],{"xmlns":1141},[1143,17999,18000,18004],{},[1146,18001,18002],{},[1149,18003,1257],{},[1153,18005,1257],{"encoding":1155}," se rozdělí na určitý počet ",[1130,18008,18009],{},"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.",[1110,18012,18013],{},"Výsledkem je tabulka četností se sloupci:",[1124,18015,18016,18096,18117,18138],{},[1127,18017,18018,18036,18037,18050,18051,18095],{},[1115,18019,18021],{"className":18020},[1137],[1139,18022,18023],{"xmlns":1141},[1143,18024,18025,18033],{},[1146,18026,18027],{},[1201,18028,18029,18031],{},[1149,18030,1278],{},[1149,18032,6318],{},[1153,18034,18035],{"encoding":1155},"I_j"," — ",[1115,18038,18040],{"className":18039},[1137],[1139,18041,18042],{"xmlns":1141},[1143,18043,18044,18048],{},[1146,18045,18046],{},[1149,18047,6318],{},[1153,18049,6318],{"encoding":1155},"-tý interval (v této kapitole vždy zleva uzavřený a zprava otevřený, ",[1115,18052,18054],{"className":18053},[1137],[1139,18055,18056],{"xmlns":1141},[1143,18057,18058,18092],{},[1146,18059,18060,18066,18068,18070,18076,18078,18090],{},[1201,18061,18062,18064],{},[1149,18063,1278],{},[1149,18065,6318],{},[1193,18067,1281],{},[1193,18069,12796],{"stretchy":1198},[1201,18071,18072,18074],{},[1149,18073,8130],{},[1149,18075,6318],{},[1193,18077,1589],{"separator":1121},[1201,18079,18080,18082],{},[1149,18081,8130],{},[1146,18083,18084,18086,18088],{},[1149,18085,6318],{},[1193,18087,1924],{},[1230,18089,1525],{},[1193,18091,1228],{"stretchy":1198},[1153,18093,18094],{"encoding":1155},"I_j = \\langle c_j; c_{j+1})","),",[1127,18097,18098,18116],{},[1115,18099,18101],{"className":18100},[1137],[1139,18102,18103],{"xmlns":1141},[1143,18104,18105,18113],{},[1146,18106,18107],{},[1201,18108,18109,18111],{},[1149,18110,13295],{},[1149,18112,6318],{},[1153,18114,18115],{"encoding":1155},"Z_j"," — střed (reprezentant) intervalu,",[1127,18118,18119,18137],{},[1115,18120,18122],{"className":18121},[1137],[1139,18123,18124],{"xmlns":1141},[1143,18125,18126,18134],{},[1146,18127,18128],{},[1201,18129,18130,18132],{},[1149,18131,1582],{},[1149,18133,6318],{},[1153,18135,18136],{"encoding":1155},"f_j"," — četnost, počet hodnot v intervalu,",[1127,18139,18140,18170,18171,1405,18199,1236],{},[1115,18141,18143],{"className":18142},[1137],[1139,18144,18145],{"xmlns":1141},[1143,18146,18147,18167],{},[1146,18148,18149,18155,18157,18163,18165],{},[1201,18150,18151,18153],{},[1149,18152,1110],{},[1149,18154,6318],{},[1193,18156,1281],{},[1201,18158,18159,18161],{},[1149,18160,1582],{},[1149,18162,6318],{},[1149,18164,5731],{"mathvariant":1854},[1149,18166,1816],{},[1153,18168,18169],{"encoding":1155},"p_j = f_j\u002Fn"," — relativní četnost, přičemž ",[1115,18172,18174],{"className":18173},[1137],[1139,18175,18176],{"xmlns":1141},[1143,18177,18178,18196],{},[1146,18179,18180,18186,18192,18194],{},[1201,18181,18182,18184],{},[1193,18183,1195],{},[1149,18185,6318],{},[1201,18187,18188,18190],{},[1149,18189,1582],{},[1149,18191,6318],{},[1193,18193,1281],{},[1149,18195,1816],{},[1153,18197,18198],{"encoding":1155},"\\sum_j f_j = n",[1115,18200,18202],{"className":18201},[1137],[1139,18203,18204],{"xmlns":1141},[1143,18205,18206,18224],{},[1146,18207,18208,18214,18220,18222],{},[1201,18209,18210,18212],{},[1193,18211,1195],{},[1149,18213,6318],{},[1201,18215,18216,18218],{},[1149,18217,1110],{},[1149,18219,6318],{},[1193,18221,1281],{},[1230,18223,1525],{},[1153,18225,18226],{"encoding":1155},"\\sum_j p_j = 1",[1110,18228,18229,18230,18233,18234,18237,18238,18241,18242,18245,18246,4053,18249,18266,18267,18270,18271,4053,18274,6250,18291,18294],{},"V R se třídění provádí příkazem ",[1332,18231,18232],{},"hist()"," — buď necháme R zvolit třídy samo (",[1332,18235,18236],{},"hist(x)","), nebo zadáme hranice přímo (",[1332,18239,18240],{},"hist(x, br = seq(0, 550, by = 50))","). Uložením výsledku do proměnné (",[1332,18243,18244],{},"y \u003C- hist(...)",") získáme jednotlivé sloupce tabulky: ",[1332,18247,18248],{},"y$counts",[1115,18250,18252],{"className":18251},[1137],[1139,18253,18254],{"xmlns":1141},[1143,18255,18256,18264],{},[1146,18257,18258],{},[1201,18259,18260,18262],{},[1149,18261,1582],{},[1149,18263,6318],{},[1153,18265,18136],{"encoding":1155},"), ",[1332,18268,18269],{},"y$breaks"," (hranice tříd), ",[1332,18272,18273],{},"y$mids",[1115,18275,18277],{"className":18276},[1137],[1139,18278,18279],{"xmlns":1141},[1143,18280,18281,18289],{},[1146,18282,18283],{},[1201,18284,18285,18287],{},[1149,18286,13295],{},[1149,18288,6318],{},[1153,18290,18115],{"encoding":1155},[1332,18292,18293],{},"y$density"," (relativní četnosti na škále hustoty).",[1110,18296,18297,18298,18315,18316,18318,18319,18355,18356,18359,18360,1236],{},"Interval ",[1115,18299,18301],{"className":18300},[1137],[1139,18302,18303],{"xmlns":1141},[1143,18304,18305,18313],{},[1146,18306,18307],{},[1201,18308,18309,18311],{},[1149,18310,1278],{},[1149,18312,6318],{},[1153,18314,18035],{"encoding":1155}," je ve výchozím nastavení ",[1332,18317,18232],{}," zleva otevřený a zprava uzavřený, ",[1115,18320,18322],{"className":18321},[1137],[1139,18323,18324],{"xmlns":1141},[1143,18325,18326,18352],{},[1146,18327,18328,18330,18336,18338,18350],{},[1193,18329,1199],{"stretchy":1198},[1201,18331,18332,18334],{},[1149,18333,8130],{},[1149,18335,6318],{},[1193,18337,1589],{"separator":1121},[1201,18339,18340,18342],{},[1149,18341,8130],{},[1146,18343,18344,18346,18348],{},[1149,18345,6318],{},[1193,18347,1924],{},[1230,18349,1525],{},[1193,18351,11815],{"stretchy":1198},[1153,18353,18354],{"encoding":1155},"(c_j; c_{j+1}\\rangle"," — opačně, než jak třídy zapisujeme v této kapitole. Parametr ",[1332,18357,18358],{},"right = FALSE"," třídy obrátí na ",[1115,18361,18363],{"className":18362},[1137],[1139,18364,18365],{"xmlns":1141},[1143,18366,18367,18393],{},[1146,18368,18369,18371,18377,18379,18391],{},[1193,18370,12796],{"stretchy":1198},[1201,18372,18373,18375],{},[1149,18374,8130],{},[1149,18376,6318],{},[1193,18378,1589],{"separator":1121},[1201,18380,18381,18383],{},[1149,18382,8130],{},[1146,18384,18385,18387,18389],{},[1149,18386,6318],{},[1193,18388,1924],{},[1230,18390,1525],{},[1193,18392,1228],{"stretchy":1198},[1153,18394,18395],{"encoding":1155},"\\langle c_j; c_{j+1})",[1110,18397,18398],{},[1864,18399],{"alt":18400,"className":18401,"src":18402},"mask-ps-histogram-trideni",[1387,1868],"\u002Fwiki-assets\u002Fmask-ps-histogram-trideni.png",[1103,18404,18406,18413],{"className":18405,"dataCallout":2932},[1106,2931],[1110,18407,18409,18412],{"className":18408},[1113],[1115,18410],{"className":18411,"ariaHidden":1121},[1118,2939,1120],"Příklad: Třídění datového souboru",[1110,18414,18415],{},"Byly provedeny zkoušky životnosti nového výrobku. Datový soubor obsahuje 68 hodnot doby do poruchy (v minutách). Určete odhady charakteristik a zákona rozdělení.",[2035,18417,18419],{"className":2037,"code":18418,"language":71,"meta":2039,"style":2039},"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",[1332,18420,18421,18478,18529,18579,18630,18680,18728,18768,18778,18798,18862,18871,18901],{"__ignoreMap":2039},[1115,18422,18423,18426,18428,18430,18432,18435,18437,18440,18442,18445,18447,18450,18452,18454,18456,18458,18460,18462,18464,18467,18469,18471,18473,18476],{"class":2044,"line":10},[1115,18424,18425],{"class":2047},"x9",[1115,18427,2052],{"class":2051},[1115,18429,2056],{"class":2055},[1115,18431,1199],{"class":2059},[1115,18433,18434],{"class":2062},"101",[1115,18436,1503],{"class":2051},[1115,18438,18439],{"class":2062}," 338",[1115,18441,1503],{"class":2051},[1115,18443,18444],{"class":2062}," 150",[1115,18446,1503],{"class":2051},[1115,18448,18449],{"class":2062}," 47",[1115,18451,1503],{"class":2051},[1115,18453,13845],{"class":2062},[1115,18455,1503],{"class":2051},[1115,18457,2067],{"class":2062},[1115,18459,1503],{"class":2051},[1115,18461,8144],{"class":2062},[1115,18463,1503],{"class":2051},[1115,18465,18466],{"class":2062}," 392",[1115,18468,1503],{"class":2051},[1115,18470,2082],{"class":2062},[1115,18472,1503],{"class":2051},[1115,18474,18475],{"class":2062}," 73",[1115,18477,8147],{"class":2051},[1115,18479,18480,18483,18485,18488,18490,18493,18495,18498,18500,18502,18504,18507,18509,18512,18514,18517,18519,18522,18524,18527],{"class":2044,"line":27},[1115,18481,18482],{"class":2062}," 367",[1115,18484,1503],{"class":2051},[1115,18486,18487],{"class":2062}," 54",[1115,18489,1503],{"class":2051},[1115,18491,18492],{"class":2062}," 114",[1115,18494,1503],{"class":2051},[1115,18496,18497],{"class":2062}," 213",[1115,18499,1503],{"class":2051},[1115,18501,8162],{"class":2062},[1115,18503,1503],{"class":2051},[1115,18505,18506],{"class":2062}," 341",[1115,18508,1503],{"class":2051},[1115,18510,18511],{"class":2062}," 313",[1115,18513,1503],{"class":2051},[1115,18515,18516],{"class":2062}," 112",[1115,18518,1503],{"class":2051},[1115,18520,18521],{"class":2062}," 343",[1115,18523,1503],{"class":2051},[1115,18525,18526],{"class":2062}," 151",[1115,18528,8147],{"class":2051},[1115,18530,18531,18534,18536,18539,18541,18544,18546,18549,18551,18554,18556,18558,18560,18563,18565,18567,18569,18572,18574,18577],{"class":2044,"line":148},[1115,18532,18533],{"class":2062}," 9",[1115,18535,1503],{"class":2051},[1115,18537,18538],{"class":2062}," 160",[1115,18540,1503],{"class":2051},[1115,18542,18543],{"class":2062}," 18",[1115,18545,1503],{"class":2051},[1115,18547,18548],{"class":2062}," 113",[1115,18550,1503],{"class":2051},[1115,18552,18553],{"class":2062}," 77",[1115,18555,1503],{"class":2051},[1115,18557,8162],{"class":2062},[1115,18559,1503],{"class":2051},[1115,18561,18562],{"class":2062}," 159",[1115,18564,1503],{"class":2051},[1115,18566,8144],{"class":2062},[1115,18568,1503],{"class":2051},[1115,18570,18571],{"class":2062}," 119",[1115,18573,1503],{"class":2051},[1115,18575,18576],{"class":2062}," 130",[1115,18578,8147],{"class":2051},[1115,18580,18581,18584,18586,18589,18591,18594,18596,18598,18600,18603,18605,18608,18610,18613,18615,18618,18620,18623,18625,18628],{"class":2044,"line":111},[1115,18582,18583],{"class":2062}," 140",[1115,18585,1503],{"class":2051},[1115,18587,18588],{"class":2062}," 161",[1115,18590,1503],{"class":2051},[1115,18592,18593],{"class":2062}," 379",[1115,18595,1503],{"class":2051},[1115,18597,18487],{"class":2062},[1115,18599,1503],{"class":2051},[1115,18601,18602],{"class":2062}," 373",[1115,18604,1503],{"class":2051},[1115,18606,18607],{"class":2062}," 168",[1115,18609,1503],{"class":2051},[1115,18611,18612],{"class":2062}," 365",[1115,18614,1503],{"class":2051},[1115,18616,18617],{"class":2062}," 110",[1115,18619,1503],{"class":2051},[1115,18621,18622],{"class":2062}," 145",[1115,18624,1503],{"class":2051},[1115,18626,18627],{"class":2062}," 88",[1115,18629,8147],{"class":2051},[1115,18631,18632,18635,18637,18640,18642,18645,18647,18650,18652,18655,18657,18659,18661,18664,18666,18668,18670,18673,18675,18678],{"class":2044,"line":96},[1115,18633,18634],{"class":2062}," 74",[1115,18636,1503],{"class":2051},[1115,18638,18639],{"class":2062}," 46",[1115,18641,1503],{"class":2051},[1115,18643,18644],{"class":2062}," 246",[1115,18646,1503],{"class":2051},[1115,18648,18649],{"class":2062}," 259",[1115,18651,1503],{"class":2051},[1115,18653,18654],{"class":2062}," 19",[1115,18656,1503],{"class":2051},[1115,18658,18571],{"class":2062},[1115,18660,1503],{"class":2051},[1115,18662,18663],{"class":2062}," 48",[1115,18665,1503],{"class":2051},[1115,18667,2072],{"class":2062},[1115,18669,1503],{"class":2051},[1115,18671,18672],{"class":2062}," 163",[1115,18674,1503],{"class":2051},[1115,18676,18677],{"class":2062}," 179",[1115,18679,8147],{"class":2051},[1115,18681,18682,18685,18687,18689,18691,18694,18696,18699,18701,18704,18706,18708,18710,18712,18714,18716,18718,18721,18723,18726],{"class":2044,"line":89},[1115,18683,18684],{"class":2062}," 194",[1115,18686,1503],{"class":2051},[1115,18688,8544],{"class":2062},[1115,18690,1503],{"class":2051},[1115,18692,18693],{"class":2062}," 49",[1115,18695,1503],{"class":2051},[1115,18697,18698],{"class":2062}," 501",[1115,18700,1503],{"class":2051},[1115,18702,18703],{"class":2062}," 193",[1115,18705,1503],{"class":2051},[1115,18707,18654],{"class":2062},[1115,18709,1503],{"class":2051},[1115,18711,2082],{"class":2062},[1115,18713,1503],{"class":2051},[1115,18715,2067],{"class":2062},[1115,18717,1503],{"class":2051},[1115,18719,18720],{"class":2062}," 221",[1115,18722,1503],{"class":2051},[1115,18724,18725],{"class":2062}," 300",[1115,18727,8147],{"class":2051},[1115,18729,18730,18733,18735,18737,18739,18742,18744,18747,18749,18752,18754,18757,18759,18761,18763,18766],{"class":2044,"line":82},[1115,18731,18732],{"class":2062}," 88",[1115,18734,1503],{"class":2051},[1115,18736,8139],{"class":2062},[1115,18738,1503],{"class":2051},[1115,18740,18741],{"class":2062}," 428",[1115,18743,1503],{"class":2051},[1115,18745,18746],{"class":2062}," 249",[1115,18748,1503],{"class":2051},[1115,18750,18751],{"class":2062}," 25",[1115,18753,1503],{"class":2051},[1115,18755,18756],{"class":2062}," 209",[1115,18758,1503],{"class":2051},[1115,18760,18487],{"class":2062},[1115,18762,1503],{"class":2051},[1115,18764,18765],{"class":2062}," 91",[1115,18767,2090],{"class":2059},[1115,18769,18770,18772,18774,18776],{"class":2044,"line":75},[1115,18771,16478],{"class":2055},[1115,18773,1199],{"class":2059},[1115,18775,18425],{"class":2047},[1115,18777,2090],{"class":2059},[1115,18779,18780,18782,18784,18786,18788,18790,18792,18794,18796],{"class":2044,"line":5577},[1115,18781,16071],{"class":2055},[1115,18783,1199],{"class":2059},[1115,18785,18425],{"class":2047},[1115,18787,8993],{"class":2059},[1115,18789,9028],{"class":2051},[1115,18791,16549],{"class":2055},[1115,18793,1199],{"class":2059},[1115,18795,18425],{"class":2047},[1115,18797,2090],{"class":2059},[1115,18799,18800,18803,18805,18808,18810,18812,18814,18817,18819,18822,18824,18826,18828,18831,18833,18836,18838,18840,18842,18844,18847,18849,18851,18853,18856,18858,18860],{"class":2044,"line":72},[1115,18801,18802],{"class":2047},"y9",[1115,18804,2052],{"class":2051},[1115,18806,18807],{"class":2055}," hist",[1115,18809,1199],{"class":2059},[1115,18811,18425],{"class":2047},[1115,18813,1503],{"class":2051},[1115,18815,18816],{"class":2047}," br",[1115,18818,2510],{"class":2051},[1115,18820,18821],{"class":2055}," seq",[1115,18823,1199],{"class":2059},[1115,18825,1597],{"class":2062},[1115,18827,1503],{"class":2051},[1115,18829,18830],{"class":2062}," 550",[1115,18832,1503],{"class":2051},[1115,18834,18835],{"class":2047}," by",[1115,18837,2510],{"class":2051},[1115,18839,10633],{"class":2062},[1115,18841,1228],{"class":2059},[1115,18843,1503],{"class":2051},[1115,18845,18846],{"class":2047}," right",[1115,18848,2510],{"class":2051},[1115,18850,10726],{"class":2062},[1115,18852,1503],{"class":2051},[1115,18854,18855],{"class":2047}," plot",[1115,18857,2510],{"class":2051},[1115,18859,10726],{"class":2062},[1115,18861,2090],{"class":2059},[1115,18863,18864,18866,18868],{"class":2044,"line":25},[1115,18865,18802],{"class":2047},[1115,18867,8317],{"class":2051},[1115,18869,18870],{"class":2047},"counts\n",[1115,18872,18873,18875,18877,18879,18881,18884,18886,18889,18891,18893,18895,18897,18899],{"class":2044,"line":65},[1115,18874,14346],{"class":2055},[1115,18876,1199],{"class":2059},[1115,18878,18802],{"class":2047},[1115,18880,8317],{"class":2051},[1115,18882,18883],{"class":2047},"counts",[1115,18885,4211],{"class":2051},[1115,18887,18888],{"class":2055}," length",[1115,18890,1199],{"class":2059},[1115,18892,18425],{"class":2047},[1115,18894,1228],{"class":2059},[1115,18896,1503],{"class":2051},[1115,18898,2072],{"class":2062},[1115,18900,2090],{"class":2059},[1115,18902,18903,18905,18907,18909,18911,18913,18915,18917],{"class":2044,"line":63},[1115,18904,16489],{"class":2055},[1115,18906,1199],{"class":2059},[1115,18908,18425],{"class":2047},[1115,18910,16528],{"class":2059},[1115,18912,16511],{"class":2055},[1115,18914,1199],{"class":2059},[1115,18916,18425],{"class":2047},[1115,18918,2090],{"class":2059},[2035,18920,18923],{"className":18921,"code":18922,"language":2169,"meta":2039},[2167],"[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",[1332,18924,18922],{"__ignoreMap":2039},[1110,18926,18927,18928,18956],{},"Variační rozpětí je ",[1115,18929,18931],{"className":18930},[1137],[1139,18932,18933],{"xmlns":1141},[1143,18934,18935,18953],{},[1146,18936,18937,18939,18941,18944,18946,18948,18950],{},[1149,18938,1257],{},[1193,18940,1281],{},[1230,18942,18943],{},"501",[1193,18945,1210],{},[1230,18947,1232],{},[1193,18949,1281],{},[1230,18951,18952],{},"499",[1153,18954,18955],{"encoding":1155},"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:",[6528,18958,18959,19055],{},[6531,18960,18961],{},[6534,18962,18963,18978,18997,19016,19035],{},[6537,18964,18965],{},[1115,18966,18968],{"className":18967},[1137],[1139,18969,18970],{"xmlns":1141},[1143,18971,18972,18976],{},[1146,18973,18974],{},[1149,18975,6318],{},[1153,18977,6318],{"encoding":1155},[6537,18979,18980],{},[1115,18981,18983],{"className":18982},[1137],[1139,18984,18985],{"xmlns":1141},[1143,18986,18987,18995],{},[1146,18988,18989],{},[1201,18990,18991,18993],{},[1149,18992,1278],{},[1149,18994,6318],{},[1153,18996,18035],{"encoding":1155},[6537,18998,18999],{},[1115,19000,19002],{"className":19001},[1137],[1139,19003,19004],{"xmlns":1141},[1143,19005,19006,19014],{},[1146,19007,19008],{},[1201,19009,19010,19012],{},[1149,19011,13295],{},[1149,19013,6318],{},[1153,19015,18115],{"encoding":1155},[6537,19017,19018],{},[1115,19019,19021],{"className":19020},[1137],[1139,19022,19023],{"xmlns":1141},[1143,19024,19025,19033],{},[1146,19026,19027],{},[1201,19028,19029,19031],{},[1149,19030,1582],{},[1149,19032,6318],{},[1153,19034,18136],{"encoding":1155},[6537,19036,19037],{},[1115,19038,19040],{"className":19039},[1137],[1139,19041,19042],{"xmlns":1141},[1143,19043,19044,19052],{},[1146,19045,19046],{},[1201,19047,19048,19050],{},[1149,19049,1110],{},[1149,19051,6318],{},[1153,19053,19054],{"encoding":1155},"p_j",[6645,19056,19057,19072,19087,19102,19115,19130,19145,19159,19174,19188,19203],{},[6534,19058,19059,19061,19064,19066,19069],{},[6650,19060,1525],{},[6650,19062,19063],{},"⟨0; 50)",[6650,19065,8457],{},[6650,19067,19068],{},"19",[6650,19070,19071],{},"0,279",[6534,19073,19074,19076,19079,19082,19084],{},[6650,19075,1232],{},[6650,19077,19078],{},"⟨50; 100)",[6650,19080,19081],{},"75",[6650,19083,6687],{},[6650,19085,19086],{},"0,162",[6534,19088,19089,19091,19094,19097,19099],{},[6650,19090,8010],{},[6650,19092,19093],{},"⟨100; 150)",[6650,19095,19096],{},"125",[6650,19098,5389],{},[6650,19100,19101],{},"0,147",[6534,19103,19104,19106,19109,19111,19113],{},[6650,19105,7961],{},[6650,19107,19108],{},"⟨150; 200)",[6650,19110,11851],{},[6650,19112,5389],{},[6650,19114,19101],{},[6534,19116,19117,19119,19122,19125,19127],{},[6650,19118,5351],{},[6650,19120,19121],{},"⟨200; 250)",[6650,19123,19124],{},"225",[6650,19126,5351],{},[6650,19128,19129],{},"0,074",[6534,19131,19132,19134,19137,19140,19142],{},[6650,19133,8365],{},[6650,19135,19136],{},"⟨250; 300)",[6650,19138,19139],{},"275",[6650,19141,1525],{},[6650,19143,19144],{},"0,015",[6534,19146,19147,19149,19152,19155,19157],{},[6650,19148,2538],{},[6650,19150,19151],{},"⟨300; 350)",[6650,19153,19154],{},"325",[6650,19156,5351],{},[6650,19158,19129],{},[6534,19160,19161,19164,19167,19170,19172],{},[6650,19162,19163],{},"8",[6650,19165,19166],{},"⟨350; 400)",[6650,19168,19169],{},"375",[6650,19171,5351],{},[6650,19173,19129],{},[6534,19175,19176,19178,19181,19184,19186],{},[6650,19177,8013],{},[6650,19179,19180],{},"⟨400; 450)",[6650,19182,19183],{},"425",[6650,19185,1525],{},[6650,19187,19144],{},[6534,19189,19190,19192,19195,19198,19200],{},[6650,19191,5389],{},[6650,19193,19194],{},"⟨450; 500)",[6650,19196,19197],{},"475",[6650,19199,1597],{},[6650,19201,19202],{},"0,000",[6534,19204,19205,19207,19210,19213,19215],{},[6650,19206,6687],{},[6650,19208,19209],{},"⟨500; ∞)",[6650,19211,19212],{},"525",[6650,19214,1525],{},[6650,19216,19144],{},[1110,19218,19219,19220,19237,19238,19255,19256,1348,19279,1348,19307,19326,19327,1348,19350,19369],{},"Asi 27,9 % výrobků vydrželo méně než 50 minut, jen asi 1,5 % mezi 250 a 300 minutami. Charakteristiky spočtené ze středů tříd ",[1115,19221,19223],{"className":19222},[1137],[1139,19224,19225],{"xmlns":1141},[1143,19226,19227,19235],{},[1146,19228,19229],{},[1201,19230,19231,19233],{},[1149,19232,13295],{},[1149,19234,6318],{},[1153,19236,18115],{"encoding":1155}," (vážený průměr a rozptyl se střední hodnotou nahrazenou ",[1115,19239,19241],{"className":19240},[1137],[1139,19242,19243],{"xmlns":1141},[1143,19244,19245,19253],{},[1146,19246,19247],{},[1201,19248,19249,19251],{},[1149,19250,13295],{},[1149,19252,6318],{},[1153,19254,18115],{"encoding":1155},") vycházejí ",[1115,19257,19259],{"className":19258},[1137],[1139,19260,19261],{"xmlns":1141},[1143,19262,19263,19276],{},[1146,19264,19265,19271,19273],{},[1214,19266,19267,19269],{"accent":1121},[1149,19268,1168],{},[1193,19270,15814],{},[1193,19272,4165],{},[1230,19274,19275],{},"149,26",[1153,19277,19278],{"encoding":1155},"\\bar{x} \\approx 149{,}26",[1115,19280,19282],{"className":19281},[1137],[1139,19283,19284],{"xmlns":1141},[1143,19285,19286,19304],{},[1146,19287,19288,19294,19296,19299,19301],{},[1224,19289,19290,19292],{},[1149,19291,4542],{},[1230,19293,1232],{},[1193,19295,4165],{},[1230,19297,19298],{},"15",[2201,19300,2203],{},[1230,19302,19303],{},"484,5",[1153,19305,19306],{"encoding":1155},"s^2 \\approx 15\\,484{,}5",[1115,19308,19310],{"className":19309},[1137],[1139,19311,19312],{"xmlns":1141},[1143,19313,19314,19323],{},[1146,19315,19316,19318,19320],{},[1149,19317,4542],{},[1193,19319,4165],{},[1230,19321,19322],{},"124,44",[1153,19324,19325],{"encoding":1155},"s \\approx 124{,}44"," — blízko hodnotám ",[1115,19328,19330],{"className":19329},[1137],[1139,19331,19332],{"xmlns":1141},[1143,19333,19334,19347],{},[1146,19335,19336,19342,19344],{},[1214,19337,19338,19340],{"accent":1121},[1149,19339,1168],{},[1193,19341,15814],{},[1193,19343,1281],{},[1230,19345,19346],{},"145,44",[1153,19348,19349],{"encoding":1155},"\\bar{x}=145{,}44",[1115,19351,19353],{"className":19352},[1137],[1139,19354,19355],{"xmlns":1141},[1143,19356,19357,19366],{},[1146,19358,19359,19361,19363],{},[1149,19360,4542],{},[1193,19362,1281],{},[1230,19364,19365],{},"126,13",[1153,19367,19368],{"encoding":1155},"s=126{,}13"," spočteným přímo z nerozdělených dat; malý rozdíl vzniká tím, že třídění nahrazuje skutečné hodnoty středy tříd.",[1110,19371,19372,19373,19376,19377,19413,19414,19432,19433,19447,19448,19474,19475,19477,19478,9256],{},"Tvar histogramu — vysoká četnost u krátkých dob, rychlý pokles — odpovídá ",[1130,19374,19375],{},"exponenciálnímu rozdělení",", které se pro dobu do poruchy používá nejčastěji. Jeho hustota je ",[1115,19378,19380],{"className":19379},[1137],[1139,19381,19382],{"xmlns":1141},[1143,19383,19384,19410],{},[1146,19385,19386,19388,19390,19392,19394,19396,19398],{},[1149,19387,1582],{},[1193,19389,1199],{"stretchy":1198},[1149,19391,1168],{},[1193,19393,1228],{"stretchy":1198},[1193,19395,1281],{},[1149,19397,14079],{},[1224,19399,19400,19402],{},[1149,19401,1754],{},[1146,19403,19404,19406,19408],{},[1193,19405,1210],{},[1149,19407,14079],{},[1149,19409,1168],{},[1153,19411,19412],{"encoding":1155},"f(x) = \\lambda e^{-\\lambda x}"," pro ",[1115,19415,19417],{"className":19416},[1137],[1139,19418,19419],{"xmlns":1141},[1143,19420,19421,19429],{},[1146,19422,19423,19425,19427],{},[1149,19424,1168],{},[1193,19426,7775],{},[1230,19428,1597],{},[1153,19430,19431],{"encoding":1155},"x \\ge 0",", s parametrem ",[1115,19434,19436],{"className":19435},[1137],[1139,19437,19438],{"xmlns":1141},[1143,19439,19440,19444],{},[1146,19441,19442],{},[1149,19443,14079],{},[1153,19445,19446],{"encoding":1155},"\\lambda"," odhadnutým jako ",[1115,19449,19451],{"className":19450},[1137],[1139,19452,19453],{"xmlns":1141},[1143,19454,19455,19471],{},[1146,19456,19457,19459,19461,19463,19465],{},[1149,19458,14079],{},[1193,19460,1281],{},[1230,19462,1525],{},[1149,19464,5731],{"mathvariant":1854},[1214,19466,19467,19469],{"accent":1121},[1149,19468,1168],{},[1193,19470,15814],{},[1153,19472,19473],{"encoding":1155},"\\lambda = 1\u002F\\bar{x}"," (v R je ",[1332,19476,14246],{}," parametrem ",[1332,19479,19480],{},"dexp()",[2035,19482,19484],{"className":2037,"code":19483,"language":71,"meta":2039,"style":2039},"rate9 \u003C- 1 \u002F mean(x9)\nrate9\n",[1332,19485,19486,19505],{"__ignoreMap":2039},[1115,19487,19488,19491,19493,19495,19497,19499,19501,19503],{"class":2044,"line":10},[1115,19489,19490],{"class":2047},"rate9",[1115,19492,2052],{"class":2051},[1115,19494,9031],{"class":2062},[1115,19496,4211],{"class":2051},[1115,19498,13600],{"class":2055},[1115,19500,1199],{"class":2059},[1115,19502,18425],{"class":2047},[1115,19504,2090],{"class":2059},[1115,19506,19507],{"class":2044,"line":27},[1115,19508,19509],{"class":2047},"rate9\n",[2035,19511,19514],{"className":19512,"code":19513,"language":2169,"meta":2039},[2167],"[1] 0.006875632\n",[1332,19515,19513],{"__ignoreMap":2039},[1110,19517,19518],{},[1864,19519],{"alt":19520,"className":19521,"src":19522},"mask-ps-hustota-fit",[1387,1868],"\u002Fwiki-assets\u002Fmask-ps-hustota-fit.png",[1110,19524,19525,19526,1236],{},"Proložená křivka dobře sleduje tvar sloupců. Zda data odpovídají exponenciálnímu rozdělení formálně, posuzuje test dobré shody popsaný v ",[1384,19527,5890],{"className":19528,"dataFsResolvedFilePath":5302,"href":5303},[1387],[1103,19530,19532,19539],{"className":19531,"dataCallout":2932},[1106,2931],[1110,19533,19535,19538],{"className":19534},[1113],[1115,19536],{"className":19537,"ariaHidden":1121},[1118,2939,1120],"Příklad: Doba života výrobku",[1110,19540,19541],{},"Sledováním doby života výrobku bylo naměřeno 50 hodnot (v minutách). Určete empirické charakteristiky, roztřiďte datový soubor a nakreslete histogram četností.",[2035,19543,19545],{"className":2037,"code":19544,"language":71,"meta":2039,"style":2039},"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",[1332,19546,19547,19607,19658,19709,19760,19812,19822,19848,19868,19926,19935,19943],{"__ignoreMap":2039},[1115,19548,19549,19552,19554,19556,19558,19561,19563,19566,19568,19571,19573,19576,19578,19581,19583,19586,19588,19591,19593,19596,19598,19601,19603,19605],{"class":2044,"line":10},[1115,19550,19551],{"class":2047},"x5",[1115,19553,2052],{"class":2051},[1115,19555,2056],{"class":2055},[1115,19557,1199],{"class":2059},[1115,19559,19560],{"class":2062},"63",[1115,19562,1503],{"class":2051},[1115,19564,19565],{"class":2062}," 156",[1115,19567,1503],{"class":2051},[1115,19569,19570],{"class":2062}," 184",[1115,19572,1503],{"class":2051},[1115,19574,19575],{"class":2062}," 786",[1115,19577,1503],{"class":2051},[1115,19579,19580],{"class":2062}," 822",[1115,19582,1503],{"class":2051},[1115,19584,19585],{"class":2062}," 278",[1115,19587,1503],{"class":2051},[1115,19589,19590],{"class":2062}," 15",[1115,19592,1503],{"class":2051},[1115,19594,19595],{"class":2062}," 561",[1115,19597,1503],{"class":2051},[1115,19599,19600],{"class":2062}," 229",[1115,19602,1503],{"class":2051},[1115,19604,2543],{"class":2062},[1115,19606,8147],{"class":2051},[1115,19608,19609,19612,19614,19617,19619,19621,19623,19626,19628,19631,19633,19636,19638,19641,19643,19646,19648,19651,19653,19656],{"class":2044,"line":27},[1115,19610,19611],{"class":2062}," 4",[1115,19613,1503],{"class":2051},[1115,19615,19616],{"class":2062}," 35",[1115,19618,1503],{"class":2051},[1115,19620,18475],{"class":2062},[1115,19622,1503],{"class":2051},[1115,19624,19625],{"class":2062}," 203",[1115,19627,1503],{"class":2051},[1115,19629,19630],{"class":2062}," 178",[1115,19632,1503],{"class":2051},[1115,19634,19635],{"class":2062}," 323",[1115,19637,1503],{"class":2051},[1115,19639,19640],{"class":2062}," 275",[1115,19642,1503],{"class":2051},[1115,19644,19645],{"class":2062}," 176",[1115,19647,1503],{"class":2051},[1115,19649,19650],{"class":2062}," 427",[1115,19652,1503],{"class":2051},[1115,19654,19655],{"class":2062}," 196",[1115,19657,8147],{"class":2051},[1115,19659,19660,19663,19665,19668,19670,19673,19675,19678,19680,19683,19685,19688,19690,19693,19695,19697,19699,19702,19704,19707],{"class":2044,"line":148},[1115,19661,19662],{"class":2062}," 415",[1115,19664,1503],{"class":2051},[1115,19666,19667],{"class":2062}," 140",[1115,19669,1503],{"class":2051},[1115,19671,19672],{"class":2062}," 17",[1115,19674,1503],{"class":2051},[1115,19676,19677],{"class":2062}," 293",[1115,19679,1503],{"class":2051},[1115,19681,19682],{"class":2062}," 991",[1115,19684,1503],{"class":2051},[1115,19686,19687],{"class":2062}," 100",[1115,19689,1503],{"class":2051},[1115,19691,19692],{"class":2062}," 189",[1115,19694,1503],{"class":2051},[1115,19696,19645],{"class":2062},[1115,19698,1503],{"class":2051},[1115,19700,19701],{"class":2062}," 672",[1115,19703,1503],{"class":2051},[1115,19705,19706],{"class":2062}," 134",[1115,19708,8147],{"class":2051},[1115,19710,19711,19714,19716,19719,19721,19724,19726,19729,19731,19733,19735,19738,19740,19743,19745,19748,19750,19753,19755,19758],{"class":2044,"line":111},[1115,19712,19713],{"class":2062}," 529",[1115,19715,1503],{"class":2051},[1115,19717,19718],{"class":2062}," 310",[1115,19720,1503],{"class":2051},[1115,19722,19723],{"class":2062}," 22",[1115,19725,1503],{"class":2051},[1115,19727,19728],{"class":2062}," 69",[1115,19730,1503],{"class":2051},[1115,19732,18576],{"class":2062},[1115,19734,1503],{"class":2051},[1115,19736,19737],{"class":2062}," 272",[1115,19739,1503],{"class":2051},[1115,19741,19742],{"class":2062}," 117",[1115,19744,1503],{"class":2051},[1115,19746,19747],{"class":2062}," 169",[1115,19749,1503],{"class":2051},[1115,19751,19752],{"class":2062}," 466",[1115,19754,1503],{"class":2051},[1115,19756,19757],{"class":2062}," 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23",[1115,19811,2090],{"class":2059},[1115,19813,19814,19816,19818,19820],{"class":2044,"line":89},[1115,19815,16478],{"class":2055},[1115,19817,1199],{"class":2059},[1115,19819,19551],{"class":2047},[1115,19821,2090],{"class":2059},[1115,19823,19824,19826,19828,19830,19832,19834,19836,19838,19840,19842,19844,19846],{"class":2044,"line":82},[1115,19825,16489],{"class":2055},[1115,19827,1199],{"class":2059},[1115,19829,19551],{"class":2047},[1115,19831,16528],{"class":2059},[1115,19833,16511],{"class":2055},[1115,19835,1199],{"class":2059},[1115,19837,19551],{"class":2047},[1115,19839,16528],{"class":2059},[1115,19841,17210],{"class":2055},[1115,19843,1199],{"class":2059},[1115,19845,19551],{"class":2047},[1115,19847,2090],{"class":2059},[1115,19849,19850,19852,19854,19856,19858,19860,19862,19864,19866],{"class":2044,"line":75},[1115,19851,16071],{"class":2055},[1115,19853,1199],{"class":2059},[1115,19855,19551],{"class":2047},[1115,19857,8993],{"class":2059},[1115,19859,9028],{"class":2051},[1115,19861,16549],{"class":2055},[1115,19863,1199],{"class":2059},[1115,19865,19551],{"class":2047},[1115,19867,2090],{"class":2059},[1115,19869,19870,19873,19875,19877,19879,19881,19883,19885,19887,19889,19891,19893,19895,19898,19900,19902,19904,19906,19908,19910,19912,19914,19916,19918,19920,19922,19924],{"class":2044,"line":5577},[1115,19871,19872],{"class":2047},"y5",[1115,19874,2052],{"class":2051},[1115,19876,18807],{"class":2055},[1115,19878,1199],{"class":2059},[1115,19880,19551],{"class":2047},[1115,19882,1503],{"class":2051},[1115,19884,18816],{"class":2047},[1115,19886,2510],{"class":2051},[1115,19888,18821],{"class":2055},[1115,19890,1199],{"class":2059},[1115,19892,1597],{"class":2062},[1115,19894,1503],{"class":2051},[1115,19896,19897],{"class":2062}," 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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",[1332,19976,19974],{"__ignoreMap":2039},[1110,19978,19979],{},"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.",[1377,19981,5681],{"id":5680},[1124,19983,19984,20002,20103,20171],{},[1127,19985,19986,1243,19989,19992,19993,19996,19997,19999,20000,1236],{},[1130,19987,19988],{},"Výchozí typ kvantilu v R.",[1332,19990,19991],{},"quantile()"," bez argumentu ",[1332,19994,19995],{},"type"," používá jiný výpočetní vzorec (",[1332,19998,16641],{},") než ruční postup v této kapitole — u některých souborů se hodnoty liší. Pro shodu s ručním výpočtem zadávejte ",[1332,20001,16637],{},[1127,20003,20004,20009,20010,20012,20013,20048,20049,20084,20085,20102],{},[1130,20005,20006,20007,1236],{},"Výchozí ohraničení tříd v ",[1332,20008,18232],{}," Bez ",[1332,20011,18358],{}," jsou třídy zprava uzavřené, ",[1115,20014,20016],{"className":20015},[1137],[1139,20017,20018],{"xmlns":1141},[1143,20019,20020,20046],{},[1146,20021,20022,20024,20030,20032,20044],{},[1193,20023,1199],{"stretchy":1198},[1201,20025,20026,20028],{},[1149,20027,8130],{},[1149,20029,6318],{},[1193,20031,1589],{"separator":1121},[1201,20033,20034,20036],{},[1149,20035,8130],{},[1146,20037,20038,20040,20042],{},[1149,20039,6318],{},[1193,20041,1924],{},[1230,20043,1525],{},[1193,20045,11815],{"stretchy":1198},[1153,20047,18354],{"encoding":1155}," — opačně než konvence ",[1115,20050,20052],{"className":20051},[1137],[1139,20053,20054],{"xmlns":1141},[1143,20055,20056,20082],{},[1146,20057,20058,20060,20066,20068,20080],{},[1193,20059,12796],{"stretchy":1198},[1201,20061,20062,20064],{},[1149,20063,8130],{},[1149,20065,6318],{},[1193,20067,1589],{"separator":1121},[1201,20069,20070,20072],{},[1149,20071,8130],{},[1146,20073,20074,20076,20078],{},[1149,20075,6318],{},[1193,20077,1924],{},[1230,20079,1525],{},[1193,20081,1228],{"stretchy":1198},[1153,20083,18395],{"encoding":1155}," použitá v tabulkách výše. Hodnota ležící přesně na hranici pak spadne do jiné třídy a četnosti ",[1115,20086,20088],{"className":20087},[1137],[1139,20089,20090],{"xmlns":1141},[1143,20091,20092,20100],{},[1146,20093,20094],{},[1201,20095,20096,20098],{},[1149,20097,1582],{},[1149,20099,6318],{},[1153,20101,18136],{"encoding":1155}," vyjdou jinak.",[1127,20104,20105,1243,20108,20126,20127,20140,20141,13417,20154,1236],{},[1130,20106,20107],{},"Rozptyl vs. směrodatná odchylka.",[1115,20109,20111],{"className":20110},[1137],[1139,20112,20113],{"xmlns":1141},[1143,20114,20115,20123],{},[1146,20116,20117],{},[1224,20118,20119,20121],{},[1149,20120,4542],{},[1230,20122,1232],{},[1153,20124,20125],{"encoding":1155},"s^2"," se udává v jednotkách znaku na druhou, ",[1115,20128,20130],{"className":20129},[1137],[1139,20131,20132],{"xmlns":1141},[1143,20133,20134,20138],{},[1146,20135,20136],{},[1149,20137,4542],{},[1153,20139,4542],{"encoding":1155}," ve stejných jednotkách jako data — pro interpretaci (např. „kolísání kolem průměru\") patří vždy ",[1115,20142,20144],{"className":20143},[1137],[1139,20145,20146],{"xmlns":1141},[1143,20147,20148,20152],{},[1146,20149,20150],{},[1149,20151,4542],{},[1153,20153,4542],{"encoding":1155},[1115,20155,20157],{"className":20156},[1137],[1139,20158,20159],{"xmlns":1141},[1143,20160,20161,20169],{},[1146,20162,20163],{},[1224,20164,20165,20167],{},[1149,20166,4542],{},[1230,20168,1232],{},[1153,20170,20125],{"encoding":1155},[1127,20172,20173,20176],{},[1130,20174,20175],{},"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.",[1377,20178,5863],{"id":5862},[1124,20180,20181,20186,20191,20196,20201,20206,20211],{},[1127,20182,20183],{},[1384,20184,1390],{"className":20185,"dataFsResolvedFilePath":1388,"href":1389},[1387],[1127,20187,20188],{},[1384,20189,5876],{"className":20190,"dataFsResolvedFilePath":5292,"href":5293},[1387],[1127,20192,20193],{},[1384,20194,5890],{"className":20195,"dataFsResolvedFilePath":5302,"href":5303},[1387],[1127,20197,20198],{},[1384,20199,1094],{"className":20200,"dataFsResolvedFilePath":11005,"href":11006},[1387],[1127,20202,20203],{},[1384,20204,5898],{"className":20205,"dataFsResolvedFilePath":5896,"href":5897},[1387],[1127,20207,20208],{},[1384,20209,5906],{"className":20210,"dataFsResolvedFilePath":5904,"href":5905},[1387],[1127,20212,20213],{},[1384,20214,5914],{"className":20215,"dataFsResolvedFilePath":5912,"href":5913},[1387],[1377,20217,5917],{"id":934},[1110,20219,5920,20220,5925],{},[5922,20221,5924],{},[5927,20223,20224],{},"html pre.shiki code .sP4rz, 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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.",[1127,24468,24469,24470,1348,24496,1405,24522,1236],{},"Regulace měřením (spojitá veličina s normálním rozdělením): diagramy ",[1115,24471,24473],{"className":24472},[1137],[1139,24474,24475],{"xmlns":1141},[1143,24476,24477,24493],{},[1146,24478,24479,24481,24487,24489,24491],{},[1193,24480,1199],{"stretchy":1198},[1214,24482,24483,24485],{"accent":1121},[1149,24484,1168],{},[1193,24486,15814],{},[1193,24488,1503],{"separator":1121},[1149,24490,1257],{},[1193,24492,1228],{"stretchy":1198},[1153,24494,24495],{"encoding":1155},"(\\bar{x}, R)",[1115,24497,24499],{"className":24498},[1137],[1139,24500,24501],{"xmlns":1141},[1143,24502,24503,24519],{},[1146,24504,24505,24507,24513,24515,24517],{},[1193,24506,1199],{"stretchy":1198},[1214,24508,24509,24511],{"accent":1121},[1149,24510,1168],{},[1193,24512,15814],{},[1193,24514,1503],{"separator":1121},[1149,24516,4542],{},[1193,24518,1228],{"stretchy":1198},[1153,24520,24521],{"encoding":1155},"(\\bar{x}, s)",[1115,24523,24525],{"className":24524},[1137],[1139,24526,24527],{"xmlns":1141},[1143,24528,24529,24558],{},[1146,24530,24531,24533,24539,24541,24556],{},[1193,24532,1199],{"stretchy":1198},[1201,24534,24535,24537],{},[1149,24536,1168],{},[1149,24538,1207],{},[1193,24540,1503],{"separator":1121},[1201,24542,24543,24545],{},[1149,24544,1257],{},[1146,24546,24547,24549,24552,24554],{},[1149,24548,11631],{},[1149,24550,24551],{},"l",[1193,24553,1503],{"separator":1121},[1149,24555,1207],{},[1193,24557,1228],{"stretchy":1198},[1153,24559,24560],{"encoding":1155},"(x_i, R_{kl,i})",[1127,24562,24563,24564,24577,24578,24591,24592,24608,24609,24622],{},"Regulace srovnáváním (diskrétní veličina): počet neshod ",[1115,24565,24567],{"className":24566},[1137],[1139,24568,24569],{"xmlns":1141},[1143,24570,24571,24575],{},[1146,24572,24573],{},[1149,24574,8130],{},[1153,24576,8130],{"encoding":1155}," (konstantní rozsah) a ",[1115,24579,24581],{"className":24580},[1137],[1139,24582,24583],{"xmlns":1141},[1143,24584,24585,24589],{},[1146,24586,24587],{},[1149,24588,15880],{},[1153,24590,15880],{"encoding":1155}," (nekonstantní rozsah), počet neshodných produktů ",[1115,24593,24595],{"className":24594},[1137],[1139,24596,24597],{"xmlns":1141},[1143,24598,24599,24605],{},[1146,24600,24601,24603],{},[1149,24602,1816],{},[1149,24604,1110],{},[1153,24606,24607],{"encoding":1155},"np"," (konstantní rozsah) a jejich podíl ",[1115,24610,24612],{"className":24611},[1137],[1139,24613,24614],{"xmlns":1141},[1143,24615,24616,24620],{},[1146,24617,24618],{},[1149,24619,1110],{},[1153,24621,1110],{"encoding":1155}," (nekonstantní rozsah).",[1127,24624,24625],{},"Podskupiny s vymezitelnou příčinou se po jejím odstranění z výpočtu vyřadí a meze se přepočítají, dokud jsou všechny body uvnitř mezí.",[1127,24627,24628,24629,1348,24648,1348,24670,1348,24692,24716,24717,24738],{},"Indexy způsobilosti ",[1115,24630,24632],{"className":24631},[1137],[1139,24633,24634],{"xmlns":1141},[1143,24635,24636,24645],{},[1146,24637,24638],{},[1201,24639,24640,24643],{},[1149,24641,24642],{},"C",[1149,24644,1110],{},[1153,24646,24647],{"encoding":1155},"C_p",[1115,24649,24651],{"className":24650},[1137],[1139,24652,24653],{"xmlns":1141},[1143,24654,24655,24667],{},[1146,24656,24657],{},[1201,24658,24659,24661],{},[1149,24660,24642],{},[1146,24662,24663,24665],{},[1149,24664,1110],{},[1149,24666,11631],{},[1153,24668,24669],{"encoding":1155},"C_{pk}",[1115,24671,24673],{"className":24672},[1137],[1139,24674,24675],{"xmlns":1141},[1143,24676,24677,24689],{},[1146,24678,24679],{},[1201,24680,24681,24683],{},[1149,24682,24642],{},[1146,24684,24685,24687],{},[1149,24686,1110],{},[1149,24688,8865],{},[1153,24690,24691],{"encoding":1155},"C_{pm}",[1115,24693,24695],{"className":24694},[1137],[1139,24696,24697],{"xmlns":1141},[1143,24698,24699,24713],{},[1146,24700,24701],{},[1201,24702,24703,24705],{},[1149,24704,24642],{},[1146,24706,24707,24709,24711],{},[1149,24708,1110],{},[1149,24710,8865],{},[1149,24712,11631],{},[1153,24714,24715],{"encoding":1155},"C_{pmk}"," posuzují, zda statisticky zvládnutý proces vyhovuje tolerančním mezím; ",[1115,24718,24720],{"className":24719},[1137],[1139,24721,24722],{"xmlns":1141},[1143,24723,24724,24736],{},[1146,24725,24726],{},[1201,24727,24728,24730],{},[1149,24729,24642],{},[1146,24731,24732,24734],{},[1149,24733,1110],{},[1149,24735,11631],{},[1153,24737,24669],{"encoding":1155}," navíc zohledňuje vychýlení střední hodnoty.",[1127,24740,24741,24742,1236],{},"V R diagramy i indexy počítá balíček ",[1332,24743,360],{},[1377,24745,24747],{"id":24746},"statistická-regulace-procesu","Statistická regulace procesu",[1110,24749,24750,24751,24753,24754,1236],{},"Tradiční zabezpečování jakosti kontroluje výrobky až po jejich vyrobení, což je neekonomické. ",[1130,24752,24747],{}," 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 ",[1130,24755,24756],{},"statisticky zvládnutém stavu",[1110,24758,24759,24760,24763],{},"Teorie regulace vychází z ",[1130,24761,24762],{},"variability"," procesu, kterou způsobují dva druhy příčin:",[6528,24765,24766,24778],{},[6531,24767,24768],{},[6534,24769,24770,24772,24775],{},[6537,24771],{},[6537,24773,24774],{},"Náhodné příčiny",[6537,24776,24777],{},"Vymezitelné příčiny",[6645,24779,24780,24791,24802],{},[6534,24781,24782,24785,24788],{},[6650,24783,24784],{},"Povaha",[6650,24786,24787],{},"široká skupina neidentifikovatelných vlivů, každý přispívá k variabilitě malou měrou",[6650,24789,24790],{},"vlivy, které za běžných podmínek na proces nepůsobí; vyvolají nepřirozené kolísání údajů",[6534,24792,24793,24796,24799],{},[6650,24794,24795],{},"Stav procesu",[6650,24797,24798],{},"ustálený, jakost výstupů je předvídatelná, není nutné zasahovat — statisticky zvládnutý",[6650,24800,24801],{},"jakost výstupů není předvídatelná, je nutné zasáhnout — proces není statisticky zvládnutý",[6534,24803,24804,24807,24810],{},[6650,24805,24806],{},"Příklady",[6650,24808,24809],{},"psychický stav pracovníka, chvění stroje, teplota ovzduší",[6650,24811,24812],{},"změna materiálu, nezaškolená obsluha",[1110,24814,24815,24816,24819,24820,24823],{},"Vymezitelné příčiny jsou ",[1130,24817,24818],{},"sporadické"," (vznikají náhle, změny trvají krátce) nebo ",[1130,24821,24822],{},"přetrvávající"," (trvají stále nebo se mění).",[1110,24825,24826],{},[1864,24827],{"alt":24828,"className":24829,"src":24830},"mask-ilu-pricin-variability",[1387,1868],"\u002Fwiki-assets\u002Fmask-ilu-pricin-variability.png",[1110,24832,24833],{},"Regulace probíhá ve třech fázích:",[5106,24835,24836,24846,24852],{},[1127,24837,24838,24841,24842,24845],{},[1130,24839,24840],{},"Fáze přípravná"," — stanoví se sledované znaky jakosti (rozměr, hmotnost, počet vad…), délka časového intervalu mezi měřeními, ",[1130,24843,24844],{},"logická podskupina"," (skupina měření, v níž se předpokládá působení pouze náhodných příčin), typ regulačního diagramu a místa kontroly v procesu.",[1127,24847,24848,24851],{},[1130,24849,24850],{},"Fáze zabezpečování statistické zvládnutosti"," — pomocí regulačních diagramů se identifikují vymezitelné příčiny a odstraní se jejich působení.",[1127,24853,24854,24857],{},[1130,24855,24856],{},"Fáze analýzy a zabezpečení způsobilosti"," — zkoumá se, zda statisticky zvládnutý proces vyhovuje požadavkům zákazníka; k tomu slouží indexy způsobilosti (níže).",[1377,24859,24861],{"id":24860},"princip-regulačního-diagramu","Princip regulačního diagramu",[1110,24863,24864,24867],{},[1130,24865,24866],{},"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.",[1124,24869,24870,24876,24882],{},[1127,24871,24872,24875],{},[1130,24873,24874],{},"CL"," — střední přímka, odpovídá požadované (referenční) hodnotě použité charakteristiky,",[1127,24877,24878,24881],{},[1130,24879,24880],{},"UCL"," — horní akční regulační mez,",[1127,24883,24884,24887],{},[1130,24885,24886],{},"LCL"," — dolní akční regulační mez.",[1110,24889,24890],{},"Akční meze vymezují pásmo působení pouze náhodných příčin variability.",[1110,24892,24893],{},[1864,24894],{"alt":24895,"className":24896,"src":24897},"mask-rd-schema",[1387,1868],"\u002Fwiki-assets\u002Fmask-rd-schema.png",[1110,24899,24900,24903],{},[1130,24901,24902],{},"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.",[1110,24905,24906,24907,24910,24911,24914],{},"Podle charakteru regulované veličiny se diagramy dělí na diagramy pro ",[1130,24908,24909],{},"regulaci měřením"," (regulovaná veličina je spojitá náhodná veličina) a pro ",[1130,24912,24913],{},"regulaci srovnáváním"," (diskrétní náhodná veličina).",[1110,24916,24917],{},"Postup při konstrukci regulačního diagramu:",[5106,24919,24920,24923,24926,24929,24932,24935,24938,24941,24944],{},[1127,24921,24922],{},"volba regulované veličiny,",[1127,24924,24925],{},"sběr a záznam dat,",[1127,24927,24928],{},"ověření požadovaných předpokladů o datech,",[1127,24930,24931],{},"volba rozsahu logických podskupin,",[1127,24933,24934],{},"volba vhodného regulačního diagramu,",[1127,24936,24937],{},"výpočet hodnot zvoleného testového kritéria pro jednotlivé výběry,",[1127,24939,24940],{},"ověření a zajištění statistické zvládnutosti procesu,",[1127,24942,24943],{},"ověření způsobilosti procesu,",[1127,24945,24946],{},"vlastní regulace procesu.",[1377,24948,24950],{"id":24949},"regulace-měřením","Regulace měřením",[1110,24952,24953],{},"Diagramy pro regulaci měřením se používají, když je regulovaná veličina měřitelná. Požaduje se, aby:",[1124,24955,24956,24959],{},[1127,24957,24958],{},"jednotlivá měření byla vzájemně nezávislá,",[1127,24960,24961,24962,24975,24976,24989,24990,25003,25004,25017],{},"regulovaná veličina byla spojitá náhodná veličina s normálním rozdělením se střední hodnotou ",[1115,24963,24965],{"className":24964},[1137],[1139,24966,24967],{"xmlns":1141},[1143,24968,24969,24973],{},[1146,24970,24971],{},[1149,24972,11264],{},[1153,24974,13166],{"encoding":1155}," a směrodatnou odchylkou ",[1115,24977,24979],{"className":24978},[1137],[1139,24980,24981],{"xmlns":1141},[1143,24982,24983,24987],{},[1146,24984,24985],{},[1149,24986,11271],{},[1153,24988,11303],{"encoding":1155}," — tyto dva parametry charakterizují statistickou stabilitu procesu; ",[1115,24991,24993],{"className":24992},[1137],[1139,24994,24995],{"xmlns":1141},[1143,24996,24997,25001],{},[1146,24998,24999],{},[1149,25000,11264],{},[1153,25002,13166],{"encoding":1155}," je hodnota, na niž je proces nastaven, ",[1115,25005,25007],{"className":25006},[1137],[1139,25008,25009],{"xmlns":1141},[1143,25010,25011,25015],{},[1146,25012,25013],{},[1149,25014,11271],{},[1153,25016,11303],{"encoding":1155}," charakterizuje jeho přesnost.",[1110,25019,25020,25021,1348,25046,1405,25071,25108],{},"Jsou-li předpoklady splněny, volí se diagramy, které současně sledují stabilitu polohy i stabilitu rozptylu: ",[1115,25022,25024],{"className":25023},[1137],[1139,25025,25026],{"xmlns":1141},[1143,25027,25028,25044],{},[1146,25029,25030,25032,25038,25040,25042],{},[1193,25031,1199],{"stretchy":1198},[1214,25033,25034,25036],{"accent":1121},[1149,25035,1168],{},[1193,25037,15814],{},[1193,25039,1503],{"separator":1121},[1149,25041,1257],{},[1193,25043,1228],{"stretchy":1198},[1153,25045,24495],{"encoding":1155},[1115,25047,25049],{"className":25048},[1137],[1139,25050,25051],{"xmlns":1141},[1143,25052,25053,25069],{},[1146,25054,25055,25057,25063,25065,25067],{},[1193,25056,1199],{"stretchy":1198},[1214,25058,25059,25061],{"accent":1121},[1149,25060,1168],{},[1193,25062,15814],{},[1193,25064,1503],{"separator":1121},[1149,25066,4542],{},[1193,25068,1228],{"stretchy":1198},[1153,25070,24521],{"encoding":1155},[1115,25072,25074],{"className":25073},[1137],[1139,25075,25076],{"xmlns":1141},[1143,25077,25078,25106],{},[1146,25079,25080,25082,25088,25090,25104],{},[1193,25081,1199],{"stretchy":1198},[1201,25083,25084,25086],{},[1149,25085,1168],{},[1149,25087,1207],{},[1193,25089,1503],{"separator":1121},[1201,25091,25092,25094],{},[1149,25093,1257],{},[1146,25095,25096,25098,25100,25102],{},[1149,25097,11631],{},[1149,25099,24551],{},[1193,25101,1503],{"separator":1121},[1149,25103,1207],{},[1193,25105,1228],{"stretchy":1198},[1153,25107,24560],{"encoding":1155},". Výsledkem jsou vždy dva diagramy.",[2019,25110,25112,25113],{"id":25111},"diagram-xˉrbarx-r","Diagram ",[1115,25114,25116],{"className":25115},[1137],[1139,25117,25118],{"xmlns":1141},[1143,25119,25120,25136],{},[1146,25121,25122,25124,25130,25132,25134],{},[1193,25123,1199],{"stretchy":1198},[1214,25125,25126,25128],{"accent":1121},[1149,25127,1168],{},[1193,25129,15814],{},[1193,25131,1503],{"separator":1121},[1149,25133,1257],{},[1193,25135,1228],{"stretchy":1198},[1153,25137,24495],{"encoding":1155},[1110,25139,25140,25141,25163,25164,25182],{},"Regulované veličiny jsou výběrové průměry ",[1115,25142,25144],{"className":25143},[1137],[1139,25145,25146],{"xmlns":1141},[1143,25147,25148,25160],{},[1146,25149,25150],{},[1201,25151,25152,25158],{},[1214,25153,25154,25156],{"accent":1121},[1149,25155,1168],{},[1193,25157,15814],{},[1149,25159,1207],{},[1153,25161,25162],{"encoding":1155},"\\bar{x}_i"," a výběrová rozpětí ",[1115,25165,25167],{"className":25166},[1137],[1139,25168,25169],{"xmlns":1141},[1143,25170,25171,25179],{},[1146,25172,25173],{},[1201,25174,25175,25177],{},[1149,25176,1257],{},[1149,25178,1207],{},[1153,25180,25181],{"encoding":1155},"R_i"," v logických podskupinách:",[1115,25184,25186],{"className":25185},[1137],[1139,25187,25188],{"xmlns":1141,"display":1796},[1143,25189,25190,25291],{},[1146,25191,25192,25202,25204,25210,25224,25234,25236,25238,25244,25246,25257,25267,25269,25279,25289],{},[1201,25193,25194,25200],{},[1214,25195,25196,25198],{"accent":1121},[1149,25197,1168],{},[1193,25199,15814],{},[1149,25201,1207],{},[1193,25203,1281],{},[3546,25205,25206,25208],{},[1230,25207,1525],{},[1149,25209,1816],{},[1802,25211,25212,25214,25222],{},[1193,25213,1195],{},[1146,25215,25216,25218,25220],{},[1149,25217,6318],{},[1193,25219,1281],{},[1230,25221,1525],{},[1149,25223,1816],{},[1201,25225,25226,25228],{},[1149,25227,1168],{},[1146,25229,25230,25232],{},[1149,25231,1207],{},[1149,25233,6318],{},[1193,25235,1503],{"separator":1121},[1936,25237],{"width":1938},[1201,25239,25240,25242],{},[1149,25241,1257],{},[1149,25243,1207],{},[1193,25245,1281],{},[25247,25248,25249,25255],"munder",{},[1146,25250,25251,25253],{},[1149,25252,16071],{},[1193,25254,1851],{},[1149,25256,6318],{},[1201,25258,25259,25261],{},[1149,25260,1168],{},[1146,25262,25263,25265],{},[1149,25264,1207],{},[1149,25266,6318],{},[1193,25268,1210],{},[25247,25270,25271,25277],{},[1146,25272,25273,25275],{},[1149,25274,1848],{},[1193,25276,1851],{},[1149,25278,6318],{},[1201,25280,25281,25283],{},[1149,25282,1168],{},[1146,25284,25285,25287],{},[1149,25286,1207],{},[1149,25288,6318],{},[1149,25290,1236],{"mathvariant":1854},[1153,25292,25293],{"encoding":1155},"\\bar{x}_i = \\frac{1}{n}\\sum_{j=1}^n x_{ij}, \\qquad R_i = \\max_j x_{ij} - \\min_j x_{ij}.",[1110,25295,25296],{},"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.",[1110,25298,25299,25300,25326,25327,25340,25341,1405,25362,25379,25380,25393,25394,25412,25413,1236],{},"Data se zapisují do tabulky: řádek ",[1115,25301,25303],{"className":25302},[1137],[1139,25304,25305],{"xmlns":1141},[1143,25306,25307,25323],{},[1146,25308,25309,25311,25313,25315,25317,25319,25321],{},[1149,25310,1207],{},[1193,25312,1281],{},[1230,25314,1525],{},[1193,25316,1503],{"separator":1121},[1193,25318,1530],{},[1193,25320,1503],{"separator":1121},[1149,25322,11631],{},[1153,25324,25325],{"encoding":1155},"i = 1, \\dots, k"," je logická podskupina v pořadí, v jakém byla získána, sloupce obsahují ",[1115,25328,25330],{"className":25329},[1137],[1139,25331,25332],{"xmlns":1141},[1143,25333,25334,25338],{},[1146,25335,25336],{},[1149,25337,1816],{},[1153,25339,1816],{"encoding":1155}," naměřených hodnot a poslední dva sloupce ",[1115,25342,25344],{"className":25343},[1137],[1139,25345,25346],{"xmlns":1141},[1143,25347,25348,25360],{},[1146,25349,25350],{},[1201,25351,25352,25358],{},[1214,25353,25354,25356],{"accent":1121},[1149,25355,1168],{},[1193,25357,15814],{},[1149,25359,1207],{},[1153,25361,25162],{"encoding":1155},[1115,25363,25365],{"className":25364},[1137],[1139,25366,25367],{"xmlns":1141},[1143,25368,25369,25377],{},[1146,25370,25371],{},[1201,25372,25373,25375],{},[1149,25374,1257],{},[1149,25376,1207],{},[1153,25378,25181],{"encoding":1155},". Pro sestrojení diagramu je potřeba aspoň 20 podskupin. Nejprve se určí diagram ",[1115,25381,25383],{"className":25382},[1137],[1139,25384,25385],{"xmlns":1141},[1143,25386,25387,25391],{},[1146,25388,25389],{},[1149,25390,1257],{},[1153,25392,1257],{"encoding":1155},", potom diagram ",[1115,25395,25397],{"className":25396},[1137],[1139,25398,25399],{"xmlns":1141},[1143,25400,25401,25409],{},[1146,25402,25403],{},[1214,25404,25405,25407],{"accent":1121},[1149,25406,1168],{},[1193,25408,15814],{},[1153,25410,25411],{"encoding":1155},"\\bar{x}"," — u obou střední přímka a akční meze. V R se diagramy konstruují funkcí ",[1332,25414,25415],{},"qcc()",[1103,25417,25419,25426],{"className":25418,"dataCallout":2932},[1106,2931],[1110,25420,25422,25425],{"className":25421},[1113],[1115,25423],{"className":25424,"ariaHidden":1121},[1118,2939,1120],"Příklad: kontrola rozměru dílu ve 20 logických podskupinách",[1110,25427,25428,25429,25442,25443,1348,25461,25479,25480,1236],{},"Naměřená data znaku jakosti ",[1115,25430,25432],{"className":25431},[1137],[1139,25433,25434],{"xmlns":1141},[1143,25435,25436,25440],{},[1146,25437,25438],{},[1149,25439,11107],{},[1153,25441,11107],{"encoding":1155}," byla získána ve 20 logických podskupinách po 4 měřeních (",[1115,25444,25446],{"className":25445},[1137],[1139,25447,25448],{"xmlns":1141},[1143,25449,25450,25458],{},[1146,25451,25452,25454,25456],{},[1149,25453,11631],{},[1193,25455,1281],{},[1230,25457,8444],{},[1153,25459,25460],{"encoding":1155},"k=20",[1115,25462,25464],{"className":25463},[1137],[1139,25465,25466],{"xmlns":1141},[1143,25467,25468,25476],{},[1146,25469,25470,25472,25474],{},[1149,25471,1816],{},[1193,25473,1281],{},[1230,25475,7961],{},[1153,25477,25478],{"encoding":1155},"n=4","); znak je měřitelný a má normální rozdělení. Sestrojte regulační diagram ",[1115,25481,25483],{"className":25482},[1137],[1139,25484,25485],{"xmlns":1141},[1143,25486,25487,25503],{},[1146,25488,25489,25491,25497,25499,25501],{},[1193,25490,1199],{"stretchy":1198},[1214,25492,25493,25495],{"accent":1121},[1149,25494,1168],{},[1193,25496,15814],{},[1193,25498,1503],{"separator":1121},[1149,25500,1257],{},[1193,25502,1228],{"stretchy":1198},[1153,25504,24495],{"encoding":1155},[6528,25506,25507,25622],{},[6531,25508,25509],{},[6534,25510,25511,25526,25550,25574,25598],{},[6537,25512,25513],{},[1115,25514,25516],{"className":25515},[1137],[1139,25517,25518],{"xmlns":1141},[1143,25519,25520,25524],{},[1146,25521,25522],{},[1149,25523,1207],{},[1153,25525,1207],{"encoding":1155},[6537,25527,25528],{},[1115,25529,25531],{"className":25530},[1137],[1139,25532,25533],{"xmlns":1141},[1143,25534,25535,25547],{},[1146,25536,25537],{},[1201,25538,25539,25541],{},[1149,25540,1168],{},[1146,25542,25543,25545],{},[1149,25544,1207],{},[1230,25546,1525],{},[1153,25548,25549],{"encoding":1155},"x_{i1}",[6537,25551,25552],{},[1115,25553,25555],{"className":25554},[1137],[1139,25556,25557],{"xmlns":1141},[1143,25558,25559,25571],{},[1146,25560,25561],{},[1201,25562,25563,25565],{},[1149,25564,1168],{},[1146,25566,25567,25569],{},[1149,25568,1207],{},[1230,25570,1232],{},[1153,25572,25573],{"encoding":1155},"x_{i2}",[6537,25575,25576],{},[1115,25577,25579],{"className":25578},[1137],[1139,25580,25581],{"xmlns":1141},[1143,25582,25583,25595],{},[1146,25584,25585],{},[1201,25586,25587,25589],{},[1149,25588,1168],{},[1146,25590,25591,25593],{},[1149,25592,1207],{},[1230,25594,8010],{},[1153,25596,25597],{"encoding":1155},"x_{i3}",[6537,25599,25600],{},[1115,25601,25603],{"className":25602},[1137],[1139,25604,25605],{"xmlns":1141},[1143,25606,25607,25619],{},[1146,25608,25609],{},[1201,25610,25611,25613],{},[1149,25612,1168],{},[1146,25614,25615,25617],{},[1149,25616,1207],{},[1230,25618,7961],{},[1153,25620,25621],{"encoding":1155},"x_{i4}",[6645,25623,25624,25638,25653,25669,25684,25696,25710,25722,25735],{},[6534,25625,25626,25628,25631,25634,25636],{},[6650,25627,1525],{},[6650,25629,25630],{},"106",[6650,25632,25633],{},"98",[6650,25635,18434],{},[6650,25637,18434],{},[6534,25639,25640,25642,25645,25648,25651],{},[6650,25641,1232],{},[6650,25643,25644],{},"95",[6650,25646,25647],{},"94",[6650,25649,25650],{},"108",[6650,25652,10512],{},[6534,25654,25655,25657,25660,25663,25666],{},[6650,25656,8010],{},[6650,25658,25659],{},"122",[6650,25661,25662],{},"105",[6650,25664,25665],{},"103",[6650,25667,25668],{},"133",[6534,25670,25671,25673,25676,25678,25681],{},[6650,25672,7961],{},[6650,25674,25675],{},"113",[6650,25677,7982],{},[6650,25679,25680],{},"128",[6650,25682,25683],{},"135",[6534,25685,25686,25688,25690,25692,25694],{},[6650,25687,5351],{},[6650,25689,18434],{},[6650,25691,10512],{},[6650,25693,25665],{},[6650,25695,10512],{},[6534,25697,25698,25700,25702,25704,25707],{},[6650,25699,8365],{},[6650,25701,25633],{},[6650,25703,25665],{},[6650,25705,25706],{},"97",[6650,25708,25709],{},"99",[6534,25711,25712,25714,25716,25718,25720],{},[6650,25713,1530],{},[6650,25715,1530],{},[6650,25717,1530],{},[6650,25719,1530],{},[6650,25721,1530],{},[6534,25723,25724,25726,25728,25730,25733],{},[6650,25725,19068],{},[6650,25727,25680],{},[6650,25729,25668],{},[6650,25731,25732],{},"120",[6650,25734,19096],{},[6534,25736,25737,25739,25741,25743,25745],{},[6650,25738,8444],{},[6650,25740,25633],{},[6650,25742,25665],{},[6650,25744,25706],{},[6650,25746,25709],{},[1110,25748,25749,25750,25771,25772,1902],{},"Pro každou podskupinu se dopočítá výběrový průměr ",[1115,25751,25753],{"className":25752},[1137],[1139,25754,25755],{"xmlns":1141},[1143,25756,25757,25769],{},[1146,25758,25759],{},[1201,25760,25761,25767],{},[1214,25762,25763,25765],{"accent":1121},[1149,25764,1168],{},[1193,25766,15814],{},[1149,25768,1207],{},[1153,25770,25162],{"encoding":1155}," a rozpětí ",[1115,25773,25775],{"className":25774},[1137],[1139,25776,25777],{"xmlns":1141},[1143,25778,25779,25787],{},[1146,25780,25781],{},[1201,25782,25783,25785],{},[1149,25784,1257],{},[1149,25786,1207],{},[1153,25788,25181],{"encoding":1155},[6528,25790,25791,25852],{},[6531,25792,25793],{},[6534,25794,25795,25810,25833],{},[6537,25796,25797],{},[1115,25798,25800],{"className":25799},[1137],[1139,25801,25802],{"xmlns":1141},[1143,25803,25804,25808],{},[1146,25805,25806],{},[1149,25807,1207],{},[1153,25809,1207],{"encoding":1155},[6537,25811,25812],{},[1115,25813,25815],{"className":25814},[1137],[1139,25816,25817],{"xmlns":1141},[1143,25818,25819,25831],{},[1146,25820,25821],{},[1201,25822,25823,25829],{},[1214,25824,25825,25827],{"accent":1121},[1149,25826,1168],{},[1193,25828,15814],{},[1149,25830,1207],{},[1153,25832,25162],{"encoding":1155},[6537,25834,25835],{},[1115,25836,25838],{"className":25837},[1137],[1139,25839,25840],{"xmlns":1141},[1143,25841,25842,25850],{},[1146,25843,25844],{},[1201,25845,25846,25848],{},[1149,25847,1257],{},[1149,25849,1207],{},[1153,25851,25181],{"encoding":1155},[6645,25853,25854,25863,25873,25883,25893,25902,25911,25919,25928],{},[6534,25855,25856,25858,25861],{},[6650,25857,1525],{},[6650,25859,25860],{},"101,50",[6650,25862,19163],{},[6534,25864,25865,25867,25870],{},[6650,25866,1232],{},[6650,25868,25869],{},"97,25",[6650,25871,25872],{},"16",[6534,25874,25875,25877,25880],{},[6650,25876,8010],{},[6650,25878,25879],{},"115,75",[6650,25881,25882],{},"30",[6534,25884,25885,25887,25890],{},[6650,25886,7961],{},[6650,25888,25889],{},"111,75",[6650,25891,25892],{},"64",[6534,25894,25895,25897,25900],{},[6650,25896,5351],{},[6650,25898,25899],{},"97,00",[6650,25901,6687],{},[6534,25903,25904,25906,25909],{},[6650,25905,8365],{},[6650,25907,25908],{},"99,25",[6650,25910,8365],{},[6534,25912,25913,25915,25917],{},[6650,25914,1530],{},[6650,25916,1530],{},[6650,25918,1530],{},[6534,25920,25921,25923,25926],{},[6650,25922,19068],{},[6650,25924,25925],{},"126,50",[6650,25927,3116],{},[6534,25929,25930,25932,25934],{},[6650,25931,8444],{},[6650,25933,25908],{},[6650,25935,8365],{},[1110,25937,25938,25939,25952,25953,1348,25981,1348,26011,26039,26040,26062,26063,1348,26090,1348,26119,26146,26147,1236],{},"Nejprve se posoudí diagram ",[1115,25940,25942],{"className":25941},[1137],[1139,25943,25944],{"xmlns":1141},[1143,25945,25946,25950],{},[1146,25947,25948],{},[1149,25949,1257],{},[1153,25951,1257],{"encoding":1155}," na všech 20 podskupinách: ",[1115,25954,25956],{"className":25955},[1137],[1139,25957,25958],{"xmlns":1141},[1143,25959,25960,25978],{},[1146,25961,25962,25964,25967,25969,25971,25973,25975],{},[1149,25963,24642],{},[1149,25965,25966],{},"L",[1193,25968,1199],{"stretchy":1198},[1149,25970,1257],{},[1193,25972,1228],{"stretchy":1198},[1193,25974,1281],{},[1230,25976,25977],{},"15,8",[1153,25979,25980],{"encoding":1155},"CL(R)=15{,}8",[1115,25982,25984],{"className":25983},[1137],[1139,25985,25986],{"xmlns":1141},[1143,25987,25988,26008],{},[1146,25989,25990,25993,25995,25997,25999,26001,26003,26005],{},[1149,25991,25992],{},"U",[1149,25994,24642],{},[1149,25996,25966],{},[1193,25998,1199],{"stretchy":1198},[1149,26000,1257],{},[1193,26002,1228],{"stretchy":1198},[1193,26004,1281],{},[1230,26006,26007],{},"36,06",[1153,26009,26010],{"encoding":1155},"UCL(R)=36{,}06",[1115,26012,26014],{"className":26013},[1137],[1139,26015,26016],{"xmlns":1141},[1143,26017,26018,26036],{},[1146,26019,26020,26022,26024,26026,26028,26030,26032,26034],{},[1149,26021,25966],{},[1149,26023,24642],{},[1149,26025,25966],{},[1193,26027,1199],{"stretchy":1198},[1149,26029,1257],{},[1193,26031,1228],{"stretchy":1198},[1193,26033,1281],{},[1230,26035,1597],{},[1153,26037,26038],{"encoding":1155},"LCL(R)=0",". Rozpětí čtvrté podskupiny (",[1115,26041,26043],{"className":26042},[1137],[1139,26044,26045],{"xmlns":1141},[1143,26046,26047,26059],{},[1146,26048,26049,26055,26057],{},[1201,26050,26051,26053],{},[1149,26052,1257],{},[1230,26054,7961],{},[1193,26056,1281],{},[1230,26058,25892],{},[1153,26060,26061],{"encoding":1155},"R_4=64",") mez překračuje; po potvrzení vymezitelné příčiny se podskupina 4 z výpočtu vyřadí a meze se přepočítají — ",[1115,26064,26066],{"className":26065},[1137],[1139,26067,26068],{"xmlns":1141},[1143,26069,26070,26087],{},[1146,26071,26072,26074,26076,26078,26080,26082,26084],{},[1149,26073,24642],{},[1149,26075,25966],{},[1193,26077,1199],{"stretchy":1198},[1149,26079,1257],{},[1193,26081,1228],{"stretchy":1198},[1193,26083,1281],{},[1230,26085,26086],{},"13,26",[1153,26088,26089],{"encoding":1155},"CL(R)=13{,}26",[1115,26091,26093],{"className":26092},[1137],[1139,26094,26095],{"xmlns":1141},[1143,26096,26097,26116],{},[1146,26098,26099,26101,26103,26105,26107,26109,26111,26113],{},[1149,26100,25992],{},[1149,26102,24642],{},[1149,26104,25966],{},[1193,26106,1199],{"stretchy":1198},[1149,26108,1257],{},[1193,26110,1228],{"stretchy":1198},[1193,26112,1281],{},[1230,26114,26115],{},"30,27",[1153,26117,26118],{"encoding":1155},"UCL(R)=30{,}27",[1115,26120,26122],{"className":26121},[1137],[1139,26123,26124],{"xmlns":1141},[1143,26125,26126,26144],{},[1146,26127,26128,26130,26132,26134,26136,26138,26140,26142],{},[1149,26129,25966],{},[1149,26131,24642],{},[1149,26133,25966],{},[1193,26135,1199],{"stretchy":1198},[1149,26137,1257],{},[1193,26139,1228],{"stretchy":1198},[1193,26141,1281],{},[1230,26143,1597],{},[1153,26145,26038],{"encoding":1155},". Diagram rozpětí je teď zvládnutý, lze tedy posoudit diagram ",[1115,26148,26150],{"className":26149},[1137],[1139,26151,26152],{"xmlns":1141},[1143,26153,26154,26162],{},[1146,26155,26156],{},[1214,26157,26158,26160],{"accent":1121},[1149,26159,1168],{},[1193,26161,15814],{},[1153,26163,25411],{"encoding":1155},[1110,26165,25112,26166,26183,26184,1348,26215,1348,26248,26281,26282,26295,26296,1348,26323,1348,26352,26379],{},[1115,26167,26169],{"className":26168},[1137],[1139,26170,26171],{"xmlns":1141},[1143,26172,26173,26181],{},[1146,26174,26175],{},[1214,26176,26177,26179],{"accent":1121},[1149,26178,1168],{},[1193,26180,15814],{},[1153,26182,25411],{"encoding":1155}," bez čtvrté podskupiny dává ",[1115,26185,26187],{"className":26186},[1137],[1139,26188,26189],{"xmlns":1141},[1143,26190,26191,26212],{},[1146,26192,26193,26195,26197,26199,26205,26207,26209],{},[1149,26194,24642],{},[1149,26196,25966],{},[1193,26198,1199],{"stretchy":1198},[1214,26200,26201,26203],{"accent":1121},[1149,26202,1168],{},[1193,26204,15814],{},[1193,26206,1228],{"stretchy":1198},[1193,26208,1281],{},[1230,26210,26211],{},"102,01",[1153,26213,26214],{"encoding":1155},"CL(\\bar{x})=102{,}01",[1115,26216,26218],{"className":26217},[1137],[1139,26219,26220],{"xmlns":1141},[1143,26221,26222,26245],{},[1146,26223,26224,26226,26228,26230,26232,26238,26240,26242],{},[1149,26225,25992],{},[1149,26227,24642],{},[1149,26229,25966],{},[1193,26231,1199],{"stretchy":1198},[1214,26233,26234,26236],{"accent":1121},[1149,26235,1168],{},[1193,26237,15814],{},[1193,26239,1228],{"stretchy":1198},[1193,26241,1281],{},[1230,26243,26244],{},"111,68",[1153,26246,26247],{"encoding":1155},"UCL(\\bar{x})=111{,}68",[1115,26249,26251],{"className":26250},[1137],[1139,26252,26253],{"xmlns":1141},[1143,26254,26255,26278],{},[1146,26256,26257,26259,26261,26263,26265,26271,26273,26275],{},[1149,26258,25966],{},[1149,26260,24642],{},[1149,26262,25966],{},[1193,26264,1199],{"stretchy":1198},[1214,26266,26267,26269],{"accent":1121},[1149,26268,1168],{},[1193,26270,15814],{},[1193,26272,1228],{"stretchy":1198},[1193,26274,1281],{},[1230,26276,26277],{},"92,34",[1153,26279,26280],{"encoding":1155},"LCL(\\bar{x})=92{,}34",". Mez teď překračují průměry podskupin 3 a 19. Po potvrzení vymezitelné příčiny se vyřadí obě najednou a meze diagramu ",[1115,26283,26285],{"className":26284},[1137],[1139,26286,26287],{"xmlns":1141},[1143,26288,26289,26293],{},[1146,26290,26291],{},[1149,26292,1257],{},[1153,26294,1257],{"encoding":1155}," se přepočítají bez podskupin 3, 4 a 19: ",[1115,26297,26299],{"className":26298},[1137],[1139,26300,26301],{"xmlns":1141},[1143,26302,26303,26320],{},[1146,26304,26305,26307,26309,26311,26313,26315,26317],{},[1149,26306,24642],{},[1149,26308,25966],{},[1193,26310,1199],{"stretchy":1198},[1149,26312,1257],{},[1193,26314,1228],{"stretchy":1198},[1193,26316,1281],{},[1230,26318,26319],{},"12,29",[1153,26321,26322],{"encoding":1155},"CL(R)=12{,}29",[1115,26324,26326],{"className":26325},[1137],[1139,26327,26328],{"xmlns":1141},[1143,26329,26330,26349],{},[1146,26331,26332,26334,26336,26338,26340,26342,26344,26346],{},[1149,26333,25992],{},[1149,26335,24642],{},[1149,26337,25966],{},[1193,26339,1199],{"stretchy":1198},[1149,26341,1257],{},[1193,26343,1228],{"stretchy":1198},[1193,26345,1281],{},[1230,26347,26348],{},"28,06",[1153,26350,26351],{"encoding":1155},"UCL(R)=28{,}06",[1115,26353,26355],{"className":26354},[1137],[1139,26356,26357],{"xmlns":1141},[1143,26358,26359,26377],{},[1146,26360,26361,26363,26365,26367,26369,26371,26373,26375],{},[1149,26362,25966],{},[1149,26364,24642],{},[1149,26366,25966],{},[1193,26368,1199],{"stretchy":1198},[1149,26370,1257],{},[1193,26372,1228],{"stretchy":1198},[1193,26374,1281],{},[1230,26376,1597],{},[1153,26378,26038],{"encoding":1155}," — žádná z 17 zbývajících podskupin mez nepřekračuje.",[1110,26381,26382,26383,26400,26401,1348,26432,1348,26465,26498],{},"Konečný diagram ",[1115,26384,26386],{"className":26385},[1137],[1139,26387,26388],{"xmlns":1141},[1143,26389,26390,26398],{},[1146,26391,26392],{},[1214,26393,26394,26396],{"accent":1121},[1149,26395,1168],{},[1193,26397,15814],{},[1153,26399,25411],{"encoding":1155}," na stejných 17 podskupinách má ",[1115,26402,26404],{"className":26403},[1137],[1139,26405,26406],{"xmlns":1141},[1143,26407,26408,26429],{},[1146,26409,26410,26412,26414,26416,26422,26424,26426],{},[1149,26411,24642],{},[1149,26413,25966],{},[1193,26415,1199],{"stretchy":1198},[1214,26417,26418,26420],{"accent":1121},[1149,26419,1168],{},[1193,26421,15814],{},[1193,26423,1228],{"stretchy":1198},[1193,26425,1281],{},[1230,26427,26428],{},"99,76",[1153,26430,26431],{"encoding":1155},"CL(\\bar{x})=99{,}76",[1115,26433,26435],{"className":26434},[1137],[1139,26436,26437],{"xmlns":1141},[1143,26438,26439,26462],{},[1146,26440,26441,26443,26445,26447,26449,26455,26457,26459],{},[1149,26442,25992],{},[1149,26444,24642],{},[1149,26446,25966],{},[1193,26448,1199],{"stretchy":1198},[1214,26450,26451,26453],{"accent":1121},[1149,26452,1168],{},[1193,26454,15814],{},[1193,26456,1228],{"stretchy":1198},[1193,26458,1281],{},[1230,26460,26461],{},"108,73",[1153,26463,26464],{"encoding":1155},"UCL(\\bar{x})=108{,}73",[1115,26466,26468],{"className":26467},[1137],[1139,26469,26470],{"xmlns":1141},[1143,26471,26472,26495],{},[1146,26473,26474,26476,26478,26480,26482,26488,26490,26492],{},[1149,26475,25966],{},[1149,26477,24642],{},[1149,26479,25966],{},[1193,26481,1199],{"stretchy":1198},[1214,26483,26484,26486],{"accent":1121},[1149,26485,1168],{},[1193,26487,15814],{},[1193,26489,1228],{"stretchy":1198},[1193,26491,1281],{},[1230,26493,26494],{},"90,80",[1153,26496,26497],{"encoding":1155},"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.",[1110,26500,26501],{},[1864,26502],{"alt":26503,"className":26504,"src":26505},"mask-rd-priklad1-meze",[1387,1868],"\u002Fwiki-assets\u002Fmask-rd-priklad1-meze.png",[1110,26507,26508,26509,26511,26512,26514],{},"V R se diagramy sestrojí funkcí ",[1332,26510,25415],{}," z balíčku ",[1332,26513,360],{},". Data jsou tabulka, v níž řádek odpovídá logické podskupině a sloupce jednotlivým měřením:",[2035,26516,26518],{"className":2037,"code":26517,"language":71,"meta":2039,"style":2039},"library(qcc)\ndata \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"R\") # diagram R\nqcc(data, type = \"xbar\") # diagram x̄\n",[1332,26519,26520,26530,26553,26576],{"__ignoreMap":2039},[1115,26521,26522,26524,26526,26528],{"class":2044,"line":10},[1115,26523,2698],{"class":2051},[1115,26525,1199],{"class":2059},[1115,26527,360],{"class":2047},[1115,26529,2090],{"class":2059},[1115,26531,26532,26534,26536,26538,26540,26543,26545,26547,26549,26551],{"class":2044,"line":27},[1115,26533,5440],{"class":2047},[1115,26535,2052],{"class":2051},[1115,26537,5445],{"class":2055},[1115,26539,1199],{"class":2059},[1115,26541,26542],{"class":2575},"\"3_2.txt\"",[1115,26544,1503],{"class":2051},[1115,26546,5455],{"class":2047},[1115,26548,2510],{"class":2051},[1115,26550,5460],{"class":2062},[1115,26552,2090],{"class":2059},[1115,26554,26555,26557,26559,26561,26563,26565,26567,26570,26573],{"class":2044,"line":148},[1115,26556,360],{"class":2055},[1115,26558,1199],{"class":2059},[1115,26560,5440],{"class":2047},[1115,26562,1503],{"class":2051},[1115,26564,16574],{"class":2047},[1115,26566,2510],{"class":2051},[1115,26568,26569],{"class":2575}," \"R\"",[1115,26571,26572],{"class":2059},") ",[1115,26574,26575],{"class":16384},"# diagram R\n",[1115,26577,26578,26580,26582,26584,26586,26588,26590,26593,26595],{"class":2044,"line":111},[1115,26579,360],{"class":2055},[1115,26581,1199],{"class":2059},[1115,26583,5440],{"class":2047},[1115,26585,1503],{"class":2051},[1115,26587,16574],{"class":2047},[1115,26589,2510],{"class":2051},[1115,26591,26592],{"class":2575}," \"xbar\"",[1115,26594,16381],{"class":2059},[1115,26596,26597],{"class":16384},"# diagram x̄\n",[1110,26599,26600,26601,26604],{},"Funkce vykreslí diagram se střední přímkou a akčními mezemi a body mimo meze zvýrazní. Podskupina s potvrzenou vymezitelnou příčinou se vyřadí z dat (například ",[1332,26602,26603],{},"data[-4, ]",") a diagram se sestrojí znovu.",[2019,26606,25112,26608],{"id":26607},"diagram-xˉsbarx-s",[1115,26609,26611],{"className":26610},[1137],[1139,26612,26613],{"xmlns":1141},[1143,26614,26615,26631],{},[1146,26616,26617,26619,26625,26627,26629],{},[1193,26618,1199],{"stretchy":1198},[1214,26620,26621,26623],{"accent":1121},[1149,26622,1168],{},[1193,26624,15814],{},[1193,26626,1503],{"separator":1121},[1149,26628,4542],{},[1193,26630,1228],{"stretchy":1198},[1153,26632,24521],{"encoding":1155},[1110,26634,25140,26635,26656,26657,26675,26676,26701],{},[1115,26636,26638],{"className":26637},[1137],[1139,26639,26640],{"xmlns":1141},[1143,26641,26642,26654],{},[1146,26643,26644],{},[1201,26645,26646,26652],{},[1214,26647,26648,26650],{"accent":1121},[1149,26649,1168],{},[1193,26651,15814],{},[1149,26653,1207],{},[1153,26655,25162],{"encoding":1155}," a výběrové směrodatné odchylky ",[1115,26658,26660],{"className":26659},[1137],[1139,26661,26662],{"xmlns":1141},[1143,26663,26664,26672],{},[1146,26665,26666],{},[1201,26667,26668,26670],{},[1149,26669,4542],{},[1149,26671,1207],{},[1153,26673,26674],{"encoding":1155},"s_i"," v logických podskupinách. Podmínky použití jsou stejné jako u ",[1115,26677,26679],{"className":26678},[1137],[1139,26680,26681],{"xmlns":1141},[1143,26682,26683,26699],{},[1146,26684,26685,26687,26693,26695,26697],{},[1193,26686,1199],{"stretchy":1198},[1214,26688,26689,26691],{"accent":1121},[1149,26690,1168],{},[1193,26692,15814],{},[1193,26694,1503],{"separator":1121},[1149,26696,1257],{},[1193,26698,1228],{"stretchy":1198},[1153,26700,24495],{"encoding":1155},", logické podskupiny ale sestávají z většího počtu měření. Data se zapisují do obdobné tabulky.",[2035,26703,26705],{"className":2037,"code":26704,"language":71,"meta":2039,"style":2039},"data \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"S\") # diagram s\nqcc(data, type = \"xbar\") # diagram x̄\n",[1332,26706,26707,26729,26751],{"__ignoreMap":2039},[1115,26708,26709,26711,26713,26715,26717,26719,26721,26723,26725,26727],{"class":2044,"line":10},[1115,26710,5440],{"class":2047},[1115,26712,2052],{"class":2051},[1115,26714,5445],{"class":2055},[1115,26716,1199],{"class":2059},[1115,26718,26542],{"class":2575},[1115,26720,1503],{"class":2051},[1115,26722,5455],{"class":2047},[1115,26724,2510],{"class":2051},[1115,26726,5460],{"class":2062},[1115,26728,2090],{"class":2059},[1115,26730,26731,26733,26735,26737,26739,26741,26743,26746,26748],{"class":2044,"line":27},[1115,26732,360],{"class":2055},[1115,26734,1199],{"class":2059},[1115,26736,5440],{"class":2047},[1115,26738,1503],{"class":2051},[1115,26740,16574],{"class":2047},[1115,26742,2510],{"class":2051},[1115,26744,26745],{"class":2575}," \"S\"",[1115,26747,26572],{"class":2059},[1115,26749,26750],{"class":16384},"# diagram s\n",[1115,26752,26753,26755,26757,26759,26761,26763,26765,26767,26769],{"class":2044,"line":148},[1115,26754,360],{"class":2055},[1115,26756,1199],{"class":2059},[1115,26758,5440],{"class":2047},[1115,26760,1503],{"class":2051},[1115,26762,16574],{"class":2047},[1115,26764,2510],{"class":2051},[1115,26766,26592],{"class":2575},[1115,26768,16381],{"class":2059},[1115,26770,26597],{"class":16384},[2019,26772,25112,26774],{"id":26773},"diagram-xirklix_i-r_kli",[1115,26775,26777],{"className":26776},[1137],[1139,26778,26779],{"xmlns":1141},[1143,26780,26781,26809],{},[1146,26782,26783,26785,26791,26793,26807],{},[1193,26784,1199],{"stretchy":1198},[1201,26786,26787,26789],{},[1149,26788,1168],{},[1149,26790,1207],{},[1193,26792,1503],{"separator":1121},[1201,26794,26795,26797],{},[1149,26796,1257],{},[1146,26798,26799,26801,26803,26805],{},[1149,26800,11631],{},[1149,26802,24551],{},[1193,26804,1503],{"separator":1121},[1149,26806,1207],{},[1193,26808,1228],{"stretchy":1198},[1153,26810,24560],{"encoding":1155},[1110,26812,26813,26814,26839,26840,1902],{},"Používá se za stejných podmínek jako ",[1115,26815,26817],{"className":26816},[1137],[1139,26818,26819],{"xmlns":1141},[1143,26820,26821,26837],{},[1146,26822,26823,26825,26831,26833,26835],{},[1193,26824,1199],{"stretchy":1198},[1214,26826,26827,26829],{"accent":1121},[1149,26828,1168],{},[1193,26830,15814],{},[1193,26832,1503],{"separator":1121},[1149,26834,1257],{},[1193,26836,1228],{"stretchy":1198},[1153,26838,24495],{"encoding":1155},", 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 ",[1130,26841,26842],{},"klouzavé rozpětí",[1115,26844,26846],{"className":26845},[1137],[1139,26847,26848],{"xmlns":1141,"display":1796},[1143,26849,26850,26977],{},[1146,26851,26852,26866,26868,26871,26877,26879,26891,26893,26895,26897,26899,26901,26903,26905,26907,26909,26911,26913,26915,26917,26919,26933,26935,26947,26961,26975],{},[1201,26853,26854,26856],{},[1149,26855,1257],{},[1146,26857,26858,26860,26862,26864],{},[1149,26859,11631],{},[1149,26861,24551],{},[1193,26863,1503],{"separator":1121},[1149,26865,1207],{},[1193,26867,1281],{},[1149,26869,26870],{"mathvariant":1854},"∣",[1201,26872,26873,26875],{},[1149,26874,1168],{},[1149,26876,1207],{},[1193,26878,1210],{},[1201,26880,26881,26883],{},[1149,26882,1168],{},[1146,26884,26885,26887,26889],{},[1149,26886,1207],{},[1193,26888,1210],{},[1230,26890,1525],{},[1149,26892,26870],{"mathvariant":1854},[1193,26894,1503],{"separator":1121},[1936,26896],{"width":3331},[1149,26898,1207],{},[1193,26900,1281],{},[1230,26902,1232],{},[1193,26904,1503],{"separator":1121},[1230,26906,8010],{},[1193,26908,1503],{"separator":1121},[1193,26910,1530],{},[1193,26912,1503],{"separator":1121},[1149,26914,11631],{},[1193,26916,1503],{"separator":1121},[1936,26918],{"width":1938},[1201,26920,26921,26927],{},[1214,26922,26923,26925],{"accent":1121},[1149,26924,1257],{},[1193,26926,15814],{},[1146,26928,26929,26931],{},[1149,26930,11631],{},[1149,26932,24551],{},[1193,26934,1281],{},[3546,26936,26937,26939],{},[1230,26938,1525],{},[1146,26940,26941,26943,26945],{},[1149,26942,11631],{},[1193,26944,1210],{},[1230,26946,1525],{},[1802,26948,26949,26951,26959],{},[1193,26950,1195],{},[1146,26952,26953,26955,26957],{},[1149,26954,1207],{},[1193,26956,1281],{},[1230,26958,1232],{},[1149,26960,11631],{},[1201,26962,26963,26965],{},[1149,26964,1257],{},[1146,26966,26967,26969,26971,26973],{},[1149,26968,11631],{},[1149,26970,24551],{},[1193,26972,1503],{"separator":1121},[1149,26974,1207],{},[1149,26976,1236],{"mathvariant":1854},[1153,26978,26979],{"encoding":1155},"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}.",[1110,26981,26982,26983,1405,27000,27026,27027,27052,27053,27070],{},"Regulované veličiny jsou hodnoty ",[1115,26984,26986],{"className":26985},[1137],[1139,26987,26988],{"xmlns":1141},[1143,26989,26990,26998],{},[1146,26991,26992],{},[1201,26993,26994,26996],{},[1149,26995,1168],{},[1149,26997,1207],{},[1153,26999,2429],{"encoding":1155},[1115,27001,27003],{"className":27002},[1137],[1139,27004,27005],{"xmlns":1141},[1143,27006,27007,27023],{},[1146,27008,27009],{},[1201,27010,27011,27013],{},[1149,27012,1257],{},[1146,27014,27015,27017,27019,27021],{},[1149,27016,11631],{},[1149,27018,24551],{},[1193,27020,1503],{"separator":1121},[1149,27022,1207],{},[1153,27024,27025],{"encoding":1155},"R_{kl,i}","; nejdříve se určí střední přímka a meze diagramu ",[1115,27028,27030],{"className":27029},[1137],[1139,27031,27032],{"xmlns":1141},[1143,27033,27034,27050],{},[1146,27035,27036],{},[1201,27037,27038,27040],{},[1149,27039,1257],{},[1146,27041,27042,27044,27046,27048],{},[1149,27043,11631],{},[1149,27045,24551],{},[1193,27047,1503],{"separator":1121},[1149,27049,1207],{},[1153,27051,27025],{"encoding":1155},", potom diagramu ",[1115,27054,27056],{"className":27055},[1137],[1139,27057,27058],{"xmlns":1141},[1143,27059,27060,27068],{},[1146,27061,27062],{},[1201,27063,27064,27066],{},[1149,27065,1168],{},[1149,27067,1207],{},[1153,27069,2429],{"encoding":1155},". Data jsou jeden vektor naměřených hodnot:",[2035,27072,27074],{"className":2037,"code":27073,"language":71,"meta":2039,"style":2039},"data \u003C- read.table(\"3_3.txt\", header = TRUE)\nqcc(data[, 1], type = \"xbar.one\")\n",[1332,27075,27076,27099],{"__ignoreMap":2039},[1115,27077,27078,27080,27082,27084,27086,27089,27091,27093,27095,27097],{"class":2044,"line":10},[1115,27079,5440],{"class":2047},[1115,27081,2052],{"class":2051},[1115,27083,5445],{"class":2055},[1115,27085,1199],{"class":2059},[1115,27087,27088],{"class":2575},"\"3_3.txt\"",[1115,27090,1503],{"class":2051},[1115,27092,5455],{"class":2047},[1115,27094,2510],{"class":2051},[1115,27096,5460],{"class":2062},[1115,27098,2090],{"class":2059},[1115,27100,27101,27103,27105,27107,27109,27111,27113,27115,27117,27119,27121,27124],{"class":2044,"line":27},[1115,27102,360],{"class":2055},[1115,27104,1199],{"class":2059},[1115,27106,5440],{"class":2047},[1115,27108,12546],{"class":2059},[1115,27110,1503],{"class":2051},[1115,27112,9031],{"class":2062},[1115,27114,12563],{"class":2059},[1115,27116,1503],{"class":2051},[1115,27118,16574],{"class":2047},[1115,27120,2510],{"class":2051},[1115,27122,27123],{"class":2575}," \"xbar.one\"",[1115,27125,2090],{"class":2059},[1377,27127,27129],{"id":27128},"regulace-srovnáváním","Regulace srovnáváním",[1110,27131,27132],{},"Diagramy pro regulaci srovnáváním se používají, sledují-li se počty neshodných produktů nebo počty neshod na produktech — regulovaná veličina je diskrétní náhodná veličina.",[6528,27134,27135,27148],{},[6531,27136,27137],{},[6534,27138,27139,27142,27145],{},[6537,27140,27141],{},"Sleduje se",[6537,27143,27144],{},"Konstantní rozsah podskupin",[6537,27146,27147],{},"Nekonstantní rozsah podskupin",[6645,27149,27150,27185],{},[6534,27151,27152,27155,27170],{},[6650,27153,27154],{},"počet neshod na produktech (např. vady na stejných tabulích skla)",[6650,27156,27157],{},[1115,27158,27160],{"className":27159},[1137],[1139,27161,27162],{"xmlns":1141},[1143,27163,27164,27168],{},[1146,27165,27166],{},[1149,27167,8130],{},[1153,27169,8130],{"encoding":1155},[6650,27171,27172],{},[1115,27173,27175],{"className":27174},[1137],[1139,27176,27177],{"xmlns":1141},[1143,27178,27179,27183],{},[1146,27180,27181],{},[1149,27182,15880],{},[1153,27184,15880],{"encoding":1155},[6534,27186,27187,27190,27207],{},[6650,27188,27189],{},"počet neshodných produktů ve výběru (např. neshodné kusy ze série na výrobní lince)",[6650,27191,27192],{},[1115,27193,27195],{"className":27194},[1137],[1139,27196,27197],{"xmlns":1141},[1143,27198,27199,27205],{},[1146,27200,27201,27203],{},[1149,27202,1816],{},[1149,27204,1110],{},[1153,27206,24607],{"encoding":1155},[6650,27208,27209],{},[1115,27210,27212],{"className":27211},[1137],[1139,27213,27214],{"xmlns":1141},[1143,27215,27216,27220],{},[1146,27217,27218],{},[1149,27219,1110],{},[1153,27221,1110],{"encoding":1155},[2019,27223,25112,27225],{"id":27224},"diagram-cc",[1115,27226,27228],{"className":27227},[1137],[1139,27229,27230],{"xmlns":1141},[1143,27231,27232,27236],{},[1146,27233,27234],{},[1149,27235,8130],{},[1153,27237,8130],{"encoding":1155},[1110,27239,27240,27241,27259,27260,27273,27274,27299,27300,27313],{},"Regulovanou veličinou ",[1115,27242,27244],{"className":27243},[1137],[1139,27245,27246],{"xmlns":1141},[1143,27247,27248,27256],{},[1146,27249,27250],{},[1201,27251,27252,27254],{},[1149,27253,8130],{},[1149,27255,1207],{},[1153,27257,27258],{"encoding":1155},"c_i"," je počet neshod na produktech v ",[1115,27261,27263],{"className":27262},[1137],[1139,27264,27265],{"xmlns":1141},[1143,27266,27267,27271],{},[1146,27268,27269],{},[1149,27270,1207],{},[1153,27272,1207],{"encoding":1155},"-té logické podskupině, ",[1115,27275,27277],{"className":27276},[1137],[1139,27278,27279],{"xmlns":1141},[1143,27280,27281,27297],{},[1146,27282,27283,27285,27287,27289,27291,27293,27295],{},[1149,27284,1207],{},[1193,27286,1281],{},[1230,27288,1525],{},[1193,27290,1503],{"separator":1121},[1193,27292,1530],{},[1193,27294,1503],{"separator":1121},[1149,27296,11631],{},[1153,27298,25325],{"encoding":1155},"; v každé podskupině je stejný počet ",[1115,27301,27303],{"className":27302},[1137],[1139,27304,27305],{"xmlns":1141},[1143,27306,27307,27311],{},[1146,27308,27309],{},[1149,27310,1816],{},[1153,27312,1816],{"encoding":1155}," 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.",[1103,27315,27317,27324],{"className":27316,"dataCallout":2932},[1106,2931],[1110,27318,27320,27323],{"className":27319},[1113],[1115,27321],{"className":27322,"ariaHidden":1121},[1118,2939,1120],"Příklad: bodové vady na pásech látky",[1110,27325,27326,27327,27344,27345,1236],{},"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 ",[1115,27328,27330],{"className":27329},[1137],[1139,27331,27332],{"xmlns":1141},[1143,27333,27334,27342],{},[1146,27335,27336],{},[1201,27337,27338,27340],{},[1149,27339,8130],{},[1149,27341,1207],{},[1153,27343,27258],{"encoding":1155},". Sestrojte regulační diagram ",[1115,27346,27348],{"className":27347},[1137],[1139,27349,27350],{"xmlns":1141},[1143,27351,27352,27356],{},[1146,27353,27354],{},[1149,27355,8130],{},[1153,27357,8130],{"encoding":1155},[2035,27359,27361],{"className":2037,"code":27360,"language":71,"meta":2039,"style":2039},"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",[1332,27362,27363,27453,27457,27482],{"__ignoreMap":2039},[1115,27364,27365,27367,27369,27371,27373,27375,27377,27379,27381,27383,27385,27387,27389,27391,27393,27395,27397,27399,27401,27403,27405,27407,27409,27411,27413,27415,27417,27419,27421,27423,27425,27427,27429,27431,27433,27435,27437,27439,27441,27443,27445,27447,27449,27451],{"class":2044,"line":10},[1115,27366,27258],{"class":2047},[1115,27368,2052],{"class":2051},[1115,27370,2056],{"class":2055},[1115,27372,1199],{"class":2059},[1115,27374,2538],{"class":2062},[1115,27376,1503],{"class":2051},[1115,27378,9031],{"class":2062},[1115,27380,1503],{"class":2051},[1115,27382,2067],{"class":2062},[1115,27384,1503],{"class":2051},[1115,27386,2082],{"class":2062},[1115,27388,1503],{"class":2051},[1115,27390,14336],{"class":2062},[1115,27392,1503],{"class":2051},[1115,27394,2087],{"class":2062},[1115,27396,1503],{"class":2051},[1115,27398,2067],{"class":2062},[1115,27400,1503],{"class":2051},[1115,27402,14336],{"class":2062},[1115,27404,1503],{"class":2051},[1115,27406,2077],{"class":2062},[1115,27408,1503],{"class":2051},[1115,27410,2077],{"class":2062},[1115,27412,1503],{"class":2051},[1115,27414,2087],{"class":2062},[1115,27416,1503],{"class":2051},[1115,27418,2072],{"class":2062},[1115,27420,1503],{"class":2051},[1115,27422,2072],{"class":2062},[1115,27424,1503],{"class":2051},[1115,27426,2072],{"class":2062},[1115,27428,1503],{"class":2051},[1115,27430,9031],{"class":2062},[1115,27432,1503],{"class":2051},[1115,27434,2087],{"class":2062},[1115,27436,1503],{"class":2051},[1115,27438,2072],{"class":2062},[1115,27440,1503],{"class":2051},[1115,27442,9031],{"class":2062},[1115,27444,1503],{"class":2051},[1115,27446,2082],{"class":2062},[1115,27448,1503],{"class":2051},[1115,27450,2087],{"class":2062},[1115,27452,2090],{"class":2059},[1115,27454,27455],{"class":2044,"line":27},[1115,27456,5548],{"emptyLinePlaceholder":5547},[1115,27458,27459,27462,27464,27467,27469,27471,27473,27475,27477,27480],{"class":2044,"line":148},[1115,27460,27461],{"class":2047},"q_c",[1115,27463,2052],{"class":2051},[1115,27465,27466],{"class":2055}," qcc",[1115,27468,1199],{"class":2059},[1115,27470,27258],{"class":2047},[1115,27472,1503],{"class":2051},[1115,27474,16574],{"class":2047},[1115,27476,2510],{"class":2051},[1115,27478,27479],{"class":2575}," \"c\"",[1115,27481,2090],{"class":2059},[1115,27483,27484,27486,27488,27490],{"class":2044,"line":111},[1115,27485,2157],{"class":2055},[1115,27487,1199],{"class":2059},[1115,27489,27461],{"class":2047},[1115,27491,2090],{"class":2059},[2035,27493,27496],{"className":27494,"code":27495,"language":2169,"meta":2039},[2167],"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",[1332,27497,27495],{"__ignoreMap":2039},[1110,27499,27500,27501,27530,27531,27554,27555,27577],{},"Průměrný počet vad na pás je ",[1115,27502,27504],{"className":27503},[1137],[1139,27505,27506],{"xmlns":1141},[1143,27507,27508,27527],{},[1146,27509,27510,27512,27514,27516,27522,27524],{},[1149,27511,24642],{},[1149,27513,25966],{},[1193,27515,1281],{},[1214,27517,27518,27520],{"accent":1121},[1149,27519,8130],{},[1193,27521,15814],{},[1193,27523,1281],{},[1230,27525,27526],{},"3,4",[1153,27528,27529],{"encoding":1155},"CL = \\bar{c} = 3{,}4",", horní mez ",[1115,27532,27534],{"className":27533},[1137],[1139,27535,27536],{"xmlns":1141},[1143,27537,27538,27551],{},[1146,27539,27540,27542,27544,27546,27548],{},[1149,27541,25992],{},[1149,27543,24642],{},[1149,27545,25966],{},[1193,27547,1281],{},[1230,27549,27550],{},"8,93",[1153,27552,27553],{"encoding":1155},"UCL = 8{,}93"," a dolní mez ",[1115,27556,27558],{"className":27557},[1137],[1139,27559,27560],{"xmlns":1141},[1143,27561,27562,27574],{},[1146,27563,27564,27566,27568,27570,27572],{},[1149,27565,25966],{},[1149,27567,24642],{},[1149,27569,25966],{},[1193,27571,1281],{},[1230,27573,1597],{},[1153,27575,27576],{"encoding":1155},"LCL = 0",". Žádný pás meze nepřekračuje — proces je zvládnutý.",[1110,27579,27580],{},[1864,27581],{"alt":27582,"className":27583,"src":27584},"mask-rd-priklad2-c",[1387,1868],"\u002Fwiki-assets\u002Fmask-rd-priklad2-c.png",[2019,27586,25112,27588],{"id":27587},"diagram-uu",[1115,27589,27591],{"className":27590},[1137],[1139,27592,27593],{"xmlns":1141},[1143,27594,27595,27599],{},[1146,27596,27597],{},[1149,27598,15880],{},[1153,27600,15880],{"encoding":1155},[1110,27602,27240,27603,27637,27638,27656],{},[1115,27604,27606],{"className":27605},[1137],[1139,27607,27608],{"xmlns":1141},[1143,27609,27610,27634],{},[1146,27611,27612,27618,27620,27626,27628],{},[1201,27613,27614,27616],{},[1149,27615,15880],{},[1149,27617,1207],{},[1193,27619,1281],{},[1201,27621,27622,27624],{},[1149,27623,8130],{},[1149,27625,1207],{},[1149,27627,5731],{"mathvariant":1854},[1201,27629,27630,27632],{},[1149,27631,1816],{},[1149,27633,1207],{},[1153,27635,27636],{"encoding":1155},"u_i = c_i\u002Fn_i"," je průměrný počet neshod přepočítaný na jeden produkt z logické podskupiny; rozsah podskupin ",[1115,27639,27641],{"className":27640},[1137],[1139,27642,27643],{"xmlns":1141},[1143,27644,27645,27653],{},[1146,27646,27647],{},[1201,27648,27649,27651],{},[1149,27650,1816],{},[1149,27652,1207],{},[1153,27654,27655],{"encoding":1155},"n_i"," není konstantní, a proto se bod od bodu mění i meze.",[1110,27658,27659,27660,27663],{},"Za ",[1332,27661,27662],{},"sizes"," se dosadí vektor rozsahů jednotlivých logických podskupin, resp. rozměr jejich jednotek:",[2035,27665,27667],{"className":2037,"code":27666,"language":71,"meta":2039,"style":2039},"data \u003C- read.table(\"3_4.txt\", header = TRUE) # počty suků a rozměry prken\nqcc(data[, 1], type = \"u\", sizes = data[, 2])\n",[1332,27668,27669,27695],{"__ignoreMap":2039},[1115,27670,27671,27673,27675,27677,27679,27682,27684,27686,27688,27690,27692],{"class":2044,"line":10},[1115,27672,5440],{"class":2047},[1115,27674,2052],{"class":2051},[1115,27676,5445],{"class":2055},[1115,27678,1199],{"class":2059},[1115,27680,27681],{"class":2575},"\"3_4.txt\"",[1115,27683,1503],{"class":2051},[1115,27685,5455],{"class":2047},[1115,27687,2510],{"class":2051},[1115,27689,5460],{"class":2062},[1115,27691,16381],{"class":2059},[1115,27693,27694],{"class":16384},"# počty suků a rozměry prken\n",[1115,27696,27697,27699,27701,27703,27705,27707,27709,27711,27713,27715,27717,27720,27722,27725,27727,27729,27731,27733,27735],{"class":2044,"line":27},[1115,27698,360],{"class":2055},[1115,27700,1199],{"class":2059},[1115,27702,5440],{"class":2047},[1115,27704,12546],{"class":2059},[1115,27706,1503],{"class":2051},[1115,27708,9031],{"class":2062},[1115,27710,12563],{"class":2059},[1115,27712,1503],{"class":2051},[1115,27714,16574],{"class":2047},[1115,27716,2510],{"class":2051},[1115,27718,27719],{"class":2575}," \"u\"",[1115,27721,1503],{"class":2051},[1115,27723,27724],{"class":2047}," sizes",[1115,27726,2510],{"class":2051},[1115,27728,5500],{"class":2047},[1115,27730,12546],{"class":2059},[1115,27732,1503],{"class":2051},[1115,27734,2067],{"class":2062},[1115,27736,27737],{"class":2059},"])\n",[2019,27739,25112,27741],{"id":27740},"diagram-npnp",[1115,27742,27744],{"className":27743},[1137],[1139,27745,27746],{"xmlns":1141},[1143,27747,27748,27754],{},[1146,27749,27750,27752],{},[1149,27751,1816],{},[1149,27753,1110],{},[1153,27755,24607],{"encoding":1155},[1110,27757,27758,27759,11154,27774,27787],{},"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 ",[1115,27760,27762],{"className":27761},[1137],[1139,27763,27764],{"xmlns":1141},[1143,27765,27766,27772],{},[1146,27767,27768,27770],{},[1149,27769,1816],{},[1149,27771,1110],{},[1153,27773,24607],{"encoding":1155},[1115,27775,27777],{"className":27776},[1137],[1139,27778,27779],{"xmlns":1141},[1143,27780,27781,27785],{},[1146,27782,27783],{},[1149,27784,1110],{},[1153,27786,1110],{"encoding":1155}," je pravděpodobnost, že vyrobený produkt je neshodný.",[1110,27789,27790,27791,1902],{},"Pro konstantní rozsah ",[1115,27792,27794],{"className":27793},[1137],[1139,27795,27796],{"xmlns":1141},[1143,27797,27798,27802],{},[1146,27799,27800],{},[1149,27801,1816],{},[1153,27803,1816],{"encoding":1155},[2035,27805,27807],{"className":2037,"code":27806,"language":71,"meta":2039,"style":2039},"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",[1332,27808,27809,27835],{"__ignoreMap":2039},[1115,27810,27811,27813,27815,27817,27819,27822,27824,27826,27828,27830,27832],{"class":2044,"line":10},[1115,27812,5440],{"class":2047},[1115,27814,2052],{"class":2051},[1115,27816,5445],{"class":2055},[1115,27818,1199],{"class":2059},[1115,27820,27821],{"class":2575},"\"3_7.txt\"",[1115,27823,1503],{"class":2051},[1115,27825,5455],{"class":2047},[1115,27827,2510],{"class":2051},[1115,27829,5460],{"class":2062},[1115,27831,16381],{"class":2059},[1115,27833,27834],{"class":16384},"# počty vadných tabletů v sériích po 100 kusech\n",[1115,27836,27837,27839,27841,27843,27845,27847,27849,27851,27853,27855,27857,27860,27862,27864,27866,27868],{"class":2044,"line":27},[1115,27838,360],{"class":2055},[1115,27840,1199],{"class":2059},[1115,27842,5440],{"class":2047},[1115,27844,12546],{"class":2059},[1115,27846,1503],{"class":2051},[1115,27848,9031],{"class":2062},[1115,27850,12563],{"class":2059},[1115,27852,1503],{"class":2051},[1115,27854,16574],{"class":2047},[1115,27856,2510],{"class":2051},[1115,27858,27859],{"class":2575}," \"np\"",[1115,27861,1503],{"class":2051},[1115,27863,27724],{"class":2047},[1115,27865,2510],{"class":2051},[1115,27867,19687],{"class":2062},[1115,27869,2090],{"class":2059},[2019,27871,25112,27873],{"id":27872},"diagram-pp",[1115,27874,27876],{"className":27875},[1137],[1139,27877,27878],{"xmlns":1141},[1143,27879,27880,27884],{},[1146,27881,27882],{},[1149,27883,1110],{},[1153,27885,1110],{"encoding":1155},[1110,27887,27888,27889,27925],{},"Regulovanou veličinou je počet neshodných produktů v logické podskupině přepočtený na jednotku, ",[1115,27890,27892],{"className":27891},[1137],[1139,27893,27894],{"xmlns":1141},[1143,27895,27896,27922],{},[1146,27897,27898,27904,27906,27908,27914,27916],{},[1201,27899,27900,27902],{},[1149,27901,1110],{},[1149,27903,1207],{},[1193,27905,1281],{},[1149,27907,1816],{},[1201,27909,27910,27912],{},[1149,27911,1110],{},[1149,27913,1207],{},[1149,27915,5731],{"mathvariant":1854},[1201,27917,27918,27920],{},[1149,27919,1816],{},[1149,27921,1207],{},[1153,27923,27924],{"encoding":1155},"p_i = np_i\u002Fn_i","; rozsahy podskupin nemusí být konstantní.",[1110,27927,27659,27928,27930],{},[1332,27929,27662],{}," se dosadí vektor rozsahů logických podskupin:",[2035,27932,27934],{"className":2037,"code":27933,"language":71,"meta":2039,"style":2039},"data \u003C- read.table(\"3_6.txt\", header = TRUE) # počty vadných tabletů a rozsahy sérií\nqcc(data[, 1], type = \"p\", sizes = data[, 2])\n",[1332,27935,27936,27962],{"__ignoreMap":2039},[1115,27937,27938,27940,27942,27944,27946,27949,27951,27953,27955,27957,27959],{"class":2044,"line":10},[1115,27939,5440],{"class":2047},[1115,27941,2052],{"class":2051},[1115,27943,5445],{"class":2055},[1115,27945,1199],{"class":2059},[1115,27947,27948],{"class":2575},"\"3_6.txt\"",[1115,27950,1503],{"class":2051},[1115,27952,5455],{"class":2047},[1115,27954,2510],{"class":2051},[1115,27956,5460],{"class":2062},[1115,27958,16381],{"class":2059},[1115,27960,27961],{"class":16384},"# počty vadných tabletů a rozsahy sérií\n",[1115,27963,27964,27966,27968,27970,27972,27974,27976,27978,27980,27982,27984,27987,27989,27991,27993,27995,27997,27999,28001],{"class":2044,"line":27},[1115,27965,360],{"class":2055},[1115,27967,1199],{"class":2059},[1115,27969,5440],{"class":2047},[1115,27971,12546],{"class":2059},[1115,27973,1503],{"class":2051},[1115,27975,9031],{"class":2062},[1115,27977,12563],{"class":2059},[1115,27979,1503],{"class":2051},[1115,27981,16574],{"class":2047},[1115,27983,2510],{"class":2051},[1115,27985,27986],{"class":2575}," \"p\"",[1115,27988,1503],{"class":2051},[1115,27990,27724],{"class":2047},[1115,27992,2510],{"class":2051},[1115,27994,5500],{"class":2047},[1115,27996,12546],{"class":2059},[1115,27998,1503],{"class":2051},[1115,28000,2067],{"class":2062},[1115,28002,27737],{"class":2059},[1377,28004,28006],{"id":28005},"indexy-způsobilosti","Indexy způsobilosti",[1110,28008,28009,28010,28029,28030,28048],{},"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 ",[1115,28011,28013],{"className":28012},[1137],[1139,28014,28015],{"xmlns":1141},[1143,28016,28017,28026],{},[1146,28018,28019,28021,28024],{},[1149,28020,25966],{},[1149,28022,28023],{},"S",[1149,28025,25966],{},[1153,28027,28028],{"encoding":1155},"LSL"," a horní meze ",[1115,28031,28033],{"className":28032},[1137],[1139,28034,28035],{"xmlns":1141},[1143,28036,28037,28045],{},[1146,28038,28039,28041,28043],{},[1149,28040,25992],{},[1149,28042,28023],{},[1149,28044,25966],{},[1153,28046,28047],{"encoding":1155},"USL",". Způsobilost se zkoumá až pro proces, který je podle regulačních diagramů statisticky zvládnutý (třetí fáze regulace).",[2019,28050,28052,28069],{"id":28051},"cpc_p-index-způsobilosti",[1115,28053,28055],{"className":28054},[1137],[1139,28056,28057],{"xmlns":1141},[1143,28058,28059,28067],{},[1146,28060,28061],{},[1201,28062,28063,28065],{},[1149,28064,24642],{},[1149,28066,1110],{},[1153,28068,24647],{"encoding":1155}," — index způsobilosti",[1110,28071,28072,28073,1902],{},"Podíl mezi délkou tolerančního intervalu a délkou intervalu, ve kterém by za normálního rozdělení mělo ležet skoro všech 99,73 % hodnot znaku, tedy ",[1115,28074,28076],{"className":28075},[1137],[1139,28077,28078],{"xmlns":1141},[1143,28079,28080,28086],{},[1146,28081,28082,28084],{},[1230,28083,8365],{},[1149,28085,11271],{},[1153,28087,28088],{"encoding":1155},"6\\sigma",[1115,28090,28092],{"className":28091},[1137],[1139,28093,28094],{"xmlns":1141,"display":1796},[1143,28095,28096,28132],{},[1146,28097,28098,28104,28106,28130],{},[1201,28099,28100,28102],{},[1149,28101,24642],{},[1149,28103,1110],{},[1193,28105,1281],{},[3546,28107,28108,28124],{},[1146,28109,28110,28112,28114,28116,28118,28120,28122],{},[1149,28111,25992],{},[1149,28113,28023],{},[1149,28115,25966],{},[1193,28117,1210],{},[1149,28119,25966],{},[1149,28121,28023],{},[1149,28123,25966],{},[1146,28125,28126,28128],{},[1230,28127,8365],{},[1149,28129,11271],{},[1149,28131,1236],{"mathvariant":1854},[1153,28133,28134],{"encoding":1155},"C_p = \\frac{USL - LSL}{6\\sigma}.",[1110,28136,28137,28154,28155,28168,28169,1236],{},[1115,28138,28140],{"className":28139},[1137],[1139,28141,28142],{"xmlns":1141},[1143,28143,28144,28152],{},[1146,28145,28146],{},[1201,28147,28148,28150],{},[1149,28149,24642],{},[1149,28151,1110],{},[1153,28153,24647],{"encoding":1155}," srovnává jen délky, nevšímá si, kde uprostřed tolerance proces leží — centrovaný i silně vychýlený proces se stejným ",[1115,28156,28158],{"className":28157},[1137],[1139,28159,28160],{"xmlns":1141},[1143,28161,28162,28166],{},[1146,28163,28164],{},[1149,28165,11271],{},[1153,28167,11303],{"encoding":1155}," mají stejné ",[1115,28170,28172],{"className":28171},[1137],[1139,28173,28174],{"xmlns":1141},[1143,28175,28176,28184],{},[1146,28177,28178],{},[1201,28179,28180,28182],{},[1149,28181,24642],{},[1149,28183,1110],{},[1153,28185,24647],{"encoding":1155},[1110,28187,28188],{},"Doplňkové charakteristiky využití tolerančního intervalu:",[1124,28190,28191,28225,28313],{},[1127,28192,28193,3096,28196,28224],{},[1130,28194,28195],{},"míra využití tolerančního intervalu",[1115,28197,28199],{"className":28198},[1137],[1139,28200,28201],{"xmlns":1141},[1143,28202,28203,28221],{},[1146,28204,28205,28217,28219],{},[3310,28206,28207],{"scriptlevel":1597,"displaystyle":1121},[3546,28208,28209,28211],{},[1230,28210,16169],{},[1201,28212,28213,28215],{},[1149,28214,24642],{},[1149,28216,1110],{},[2201,28218,2203],{},[1149,28220,16176],{"mathvariant":1854},[1153,28222,28223],{"encoding":1155},"\\dfrac{100}{C_p}\\,\\%"," — na kolik procent je toleranční interval využíván sledovaným znakem,",[1127,28226,28227,28230,28231,28248,28249,1405,28281,1503],{},[1130,28228,28229],{},"robustnost procesu",": rezerva, kterou máme v tolerančních mezích, než index ",[1115,28232,28234],{"className":28233},[1137],[1139,28235,28236],{"xmlns":1141},[1143,28237,28238,28246],{},[1146,28239,28240],{},[1201,28241,28242,28244],{},[1149,28243,24642],{},[1149,28245,1110],{},[1153,28247,24647],{"encoding":1155}," nabyde hodnotu 1 — rovná se menší hodnotě z výrazů ",[1115,28250,28252],{"className":28251},[1137],[1139,28253,28254],{"xmlns":1141},[1143,28255,28256,28278],{},[1146,28257,28258,28260,28262,28264,28266,28268,28270,28272,28274,28276],{},[1149,28259,25992],{},[1149,28261,28023],{},[1149,28263,25966],{},[1193,28265,1210],{},[1193,28267,1199],{"stretchy":1198},[1149,28269,11264],{},[1193,28271,1924],{},[1230,28273,8010],{},[1149,28275,11271],{},[1193,28277,1228],{"stretchy":1198},[1153,28279,28280],{"encoding":1155},"USL-(\\mu+3\\sigma)",[1115,28282,28284],{"className":28283},[1137],[1139,28285,28286],{"xmlns":1141},[1143,28287,28288,28310],{},[1146,28289,28290,28292,28294,28296,28298,28300,28302,28304,28306,28308],{},[1193,28291,1199],{"stretchy":1198},[1149,28293,11264],{},[1193,28295,1210],{},[1230,28297,8010],{},[1149,28299,11271],{},[1193,28301,1228],{"stretchy":1198},[1193,28303,1210],{},[1149,28305,25966],{},[1149,28307,28023],{},[1149,28309,25966],{},[1153,28311,28312],{"encoding":1155},"(\\mu-3\\sigma)-LSL",[1127,28314,28315,3096,28318,11154,28358,28372],{},[1130,28316,28317],{},"podíl zmetků",[1115,28319,28321],{"className":28320},[1137],[1139,28322,28323],{"xmlns":1141},[1143,28324,28325,28355],{},[1146,28326,28327,28334,28336,28338,28341,28343,28345,28347,28353],{},[1201,28328,28329,28331],{},[1149,28330,11102],{},[1149,28332,28333],{},"z",[1193,28335,1281],{},[1230,28337,1232],{},[1149,28339,28340],{"mathvariant":1854},"Φ",[1193,28342,1199],{"stretchy":1198},[1193,28344,1210],{},[1230,28346,8010],{},[1201,28348,28349,28351],{},[1149,28350,24642],{},[1149,28352,1110],{},[1193,28354,1228],{"stretchy":1198},[1153,28356,28357],{"encoding":1155},"P_z = 2\\Phi(-3C_p)",[1115,28359,28361],{"className":28360},[1137],[1139,28362,28363],{"xmlns":1141},[1143,28364,28365,28369],{},[1146,28366,28367],{},[1149,28368,28340],{"mathvariant":1854},[1153,28370,28371],{"encoding":1155},"\\Phi"," je distribuční funkce normovaného normálního rozdělení.",[2019,28374,28376,28397],{"id":28375},"cpkc_pk-index-způsobilosti-s-ohledem-na-vychýlení",[1115,28377,28379],{"className":28378},[1137],[1139,28380,28381],{"xmlns":1141},[1143,28382,28383,28395],{},[1146,28384,28385],{},[1201,28386,28387,28389],{},[1149,28388,24642],{},[1146,28390,28391,28393],{},[1149,28392,1110],{},[1149,28394,11631],{},[1153,28396,24669],{"encoding":1155}," — index způsobilosti s ohledem na vychýlení",[1110,28399,28400],{},"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:",[1115,28402,28404],{"className":28403},[1137],[1139,28405,28406],{"xmlns":1141,"display":1796},[1143,28407,28408,28478],{},[1146,28409,28410,28420,28422,28424,28426,28476],{},[1201,28411,28412,28414],{},[1149,28413,24642],{},[1146,28415,28416,28418],{},[1149,28417,1110],{},[1149,28419,11631],{},[1193,28421,1281],{},[1149,28423,1848],{},[1193,28425,1851],{},[1146,28427,28428,28430,28450,28452,28454,28474],{},[1193,28429,1199],{"fence":1121},[3546,28431,28432,28444],{},[1146,28433,28434,28436,28438,28440,28442],{},[1149,28435,25992],{},[1149,28437,28023],{},[1149,28439,25966],{},[1193,28441,1210],{},[1149,28443,11264],{},[1146,28445,28446,28448],{},[1230,28447,8010],{},[1149,28449,11271],{},[1193,28451,1503],{"separator":1121},[2201,28453,15670],{},[3546,28455,28456,28468],{},[1146,28457,28458,28460,28462,28464,28466],{},[1149,28459,11264],{},[1193,28461,1210],{},[1149,28463,25966],{},[1149,28465,28023],{},[1149,28467,25966],{},[1146,28469,28470,28472],{},[1230,28471,8010],{},[1149,28473,11271],{},[1193,28475,1228],{"fence":1121},[1149,28477,1236],{"mathvariant":1854},[1153,28479,28480],{"encoding":1155},"C_{pk} = \\min\\left(\\frac{USL-\\mu}{3\\sigma},\\ \\frac{\\mu-LSL}{3\\sigma}\\right).",[1110,28482,28483,28484,28497,28498,28528,28529,28550,28551,1236],{},"Vyjde-li některý z obou podílů záporný, položí se roven nule; to nastane, když střední hodnota ",[1115,28485,28487],{"className":28486},[1137],[1139,28488,28489],{"xmlns":1141},[1143,28490,28491,28495],{},[1146,28492,28493],{},[1149,28494,11264],{},[1153,28496,13166],{"encoding":1155}," leží mimo toleranční interval, a proces pak není pod statistickou kontrolou. U centrovaného procesu jsou oba podíly stejné a ",[1115,28499,28501],{"className":28500},[1137],[1139,28502,28503],{"xmlns":1141},[1143,28504,28505,28525],{},[1146,28506,28507,28517,28519],{},[1201,28508,28509,28511],{},[1149,28510,24642],{},[1146,28512,28513,28515],{},[1149,28514,1110],{},[1149,28516,11631],{},[1193,28518,1281],{},[1201,28520,28521,28523],{},[1149,28522,24642],{},[1149,28524,1110],{},[1153,28526,28527],{"encoding":1155},"C_{pk} = C_p","; čím víc je proces vychýlený, tím víc je ",[1115,28530,28532],{"className":28531},[1137],[1139,28533,28534],{"xmlns":1141},[1143,28535,28536,28548],{},[1146,28537,28538],{},[1201,28539,28540,28542],{},[1149,28541,24642],{},[1146,28543,28544,28546],{},[1149,28545,1110],{},[1149,28547,11631],{},[1153,28549,24669],{"encoding":1155}," menší než ",[1115,28552,28554],{"className":28553},[1137],[1139,28555,28556],{"xmlns":1141},[1143,28557,28558,28566],{},[1146,28559,28560],{},[1201,28561,28562,28564],{},[1149,28563,24642],{},[1149,28565,1110],{},[1153,28567,24647],{"encoding":1155},[2019,28569,28571,1405,28592,28615],{"id":28570},"cpmc_pm-a-cpmkc_pmk-indexy-vztažené-k-cíli",[1115,28572,28574],{"className":28573},[1137],[1139,28575,28576],{"xmlns":1141},[1143,28577,28578,28590],{},[1146,28579,28580],{},[1201,28581,28582,28584],{},[1149,28583,24642],{},[1146,28585,28586,28588],{},[1149,28587,1110],{},[1149,28589,8865],{},[1153,28591,24691],{"encoding":1155},[1115,28593,28595],{"className":28594},[1137],[1139,28596,28597],{"xmlns":1141},[1143,28598,28599,28613],{},[1146,28600,28601],{},[1201,28602,28603,28605],{},[1149,28604,24642],{},[1146,28606,28607,28609,28611],{},[1149,28608,1110],{},[1149,28610,8865],{},[1149,28612,11631],{},[1153,28614,24715],{"encoding":1155}," — indexy vztažené k cíli",[1110,28617,28618,28619,28632,28633,28646,28647,28690,28691,1902],{},"Pokud má proces zadaný cílový střed ",[1115,28620,28622],{"className":28621},[1137],[1139,28623,28624],{"xmlns":1141},[1143,28625,28626,28630],{},[1146,28627,28628],{},[1149,28629,11474],{},[1153,28631,11474],{"encoding":1155}," (ne nutně střed tolerance), nahradí se ",[1115,28634,28636],{"className":28635},[1137],[1139,28637,28638],{"xmlns":1141},[1143,28639,28640,28644],{},[1146,28641,28642],{},[1149,28643,11271],{},[1153,28645,11303],{"encoding":1155}," odmocninou ze střední čtvercové odchylky od cíle ",[1115,28648,28650],{"className":28649},[1137],[1139,28651,28652],{"xmlns":1141},[1143,28653,28654,28687],{},[1146,28655,28656,28659,28661],{},[1149,28657,28658],{},"τ",[1193,28660,1281],{},[1283,28662,28663],{},[1146,28664,28665,28671,28673,28675,28677,28679,28681],{},[1224,28666,28667,28669],{},[1149,28668,11271],{},[1230,28670,1232],{},[1193,28672,1924],{},[1193,28674,1199],{"stretchy":1198},[1149,28676,11264],{},[1193,28678,1210],{},[1149,28680,11474],{},[1224,28682,28683,28685],{},[1193,28684,1228],{"stretchy":1198},[1230,28686,1232],{},[1153,28688,28689],{"encoding":1155},"\\tau = \\sqrt{\\sigma^2+(\\mu-T)^2}",", která trestá i vychýlení od ",[1115,28692,28694],{"className":28693},[1137],[1139,28695,28696],{"xmlns":1141},[1143,28697,28698,28702],{},[1146,28699,28700],{},[1149,28701,11474],{},[1153,28703,11474],{"encoding":1155},[1115,28705,28707],{"className":28706},[1137],[1139,28708,28709],{"xmlns":1141,"display":1796},[1143,28710,28711,28823],{},[1146,28712,28713,28723,28725,28749,28751,28753,28765,28767,28769,28771,28821],{},[1201,28714,28715,28717],{},[1149,28716,24642],{},[1146,28718,28719,28721],{},[1149,28720,1110],{},[1149,28722,8865],{},[1193,28724,1281],{},[3546,28726,28727,28743],{},[1146,28728,28729,28731,28733,28735,28737,28739,28741],{},[1149,28730,25992],{},[1149,28732,28023],{},[1149,28734,25966],{},[1193,28736,1210],{},[1149,28738,25966],{},[1149,28740,28023],{},[1149,28742,25966],{},[1146,28744,28745,28747],{},[1230,28746,8365],{},[1149,28748,28658],{},[1193,28750,1503],{"separator":1121},[1936,28752],{"width":1938},[1201,28754,28755,28757],{},[1149,28756,24642],{},[1146,28758,28759,28761,28763],{},[1149,28760,1110],{},[1149,28762,8865],{},[1149,28764,11631],{},[1193,28766,1281],{},[1149,28768,1848],{},[1193,28770,1851],{},[1146,28772,28773,28775,28795,28797,28799,28819],{},[1193,28774,1199],{"fence":1121},[3546,28776,28777,28789],{},[1146,28778,28779,28781,28783,28785,28787],{},[1149,28780,25992],{},[1149,28782,28023],{},[1149,28784,25966],{},[1193,28786,1210],{},[1149,28788,11264],{},[1146,28790,28791,28793],{},[1230,28792,8010],{},[1149,28794,28658],{},[1193,28796,1503],{"separator":1121},[2201,28798,15670],{},[3546,28800,28801,28813],{},[1146,28802,28803,28805,28807,28809,28811],{},[1149,28804,11264],{},[1193,28806,1210],{},[1149,28808,25966],{},[1149,28810,28023],{},[1149,28812,25966],{},[1146,28814,28815,28817],{},[1230,28816,8010],{},[1149,28818,28658],{},[1193,28820,1228],{"fence":1121},[1149,28822,1236],{"mathvariant":1854},[1153,28824,28825],{"encoding":1155},"C_{pm} = \\frac{USL-LSL}{6\\tau}, \\qquad C_{pmk} = \\min\\left(\\frac{USL-\\mu}{3\\tau},\\ \\frac{\\mu-LSL}{3\\tau}\\right).",[2019,28827,28829],{"id":28828},"interpretace","Interpretace",[6528,28831,28832,28859],{},[6531,28833,28834],{},[6534,28835,28836,28856],{},[6537,28837,28838,28839],{},"Hodnota ",[1115,28840,28842],{"className":28841},[1137],[1139,28843,28844],{"xmlns":1141},[1143,28845,28846,28854],{},[1146,28847,28848],{},[1201,28849,28850,28852],{},[1149,28851,24642],{},[1149,28853,1110],{},[1153,28855,24647],{"encoding":1155},[6537,28857,28858],{},"Způsobilost procesu",[6645,28860,28861,28890,28933],{},[6534,28862,28863,28887],{},[6650,28864,28865],{},[1115,28866,28868],{"className":28867},[1137],[1139,28869,28870],{"xmlns":1141},[1143,28871,28872,28884],{},[1146,28873,28874,28880,28882],{},[1201,28875,28876,28878],{},[1149,28877,24642],{},[1149,28879,1110],{},[1193,28881,5343],{},[1230,28883,1525],{},[1153,28885,28886],{"encoding":1155},"C_p \u003C 1",[6650,28888,28889],{},"dosahovaná přesnost je menší než předepsaná — proces je nezpůsobilý",[6534,28891,28892,28916],{},[6650,28893,28894],{},[1115,28895,28897],{"className":28896},[1137],[1139,28898,28899],{"xmlns":1141},[1143,28900,28901,28913],{},[1146,28902,28903,28909,28911],{},[1201,28904,28905,28907],{},[1149,28906,24642],{},[1149,28908,1110],{},[1193,28910,1281],{},[1230,28912,1525],{},[1153,28914,28915],{"encoding":1155},"C_p = 1",[6650,28917,28918,28919,28932],{},"dosahovaná přesnost je rovna předepsané — proces je způsobilý, ale sebemenší zvětšení ",[1115,28920,28922],{"className":28921},[1137],[1139,28923,28924],{"xmlns":1141},[1143,28925,28926,28930],{},[1146,28927,28928],{},[1149,28929,11271],{},[1153,28931,11303],{"encoding":1155}," jej posune na nezpůsobilý",[6534,28934,28935,28959],{},[6650,28936,28937],{},[1115,28938,28940],{"className":28939},[1137],[1139,28941,28942],{"xmlns":1141},[1143,28943,28944,28956],{},[1146,28945,28946,28952,28954],{},[1201,28947,28948,28950],{},[1149,28949,24642],{},[1149,28951,1110],{},[1193,28953,5369],{},[1230,28955,1525],{},[1153,28957,28958],{"encoding":1155},"C_p > 1",[6650,28960,28961],{},"dosahovaná přesnost je větší než předepsaná — proces je způsobilý",[1110,28963,28964,28965,28986,28987,1236],{},"U indexu ",[1115,28966,28968],{"className":28967},[1137],[1139,28969,28970],{"xmlns":1141},[1143,28971,28972,28984],{},[1146,28973,28974],{},[1201,28975,28976,28978],{},[1149,28977,24642],{},[1146,28979,28980,28982],{},[1149,28981,1110],{},[1149,28983,11631],{},[1153,28985,24669],{"encoding":1155}," se v praxi požaduje víc než jen hodnota nad 1: s rozvojem technologií roste nárok na rezervu, a běžně se dnes vyžaduje hodnota alespoň ",[1115,28988,28990],{"className":28989},[1137],[1139,28991,28992],{"xmlns":1141},[1143,28993,28994,28999],{},[1146,28995,28996],{},[1230,28997,28998],{},"1,5",[1153,29000,29001],{"encoding":1155},"1{,}5",[1110,29003,29004],{},[1864,29005],{"alt":29006,"className":29007,"src":29008},"mask-rd-cp-panely",[1387,1868],"\u002Fwiki-assets\u002Fmask-rd-cp-panely.png",[1110,29010,29011],{},[1864,29012],{"alt":29013,"className":29014,"src":29015},"mask-rd-cpk-off-centre",[1387,1868],"\u002Fwiki-assets\u002Fmask-rd-cpk-off-centre.png",[2019,29017,29019],{"id":29018},"výpočet-v-r","Výpočet v R",[1110,29021,29022,29023,29026,29027,29030,29031,29034,29035,1405,29052,1348,29069,29072,29073,29086],{},"Indexy způsobilosti počítá ",[1332,29024,29025],{},"process.capability()"," z výstupu regulačního diagramu ",[1332,29028,29029],{},"q","; ",[1332,29032,29033],{},"spec.limits"," jsou toleranční meze ",[1115,29036,29038],{"className":29037},[1137],[1139,29039,29040],{"xmlns":1141},[1143,29041,29042,29050],{},[1146,29043,29044,29046,29048],{},[1149,29045,25966],{},[1149,29047,28023],{},[1149,29049,25966],{},[1153,29051,28028],{"encoding":1155},[1115,29053,29055],{"className":29054},[1137],[1139,29056,29057],{"xmlns":1141},[1143,29058,29059,29067],{},[1146,29060,29061,29063,29065],{},[1149,29062,25992],{},[1149,29064,28023],{},[1149,29066,25966],{},[1153,29068,28047],{"encoding":1155},[1332,29070,29071],{},"target"," cílová hodnota ",[1115,29074,29076],{"className":29075},[1137],[1139,29077,29078],{"xmlns":1141},[1143,29079,29080,29084],{},[1146,29081,29082],{},[1149,29083,11474],{},[1153,29085,11474],{"encoding":1155},". Pro velikost výrobku v mm s tolerančními mezemi 100 a 110 mm a cílovou hodnotou 105 mm:",[2035,29088,29090],{"className":2037,"code":29089,"language":71,"meta":2039,"style":2039},"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",[1332,29091,29092,29102,29125,29140,29162],{"__ignoreMap":2039},[1115,29093,29094,29096,29098,29100],{"class":2044,"line":10},[1115,29095,2698],{"class":2051},[1115,29097,1199],{"class":2059},[1115,29099,360],{"class":2047},[1115,29101,2090],{"class":2059},[1115,29103,29104,29106,29108,29110,29112,29115,29117,29119,29121,29123],{"class":2044,"line":27},[1115,29105,5440],{"class":2047},[1115,29107,2052],{"class":2051},[1115,29109,5445],{"class":2055},[1115,29111,1199],{"class":2059},[1115,29113,29114],{"class":2575},"\"3_8.txt\"",[1115,29116,1503],{"class":2051},[1115,29118,5455],{"class":2047},[1115,29120,2510],{"class":2051},[1115,29122,5460],{"class":2062},[1115,29124,2090],{"class":2059},[1115,29126,29127,29129,29131,29134,29136,29138],{"class":2044,"line":148},[1115,29128,1168],{"class":2047},[1115,29130,2052],{"class":2051},[1115,29132,29133],{"class":2055}," as.matrix",[1115,29135,1199],{"class":2059},[1115,29137,5440],{"class":2047},[1115,29139,2090],{"class":2059},[1115,29141,29142,29144,29146,29148,29150,29152,29154,29156,29158,29160],{"class":2044,"line":111},[1115,29143,29029],{"class":2047},[1115,29145,2052],{"class":2051},[1115,29147,27466],{"class":2055},[1115,29149,1199],{"class":2059},[1115,29151,1168],{"class":2047},[1115,29153,1503],{"class":2051},[1115,29155,16574],{"class":2047},[1115,29157,2510],{"class":2051},[1115,29159,26592],{"class":2575},[1115,29161,2090],{"class":2059},[1115,29163,29164,29167,29169,29171,29173,29176,29178,29180,29182,29184,29186,29188,29190,29192,29195,29197,29200,29202,29205,29207,29209,29211,29213],{"class":2044,"line":96},[1115,29165,29166],{"class":2055},"process.capability",[1115,29168,1199],{"class":2059},[1115,29170,29029],{"class":2047},[1115,29172,1503],{"class":2051},[1115,29174,29175],{"class":2047}," spec.limits",[1115,29177,2510],{"class":2051},[1115,29179,2056],{"class":2055},[1115,29181,1199],{"class":2059},[1115,29183,16169],{"class":2062},[1115,29185,1503],{"class":2051},[1115,29187,18617],{"class":2062},[1115,29189,1228],{"class":2059},[1115,29191,1503],{"class":2051},[1115,29193,29194],{"class":2047}," target",[1115,29196,2510],{"class":2051},[1115,29198,29199],{"class":2062}," 105",[1115,29201,1503],{"class":2051},[1115,29203,29204],{"class":2047}," std.dev",[1115,29206,2510],{"class":2051},[1115,29208,13610],{"class":2055},[1115,29210,1199],{"class":2059},[1115,29212,1168],{"class":2047},[1115,29214,2546],{"class":2059},[1110,29216,29217,29218,1348,29221,1348,29224,1348,29227,1405,29230,29233,29234,1405,29236,29238,29239,29260,29261,29284],{},"Výpis obsahuje řádky ",[1332,29219,29220],{},"Cp",[1332,29222,29223],{},"Cp_l",[1332,29225,29226],{},"Cp_u",[1332,29228,29229],{},"Cp_k",[1332,29231,29232],{},"Cpm"," s hodnotou indexu a 95% intervalem spolehlivosti. ",[1332,29235,29223],{},[1332,29237,29226],{}," jsou dílčí poměry k dolní a horní mezi, jejich minimum je ",[1115,29240,29242],{"className":29241},[1137],[1139,29243,29244],{"xmlns":1141},[1143,29245,29246,29258],{},[1146,29247,29248],{},[1201,29249,29250,29252],{},[1149,29251,24642],{},[1146,29253,29254,29256],{},[1149,29255,1110],{},[1149,29257,11631],{},[1153,29259,24669],{"encoding":1155},". Index ",[1115,29262,29264],{"className":29263},[1137],[1139,29265,29266],{"xmlns":1141},[1143,29267,29268,29282],{},[1146,29269,29270],{},[1201,29271,29272,29274],{},[1149,29273,24642],{},[1146,29275,29276,29278,29280],{},[1149,29277,1110],{},[1149,29279,8865],{},[1149,29281,11631],{},[1153,29283,24715],{"encoding":1155}," a doplňkové charakteristiky se dopočítají ze vzorců výše:",[2035,29286,29288],{"className":2037,"code":29287,"language":71,"meta":2039,"style":2039},"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",[1332,29289,29290,29317,29342,29379,29409,29467,29481,29532],{"__ignoreMap":2039},[1115,29291,29292,29295,29297,29299,29301,29303,29305,29307,29309,29311,29313,29315],{"class":2044,"line":10},[1115,29293,29294],{"class":2047},"mu",[1115,29296,2052],{"class":2051},[1115,29298,13600],{"class":2055},[1115,29300,1199],{"class":2059},[1115,29302,1168],{"class":2047},[1115,29304,16528],{"class":2059},[1115,29306,380],{"class":2047},[1115,29308,2052],{"class":2051},[1115,29310,13610],{"class":2055},[1115,29312,1199],{"class":2059},[1115,29314,1168],{"class":2047},[1115,29316,2090],{"class":2059},[1115,29318,29319,29321,29323,29325,29327,29329,29331,29333,29335,29337,29339],{"class":2044,"line":27},[1115,29320,28028],{"class":2047},[1115,29322,2052],{"class":2051},[1115,29324,19687],{"class":2062},[1115,29326,29030],{"class":2059},[1115,29328,28047],{"class":2047},[1115,29330,2052],{"class":2051},[1115,29332,18617],{"class":2062},[1115,29334,29030],{"class":2059},[1115,29336,11474],{"class":2047},[1115,29338,2052],{"class":2051},[1115,29340,29341],{"class":2062}," 105\n",[1115,29343,29344,29347,29349,29351,29353,29355,29357,29359,29361,29363,29365,29368,29371,29373,29375,29377],{"class":2044,"line":148},[1115,29345,29346],{"class":2047},"tau",[1115,29348,2052],{"class":2051},[1115,29350,8970],{"class":2055},[1115,29352,1199],{"class":2059},[1115,29354,380],{"class":2047},[1115,29356,1220],{"class":2051},[1115,29358,1232],{"class":2062},[1115,29360,3832],{"class":2051},[1115,29362,4053],{"class":2059},[1115,29364,29294],{"class":2047},[1115,29366,29367],{"class":2051}," -",[1115,29369,29370],{"class":2047}," T",[1115,29372,1228],{"class":2059},[1115,29374,1220],{"class":2051},[1115,29376,1232],{"class":2062},[1115,29378,2090],{"class":2059},[1115,29380,29381,29383,29385,29387,29389,29391,29394,29396,29398,29400,29402,29404,29407],{"class":2044,"line":111},[1115,29382,29220],{"class":2047},[1115,29384,2052],{"class":2051},[1115,29386,4053],{"class":2059},[1115,29388,28047],{"class":2047},[1115,29390,29367],{"class":2051},[1115,29392,29393],{"class":2047}," LSL",[1115,29395,8993],{"class":2059},[1115,29397,5731],{"class":2051},[1115,29399,4053],{"class":2059},[1115,29401,8365],{"class":2062},[1115,29403,3957],{"class":2051},[1115,29405,29406],{"class":2047}," sigma",[1115,29408,2090],{"class":2059},[1115,29410,29411,29414,29416,29418,29421,29423,29425,29428,29430,29432,29434,29436,29438,29441,29443,29445,29447,29449,29451,29453,29455,29457,29459,29461,29463,29465],{"class":2044,"line":96},[1115,29412,29413],{"class":2047},"Cpmk",[1115,29415,2052],{"class":2051},[1115,29417,16549],{"class":2055},[1115,29419,29420],{"class":2059},"((",[1115,29422,28047],{"class":2047},[1115,29424,29367],{"class":2051},[1115,29426,29427],{"class":2047}," mu",[1115,29429,8993],{"class":2059},[1115,29431,5731],{"class":2051},[1115,29433,4053],{"class":2059},[1115,29435,8010],{"class":2062},[1115,29437,3957],{"class":2051},[1115,29439,29440],{"class":2047}," tau",[1115,29442,1228],{"class":2059},[1115,29444,1503],{"class":2051},[1115,29446,4053],{"class":2059},[1115,29448,29294],{"class":2047},[1115,29450,29367],{"class":2051},[1115,29452,29393],{"class":2047},[1115,29454,8993],{"class":2059},[1115,29456,5731],{"class":2051},[1115,29458,4053],{"class":2059},[1115,29460,8010],{"class":2062},[1115,29462,3957],{"class":2051},[1115,29464,29440],{"class":2047},[1115,29466,2546],{"class":2059},[1115,29468,29469,29472,29474,29476,29478],{"class":2044,"line":89},[1115,29470,29471],{"class":2047},"miravyuziti",[1115,29473,2052],{"class":2051},[1115,29475,19687],{"class":2062},[1115,29477,4211],{"class":2051},[1115,29479,29480],{"class":2047}," Cp\n",[1115,29482,29483,29486,29488,29490,29492,29494,29496,29498,29500,29502,29504,29506,29508,29510,29512,29514,29516,29518,29520,29522,29524,29526,29528,29530],{"class":2044,"line":82},[1115,29484,29485],{"class":2047},"robustnost",[1115,29487,2052],{"class":2051},[1115,29489,16549],{"class":2055},[1115,29491,1199],{"class":2059},[1115,29493,28047],{"class":2047},[1115,29495,29367],{"class":2051},[1115,29497,4053],{"class":2059},[1115,29499,29294],{"class":2047},[1115,29501,3832],{"class":2051},[1115,29503,2072],{"class":2062},[1115,29505,3957],{"class":2051},[1115,29507,29406],{"class":2047},[1115,29509,1228],{"class":2059},[1115,29511,1503],{"class":2051},[1115,29513,4053],{"class":2059},[1115,29515,29294],{"class":2047},[1115,29517,29367],{"class":2051},[1115,29519,2072],{"class":2062},[1115,29521,3957],{"class":2051},[1115,29523,29406],{"class":2047},[1115,29525,8993],{"class":2059},[1115,29527,9028],{"class":2051},[1115,29529,29393],{"class":2047},[1115,29531,2090],{"class":2059},[1115,29533,29534,29537,29539,29541,29543,29545,29547,29549,29551,29553,29556],{"class":2044,"line":75},[1115,29535,29536],{"class":2047},"Pz",[1115,29538,2052],{"class":2051},[1115,29540,2067],{"class":2062},[1115,29542,3957],{"class":2051},[1115,29544,13720],{"class":2055},[1115,29546,1199],{"class":2059},[1115,29548,9028],{"class":2051},[1115,29550,8010],{"class":2062},[1115,29552,3957],{"class":2051},[1115,29554,29555],{"class":2047}," Cp",[1115,29557,2090],{"class":2059},[1377,29559,5681],{"id":5680},[1124,29561,29562,29565,29625,29716,29782],{},[1127,29563,29564],{},"Počítat indexy způsobilosti pro proces, který není statisticky zvládnutý — způsobilost se zkoumá až ve třetí fázi regulace.",[1127,29566,29567,29568,29585,29586,29603,29604,1236],{},"Posuzovat jen ",[1115,29569,29571],{"className":29570},[1137],[1139,29572,29573],{"xmlns":1141},[1143,29574,29575,29583],{},[1146,29576,29577],{},[1201,29578,29579,29581],{},[1149,29580,24642],{},[1149,29582,1110],{},[1153,29584,24647],{"encoding":1155}," u vychýleného procesu — ",[1115,29587,29589],{"className":29588},[1137],[1139,29590,29591],{"xmlns":1141},[1143,29592,29593,29601],{},[1146,29594,29595],{},[1201,29596,29597,29599],{},[1149,29598,24642],{},[1149,29600,1110],{},[1153,29602,24647],{"encoding":1155}," polohu střední hodnoty nezohledňuje, vychýlení zachytí až ",[1115,29605,29607],{"className":29606},[1137],[1139,29608,29609],{"xmlns":1141},[1143,29610,29611,29623],{},[1146,29612,29613],{},[1201,29614,29615,29617],{},[1149,29616,24642],{},[1146,29618,29619,29621],{},[1149,29620,1110],{},[1149,29622,11631],{},[1153,29624,24669],{"encoding":1155},[1127,29626,29627,29628,29641,29642,29655,29656,29641,29671,29684,29685,29698,29699,29712,29713,29715],{},"Zaměnit diagram ",[1115,29629,29631],{"className":29630},[1137],[1139,29632,29633],{"xmlns":1141},[1143,29634,29635,29639],{},[1146,29636,29637],{},[1149,29638,8130],{},[1153,29640,8130],{"encoding":1155}," s diagramem ",[1115,29643,29645],{"className":29644},[1137],[1139,29646,29647],{"xmlns":1141},[1143,29648,29649,29653],{},[1146,29650,29651],{},[1149,29652,15880],{},[1153,29654,15880],{"encoding":1155}," nebo diagram ",[1115,29657,29659],{"className":29658},[1137],[1139,29660,29661],{"xmlns":1141},[1143,29662,29663,29669],{},[1146,29664,29665,29667],{},[1149,29666,1816],{},[1149,29668,1110],{},[1153,29670,24607],{"encoding":1155},[1115,29672,29674],{"className":29673},[1137],[1139,29675,29676],{"xmlns":1141},[1143,29677,29678,29682],{},[1146,29679,29680],{},[1149,29681,1110],{},[1153,29683,1110],{"encoding":1155}," — při nekonstantním rozsahu podskupin se volí ",[1115,29686,29688],{"className":29687},[1137],[1139,29689,29690],{"xmlns":1141},[1143,29691,29692,29696],{},[1146,29693,29694],{},[1149,29695,15880],{},[1153,29697,15880],{"encoding":1155},", resp. ",[1115,29700,29702],{"className":29701},[1137],[1139,29703,29704],{"xmlns":1141},[1143,29705,29706,29710],{},[1146,29707,29708],{},[1149,29709,1110],{},[1153,29711,1110],{"encoding":1155},", a do ",[1332,29714,27662],{}," se zadává vektor rozsahů.",[1127,29717,29718,29719,29736,29737,29750,29751,29764,29765,1236],{},"Posuzovat diagram ",[1115,29720,29722],{"className":29721},[1137],[1139,29723,29724],{"xmlns":1141},[1143,29725,29726,29734],{},[1146,29727,29728],{},[1214,29729,29730,29732],{"accent":1121},[1149,29731,1168],{},[1193,29733,15814],{},[1153,29735,25411],{"encoding":1155}," dřív než diagram rozpětí — nejprve se určí a stabilizuje diagram ",[1115,29738,29740],{"className":29739},[1137],[1139,29741,29742],{"xmlns":1141},[1143,29743,29744,29748],{},[1146,29745,29746],{},[1149,29747,1257],{},[1153,29749,1257],{"encoding":1155}," (resp. ",[1115,29752,29754],{"className":29753},[1137],[1139,29755,29756],{"xmlns":1141},[1143,29757,29758,29762],{},[1146,29759,29760],{},[1149,29761,4542],{},[1153,29763,4542],{"encoding":1155},"), potom diagram ",[1115,29766,29768],{"className":29767},[1137],[1139,29769,29770],{"xmlns":1141},[1143,29771,29772,29780],{},[1146,29773,29774],{},[1214,29775,29776,29778],{"accent":1121},[1149,29777,1168],{},[1193,29779,15814],{},[1153,29781,25411],{"encoding":1155},[1127,29783,29784],{},"Vyřadit podskupinu jen podle polohy bodu — vyřazuje se až po zjištění a odstranění vymezitelné příčiny.",[1377,29786,5863],{"id":5862},[1124,29788,29789,29794,29799,29805,29810,29815,29820],{},[1127,29790,29791],{},[1384,29792,1390],{"className":29793,"dataFsResolvedFilePath":1388,"href":1389},[1387],[1127,29795,29796],{},[1384,29797,886],{"className":29798,"dataFsResolvedFilePath":5882,"href":5883},[1387],[1127,29800,29801],{},[1384,29802,29804],{"className":29803,"dataFsResolvedFilePath":5292,"href":5293},[1387],"nahodne-veliciny-a-rozdeleni",[1127,29806,29807],{},[1384,29808,141],{"className":29809,"dataFsResolvedFilePath":5302,"href":5303},[1387],[1127,29811,29812],{},[1384,29813,15444],{"className":29814,"dataFsResolvedFilePath":11005,"href":11006},[1387],[1127,29816,29817],{},[1384,29818,716],{"className":29819,"dataFsResolvedFilePath":5896,"href":5897},[1387],[1127,29821,29822],{},[1384,29823,5914],{"className":29824,"dataFsResolvedFilePath":5912,"href":5913},[1387],[1377,29826,5917],{"id":934},[1110,29828,5920,29829,5925],{},[5922,29830,5924],{},[1110,29832,29833,29834,29837],{},"MONTGOMERY, D. C. ",[5922,29835,29836],{},"Introduction to Statistical Quality Control",". 6. vyd. John Wiley & Sons, 2005.",[1110,29839,29840,29841,29844],{},"ČSN ISO 8258. ",[5922,29842,29843],{},"Shewhartovy regulační diagramy",". Praha: Český normalizační institut, 1994.",[1110,29846,29847,29848,29851],{},"KUPKA, K. ",[5922,29849,29850],{},"Statistické řízení jakosti",". Pardubice: TriloByte, 1997.",[5927,29853,29854],{},"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: 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pp",{"id":28005,"depth":27,"text":28006,"children":29878},[29879,29881,29883,29885,29886],{"id":28051,"depth":148,"text":29880},"CpC_p — index způsobilosti",{"id":28375,"depth":148,"text":29882},"CpkC_{pk} — index způsobilosti s ohledem na vychýlení",{"id":28570,"depth":148,"text":29884},"CpmC_{pm} a CpmkC_{pmk} — indexy vztažené k cíli",{"id":28828,"depth":148,"text":28829},{"id":29018,"depth":148,"text":29019},{"id":5680,"depth":27,"text":5681},{"id":5862,"depth":27,"text":5863},{"id":934,"depth":27,"text":5917},{},"\u002Ftopics\u002Fregulacni-diagramy-a-indexy-zpusobilosti",{"title":5906,"description":2039},[29894,29895,29896,29897],"raw\u002Fmask\u002F06 regulační diagramy.pdf","raw\u002Fmask\u002F07 indexy způsobilosti.pdf","raw\u002Fmask\u002Fnávod 06 a 07.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":29902,"title":5890,"body":29903,"course":23,"courses":5957,"created":5958,"description":2039,"extension":5959,"meta":39714,"navigation":5547,"path":39715,"seo":39716,"sources":39717,"stem":39723,"tags":39724,"type":5968,"updated":5958,"__hash__":39725},"topics\u002Ftopics\u002Ftestovani-hypotez.md",{"type":1096,"value":29904,"toc":39687},[29905,29908,30107,30151,30155,30165,30168,30234,30284,30437,30441,30444,30538,30688,30707,30714,30803,30807,30842,30879,30917,30952,30956,30963,31181,31300,31304,31436,31490,31512,31854,31861,31949,31955,31996,32281,32290,32405,32411,32418,32423,32429,32523,32529,32555,32561,32653,32659,32709,32713,32909,32969,33331,33670,33769,33775,34003,34007,34273,34277,34280,34346,34393,34849,34853,34856,35043,35076,35298,35617,35656,35663,36320,36459,36465,36621,36627,36634,36687,36693,36866,36872,36936,36941,37126,37132,37177,37181,37184,37188,37235,37463,37479,37568,37574,37600,37604,37607,37679,37772,37841,37847,37870,38317,38324,38328,38358,38362,38612,38631,38692,38701,38857,38863,38889,39064,39068,39089,39120,39124,39148,39178,39182,39242,39300,39304,39311,39484,39486,39639,39641,39678,39680,39684],[1099,29906,5890],{"id":29907},"testování-statistických-hypotéz",[1103,29909,29911,29917],{"className":29910,"dataCallout":1108},[1106,1107],[1110,29912,29914,1122],{"className":29913},[1113],[1115,29915],{"className":29916,"ariaHidden":1121},[1118,1119,1120],[1124,29918,29919,29989,30071,30074,30077],{},[1127,29920,29921,29922,29939,29940,29957,29958,1348,29971,29988],{},"Test porovnává tvrzení ",[1115,29923,29925],{"className":29924},[1137],[1139,29926,29927],{"xmlns":1141},[1143,29928,29929,29937],{},[1146,29930,29931],{},[1201,29932,29933,29935],{},[1149,29934,2227],{},[1230,29936,1597],{},[1153,29938,2743],{"encoding":1155}," s alternativou ",[1115,29941,29943],{"className":29942},[1137],[1139,29944,29945],{"xmlns":1141},[1143,29946,29947,29955],{},[1146,29948,29949],{},[1201,29950,29951,29953],{},[1149,29952,2227],{},[1230,29954,1525],{},[1153,29956,2762],{"encoding":1155}," pomocí testového kritéria spočteného z výběru; padne-li kritérium do kritického oboru ",[1115,29959,29961],{"className":29960},[1137],[1139,29962,29963],{"xmlns":1141},[1143,29964,29965,29969],{},[1146,29966,29967],{},[1149,29968,6052],{},[1153,29970,6052],{"encoding":1155},[1115,29972,29974],{"className":29973},[1137],[1139,29975,29976],{"xmlns":1141},[1143,29977,29978,29986],{},[1146,29979,29980],{},[1201,29981,29982,29984],{},[1149,29983,2227],{},[1230,29985,1597],{},[1153,29987,2743],{"encoding":1155}," zamítáme.",[1127,29990,29991,29992,30005,30006,30023,30024,30038,30039,30056,30057,30070],{},"Rozhodnutí nese dva typy chyb: chybu I. druhu (",[1115,29993,29995],{"className":29994},[1137],[1139,29996,29997],{"xmlns":1141},[1143,29998,29999,30003],{},[1146,30000,30001],{},[1149,30002,7788],{},[1153,30004,7851],{"encoding":1155},", zamítnutí platné ",[1115,30007,30009],{"className":30008},[1137],[1139,30010,30011],{"xmlns":1141},[1143,30012,30013,30021],{},[1146,30014,30015],{},[1201,30016,30017,30019],{},[1149,30018,2227],{},[1230,30020,1597],{},[1153,30022,2743],{"encoding":1155},") a chybu II. druhu (",[1115,30025,30027],{"className":30026},[1137],[1139,30028,30029],{"xmlns":1141},[1143,30030,30031,30035],{},[1146,30032,30033],{},[1149,30034,1594],{},[1153,30036,30037],{"encoding":1155},"\\beta",", přijetí neplatné ",[1115,30040,30042],{"className":30041},[1137],[1139,30043,30044],{"xmlns":1141},[1143,30045,30046,30054],{},[1146,30047,30048],{},[1201,30049,30050,30052],{},[1149,30051,2227],{},[1230,30053,1597],{},[1153,30055,2743],{"encoding":1155},"). Hladina významnosti ",[1115,30058,30060],{"className":30059},[1137],[1139,30061,30062],{"xmlns":1141},[1143,30063,30064,30068],{},[1146,30065,30066],{},[1149,30067,7788],{},[1153,30069,7851],{"encoding":1155}," se volí předem, obvykle 0,05.",[1127,30072,30073],{},"Pro střední hodnotu normálního rozdělení slouží jednovýběrový a párový t-test; pro srovnání dvou souborů F-test (rozptyly) a dvouvýběrový t-test (střední hodnoty).",[1127,30075,30076],{},"Normalitu ověřuje Shapiro-Wilkův test, shodu s libovolným rozdělením Kolmogorov-Smirnovův test; při porušené normalitě nastupují neparametrické testy (Wilcoxonovy, Kruskalův-Wallisův, mediánový, Friedmanův).",[1127,30078,30079,30080,30093,30094,1236],{},"Rozhodnutí lze číst dvěma rovnocennými způsoby — podle polohy kritéria vůči ",[1115,30081,30083],{"className":30082},[1137],[1139,30084,30085],{"xmlns":1141},[1143,30086,30087,30091],{},[1146,30088,30089],{},[1149,30090,6052],{},[1153,30092,6052],{"encoding":1155},", nebo podle p-hodnoty vůči ",[1115,30095,30097],{"className":30096},[1137],[1139,30098,30099],{"xmlns":1141},[1143,30100,30101,30105],{},[1146,30102,30103],{},[1149,30104,7788],{},[1153,30106,7851],{"encoding":1155},[1110,30108,30109,30110,30114,30115,30119,30120,30124,30125,1348,30138,1335],{},"Testy statistických hypotéz jsou nástroj ",[1384,30111,30113],{"className":30112,"dataFsResolvedFilePath":1388,"href":1389},[1387],"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 ",[1384,30116,30118],{"className":30117,"dataFsResolvedFilePath":5882,"href":5883},[1387],"popisnou statistiku"," výběru, a z rozdělení uvedených u ",[1384,30121,30123],{"className":30122,"dataFsResolvedFilePath":5292,"href":5293},[1387],"náhodných veličin"," (normální, ",[1115,30126,30128],{"className":30127},[1137],[1139,30129,30130],{"xmlns":1141},[1143,30131,30132,30136],{},[1146,30133,30134],{},[1149,30135,11515],{},[1153,30137,11515],{"encoding":1155},[1115,30139,30141],{"className":30140},[1137],[1139,30142,30143],{"xmlns":1141},[1143,30144,30145,30149],{},[1146,30146,30147],{},[1149,30148,11091],{},[1153,30150,11091],{"encoding":1155},[1377,30152,30154],{"id":30153},"statistická-hypotéza-a-její-test","Statistická hypotéza a její test",[1110,30156,30157,30160,30161,30164],{},[1130,30158,30159],{},"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. ",[1130,30162,30163],{},"Testování hypotéz"," je proces ověření správnosti nebo nesprávnosti hypotézy pomocí výsledků získaných náhodným výběrem.",[1110,30166,30167],{},"Proti sobě stojí dvě hypotézy:",[1124,30169,30170,30193],{},[1127,30171,30172,30192],{},[1130,30173,30174,30175],{},"Nulová hypotéza ",[1115,30176,30178],{"className":30177},[1137],[1139,30179,30180],{"xmlns":1141},[1143,30181,30182,30190],{},[1146,30183,30184],{},[1201,30185,30186,30188],{},[1149,30187,2227],{},[1230,30189,1597],{},[1153,30191,2743],{"encoding":1155}," — tvrzení o parametru nebo rozdělení, které chceme ověřit.",[1127,30194,30195,30215,30216,30233],{},[1130,30196,30197,30198],{},"Alternativní hypotéza ",[1115,30199,30201],{"className":30200},[1137],[1139,30202,30203],{"xmlns":1141},[1143,30204,30205,30213],{},[1146,30206,30207],{},[1201,30208,30209,30211],{},[1149,30210,2227],{},[1230,30212,1525],{},[1153,30214,2762],{"encoding":1155}," — staví se proti ",[1115,30217,30219],{"className":30218},[1137],[1139,30220,30221],{"xmlns":1141},[1143,30222,30223,30231],{},[1146,30224,30225],{},[1201,30226,30227,30229],{},[1149,30228,2227],{},[1230,30230,1597],{},[1153,30232,2743],{"encoding":1155}," a určitým způsobem popírá její tvrzení.",[1110,30235,6142,30236,30266,30267,1902],{},[1115,30237,30239],{"className":30238},[1137],[1139,30240,30241],{"xmlns":1141},[1143,30242,30243,30263],{},[1146,30244,30245,30251,30253,30255,30257],{},[1201,30246,30247,30249],{},[1149,30248,2227],{},[1230,30250,1597],{},[1193,30252,1902],{},[1149,30254,11264],{},[1193,30256,1281],{},[1201,30258,30259,30261],{},[1149,30260,11264],{},[1230,30262,1597],{},[1153,30264,30265],{"encoding":1155},"H_0: \\mu = \\mu_0"," existují tři varianty ",[1115,30268,30270],{"className":30269},[1137],[1139,30271,30272],{"xmlns":1141},[1143,30273,30274,30282],{},[1146,30275,30276],{},[1201,30277,30278,30280],{},[1149,30279,2227],{},[1230,30281,1525],{},[1153,30283,2762],{"encoding":1155},[6528,30285,30286,30316],{},[6531,30287,30288],{},[6534,30289,30290,30310,30313],{},[6537,30291,30292,30293],{},"Tvar ",[1115,30294,30296],{"className":30295},[1137],[1139,30297,30298],{"xmlns":1141},[1143,30299,30300,30308],{},[1146,30301,30302],{},[1201,30303,30304,30306],{},[1149,30305,2227],{},[1230,30307,1525],{},[1153,30309,2762],{"encoding":1155},[6537,30311,30312],{},"Zápis",[6537,30314,30315],{},"Typ",[6645,30317,30318,30358,30398],{},[6534,30319,30320,30323,30355],{},[6650,30321,30322],{},"nerovnost",[6650,30324,30325],{},[1115,30326,30328],{"className":30327},[1137],[1139,30329,30330],{"xmlns":1141},[1143,30331,30332,30352],{},[1146,30333,30334,30340,30342,30344,30346],{},[1201,30335,30336,30338],{},[1149,30337,2227],{},[1230,30339,1525],{},[1193,30341,1902],{},[1149,30343,11264],{},[1193,30345,2271],{"mathvariant":1854},[1201,30347,30348,30350],{},[1149,30349,11264],{},[1230,30351,1597],{},[1153,30353,30354],{"encoding":1155},"H_1: \\mu \\neq \\mu_0",[6650,30356,30357],{},"dvoustranná",[6534,30359,30360,30363,30395],{},[6650,30361,30362],{},"větší",[6650,30364,30365],{},[1115,30366,30368],{"className":30367},[1137],[1139,30369,30370],{"xmlns":1141},[1143,30371,30372,30392],{},[1146,30373,30374,30380,30382,30384,30386],{},[1201,30375,30376,30378],{},[1149,30377,2227],{},[1230,30379,1525],{},[1193,30381,1902],{},[1149,30383,11264],{},[1193,30385,5369],{},[1201,30387,30388,30390],{},[1149,30389,11264],{},[1230,30391,1597],{},[1153,30393,30394],{"encoding":1155},"H_1: \\mu > \\mu_0",[6650,30396,30397],{},"jednostranná",[6534,30399,30400,30403,30435],{},[6650,30401,30402],{},"menší",[6650,30404,30405],{},[1115,30406,30408],{"className":30407},[1137],[1139,30409,30410],{"xmlns":1141},[1143,30411,30412,30432],{},[1146,30413,30414,30420,30422,30424,30426],{},[1201,30415,30416,30418],{},[1149,30417,2227],{},[1230,30419,1525],{},[1193,30421,1902],{},[1149,30423,11264],{},[1193,30425,5343],{},[1201,30427,30428,30430],{},[1149,30429,11264],{},[1230,30431,1597],{},[1153,30433,30434],{"encoding":1155},"H_1: \\mu \u003C \\mu_0",[6650,30436,30397],{},[2019,30438,30440],{"id":30439},"chyba-i-a-ii-druhu","Chyba I. a II. druhu",[1110,30442,30443],{},"Protože je úsudek odvozen z náhodného výběru, může vést ke dvěma typům chybného rozhodnutí:",[1124,30445,30446,30483],{},[1127,30447,30448,30451,30452,30469,30470,1236],{},[1130,30449,30450],{},"Chyba I. druhu"," — zamítnutí ",[1115,30453,30455],{"className":30454},[1137],[1139,30456,30457],{"xmlns":1141},[1143,30458,30459,30467],{},[1146,30460,30461],{},[1201,30462,30463,30465],{},[1149,30464,2227],{},[1230,30466,1597],{},[1153,30468,2743],{"encoding":1155},", ačkoliv ve skutečnosti platí. Pravděpodobnost ",[1115,30471,30473],{"className":30472},[1137],[1139,30474,30475],{"xmlns":1141},[1143,30476,30477,30481],{},[1146,30478,30479],{},[1149,30480,7788],{},[1153,30482,7851],{"encoding":1155},[1127,30484,30485,30488,30489,30506,30507,30524,30525,1236],{},[1130,30486,30487],{},"Chyba II. druhu"," — přijetí ",[1115,30490,30492],{"className":30491},[1137],[1139,30493,30494],{"xmlns":1141},[1143,30495,30496,30504],{},[1146,30497,30498],{},[1201,30499,30500,30502],{},[1149,30501,2227],{},[1230,30503,1597],{},[1153,30505,2743],{"encoding":1155},", ačkoliv platí ",[1115,30508,30510],{"className":30509},[1137],[1139,30511,30512],{"xmlns":1141},[1143,30513,30514,30522],{},[1146,30515,30516],{},[1201,30517,30518,30520],{},[1149,30519,2227],{},[1230,30521,1525],{},[1153,30523,2762],{"encoding":1155},". Pravděpodobnost ",[1115,30526,30528],{"className":30527},[1137],[1139,30529,30530],{"xmlns":1141},[1143,30531,30532,30536],{},[1146,30533,30534],{},[1149,30535,1594],{},[1153,30537,30037],{"encoding":1155},[6528,30539,30540,30603],{},[6531,30541,30542],{},[6534,30543,30544,30564,30583],{},[6537,30545,30546,30547],{},"Úsudek o ",[1115,30548,30550],{"className":30549},[1137],[1139,30551,30552],{"xmlns":1141},[1143,30553,30554,30562],{},[1146,30555,30556],{},[1201,30557,30558,30560],{},[1149,30559,2227],{},[1230,30561,1597],{},[1153,30563,2743],{"encoding":1155},[6537,30565,30566,12722],{},[1115,30567,30569],{"className":30568},[1137],[1139,30570,30571],{"xmlns":1141},[1143,30572,30573,30581],{},[1146,30574,30575],{},[1201,30576,30577,30579],{},[1149,30578,2227],{},[1230,30580,1597],{},[1153,30582,2743],{"encoding":1155},[6537,30584,30585,30602],{},[1115,30586,30588],{"className":30587},[1137],[1139,30589,30590],{"xmlns":1141},[1143,30591,30592,30600],{},[1146,30593,30594],{},[1201,30595,30596,30598],{},[1149,30597,2227],{},[1230,30599,1597],{},[1153,30601,2743],{"encoding":1155}," neplatí",[6645,30604,30605,30647],{},[6534,30606,30607,30610,30631],{},[6650,30608,30609],{},"Nezamítá se",[6650,30611,30612,30613],{},"správné rozhodnutí, ",[1115,30614,30616],{"className":30615},[1137],[1139,30617,30618],{"xmlns":1141},[1143,30619,30620,30628],{},[1146,30621,30622,30624,30626],{},[1230,30623,1525],{},[1193,30625,1210],{},[1149,30627,7788],{},[1153,30629,30630],{"encoding":1155},"1-\\alpha",[6650,30632,30633,30634],{},"chyba II. druhu, ",[1115,30635,30637],{"className":30636},[1137],[1139,30638,30639],{"xmlns":1141},[1143,30640,30641,30645],{},[1146,30642,30643],{},[1149,30644,1594],{},[1153,30646,30037],{"encoding":1155},[6534,30648,30649,30652,30668],{},[6650,30650,30651],{},"Zamítá se",[6650,30653,30654,30655],{},"chyba I. druhu, ",[1115,30656,30658],{"className":30657},[1137],[1139,30659,30660],{"xmlns":1141},[1143,30661,30662,30666],{},[1146,30663,30664],{},[1149,30665,7788],{},[1153,30667,7851],{"encoding":1155},[6650,30669,30612,30670],{},[1115,30671,30673],{"className":30672},[1137],[1139,30674,30675],{"xmlns":1141},[1143,30676,30677,30685],{},[1146,30678,30679,30681,30683],{},[1230,30680,1525],{},[1193,30682,1210],{},[1149,30684,1594],{},[1153,30686,30687],{"encoding":1155},"1-\\beta",[1110,30689,30690,1243,30693,30706],{},[1130,30691,30692],{},"Hladina významnosti",[1115,30694,30696],{"className":30695},[1137],[1139,30697,30698],{"xmlns":1141},[1143,30699,30700,30704],{},[1146,30701,30702],{},[1149,30703,7788],{},[1153,30705,7851],{"encoding":1155}," 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.",[1110,30708,30709],{},[1864,30710],{"alt":30711,"className":30712,"src":30713},"mask-th-chyba-i-ii",[1387,1868],"\u002Fwiki-assets\u002Fmask-th-chyba-i-ii.png",[1110,30715,30716,30717,30730,30731,30744,30745,30758,30759,6324,30772,30785,30786,1236],{},"Obrázek ukazuje, proč jde o kompromis: posunutí kritické hodnoty ",[1115,30718,30720],{"className":30719},[1137],[1139,30721,30722],{"xmlns":1141},[1143,30723,30724,30728],{},[1146,30725,30726],{},[1149,30727,8130],{},[1153,30729,8130],{"encoding":1155}," doleva zmenší ",[1115,30732,30734],{"className":30733},[1137],[1139,30735,30736],{"xmlns":1141},[1143,30737,30738,30742],{},[1146,30739,30740],{},[1149,30741,1594],{},[1153,30743,30037],{"encoding":1155},", ale zvětší ",[1115,30746,30748],{"className":30747},[1137],[1139,30749,30750],{"xmlns":1141},[1143,30751,30752,30756],{},[1146,30753,30754],{},[1149,30755,7788],{},[1153,30757,7851],{"encoding":1155},", a naopak. Pro danou hladinu ",[1115,30760,30762],{"className":30761},[1137],[1139,30763,30764],{"xmlns":1141},[1143,30765,30766,30770],{},[1146,30767,30768],{},[1149,30769,7788],{},[1153,30771,7851],{"encoding":1155},[1115,30773,30775],{"className":30774},[1137],[1139,30776,30777],{"xmlns":1141},[1143,30778,30779,30783],{},[1146,30780,30781],{},[1149,30782,8130],{},[1153,30784,8130],{"encoding":1155}," jednoznačně určena rozdělením kritéria za platnosti ",[1115,30787,30789],{"className":30788},[1137],[1139,30790,30791],{"xmlns":1141},[1143,30792,30793,30801],{},[1146,30794,30795],{},[1201,30796,30797,30799],{},[1149,30798,2227],{},[1230,30800,1597],{},[1153,30802,2743],{"encoding":1155},[2019,30804,30806],{"id":30805},"testové-kritérium-a-kritický-obor","Testové kritérium a kritický obor",[1110,30808,30809,1243,30811,30824,30825,1236],{},[1130,30810,7426],{},[1115,30812,30814],{"className":30813},[1137],[1139,30815,30816],{"xmlns":1141},[1143,30817,30818,30822],{},[1146,30819,30820],{},[1149,30821,11474],{},[1153,30823,11474],{"encoding":1155}," je statistika spočtená z výběru; aby bylo možné test provést, musí být známo jeho rozdělení za platnosti ",[1115,30826,30828],{"className":30827},[1137],[1139,30829,30830],{"xmlns":1141},[1143,30831,30832,30840],{},[1146,30833,30834],{},[1201,30835,30836,30838],{},[1149,30837,2227],{},[1230,30839,1597],{},[1153,30841,2743],{"encoding":1155},[1110,30843,30844,1243,30847,30860,30861,30878],{},[1130,30845,30846],{},"Kritický obor",[1115,30848,30850],{"className":30849},[1137],[1139,30851,30852],{"xmlns":1141},[1143,30853,30854,30858],{},[1146,30855,30856],{},[1149,30857,6052],{},[1153,30859,6052],{"encoding":1155}," je množina hodnot svědčících pro ",[1115,30862,30864],{"className":30863},[1137],[1139,30865,30866],{"xmlns":1141},[1143,30867,30868,30876],{},[1146,30869,30870],{},[1201,30871,30872,30874],{},[1149,30873,2227],{},[1230,30875,1525],{},[1153,30877,2762],{"encoding":1155},". Je zkonstruován tak, aby",[1115,30880,30882],{"className":30881},[1137],[1139,30883,30884],{"xmlns":1141,"display":1796},[1143,30885,30886,30914],{},[1146,30887,30888,30890,30892,30894,30896,30898,30900,30906,30908,30910,30912],{},[1149,30889,11102],{},[1193,30891,1199],{"stretchy":1198},[1149,30893,11474],{},[1193,30895,11391],{},[1149,30897,6052],{},[1193,30899,26870],{},[1201,30901,30902,30904],{},[1149,30903,2227],{},[1230,30905,1597],{},[1193,30907,1228],{"stretchy":1198},[1193,30909,1281],{},[1149,30911,7788],{},[1193,30913,1503],{"separator":1121},[1153,30915,30916],{"encoding":1155},"P(T \\in W \\mid H_0) = \\alpha,",[1110,30918,30919,30920,30933,30934,30951],{},"tedy aby pravděpodobnost, že výběr dá hodnotu kritéria v ",[1115,30921,30923],{"className":30922},[1137],[1139,30924,30925],{"xmlns":1141},[1143,30926,30927,30931],{},[1146,30928,30929],{},[1149,30930,6052],{},[1153,30932,6052],{"encoding":1155}," i při platné ",[1115,30935,30937],{"className":30936},[1137],[1139,30938,30939],{"xmlns":1141},[1143,30940,30941,30949],{},[1146,30942,30943],{},[1201,30944,30945,30947],{},[1149,30946,2227],{},[1230,30948,1597],{},[1153,30950,2743],{"encoding":1155},", byla rovna zvolené hladině významnosti.",[2019,30953,30955],{"id":30954},"postup-testování-hypotézy","Postup testování hypotézy",[1110,30957,30958],{},[1864,30959],{"alt":30960,"className":30961,"src":30962},"mask-ilu-postup-testovani",[1387,1868],"\u002Fwiki-assets\u002Fmask-ilu-postup-testovani.png",[5106,30964,30965,31002,31005,31021],{},[1127,30966,30967,30968,1405,30985,1236],{},"Formulace hypotéz ",[1115,30969,30971],{"className":30970},[1137],[1139,30972,30973],{"xmlns":1141},[1143,30974,30975,30983],{},[1146,30976,30977],{},[1201,30978,30979,30981],{},[1149,30980,2227],{},[1230,30982,1597],{},[1153,30984,2743],{"encoding":1155},[1115,30986,30988],{"className":30987},[1137],[1139,30989,30990],{"xmlns":1141},[1143,30991,30992,31000],{},[1146,30993,30994],{},[1201,30995,30996,30998],{},[1149,30997,2227],{},[1230,30999,1525],{},[1153,31001,2762],{"encoding":1155},[1127,31003,31004],{},"Volba testového kritéria a výpočet jeho hodnoty.",[1127,31006,31007,31008,1236],{},"Volba hladiny významnosti a sestrojení příslušného kritického oboru ",[1115,31009,31011],{"className":31010},[1137],[1139,31012,31013],{"xmlns":1141},[1143,31014,31015,31019],{},[1146,31016,31017],{},[1149,31018,6052],{},[1153,31020,6052],{"encoding":1155},[1127,31022,31023,31024],{},"Formulace závěru:\n",[1124,31025,31026,31104],{},[1127,31027,31028,31029,3096,31047,31064,31065,31085,31086,31103],{},"pokud ",[1115,31030,31032],{"className":31031},[1137],[1139,31033,31034],{"xmlns":1141},[1143,31035,31036,31044],{},[1146,31037,31038,31040,31042],{},[1149,31039,11474],{},[1193,31041,11391],{},[1149,31043,6052],{},[1153,31045,31046],{"encoding":1155},"T \\in W",[1115,31048,31050],{"className":31049},[1137],[1139,31051,31052],{"xmlns":1141},[1143,31053,31054,31062],{},[1146,31055,31056],{},[1201,31057,31058,31060],{},[1149,31059,2227],{},[1230,31061,1525],{},[1153,31063,2762],{"encoding":1155}," je testem prokázána na hladině významnosti ",[1115,31066,31068],{"className":31067},[1137],[1139,31069,31070],{"xmlns":1141},[1143,31071,31072,31082],{},[1146,31073,31074,31076,31078,31080],{},[1230,31075,16169],{},[1149,31077,7788],{},[2201,31079,2203],{},[1149,31081,16176],{"mathvariant":1854},[1153,31083,31084],{"encoding":1155},"100\\alpha\\,\\%"," (zamítáme ",[1115,31087,31089],{"className":31088},[1137],[1139,31090,31091],{"xmlns":1141},[1143,31092,31093,31101],{},[1146,31094,31095],{},[1201,31096,31097,31099],{},[1149,31098,2227],{},[1230,31100,1597],{},[1153,31102,2743],{"encoding":1155},");",[1127,31105,31028,31106,3096,31125,31142,31143,31162,31163,31180],{},[1115,31107,31109],{"className":31108},[1137],[1139,31110,31111],{"xmlns":1141},[1143,31112,31113,31122],{},[1146,31114,31115,31117,31120],{},[1149,31116,11474],{},[1193,31118,31119],{"mathvariant":1854},"∉",[1149,31121,6052],{},[1153,31123,31124],{"encoding":1155},"T \\notin W",[1115,31126,31128],{"className":31127},[1137],[1139,31129,31130],{"xmlns":1141},[1143,31131,31132,31140],{},[1146,31133,31134],{},[1201,31135,31136,31138],{},[1149,31137,2227],{},[1230,31139,1525],{},[1153,31141,2762],{"encoding":1155}," není testem prokázána na hladině významnosti ",[1115,31144,31146],{"className":31145},[1137],[1139,31147,31148],{"xmlns":1141},[1143,31149,31150,31160],{},[1146,31151,31152,31154,31156,31158],{},[1230,31153,16169],{},[1149,31155,7788],{},[2201,31157,2203],{},[1149,31159,16176],{"mathvariant":1854},[1153,31161,31084],{"encoding":1155}," ; ",[1115,31164,31166],{"className":31165},[1137],[1139,31167,31168],{"xmlns":1141},[1143,31169,31170,31178],{},[1146,31171,31172],{},[1201,31173,31174,31176],{},[1149,31175,2227],{},[1230,31177,1597],{},[1153,31179,2743],{"encoding":1155}," nezamítáme.",[1110,31182,31183,31184,31187,31188,31205,31206,31223,31224,31244,31245,29030,31262,1243,31282,31299],{},"Rovnocennou alternativou je ",[1130,31185,31186],{},"p-hodnota",": udává, nakolik jsou data slučitelná s ",[1115,31189,31191],{"className":31190},[1137],[1139,31192,31193],{"xmlns":1141},[1143,31194,31195,31203],{},[1146,31196,31197],{},[1201,31198,31199,31201],{},[1149,31200,2227],{},[1230,31202,1597],{},[1153,31204,2743],{"encoding":1155},". Čím menší p-hodnota, tím více data svědčí proti ",[1115,31207,31209],{"className":31208},[1137],[1139,31210,31211],{"xmlns":1141},[1143,31212,31213,31221],{},[1146,31214,31215],{},[1201,31216,31217,31219],{},[1149,31218,2227],{},[1230,31220,1597],{},[1153,31222,2743],{"encoding":1155},". Rozhodovací pravidlo: ",[1115,31225,31227],{"className":31226},[1137],[1139,31228,31229],{"xmlns":1141},[1143,31230,31231,31241],{},[1146,31232,31233,31235,31237,31239],{},[1149,31234,1110],{},[1193,31236,11110],{},[1149,31238,7788],{},[1193,31240,11921],{},[1153,31242,31243],{"encoding":1155},"p \\le \\alpha \\Rightarrow"," zamítáme ",[1115,31246,31248],{"className":31247},[1137],[1139,31249,31250],{"xmlns":1141},[1143,31251,31252,31260],{},[1146,31253,31254],{},[1201,31255,31256,31258],{},[1149,31257,2227],{},[1230,31259,1597],{},[1153,31261,2743],{"encoding":1155},[1115,31263,31265],{"className":31264},[1137],[1139,31266,31267],{"xmlns":1141},[1143,31268,31269,31279],{},[1146,31270,31271,31273,31275,31277],{},[1149,31272,1110],{},[1193,31274,5369],{},[1149,31276,7788],{},[1193,31278,11921],{},[1153,31280,31281],{"encoding":1155},"p > \\alpha \\Rightarrow",[1115,31283,31285],{"className":31284},[1137],[1139,31286,31287],{"xmlns":1141},[1143,31288,31289,31297],{},[1146,31290,31291],{},[1201,31292,31293,31295],{},[1149,31294,2227],{},[1230,31296,1597],{},[1153,31298,2743],{"encoding":1155}," nezamítáme. Obě cesty — kritický obor i p-hodnota — vedou vždy ke stejnému závěru; R u všech testů vrací p-hodnotu přímo.",[1377,31301,31303],{"id":31302},"jednovýběrový-t-test","Jednovýběrový t-test",[1110,31305,31306,31307,31320,31321,31353,31354,31367,31368,1405,31385,31402,31403,31421,31422,31435],{},"Test o střední hodnotě ",[1115,31308,31310],{"className":31309},[1137],[1139,31311,31312],{"xmlns":1141},[1143,31313,31314,31318],{},[1146,31315,31316],{},[1149,31317,11264],{},[1153,31319,13166],{"encoding":1155}," rozdělení ",[1115,31322,31324],{"className":31323},[1137],[1139,31325,31326],{"xmlns":1141},[1143,31327,31328,31350],{},[1146,31329,31330,31332,31334,31336,31338,31340,31342,31348],{},[1149,31331,11107],{},[1193,31333,13552],{},[1149,31335,11259],{},[1193,31337,1199],{"stretchy":1198},[1149,31339,11264],{},[1193,31341,1503],{"separator":1121},[1224,31343,31344,31346],{},[1149,31345,11271],{},[1230,31347,1232],{},[1193,31349,1228],{"stretchy":1198},[1153,31351,31352],{"encoding":1155},"X \\sim N(\\mu, \\sigma^2)",". Z výběru o rozsahu ",[1115,31355,31357],{"className":31356},[1137],[1139,31358,31359],{"xmlns":1141},[1143,31360,31361,31365],{},[1146,31362,31363],{},[1149,31364,1816],{},[1153,31366,1816],{"encoding":1155}," se určí charakteristiky ",[1115,31369,31371],{"className":31370},[1137],[1139,31372,31373],{"xmlns":1141},[1143,31374,31375,31383],{},[1146,31376,31377],{},[1214,31378,31379,31381],{"accent":1121},[1149,31380,1168],{},[1193,31382,15814],{},[1153,31384,25411],{"encoding":1155},[1115,31386,31388],{"className":31387},[1137],[1139,31389,31390],{"xmlns":1141},[1143,31391,31392,31400],{},[1146,31393,31394],{},[1224,31395,31396,31398],{},[1149,31397,4542],{},[1230,31399,1232],{},[1153,31401,20125],{"encoding":1155},"; testem se posuzuje vztah mezi zvoleným číslem ",[1115,31404,31406],{"className":31405},[1137],[1139,31407,31408],{"xmlns":1141},[1143,31409,31410,31418],{},[1146,31411,31412],{},[1201,31413,31414,31416],{},[1149,31415,11264],{},[1230,31417,1597],{},[1153,31419,31420],{"encoding":1155},"\\mu_0"," a neznámou hodnotou ",[1115,31423,31425],{"className":31424},[1137],[1139,31426,31427],{"xmlns":1141},[1143,31428,31429,31433],{},[1146,31430,31431],{},[1149,31432,11264],{},[1153,31434,13166],{"encoding":1155},". Testové kritérium",[1115,31437,31439],{"className":31438},[1137],[1139,31440,31441],{"xmlns":1141,"display":1796},[1143,31442,31443,31487],{},[1146,31444,31445,31447,31449,31469,31473,31475],{},[1149,31446,11474],{},[1193,31448,1281],{},[3546,31450,31451,31467],{},[1146,31452,31453,31459,31461],{},[1214,31454,31455,31457],{"accent":1121},[1149,31456,1168],{},[1193,31458,15814],{},[1193,31460,1210],{},[1201,31462,31463,31465],{},[1149,31464,11264],{},[1230,31466,1597],{},[1149,31468,4542],{},[1283,31470,31471],{},[1149,31472,1816],{},[1193,31474,13552],{},[1201,31476,31477,31479],{},[1149,31478,11515],{},[1146,31480,31481,31483,31485],{},[1149,31482,1816],{},[1193,31484,1210],{},[1230,31486,1525],{},[1153,31488,31489],{"encoding":1155},"T = \\frac{\\bar{x} - \\mu_0}{s}\\sqrt{n} \\sim t_{n-1}",[1110,31491,31492,31493,31511],{},"má Studentovo rozdělení o ",[1115,31494,31496],{"className":31495},[1137],[1139,31497,31498],{"xmlns":1141},[1143,31499,31500,31508],{},[1146,31501,31502,31504,31506],{},[1149,31503,1816],{},[1193,31505,1210],{},[1230,31507,1525],{},[1153,31509,31510],{"encoding":1155},"n-1"," stupních volnosti.",[6528,31513,31514,31572],{},[6531,31515,31516],{},[6534,31517,31518,31537,31556],{},[6537,31519,31520],{},[1115,31521,31523],{"className":31522},[1137],[1139,31524,31525],{"xmlns":1141},[1143,31526,31527,31535],{},[1146,31528,31529],{},[1201,31530,31531,31533],{},[1149,31532,2227],{},[1230,31534,1597],{},[1153,31536,2743],{"encoding":1155},[6537,31538,31539],{},[1115,31540,31542],{"className":31541},[1137],[1139,31543,31544],{"xmlns":1141},[1143,31545,31546,31554],{},[1146,31547,31548],{},[1201,31549,31550,31552],{},[1149,31551,2227],{},[1230,31553,1525],{},[1153,31555,2762],{"encoding":1155},[6537,31557,31558,31559],{},"Kritický obor ",[1115,31560,31562],{"className":31561},[1137],[1139,31563,31564],{"xmlns":1141},[1143,31565,31566,31570],{},[1146,31567,31568],{},[1149,31569,6052],{},[1153,31571,6052],{"encoding":1155},[6645,31573,31574,31664,31762],{},[6534,31575,31576,31600,31624],{},[6650,31577,31578],{},[1115,31579,31581],{"className":31580},[1137],[1139,31582,31583],{"xmlns":1141},[1143,31584,31585,31597],{},[1146,31586,31587,31589,31591],{},[1149,31588,11264],{},[1193,31590,11110],{},[1201,31592,31593,31595],{},[1149,31594,11264],{},[1230,31596,1597],{},[1153,31598,31599],{"encoding":1155},"\\mu \\le \\mu_0",[6650,31601,31602],{},[1115,31603,31605],{"className":31604},[1137],[1139,31606,31607],{"xmlns":1141},[1143,31608,31609,31621],{},[1146,31610,31611,31613,31615],{},[1149,31612,11264],{},[1193,31614,5369],{},[1201,31616,31617,31619],{},[1149,31618,11264],{},[1230,31620,1597],{},[1153,31622,31623],{"encoding":1155},"\\mu > \\mu_0",[6650,31625,31626],{},[1115,31627,31629],{"className":31628},[1137],[1139,31630,31631],{"xmlns":1141},[1143,31632,31633,31661],{},[1146,31634,31635,31637,31639,31651,31653,31655,31657,31659],{},[1149,31636,11515],{},[1193,31638,7775],{},[1201,31640,31641,31643],{},[1149,31642,11515],{},[1146,31644,31645,31647,31649],{},[1230,31646,1525],{},[1193,31648,1210],{},[1149,31650,7788],{},[1193,31652,1199],{"stretchy":1198},[1149,31654,1816],{},[1193,31656,1210],{},[1230,31658,1525],{},[1193,31660,1228],{"stretchy":1198},[1153,31662,31663],{"encoding":1155},"t \\ge t_{1-\\alpha}(n-1)",[6534,31665,31666,31690,31714],{},[6650,31667,31668],{},[1115,31669,31671],{"className":31670},[1137],[1139,31672,31673],{"xmlns":1141},[1143,31674,31675,31687],{},[1146,31676,31677,31679,31681],{},[1149,31678,11264],{},[1193,31680,1281],{},[1201,31682,31683,31685],{},[1149,31684,11264],{},[1230,31686,1597],{},[1153,31688,31689],{"encoding":1155},"\\mu = \\mu_0",[6650,31691,31692],{},[1115,31693,31695],{"className":31694},[1137],[1139,31696,31697],{"xmlns":1141},[1143,31698,31699,31711],{},[1146,31700,31701,31703,31705],{},[1149,31702,11264],{},[1193,31704,2271],{"mathvariant":1854},[1201,31706,31707,31709],{},[1149,31708,11264],{},[1230,31710,1597],{},[1153,31712,31713],{"encoding":1155},"\\mu \\neq \\mu_0",[6650,31715,31716],{},[1115,31717,31719],{"className":31718},[1137],[1139,31720,31721],{"xmlns":1141},[1143,31722,31723,31759],{},[1146,31724,31725,31727,31729,31731,31733,31749,31751,31753,31755,31757],{},[1193,31726,26870],{"stretchy":1198},[1149,31728,11515],{},[1193,31730,26870],{"stretchy":1198},[1193,31732,7775],{},[1201,31734,31735,31737],{},[1149,31736,11515],{},[1146,31738,31739,31741,31743,31745,31747],{},[1230,31740,1525],{},[1193,31742,1210],{},[1149,31744,7788],{},[1149,31746,5731],{"mathvariant":1854},[1230,31748,1232],{},[1193,31750,1199],{"stretchy":1198},[1149,31752,1816],{},[1193,31754,1210],{},[1230,31756,1525],{},[1193,31758,1228],{"stretchy":1198},[1153,31760,31761],{"encoding":1155},"\\lvert t \\rvert \\ge t_{1-\\alpha\u002F2}(n-1)",[6534,31763,31764,31788,31812],{},[6650,31765,31766],{},[1115,31767,31769],{"className":31768},[1137],[1139,31770,31771],{"xmlns":1141},[1143,31772,31773,31785],{},[1146,31774,31775,31777,31779],{},[1149,31776,11264],{},[1193,31778,7775],{},[1201,31780,31781,31783],{},[1149,31782,11264],{},[1230,31784,1597],{},[1153,31786,31787],{"encoding":1155},"\\mu \\ge \\mu_0",[6650,31789,31790],{},[1115,31791,31793],{"className":31792},[1137],[1139,31794,31795],{"xmlns":1141},[1143,31796,31797,31809],{},[1146,31798,31799,31801,31803],{},[1149,31800,11264],{},[1193,31802,5343],{},[1201,31804,31805,31807],{},[1149,31806,11264],{},[1230,31808,1597],{},[1153,31810,31811],{"encoding":1155},"\\mu \u003C \\mu_0",[6650,31813,31814],{},[1115,31815,31817],{"className":31816},[1137],[1139,31818,31819],{"xmlns":1141},[1143,31820,31821,31851],{},[1146,31822,31823,31825,31827,31829,31841,31843,31845,31847,31849],{},[1149,31824,11515],{},[1193,31826,11110],{},[1193,31828,1210],{},[1201,31830,31831,31833],{},[1149,31832,11515],{},[1146,31834,31835,31837,31839],{},[1230,31836,1525],{},[1193,31838,1210],{},[1149,31840,7788],{},[1193,31842,1199],{"stretchy":1198},[1149,31844,1816],{},[1193,31846,1210],{},[1230,31848,1525],{},[1193,31850,1228],{"stretchy":1198},[1153,31852,31853],{"encoding":1155},"t \\le -t_{1-\\alpha}(n-1)",[1110,31855,31856,31857,31860],{},"V R test provádí ",[1332,31858,31859],{},"t.test()",". 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?",[2035,31862,31864],{"className":2037,"code":31863,"language":71,"meta":2039,"style":2039},"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",[1332,31865,31866,31920],{"__ignoreMap":2039},[1115,31867,31868,31870,31872,31874,31876,31879,31881,31884,31886,31889,31891,31894,31896,31899,31901,31904,31906,31908,31910,31913,31915,31918],{"class":2044,"line":10},[1115,31869,1168],{"class":2047},[1115,31871,2052],{"class":2051},[1115,31873,2056],{"class":2055},[1115,31875,1199],{"class":2059},[1115,31877,31878],{"class":2062},"12.5",[1115,31880,1503],{"class":2051},[1115,31882,31883],{"class":2062}," 13.5",[1115,31885,1503],{"class":2051},[1115,31887,31888],{"class":2062}," 11.9",[1115,31890,1503],{"class":2051},[1115,31892,31893],{"class":2062}," 12.2",[1115,31895,1503],{"class":2051},[1115,31897,31898],{"class":2062}," 13.0",[1115,31900,1503],{"class":2051},[1115,31902,31903],{"class":2062}," 14.3",[1115,31905,1503],{"class":2051},[1115,31907,31893],{"class":2062},[1115,31909,1503],{"class":2051},[1115,31911,31912],{"class":2062}," 11.8",[1115,31914,1503],{"class":2051},[1115,31916,31917],{"class":2062}," 14.0",[1115,31919,2090],{"class":2059},[1115,31921,31922,31925,31927,31929,31931,31933,31935,31937,31939,31942,31944,31947],{"class":2044,"line":27},[1115,31923,31924],{"class":2055},"t.test",[1115,31926,1199],{"class":2059},[1115,31928,1168],{"class":2047},[1115,31930,1503],{"class":2051},[1115,31932,29427],{"class":2047},[1115,31934,2510],{"class":2051},[1115,31936,8144],{"class":2062},[1115,31938,1503],{"class":2051},[1115,31940,31941],{"class":2047}," alternative",[1115,31943,2510],{"class":2051},[1115,31945,31946],{"class":2575}," \"two.sided\"",[1115,31948,2090],{"class":2059},[2035,31950,31953],{"className":31951,"code":31952,"language":2169,"meta":2039},[2167]," 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",[1332,31954,31952],{"__ignoreMap":2039},[1110,31956,31957,31959,31960,31963,31964,31967,31968,31971,31972,31995],{},[1332,31958,11515],{}," je testové kritérium, ",[1332,31961,31962],{},"df"," stupně volnosti, ",[1332,31965,31966],{},"p-value"," p-hodnota pro zvolenou alternativu a ",[1332,31969,31970],{},"mean of x"," výběrový průměr. Zde ",[1115,31973,31975],{"className":31974},[1137],[1139,31976,31977],{"xmlns":1141},[1143,31978,31979,31992],{},[1146,31980,31981,31983,31985,31988,31990],{},[1149,31982,1110],{},[1193,31984,1281],{},[1230,31986,31987],{},"0,02843",[1193,31989,5343],{},[1230,31991,4370],{},[1153,31993,31994],{"encoding":1155},"p = 0{,}02843 \u003C 0{,}05",": úprava trasy průměrnou dobu jízdy (původně 12 minut) statisticky významně změnila.",[1103,31997,31999,32006,32094,32150,32242],{"className":31998,"dataCallout":2932},[1106,2931],[1110,32000,32002,32005],{"className":32001},[1113],[1115,32003],{"className":32004,"ariaHidden":1121},[1118,2939,1120],"Příklad: Kontrola objemu lahví",[1110,32007,32008,32009,32031,32032,32050,32051,32074,32075,32093],{},"Pivovar plní lahve, deklarovaný objem je ",[1115,32010,32012],{"className":32011},[1137],[1139,32013,32014],{"xmlns":1141},[1143,32015,32016,32028],{},[1146,32017,32018,32024,32026],{},[1201,32019,32020,32022],{},[1149,32021,11264],{},[1230,32023,1597],{},[1193,32025,1281],{},[1230,32027,12828],{},[1153,32029,32030],{"encoding":1155},"\\mu_0 = 0{,}5"," l. Náhodný výběr ",[1115,32033,32035],{"className":32034},[1137],[1139,32036,32037],{"xmlns":1141},[1143,32038,32039,32047],{},[1146,32040,32041,32043,32045],{},[1149,32042,1816],{},[1193,32044,1281],{},[1230,32046,8444],{},[1153,32048,32049],{"encoding":1155},"n = 20"," lahví dal ",[1115,32052,32054],{"className":32053},[1137],[1139,32055,32056],{"xmlns":1141},[1143,32057,32058,32071],{},[1146,32059,32060,32066,32068],{},[1214,32061,32062,32064],{"accent":1121},[1149,32063,1168],{},[1193,32065,15814],{},[1193,32067,1281],{},[1230,32069,32070],{},"0,492",[1153,32072,32073],{"encoding":1155},"\\bar{x} = 0{,}492"," l, ",[1115,32076,32078],{"className":32077},[1137],[1139,32079,32080],{"xmlns":1141},[1143,32081,32082,32090],{},[1146,32083,32084,32086,32088],{},[1149,32085,4542],{},[1193,32087,1281],{},[1230,32089,19144],{},[1153,32091,32092],{"encoding":1155},"s = 0{,}015"," l. Na hladině významnosti 5 % ověřte podezření, že pivovar lahve nedoplňuje.",[1110,32095,32096,32122,32123,32149],{},[1115,32097,32099],{"className":32098},[1137],[1139,32100,32101],{"xmlns":1141},[1143,32102,32103,32119],{},[1146,32104,32105,32111,32113,32115,32117],{},[1201,32106,32107,32109],{},[1149,32108,2227],{},[1230,32110,1597],{},[1193,32112,1902],{},[1149,32114,11264],{},[1193,32116,7775],{},[1230,32118,12828],{},[1153,32120,32121],{"encoding":1155},"H_0: \\mu \\ge 0{,}5"," l (objem je v pořádku nebo větší), ",[1115,32124,32126],{"className":32125},[1137],[1139,32127,32128],{"xmlns":1141},[1143,32129,32130,32146],{},[1146,32131,32132,32138,32140,32142,32144],{},[1201,32133,32134,32136],{},[1149,32135,2227],{},[1230,32137,1525],{},[1193,32139,1902],{},[1149,32141,11264],{},[1193,32143,5343],{},[1230,32145,12828],{},[1153,32147,32148],{"encoding":1155},"H_1: \\mu \u003C 0{,}5"," l (lahve jsou nedoplněné).",[1110,32151,32152],{},[1115,32153,32155],{"className":32154},[1137],[1139,32156,32157],{"xmlns":1141},[1143,32158,32159,32239],{},[1146,32160,32161,32163,32165,32177,32181,32183,32185,32188,32190,32192,32194,32196,32198,32200,32202,32204,32216,32218,32220,32222,32224,32226,32228,32230,32232,32234,32237],{},[1149,32162,11515],{},[1193,32164,1281],{},[3546,32166,32167,32175],{},[1146,32168,32169,32171,32173],{},[1230,32170,32070],{},[1193,32172,1210],{},[1230,32174,12828],{},[1230,32176,19144],{},[1283,32178,32179],{},[1230,32180,8444],{},[1193,32182,1281],{},[1193,32184,1210],{},[1230,32186,32187],{},"2,385",[1193,32189,1503],{"separator":1121},[1936,32191],{"width":1938},[1149,32193,6052],{},[1193,32195,1281],{},[1193,32197,7758],{"stretchy":1198},[1149,32199,11515],{},[1193,32201,11110],{},[1193,32203,1210],{},[1201,32205,32206,32208],{},[1149,32207,11515],{},[1146,32209,32210,32212,32214],{},[1230,32211,1597],{},[1193,32213,1503],{"separator":1121},[1230,32215,25644],{},[1193,32217,1199],{"stretchy":1198},[1230,32219,19068],{},[1193,32221,1228],{"stretchy":1198},[1193,32223,7817],{"stretchy":1198},[1193,32225,1281],{},[1193,32227,7758],{"stretchy":1198},[1149,32229,11515],{},[1193,32231,11110],{},[1193,32233,1210],{},[1230,32235,32236],{},"1,729",[1193,32238,7817],{"stretchy":1198},[1153,32240,32241],{"encoding":1155},"t = \\frac{0{,}492 - 0{,}5}{0{,}015}\\sqrt{20} = -2{,}385, \\qquad W = \\{t \\le -t_{0,95}(19)\\} = \\{t \\le -1{,}729\\}",[1110,32243,32244,32245,10395,32263,32280],{},"Protože ",[1115,32246,32248],{"className":32247},[1137],[1139,32249,32250],{"xmlns":1141},[1143,32251,32252,32260],{},[1146,32253,32254,32256,32258],{},[1149,32255,11515],{},[1193,32257,11391],{},[1149,32259,6052],{},[1153,32261,32262],{"encoding":1155},"t \\in W",[1115,32264,32266],{"className":32265},[1137],[1139,32267,32268],{"xmlns":1141},[1143,32269,32270,32278],{},[1146,32271,32272],{},[1201,32273,32274,32276],{},[1149,32275,2227],{},[1230,32277,1597],{},[1153,32279,2743],{"encoding":1155},": na hladině významnosti 5 % se potvrdilo, že pivovar plní lahve pod deklarovaný objem.",[1110,32282,32283,32284,32286,32287,1902],{},"Ze souhrnných charakteristik bez surových dat ",[1332,32285,31859],{}," spustit nelze — kritérium a kritická hodnota se dopočítají přímo z definice pomocí ",[1332,32288,32289],{},"qt()",[2035,32291,32293],{"className":2037,"code":32292,"language":71,"meta":2039,"style":2039},"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",[1332,32294,32295,32333,32365,32395,32400],{"__ignoreMap":2039},[1115,32296,32297,32300,32302,32305,32307,32309,32311,32314,32316,32318,32320,32323,32325,32328,32330],{"class":2044,"line":10},[1115,32298,32299],{"class":2047},"xbar",[1115,32301,2052],{"class":2051},[1115,32303,32304],{"class":2062}," 0.492",[1115,32306,29030],{"class":2059},[1115,32308,4542],{"class":2047},[1115,32310,2052],{"class":2051},[1115,32312,32313],{"class":2062}," 0.015",[1115,32315,29030],{"class":2059},[1115,32317,1816],{"class":2047},[1115,32319,2052],{"class":2051},[1115,32321,32322],{"class":2062}," 20",[1115,32324,29030],{"class":2059},[1115,32326,32327],{"class":2047},"mu0",[1115,32329,2052],{"class":2051},[1115,32331,32332],{"class":2062}," 0.5\n",[1115,32334,32335,32337,32339,32341,32343,32345,32348,32350,32352,32355,32357,32359,32361,32363],{"class":2044,"line":27},[1115,32336,11515],{"class":2047},[1115,32338,2052],{"class":2051},[1115,32340,4053],{"class":2059},[1115,32342,32299],{"class":2047},[1115,32344,29367],{"class":2051},[1115,32346,32347],{"class":2047}," mu0",[1115,32349,8993],{"class":2059},[1115,32351,5731],{"class":2051},[1115,32353,32354],{"class":2047}," s",[1115,32356,3957],{"class":2051},[1115,32358,8970],{"class":2055},[1115,32360,1199],{"class":2059},[1115,32362,1816],{"class":2047},[1115,32364,2090],{"class":2059},[1115,32366,32367,32370,32372,32375,32377,32380,32382,32384,32386,32389,32391,32393],{"class":2044,"line":148},[1115,32368,32369],{"class":2047},"t_krit",[1115,32371,2052],{"class":2051},[1115,32373,32374],{"class":2055}," qt",[1115,32376,1199],{"class":2059},[1115,32378,32379],{"class":2062},"0.05",[1115,32381,1503],{"class":2051},[1115,32383,15170],{"class":2047},[1115,32385,2510],{"class":2051},[1115,32387,32388],{"class":2047}," n",[1115,32390,29367],{"class":2051},[1115,32392,9031],{"class":2062},[1115,32394,2090],{"class":2059},[1115,32396,32397],{"class":2044,"line":111},[1115,32398,32399],{"class":2047},"t\n",[1115,32401,32402],{"class":2044,"line":96},[1115,32403,32404],{"class":2047},"t_krit\n",[2035,32406,32409],{"className":32407,"code":32408,"language":2169,"meta":2039},[2167],"[1] -2.385139\n[1] -1.729133\n",[1332,32410,32408],{"__ignoreMap":2039},[1110,32412,32413],{},[1864,32414],{"alt":32415,"className":32416,"src":32417},"mask-th-t-jednostranny",[1387,1868],"\u002Fwiki-assets\u002Fmask-th-t-jednostranny.png",[1110,32419,32420,32421,1902],{},"Další dva příklady mají k dispozici surová data, takže je lze otestovat přímo ",[1332,32422,31859],{},[1110,32424,32425,32428],{},[1130,32426,32427],{},"Životnost baterií."," Výrobce udává průměrnou životnost 10 hodin, na 11 bateriích byly naměřeny hodnoty v hodinách.",[2035,32430,32432],{"className":2037,"code":32431,"language":71,"meta":2039,"style":2039},"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",[1332,32433,32434,32497],{"__ignoreMap":2039},[1115,32435,32436,32439,32441,32443,32445,32448,32450,32453,32455,32458,32460,32463,32465,32468,32470,32473,32475,32477,32479,32482,32484,32486,32488,32491,32493,32495],{"class":2044,"line":10},[1115,32437,32438],{"class":2047},"x2",[1115,32440,2052],{"class":2051},[1115,32442,2056],{"class":2055},[1115,32444,1199],{"class":2059},[1115,32446,32447],{"class":2062},"9.5",[1115,32449,1503],{"class":2051},[1115,32451,32452],{"class":2062}," 10.5",[1115,32454,1503],{"class":2051},[1115,32456,32457],{"class":2062}," 8.9",[1115,32459,1503],{"class":2051},[1115,32461,32462],{"class":2062}," 9.2",[1115,32464,1503],{"class":2051},[1115,32466,32467],{"class":2062}," 10.0",[1115,32469,1503],{"class":2051},[1115,32471,32472],{"class":2062}," 8.5",[1115,32474,1503],{"class":2051},[1115,32476,32462],{"class":2062},[1115,32478,1503],{"class":2051},[1115,32480,32481],{"class":2062}," 8.8",[1115,32483,1503],{"class":2051},[1115,32485,32467],{"class":2062},[1115,32487,1503],{"class":2051},[1115,32489,32490],{"class":2062}," 9.5",[1115,32492,1503],{"class":2051},[1115,32494,32462],{"class":2062},[1115,32496,2090],{"class":2059},[1115,32498,32499,32501,32503,32505,32507,32509,32511,32513,32515,32517,32519,32521],{"class":2044,"line":27},[1115,32500,31924],{"class":2055},[1115,32502,1199],{"class":2059},[1115,32504,32438],{"class":2047},[1115,32506,1503],{"class":2051},[1115,32508,29427],{"class":2047},[1115,32510,2510],{"class":2051},[1115,32512,13845],{"class":2062},[1115,32514,1503],{"class":2051},[1115,32516,31941],{"class":2047},[1115,32518,2510],{"class":2051},[1115,32520,31946],{"class":2575},[1115,32522,2090],{"class":2059},[2035,32524,32527],{"className":32525,"code":32526,"language":2169,"meta":2039},[2167]," 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",[1332,32528,32526],{"__ignoreMap":2039},[1110,32530,32531,32554],{},[1115,32532,32534],{"className":32533},[1137],[1139,32535,32536],{"xmlns":1141},[1143,32537,32538,32551],{},[1146,32539,32540,32542,32544,32547,32549],{},[1149,32541,1110],{},[1193,32543,1281],{},[1230,32545,32546],{},"0,006548",[1193,32548,5343],{},[1230,32550,4370],{},[1153,32552,32553],{"encoding":1155},"p = 0{,}006548 \u003C 0{,}05",": skutečná životnost se od deklarovaných 10 hodin statisticky významně liší (baterie vydrží méně).",[1110,32556,32557,32560],{},[1130,32558,32559],{},"Odpad materiálu."," Na deseti obráběných kusech byl naměřen odpad materiálu v procentech; testuje se rozdíl proti 4 % a zároveň normalita dat.",[2035,32562,32564],{"className":2037,"code":32563,"language":71,"meta":2039,"style":2039},"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",[1332,32565,32566,32617,32643],{"__ignoreMap":2039},[1115,32567,32568,32571,32573,32575,32577,32579,32581,32583,32585,32587,32589,32591,32593,32595,32597,32599,32601,32603,32605,32607,32609,32611,32613,32615],{"class":2044,"line":10},[1115,32569,32570],{"class":2047},"x3",[1115,32572,2052],{"class":2051},[1115,32574,2056],{"class":2055},[1115,32576,1199],{"class":2059},[1115,32578,16337],{"class":2062},[1115,32580,1503],{"class":2051},[1115,32582,16342],{"class":2062},[1115,32584,1503],{"class":2051},[1115,32586,16347],{"class":2062},[1115,32588,1503],{"class":2051},[1115,32590,16352],{"class":2062},[1115,32592,1503],{"class":2051},[1115,32594,16347],{"class":2062},[1115,32596,1503],{"class":2051},[1115,32598,16347],{"class":2062},[1115,32600,1503],{"class":2051},[1115,32602,16365],{"class":2062},[1115,32604,1503],{"class":2051},[1115,32606,16370],{"class":2062},[1115,32608,1503],{"class":2051},[1115,32610,16342],{"class":2062},[1115,32612,1503],{"class":2051},[1115,32614,16342],{"class":2062},[1115,32616,2090],{"class":2059},[1115,32618,32619,32621,32623,32625,32627,32629,32631,32633,32635,32637,32639,32641],{"class":2044,"line":27},[1115,32620,31924],{"class":2055},[1115,32622,1199],{"class":2059},[1115,32624,32570],{"class":2047},[1115,32626,1503],{"class":2051},[1115,32628,29427],{"class":2047},[1115,32630,2510],{"class":2051},[1115,32632,2077],{"class":2062},[1115,32634,1503],{"class":2051},[1115,32636,31941],{"class":2047},[1115,32638,2510],{"class":2051},[1115,32640,31946],{"class":2575},[1115,32642,2090],{"class":2059},[1115,32644,32645,32647,32649,32651],{"class":2044,"line":148},[1115,32646,2880],{"class":2055},[1115,32648,1199],{"class":2059},[1115,32650,32570],{"class":2047},[1115,32652,2090],{"class":2059},[2035,32654,32657],{"className":32655,"code":32656,"language":2169,"meta":2039},[2167]," 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",[1332,32658,32656],{"__ignoreMap":2039},[1110,32660,32661,32684,32685,32708],{},[1115,32662,32664],{"className":32663},[1137],[1139,32665,32666],{"xmlns":1141},[1143,32667,32668,32681],{},[1146,32669,32670,32672,32674,32677,32679],{},[1149,32671,1110],{},[1193,32673,1281],{},[1230,32675,32676],{},"0,0343",[1193,32678,5343],{},[1230,32680,4370],{},[1153,32682,32683],{"encoding":1155},"p = 0{,}0343 \u003C 0{,}05",": průměrný odpad se od 4 % statisticky významně liší (výběrový průměr 3,86 %). Shapiro-Wilkův test dává ",[1115,32686,32688],{"className":32687},[1137],[1139,32689,32690],{"xmlns":1141},[1143,32691,32692,32705],{},[1146,32693,32694,32696,32698,32701,32703],{},[1149,32695,1110],{},[1193,32697,1281],{},[1230,32699,32700],{},"0,4634",[1193,32702,5369],{},[1230,32704,4370],{},[1153,32706,32707],{"encoding":1155},"p = 0{,}4634 > 0{,}05",", předpoklad normality pro t-test je v pořádku.",[1377,32710,32712],{"id":32711},"párový-t-test","Párový t-test",[1110,32714,32715,32716,32746,32747,11154,32781,32819,32820,32833,32834,1405,32852,32872,32873,32890,32891,31435],{},"Používá se, když jsou měření závislá — na stejných objektech se měří dvě hodnoty ",[1115,32717,32719],{"className":32718},[1137],[1139,32720,32721],{"xmlns":1141},[1143,32722,32723,32743],{},[1146,32724,32725,32727,32733,32735,32741],{},[1193,32726,1199],{"stretchy":1198},[1201,32728,32729,32731],{},[1149,32730,11107],{},[1149,32732,1207],{},[1193,32734,1503],{"separator":1121},[1201,32736,32737,32739],{},[1149,32738,11460],{},[1149,32740,1207],{},[1193,32742,1228],{"stretchy":1198},[1153,32744,32745],{"encoding":1155},"(X_i, Y_i)"," a vyhodnocují se jejich diference ",[1115,32748,32750],{"className":32749},[1137],[1139,32751,32752],{"xmlns":1141},[1143,32753,32754,32778],{},[1146,32755,32756,32762,32764,32770,32772],{},[1201,32757,32758,32760],{},[1149,32759,12523],{},[1149,32761,1207],{},[1193,32763,1281],{},[1201,32765,32766,32768],{},[1149,32767,11107],{},[1149,32769,1207],{},[1193,32771,1210],{},[1201,32773,32774,32776],{},[1149,32775,11460],{},[1149,32777,1207],{},[1153,32779,32780],{"encoding":1155},"D_i = X_i - Y_i",[1115,32782,32784],{"className":32783},[1137],[1139,32785,32786],{"xmlns":1141},[1143,32787,32788,32816],{},[1146,32789,32790,32792,32794,32796,32798,32804,32806,32814],{},[1149,32791,12523],{},[1193,32793,13552],{},[1149,32795,11259],{},[1193,32797,1199],{"stretchy":1198},[1201,32799,32800,32802],{},[1149,32801,11264],{},[1149,32803,12523],{},[1193,32805,1503],{"separator":1121},[3698,32807,32808,32810,32812],{},[1149,32809,11271],{},[1149,32811,12523],{},[1230,32813,1232],{},[1193,32815,1228],{"stretchy":1198},[1153,32817,32818],{"encoding":1155},"D \\sim N(\\mu_D, \\sigma_D^2)",". Z ",[1115,32821,32823],{"className":32822},[1137],[1139,32824,32825],{"xmlns":1141},[1143,32826,32827,32831],{},[1146,32828,32829],{},[1149,32830,1816],{},[1153,32832,1816],{"encoding":1155}," dvojic se určí ",[1115,32835,32837],{"className":32836},[1137],[1139,32838,32839],{"xmlns":1141},[1143,32840,32841,32849],{},[1146,32842,32843],{},[1214,32844,32845,32847],{"accent":1121},[1149,32846,12167],{},[1193,32848,15814],{},[1153,32850,32851],{"encoding":1155},"\\bar{d}",[1115,32853,32855],{"className":32854},[1137],[1139,32856,32857],{"xmlns":1141},[1143,32858,32859,32869],{},[1146,32860,32861],{},[3698,32862,32863,32865,32867],{},[1149,32864,4542],{},[1149,32866,12167],{},[1230,32868,1232],{},[1153,32870,32871],{"encoding":1155},"s_d^2","; testuje se vztah mezi zvoleným číslem ",[1115,32874,32876],{"className":32875},[1137],[1139,32877,32878],{"xmlns":1141},[1143,32879,32880,32888],{},[1146,32881,32882],{},[1201,32883,32884,32886],{},[1149,32885,11264],{},[1230,32887,1597],{},[1153,32889,31420],{"encoding":1155}," (obvykle 0) a ",[1115,32892,32894],{"className":32893},[1137],[1139,32895,32896],{"xmlns":1141},[1143,32897,32898,32906],{},[1146,32899,32900],{},[1201,32901,32902,32904],{},[1149,32903,11264],{},[1149,32905,12523],{},[1153,32907,32908],{"encoding":1155},"\\mu_D",[1115,32910,32912],{"className":32911},[1137],[1139,32913,32914],{"xmlns":1141,"display":1796},[1143,32915,32916,32966],{},[1146,32917,32918,32920,32922,32946,32950,32952,32964],{},[1149,32919,11474],{},[1193,32921,1281],{},[3546,32923,32924,32940],{},[1146,32925,32926,32932,32934],{},[1214,32927,32928,32930],{"accent":1121},[1149,32929,12167],{},[1193,32931,15814],{},[1193,32933,1210],{},[1201,32935,32936,32938],{},[1149,32937,11264],{},[1230,32939,1597],{},[1201,32941,32942,32944],{},[1149,32943,4542],{},[1149,32945,12167],{},[1283,32947,32948],{},[1149,32949,1816],{},[1193,32951,13552],{},[1201,32953,32954,32956],{},[1149,32955,11515],{},[1146,32957,32958,32960,32962],{},[1149,32959,1816],{},[1193,32961,1210],{},[1230,32963,1525],{},[1149,32965,1236],{"mathvariant":1854},[1153,32967,32968],{"encoding":1155},"T = \\frac{\\bar{d} - \\mu_0}{s_d}\\sqrt{n} \\sim t_{n-1}.",[6528,32970,32971,33028],{},[6531,32972,32973],{},[6534,32974,32975,32994,33013],{},[6537,32976,32977],{},[1115,32978,32980],{"className":32979},[1137],[1139,32981,32982],{"xmlns":1141},[1143,32983,32984,32992],{},[1146,32985,32986],{},[1201,32987,32988,32990],{},[1149,32989,2227],{},[1230,32991,1597],{},[1153,32993,2743],{"encoding":1155},[6537,32995,32996],{},[1115,32997,32999],{"className":32998},[1137],[1139,33000,33001],{"xmlns":1141},[1143,33002,33003,33011],{},[1146,33004,33005],{},[1201,33006,33007,33009],{},[1149,33008,2227],{},[1230,33010,1525],{},[1153,33012,2762],{"encoding":1155},[6537,33014,31558,33015],{},[1115,33016,33018],{"className":33017},[1137],[1139,33019,33020],{"xmlns":1141},[1143,33021,33022,33026],{},[1146,33023,33024],{},[1149,33025,6052],{},[1153,33027,6052],{"encoding":1155},[6645,33029,33030,33127,33232],{},[6534,33031,33032,33060,33088],{},[6650,33033,33034],{},[1115,33035,33037],{"className":33036},[1137],[1139,33038,33039],{"xmlns":1141},[1143,33040,33041,33057],{},[1146,33042,33043,33049,33051],{},[1201,33044,33045,33047],{},[1149,33046,11264],{},[1149,33048,12523],{},[1193,33050,11110],{},[1201,33052,33053,33055],{},[1149,33054,11264],{},[1230,33056,1597],{},[1153,33058,33059],{"encoding":1155},"\\mu_D \\le \\mu_0",[6650,33061,33062],{},[1115,33063,33065],{"className":33064},[1137],[1139,33066,33067],{"xmlns":1141},[1143,33068,33069,33085],{},[1146,33070,33071,33077,33079],{},[1201,33072,33073,33075],{},[1149,33074,11264],{},[1149,33076,12523],{},[1193,33078,5369],{},[1201,33080,33081,33083],{},[1149,33082,11264],{},[1230,33084,1597],{},[1153,33086,33087],{"encoding":1155},"\\mu_D > \\mu_0",[6650,33089,33090],{},[1115,33091,33093],{"className":33092},[1137],[1139,33094,33095],{"xmlns":1141},[1143,33096,33097,33125],{},[1146,33098,33099,33101,33103,33115,33117,33119,33121,33123],{},[1149,33100,11515],{},[1193,33102,7775],{},[1201,33104,33105,33107],{},[1149,33106,11515],{},[1146,33108,33109,33111,33113],{},[1230,33110,1525],{},[1193,33112,1210],{},[1149,33114,7788],{},[1193,33116,1199],{"stretchy":1198},[1149,33118,1816],{},[1193,33120,1210],{},[1230,33122,1525],{},[1193,33124,1228],{"stretchy":1198},[1153,33126,31663],{"encoding":1155},[6534,33128,33129,33157,33185],{},[6650,33130,33131],{},[1115,33132,33134],{"className":33133},[1137],[1139,33135,33136],{"xmlns":1141},[1143,33137,33138,33154],{},[1146,33139,33140,33146,33148],{},[1201,33141,33142,33144],{},[1149,33143,11264],{},[1149,33145,12523],{},[1193,33147,1281],{},[1201,33149,33150,33152],{},[1149,33151,11264],{},[1230,33153,1597],{},[1153,33155,33156],{"encoding":1155},"\\mu_D = \\mu_0",[6650,33158,33159],{},[1115,33160,33162],{"className":33161},[1137],[1139,33163,33164],{"xmlns":1141},[1143,33165,33166,33182],{},[1146,33167,33168,33174,33176],{},[1201,33169,33170,33172],{},[1149,33171,11264],{},[1149,33173,12523],{},[1193,33175,2271],{"mathvariant":1854},[1201,33177,33178,33180],{},[1149,33179,11264],{},[1230,33181,1597],{},[1153,33183,33184],{"encoding":1155},"\\mu_D \\neq \\mu_0",[6650,33186,33187],{},[1115,33188,33190],{"className":33189},[1137],[1139,33191,33192],{"xmlns":1141},[1143,33193,33194,33230],{},[1146,33195,33196,33198,33200,33202,33204,33220,33222,33224,33226,33228],{},[1193,33197,26870],{"stretchy":1198},[1149,33199,11515],{},[1193,33201,26870],{"stretchy":1198},[1193,33203,7775],{},[1201,33205,33206,33208],{},[1149,33207,11515],{},[1146,33209,33210,33212,33214,33216,33218],{},[1230,33211,1525],{},[1193,33213,1210],{},[1149,33215,7788],{},[1149,33217,5731],{"mathvariant":1854},[1230,33219,1232],{},[1193,33221,1199],{"stretchy":1198},[1149,33223,1816],{},[1193,33225,1210],{},[1230,33227,1525],{},[1193,33229,1228],{"stretchy":1198},[1153,33231,31761],{"encoding":1155},[6534,33233,33234,33262,33290],{},[6650,33235,33236],{},[1115,33237,33239],{"className":33238},[1137],[1139,33240,33241],{"xmlns":1141},[1143,33242,33243,33259],{},[1146,33244,33245,33251,33253],{},[1201,33246,33247,33249],{},[1149,33248,11264],{},[1149,33250,12523],{},[1193,33252,7775],{},[1201,33254,33255,33257],{},[1149,33256,11264],{},[1230,33258,1597],{},[1153,33260,33261],{"encoding":1155},"\\mu_D \\ge \\mu_0",[6650,33263,33264],{},[1115,33265,33267],{"className":33266},[1137],[1139,33268,33269],{"xmlns":1141},[1143,33270,33271,33287],{},[1146,33272,33273,33279,33281],{},[1201,33274,33275,33277],{},[1149,33276,11264],{},[1149,33278,12523],{},[1193,33280,5343],{},[1201,33282,33283,33285],{},[1149,33284,11264],{},[1230,33286,1597],{},[1153,33288,33289],{"encoding":1155},"\\mu_D \u003C \\mu_0",[6650,33291,33292],{},[1115,33293,33295],{"className":33294},[1137],[1139,33296,33297],{"xmlns":1141},[1143,33298,33299,33329],{},[1146,33300,33301,33303,33305,33307,33319,33321,33323,33325,33327],{},[1149,33302,11515],{},[1193,33304,11110],{},[1193,33306,1210],{},[1201,33308,33309,33311],{},[1149,33310,11515],{},[1146,33312,33313,33315,33317],{},[1230,33314,1525],{},[1193,33316,1210],{},[1149,33318,7788],{},[1193,33320,1199],{"stretchy":1198},[1149,33322,1816],{},[1193,33324,1210],{},[1230,33326,1525],{},[1193,33328,1228],{"stretchy":1198},[1153,33330,31853],{"encoding":1155},[1103,33332,33334,33341,33483,33547,33633],{"className":33333,"dataCallout":2932},[1106,2931],[1110,33335,33337,33340],{"className":33336},[1113],[1115,33338],{"className":33339,"ariaHidden":1121},[1118,2939,1120],"Příklad: Snížení spotřeby paliva aditivem",[1110,33342,33343,33344,33362,33363,33381,33382,33400,33401,33434,33435,33458,33459,33482],{},"U ",[1115,33345,33347],{"className":33346},[1137],[1139,33348,33349],{"xmlns":1141},[1143,33350,33351,33359],{},[1146,33352,33353,33355,33357],{},[1149,33354,1816],{},[1193,33356,1281],{},[1230,33358,5389],{},[1153,33360,33361],{"encoding":1155},"n = 10"," vozů se změřila spotřeba před přidáním aditiva (",[1115,33364,33366],{"className":33365},[1137],[1139,33367,33368],{"xmlns":1141},[1143,33369,33370,33378],{},[1146,33371,33372],{},[1201,33373,33374,33376],{},[1149,33375,11107],{},[1149,33377,1207],{},[1153,33379,33380],{"encoding":1155},"X_i",") a po něm (",[1115,33383,33385],{"className":33384},[1137],[1139,33386,33387],{"xmlns":1141},[1143,33388,33389,33397],{},[1146,33390,33391],{},[1201,33392,33393,33395],{},[1149,33394,11460],{},[1149,33396,1207],{},[1153,33398,33399],{"encoding":1155},"Y_i","), diference ",[1115,33402,33404],{"className":33403},[1137],[1139,33405,33406],{"xmlns":1141},[1143,33407,33408,33432],{},[1146,33409,33410,33416,33418,33424,33426],{},[1201,33411,33412,33414],{},[1149,33413,12523],{},[1149,33415,1207],{},[1193,33417,1281],{},[1201,33419,33420,33422],{},[1149,33421,11107],{},[1149,33423,1207],{},[1193,33425,1210],{},[1201,33427,33428,33430],{},[1149,33429,11460],{},[1149,33431,1207],{},[1153,33433,32780],{"encoding":1155}," představují úsporu paliva. Z dat vyšla průměrná úspora ",[1115,33436,33438],{"className":33437},[1137],[1139,33439,33440],{"xmlns":1141},[1143,33441,33442,33455],{},[1146,33443,33444,33450,33452],{},[1214,33445,33446,33448],{"accent":1121},[1149,33447,12167],{},[1193,33449,15814],{},[1193,33451,1281],{},[1230,33453,33454],{},"0,4",[1153,33456,33457],{"encoding":1155},"\\bar{d} = 0{,}4"," l\u002F100 km, ",[1115,33460,33462],{"className":33461},[1137],[1139,33463,33464],{"xmlns":1141},[1143,33465,33466,33479],{},[1146,33467,33468,33474,33476],{},[1201,33469,33470,33472],{},[1149,33471,4542],{},[1149,33473,12167],{},[1193,33475,1281],{},[1230,33477,33478],{},"0,35",[1153,33480,33481],{"encoding":1155},"s_d = 0{,}35"," l\u002F100 km. Ověřte, že aditivum spotřebu statisticky významně snižuje.",[1110,33484,33485,33515,33516,33546],{},[1115,33486,33488],{"className":33487},[1137],[1139,33489,33490],{"xmlns":1141},[1143,33491,33492,33512],{},[1146,33493,33494,33500,33502,33508,33510],{},[1201,33495,33496,33498],{},[1149,33497,2227],{},[1230,33499,1597],{},[1193,33501,1902],{},[1201,33503,33504,33506],{},[1149,33505,11264],{},[1149,33507,12523],{},[1193,33509,11110],{},[1230,33511,1597],{},[1153,33513,33514],{"encoding":1155},"H_0: \\mu_D \\le 0"," (aditivum nemá vliv nebo spotřebu zvyšuje), ",[1115,33517,33519],{"className":33518},[1137],[1139,33520,33521],{"xmlns":1141},[1143,33522,33523,33543],{},[1146,33524,33525,33531,33533,33539,33541],{},[1201,33526,33527,33529],{},[1149,33528,2227],{},[1230,33530,1525],{},[1193,33532,1902],{},[1201,33534,33535,33537],{},[1149,33536,11264],{},[1149,33538,12523],{},[1193,33540,5369],{},[1230,33542,1597],{},[1153,33544,33545],{"encoding":1155},"H_1: \\mu_D > 0"," (aditivum spotřebu snižuje).",[1110,33548,33549],{},[1115,33550,33552],{"className":33551},[1137],[1139,33553,33554],{"xmlns":1141},[1143,33555,33556,33630],{},[1146,33557,33558,33560,33562,33574,33578,33580,33583,33585,33587,33589,33591,33593,33595,33597,33609,33611,33613,33615,33617,33619,33621,33623,33625,33628],{},[1149,33559,11515],{},[1193,33561,1281],{},[3546,33563,33564,33572],{},[1146,33565,33566,33568,33570],{},[1230,33567,33454],{},[1193,33569,1210],{},[1230,33571,1597],{},[1230,33573,33478],{},[1283,33575,33576],{},[1230,33577,5389],{},[1193,33579,1281],{},[1230,33581,33582],{},"3,614",[1193,33584,1503],{"separator":1121},[1936,33586],{"width":1938},[1149,33588,6052],{},[1193,33590,1281],{},[1193,33592,7758],{"stretchy":1198},[1149,33594,11515],{},[1193,33596,7775],{},[1201,33598,33599,33601],{},[1149,33600,11515],{},[1146,33602,33603,33605,33607],{},[1230,33604,1597],{},[1193,33606,1503],{"separator":1121},[1230,33608,25644],{},[1193,33610,1199],{"stretchy":1198},[1230,33612,8013],{},[1193,33614,1228],{"stretchy":1198},[1193,33616,7817],{"stretchy":1198},[1193,33618,1281],{},[1193,33620,7758],{"stretchy":1198},[1149,33622,11515],{},[1193,33624,7775],{},[1230,33626,33627],{},"1,833",[1193,33629,7817],{"stretchy":1198},[1153,33631,33632],{"encoding":1155},"t = \\frac{0{,}4 - 0}{0{,}35}\\sqrt{10} = 3{,}614, \\qquad W = \\{t \\ge t_{0,95}(9)\\} = \\{t \\ge 1{,}833\\}",[1110,33634,32244,33635,10395,33652,33669],{},[1115,33636,33638],{"className":33637},[1137],[1139,33639,33640],{"xmlns":1141},[1143,33641,33642,33650],{},[1146,33643,33644,33646,33648],{},[1149,33645,11515],{},[1193,33647,11391],{},[1149,33649,6052],{},[1153,33651,32262],{"encoding":1155},[1115,33653,33655],{"className":33654},[1137],[1139,33656,33657],{"xmlns":1141},[1143,33658,33659,33667],{},[1146,33660,33661],{},[1201,33662,33663,33665],{},[1149,33664,2227],{},[1230,33666,1597],{},[1153,33668,2743],{"encoding":1155},": aditivum prokazatelně snižuje průměrnou spotřebu paliva.",[2035,33671,33673],{"className":2037,"code":33672,"language":71,"meta":2039,"style":2039},"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",[1332,33674,33675,33704,33735,33761,33765],{"__ignoreMap":2039},[1115,33676,33677,33680,33682,33685,33687,33690,33692,33695,33697,33699,33701],{"class":2044,"line":10},[1115,33678,33679],{"class":2047},"dbar",[1115,33681,2052],{"class":2051},[1115,33683,33684],{"class":2062}," 0.4",[1115,33686,29030],{"class":2059},[1115,33688,33689],{"class":2047},"sd_d",[1115,33691,2052],{"class":2051},[1115,33693,33694],{"class":2062}," 0.35",[1115,33696,29030],{"class":2059},[1115,33698,1816],{"class":2047},[1115,33700,2052],{"class":2051},[1115,33702,33703],{"class":2062}," 10\n",[1115,33705,33706,33708,33710,33712,33714,33716,33718,33720,33722,33725,33727,33729,33731,33733],{"class":2044,"line":27},[1115,33707,11515],{"class":2047},[1115,33709,2052],{"class":2051},[1115,33711,4053],{"class":2059},[1115,33713,33679],{"class":2047},[1115,33715,29367],{"class":2051},[1115,33717,14336],{"class":2062},[1115,33719,8993],{"class":2059},[1115,33721,5731],{"class":2051},[1115,33723,33724],{"class":2047}," sd_d",[1115,33726,3957],{"class":2051},[1115,33728,8970],{"class":2055},[1115,33730,1199],{"class":2059},[1115,33732,1816],{"class":2047},[1115,33734,2090],{"class":2059},[1115,33736,33737,33739,33741,33743,33745,33747,33749,33751,33753,33755,33757,33759],{"class":2044,"line":148},[1115,33738,32369],{"class":2047},[1115,33740,2052],{"class":2051},[1115,33742,32374],{"class":2055},[1115,33744,1199],{"class":2059},[1115,33746,15187],{"class":2062},[1115,33748,1503],{"class":2051},[1115,33750,15170],{"class":2047},[1115,33752,2510],{"class":2051},[1115,33754,32388],{"class":2047},[1115,33756,29367],{"class":2051},[1115,33758,9031],{"class":2062},[1115,33760,2090],{"class":2059},[1115,33762,33763],{"class":2044,"line":111},[1115,33764,32399],{"class":2047},[1115,33766,33767],{"class":2044,"line":96},[1115,33768,32404],{"class":2047},[2035,33770,33773],{"className":33771,"code":33772,"language":2169,"meta":2039},[2167],"[1] 3.614032\n[1] 1.833113\n",[1332,33774,33772],{"__ignoreMap":2039},[1103,33776,33778,33785,33788,33933,33939],{"className":33777,"dataCallout":5686},[1106,5685],[1110,33779,33781,33784],{"className":33780},[1113],[1115,33782],{"className":33783,"ariaHidden":1121},[1118,5693,1120],"Ověřte normalitu diferencí, ne jen výsledek testu",[1110,33786,33787],{},"Realitní kancelář nechala dva odhadce ocenit osm nemovitostí (tisíce Kč):",[2035,33789,33791],{"className":2037,"code":33790,"language":71,"meta":2039,"style":2039},"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",[1332,33792,33793,33844,33895,33919],{"__ignoreMap":2039},[1115,33794,33795,33798,33800,33802,33804,33807,33809,33812,33814,33817,33819,33822,33824,33827,33829,33832,33834,33837,33839,33842],{"class":2044,"line":10},[1115,33796,33797],{"class":2047},"estA",[1115,33799,2052],{"class":2051},[1115,33801,2056],{"class":2055},[1115,33803,1199],{"class":2059},[1115,33805,33806],{"class":2062},"3282",[1115,33808,1503],{"class":2051},[1115,33810,33811],{"class":2062}," 2506",[1115,33813,1503],{"class":2051},[1115,33815,33816],{"class":2062}," 2812",[1115,33818,1503],{"class":2051},[1115,33820,33821],{"class":2062}," 5453",[1115,33823,1503],{"class":2051},[1115,33825,33826],{"class":2062}," 3263",[1115,33828,1503],{"class":2051},[1115,33830,33831],{"class":2062}," 4571",[1115,33833,1503],{"class":2051},[1115,33835,33836],{"class":2062}," 3121",[1115,33838,1503],{"class":2051},[1115,33840,33841],{"class":2062}," 2963",[1115,33843,2090],{"class":2059},[1115,33845,33846,33849,33851,33853,33855,33858,33860,33863,33865,33868,33870,33873,33875,33878,33880,33883,33885,33888,33890,33893],{"class":2044,"line":27},[1115,33847,33848],{"class":2047},"estB",[1115,33850,2052],{"class":2051},[1115,33852,2056],{"class":2055},[1115,33854,1199],{"class":2059},[1115,33856,33857],{"class":2062},"3271",[1115,33859,1503],{"class":2051},[1115,33861,33862],{"class":2062}," 2531",[1115,33864,1503],{"class":2051},[1115,33866,33867],{"class":2062}," 2799",[1115,33869,1503],{"class":2051},[1115,33871,33872],{"class":2062}," 5471",[1115,33874,1503],{"class":2051},[1115,33876,33877],{"class":2062}," 3285",[1115,33879,1503],{"class":2051},[1115,33881,33882],{"class":2062}," 4557",[1115,33884,1503],{"class":2051},[1115,33886,33887],{"class":2062}," 3139",[1115,33889,1503],{"class":2051},[1115,33891,33892],{"class":2062}," 2976",[1115,33894,2090],{"class":2059},[1115,33896,33897,33899,33901,33903,33905,33908,33910,33913,33915,33917],{"class":2044,"line":148},[1115,33898,31924],{"class":2055},[1115,33900,1199],{"class":2059},[1115,33902,33797],{"class":2047},[1115,33904,1503],{"class":2051},[1115,33906,33907],{"class":2047}," estB",[1115,33909,1503],{"class":2051},[1115,33911,33912],{"class":2047}," paired",[1115,33914,2510],{"class":2051},[1115,33916,5460],{"class":2062},[1115,33918,2090],{"class":2059},[1115,33920,33921,33923,33925,33927,33929,33931],{"class":2044,"line":111},[1115,33922,2880],{"class":2055},[1115,33924,1199],{"class":2059},[1115,33926,33797],{"class":2047},[1115,33928,29367],{"class":2051},[1115,33930,33907],{"class":2047},[1115,33932,2090],{"class":2059},[2035,33934,33937],{"className":33935,"code":33936,"language":2169,"meta":2039},[2167]," 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",[1332,33938,33936],{"__ignoreMap":2039},[1110,33940,33941,33942,4053,33959,33978,33979,34002],{},"Párový t-test sám nezamítá ",[1115,33943,33945],{"className":33944},[1137],[1139,33946,33947],{"xmlns":1141},[1143,33948,33949,33957],{},[1146,33950,33951],{},[1201,33952,33953,33955],{},[1149,33954,2227],{},[1230,33956,1597],{},[1153,33958,2743],{"encoding":1155},[1115,33960,33962],{"className":33961},[1137],[1139,33963,33964],{"xmlns":1141},[1143,33965,33966,33975],{},[1146,33967,33968,33970,33972],{},[1149,33969,1110],{},[1193,33971,1281],{},[1230,33973,33974],{},"0,2635",[1153,33976,33977],{"encoding":1155},"p = 0{,}2635","): odhadci se podle něj neliší. Shapiro-Wilkův test na diferencích ale dává ",[1115,33980,33982],{"className":33981},[1137],[1139,33983,33984],{"xmlns":1141},[1143,33985,33986,33999],{},[1146,33987,33988,33990,33992,33995,33997],{},[1149,33989,1110],{},[1193,33991,1281],{},[1230,33993,33994],{},"0,03203",[1193,33996,5343],{},[1230,33998,4370],{},[1153,34000,34001],{"encoding":1155},"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).",[1377,34004,34006],{"id":34005},"testy-o-dvou-základních-souborech","Testy o dvou základních souborech",[1110,34008,34009,34010,34036,34037,34075,34076,1405,34094,34075,34132,34150,34151,1405,34183,34215,34216,34242,34243,1236],{},"Uvažují se dva nezávislé základní soubory ",[1115,34011,34013],{"className":34012},[1137],[1139,34014,34015],{"xmlns":1141},[1143,34016,34017,34033],{},[1146,34018,34019,34025,34027],{},[1201,34020,34021,34023],{},[1149,34022,13295],{},[1230,34024,1525],{},[1193,34026,1503],{"separator":1121},[1201,34028,34029,34031],{},[1149,34030,13295],{},[1230,34032,1232],{},[1153,34034,34035],{"encoding":1155},"Z_1, Z_2"," se znakem ",[1115,34038,34040],{"className":34039},[1137],[1139,34041,34042],{"xmlns":1141},[1143,34043,34044,34072],{},[1146,34045,34046,34048,34050,34052,34054,34060,34062,34070],{},[1149,34047,11107],{},[1193,34049,13552],{},[1149,34051,11259],{},[1193,34053,1199],{"stretchy":1198},[1201,34055,34056,34058],{},[1149,34057,11264],{},[1230,34059,1525],{},[1193,34061,1503],{"separator":1121},[3698,34063,34064,34066,34068],{},[1149,34065,11271],{},[1230,34067,1525],{},[1230,34069,1232],{},[1193,34071,1228],{"stretchy":1198},[1153,34073,34074],{"encoding":1155},"X \\sim N(\\mu_1, \\sigma_1^2)"," v ",[1115,34077,34079],{"className":34078},[1137],[1139,34080,34081],{"xmlns":1141},[1143,34082,34083,34091],{},[1146,34084,34085],{},[1201,34086,34087,34089],{},[1149,34088,13295],{},[1230,34090,1525],{},[1153,34092,34093],{"encoding":1155},"Z_1",[1115,34095,34097],{"className":34096},[1137],[1139,34098,34099],{"xmlns":1141},[1143,34100,34101,34129],{},[1146,34102,34103,34105,34107,34109,34111,34117,34119,34127],{},[1149,34104,11107],{},[1193,34106,13552],{},[1149,34108,11259],{},[1193,34110,1199],{"stretchy":1198},[1201,34112,34113,34115],{},[1149,34114,11264],{},[1230,34116,1232],{},[1193,34118,1503],{"separator":1121},[3698,34120,34121,34123,34125],{},[1149,34122,11271],{},[1230,34124,1232],{},[1230,34126,1232],{},[1193,34128,1228],{"stretchy":1198},[1153,34130,34131],{"encoding":1155},"X \\sim N(\\mu_2, \\sigma_2^2)",[1115,34133,34135],{"className":34134},[1137],[1139,34136,34137],{"xmlns":1141},[1143,34138,34139,34147],{},[1146,34140,34141],{},[1201,34142,34143,34145],{},[1149,34144,13295],{},[1230,34146,1232],{},[1153,34148,34149],{"encoding":1155},"Z_2",". Z výběrů se určí ",[1115,34152,34154],{"className":34153},[1137],[1139,34155,34156],{"xmlns":1141},[1143,34157,34158,34180],{},[1146,34159,34160,34170,34172],{},[1201,34161,34162,34168],{},[1214,34163,34164,34166],{"accent":1121},[1149,34165,1168],{},[1193,34167,15814],{},[1230,34169,1525],{},[1193,34171,1503],{"separator":1121},[3698,34173,34174,34176,34178],{},[1149,34175,4542],{},[1230,34177,1525],{},[1230,34179,1232],{},[1153,34181,34182],{"encoding":1155},"\\bar{x}_1, s_1^2",[1115,34184,34186],{"className":34185},[1137],[1139,34187,34188],{"xmlns":1141},[1143,34189,34190,34212],{},[1146,34191,34192,34202,34204],{},[1201,34193,34194,34200],{},[1214,34195,34196,34198],{"accent":1121},[1149,34197,1168],{},[1193,34199,15814],{},[1230,34201,1232],{},[1193,34203,1503],{"separator":1121},[3698,34205,34206,34208,34210],{},[1149,34207,4542],{},[1230,34209,1232],{},[1230,34211,1232],{},[1153,34213,34214],{"encoding":1155},"\\bar{x}_2, s_2^2",". Testují se varianty vztahů mezi ",[1115,34217,34219],{"className":34218},[1137],[1139,34220,34221],{"xmlns":1141},[1143,34222,34223,34239],{},[1146,34224,34225,34231,34233],{},[1201,34226,34227,34229],{},[1149,34228,11264],{},[1230,34230,1525],{},[1193,34232,1503],{"separator":1121},[1201,34234,34235,34237],{},[1149,34236,11264],{},[1230,34238,1232],{},[1153,34240,34241],{"encoding":1155},"\\mu_1, \\mu_2",", resp. mezi ",[1115,34244,34246],{"className":34245},[1137],[1139,34247,34248],{"xmlns":1141},[1143,34249,34250,34270],{},[1146,34251,34252,34260,34262],{},[3698,34253,34254,34256,34258],{},[1149,34255,11271],{},[1230,34257,1525],{},[1230,34259,1232],{},[1193,34261,1503],{"separator":1121},[3698,34263,34264,34266,34268],{},[1149,34265,11271],{},[1230,34267,1232],{},[1230,34269,1232],{},[1153,34271,34272],{"encoding":1155},"\\sigma_1^2, \\sigma_2^2",[2019,34274,34276],{"id":34275},"f-test-o-rozptylech","F-test o rozptylech",[1110,34278,34279],{},"Statistika",[1115,34281,34283],{"className":34282},[1137],[1139,34284,34285],{"xmlns":1141,"display":1796},[1143,34286,34287,34343],{},[1146,34288,34289,34291,34293,34311,34313],{},[1149,34290,11091],{},[1193,34292,1281],{},[3546,34294,34295,34303],{},[3698,34296,34297,34299,34301],{},[1149,34298,4542],{},[1230,34300,1525],{},[1230,34302,1232],{},[3698,34304,34305,34307,34309],{},[1149,34306,4542],{},[1230,34308,1232],{},[1230,34310,1232],{},[1193,34312,13552],{},[1201,34314,34315,34317],{},[1149,34316,11091],{},[1146,34318,34319,34325,34327,34329,34331,34333,34339,34341],{},[1201,34320,34321,34323],{},[1149,34322,1816],{},[1230,34324,1525],{},[1193,34326,1210],{},[1230,34328,1525],{},[1193,34330,1503],{"separator":1121},[2201,34332,2203],{},[1201,34334,34335,34337],{},[1149,34336,1816],{},[1230,34338,1232],{},[1193,34340,1210],{},[1230,34342,1525],{},[1153,34344,34345],{"encoding":1155},"F = \\frac{s_1^2}{s_2^2} \\sim F_{n_1-1,\\,n_2-1}",[1110,34347,34348,34349,1405,34371,31511],{},"má Fisherovo-Snedecorovo rozdělení o ",[1115,34350,34352],{"className":34351},[1137],[1139,34353,34354],{"xmlns":1141},[1143,34355,34356,34368],{},[1146,34357,34358,34364,34366],{},[1201,34359,34360,34362],{},[1149,34361,1816],{},[1230,34363,1525],{},[1193,34365,1210],{},[1230,34367,1525],{},[1153,34369,34370],{"encoding":1155},"n_1-1",[1115,34372,34374],{"className":34373},[1137],[1139,34375,34376],{"xmlns":1141},[1143,34377,34378,34390],{},[1146,34379,34380,34386,34388],{},[1201,34381,34382,34384],{},[1149,34383,1816],{},[1230,34385,1232],{},[1193,34387,1210],{},[1230,34389,1525],{},[1153,34391,34392],{"encoding":1155},"n_2-1",[6528,34394,34395,34452],{},[6531,34396,34397],{},[6534,34398,34399,34418,34437],{},[6537,34400,34401],{},[1115,34402,34404],{"className":34403},[1137],[1139,34405,34406],{"xmlns":1141},[1143,34407,34408,34416],{},[1146,34409,34410],{},[1201,34411,34412,34414],{},[1149,34413,2227],{},[1230,34415,1597],{},[1153,34417,2743],{"encoding":1155},[6537,34419,34420],{},[1115,34421,34423],{"className":34422},[1137],[1139,34424,34425],{"xmlns":1141},[1143,34426,34427,34435],{},[1146,34428,34429],{},[1201,34430,34431,34433],{},[1149,34432,2227],{},[1230,34434,1525],{},[1153,34436,2762],{"encoding":1155},[6537,34438,31558,34439],{},[1115,34440,34442],{"className":34441},[1137],[1139,34443,34444],{"xmlns":1141},[1143,34445,34446,34450],{},[1146,34447,34448],{},[1149,34449,6052],{},[1153,34451,6052],{"encoding":1155},[6645,34453,34454,34568,34741],{},[6534,34455,34456,34484,34512],{},[6650,34457,34458],{},[1115,34459,34461],{"className":34460},[1137],[1139,34462,34463],{"xmlns":1141},[1143,34464,34465,34481],{},[1146,34466,34467,34473,34475],{},[1201,34468,34469,34471],{},[1149,34470,11271],{},[1230,34472,1525],{},[1193,34474,11110],{},[1201,34476,34477,34479],{},[1149,34478,11271],{},[1230,34480,1232],{},[1153,34482,34483],{"encoding":1155},"\\sigma_1 \\le \\sigma_2",[6650,34485,34486],{},[1115,34487,34489],{"className":34488},[1137],[1139,34490,34491],{"xmlns":1141},[1143,34492,34493,34509],{},[1146,34494,34495,34501,34503],{},[1201,34496,34497,34499],{},[1149,34498,11271],{},[1230,34500,1525],{},[1193,34502,5369],{},[1201,34504,34505,34507],{},[1149,34506,11271],{},[1230,34508,1232],{},[1153,34510,34511],{"encoding":1155},"\\sigma_1 > \\sigma_2",[6650,34513,34514],{},[1115,34515,34517],{"className":34516},[1137],[1139,34518,34519],{"xmlns":1141},[1143,34520,34521,34565],{},[1146,34522,34523,34525,34527,34539,34541,34547,34549,34551,34553,34559,34561,34563],{},[1149,34524,11091],{},[1193,34526,7775],{},[1201,34528,34529,34531],{},[1149,34530,11091],{},[1146,34532,34533,34535,34537],{},[1230,34534,1525],{},[1193,34536,1210],{},[1149,34538,7788],{},[1193,34540,1199],{"stretchy":1198},[1201,34542,34543,34545],{},[1149,34544,1816],{},[1230,34546,1525],{},[1193,34548,1210],{},[1230,34550,1525],{},[1193,34552,1503],{"separator":1121},[1201,34554,34555,34557],{},[1149,34556,1816],{},[1230,34558,1232],{},[1193,34560,1210],{},[1230,34562,1525],{},[1193,34564,1228],{"stretchy":1198},[1153,34566,34567],{"encoding":1155},"F \\ge F_{1-\\alpha}(n_1-1, n_2-1)",[6534,34569,34570,34598,34626],{},[6650,34571,34572],{},[1115,34573,34575],{"className":34574},[1137],[1139,34576,34577],{"xmlns":1141},[1143,34578,34579,34595],{},[1146,34580,34581,34587,34589],{},[1201,34582,34583,34585],{},[1149,34584,11271],{},[1230,34586,1525],{},[1193,34588,1281],{},[1201,34590,34591,34593],{},[1149,34592,11271],{},[1230,34594,1232],{},[1153,34596,34597],{"encoding":1155},"\\sigma_1 = \\sigma_2",[6650,34599,34600],{},[1115,34601,34603],{"className":34602},[1137],[1139,34604,34605],{"xmlns":1141},[1143,34606,34607,34623],{},[1146,34608,34609,34615,34617],{},[1201,34610,34611,34613],{},[1149,34612,11271],{},[1230,34614,1525],{},[1193,34616,2271],{"mathvariant":1854},[1201,34618,34619,34621],{},[1149,34620,11271],{},[1230,34622,1232],{},[1153,34624,34625],{"encoding":1155},"\\sigma_1 \\neq \\sigma_2",[6650,34627,34628,34682,34683],{},[1115,34629,34631],{"className":34630},[1137],[1139,34632,34633],{"xmlns":1141},[1143,34634,34635,34679],{},[1146,34636,34637,34639,34641,34653,34655,34661,34663,34665,34667,34673,34675,34677],{},[1149,34638,11091],{},[1193,34640,11110],{},[1201,34642,34643,34645],{},[1149,34644,11091],{},[1146,34646,34647,34649,34651],{},[1149,34648,7788],{},[1149,34650,5731],{"mathvariant":1854},[1230,34652,1232],{},[1193,34654,1199],{"stretchy":1198},[1201,34656,34657,34659],{},[1149,34658,1816],{},[1230,34660,1525],{},[1193,34662,1210],{},[1230,34664,1525],{},[1193,34666,1503],{"separator":1121},[1201,34668,34669,34671],{},[1149,34670,1816],{},[1230,34672,1232],{},[1193,34674,1210],{},[1230,34676,1525],{},[1193,34678,1228],{"stretchy":1198},[1153,34680,34681],{"encoding":1155},"F \\le F_{\\alpha\u002F2}(n_1-1, n_2-1)"," nebo ",[1115,34684,34686],{"className":34685},[1137],[1139,34687,34688],{"xmlns":1141},[1143,34689,34690,34738],{},[1146,34691,34692,34694,34696,34712,34714,34720,34722,34724,34726,34732,34734,34736],{},[1149,34693,11091],{},[1193,34695,7775],{},[1201,34697,34698,34700],{},[1149,34699,11091],{},[1146,34701,34702,34704,34706,34708,34710],{},[1230,34703,1525],{},[1193,34705,1210],{},[1149,34707,7788],{},[1149,34709,5731],{"mathvariant":1854},[1230,34711,1232],{},[1193,34713,1199],{"stretchy":1198},[1201,34715,34716,34718],{},[1149,34717,1816],{},[1230,34719,1525],{},[1193,34721,1210],{},[1230,34723,1525],{},[1193,34725,1503],{"separator":1121},[1201,34727,34728,34730],{},[1149,34729,1816],{},[1230,34731,1232],{},[1193,34733,1210],{},[1230,34735,1525],{},[1193,34737,1228],{"stretchy":1198},[1153,34739,34740],{"encoding":1155},"F \\ge F_{1-\\alpha\u002F2}(n_1-1, n_2-1)",[6534,34742,34743,34771,34799],{},[6650,34744,34745],{},[1115,34746,34748],{"className":34747},[1137],[1139,34749,34750],{"xmlns":1141},[1143,34751,34752,34768],{},[1146,34753,34754,34760,34762],{},[1201,34755,34756,34758],{},[1149,34757,11271],{},[1230,34759,1525],{},[1193,34761,7775],{},[1201,34763,34764,34766],{},[1149,34765,11271],{},[1230,34767,1232],{},[1153,34769,34770],{"encoding":1155},"\\sigma_1 \\ge \\sigma_2",[6650,34772,34773],{},[1115,34774,34776],{"className":34775},[1137],[1139,34777,34778],{"xmlns":1141},[1143,34779,34780,34796],{},[1146,34781,34782,34788,34790],{},[1201,34783,34784,34786],{},[1149,34785,11271],{},[1230,34787,1525],{},[1193,34789,5343],{},[1201,34791,34792,34794],{},[1149,34793,11271],{},[1230,34795,1232],{},[1153,34797,34798],{"encoding":1155},"\\sigma_1 \u003C \\sigma_2",[6650,34800,34801],{},[1115,34802,34804],{"className":34803},[1137],[1139,34805,34806],{"xmlns":1141},[1143,34807,34808,34846],{},[1146,34809,34810,34812,34814,34820,34822,34828,34830,34832,34834,34840,34842,34844],{},[1149,34811,11091],{},[1193,34813,11110],{},[1201,34815,34816,34818],{},[1149,34817,11091],{},[1149,34819,7788],{},[1193,34821,1199],{"stretchy":1198},[1201,34823,34824,34826],{},[1149,34825,1816],{},[1230,34827,1525],{},[1193,34829,1210],{},[1230,34831,1525],{},[1193,34833,1503],{"separator":1121},[1201,34835,34836,34838],{},[1149,34837,1816],{},[1230,34839,1232],{},[1193,34841,1210],{},[1230,34843,1525],{},[1193,34845,1228],{"stretchy":1198},[1153,34847,34848],{"encoding":1155},"F \\le F_{\\alpha}(n_1-1, n_2-1)",[2019,34850,34852],{"id":34851},"dvouvýběrový-t-test-o-středních-hodnotách","Dvouvýběrový t-test o středních hodnotách",[1110,34854,34855],{},"Volba statistiky závisí na tom, zda jsou rozptyly považovány za shodné:",[1115,34857,34859],{"className":34858},[1137],[1139,34860,34861],{"xmlns":1141,"display":1796},[1143,34862,34863,35040],{},[1146,34864,34865,34871,34873,34949,34997,34999,35001,35010,35012,35018,35020,35026,35028,35034,35036,35038],{},[1201,34866,34867,34869],{},[1149,34868,11474],{},[1230,34870,1525],{},[1193,34872,1281],{},[3546,34874,34875,34899],{},[1146,34876,34877,34887,34889],{},[1201,34878,34879,34885],{},[1214,34880,34881,34883],{"accent":1121},[1149,34882,1168],{},[1193,34884,15814],{},[1230,34886,1525],{},[1193,34888,1210],{},[1201,34890,34891,34897],{},[1214,34892,34893,34895],{"accent":1121},[1149,34894,1168],{},[1193,34896,15814],{},[1230,34898,1232],{},[1283,34900,34901],{},[1146,34902,34903,34905,34911,34913,34915,34917,34925,34927,34929,34935,34937,34939,34941],{},[1193,34904,1199],{"stretchy":1198},[1201,34906,34907,34909],{},[1149,34908,1816],{},[1230,34910,1525],{},[1193,34912,1210],{},[1230,34914,1525],{},[1193,34916,1228],{"stretchy":1198},[3698,34918,34919,34921,34923],{},[1149,34920,4542],{},[1230,34922,1525],{},[1230,34924,1232],{},[1193,34926,1924],{},[1193,34928,1199],{"stretchy":1198},[1201,34930,34931,34933],{},[1149,34932,1816],{},[1230,34934,1232],{},[1193,34936,1210],{},[1230,34938,1525],{},[1193,34940,1228],{"stretchy":1198},[3698,34942,34943,34945,34947],{},[1149,34944,4542],{},[1230,34946,1232],{},[1230,34948,1232],{},[1283,34950,34951],{},[3546,34952,34953,34973],{},[1146,34954,34955,34961,34963,34969,34971],{},[1201,34956,34957,34959],{},[1149,34958,1816],{},[1230,34960,1525],{},[1193,34962,1924],{},[1201,34964,34965,34967],{},[1149,34966,1816],{},[1230,34968,1232],{},[1193,34970,1210],{},[1230,34972,1232],{},[1146,34974,34975,34985,34987],{},[3546,34976,34977,34979],{},[1230,34978,1525],{},[1201,34980,34981,34983],{},[1149,34982,1816],{},[1230,34984,1525],{},[1193,34986,1924],{},[3546,34988,34989,34991],{},[1230,34990,1525],{},[1201,34992,34993,34995],{},[1149,34994,1816],{},[1230,34996,1232],{},[1193,34998,1503],{"separator":1121},[1936,35000],{"width":1938},[3698,35002,35003,35005,35007],{},[1149,35004,11515],{},[1149,35006,1110],{},[1193,35008,35009],{},"∗",[1193,35011,1281],{},[1201,35013,35014,35016],{},[1149,35015,11515],{},[1149,35017,1110],{},[1193,35019,1199],{"stretchy":1198},[1201,35021,35022,35024],{},[1149,35023,1816],{},[1230,35025,1525],{},[1193,35027,1924],{},[1201,35029,35030,35032],{},[1149,35031,1816],{},[1230,35033,1232],{},[1193,35035,1210],{},[1230,35037,1232],{},[1193,35039,1228],{"stretchy":1198},[1153,35041,35042],{"encoding":1155},"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)",[1110,35044,35045,35046,35075],{},"se použije, pokud jsou rozptyly ",[1115,35047,35049],{"className":35048},[1137],[1139,35050,35051],{"xmlns":1141},[1143,35052,35053,35073],{},[1146,35054,35055,35063,35065],{},[3698,35056,35057,35059,35061],{},[1149,35058,11271],{},[1230,35060,1525],{},[1230,35062,1232],{},[1193,35064,1503],{"separator":1121},[3698,35066,35067,35069,35071],{},[1149,35068,11271],{},[1230,35070,1232],{},[1230,35072,1232],{},[1153,35074,34272],{"encoding":1155}," alespoň přibližně shodné; při rozdílných rozptylech",[1115,35077,35079],{"className":35078},[1137],[1139,35080,35081],{"xmlns":1141,"display":1796},[1143,35082,35083,35295],{},[1146,35084,35085,35091,35093,35157,35159,35161,35169,35171,35293],{},[1201,35086,35087,35089],{},[1149,35088,11474],{},[1230,35090,1232],{},[1193,35092,1281],{},[3546,35094,35095,35119],{},[1146,35096,35097,35107,35109],{},[1201,35098,35099,35105],{},[1214,35100,35101,35103],{"accent":1121},[1149,35102,1168],{},[1193,35104,15814],{},[1230,35106,1525],{},[1193,35108,1210],{},[1201,35110,35111,35117],{},[1214,35112,35113,35115],{"accent":1121},[1149,35114,1168],{},[1193,35116,15814],{},[1230,35118,1232],{},[1283,35120,35121],{},[1146,35122,35123,35131,35133,35139,35141,35149,35151],{},[3698,35124,35125,35127,35129],{},[1149,35126,4542],{},[1230,35128,1525],{},[1230,35130,1232],{},[1149,35132,5731],{"mathvariant":1854},[1201,35134,35135,35137],{},[1149,35136,1816],{},[1230,35138,1525],{},[1193,35140,1924],{},[3698,35142,35143,35145,35147],{},[1149,35144,4542],{},[1230,35146,1232],{},[1230,35148,1232],{},[1149,35150,5731],{"mathvariant":1854},[1201,35152,35153,35155],{},[1149,35154,1816],{},[1230,35156,1232],{},[1193,35158,1503],{"separator":1121},[1936,35160],{"width":1938},[3698,35162,35163,35165,35167],{},[1149,35164,11515],{},[1149,35166,1110],{},[1193,35168,35009],{},[1193,35170,1281],{},[3546,35172,35173,35253],{},[1146,35174,35175,35193,35199,35201,35207,35209,35211,35213,35215,35233,35239,35241,35247,35249,35251],{},[3310,35176,35177],{"scriptlevel":1597,"displaystyle":1121},[3546,35178,35179,35187],{},[3698,35180,35181,35183,35185],{},[1149,35182,4542],{},[1230,35184,1525],{},[1230,35186,1232],{},[1201,35188,35189,35191],{},[1149,35190,1816],{},[1230,35192,1525],{},[1201,35194,35195,35197],{},[1149,35196,11515],{},[1149,35198,1110],{},[1193,35200,1199],{"stretchy":1198},[1201,35202,35203,35205],{},[1149,35204,1816],{},[1230,35206,1525],{},[1193,35208,1210],{},[1230,35210,1525],{},[1193,35212,1228],{"stretchy":1198},[1193,35214,1924],{},[3310,35216,35217],{"scriptlevel":1597,"displaystyle":1121},[3546,35218,35219,35227],{},[3698,35220,35221,35223,35225],{},[1149,35222,4542],{},[1230,35224,1232],{},[1230,35226,1232],{},[1201,35228,35229,35231],{},[1149,35230,1816],{},[1230,35232,1232],{},[1201,35234,35235,35237],{},[1149,35236,11515],{},[1149,35238,1110],{},[1193,35240,1199],{"stretchy":1198},[1201,35242,35243,35245],{},[1149,35244,1816],{},[1230,35246,1232],{},[1193,35248,1210],{},[1230,35250,1525],{},[1193,35252,1228],{"stretchy":1198},[1146,35254,35255,35273,35275],{},[3310,35256,35257],{"scriptlevel":1597,"displaystyle":1121},[3546,35258,35259,35267],{},[3698,35260,35261,35263,35265],{},[1149,35262,4542],{},[1230,35264,1525],{},[1230,35266,1232],{},[1201,35268,35269,35271],{},[1149,35270,1816],{},[1230,35272,1525],{},[1193,35274,1924],{},[3310,35276,35277],{"scriptlevel":1597,"displaystyle":1121},[3546,35278,35279,35287],{},[3698,35280,35281,35283,35285],{},[1149,35282,4542],{},[1230,35284,1232],{},[1230,35286,1232],{},[1201,35288,35289,35291],{},[1149,35290,1816],{},[1230,35292,1232],{},[1149,35294,1236],{"mathvariant":1854},[1153,35296,35297],{"encoding":1155},"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}}.",[6528,35299,35300,35357],{},[6531,35301,35302],{},[6534,35303,35304,35323,35342],{},[6537,35305,35306],{},[1115,35307,35309],{"className":35308},[1137],[1139,35310,35311],{"xmlns":1141},[1143,35312,35313,35321],{},[1146,35314,35315],{},[1201,35316,35317,35319],{},[1149,35318,2227],{},[1230,35320,1597],{},[1153,35322,2743],{"encoding":1155},[6537,35324,35325],{},[1115,35326,35328],{"className":35327},[1137],[1139,35329,35330],{"xmlns":1141},[1143,35331,35332,35340],{},[1146,35333,35334],{},[1201,35335,35336,35338],{},[1149,35337,2227],{},[1230,35339,1525],{},[1153,35341,2762],{"encoding":1155},[6537,35343,31558,35344],{},[1115,35345,35347],{"className":35346},[1137],[1139,35348,35349],{"xmlns":1141},[1143,35350,35351,35355],{},[1146,35352,35353],{},[1149,35354,6052],{},[1153,35356,6052],{"encoding":1155},[6645,35358,35359,35443,35531],{},[6534,35360,35361,35389,35417],{},[6650,35362,35363],{},[1115,35364,35366],{"className":35365},[1137],[1139,35367,35368],{"xmlns":1141},[1143,35369,35370,35386],{},[1146,35371,35372,35378,35380],{},[1201,35373,35374,35376],{},[1149,35375,11264],{},[1230,35377,1525],{},[1193,35379,11110],{},[1201,35381,35382,35384],{},[1149,35383,11264],{},[1230,35385,1232],{},[1153,35387,35388],{"encoding":1155},"\\mu_1 \\le \\mu_2",[6650,35390,35391],{},[1115,35392,35394],{"className":35393},[1137],[1139,35395,35396],{"xmlns":1141},[1143,35397,35398,35414],{},[1146,35399,35400,35406,35408],{},[1201,35401,35402,35404],{},[1149,35403,11264],{},[1230,35405,1525],{},[1193,35407,5369],{},[1201,35409,35410,35412],{},[1149,35411,11264],{},[1230,35413,1232],{},[1153,35415,35416],{"encoding":1155},"\\mu_1 > \\mu_2",[6650,35418,35419],{},[1115,35420,35422],{"className":35421},[1137],[1139,35423,35424],{"xmlns":1141},[1143,35425,35426,35440],{},[1146,35427,35428,35430,35432],{},[1149,35429,11515],{},[1193,35431,7775],{},[3698,35433,35434,35436,35438],{},[1149,35435,11515],{},[1149,35437,1110],{},[1193,35439,35009],{},[1153,35441,35442],{"encoding":1155},"t \\ge t_p^*",[6534,35444,35445,35473,35501],{},[6650,35446,35447],{},[1115,35448,35450],{"className":35449},[1137],[1139,35451,35452],{"xmlns":1141},[1143,35453,35454,35470],{},[1146,35455,35456,35462,35464],{},[1201,35457,35458,35460],{},[1149,35459,11264],{},[1230,35461,1525],{},[1193,35463,1281],{},[1201,35465,35466,35468],{},[1149,35467,11264],{},[1230,35469,1232],{},[1153,35471,35472],{"encoding":1155},"\\mu_1 = \\mu_2",[6650,35474,35475],{},[1115,35476,35478],{"className":35477},[1137],[1139,35479,35480],{"xmlns":1141},[1143,35481,35482,35498],{},[1146,35483,35484,35490,35492],{},[1201,35485,35486,35488],{},[1149,35487,11264],{},[1230,35489,1525],{},[1193,35491,2271],{"mathvariant":1854},[1201,35493,35494,35496],{},[1149,35495,11264],{},[1230,35497,1232],{},[1153,35499,35500],{"encoding":1155},"\\mu_1 \\neq \\mu_2",[6650,35502,35503],{},[1115,35504,35506],{"className":35505},[1137],[1139,35507,35508],{"xmlns":1141},[1143,35509,35510,35528],{},[1146,35511,35512,35514,35516,35518,35520],{},[1193,35513,26870],{"stretchy":1198},[1149,35515,11515],{},[1193,35517,26870],{"stretchy":1198},[1193,35519,7775],{},[3698,35521,35522,35524,35526],{},[1149,35523,11515],{},[1149,35525,1110],{},[1193,35527,35009],{},[1153,35529,35530],{"encoding":1155},"\\lvert t \\rvert \\ge t_p^*",[6534,35532,35533,35561,35589],{},[6650,35534,35535],{},[1115,35536,35538],{"className":35537},[1137],[1139,35539,35540],{"xmlns":1141},[1143,35541,35542,35558],{},[1146,35543,35544,35550,35552],{},[1201,35545,35546,35548],{},[1149,35547,11264],{},[1230,35549,1525],{},[1193,35551,7775],{},[1201,35553,35554,35556],{},[1149,35555,11264],{},[1230,35557,1232],{},[1153,35559,35560],{"encoding":1155},"\\mu_1 \\ge \\mu_2",[6650,35562,35563],{},[1115,35564,35566],{"className":35565},[1137],[1139,35567,35568],{"xmlns":1141},[1143,35569,35570,35586],{},[1146,35571,35572,35578,35580],{},[1201,35573,35574,35576],{},[1149,35575,11264],{},[1230,35577,1525],{},[1193,35579,5343],{},[1201,35581,35582,35584],{},[1149,35583,11264],{},[1230,35585,1232],{},[1153,35587,35588],{"encoding":1155},"\\mu_1 \u003C \\mu_2",[6650,35590,35591],{},[1115,35592,35594],{"className":35593},[1137],[1139,35595,35596],{"xmlns":1141},[1143,35597,35598,35614],{},[1146,35599,35600,35602,35604,35606],{},[1149,35601,11515],{},[1193,35603,11110],{},[1193,35605,1210],{},[3698,35607,35608,35610,35612],{},[1149,35609,11515],{},[1149,35611,1110],{},[1193,35613,35009],{},[1153,35615,35616],{"encoding":1155},"t \\le -t_p^*",[1110,35618,35619,35620,34682,35638,1236],{},"Postup je dvoukrokový: nejprve F-test rozhodne o shodě rozptylů, pak se podle výsledku zvolí ",[1115,35621,35623],{"className":35622},[1137],[1139,35624,35625],{"xmlns":1141},[1143,35626,35627,35635],{},[1146,35628,35629],{},[1201,35630,35631,35633],{},[1149,35632,11474],{},[1230,35634,1525],{},[1153,35636,35637],{"encoding":1155},"T_1",[1115,35639,35641],{"className":35640},[1137],[1139,35642,35643],{"xmlns":1141},[1143,35644,35645,35653],{},[1146,35646,35647],{},[1201,35648,35649,35651],{},[1149,35650,11474],{},[1230,35652,1232],{},[1153,35654,35655],{"encoding":1155},"T_2",[1110,35657,35658],{},[1864,35659],{"alt":35660,"className":35661,"src":35662},"mask-th-f-kriticky-obor",[1387,1868],"\u002Fwiki-assets\u002Fmask-th-f-kriticky-obor.png",[1103,35664,35666,35673,35823,35904,36033,36071,36144,36283],{"className":35665,"dataCallout":2932},[1106,2931],[1110,35667,35669,35672],{"className":35668},[1113],[1115,35670],{"className":35671,"ariaHidden":1121},[1118,2939,1120],"Příklad: Porovnání dvou dodavatelů součástek",[1110,35674,35675,35676,1348,35698,35724,35725,35749,35750,1348,35772,35724,35798,35822],{},"Pevnost plastových dílů: dodavatel A (",[1115,35677,35679],{"className":35678},[1137],[1139,35680,35681],{"xmlns":1141},[1143,35682,35683,35695],{},[1146,35684,35685,35691,35693],{},[1201,35686,35687,35689],{},[1149,35688,1816],{},[1230,35690,1525],{},[1193,35692,1281],{},[1230,35694,5389],{},[1153,35696,35697],{"encoding":1155},"n_1 = 10",[1115,35699,35701],{"className":35700},[1137],[1139,35702,35703],{"xmlns":1141},[1143,35704,35705,35721],{},[1146,35706,35707,35717,35719],{},[1201,35708,35709,35715],{},[1214,35710,35711,35713],{"accent":1121},[1149,35712,1168],{},[1193,35714,15814],{},[1230,35716,1525],{},[1193,35718,1281],{},[1230,35720,8046],{},[1153,35722,35723],{"encoding":1155},"\\bar{x}_1 = 82"," MPa, ",[1115,35726,35728],{"className":35727},[1137],[1139,35729,35730],{"xmlns":1141},[1143,35731,35732,35746],{},[1146,35733,35734,35742,35744],{},[3698,35735,35736,35738,35740],{},[1149,35737,4542],{},[1230,35739,1525],{},[1230,35741,1232],{},[1193,35743,1281],{},[1230,35745,8457],{},[1153,35747,35748],{"encoding":1155},"s_1^2 = 25","), dodavatel B (",[1115,35751,35753],{"className":35752},[1137],[1139,35754,35755],{"xmlns":1141},[1143,35756,35757,35769],{},[1146,35758,35759,35765,35767],{},[1201,35760,35761,35763],{},[1149,35762,1816],{},[1230,35764,1232],{},[1193,35766,1281],{},[1230,35768,6708],{},[1153,35770,35771],{"encoding":1155},"n_2 = 12",[1115,35773,35775],{"className":35774},[1137],[1139,35776,35777],{"xmlns":1141},[1143,35778,35779,35795],{},[1146,35780,35781,35791,35793],{},[1201,35782,35783,35789],{},[1214,35784,35785,35787],{"accent":1121},[1149,35786,1168],{},[1193,35788,15814],{},[1230,35790,1232],{},[1193,35792,1281],{},[1230,35794,19081],{},[1153,35796,35797],{"encoding":1155},"\\bar{x}_2 = 75",[1115,35799,35801],{"className":35800},[1137],[1139,35802,35803],{"xmlns":1141},[1143,35804,35805,35819],{},[1146,35806,35807,35815,35817],{},[3698,35808,35809,35811,35813],{},[1149,35810,4542],{},[1230,35812,1232],{},[1230,35814,1232],{},[1193,35816,1281],{},[1230,35818,25872],{},[1153,35820,35821],{"encoding":1155},"s_2^2 = 16","). Předpokládá se normalita obou rozdělení.",[1110,35824,35825,1243,35828,1348,35866,1236],{},[1130,35826,35827],{},"Krok 1 — F-test rozptylů.",[1115,35829,35831],{"className":35830},[1137],[1139,35832,35833],{"xmlns":1141},[1143,35834,35835,35863],{},[1146,35836,35837,35843,35845,35853,35855],{},[1201,35838,35839,35841],{},[1149,35840,2227],{},[1230,35842,1597],{},[1193,35844,1902],{},[3698,35846,35847,35849,35851],{},[1149,35848,11271],{},[1230,35850,1525],{},[1230,35852,1232],{},[1193,35854,1281],{},[3698,35856,35857,35859,35861],{},[1149,35858,11271],{},[1230,35860,1232],{},[1230,35862,1232],{},[1153,35864,35865],{"encoding":1155},"H_0: \\sigma_1^2 = \\sigma_2^2",[1115,35867,35869],{"className":35868},[1137],[1139,35870,35871],{"xmlns":1141},[1143,35872,35873,35901],{},[1146,35874,35875,35881,35883,35891,35893],{},[1201,35876,35877,35879],{},[1149,35878,2227],{},[1230,35880,1525],{},[1193,35882,1902],{},[3698,35884,35885,35887,35889],{},[1149,35886,11271],{},[1230,35888,1525],{},[1230,35890,1232],{},[1193,35892,2271],{"mathvariant":1854},[3698,35894,35895,35897,35899],{},[1149,35896,11271],{},[1230,35898,1232],{},[1230,35900,1232],{},[1153,35902,35903],{"encoding":1155},"H_1: \\sigma_1^2 \\neq \\sigma_2^2",[1110,35905,35906],{},[1115,35907,35909],{"className":35908},[1137],[1139,35910,35911],{"xmlns":1141},[1143,35912,35913,36030],{},[1146,35914,35915,35917,35919,35925,35927,35930,35932,35934,35936,35938,35940,35942,35944,35957,35959,35961,35963,35965,35967,35970,35973,35975,35977,35979,35992,35994,35996,35998,36000,36002,36004,36006,36008,36010,36012,36015,36017,36019,36021,36023,36025,36028],{},[1149,35916,11091],{},[1193,35918,1281],{},[3546,35920,35921,35923],{},[1230,35922,8457],{},[1230,35924,25872],{},[1193,35926,1281],{},[1230,35928,35929],{},"1,5625",[1193,35931,1503],{"separator":1121},[1936,35933],{"width":1938},[1149,35935,6052],{},[1193,35937,1281],{},[1193,35939,7758],{"stretchy":1198},[1149,35941,11091],{},[1193,35943,11110],{},[1201,35945,35946,35948],{},[1149,35947,11091],{},[1146,35949,35950,35952,35954],{},[1230,35951,1597],{},[1193,35953,1503],{"separator":1121},[1230,35955,35956],{},"025",[1193,35958,1199],{"stretchy":1198},[1230,35960,8013],{},[1193,35962,1503],{"separator":1121},[1230,35964,6687],{},[1193,35966,1228],{"stretchy":1198},[2201,35968,35969],{},"  ",[2201,35971,35972],{},"nebo",[2201,35974,35969],{},[1149,35976,11091],{},[1193,35978,7775],{},[1201,35980,35981,35983],{},[1149,35982,11091],{},[1146,35984,35985,35987,35989],{},[1230,35986,1597],{},[1193,35988,1503],{"separator":1121},[1230,35990,35991],{},"975",[1193,35993,1199],{"stretchy":1198},[1230,35995,8013],{},[1193,35997,1503],{"separator":1121},[1230,35999,6687],{},[1193,36001,1228],{"stretchy":1198},[1193,36003,7817],{"stretchy":1198},[1193,36005,1281],{},[1193,36007,7758],{"stretchy":1198},[1149,36009,11091],{},[1193,36011,11110],{},[1230,36013,36014],{},"0,256",[2201,36016,35969],{},[2201,36018,35972],{},[2201,36020,35969],{},[1149,36022,11091],{},[1193,36024,7775],{},[1230,36026,36027],{},"3,588",[1193,36029,7817],{"stretchy":1198},[1153,36031,36032],{"encoding":1155},"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\\}",[1110,36034,36035,36053,36054,1236],{},[1115,36036,36038],{"className":36037},[1137],[1139,36039,36040],{"xmlns":1141},[1143,36041,36042,36050],{},[1146,36043,36044,36046,36048],{},[1149,36045,11091],{},[1193,36047,31119],{"mathvariant":1854},[1149,36049,6052],{},[1153,36051,36052],{"encoding":1155},"F \\notin W",", rozptyly nezamítáme jako shodné — pro t-test se použije ",[1115,36055,36057],{"className":36056},[1137],[1139,36058,36059],{"xmlns":1141},[1143,36060,36061,36069],{},[1146,36062,36063],{},[1201,36064,36065,36067],{},[1149,36066,11474],{},[1230,36068,1525],{},[1153,36070,35637],{"encoding":1155},[1110,36072,36073,1243,36076,1348,36110,1236],{},[1130,36074,36075],{},"Krok 2 — dvouvýběrový t-test středních hodnot.",[1115,36077,36079],{"className":36078},[1137],[1139,36080,36081],{"xmlns":1141},[1143,36082,36083,36107],{},[1146,36084,36085,36091,36093,36099,36101],{},[1201,36086,36087,36089],{},[1149,36088,2227],{},[1230,36090,1597],{},[1193,36092,1902],{},[1201,36094,36095,36097],{},[1149,36096,11264],{},[1230,36098,1525],{},[1193,36100,1281],{},[1201,36102,36103,36105],{},[1149,36104,11264],{},[1230,36106,1232],{},[1153,36108,36109],{"encoding":1155},"H_0: \\mu_1 = \\mu_2",[1115,36111,36113],{"className":36112},[1137],[1139,36114,36115],{"xmlns":1141},[1143,36116,36117,36141],{},[1146,36118,36119,36125,36127,36133,36135],{},[1201,36120,36121,36123],{},[1149,36122,2227],{},[1230,36124,1525],{},[1193,36126,1902],{},[1201,36128,36129,36131],{},[1149,36130,11264],{},[1230,36132,1525],{},[1193,36134,2271],{"mathvariant":1854},[1201,36136,36137,36139],{},[1149,36138,11264],{},[1230,36140,1232],{},[1153,36142,36143],{"encoding":1155},"H_1: \\mu_1 \\neq \\mu_2",[1110,36145,36146],{},[1115,36147,36149],{"className":36148},[1137],[1139,36150,36151],{"xmlns":1141},[1143,36152,36153,36280],{},[1146,36154,36155,36163,36165,36185,36187,36190,36192,36194,36196,36198,36212,36220,36222,36225,36227,36229,36231,36233,36235,36237,36239,36241,36243,36255,36257,36259,36261,36263,36265,36267,36269,36271,36273,36275,36278],{},[3698,36156,36157,36159,36161],{},[1149,36158,4542],{},[1149,36160,1110],{},[1230,36162,1232],{},[1193,36164,1281],{},[3546,36166,36167,36183],{},[1146,36168,36169,36171,36173,36175,36177,36179,36181],{},[1230,36170,8013],{},[1193,36172,3045],{},[1230,36174,8457],{},[1193,36176,1924],{},[1230,36178,6687],{},[1193,36180,3045],{},[1230,36182,25872],{},[1230,36184,8444],{},[1193,36186,1281],{},[1230,36188,36189],{},"20,05",[1193,36191,1503],{"separator":1121},[1936,36193],{"width":1938},[1149,36195,11515],{},[1193,36197,1281],{},[3546,36199,36200,36208],{},[1146,36201,36202,36204,36206],{},[1230,36203,8046],{},[1193,36205,1210],{},[1230,36207,19081],{},[1283,36209,36210],{},[1230,36211,36189],{},[1283,36213,36214],{},[3546,36215,36216,36218],{},[1230,36217,25732],{},[1230,36219,6822],{},[1193,36221,4165],{},[1230,36223,36224],{},"3,651",[1193,36226,1503],{"separator":1121},[1936,36228],{"width":1938},[1149,36230,6052],{},[1193,36232,1281],{},[1193,36234,7758],{"stretchy":1198},[1193,36236,26870],{"stretchy":1198},[1149,36238,11515],{},[1193,36240,26870],{"stretchy":1198},[1193,36242,7775],{},[1201,36244,36245,36247],{},[1149,36246,11515],{},[1146,36248,36249,36251,36253],{},[1230,36250,1597],{},[1193,36252,1503],{"separator":1121},[1230,36254,35991],{},[1193,36256,1199],{"stretchy":1198},[1230,36258,8444],{},[1193,36260,1228],{"stretchy":1198},[1193,36262,7817],{"stretchy":1198},[1193,36264,1281],{},[1193,36266,7758],{"stretchy":1198},[1193,36268,26870],{"stretchy":1198},[1149,36270,11515],{},[1193,36272,26870],{"stretchy":1198},[1193,36274,7775],{},[1230,36276,36277],{},"2,086",[1193,36279,7817],{"stretchy":1198},[1153,36281,36282],{"encoding":1155},"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\\}",[1110,36284,36285,10395,36302,36319],{},[1115,36286,36288],{"className":36287},[1137],[1139,36289,36290],{"xmlns":1141},[1143,36291,36292,36300],{},[1146,36293,36294,36296,36298],{},[1149,36295,11515],{},[1193,36297,11391],{},[1149,36299,6052],{},[1153,36301,32262],{"encoding":1155},[1115,36303,36305],{"className":36304},[1137],[1139,36306,36307],{"xmlns":1141},[1143,36308,36309,36317],{},[1146,36310,36311],{},[1201,36312,36313,36315],{},[1149,36314,2227],{},[1230,36316,1597],{},[1153,36318,2743],{"encoding":1155},": pevnost součástek od obou dodavatelů se statisticky významně liší.",[2035,36321,36323],{"className":2037,"code":36322,"language":71,"meta":2039,"style":2039},"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",[1332,36324,36325,36343,36363,36378,36413,36444,36449,36454],{"__ignoreMap":2039},[1115,36326,36327,36330,36332,36334,36336,36339,36341],{"class":2044,"line":10},[1115,36328,36329],{"class":2047},"s1",[1115,36331,2052],{"class":2051},[1115,36333,18751],{"class":2062},[1115,36335,29030],{"class":2059},[1115,36337,36338],{"class":2047},"n1",[1115,36340,2052],{"class":2051},[1115,36342,33703],{"class":2062},[1115,36344,36345,36348,36350,36353,36355,36358,36360],{"class":2044,"line":27},[1115,36346,36347],{"class":2047},"s2",[1115,36349,2052],{"class":2051},[1115,36351,36352],{"class":2062}," 16",[1115,36354,29030],{"class":2059},[1115,36356,36357],{"class":2047},"n2",[1115,36359,2052],{"class":2051},[1115,36361,36362],{"class":2062}," 12\n",[1115,36364,36365,36368,36370,36373,36375],{"class":2044,"line":148},[1115,36366,36367],{"class":2047},"Fstat",[1115,36369,2052],{"class":2051},[1115,36371,36372],{"class":2047}," s1",[1115,36374,4211],{"class":2051},[1115,36376,36377],{"class":2047}," s2\n",[1115,36379,36380,36383,36385,36388,36390,36393,36395,36398,36400,36402,36404,36407,36409,36411],{"class":2044,"line":111},[1115,36381,36382],{"class":2047},"F_dolni",[1115,36384,2052],{"class":2051},[1115,36386,36387],{"class":2055}," qf",[1115,36389,1199],{"class":2059},[1115,36391,36392],{"class":2062},"0.025",[1115,36394,1503],{"class":2051},[1115,36396,36397],{"class":2047}," n1",[1115,36399,29367],{"class":2051},[1115,36401,9031],{"class":2062},[1115,36403,1503],{"class":2051},[1115,36405,36406],{"class":2047}," n2",[1115,36408,29367],{"class":2051},[1115,36410,9031],{"class":2062},[1115,36412,2090],{"class":2059},[1115,36414,36415,36418,36420,36422,36424,36426,36428,36430,36432,36434,36436,36438,36440,36442],{"class":2044,"line":96},[1115,36416,36417],{"class":2047},"F_horni",[1115,36419,2052],{"class":2051},[1115,36421,36387],{"class":2055},[1115,36423,1199],{"class":2059},[1115,36425,13458],{"class":2062},[1115,36427,1503],{"class":2051},[1115,36429,36397],{"class":2047},[1115,36431,29367],{"class":2051},[1115,36433,9031],{"class":2062},[1115,36435,1503],{"class":2051},[1115,36437,36406],{"class":2047},[1115,36439,29367],{"class":2051},[1115,36441,9031],{"class":2062},[1115,36443,2090],{"class":2059},[1115,36445,36446],{"class":2044,"line":89},[1115,36447,36448],{"class":2047},"Fstat\n",[1115,36450,36451],{"class":2044,"line":82},[1115,36452,36453],{"class":2047},"F_dolni\n",[1115,36455,36456],{"class":2044,"line":75},[1115,36457,36458],{"class":2047},"F_horni\n",[2035,36460,36463],{"className":36461,"code":36462,"language":2169,"meta":2039},[2167],"[1] 1.5625\n[1] 0.2556189\n[1] 3.587899\n",[1332,36464,36462],{"__ignoreMap":2039},[2035,36466,36468],{"className":2037,"code":36467,"language":71,"meta":2039,"style":2039},"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",[1332,36469,36470,36527,36578,36608,36613,36617],{"__ignoreMap":2039},[1115,36471,36472,36475,36477,36480,36482,36484,36486,36488,36490,36492,36494,36496,36498,36500,36502,36504,36506,36509,36511,36513,36515,36517,36519,36521,36523,36525],{"class":2044,"line":10},[1115,36473,36474],{"class":2047},"sp2",[1115,36476,2052],{"class":2051},[1115,36478,36479],{"class":2059}," ((",[1115,36481,36338],{"class":2047},[1115,36483,29367],{"class":2051},[1115,36485,9031],{"class":2062},[1115,36487,8993],{"class":2059},[1115,36489,9009],{"class":2051},[1115,36491,36372],{"class":2047},[1115,36493,3832],{"class":2051},[1115,36495,4053],{"class":2059},[1115,36497,36357],{"class":2047},[1115,36499,29367],{"class":2051},[1115,36501,9031],{"class":2062},[1115,36503,8993],{"class":2059},[1115,36505,9009],{"class":2051},[1115,36507,36508],{"class":2047}," s2",[1115,36510,8993],{"class":2059},[1115,36512,5731],{"class":2051},[1115,36514,4053],{"class":2059},[1115,36516,36338],{"class":2047},[1115,36518,3832],{"class":2051},[1115,36520,36406],{"class":2047},[1115,36522,29367],{"class":2051},[1115,36524,2067],{"class":2062},[1115,36526,2090],{"class":2059},[1115,36528,36529,36531,36533,36535,36537,36539,36542,36544,36546,36548,36550,36552,36554,36556,36558,36560,36562,36564,36566,36568,36570,36572,36574,36576],{"class":2044,"line":27},[1115,36530,11515],{"class":2047},[1115,36532,2052],{"class":2051},[1115,36534,4053],{"class":2059},[1115,36536,8046],{"class":2062},[1115,36538,29367],{"class":2051},[1115,36540,36541],{"class":2062}," 75",[1115,36543,8993],{"class":2059},[1115,36545,5731],{"class":2051},[1115,36547,8970],{"class":2055},[1115,36549,1199],{"class":2059},[1115,36551,36474],{"class":2047},[1115,36553,8993],{"class":2059},[1115,36555,9009],{"class":2051},[1115,36557,8970],{"class":2055},[1115,36559,1199],{"class":2059},[1115,36561,36338],{"class":2047},[1115,36563,3957],{"class":2051},[1115,36565,36406],{"class":2047},[1115,36567,4211],{"class":2051},[1115,36569,4053],{"class":2059},[1115,36571,36338],{"class":2047},[1115,36573,3832],{"class":2051},[1115,36575,36406],{"class":2047},[1115,36577,2546],{"class":2059},[1115,36579,36580,36582,36584,36586,36588,36590,36592,36594,36596,36598,36600,36602,36604,36606],{"class":2044,"line":148},[1115,36581,32369],{"class":2047},[1115,36583,2052],{"class":2051},[1115,36585,32374],{"class":2055},[1115,36587,1199],{"class":2059},[1115,36589,13458],{"class":2062},[1115,36591,1503],{"class":2051},[1115,36593,15170],{"class":2047},[1115,36595,2510],{"class":2051},[1115,36597,36397],{"class":2047},[1115,36599,3832],{"class":2051},[1115,36601,36406],{"class":2047},[1115,36603,29367],{"class":2051},[1115,36605,2067],{"class":2062},[1115,36607,2090],{"class":2059},[1115,36609,36610],{"class":2044,"line":111},[1115,36611,36612],{"class":2047},"sp2\n",[1115,36614,36615],{"class":2044,"line":96},[1115,36616,32399],{"class":2047},[1115,36618,36619],{"class":2044,"line":89},[1115,36620,32404],{"class":2047},[2035,36622,36625],{"className":36623,"code":36624,"language":2169,"meta":2039},[2167],"[1] 20.05\n[1] 3.65107\n[1] 2.085963\n",[1332,36626,36624],{"__ignoreMap":2039},[1110,36628,36629],{},[1864,36630],{"alt":36631,"className":36632,"src":36633},"mask-th-t-dvoustranny",[1387,1868],"\u002Fwiki-assets\u002Fmask-th-t-dvoustranny.png",[1110,36635,36636,36637,1405,36640,36642,36643,36646,36647,1405,36664,3096,36681,36683,36684,36686],{},"V R provede obě kroky ",[1332,36638,36639],{},"var.test()",[1332,36641,31859],{},". Parametr ",[1332,36644,36645],{},"var.equal"," nastavuje volbu mezi ",[1115,36648,36650],{"className":36649},[1137],[1139,36651,36652],{"xmlns":1141},[1143,36653,36654,36662],{},[1146,36655,36656],{},[1201,36657,36658,36660],{},[1149,36659,11474],{},[1230,36661,1525],{},[1153,36663,35637],{"encoding":1155},[1115,36665,36667],{"className":36666},[1137],[1139,36668,36669],{"xmlns":1141},[1143,36670,36671,36679],{},[1146,36672,36673],{},[1201,36674,36675,36677],{},[1149,36676,11474],{},[1230,36678,1232],{},[1153,36680,35655],{"encoding":1155},[1332,36682,13891],{}," znamená předpoklad shodných rozptylů (podle výsledku F-testu), ",[1332,36685,13894],{}," předpoklad rozdílných rozptylů.",[1110,36688,36689,36692],{},[1130,36690,36691],{},"Kabely A\u002FB."," Pevnost v tahu dvou výrobců (MPa, 12 kabelů od každého):",[2035,36694,36696],{"className":2037,"code":36695,"language":71,"meta":2039,"style":2039},"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",[1332,36697,36698,36764,36827,36843],{"__ignoreMap":2039},[1115,36699,36700,36702,36704,36706,36708,36711,36713,36716,36718,36721,36723,36726,36728,36730,36732,36735,36737,36740,36742,36744,36746,36749,36751,36753,36755,36758,36760,36762],{"class":2044,"line":10},[1115,36701,6216],{"class":2047},[1115,36703,2052],{"class":2051},[1115,36705,2056],{"class":2055},[1115,36707,1199],{"class":2059},[1115,36709,36710],{"class":2062},"313",[1115,36712,1503],{"class":2051},[1115,36714,36715],{"class":2062}," 299",[1115,36717,1503],{"class":2051},[1115,36719,36720],{"class":2062}," 315",[1115,36722,1503],{"class":2051},[1115,36724,36725],{"class":2062}," 312",[1115,36727,1503],{"class":2051},[1115,36729,19718],{"class":2062},[1115,36731,1503],{"class":2051},[1115,36733,36734],{"class":2062}," 308",[1115,36736,1503],{"class":2051},[1115,36738,36739],{"class":2062}," 314",[1115,36741,1503],{"class":2051},[1115,36743,18511],{"class":2062},[1115,36745,1503],{"class":2051},[1115,36747,36748],{"class":2062}," 305",[1115,36750,1503],{"class":2051},[1115,36752,19718],{"class":2062},[1115,36754,1503],{"class":2051},[1115,36756,36757],{"class":2062}," 309",[1115,36759,1503],{"class":2051},[1115,36761,36739],{"class":2062},[1115,36763,2090],{"class":2059},[1115,36765,36766,36768,36770,36772,36774,36777,36779,36782,36784,36786,36788,36790,36792,36795,36797,36800,36802,36804,36806,36808,36810,36812,36814,36817,36819,36821,36823,36825],{"class":2044,"line":27},[1115,36767,6262],{"class":2047},[1115,36769,2052],{"class":2051},[1115,36771,2056],{"class":2055},[1115,36773,1199],{"class":2059},[1115,36775,36776],{"class":2062},"307",[1115,36778,1503],{"class":2051},[1115,36780,36781],{"class":2062}," 322",[1115,36783,1503],{"class":2051},[1115,36785,18511],{"class":2062},[1115,36787,1503],{"class":2051},[1115,36789,18511],{"class":2062},[1115,36791,1503],{"class":2051},[1115,36793,36794],{"class":2062}," 311",[1115,36796,1503],{"class":2051},[1115,36798,36799],{"class":2062}," 316",[1115,36801,1503],{"class":2051},[1115,36803,36720],{"class":2062},[1115,36805,1503],{"class":2051},[1115,36807,36739],{"class":2062},[1115,36809,1503],{"class":2051},[1115,36811,36734],{"class":2062},[1115,36813,1503],{"class":2051},[1115,36815,36816],{"class":2062}," 319",[1115,36818,1503],{"class":2051},[1115,36820,18511],{"class":2062},[1115,36822,1503],{"class":2051},[1115,36824,36725],{"class":2062},[1115,36826,2090],{"class":2059},[1115,36828,36829,36832,36834,36836,36838,36841],{"class":2044,"line":148},[1115,36830,36831],{"class":2055},"var.test",[1115,36833,1199],{"class":2059},[1115,36835,6216],{"class":2047},[1115,36837,1503],{"class":2051},[1115,36839,36840],{"class":2047}," B",[1115,36842,2090],{"class":2059},[1115,36844,36845,36847,36849,36851,36853,36855,36857,36860,36862,36864],{"class":2044,"line":111},[1115,36846,31924],{"class":2055},[1115,36848,1199],{"class":2059},[1115,36850,6216],{"class":2047},[1115,36852,1503],{"class":2051},[1115,36854,36840],{"class":2047},[1115,36856,1503],{"class":2051},[1115,36858,36859],{"class":2047}," var.equal",[1115,36861,2510],{"class":2051},[1115,36863,5460],{"class":2062},[1115,36865,2090],{"class":2059},[2035,36867,36870],{"className":36868,"code":36869,"language":2169,"meta":2039},[2167]," 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",[1332,36871,36869],{"__ignoreMap":2039},[1110,36873,36874,36875,16405,36894,36897,36898,36917,36918,36935],{},"F-test shodu rozptylů nezamítá (",[1115,36876,36878],{"className":36877},[1137],[1139,36879,36880],{"xmlns":1141},[1143,36881,36882,36891],{},[1146,36883,36884,36886,36888],{},[1149,36885,1110],{},[1193,36887,1281],{},[1230,36889,36890],{},"0,7776",[1153,36892,36893],{"encoding":1155},"p = 0{,}7776",[1332,36895,36896],{},"var.equal = TRUE",". Výsledný t-test dává ",[1115,36899,36901],{"className":36900},[1137],[1139,36902,36903],{"xmlns":1141},[1143,36904,36905,36914],{},[1146,36906,36907,36909,36911],{},[1149,36908,1110],{},[1193,36910,1281],{},[1230,36912,36913],{},"0,06932",[1153,36915,36916],{"encoding":1155},"p = 0{,}06932"," — na hladině 5 % se ",[1115,36919,36921],{"className":36920},[1137],[1139,36922,36923],{"xmlns":1141},[1143,36924,36925,36933],{},[1146,36926,36927],{},[1201,36928,36929,36931],{},[1149,36930,2227],{},[1230,36932,1597],{},[1153,36934,2743],{"encoding":1155}," nezamítá, ale hodnota je těsně nad hranicí.",[1110,36937,36938],{},[1130,36939,36940],{},"Výšky chlapců a dívek v páté třídě:",[2035,36942,36944],{"className":2037,"code":36943,"language":71,"meta":2039,"style":2039},"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",[1332,36945,36946,37026,37089,37104],{"__ignoreMap":2039},[1115,36947,36948,36951,36953,36955,36957,36960,36962,36964,36966,36969,36971,36974,36976,36979,36981,36984,36986,36988,36990,36992,36994,36996,36998,37000,37002,37005,37007,37010,37012,37015,37017,37019,37021,37024],{"class":2044,"line":10},[1115,36949,36950],{"class":2047},"boys",[1115,36952,2052],{"class":2051},[1115,36954,2056],{"class":2055},[1115,36956,1199],{"class":2059},[1115,36958,36959],{"class":2062},"130",[1115,36961,1503],{"class":2051},[1115,36963,19667],{"class":2062},[1115,36965,1503],{"class":2051},[1115,36967,36968],{"class":2062}," 136",[1115,36970,1503],{"class":2051},[1115,36972,36973],{"class":2062}," 141",[1115,36975,1503],{"class":2051},[1115,36977,36978],{"class":2062}," 139",[1115,36980,1503],{"class":2051},[1115,36982,36983],{"class":2062}," 133",[1115,36985,1503],{"class":2051},[1115,36987,3789],{"class":2062},[1115,36989,1503],{"class":2051},[1115,36991,18526],{"class":2062},[1115,36993,1503],{"class":2051},[1115,36995,36978],{"class":2062},[1115,36997,1503],{"class":2051},[1115,36999,36968],{"class":2062},[1115,37001,1503],{"class":2051},[1115,37003,37004],{"class":2062}," 138",[1115,37006,1503],{"class":2051},[1115,37008,37009],{"class":2062}," 142",[1115,37011,1503],{"class":2051},[1115,37013,37014],{"class":2062}," 127",[1115,37016,1503],{"class":2051},[1115,37018,36978],{"class":2062},[1115,37020,1503],{"class":2051},[1115,37022,37023],{"class":2062}," 147",[1115,37025,2090],{"class":2059},[1115,37027,37028,37031,37033,37035,37037,37039,37041,37043,37045,37048,37050,37053,37055,37058,37060,37062,37064,37066,37068,37070,37072,37074,37076,37079,37081,37083,37085,37087],{"class":2044,"line":27},[1115,37029,37030],{"class":2047},"girls",[1115,37032,2052],{"class":2051},[1115,37034,2056],{"class":2055},[1115,37036,1199],{"class":2059},[1115,37038,25683],{"class":2062},[1115,37040,1503],{"class":2051},[1115,37042,36973],{"class":2062},[1115,37044,1503],{"class":2051},[1115,37046,37047],{"class":2062}," 143",[1115,37049,1503],{"class":2051},[1115,37051,37052],{"class":2062}," 132",[1115,37054,1503],{"class":2051},[1115,37056,37057],{"class":2062}," 146",[1115,37059,1503],{"class":2051},[1115,37061,37057],{"class":2062},[1115,37063,1503],{"class":2051},[1115,37065,18526],{"class":2062},[1115,37067,1503],{"class":2051},[1115,37069,36973],{"class":2062},[1115,37071,1503],{"class":2051},[1115,37073,36973],{"class":2062},[1115,37075,1503],{"class":2051},[1115,37077,37078],{"class":2062}," 131",[1115,37080,1503],{"class":2051},[1115,37082,37009],{"class":2062},[1115,37084,1503],{"class":2051},[1115,37086,36973],{"class":2062},[1115,37088,2090],{"class":2059},[1115,37090,37091,37093,37095,37097,37099,37102],{"class":2044,"line":148},[1115,37092,36831],{"class":2055},[1115,37094,1199],{"class":2059},[1115,37096,36950],{"class":2047},[1115,37098,1503],{"class":2051},[1115,37100,37101],{"class":2047}," girls",[1115,37103,2090],{"class":2059},[1115,37105,37106,37108,37110,37112,37114,37116,37118,37120,37122,37124],{"class":2044,"line":111},[1115,37107,31924],{"class":2055},[1115,37109,1199],{"class":2059},[1115,37111,36950],{"class":2047},[1115,37113,1503],{"class":2051},[1115,37115,37101],{"class":2047},[1115,37117,1503],{"class":2051},[1115,37119,36859],{"class":2047},[1115,37121,2510],{"class":2051},[1115,37123,5460],{"class":2062},[1115,37125,2090],{"class":2059},[2035,37127,37130],{"className":37128,"code":37129,"language":2169,"meta":2039},[2167]," 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",[1332,37131,37129],{"__ignoreMap":2039},[1110,37133,36874,37134,37153,37154,37156,37157,37176],{},[1115,37135,37137],{"className":37136},[1137],[1139,37138,37139],{"xmlns":1141},[1143,37140,37141,37150],{},[1146,37142,37143,37145,37147],{},[1149,37144,1110],{},[1193,37146,1281],{},[1230,37148,37149],{},"0,6977",[1153,37151,37152],{"encoding":1155},"p = 0{,}6977","), t-test s ",[1332,37155,36896],{}," dává ",[1115,37158,37160],{"className":37159},[1137],[1139,37161,37162],{"xmlns":1141},[1143,37163,37164,37173],{},[1146,37165,37166,37168,37170],{},[1149,37167,1110],{},[1193,37169,1281],{},[1230,37171,37172],{},"0,4883",[1153,37174,37175],{"encoding":1155},"p = 0{,}4883",": na hladině 5 % se rozdíl průměrných výšek chlapců a dívek neprokázal.",[1377,37178,37180],{"id":37179},"testy-dobré-shody-a-normalita","Testy dobré shody a normalita",[1110,37182,37183],{},"Testy dobré shody ověřují, zda datový soubor pochází ze základního souboru s určitým typem rozdělení (normální, exponenciální apod.).",[2019,37185,37187],{"id":37186},"kolmogorovův-smirnovův-test","Kolmogorovův-Smirnovův test",[1110,37189,37190,37191,37214,37215,37234],{},"Univerzální test pro spojitá rozdělení. Porovnává empirickou distribuční funkci ",[1115,37192,37194],{"className":37193},[1137],[1139,37195,37196],{"xmlns":1141},[1143,37197,37198,37212],{},[1146,37199,37200,37206,37208,37210],{},[1201,37201,37202,37204],{},[1149,37203,11091],{},[1149,37205,1816],{},[1193,37207,1199],{"stretchy":1198},[1149,37209,1168],{},[1193,37211,1228],{"stretchy":1198},[1153,37213,15542],{"encoding":1155}," s teoretickou distribuční funkcí ",[1115,37216,37218],{"className":37217},[1137],[1139,37219,37220],{"xmlns":1141},[1143,37221,37222,37232],{},[1146,37223,37224,37226,37228,37230],{},[1149,37225,11091],{},[1193,37227,1199],{"stretchy":1198},[1149,37229,1168],{},[1193,37231,1228],{"stretchy":1198},[1153,37233,11707],{"encoding":1155}," testovaného rozdělení.",[1124,37236,37237,37300,37320,37376],{},[1127,37238,37239,37256,37257,1405,37280,37299],{},[1115,37240,37242],{"className":37241},[1137],[1139,37243,37244],{"xmlns":1141},[1143,37245,37246,37254],{},[1146,37247,37248],{},[1201,37249,37250,37252],{},[1149,37251,2227],{},[1230,37253,1597],{},[1153,37255,2743],{"encoding":1155},": odchylky mezi ",[1115,37258,37260],{"className":37259},[1137],[1139,37261,37262],{"xmlns":1141},[1143,37263,37264,37278],{},[1146,37265,37266,37272,37274,37276],{},[1201,37267,37268,37270],{},[1149,37269,11091],{},[1149,37271,1816],{},[1193,37273,1199],{"stretchy":1198},[1149,37275,1168],{},[1193,37277,1228],{"stretchy":1198},[1153,37279,15542],{"encoding":1155},[1115,37281,37283],{"className":37282},[1137],[1139,37284,37285],{"xmlns":1141},[1143,37286,37287,37297],{},[1146,37288,37289,37291,37293,37295],{},[1149,37290,11091],{},[1193,37292,1199],{"stretchy":1198},[1149,37294,1168],{},[1193,37296,1228],{"stretchy":1198},[1153,37298,11707],{"encoding":1155}," jsou náhodné (data mají dané rozdělení).",[1127,37301,37302,37319],{},[1115,37303,37305],{"className":37304},[1137],[1139,37306,37307],{"xmlns":1141},[1143,37308,37309,37317],{},[1146,37310,37311],{},[1201,37312,37313,37315],{},[1149,37314,2227],{},[1230,37316,1525],{},[1153,37318,2762],{"encoding":1155},": data nemají dané rozdělení.",[1127,37321,37322,37323,1236],{},"Testové kritérium: ",[1115,37324,37326],{"className":37325},[1137],[1139,37327,37328],{"xmlns":1141},[1143,37329,37330,37373],{},[1146,37331,37332,37334,37336,37347,37349,37355,37357,37359,37361,37363,37365,37367,37369,37371],{},[1149,37333,12523],{},[1193,37335,1281],{},[1201,37337,37338,37345],{},[1146,37339,37340,37343],{},[1149,37341,37342],{},"sup",[1193,37344,1851],{},[1149,37346,1168],{},[1193,37348,26870],{"stretchy":1198},[1201,37350,37351,37353],{},[1149,37352,11091],{},[1149,37354,1816],{},[1193,37356,1199],{"stretchy":1198},[1149,37358,1168],{},[1193,37360,1228],{"stretchy":1198},[1193,37362,1210],{},[1149,37364,11091],{},[1193,37366,1199],{"stretchy":1198},[1149,37368,1168],{},[1193,37370,1228],{"stretchy":1198},[1193,37372,26870],{"stretchy":1198},[1153,37374,37375],{"encoding":1155},"D = \\sup_x \\lvert F_n(x) - F(x) \\rvert",[1127,37377,7742,37378,37422,37423,37441,37442,1236],{},[1115,37379,37381],{"className":37380},[1137],[1139,37382,37383],{"xmlns":1141},[1143,37384,37385,37419],{},[1146,37386,37387,37393,37395,37397,37399,37401,37403,37405,37411,37413,37415,37417],{},[1201,37388,37389,37391],{},[1149,37390,6052],{},[1149,37392,7788],{},[1193,37394,1281],{},[1193,37396,7758],{"stretchy":1198},[1149,37398,12167],{},[1193,37400,1902],{},[1149,37402,12167],{},[1193,37404,5369],{},[1201,37406,37407,37409],{},[1149,37408,12523],{},[1149,37410,7788],{},[1193,37412,1199],{"stretchy":1198},[1149,37414,1816],{},[1193,37416,1228],{"stretchy":1198},[1193,37418,7817],{"stretchy":1198},[1153,37420,37421],{"encoding":1155},"W_\\alpha = \\{d : d > D_\\alpha(n)\\}","; pro ",[1115,37424,37426],{"className":37425},[1137],[1139,37427,37428],{"xmlns":1141},[1143,37429,37430,37438],{},[1146,37431,37432,37434,37436],{},[1149,37433,1816],{},[1193,37435,5369],{},[1230,37437,25882],{},[1153,37439,37440],{"encoding":1155},"n>30"," se kritická hodnota aproximuje zlomkem ",[1115,37443,37445],{"className":37444},[1137],[1139,37446,37447],{"xmlns":1141},[1143,37448,37449,37460],{},[1146,37450,37451,37454,37456],{},[1230,37452,37453],{},"1,36",[1149,37455,5731],{"mathvariant":1854},[1283,37457,37458],{},[1149,37459,1816],{},[1153,37461,37462],{"encoding":1155},"1{,}36\u002F\\sqrt{n}",[1110,37464,31856,37465,37468,37469,37471,37472,1348,37475,37478],{},[1332,37466,37467],{},"ks.test()",", kde se za ",[1332,37470,11707],{}," dosadí příslušná distribuční funkce (",[1332,37473,37474],{},"\"pnorm\"",[1332,37476,37477],{},"\"pexp\"",", …) s jejími parametry:",[2035,37480,37482],{"className":2037,"code":37481,"language":71,"meta":2039,"style":2039},"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",[1332,37483,37484,37534],{"__ignoreMap":2039},[1115,37485,37486,37488,37490,37492,37494,37496,37498,37500,37502,37504,37506,37508,37510,37512,37514,37516,37518,37520,37522,37524,37526,37528,37530,37532],{"class":2044,"line":10},[1115,37487,32570],{"class":2047},[1115,37489,2052],{"class":2051},[1115,37491,2056],{"class":2055},[1115,37493,1199],{"class":2059},[1115,37495,16337],{"class":2062},[1115,37497,1503],{"class":2051},[1115,37499,16342],{"class":2062},[1115,37501,1503],{"class":2051},[1115,37503,16347],{"class":2062},[1115,37505,1503],{"class":2051},[1115,37507,16352],{"class":2062},[1115,37509,1503],{"class":2051},[1115,37511,16347],{"class":2062},[1115,37513,1503],{"class":2051},[1115,37515,16347],{"class":2062},[1115,37517,1503],{"class":2051},[1115,37519,16365],{"class":2062},[1115,37521,1503],{"class":2051},[1115,37523,16370],{"class":2062},[1115,37525,1503],{"class":2051},[1115,37527,16342],{"class":2062},[1115,37529,1503],{"class":2051},[1115,37531,16342],{"class":2062},[1115,37533,2090],{"class":2059},[1115,37535,37536,37539,37541,37543,37545,37548,37550,37552,37554,37556,37558,37560,37562,37564,37566],{"class":2044,"line":27},[1115,37537,37538],{"class":2055},"ks.test",[1115,37540,1199],{"class":2059},[1115,37542,32570],{"class":2047},[1115,37544,1503],{"class":2051},[1115,37546,37547],{"class":2575}," \"pnorm\"",[1115,37549,1503],{"class":2051},[1115,37551,13600],{"class":2055},[1115,37553,1199],{"class":2059},[1115,37555,32570],{"class":2047},[1115,37557,1228],{"class":2059},[1115,37559,1503],{"class":2051},[1115,37561,13610],{"class":2055},[1115,37563,1199],{"class":2059},[1115,37565,32570],{"class":2047},[1115,37567,2546],{"class":2059},[2035,37569,37572],{"className":37570,"code":37571,"language":2169,"meta":2039},[2167]," Asymptotic one-sample Kolmogorov-Smirnov test\n\ndata: x3\nD = 0.18469, p-value = 0.8847\nalternative hypothesis: two-sided\n",[1332,37573,37571],{"__ignoreMap":2039},[1110,37575,37576,37599],{},[1115,37577,37579],{"className":37578},[1137],[1139,37580,37581],{"xmlns":1141},[1143,37582,37583,37596],{},[1146,37584,37585,37587,37589,37592,37594],{},[1149,37586,1110],{},[1193,37588,1281],{},[1230,37590,37591],{},"0,8847",[1193,37593,5369],{},[1230,37595,4370],{},[1153,37597,37598],{"encoding":1155},"p = 0{,}8847 > 0{,}05",": odpad materiálu je slučitelný s normálním rozdělením se stejným průměrem a směrodatnou odchylkou.",[2019,37601,37603],{"id":37602},"shapiro-wilkův-test","Shapiro-Wilkův test",[1110,37605,37606],{},"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.",[1124,37608,37609,37629,37649],{},[1127,37610,37611,37628],{},[1115,37612,37614],{"className":37613},[1137],[1139,37615,37616],{"xmlns":1141},[1143,37617,37618,37626],{},[1146,37619,37620],{},[1201,37621,37622,37624],{},[1149,37623,2227],{},[1230,37625,1597],{},[1153,37627,2743],{"encoding":1155},": data mají normální rozdělení.",[1127,37630,37631,37648],{},[1115,37632,37634],{"className":37633},[1137],[1139,37635,37636],{"xmlns":1141},[1143,37637,37638,37646],{},[1146,37639,37640],{},[1201,37641,37642,37644],{},[1149,37643,2227],{},[1230,37645,1525],{},[1153,37647,2762],{"encoding":1155},": data nemají normální rozdělení.",[1127,37650,37651,37652,37678],{},"Testová statistika ",[1115,37653,37655],{"className":37654},[1137],[1139,37656,37657],{"xmlns":1141},[1143,37658,37659,37675],{},[1146,37660,37661,37663,37665,37667,37669,37671,37673],{},[1149,37662,6052],{},[1193,37664,11391],{},[1193,37666,12796],{"stretchy":1198},[1230,37668,1597],{},[1193,37670,1503],{"separator":1121},[1230,37672,1525],{},[1193,37674,11815],{"stretchy":1198},[1153,37676,37677],{"encoding":1155},"W \\in \\langle 0,1 \\rangle","; hodnoty blízké 1 indikují shodu s normalitou.",[1110,37680,37681,37682,37695,37696,1243,37716,37733,37734,1243,37754,37771],{},"Na rozdíl od ostatních testů v této kapitole se Shapiro-Wilkův test v praxi vyhodnocuje pouze přes p-hodnotu (tabulka kritických hodnot pro ",[1115,37683,37685],{"className":37684},[1137],[1139,37686,37687],{"xmlns":1141},[1143,37688,37689,37693],{},[1146,37690,37691],{},[1149,37692,6052],{},[1153,37694,6052],{"encoding":1155}," se běžně neudává): ",[1115,37697,37699],{"className":37698},[1137],[1139,37700,37701],{"xmlns":1141},[1143,37702,37703,37713],{},[1146,37704,37705,37707,37709,37711],{},[1149,37706,1110],{},[1193,37708,7775],{},[1149,37710,7788],{},[1193,37712,11921],{},[1153,37714,37715],{"encoding":1155},"p \\ge \\alpha \\Rightarrow",[1115,37717,37719],{"className":37718},[1137],[1139,37720,37721],{"xmlns":1141},[1143,37722,37723,37731],{},[1146,37724,37725],{},[1201,37726,37727,37729],{},[1149,37728,2227],{},[1230,37730,1597],{},[1153,37732,2743],{"encoding":1155}," nezamítáme (normalitu lze předpokládat); ",[1115,37735,37737],{"className":37736},[1137],[1139,37738,37739],{"xmlns":1141},[1143,37740,37741,37751],{},[1146,37742,37743,37745,37747,37749],{},[1149,37744,1110],{},[1193,37746,5343],{},[1149,37748,7788],{},[1193,37750,11921],{},[1153,37752,37753],{"encoding":1155},"p \u003C \\alpha \\Rightarrow",[1115,37755,37757],{"className":37756},[1137],[1139,37758,37759],{"xmlns":1141},[1143,37760,37761,37769],{},[1146,37762,37763],{},[1201,37764,37765,37767],{},[1149,37766,2227],{},[1230,37768,1597],{},[1153,37770,2743],{"encoding":1155}," zamítáme (předpoklad normality je porušen).",[2035,37773,37775],{"className":2037,"code":37774,"language":71,"meta":2039,"style":2039},"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",[1332,37776,37777,37831],{"__ignoreMap":2039},[1115,37778,37779,37781,37783,37785,37787,37789,37791,37793,37795,37797,37799,37801,37803,37805,37807,37809,37811,37813,37815,37817,37819,37821,37823,37825,37827,37829],{"class":2044,"line":10},[1115,37780,32438],{"class":2047},[1115,37782,2052],{"class":2051},[1115,37784,2056],{"class":2055},[1115,37786,1199],{"class":2059},[1115,37788,32447],{"class":2062},[1115,37790,1503],{"class":2051},[1115,37792,32452],{"class":2062},[1115,37794,1503],{"class":2051},[1115,37796,32457],{"class":2062},[1115,37798,1503],{"class":2051},[1115,37800,32462],{"class":2062},[1115,37802,1503],{"class":2051},[1115,37804,32467],{"class":2062},[1115,37806,1503],{"class":2051},[1115,37808,32472],{"class":2062},[1115,37810,1503],{"class":2051},[1115,37812,32462],{"class":2062},[1115,37814,1503],{"class":2051},[1115,37816,32481],{"class":2062},[1115,37818,1503],{"class":2051},[1115,37820,32467],{"class":2062},[1115,37822,1503],{"class":2051},[1115,37824,32490],{"class":2062},[1115,37826,1503],{"class":2051},[1115,37828,32462],{"class":2062},[1115,37830,2090],{"class":2059},[1115,37832,37833,37835,37837,37839],{"class":2044,"line":27},[1115,37834,2880],{"class":2055},[1115,37836,1199],{"class":2059},[1115,37838,32438],{"class":2047},[1115,37840,2090],{"class":2059},[2035,37842,37845],{"className":37843,"code":37844,"language":2169,"meta":2039},[2167]," Shapiro-Wilk normality test\n\ndata: x2\nW = 0.96022, p-value = 0.7744\n",[1332,37846,37844],{"__ignoreMap":2039},[1110,37848,37849,37850,37869],{},"U dat o životnosti baterií se normalita nezamítá (",[1115,37851,37853],{"className":37852},[1137],[1139,37854,37855],{"xmlns":1141},[1143,37856,37857,37866],{},[1146,37858,37859,37861,37863],{},[1149,37860,1110],{},[1193,37862,1281],{},[1230,37864,37865],{},"0,7744",[1153,37867,37868],{"encoding":1155},"p = 0{,}7744","), předpoklad t-testu je tedy splněn.",[1103,37871,37873,37880,37883,38250,38256],{"className":37872,"dataCallout":2932},[1106,2931],[1110,37874,37876,37879],{"className":37875},[1113],[1115,37877],{"className":37878,"ariaHidden":1121},[1118,2939,1120],"Příklad: Doba do poruchy výrobku",[1110,37881,37882],{},"Zkoušky životnosti nového výrobku daly soubor 68 hodnot doby do poruchy (v minutách). Odhadněte charakteristiky a zákon rozdělení.",[2035,37884,37886],{"className":2037,"code":37885,"language":71,"meta":2039,"style":2039},"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",[1332,37887,37888,37979,38057,38145,38179,38189,38199,38209,38219],{"__ignoreMap":2039},[1115,37889,37890,37892,37894,37896,37898,37900,37902,37904,37906,37908,37910,37912,37914,37916,37918,37920,37922,37924,37926,37928,37930,37932,37934,37936,37938,37941,37943,37945,37947,37949,37951,37953,37955,37957,37959,37961,37963,37965,37967,37969,37971,37973,37975,37977],{"class":2044,"line":10},[1115,37891,18425],{"class":2047},[1115,37893,2052],{"class":2051},[1115,37895,2056],{"class":2055},[1115,37897,1199],{"class":2059},[1115,37899,18434],{"class":2062},[1115,37901,1503],{"class":2051},[1115,37903,18439],{"class":2062},[1115,37905,1503],{"class":2051},[1115,37907,18444],{"class":2062},[1115,37909,1503],{"class":2051},[1115,37911,18449],{"class":2062},[1115,37913,1503],{"class":2051},[1115,37915,13845],{"class":2062},[1115,37917,1503],{"class":2051},[1115,37919,2067],{"class":2062},[1115,37921,1503],{"class":2051},[1115,37923,8144],{"class":2062},[1115,37925,1503],{"class":2051},[1115,37927,18466],{"class":2062},[1115,37929,1503],{"class":2051},[1115,37931,2082],{"class":2062},[1115,37933,1503],{"class":2051},[1115,37935,18475],{"class":2062},[1115,37937,1503],{"class":2051},[1115,37939,37940],{"class":2062}," 367",[1115,37942,1503],{"class":2051},[1115,37944,18487],{"class":2062},[1115,37946,1503],{"class":2051},[1115,37948,18492],{"class":2062},[1115,37950,1503],{"class":2051},[1115,37952,18497],{"class":2062},[1115,37954,1503],{"class":2051},[1115,37956,8162],{"class":2062},[1115,37958,1503],{"class":2051},[1115,37960,18506],{"class":2062},[1115,37962,1503],{"class":2051},[1115,37964,18511],{"class":2062},[1115,37966,1503],{"class":2051},[1115,37968,18516],{"class":2062},[1115,37970,1503],{"class":2051},[1115,37972,18521],{"class":2062},[1115,37974,1503],{"class":2051},[1115,37976,18526],{"class":2062},[1115,37978,8147],{"class":2051},[1115,37980,37981,37983,37985,37987,37989,37991,37993,37995,37997,37999,38001,38003,38005,38007,38009,38011,38013,38015,38017,38019,38021,38023,38025,38027,38029,38031,38033,38035,38037,38039,38041,38043,38045,38047,38049,38051,38053,38055],{"class":2044,"line":27},[1115,37982,18533],{"class":2062},[1115,37984,1503],{"class":2051},[1115,37986,18538],{"class":2062},[1115,37988,1503],{"class":2051},[1115,37990,18543],{"class":2062},[1115,37992,1503],{"class":2051},[1115,37994,18548],{"class":2062},[1115,37996,1503],{"class":2051},[1115,37998,18553],{"class":2062},[1115,38000,1503],{"class":2051},[1115,38002,8162],{"class":2062},[1115,38004,1503],{"class":2051},[1115,38006,18562],{"class":2062},[1115,38008,1503],{"class":2051},[1115,38010,8144],{"class":2062},[1115,38012,1503],{"class":2051},[1115,38014,18571],{"class":2062},[1115,38016,1503],{"class":2051},[1115,38018,18576],{"class":2062},[1115,38020,1503],{"class":2051},[1115,38022,19667],{"class":2062},[1115,38024,1503],{"class":2051},[1115,38026,18588],{"class":2062},[1115,38028,1503],{"class":2051},[1115,38030,18593],{"class":2062},[1115,38032,1503],{"class":2051},[1115,38034,18487],{"class":2062},[1115,38036,1503],{"class":2051},[1115,38038,18602],{"class":2062},[1115,38040,1503],{"class":2051},[1115,38042,18607],{"class":2062},[1115,38044,1503],{"class":2051},[1115,38046,18612],{"class":2062},[1115,38048,1503],{"class":2051},[1115,38050,18617],{"class":2062},[1115,38052,1503],{"class":2051},[1115,38054,18622],{"class":2062},[1115,38056,8147],{"class":2051},[1115,38058,38059,38061,38063,38066,38068,38070,38072,38074,38076,38078,38080,38082,38084,38086,38088,38090,38092,38094,38096,38098,38100,38102,38104,38107,38109,38111,38113,38115,38117,38119,38121,38123,38125,38127,38129,38131,38133,38135,38137,38139,38141,38143],{"class":2044,"line":148},[1115,38060,18732],{"class":2062},[1115,38062,1503],{"class":2051},[1115,38064,38065],{"class":2062}," 74",[1115,38067,1503],{"class":2051},[1115,38069,18639],{"class":2062},[1115,38071,1503],{"class":2051},[1115,38073,18644],{"class":2062},[1115,38075,1503],{"class":2051},[1115,38077,18649],{"class":2062},[1115,38079,1503],{"class":2051},[1115,38081,18654],{"class":2062},[1115,38083,1503],{"class":2051},[1115,38085,18571],{"class":2062},[1115,38087,1503],{"class":2051},[1115,38089,18663],{"class":2062},[1115,38091,1503],{"class":2051},[1115,38093,2072],{"class":2062},[1115,38095,1503],{"class":2051},[1115,38097,18672],{"class":2062},[1115,38099,1503],{"class":2051},[1115,38101,18677],{"class":2062},[1115,38103,1503],{"class":2051},[1115,38105,38106],{"class":2062}," 194",[1115,38108,1503],{"class":2051},[1115,38110,8544],{"class":2062},[1115,38112,1503],{"class":2051},[1115,38114,18693],{"class":2062},[1115,38116,1503],{"class":2051},[1115,38118,18698],{"class":2062},[1115,38120,1503],{"class":2051},[1115,38122,18703],{"class":2062},[1115,38124,1503],{"class":2051},[1115,38126,18654],{"class":2062},[1115,38128,1503],{"class":2051},[1115,38130,2082],{"class":2062},[1115,38132,1503],{"class":2051},[1115,38134,2067],{"class":2062},[1115,38136,1503],{"class":2051},[1115,38138,18720],{"class":2062},[1115,38140,1503],{"class":2051},[1115,38142,18725],{"class":2062},[1115,38144,8147],{"class":2051},[1115,38146,38147,38149,38151,38153,38155,38157,38159,38161,38163,38165,38167,38169,38171,38173,38175,38177],{"class":2044,"line":111},[1115,38148,18732],{"class":2062},[1115,38150,1503],{"class":2051},[1115,38152,8139],{"class":2062},[1115,38154,1503],{"class":2051},[1115,38156,18741],{"class":2062},[1115,38158,1503],{"class":2051},[1115,38160,18746],{"class":2062},[1115,38162,1503],{"class":2051},[1115,38164,18751],{"class":2062},[1115,38166,1503],{"class":2051},[1115,38168,18756],{"class":2062},[1115,38170,1503],{"class":2051},[1115,38172,18487],{"class":2062},[1115,38174,1503],{"class":2051},[1115,38176,18765],{"class":2062},[1115,38178,2090],{"class":2059},[1115,38180,38181,38183,38185,38187],{"class":2044,"line":96},[1115,38182,16489],{"class":2055},[1115,38184,1199],{"class":2059},[1115,38186,18425],{"class":2047},[1115,38188,2090],{"class":2059},[1115,38190,38191,38193,38195,38197],{"class":2044,"line":89},[1115,38192,16511],{"class":2055},[1115,38194,1199],{"class":2059},[1115,38196,18425],{"class":2047},[1115,38198,2090],{"class":2059},[1115,38200,38201,38203,38205,38207],{"class":2044,"line":82},[1115,38202,17210],{"class":2055},[1115,38204,1199],{"class":2059},[1115,38206,18425],{"class":2047},[1115,38208,2090],{"class":2059},[1115,38210,38211,38213,38215,38217],{"class":2044,"line":75},[1115,38212,2880],{"class":2055},[1115,38214,1199],{"class":2059},[1115,38216,18425],{"class":2047},[1115,38218,2090],{"class":2059},[1115,38220,38221,38223,38225,38227,38229,38232,38234,38236,38238,38240,38242,38244,38246,38248],{"class":2044,"line":5577},[1115,38222,37538],{"class":2055},[1115,38224,1199],{"class":2059},[1115,38226,18425],{"class":2047},[1115,38228,1503],{"class":2051},[1115,38230,38231],{"class":2575}," \"pexp\"",[1115,38233,1503],{"class":2051},[1115,38235,14431],{"class":2047},[1115,38237,2510],{"class":2051},[1115,38239,9031],{"class":2062},[1115,38241,4211],{"class":2051},[1115,38243,13600],{"class":2055},[1115,38245,1199],{"class":2059},[1115,38247,18425],{"class":2047},[1115,38249,2546],{"class":2059},[2035,38251,38254],{"className":38252,"code":38253,"language":2169,"meta":2039},[2167],"[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",[1332,38255,38253],{"__ignoreMap":2039},[1110,38257,38258,38259,38278,38279,38296,38297,38316],{},"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 (",[1115,38260,38262],{"className":38261},[1137],[1139,38263,38264],{"xmlns":1141},[1143,38265,38266,38275],{},[1146,38267,38268,38270,38272],{},[1149,38269,1110],{},[1193,38271,5343],{},[1230,38273,38274],{},"0,0001",[1153,38276,38277],{"encoding":1155},"p \u003C 0{,}0001","), zatímco Kolmogorov-Smirnovův test proti exponenciálnímu rozdělení se střední hodnotou ",[1115,38280,38282],{"className":38281},[1137],[1139,38283,38284],{"xmlns":1141},[1143,38285,38286,38294],{},[1146,38287,38288],{},[1214,38289,38290,38292],{"accent":1121},[1149,38291,1168],{},[1193,38293,15814],{},[1153,38295,25411],{"encoding":1155}," shodu nezamítá (",[1115,38298,38300],{"className":38299},[1137],[1139,38301,38302],{"xmlns":1141},[1143,38303,38304,38313],{},[1146,38305,38306,38308,38310],{},[1149,38307,1110],{},[1193,38309,1281],{},[1230,38311,38312],{},"0,8421",[1153,38314,38315],{"encoding":1155},"p = 0{,}8421","): data odpovídají spíše exponenciálnímu rozdělení než normálnímu.",[1110,38318,38319],{},[1864,38320],{"alt":38321,"className":38322,"src":38323},"mask-th-exponencialni-shoda",[1387,1868],"\u002Fwiki-assets\u002Fmask-th-exponencialni-shoda.png",[1377,38325,38327],{"id":38326},"neparametrické-testy","Neparametrické testy",[1110,38329,38330,38331,4053,38333,38357],{},"Když předpoklad normality neplatí, nahrazují t-testy jejich neparametrické obdoby — Wilcoxonovy testy posuzují ",[1130,38332,15903],{},[1115,38334,38336],{"className":38335},[1137],[1139,38337,38338],{"xmlns":1141},[1143,38339,38340,38354],{},[1146,38341,38342],{},[1201,38343,38344,38346],{},[1149,38345,1168],{},[1146,38347,38348,38350,38352],{},[1230,38349,1597],{},[1193,38351,1503],{"separator":1121},[1230,38353,5351],{},[1153,38355,38356],{"encoding":1155},"x_{0,5}",") místo střední hodnoty a nevyžadují normalitu dat.",[2019,38359,38361],{"id":38360},"wilcoxonovy-testy","Wilcoxonovy testy",[6528,38363,38364,38409],{},[6531,38365,38366],{},[6534,38367,38368,38387,38406],{},[6537,38369,38370],{},[1115,38371,38373],{"className":38372},[1137],[1139,38374,38375],{"xmlns":1141},[1143,38376,38377,38385],{},[1146,38378,38379],{},[1201,38380,38381,38383],{},[1149,38382,2227],{},[1230,38384,1597],{},[1153,38386,2743],{"encoding":1155},[6537,38388,38389],{},[1115,38390,38392],{"className":38391},[1137],[1139,38393,38394],{"xmlns":1141},[1143,38395,38396,38404],{},[1146,38397,38398],{},[1201,38399,38400,38402],{},[1149,38401,2227],{},[1230,38403,1525],{},[1153,38405,2762],{"encoding":1155},[6537,38407,38408],{},"Příkaz v R",[6645,38410,38411,38478,38545],{},[6534,38412,38413,38443,38473],{},[6650,38414,38415],{},[1115,38416,38418],{"className":38417},[1137],[1139,38419,38420],{"xmlns":1141},[1143,38421,38422,38440],{},[1146,38423,38424,38436,38438],{},[1201,38425,38426,38428],{},[1149,38427,1168],{},[1146,38429,38430,38432,38434],{},[1230,38431,1597],{},[1193,38433,1503],{"separator":1121},[1230,38435,5351],{},[1193,38437,11110],{},[1149,38439,8130],{},[1153,38441,38442],{"encoding":1155},"x_{0,5} \\le c",[6650,38444,38445],{},[1115,38446,38448],{"className":38447},[1137],[1139,38449,38450],{"xmlns":1141},[1143,38451,38452,38470],{},[1146,38453,38454,38466,38468],{},[1201,38455,38456,38458],{},[1149,38457,1168],{},[1146,38459,38460,38462,38464],{},[1230,38461,1597],{},[1193,38463,1503],{"separator":1121},[1230,38465,5351],{},[1193,38467,5369],{},[1149,38469,8130],{},[1153,38471,38472],{"encoding":1155},"x_{0,5} > c",[6650,38474,38475],{},[1332,38476,38477],{},"wilcox.test(x, alternative = \"greater\", mu = c)",[6534,38479,38480,38510,38540],{},[6650,38481,38482],{},[1115,38483,38485],{"className":38484},[1137],[1139,38486,38487],{"xmlns":1141},[1143,38488,38489,38507],{},[1146,38490,38491,38503,38505],{},[1201,38492,38493,38495],{},[1149,38494,1168],{},[1146,38496,38497,38499,38501],{},[1230,38498,1597],{},[1193,38500,1503],{"separator":1121},[1230,38502,5351],{},[1193,38504,1281],{},[1149,38506,8130],{},[1153,38508,38509],{"encoding":1155},"x_{0,5} = c",[6650,38511,38512],{},[1115,38513,38515],{"className":38514},[1137],[1139,38516,38517],{"xmlns":1141},[1143,38518,38519,38537],{},[1146,38520,38521,38533,38535],{},[1201,38522,38523,38525],{},[1149,38524,1168],{},[1146,38526,38527,38529,38531],{},[1230,38528,1597],{},[1193,38530,1503],{"separator":1121},[1230,38532,5351],{},[1193,38534,2271],{"mathvariant":1854},[1149,38536,8130],{},[1153,38538,38539],{"encoding":1155},"x_{0,5} \\neq c",[6650,38541,38542],{},[1332,38543,38544],{},"wilcox.test(x, alternative = \"two.sided\", mu = c)",[6534,38546,38547,38577,38607],{},[6650,38548,38549],{},[1115,38550,38552],{"className":38551},[1137],[1139,38553,38554],{"xmlns":1141},[1143,38555,38556,38574],{},[1146,38557,38558,38570,38572],{},[1201,38559,38560,38562],{},[1149,38561,1168],{},[1146,38563,38564,38566,38568],{},[1230,38565,1597],{},[1193,38567,1503],{"separator":1121},[1230,38569,5351],{},[1193,38571,7775],{},[1149,38573,8130],{},[1153,38575,38576],{"encoding":1155},"x_{0,5} \\ge c",[6650,38578,38579],{},[1115,38580,38582],{"className":38581},[1137],[1139,38583,38584],{"xmlns":1141},[1143,38585,38586,38604],{},[1146,38587,38588,38600,38602],{},[1201,38589,38590,38592],{},[1149,38591,1168],{},[1146,38593,38594,38596,38598],{},[1230,38595,1597],{},[1193,38597,1503],{"separator":1121},[1230,38599,5351],{},[1193,38601,5343],{},[1149,38603,8130],{},[1153,38605,38606],{"encoding":1155},"x_{0,5} \u003C c",[6650,38608,38609],{},[1332,38610,38611],{},"wilcox.test(x, alternative = \"less\", mu = c)",[1110,38613,38614,38617,38618,1236],{},[5922,38615,38616],{},"Jednovýběrový Wilcoxonův test"," (obdoba t-testu) posuzuje odchylku mediánu od konstanty ",[1115,38619,38621],{"className":38620},[1137],[1139,38622,38623],{"xmlns":1141},[1143,38624,38625,38629],{},[1146,38626,38627],{},[1149,38628,8130],{},[1153,38630,8130],{"encoding":1155},[1110,38632,38633,38636,38637,13204,38675,38688,38689,1236],{},[5922,38634,38635],{},"Jednovýběrový Wilcoxonův test na diferencích"," (obdoba párového t-testu) posuzuje odchylku mediánu rozdílu ",[1115,38638,38640],{"className":38639},[1137],[1139,38641,38642],{"xmlns":1141},[1143,38643,38644,38672],{},[1146,38645,38646,38658,38660],{},[1201,38647,38648,38650],{},[1149,38649,1168],{},[1146,38651,38652,38654,38656],{},[1230,38653,1597],{},[1193,38655,1503],{"separator":1121},[1230,38657,5351],{},[1193,38659,1210],{},[1201,38661,38662,38664],{},[1149,38663,1151],{},[1146,38665,38666,38668,38670],{},[1230,38667,1597],{},[1193,38669,1503],{"separator":1121},[1230,38671,5351],{},[1153,38673,38674],{"encoding":1155},"x_{0,5}-y_{0,5}",[1115,38676,38678],{"className":38677},[1137],[1139,38679,38680],{"xmlns":1141},[1143,38681,38682,38686],{},[1146,38683,38684],{},[1149,38685,8130],{},[1153,38687,8130],{"encoding":1155},"; v R se volá se stejnými argumenty jako výše a navíc ",[1332,38690,38691],{},"paired = TRUE",[1110,38693,38694,38697,38698,38700],{},[5922,38695,38696],{},"Dvouvýběrový Wilcoxonův test"," (obdoba dvouvýběrového t-testu) posuzuje odchylku mediánů dvou nezávislých výběrů; argument ",[1332,38699,29294],{}," odpadá. Pro výšky chlapců a dívek z příkladu výše:",[2035,38702,38704],{"className":2037,"code":38703,"language":71,"meta":2039,"style":2039},"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",[1332,38705,38706,38776,38834],{"__ignoreMap":2039},[1115,38707,38708,38710,38712,38714,38716,38718,38720,38722,38724,38726,38728,38730,38732,38734,38736,38738,38740,38742,38744,38746,38748,38750,38752,38754,38756,38758,38760,38762,38764,38766,38768,38770,38772,38774],{"class":2044,"line":10},[1115,38709,36950],{"class":2047},[1115,38711,2052],{"class":2051},[1115,38713,2056],{"class":2055},[1115,38715,1199],{"class":2059},[1115,38717,36959],{"class":2062},[1115,38719,1503],{"class":2051},[1115,38721,19667],{"class":2062},[1115,38723,1503],{"class":2051},[1115,38725,36968],{"class":2062},[1115,38727,1503],{"class":2051},[1115,38729,36973],{"class":2062},[1115,38731,1503],{"class":2051},[1115,38733,36978],{"class":2062},[1115,38735,1503],{"class":2051},[1115,38737,36983],{"class":2062},[1115,38739,1503],{"class":2051},[1115,38741,3789],{"class":2062},[1115,38743,1503],{"class":2051},[1115,38745,18526],{"class":2062},[1115,38747,1503],{"class":2051},[1115,38749,36978],{"class":2062},[1115,38751,1503],{"class":2051},[1115,38753,36968],{"class":2062},[1115,38755,1503],{"class":2051},[1115,38757,37004],{"class":2062},[1115,38759,1503],{"class":2051},[1115,38761,37009],{"class":2062},[1115,38763,1503],{"class":2051},[1115,38765,37014],{"class":2062},[1115,38767,1503],{"class":2051},[1115,38769,36978],{"class":2062},[1115,38771,1503],{"class":2051},[1115,38773,37023],{"class":2062},[1115,38775,2090],{"class":2059},[1115,38777,38778,38780,38782,38784,38786,38788,38790,38792,38794,38796,38798,38800,38802,38804,38806,38808,38810,38812,38814,38816,38818,38820,38822,38824,38826,38828,38830,38832],{"class":2044,"line":27},[1115,38779,37030],{"class":2047},[1115,38781,2052],{"class":2051},[1115,38783,2056],{"class":2055},[1115,38785,1199],{"class":2059},[1115,38787,25683],{"class":2062},[1115,38789,1503],{"class":2051},[1115,38791,36973],{"class":2062},[1115,38793,1503],{"class":2051},[1115,38795,37047],{"class":2062},[1115,38797,1503],{"class":2051},[1115,38799,37052],{"class":2062},[1115,38801,1503],{"class":2051},[1115,38803,37057],{"class":2062},[1115,38805,1503],{"class":2051},[1115,38807,37057],{"class":2062},[1115,38809,1503],{"class":2051},[1115,38811,18526],{"class":2062},[1115,38813,1503],{"class":2051},[1115,38815,36973],{"class":2062},[1115,38817,1503],{"class":2051},[1115,38819,36973],{"class":2062},[1115,38821,1503],{"class":2051},[1115,38823,37078],{"class":2062},[1115,38825,1503],{"class":2051},[1115,38827,37009],{"class":2062},[1115,38829,1503],{"class":2051},[1115,38831,36973],{"class":2062},[1115,38833,2090],{"class":2059},[1115,38835,38836,38839,38841,38843,38845,38847,38849,38851,38853,38855],{"class":2044,"line":148},[1115,38837,38838],{"class":2055},"wilcox.test",[1115,38840,1199],{"class":2059},[1115,38842,36950],{"class":2047},[1115,38844,1503],{"class":2051},[1115,38846,37101],{"class":2047},[1115,38848,1503],{"class":2051},[1115,38850,31941],{"class":2047},[1115,38852,2510],{"class":2051},[1115,38854,31946],{"class":2575},[1115,38856,2090],{"class":2059},[2035,38858,38861],{"className":38859,"code":38860,"language":2169,"meta":2039},[2167]," 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",[1332,38862,38860],{"__ignoreMap":2039},[1110,38864,38865,38888],{},[1115,38866,38868],{"className":38867},[1137],[1139,38869,38870],{"xmlns":1141},[1143,38871,38872,38885],{},[1146,38873,38874,38876,38878,38881,38883],{},[1149,38875,1110],{},[1193,38877,1281],{},[1230,38879,38880],{},"0,315",[1193,38882,5369],{},[1230,38884,4370],{},[1153,38886,38887],{"encoding":1155},"p = 0{,}315 > 0{,}05",": mediány výšek chlapců a dívek se statisticky významně neliší — stejný závěr jako u dvouvýběrového t-testu.",[1103,38890,38892,38899,38921,39032,39038],{"className":38891,"dataCallout":2932},[1106,2931],[1110,38893,38895,38898],{"className":38894},[1113],[1115,38896],{"className":38897,"ariaHidden":1121},[1118,2939,1120],"Příklad: Realitní odhadci — neparametrická alternativa",[1110,38900,38901,38902,38920],{},"U odhadů cen z párového t-testu výše normalita diferencí neplatí (",[1115,38903,38905],{"className":38904},[1137],[1139,38906,38907],{"xmlns":1141},[1143,38908,38909,38917],{},[1146,38910,38911,38913,38915],{},[1149,38912,1110],{},[1193,38914,1281],{},[1230,38916,33994],{},[1153,38918,38919],{"encoding":1155},"p = 0{,}03203","). Správnou volbou je párový Wilcoxonův test:",[2035,38922,38924],{"className":2037,"code":38923,"language":71,"meta":2039,"style":2039},"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",[1332,38925,38926,38968,39010],{"__ignoreMap":2039},[1115,38927,38928,38930,38932,38934,38936,38938,38940,38942,38944,38946,38948,38950,38952,38954,38956,38958,38960,38962,38964,38966],{"class":2044,"line":10},[1115,38929,33797],{"class":2047},[1115,38931,2052],{"class":2051},[1115,38933,2056],{"class":2055},[1115,38935,1199],{"class":2059},[1115,38937,33806],{"class":2062},[1115,38939,1503],{"class":2051},[1115,38941,33811],{"class":2062},[1115,38943,1503],{"class":2051},[1115,38945,33816],{"class":2062},[1115,38947,1503],{"class":2051},[1115,38949,33821],{"class":2062},[1115,38951,1503],{"class":2051},[1115,38953,33826],{"class":2062},[1115,38955,1503],{"class":2051},[1115,38957,33831],{"class":2062},[1115,38959,1503],{"class":2051},[1115,38961,33836],{"class":2062},[1115,38963,1503],{"class":2051},[1115,38965,33841],{"class":2062},[1115,38967,2090],{"class":2059},[1115,38969,38970,38972,38974,38976,38978,38980,38982,38984,38986,38988,38990,38992,38994,38996,38998,39000,39002,39004,39006,39008],{"class":2044,"line":27},[1115,38971,33848],{"class":2047},[1115,38973,2052],{"class":2051},[1115,38975,2056],{"class":2055},[1115,38977,1199],{"class":2059},[1115,38979,33857],{"class":2062},[1115,38981,1503],{"class":2051},[1115,38983,33862],{"class":2062},[1115,38985,1503],{"class":2051},[1115,38987,33867],{"class":2062},[1115,38989,1503],{"class":2051},[1115,38991,33872],{"class":2062},[1115,38993,1503],{"class":2051},[1115,38995,33877],{"class":2062},[1115,38997,1503],{"class":2051},[1115,38999,33882],{"class":2062},[1115,39001,1503],{"class":2051},[1115,39003,33887],{"class":2062},[1115,39005,1503],{"class":2051},[1115,39007,33892],{"class":2062},[1115,39009,2090],{"class":2059},[1115,39011,39012,39014,39016,39018,39020,39022,39024,39026,39028,39030],{"class":2044,"line":148},[1115,39013,38838],{"class":2055},[1115,39015,1199],{"class":2059},[1115,39017,33797],{"class":2047},[1115,39019,1503],{"class":2051},[1115,39021,33907],{"class":2047},[1115,39023,1503],{"class":2051},[1115,39025,33912],{"class":2047},[1115,39027,2510],{"class":2051},[1115,39029,5460],{"class":2062},[1115,39031,2090],{"class":2059},[2035,39033,39036],{"className":39034,"code":39035,"language":2169,"meta":2039},[2167]," 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",[1332,39037,39035],{"__ignoreMap":2039},[1110,39039,39040,39063],{},[1115,39041,39043],{"className":39042},[1137],[1139,39044,39045],{"xmlns":1141},[1143,39046,39047,39060],{},[1146,39048,39049,39051,39053,39056,39058],{},[1149,39050,1110],{},[1193,39052,1281],{},[1230,39054,39055],{},"0,1484",[1193,39057,5369],{},[1230,39059,4370],{},[1153,39061,39062],{"encoding":1155},"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.",[2019,39065,39067],{"id":39066},"kruskalův-wallisův-test","Kruskalův-Wallisův test",[1110,39069,39070,39071,39088],{},"Zobecnění dvouvýběrového Wilcoxonova testu, neparametrická obdoba analýzy rozptylu jednoduchého třídění. ",[1115,39072,39074],{"className":39073},[1137],[1139,39075,39076],{"xmlns":1141},[1143,39077,39078,39086],{},[1146,39079,39080],{},[1201,39081,39082,39084],{},[1149,39083,2227],{},[1230,39085,1597],{},[1153,39087,2743],{"encoding":1155},": všechny výběry pocházejí ze stejného rozdělení.",[2035,39090,39092],{"className":2037,"code":39091,"language":71,"meta":2039,"style":2039},"kruskal.test(kvantitativní_proměnná ~ faktor, data = soubor)\n",[1332,39093,39094],{"__ignoreMap":2039},[1115,39095,39096,39099,39101,39104,39106,39109,39111,39113,39115,39118],{"class":2044,"line":10},[1115,39097,39098],{"class":2055},"kruskal.test",[1115,39100,1199],{"class":2059},[1115,39102,39103],{"class":2047},"kvantitativní_proměnná",[1115,39105,2147],{"class":2051},[1115,39107,39108],{"class":2047}," faktor",[1115,39110,1503],{"class":2051},[1115,39112,5500],{"class":2047},[1115,39114,2510],{"class":2051},[1115,39116,39117],{"class":2047}," soubor",[1115,39119,2090],{"class":2059},[2019,39121,39123],{"id":39122},"mediánový-test","Mediánový test",[1110,39125,39126,39127,39144,39145,1902],{},"Má stejný účel jako Kruskalův-Wallisův test (obdoba analýzy rozptylu jednoduchého třídění, ",[1115,39128,39130],{"className":39129},[1137],[1139,39131,39132],{"xmlns":1141},[1143,39133,39134,39142],{},[1146,39135,39136],{},[1201,39137,39138,39140],{},[1149,39139,2227],{},[1230,39141,1597],{},[1153,39143,2743],{"encoding":1155},": všechny výběry pocházejí ze stejného rozdělení) a je součástí balíčku ",[1332,39146,39147],{},"agricolae",[2035,39149,39151],{"className":2037,"code":39150,"language":71,"meta":2039,"style":2039},"library(agricolae)\nMedian.test(kvantitativní_proměnná, faktor)\n",[1332,39152,39153,39163],{"__ignoreMap":2039},[1115,39154,39155,39157,39159,39161],{"class":2044,"line":10},[1115,39156,2698],{"class":2051},[1115,39158,1199],{"class":2059},[1115,39160,39147],{"class":2047},[1115,39162,2090],{"class":2059},[1115,39164,39165,39168,39170,39172,39174,39176],{"class":2044,"line":27},[1115,39166,39167],{"class":2055},"Median.test",[1115,39169,1199],{"class":2059},[1115,39171,39103],{"class":2047},[1115,39173,1503],{"class":2051},[1115,39175,39108],{"class":2047},[1115,39177,2090],{"class":2059},[2019,39179,39181],{"id":39180},"friedmanův-test","Friedmanův test",[1110,39183,39184,39185,39202,39203,39241],{},"Neparametrická obdoba analýzy rozptylu dvojného třídění s jedním pozorováním v každé podtřídě. ",[1115,39186,39188],{"className":39187},[1137],[1139,39189,39190],{"xmlns":1141},[1143,39191,39192,39200],{},[1146,39193,39194],{},[1201,39195,39196,39198],{},[1149,39197,2227],{},[1230,39199,1597],{},[1153,39201,2743],{"encoding":1155},": distribuční funkce veličin ",[1115,39204,39206],{"className":39205},[1137],[1139,39207,39208],{"xmlns":1141},[1143,39209,39210,39238],{},[1146,39211,39212,39222,39224,39226,39228],{},[1201,39213,39214,39216],{},[1149,39215,11107],{},[1146,39217,39218,39220],{},[1149,39219,1207],{},[1230,39221,1525],{},[1193,39223,1503],{"separator":1121},[1193,39225,1530],{},[1193,39227,1503],{"separator":1121},[1201,39229,39230,39232],{},[1149,39231,11107],{},[1146,39233,39234,39236],{},[1149,39235,1207],{},[1149,39237,11631],{},[1153,39239,39240],{"encoding":1155},"X_{i1}, \\dots, X_{ik}"," jsou totožné.",[2035,39243,39245],{"className":2037,"code":39244,"language":71,"meta":2039,"style":2039},"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",[1332,39246,39247,39277,39282],{"__ignoreMap":2039},[1115,39248,39249,39252,39254,39256,39258,39261,39264,39267,39269,39271,39273,39275],{"class":2044,"line":10},[1115,39250,39251],{"class":2055},"friedman.test",[1115,39253,1199],{"class":2059},[1115,39255,39103],{"class":2047},[1115,39257,2147],{"class":2051},[1115,39259,39260],{"class":2047}," faktor_A",[1115,39262,39263],{"class":2051}," |",[1115,39265,39266],{"class":2047}," faktor_B",[1115,39268,1503],{"class":2051},[1115,39270,5500],{"class":2047},[1115,39272,2510],{"class":2051},[1115,39274,39117],{"class":2047},[1115,39276,2090],{"class":2059},[1115,39278,39279],{"class":2044,"line":27},[1115,39280,39281],{"class":16384},"# jsou-li proměnné samostatné vektory (bez argumentu data):\n",[1115,39283,39284,39286,39288,39290,39292,39294,39296,39298],{"class":2044,"line":148},[1115,39285,39251],{"class":2055},[1115,39287,1199],{"class":2059},[1115,39289,39103],{"class":2047},[1115,39291,1503],{"class":2051},[1115,39293,39260],{"class":2047},[1115,39295,1503],{"class":2051},[1115,39297,39266],{"class":2047},[1115,39299,2090],{"class":2059},[1377,39301,39303],{"id":39302},"přehled-testů","Přehled testů",[1110,39305,39306],{},[1864,39307],{"alt":39308,"className":39309,"src":39310},"mask-ilu-volba-testu",[1387,1868],"\u002Fwiki-assets\u002Fmask-ilu-volba-testu.png",[6528,39312,39313,39326],{},[6531,39314,39315],{},[6534,39316,39317,39320,39323],{},[6537,39318,39319],{},"Situace",[6537,39321,39322],{},"Test",[6537,39324,39325],{},"R funkce",[6645,39327,39328,39341,39354,39366,39379,39394,39406,39419,39432,39445,39457,39472],{},[6534,39329,39330,39333,39336],{},[6650,39331,39332],{},"Jedna střední hodnota vs. zadané číslo, normální data",[6650,39334,39335],{},"jednovýběrový t-test",[6650,39337,39338],{},[1332,39339,39340],{},"t.test(x, mu = ..., alternative = ...)",[6534,39342,39343,39346,39349],{},[6650,39344,39345],{},"Rozdíl dvou závislých měření, diference normální",[6650,39347,39348],{},"párový t-test",[6650,39350,39351],{},[1332,39352,39353],{},"t.test(x, y, paired = TRUE)",[6534,39355,39356,39359,39361],{},[6650,39357,39358],{},"Shoda rozptylů dvou nezávislých normálních výběrů",[6650,39360,5407],{},[6650,39362,39363],{},[1332,39364,39365],{},"var.test(x, y)",[6534,39367,39368,39371,39374],{},[6650,39369,39370],{},"Shoda středních hodnot dvou nezávislých normálních výběrů",[6650,39372,39373],{},"dvouvýběrový t-test",[6650,39375,39376],{},[1332,39377,39378],{},"t.test(x, y, var.equal = TRUE\u002FFALSE)",[6534,39380,39381,39384,39386],{},[6650,39382,39383],{},"Shoda dat se zadaným typem rozdělení (normální, exponenciální, …)",[6650,39385,37187],{},[6650,39387,39388,1348,39391],{},[1332,39389,39390],{},"ks.test(x, \"pnorm\", mu, sigma)",[1332,39392,39393],{},"ks.test(x, \"pexp\", 1\u002Fdelta)",[6534,39395,39396,39399,39401],{},[6650,39397,39398],{},"Normalita dat",[6650,39400,37603],{},[6650,39402,39403],{},[1332,39404,39405],{},"shapiro.test(x)",[6534,39407,39408,39411,39414],{},[6650,39409,39410],{},"Medián jednoho výběru vs. konstanta, data nejsou normální",[6650,39412,39413],{},"jednovýběrový Wilcoxonův test",[6650,39415,39416],{},[1332,39417,39418],{},"wilcox.test(x, mu = c, alternative = ...)",[6534,39420,39421,39424,39427],{},[6650,39422,39423],{},"Medián diferencí dvou závislých měření, data nejsou normální",[6650,39425,39426],{},"párový Wilcoxonův test",[6650,39428,39429],{},[1332,39430,39431],{},"wilcox.test(x, y, paired = TRUE, mu = c)",[6534,39433,39434,39437,39440],{},[6650,39435,39436],{},"Mediány dvou nezávislých výběrů, data nejsou normální",[6650,39438,39439],{},"dvouvýběrový Wilcoxonův test",[6650,39441,39442],{},[1332,39443,39444],{},"wilcox.test(x, y)",[6534,39446,39447,39450,39452],{},[6650,39448,39449],{},"Více než dva nezávislé výběry, data nejsou normální",[6650,39451,39067],{},[6650,39453,39454],{},[1332,39455,39456],{},"kruskal.test(y ~ faktor, data)",[6534,39458,39459,39462,39465],{},[6650,39460,39461],{},"Více než dva nezávislé výběry, data nejsou normální (alternativa)",[6650,39463,39464],{},"mediánový test",[6650,39466,39467,26511,39470],{},[1332,39468,39469],{},"Median.test(y, faktor)",[1332,39471,39147],{},[6534,39473,39474,39477,39479],{},[6650,39475,39476],{},"Více než dva závislé výběry (dvojné třídění, jedno pozorování na podtřídu)",[6650,39478,39181],{},[6650,39480,39481],{},[1332,39482,39483],{},"friedman.test(y ~ A | B, data)",[1377,39485,5681],{"id":5680},[1124,39487,39488,39565,39571,39588,39619],{},[1127,39489,39490,39529,39530,36917,39547,39564],{},[1130,39491,39492,39493,39510,39511,39528],{},"Nezamítnutí ",[1115,39494,39496],{"className":39495},[1137],[1139,39497,39498],{"xmlns":1141},[1143,39499,39500,39508],{},[1146,39501,39502],{},[1201,39503,39504,39506],{},[1149,39505,2227],{},[1230,39507,1597],{},[1153,39509,2743],{"encoding":1155}," není důkaz, že ",[1115,39512,39514],{"className":39513},[1137],[1139,39515,39516],{"xmlns":1141},[1143,39517,39518,39526],{},[1146,39519,39520],{},[1201,39521,39522,39524],{},[1149,39523,2227],{},[1230,39525,1597],{},[1153,39527,2743],{"encoding":1155}," platí."," U kabelů A\u002FB vyšlo ",[1115,39531,39533],{"className":39532},[1137],[1139,39534,39535],{"xmlns":1141},[1143,39536,39537,39545],{},[1146,39538,39539,39541,39543],{},[1149,39540,1110],{},[1193,39542,1281],{},[1230,39544,36913],{},[1153,39546,36916],{"encoding":1155},[1115,39548,39550],{"className":39549},[1137],[1139,39551,39552],{"xmlns":1141},[1143,39553,39554,39562],{},[1146,39555,39556],{},[1201,39557,39558,39560],{},[1149,39559,2227],{},[1230,39561,1597],{},[1153,39563,2743],{"encoding":1155}," nezamítá, ale hodnota je blízko hranice; správná interpretace je „data rovnost průměrů nevyvracejí“, ne „rovnost je prokázána“.",[1127,39566,39567,39570],{},[1130,39568,39569],{},"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.",[1127,39572,39573,39580,39581,39584,39585,39587],{},[1130,39574,39575,34075,39577,39579],{},[1332,39576,36645],{},[1332,39578,31859],{}," se volí podle F-testu, ne podle výchozí hodnoty."," Výchozí nastavení R je ",[1332,39582,39583],{},"var.equal = FALSE"," (Welchova varianta); pokud F-test potvrdí shodné rozptyly, je třeba explicitně napsat ",[1332,39586,36896],{},", jinak se použije jiná statistika a jiné stupně volnosti.",[1127,39589,39590,39593,39594,39597,39598,39615,39616,1236],{},[1130,39591,39592],{},"Jednostranná vs. dvoustranná alternativa mění kritický obor i závěr."," Volba ",[1332,39595,39596],{},"alternative = \"greater\"\u002F\"less\"\u002F\"two.sided\""," musí odpovídat formulaci ",[1115,39599,39601],{"className":39600},[1137],[1139,39602,39603],{"xmlns":1141},[1143,39604,39605,39613],{},[1146,39606,39607],{},[1201,39608,39609,39611],{},[1149,39610,2227],{},[1230,39612,1525],{},[1153,39614,2762],{"encoding":1155}," v zadání, ne být ponechána na výchozí hodnotě ",[1332,39617,39618],{},"\"two.sided\"",[1127,39620,39621,39624,39625,39638],{},[1130,39622,39623],{},"Shapiro-Wilkův test se vyhodnocuje jen přes p-hodnotu",", ne porovnáním ",[1115,39626,39628],{"className":39627},[1137],[1139,39629,39630],{"xmlns":1141},[1143,39631,39632,39636],{},[1146,39633,39634],{},[1149,39635,6052],{},[1153,39637,6052],{"encoding":1155}," s tabulkovou kritickou hodnotou jako u ostatních testů v této kapitole.",[1377,39640,5863],{"id":5862},[1124,39642,39643,39648,39653,39658,39663,39668,39673],{},[1127,39644,39645],{},[1384,39646,1390],{"className":39647,"dataFsResolvedFilePath":1388,"href":1389},[1387],[1127,39649,39650],{},[1384,39651,5876],{"className":39652,"dataFsResolvedFilePath":5292,"href":5293},[1387],[1127,39654,39655],{},[1384,39656,5884],{"className":39657,"dataFsResolvedFilePath":5882,"href":5883},[1387],[1127,39659,39660],{},[1384,39661,1094],{"className":39662,"dataFsResolvedFilePath":11005,"href":11006},[1387],[1127,39664,39665],{},[1384,39666,5898],{"className":39667,"dataFsResolvedFilePath":5896,"href":5897},[1387],[1127,39669,39670],{},[1384,39671,5906],{"className":39672,"dataFsResolvedFilePath":5904,"href":5905},[1387],[1127,39674,39675],{},[1384,39676,5914],{"className":39677,"dataFsResolvedFilePath":5912,"href":5913},[1387],[1377,39679,5917],{"id":934},[1110,39681,5920,39682,5925],{},[5922,39683,5924],{},[5927,39685,39686],{},"html pre.shiki code .sP4rz, 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