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statistika a datové soubory",{"type":1096,"value":1097,"toc":6031},"minimark",[1098,1102,1231,1236,1252,1390,1399,1410,1414,1458,1463,1578,1588,1593,1738,1819,1824,1926,2011,2019,2101,2120,2123,2344,2352,2362,2369,2372,2427,2433,2443,2459,2606,2609,2622,2944,2950,2953,2957,3037,3072,3102,3104,3183,3189,3251,3258,3271,3349,3475,3526,3539,3695,3701,3728,3732,3757,3760,3975,4045,4147,4154,4167,4684,4690,4722,4986,5140,5255,5286,5292,5299,5308,5321,5751,5757,5760,5764,5960,5964,6016,6019,6027],[1099,1100,1094],"h1",{"id":1101},"popisná-statistika-a-datové-soubory",[1103,1104,1109,1123],"aside",{"className":1105,"dataCallout":1108},[1106,1107],"callout","callout-default","tldr",[1110,1111,1114,1122],"p",{"className":1112},[1113],"callout-title",[1115,1116],"span",{"className":1117,"ariaHidden":1121},[1118,1119,1120],"iconify","i-lucide:info","callout-icon","true","V kostce",[1124,1125,1126,1130,1133,1177,1228],"ul",{},[1127,1128,1129],"li",{},"Rozlišit základní a výběrový soubor, typ statistického znaku (kvantitativní\u002Fkvalitativní, diskrétní\u002Fspojitý) a požadavek reprezentativity a nezávislého výběru.",[1127,1131,1132],{},"Spočítat výběrový průměr, rozptyl, směrodatnou odchylku a variační rozpětí; interpretovat je jako bodové odhady charakteristik náhodné veličiny.",[1127,1134,1135,1136,1176],{},"Určit medián a kvartily a číst empirickou distribuční funkci ",[1115,1137,1140],{"className":1138},[1139],"katex",[1141,1142,1144],"math",{"xmlns":1143},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1145,1146,1147,1171],"semantics",{},[1148,1149,1150,1160,1165,1168],"mrow",{},[1151,1152,1153,1157],"msub",{},[1154,1155,1156],"mi",{},"F",[1154,1158,1159],{},"n",[1161,1162,1164],"mo",{"stretchy":1163},"false","(",[1154,1166,1167],{},"x",[1161,1169,1170],{"stretchy":1163},")",[1172,1173,1175],"annotation",{"encoding":1174},"application\u002Fx-tex","F_n(x)",".",[1127,1178,1179,1180,1227],{},"Roztřídit velký datový soubor do tříd (intervalové rozdělení četností), sestavit tabulku ",[1115,1181,1183],{"className":1182},[1139],[1141,1184,1185],{"xmlns":1143},[1145,1186,1187,1224],{},[1148,1188,1189,1197,1200,1207,1209,1216,1218],{},[1151,1190,1191,1194],{},[1154,1192,1193],{},"I",[1154,1195,1196],{},"j",[1161,1198,1199],{"separator":1121},",",[1151,1201,1202,1205],{},[1154,1203,1204],{},"Z",[1154,1206,1196],{},[1161,1208,1199],{"separator":1121},[1151,1210,1211,1214],{},[1154,1212,1213],{},"f",[1154,1215,1196],{},[1161,1217,1199],{"separator":1121},[1151,1219,1220,1222],{},[1154,1221,1110],{},[1154,1223,1196],{},[1172,1225,1226],{"encoding":1174},"I_j, Z_j, f_j, p_j"," a nakreslit histogram.",[1127,1229,1230],{},"Z histogramu odhadnout zákon rozdělení dat; formální test shody patří do testování hypotéz.",[1232,1233,1235],"h2",{"id":1234},"základní-pojmy","Základní pojmy",[1110,1237,1238,1246,1247,1251],{},[1239,1240,1245],"a",{"className":1241,"dataFsResolvedFilePath":1243,"href":1244},[1242],"wikilink","courses\u002Fmask.md","\u002Fwiki\u002Fmask","Metody aplikované statistiky"," pracuje s ",[1248,1249,1250],"strong",{},"datovými soubory"," — konkrétními hodnotami, které popisují vlastnost zkoumaných prvků.",[1124,1253,1254,1260,1288,1294,1375],{},[1127,1255,1256,1259],{},[1248,1257,1258],{},"Základní soubor"," — množina prvků, na nichž provádíme šetření (např. všichni výdělečně činní obyvatelé ČR).",[1127,1261,1262,1265,1266],{},[1248,1263,1264],{},"Statistický znak"," — funkce, která vyjadřuje určitou vlastnost prvku (např. velikost platu). Znaky dělíme na:\n",[1124,1267,1268,1282],{},[1127,1269,1270,1273,1274,1277,1278,1281],{},[1248,1271,1272],{},"kvantitativní"," (vyjádřitelné číslem) — dále ",[1248,1275,1276],{},"diskrétní"," (spočetně mnoho hodnot) nebo ",[1248,1279,1280],{},"spojité"," (libovolná hodnota v intervalu);",[1127,1283,1284,1287],{},[1248,1285,1286],{},"kvalitativní"," (vyjádřitelné slovně).",[1127,1289,1290,1293],{},[1248,1291,1292],{},"Výběrový soubor"," — podmnožina prvků základního souboru, na níž znak skutečně zjišťujeme (např. 5 náhodně vybraných obyvatel).",[1127,1295,1296,1299,1300,1176],{},[1248,1297,1298],{},"Datový soubor"," — n-tice naměřených hodnot zkoumaného znaku, např. ",[1115,1301,1303],{"className":1302},[1139],[1141,1304,1305],{"xmlns":1143},[1145,1306,1307,1372],{},[1148,1308,1309,1311,1315,1319,1322,1324,1327,1330,1332,1335,1337,1339,1342,1344,1347,1349,1351,1354,1356,1358,1360,1362,1365,1367,1370],{},[1161,1310,1164],{"stretchy":1163},[1312,1313,1314],"mn",{},"29",[1316,1317,1318],"mtext",{}," ",[1312,1320,1321],{},"500",[1161,1323,1199],{"separator":1121},[1316,1325,1326],{}," ",[1312,1328,1329],{},"38",[1316,1331,1318],{},[1312,1333,1334],{},"000",[1161,1336,1199],{"separator":1121},[1316,1338,1326],{},[1312,1340,1341],{},"37",[1316,1343,1318],{},[1312,1345,1346],{},"800",[1161,1348,1199],{"separator":1121},[1316,1350,1326],{},[1312,1352,1353],{},"41",[1316,1355,1318],{},[1312,1357,1334],{},[1161,1359,1199],{"separator":1121},[1316,1361,1326],{},[1312,1363,1364],{},"31",[1316,1366,1318],{},[1312,1368,1369],{},"200",[1161,1371,1170],{"stretchy":1163},[1172,1373,1374],{"encoding":1174},"(29\\,500,\\ 38\\,000,\\ 37\\,800,\\ 41\\,000,\\ 31\\,200)",[1127,1376,1377,1378,1381,1382,1385,1386,1389],{},"Podle počtu sledovaných znaků rozlišujeme ",[1248,1379,1380],{},"jednorozměrné",", ",[1248,1383,1384],{},"dvourozměrné"," a ",[1248,1387,1388],{},"vícerozměrné"," datové soubory.",[1110,1391,1392],{},[1393,1394],"img",{"alt":1395,"className":1396,"src":1398},"mask-ilu-zakladni-soubor-vyber",[1242,1397],"wikilink-broken","\u002Fwiki-assets\u002Fmask-ilu-zakladni-soubor-vyber.png",[1110,1400,1401,1402,1405,1406,1409],{},"Aby výběrový soubor dobře vypovídal o základním souboru, měl by být ",[1248,1403,1404],{},"reprezentativní"," (podobný základnímu souboru svým složením). Není-li to možné zajistit přímo, volí se prvky do výběru náhodně — ",[1248,1407,1408],{},"nezávislý výběr",". Bez náhodnosti výběru nelze vlastnosti základního souboru správně vystihnout.",[1232,1411,1413],{"id":1412},"empirické-charakteristiky","Empirické charakteristiky",[1110,1415,1416,1417,1420,1421,1424,1425,1439,1440,1443,1444,1457],{},"Zpracováním datového souboru získáme ",[1248,1418,1419],{},"empirické charakteristiky"," a odhad ",[1248,1422,1423],{},"zákona rozdělení"," zkoumané náhodné veličiny ",[1115,1426,1428],{"className":1427},[1139],[1141,1429,1430],{"xmlns":1143},[1145,1431,1432,1437],{},[1148,1433,1434],{},[1154,1435,1436],{},"X",[1172,1438,1436],{"encoding":1174},". Jde o ",[1248,1441,1442],{},"bodové odhady"," charakteristik ",[1115,1445,1447],{"className":1446},[1139],[1141,1448,1449],{"xmlns":1143},[1145,1450,1451,1455],{},[1148,1452,1453],{},[1154,1454,1436],{},[1172,1456,1436],{"encoding":1174},"; ruční výpočet podle vzorců níže je potřeba jen bez dostupného softwaru.",[1110,1459,1460],{},[1248,1461,1462],{},"Míry polohy",[1115,1464,1466],{"className":1465},[1139],[1141,1467,1469],{"xmlns":1143,"display":1468},"block",[1145,1470,1471,1575],{},[1148,1472,1473,1481,1484,1492,1509,1515,1519],{},[1474,1475,1476,1478],"mover",{"accent":1121},[1154,1477,1167],{},[1161,1479,1480],{},"ˉ",[1161,1482,1483],{},"=",[1485,1486,1487,1490],"mfrac",{},[1312,1488,1489],{},"1",[1154,1491,1159],{},[1493,1494,1495,1498,1507],"munderover",{},[1161,1496,1497],{},"∑",[1148,1499,1500,1503,1505],{},[1154,1501,1502],{},"i",[1161,1504,1483],{},[1312,1506,1489],{},[1154,1508,1159],{},[1151,1510,1511,1513],{},[1154,1512,1167],{},[1154,1514,1502],{},[1516,1517],"mspace",{"width":1518},"2em",[1148,1520,1521,1524,1532,1535,1543,1546,1552,1555,1563,1566,1572],{},[1316,1522,1523],{},"(v",[1474,1525,1526,1529],{"accent":1121},[1316,1527,1528],{},"y",[1161,1530,1531],{},"ˊ",[1316,1533,1534],{},"b",[1474,1536,1537,1540],{"accent":1121},[1316,1538,1539],{},"e",[1161,1541,1542],{},"ˇ",[1316,1544,1545],{},"rov",[1474,1547,1548,1550],{"accent":1121},[1316,1549,1528],{},[1161,1551,1531],{},[1316,1553,1554],{}," pr",[1474,1556,1557,1560],{"accent":1121},[1316,1558,1559],{},"u",[1161,1561,1562],{},"˚",[1316,1564,1565],{},"m",[1474,1567,1568,1570],{"accent":1121},[1316,1569,1539],{},[1161,1571,1542],{},[1316,1573,1574],{},"r)",[1172,1576,1577],{"encoding":1174},"\\bar{x} = \\frac{1}{n}\\sum_{i=1}^{n} x_i \\qquad \\text{(výběrový průměr)}",[1110,1579,1580,1581,1385,1584,1587],{},"Dalšími mírami polohy jsou ",[1248,1582,1583],{},"medián",[1248,1585,1586],{},"modus"," (nejčetnější hodnota výběru).",[1110,1589,1590],{},[1248,1591,1592],{},"Míry variability",[1115,1594,1596],{"className":1595},[1139],[1141,1597,1598],{"xmlns":1143,"display":1468},[1145,1599,1600,1735],{},[1148,1601,1602,1611,1613,1626,1669,1671,1673,1675,1677,1686,1688],{},[1603,1604,1605,1608],"msup",{},[1154,1606,1607],{},"s",[1312,1609,1610],{},"2",[1161,1612,1483],{},[1485,1614,1615,1617],{},[1312,1616,1489],{},[1148,1618,1619,1621,1624],{},[1154,1620,1159],{},[1161,1622,1623],{},"−",[1312,1625,1489],{},[1148,1627,1628,1630,1644,1653,1655,1657,1667],{},[1161,1629,1164],{"fence":1121},[1493,1631,1632,1634,1642],{},[1161,1633,1497],{},[1148,1635,1636,1638,1640],{},[1154,1637,1502],{},[1161,1639,1483],{},[1312,1641,1489],{},[1154,1643,1159],{},[1645,1646,1647,1649,1651],"msubsup",{},[1154,1648,1167],{},[1154,1650,1502],{},[1312,1652,1610],{},[1161,1654,1623],{},[1154,1656,1159],{},[1603,1658,1659,1665],{},[1474,1660,1661,1663],{"accent":1121},[1154,1662,1167],{},[1161,1664,1480],{},[1312,1666,1610],{},[1161,1668,1170],{"fence":1121},[1161,1670,1199],{"separator":1121},[1516,1672],{"width":1518},[1154,1674,1607],{},[1161,1676,1483],{},[1678,1679,1680],"msqrt",{},[1603,1681,1682,1684],{},[1154,1683,1607],{},[1312,1685,1610],{},[1516,1687],{"width":1518},[1148,1689,1690,1692,1698,1700,1706,1708,1714,1717,1723,1726,1732],{},[1316,1691,1523],{},[1474,1693,1694,1696],{"accent":1121},[1316,1695,1528],{},[1161,1697,1531],{},[1316,1699,1534],{},[1474,1701,1702,1704],{"accent":1121},[1316,1703,1539],{},[1161,1705,1542],{},[1316,1707,1545],{},[1474,1709,1710,1712],{"accent":1121},[1316,1711,1528],{},[1161,1713,1531],{},[1316,1715,1716],{}," rozptyl, sm",[1474,1718,1719,1721],{"accent":1121},[1316,1720,1539],{},[1161,1722,1542],{},[1316,1724,1725],{},"rodatn",[1474,1727,1728,1730],{"accent":1121},[1316,1729,1239],{},[1161,1731,1531],{},[1316,1733,1734],{}," odchylka)",[1172,1736,1737],{"encoding":1174},"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)}",[1115,1739,1741],{"className":1740},[1139],[1141,1742,1743],{"xmlns":1143,"display":1468},[1145,1744,1745,1816],{},[1148,1746,1747,1750,1752,1762,1764,1773,1775],{},[1154,1748,1749],{},"R",[1161,1751,1483],{},[1151,1753,1754,1756,1759],{},[1154,1755,1167],{},[1154,1757,1758],{},"max",[1161,1760,1761],{},"⁡",[1161,1763,1623],{},[1151,1765,1766,1768,1771],{},[1154,1767,1167],{},[1154,1769,1770],{},"min",[1161,1772,1761],{},[1516,1774],{"width":1518},[1148,1776,1777,1780,1787,1789,1796,1799,1805,1808,1814],{},[1316,1778,1779],{},"(varia",[1474,1781,1782,1785],{"accent":1121},[1316,1783,1784],{},"c",[1161,1786,1542],{},[1316,1788,1159],{},[1474,1790,1791,1794],{"accent":1121},[1316,1792,1793],{},"ı",[1161,1795,1531],{},[1316,1797,1798],{}," rozp",[1474,1800,1801,1803],{"accent":1121},[1316,1802,1539],{},[1161,1804,1542],{},[1316,1806,1807],{},"t",[1474,1809,1810,1812],{"accent":1121},[1316,1811,1793],{},[1161,1813,1531],{},[1316,1815,1170],{},[1172,1817,1818],{"encoding":1174},"R = x_{\\max} - x_{\\min} \\qquad \\text{(variační rozpětí)}",[1110,1820,1821],{},[1248,1822,1823],{},"Kvantily",[1110,1825,1826,1827,1850,1851,1874,1875,1896,1897,1925],{},"Kvantil ",[1115,1828,1830],{"className":1829},[1139],[1141,1831,1832],{"xmlns":1143},[1145,1833,1834,1847],{},[1148,1835,1836],{},[1151,1837,1838,1845],{},[1474,1839,1840,1842],{"accent":1121},[1154,1841,1167],{},[1161,1843,1844],{},"~",[1154,1846,1110],{},[1172,1848,1849],{"encoding":1174},"\\tilde{x}_p"," dělí hodnoty datového souboru na dvě části: ",[1115,1852,1854],{"className":1853},[1139],[1141,1855,1856],{"xmlns":1143},[1145,1857,1858,1871],{},[1148,1859,1860,1863,1865,1867],{},[1312,1861,1862],{},"100",[1154,1864,1110],{},[1316,1866,1318],{},[1154,1868,1870],{"mathvariant":1869},"normal","%",[1172,1872,1873],{"encoding":1174},"100p\\,\\%"," hodnot je menších nebo rovných ",[1115,1876,1878],{"className":1877},[1139],[1141,1879,1880],{"xmlns":1143},[1145,1881,1882,1894],{},[1148,1883,1884],{},[1151,1885,1886,1892],{},[1474,1887,1888,1890],{"accent":1121},[1154,1889,1167],{},[1161,1891,1844],{},[1154,1893,1110],{},[1172,1895,1849],{"encoding":1174},", zbylých ",[1115,1898,1900],{"className":1899},[1139],[1141,1901,1902],{"xmlns":1143},[1145,1903,1904,1922],{},[1148,1905,1906,1908,1910,1912,1914,1916,1918,1920],{},[1312,1907,1862],{},[1161,1909,1164],{"stretchy":1163},[1312,1911,1489],{},[1161,1913,1623],{},[1154,1915,1110],{},[1161,1917,1170],{"stretchy":1163},[1316,1919,1318],{},[1154,1921,1870],{"mathvariant":1869},[1172,1923,1924],{"encoding":1174},"100(1-p)\\,\\%"," je větších. Nejdůležitější kvantily:",[1124,1927,1928,1957],{},[1127,1929,1930,1932,1933,1956],{},[1248,1931,1583],{}," ",[1115,1934,1936],{"className":1935},[1139],[1141,1937,1938],{"xmlns":1143},[1145,1939,1940,1953],{},[1148,1941,1942],{},[1151,1943,1944,1950],{},[1474,1945,1946,1948],{"accent":1121},[1154,1947,1167],{},[1161,1949,1844],{},[1312,1951,1952],{},"0,5",[1172,1954,1955],{"encoding":1174},"\\tilde{x}_{0{,}5}"," — pro lichý počet prvků uspořádaného souboru prostřední prvek, pro sudý počet průměr dvou prostředních prvků;",[1127,1958,1959,1932,1962,1385,1985,1932,1988,1176],{},[1248,1960,1961],{},"dolní kvartil",[1115,1963,1965],{"className":1964},[1139],[1141,1966,1967],{"xmlns":1143},[1145,1968,1969,1982],{},[1148,1970,1971],{},[1151,1972,1973,1979],{},[1474,1974,1975,1977],{"accent":1121},[1154,1976,1167],{},[1161,1978,1844],{},[1312,1980,1981],{},"0,25",[1172,1983,1984],{"encoding":1174},"\\tilde{x}_{0{,}25}",[1248,1986,1987],{},"horní kvartil",[1115,1989,1991],{"className":1990},[1139],[1141,1992,1993],{"xmlns":1143},[1145,1994,1995,2008],{},[1148,1996,1997],{},[1151,1998,1999,2005],{},[1474,2000,2001,2003],{"accent":1121},[1154,2002,1167],{},[1161,2004,1844],{},[1312,2006,2007],{},"0,75",[1172,2009,2010],{"encoding":1174},"\\tilde{x}_{0{,}75}",[1110,2012,2013,2014,2018],{},"Datový soubor se do R zadává buď přímo (",[2015,2016,2017],"code",{},"x \u003C- c(...)","), nebo načtením ze souboru:",[2020,2021,2025],"pre",{"className":2022,"code":2023,"language":71,"meta":2024,"style":2024},"language-r shiki shiki-themes github-light github-light github-dark","x \u003C- c(4.1, 4.0, 3.8, 3.9, 3.8, 3.8, 3.5, 3.7, 4.0, 4.0)   # přímé zadání hodnot\n# x \u003C- read.table(\"data.txt\")[, 1]                       # načtení prvního sloupce ze souboru\n","",[2015,2026,2027,2096],{"__ignoreMap":2024},[1115,2028,2030,2033,2037,2041,2044,2048,2050,2053,2055,2058,2060,2063,2065,2067,2069,2071,2073,2076,2078,2081,2083,2085,2087,2089,2092],{"class":2029,"line":10},"line",[1115,2031,1167],{"class":2032},"sP4rz",[1115,2034,2036],{"class":2035},"s8jYJ"," \u003C-",[1115,2038,2040],{"class":2039},"snPdu"," c",[1115,2042,1164],{"class":2043},"sxrX7",[1115,2045,2047],{"class":2046},"sBjJW","4.1",[1115,2049,1199],{"class":2035},[1115,2051,2052],{"class":2046}," 4.0",[1115,2054,1199],{"class":2035},[1115,2056,2057],{"class":2046}," 3.8",[1115,2059,1199],{"class":2035},[1115,2061,2062],{"class":2046}," 3.9",[1115,2064,1199],{"class":2035},[1115,2066,2057],{"class":2046},[1115,2068,1199],{"class":2035},[1115,2070,2057],{"class":2046},[1115,2072,1199],{"class":2035},[1115,2074,2075],{"class":2046}," 3.5",[1115,2077,1199],{"class":2035},[1115,2079,2080],{"class":2046}," 3.7",[1115,2082,1199],{"class":2035},[1115,2084,2052],{"class":2046},[1115,2086,1199],{"class":2035},[1115,2088,2052],{"class":2046},[1115,2090,2091],{"class":2043},")   ",[1115,2093,2095],{"class":2094},"sCsY4","# přímé zadání hodnot\n",[1115,2097,2098],{"class":2029,"line":27},[1115,2099,2100],{"class":2094},"# x \u003C- read.table(\"data.txt\")[, 1]                       # načtení prvního sloupce ze souboru\n",[1110,2102,2103,2104,2107,2108,2111,2112,2115,2116,2119],{},"Řádek s načtením ze souboru je zakomentovaný znakem ",[2015,2105,2106],{},"#",": soubor musí ležet v pracovním adresáři R. ",[2015,2109,2110],{},"read.table()"," vrací datovou tabulku (",[2015,2113,2114],{},"data.frame","), proto ",[2015,2117,2118],{},"[, 1]"," vybere její první sloupec jako vektor.",[1110,2121,2122],{},"V R:",[2020,2124,2126],{"className":2022,"code":2125,"language":71,"meta":2024,"style":2024},"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",[2015,2127,2128,2186,2197,2208,2219,2230,2270,2297,2320],{"__ignoreMap":2024},[1115,2129,2130,2132,2134,2136,2138,2141,2143,2146,2148,2151,2153,2156,2158,2160,2162,2165,2167,2169,2171,2174,2176,2179,2181,2183],{"class":2029,"line":10},[1115,2131,1167],{"class":2032},[1115,2133,2036],{"class":2035},[1115,2135,2040],{"class":2039},[1115,2137,1164],{"class":2043},[1115,2139,2140],{"class":2046},"11.1",[1115,2142,1199],{"class":2035},[1115,2144,2145],{"class":2046}," 12.7",[1115,2147,1199],{"class":2035},[1115,2149,2150],{"class":2046}," 10.8",[1115,2152,1199],{"class":2035},[1115,2154,2155],{"class":2046}," 13.2",[1115,2157,1199],{"class":2035},[1115,2159,2145],{"class":2046},[1115,2161,1199],{"class":2035},[1115,2163,2164],{"class":2046}," 13.4",[1115,2166,1199],{"class":2035},[1115,2168,2145],{"class":2046},[1115,2170,1199],{"class":2035},[1115,2172,2173],{"class":2046}," 14.4",[1115,2175,1199],{"class":2035},[1115,2177,2178],{"class":2046}," 14.7",[1115,2180,1199],{"class":2035},[1115,2182,2173],{"class":2046},[1115,2184,2185],{"class":2043},")\n",[1115,2187,2188,2191,2193,2195],{"class":2029,"line":27},[1115,2189,2190],{"class":2039},"length",[1115,2192,1164],{"class":2043},[1115,2194,1167],{"class":2032},[1115,2196,2185],{"class":2043},[1115,2198,2199,2202,2204,2206],{"class":2029,"line":148},[1115,2200,2201],{"class":2039},"mean",[1115,2203,1164],{"class":2043},[1115,2205,1167],{"class":2032},[1115,2207,2185],{"class":2043},[1115,2209,2210,2213,2215,2217],{"class":2029,"line":111},[1115,2211,2212],{"class":2039},"var",[1115,2214,1164],{"class":2043},[1115,2216,1167],{"class":2032},[1115,2218,2185],{"class":2043},[1115,2220,2221,2224,2226,2228],{"class":2029,"line":96},[1115,2222,2223],{"class":2039},"sd",[1115,2225,1164],{"class":2043},[1115,2227,1167],{"class":2032},[1115,2229,2185],{"class":2043},[1115,2231,2232,2234,2236,2238,2241,2243,2245,2247,2249,2251,2253,2255,2258,2261,2264,2266,2268],{"class":2029,"line":89},[1115,2233,1770],{"class":2039},[1115,2235,1164],{"class":2043},[1115,2237,1167],{"class":2032},[1115,2239,2240],{"class":2043},"); ",[1115,2242,1758],{"class":2039},[1115,2244,1164],{"class":2043},[1115,2246,1167],{"class":2032},[1115,2248,2240],{"class":2043},[1115,2250,1758],{"class":2039},[1115,2252,1164],{"class":2043},[1115,2254,1167],{"class":2032},[1115,2256,2257],{"class":2043},") ",[1115,2259,2260],{"class":2035},"-",[1115,2262,2263],{"class":2039}," min",[1115,2265,1164],{"class":2043},[1115,2267,1167],{"class":2032},[1115,2269,2185],{"class":2043},[1115,2271,2272,2275,2277,2279,2281,2284,2286,2289,2292,2295],{"class":2029,"line":82},[1115,2273,2274],{"class":2039},"quantile",[1115,2276,1164],{"class":2043},[1115,2278,1167],{"class":2032},[1115,2280,1199],{"class":2035},[1115,2282,2283],{"class":2046}," 0.5",[1115,2285,1199],{"class":2035},[1115,2287,2288],{"class":2032}," type",[1115,2290,2291],{"class":2035}," =",[1115,2293,2294],{"class":2046}," 6",[1115,2296,2185],{"class":2043},[1115,2298,2299,2301,2303,2305,2307,2310,2312,2314,2316,2318],{"class":2029,"line":75},[1115,2300,2274],{"class":2039},[1115,2302,1164],{"class":2043},[1115,2304,1167],{"class":2032},[1115,2306,1199],{"class":2035},[1115,2308,2309],{"class":2046}," 0.25",[1115,2311,1199],{"class":2035},[1115,2313,2288],{"class":2032},[1115,2315,2291],{"class":2035},[1115,2317,2294],{"class":2046},[1115,2319,2185],{"class":2043},[1115,2321,2323,2325,2327,2329,2331,2334,2336,2338,2340,2342],{"class":2029,"line":2322},9,[1115,2324,2274],{"class":2039},[1115,2326,1164],{"class":2043},[1115,2328,1167],{"class":2032},[1115,2330,1199],{"class":2035},[1115,2332,2333],{"class":2046}," 0.75",[1115,2335,1199],{"class":2035},[1115,2337,2288],{"class":2032},[1115,2339,2291],{"class":2035},[1115,2341,2294],{"class":2046},[1115,2343,2185],{"class":2043},[2020,2345,2350],{"className":2346,"code":2348,"language":2349,"meta":2024},[2347],"language-text","[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","text",[2015,2351,2348],{"__ignoreMap":2024},[1110,2353,2354,2357,2358,2361],{},[2015,2355,2356],{},"quantile(x, p, type = 6)"," je potřeba zadat explicitně — výchozí typ v R (",[2015,2359,2360],{},"type = 7",") by u některých souborů dal mírně odlišné hodnoty kvantilů než ruční výpočet použitý v této kapitole.",[1110,2363,2364],{},[1393,2365],{"alt":2366,"className":2367,"src":2368},"mask-ps-kvantily",[1242,1397],"\u002Fwiki-assets\u002Fmask-ps-kvantily.png",[1110,2370,2371],{},"Seřazení souboru a krabicový graf:",[2020,2373,2375],{"className":2022,"code":2374,"language":71,"meta":2024,"style":2024},"sort(x)                     # vzestupně\nsort(x, decreasing = TRUE)  # sestupně\nboxplot(x)\n",[2015,2376,2377,2392,2416],{"__ignoreMap":2024},[1115,2378,2379,2382,2384,2386,2389],{"class":2029,"line":10},[1115,2380,2381],{"class":2039},"sort",[1115,2383,1164],{"class":2043},[1115,2385,1167],{"class":2032},[1115,2387,2388],{"class":2043},")                     ",[1115,2390,2391],{"class":2094},"# vzestupně\n",[1115,2393,2394,2396,2398,2400,2402,2405,2407,2410,2413],{"class":2029,"line":27},[1115,2395,2381],{"class":2039},[1115,2397,1164],{"class":2043},[1115,2399,1167],{"class":2032},[1115,2401,1199],{"class":2035},[1115,2403,2404],{"class":2032}," decreasing",[1115,2406,2291],{"class":2035},[1115,2408,2409],{"class":2046}," TRUE",[1115,2411,2412],{"class":2043},")  ",[1115,2414,2415],{"class":2094},"# sestupně\n",[1115,2417,2418,2421,2423,2425],{"class":2029,"line":148},[1115,2419,2420],{"class":2039},"boxplot",[1115,2422,1164],{"class":2043},[1115,2424,1167],{"class":2032},[1115,2426,2185],{"class":2043},[2020,2428,2431],{"className":2429,"code":2430,"language":2349,"meta":2024},[2347]," [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",[2015,2432,2430],{"__ignoreMap":2024},[1110,2434,2435,2438,2439,2442],{},[2015,2436,2437],{},"boxplot()"," kreslí krabici mezi hodnotami ",[2015,2440,2441],{},"fivenum(x)"," (zde 12,7 a 14,4), které se od kvartilů typu 6 mohou mírně lišit.",[1103,2444,2448,2456],{"className":2445,"dataCallout":2447},[1106,2446],"callout-example","example",[1110,2449,2451,2455],{"className":2450},[1113],[1115,2452],{"className":2453,"ariaHidden":1121},[1118,2454,1120],"i-lucide:flask-conical","Příklad: Empirické charakteristiky",[1110,2457,2458],{},"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.",[1110,2460,2461,2462,1381,2485,1381,2508,1381,2527,2546,2547,2574,2575,2590,2591,1176],{},"Výstup R kódu výše dává ",[1115,2463,2465],{"className":2464},[1139],[1141,2466,2467],{"xmlns":1143},[1145,2468,2469,2482],{},[1148,2470,2471,2477,2479],{},[1474,2472,2473,2475],{"accent":1121},[1154,2474,1167],{},[1161,2476,1480],{},[1161,2478,1483],{},[1312,2480,2481],{},"13,01",[1172,2483,2484],{"encoding":1174},"\\bar{x}=13{,}01",[1115,2486,2488],{"className":2487},[1139],[1141,2489,2490],{"xmlns":1143},[1145,2491,2492,2505],{},[1148,2493,2494,2500,2502],{},[1603,2495,2496,2498],{},[1154,2497,1607],{},[1312,2499,1610],{},[1161,2501,1483],{},[1312,2503,2504],{},"1,75",[1172,2506,2507],{"encoding":1174},"s^2=1{,}75",[1115,2509,2511],{"className":2510},[1139],[1141,2512,2513],{"xmlns":1143},[1145,2514,2515,2524],{},[1148,2516,2517,2519,2521],{},[1154,2518,1607],{},[1161,2520,1483],{},[1312,2522,2523],{},"1,32",[1172,2525,2526],{"encoding":1174},"s=1{,}32",[1115,2528,2530],{"className":2529},[1139],[1141,2531,2532],{"xmlns":1143},[1145,2533,2534,2543],{},[1148,2535,2536,2538,2540],{},[1154,2537,1749],{},[1161,2539,1483],{},[1312,2541,2542],{},"3,9",[1172,2544,2545],{"encoding":1174},"R=3{,}9",", medián ",[1115,2548,2550],{"className":2549},[1139],[1141,2551,2552],{"xmlns":1143},[1145,2553,2554,2571],{},[1148,2555,2556,2566,2568],{},[1151,2557,2558,2564],{},[1474,2559,2560,2562],{"accent":1121},[1154,2561,1167],{},[1161,2563,1844],{},[1312,2565,1952],{},[1161,2567,1483],{},[1312,2569,2570],{},"12,95",[1172,2572,2573],{"encoding":1174},"\\tilde{x}_{0{,}5}=12{,}95",", dolní kvartil ",[1115,2576,2578],{"className":2577},[1139],[1141,2579,2580],{"xmlns":1143},[1145,2581,2582,2587],{},[1148,2583,2584],{},[1312,2585,2586],{},"12,3",[1172,2588,2589],{"encoding":1174},"12{,}3",", horní kvartil ",[1115,2592,2594],{"className":2593},[1139],[1141,2595,2596],{"xmlns":1143},[1145,2597,2598,2603],{},[1148,2599,2600],{},[1312,2601,2602],{},"14,4",[1172,2604,2605],{"encoding":1174},"14{,}4",[1110,2607,2608],{},"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.",[1103,2610,2612,2619],{"className":2611,"dataCallout":2447},[1106,2446],[1110,2613,2615,2618],{"className":2614},[1113],[1115,2616],{"className":2617,"ariaHidden":1121},[1118,2454,1120],"Příklad: Doba oprav televizorů",[1110,2620,2621],{},"Při 50 opravách určité závady televizoru byly naměřeny časy (v minutách). Určete empirické charakteristiky.",[2020,2623,2625],{"className":2022,"code":2624,"language":71,"meta":2024,"style":2024},"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",[2015,2626,2627,2689,2741,2788,2835,2883,2893,2903,2913,2933],{"__ignoreMap":2024},[1115,2628,2629,2632,2634,2636,2638,2641,2643,2646,2648,2651,2653,2656,2658,2661,2663,2666,2668,2671,2673,2676,2678,2681,2683,2686],{"class":2029,"line":10},[1115,2630,2631],{"class":2032},"x6",[1115,2633,2036],{"class":2035},[1115,2635,2040],{"class":2039},[1115,2637,1164],{"class":2043},[1115,2639,2640],{"class":2046},"44",[1115,2642,1199],{"class":2035},[1115,2644,2645],{"class":2046}," 40.2",[1115,2647,1199],{"class":2035},[1115,2649,2650],{"class":2046}," 41.9",[1115,2652,1199],{"class":2035},[1115,2654,2655],{"class":2046}," 43.4",[1115,2657,1199],{"class":2035},[1115,2659,2660],{"class":2046}," 42.8",[1115,2662,1199],{"class":2035},[1115,2664,2665],{"class":2046}," 42.3",[1115,2667,1199],{"class":2035},[1115,2669,2670],{"class":2046}," 43.2",[1115,2672,1199],{"class":2035},[1115,2674,2675],{"class":2046}," 45",[1115,2677,1199],{"class":2035},[1115,2679,2680],{"class":2046}," 41.5",[1115,2682,1199],{"class":2035},[1115,2684,2685],{"class":2046}," 42.7",[1115,2687,2688],{"class":2035},",\n",[1115,2690,2691,2694,2696,2699,2701,2704,2706,2709,2711,2714,2716,2719,2721,2724,2726,2729,2731,2734,2736,2739],{"class":2029,"line":27},[1115,2692,2693],{"class":2046},"        43.9",[1115,2695,1199],{"class":2035},[1115,2697,2698],{"class":2046}," 40.1",[1115,2700,1199],{"class":2035},[1115,2702,2703],{"class":2046}," 43.3",[1115,2705,1199],{"class":2035},[1115,2707,2708],{"class":2046}," 41.1",[1115,2710,1199],{"class":2035},[1115,2712,2713],{"class":2046}," 42.5",[1115,2715,1199],{"class":2035},[1115,2717,2718],{"class":2046}," 42.4",[1115,2720,1199],{"class":2035},[1115,2722,2723],{"class":2046}," 41.4",[1115,2725,1199],{"class":2035},[1115,2727,2728],{"class":2046}," 40.8",[1115,2730,1199],{"class":2035},[1115,2732,2733],{"class":2046}," 42",[1115,2735,1199],{"class":2035},[1115,2737,2738],{"class":2046}," 44.7",[1115,2740,2688],{"class":2035},[1115,2742,2743,2746,2748,2750,2752,2754,2756,2759,2761,2764,2766,2769,2771,2773,2775,2778,2780,2782,2784,2786],{"class":2029,"line":148},[1115,2744,2745],{"class":2046},"        41.2",[1115,2747,1199],{"class":2035},[1115,2749,2650],{"class":2046},[1115,2751,1199],{"class":2035},[1115,2753,2718],{"class":2046},[1115,2755,1199],{"class":2035},[1115,2757,2758],{"class":2046}," 44.4",[1115,2760,1199],{"class":2035},[1115,2762,2763],{"class":2046}," 40.5",[1115,2765,1199],{"class":2035},[1115,2767,2768],{"class":2046}," 39.7",[1115,2770,1199],{"class":2035},[1115,2772,2708],{"class":2046},[1115,2774,1199],{"class":2035},[1115,2776,2777],{"class":2046}," 41",[1115,2779,1199],{"class":2035},[1115,2781,2650],{"class":2046},[1115,2783,1199],{"class":2035},[1115,2785,2728],{"class":2046},[1115,2787,2688],{"class":2035},[1115,2789,2790,2793,2795,2797,2799,2802,2804,2806,2808,2810,2812,2815,2817,2820,2822,2824,2826,2829,2831,2833],{"class":2029,"line":111},[1115,2791,2792],{"class":2046},"        43",[1115,2794,1199],{"class":2035},[1115,2796,2660],{"class":2046},[1115,2798,1199],{"class":2035},[1115,2800,2801],{"class":2046}," 42.9",[1115,2803,1199],{"class":2035},[1115,2805,2685],{"class":2046},[1115,2807,1199],{"class":2035},[1115,2809,2703],{"class":2046},[1115,2811,1199],{"class":2035},[1115,2813,2814],{"class":2046}," 42.2",[1115,2816,1199],{"class":2035},[1115,2818,2819],{"class":2046}," 39.2",[1115,2821,1199],{"class":2035},[1115,2823,2680],{"class":2046},[1115,2825,1199],{"class":2035},[1115,2827,2828],{"class":2046}," 41.6",[1115,2830,1199],{"class":2035},[1115,2832,2685],{"class":2046},[1115,2834,2688],{"class":2035},[1115,2836,2837,2840,2842,2844,2846,2849,2851,2853,2855,2858,2860,2863,2865,2868,2870,2872,2874,2877,2879,2881],{"class":2029,"line":96},[1115,2838,2839],{"class":2046},"        45",[1115,2841,1199],{"class":2035},[1115,2843,2665],{"class":2046},[1115,2845,1199],{"class":2035},[1115,2847,2848],{"class":2046}," 43.6",[1115,2850,1199],{"class":2035},[1115,2852,2670],{"class":2046},[1115,2854,1199],{"class":2035},[1115,2856,2857],{"class":2046}," 38.8",[1115,2859,1199],{"class":2035},[1115,2861,2862],{"class":2046}," 43",[1115,2864,1199],{"class":2035},[1115,2866,2867],{"class":2046}," 44.2",[1115,2869,1199],{"class":2035},[1115,2871,2862],{"class":2046},[1115,2873,1199],{"class":2035},[1115,2875,2876],{"class":2046}," 40",[1115,2878,1199],{"class":2035},[1115,2880,2758],{"class":2046},[1115,2882,2185],{"class":2043},[1115,2884,2885,2887,2889,2891],{"class":2029,"line":89},[1115,2886,2190],{"class":2039},[1115,2888,1164],{"class":2043},[1115,2890,2631],{"class":2032},[1115,2892,2185],{"class":2043},[1115,2894,2895,2897,2899,2901],{"class":2029,"line":82},[1115,2896,2201],{"class":2039},[1115,2898,1164],{"class":2043},[1115,2900,2631],{"class":2032},[1115,2902,2185],{"class":2043},[1115,2904,2905,2907,2909,2911],{"class":2029,"line":75},[1115,2906,2223],{"class":2039},[1115,2908,1164],{"class":2043},[1115,2910,2631],{"class":2032},[1115,2912,2185],{"class":2043},[1115,2914,2915,2917,2919,2921,2923,2925,2927,2929,2931],{"class":2029,"line":2322},[1115,2916,1758],{"class":2039},[1115,2918,1164],{"class":2043},[1115,2920,2631],{"class":2032},[1115,2922,2257],{"class":2043},[1115,2924,2260],{"class":2035},[1115,2926,2263],{"class":2039},[1115,2928,1164],{"class":2043},[1115,2930,2631],{"class":2032},[1115,2932,2185],{"class":2043},[1115,2934,2935,2938,2940,2942],{"class":2029,"line":72},[1115,2936,2937],{"class":2039},"median",[1115,2939,1164],{"class":2043},[1115,2941,2631],{"class":2032},[1115,2943,2185],{"class":2043},[2020,2945,2948],{"className":2946,"code":2947,"language":2349,"meta":2024},[2347],"[1] 50\n[1] 42.27\n[1] 1.48052\n[1] 6.2\n[1] 42.4\n",[2015,2949,2947],{"__ignoreMap":2024},[1110,2951,2952],{},"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.",[1232,2954,2956],{"id":2955},"empirická-distribuční-funkce","Empirická distribuční funkce",[1110,2958,2959,2960,2973,2974,1932,2977,3000,3001,3036],{},"Pro libovolný rozsah datového souboru, diskrétní i spojitou náhodnou veličinu ",[1115,2961,2963],{"className":2962},[1139],[1141,2964,2965],{"xmlns":1143},[1145,2966,2967,2971],{},[1148,2968,2969],{},[1154,2970,1436],{},[1172,2972,1436],{"encoding":1174},", lze sestrojit ",[1248,2975,2976],{},"empirickou distribuční funkci",[1115,2978,2980],{"className":2979},[1139],[1141,2981,2982],{"xmlns":1143},[1145,2983,2984,2998],{},[1148,2985,2986,2992,2994,2996],{},[1151,2987,2988,2990],{},[1154,2989,1156],{},[1154,2991,1159],{},[1161,2993,1164],{"stretchy":1163},[1154,2995,1167],{},[1161,2997,1170],{"stretchy":1163},[1172,2999,1175],{"encoding":1174},". Pro datový soubor ",[1115,3002,3004],{"className":3003},[1139],[1141,3005,3006],{"xmlns":1143},[1145,3007,3008,3033],{},[1148,3009,3010,3012,3018,3020,3023,3025,3031],{},[1161,3011,1164],{"stretchy":1163},[1151,3013,3014,3016],{},[1154,3015,1167],{},[1312,3017,1489],{},[1161,3019,1199],{"separator":1121},[1161,3021,3022],{},"…",[1161,3024,1199],{"separator":1121},[1151,3026,3027,3029],{},[1154,3028,1167],{},[1154,3030,1159],{},[1161,3032,1170],{"stretchy":1163},[1172,3034,3035],{"encoding":1174},"(x_1,\\dots,x_n)"," je",[1115,3038,3040],{"className":3039},[1139],[1141,3041,3042],{"xmlns":1143,"display":1468},[1145,3043,3044,3069],{},[1148,3045,3046,3052,3054,3056,3058,3060,3067],{},[1151,3047,3048,3050],{},[1154,3049,1156],{},[1154,3051,1159],{},[1161,3053,1164],{"stretchy":1163},[1154,3055,1167],{},[1161,3057,1170],{"stretchy":1163},[1161,3059,1483],{},[1485,3061,3062,3065],{},[1154,3063,3064],{},"k",[1154,3066,1159],{},[1161,3068,1199],{"separator":1121},[1172,3070,3071],{"encoding":1174},"F_n(x) = \\frac{k}{n},",[1110,3073,3074,3075,3088,3089,1176],{},"kde ",[1115,3076,3078],{"className":3077},[1139],[1141,3079,3080],{"xmlns":1143},[1145,3081,3082,3086],{},[1148,3083,3084],{},[1154,3085,3064],{},[1172,3087,3064],{"encoding":1174}," je počet prvků datového souboru menších nebo rovných číslu ",[1115,3090,3092],{"className":3091},[1139],[1141,3093,3094],{"xmlns":1143},[1145,3095,3096,3100],{},[1148,3097,3098],{},[1154,3099,1167],{},[1172,3101,1167],{"encoding":1174},[1110,3103,2122],{},[2020,3105,3107],{"className":2022,"code":3106,"language":71,"meta":2024,"style":2024},"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",[2015,3108,3109,3124,3139,3157,3172],{"__ignoreMap":2024},[1115,3110,3111,3113,3115,3118,3120,3122],{"class":2029,"line":10},[1115,3112,1213],{"class":2032},[1115,3114,2036],{"class":2035},[1115,3116,3117],{"class":2039}," ecdf",[1115,3119,1164],{"class":2043},[1115,3121,1167],{"class":2032},[1115,3123,2185],{"class":2043},[1115,3125,3126,3129,3131,3133,3136],{"class":2029,"line":27},[1115,3127,3128],{"class":2039},"knots",[1115,3130,1164],{"class":2043},[1115,3132,1213],{"class":2032},[1115,3134,3135],{"class":2043},")        ",[1115,3137,3138],{"class":2094},"# vzestupně seřazené různé hodnoty datového souboru\n",[1115,3140,3141,3143,3145,3147,3149,3151,3154],{"class":2029,"line":148},[1115,3142,1213],{"class":2039},[1115,3144,1164],{"class":2043},[1115,3146,3128],{"class":2039},[1115,3148,1164],{"class":2043},[1115,3150,1213],{"class":2032},[1115,3152,3153],{"class":2043},"))      ",[1115,3155,3156],{"class":2094},"# hodnoty Fn(x) v těchto bodech\n",[1115,3158,3159,3161,3163,3166,3169],{"class":2029,"line":111},[1115,3160,1213],{"class":2039},[1115,3162,1164],{"class":2043},[1115,3164,3165],{"class":2046},"13",[1115,3167,3168],{"class":2043},")            ",[1115,3170,3171],{"class":2094},"# Fn v libovolném bodě\n",[1115,3173,3174,3177,3179,3181],{"class":2029,"line":96},[1115,3175,3176],{"class":2039},"plot",[1115,3178,1164],{"class":2043},[1115,3180,1213],{"class":2032},[1115,3182,2185],{"class":2043},[2020,3184,3187],{"className":3185,"code":3186,"language":2349,"meta":2024},[2347],"[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",[2015,3188,3186],{"__ignoreMap":2024},[1110,3190,3191,3194,3195,3213,3214,3217,3218,3231,3232,1176],{},[2015,3192,3193],{},"knots()"," vrací jen různé hodnoty (opakující se hodnota 12,7 je ve výpočtu ",[1115,3196,3198],{"className":3197},[1139],[1141,3199,3200],{"xmlns":1143},[1145,3201,3202,3210],{},[1148,3203,3204],{},[1151,3205,3206,3208],{},[1154,3207,1156],{},[1154,3209,1159],{},[1172,3211,3212],{"encoding":1174},"F_n"," započtena třikrát, v seznamu uzlů je ale jen jednou); ",[2015,3215,3216],{},"plot(f)"," nakreslí schodovitý graf, který v každém uzlu skáče o ",[1115,3219,3221],{"className":3220},[1139],[1141,3222,3223],{"xmlns":1143},[1145,3224,3225,3229],{},[1148,3226,3227],{},[1154,3228,3064],{},[1172,3230,3064],{"encoding":1174},"-násobek ",[1115,3233,3235],{"className":3234},[1139],[1141,3236,3237],{"xmlns":1143},[1145,3238,3239,3248],{},[1148,3240,3241,3243,3246],{},[1312,3242,1489],{},[1154,3244,3245],{"mathvariant":1869},"\u002F",[1154,3247,1159],{},[1172,3249,3250],{"encoding":1174},"1\u002Fn",[1110,3252,3253],{},[1393,3254],{"alt":3255,"className":3256,"src":3257},"mask-ps-ecdf",[1242,1397],"\u002Fwiki-assets\u002Fmask-ps-ecdf.png",[1103,3259,3261,3268],{"className":3260,"dataCallout":2447},[1106,2446],[1110,3262,3264,3267],{"className":3263},[1113],[1115,3265],{"className":3266,"ariaHidden":1121},[1118,2454,1120],"Příklad: Empirická distribuční funkce",[1110,3269,3270],{},"Pro předchozí datový soubor (doba opravy součástky) určete empirickou distribuční funkci.",[1110,3272,3273,3274,1176],{},"Uspořádaný soubor je ",[1115,3275,3277],{"className":3276},[1139],[1141,3278,3279],{"xmlns":1143},[1145,3280,3281,3346],{},[1148,3282,3283,3286,3289,3291,3294,3296,3298,3301,3303,3305,3307,3309,3311,3313,3315,3317,3320,3322,3324,3327,3329,3331,3333,3335,3337,3339,3341,3343],{},[1312,3284,3285],{},"10,8",[1161,3287,3288],{"separator":1121},";",[1316,3290,1326],{},[1312,3292,3293],{},"11,1",[1161,3295,3288],{"separator":1121},[1316,3297,1326],{},[1312,3299,3300],{},"12,7",[1161,3302,3288],{"separator":1121},[1316,3304,1326],{},[1312,3306,3300],{},[1161,3308,3288],{"separator":1121},[1316,3310,1326],{},[1312,3312,3300],{},[1161,3314,3288],{"separator":1121},[1316,3316,1326],{},[1312,3318,3319],{},"13,2",[1161,3321,3288],{"separator":1121},[1316,3323,1326],{},[1312,3325,3326],{},"13,4",[1161,3328,3288],{"separator":1121},[1316,3330,1326],{},[1312,3332,2602],{},[1161,3334,3288],{"separator":1121},[1316,3336,1326],{},[1312,3338,2602],{},[1161,3340,3288],{"separator":1121},[1316,3342,1326],{},[1312,3344,3345],{},"14,7",[1172,3347,3348],{"encoding":1174},"10{,}8;\\ 11{,}1;\\ 12{,}7;\\ 12{,}7;\\ 12{,}7;\\ 13{,}2;\\ 13{,}4;\\ 14{,}4;\\ 14{,}4;\\ 14{,}7",[3350,3351,3352,3388],"table",{},[3353,3354,3355],"thead",{},[3356,3357,3358,3374,3376,3378,3380,3382,3384,3386],"tr",{},[3359,3360,3361],"th",{},[1115,3362,3364],{"className":3363},[1139],[1141,3365,3366],{"xmlns":1143},[1145,3367,3368,3372],{},[1148,3369,3370],{},[1154,3371,1167],{},[1172,3373,1167],{"encoding":1174},[3359,3375,3285],{},[3359,3377,3293],{},[3359,3379,3300],{},[3359,3381,3319],{},[3359,3383,3326],{},[3359,3385,2602],{},[3359,3387,3345],{},[3389,3390,3391,3428],"tbody",{},[3356,3392,3393,3409,3411,3413,3416,3419,3422,3425],{},[3394,3395,3396],"td",{},[1115,3397,3399],{"className":3398},[1139],[1141,3400,3401],{"xmlns":1143},[1145,3402,3403,3407],{},[1148,3404,3405],{},[1154,3406,3064],{},[1172,3408,3064],{"encoding":1174},[3394,3410,1489],{},[3394,3412,1610],{},[3394,3414,3415],{},"5",[3394,3417,3418],{},"6",[3394,3420,3421],{},"7",[3394,3423,3424],{},"9",[3394,3426,3427],{},"10",[3356,3429,3430,3455,3458,3461,3463,3466,3469,3472],{},[3394,3431,3432],{},[1115,3433,3435],{"className":3434},[1139],[1141,3436,3437],{"xmlns":1143},[1145,3438,3439,3453],{},[1148,3440,3441,3447,3449,3451],{},[1151,3442,3443,3445],{},[1154,3444,1156],{},[1154,3446,1159],{},[1161,3448,1164],{"stretchy":1163},[1154,3450,1167],{},[1161,3452,1170],{"stretchy":1163},[1172,3454,1175],{"encoding":1174},[3394,3456,3457],{},"0,1",[3394,3459,3460],{},"0,2",[3394,3462,1952],{},[3394,3464,3465],{},"0,6",[3394,3467,3468],{},"0,7",[3394,3470,3471],{},"0,9",[3394,3473,3474],{},"1,0",[1110,3476,3477,3478,3500,3501,3525],{},"Graf (levý panel výše) odpovídá tabulce: funkce je nulová pod 10,8, skáče o ",[1115,3479,3481],{"className":3480},[1139],[1141,3482,3483],{"xmlns":1143},[1145,3484,3485,3497],{},[1148,3486,3487,3489,3491,3493,3495],{},[1312,3488,1489],{},[1154,3490,3245],{"mathvariant":1869},[1154,3492,1159],{},[1161,3494,1483],{},[1312,3496,3457],{},[1172,3498,3499],{"encoding":1174},"1\u002Fn = 0{,}1"," v každé jednoduché hodnotě a o ",[1115,3502,3504],{"className":3503},[1139],[1141,3505,3506],{"xmlns":1143},[1145,3507,3508,3522],{},[1148,3509,3510,3513,3515,3517,3519],{},[1312,3511,3512],{},"3",[1154,3514,3245],{"mathvariant":1869},[1154,3516,1159],{},[1161,3518,1483],{},[1312,3520,3521],{},"0,3",[1172,3523,3524],{"encoding":1174},"3\u002Fn = 0{,}3"," v bodě 12,7, kde se hodnota opakuje třikrát.",[1103,3527,3529,3536],{"className":3528,"dataCallout":2447},[1106,2446],[1110,3530,3532,3535],{"className":3531},[1113],[1115,3533],{"className":3534,"ariaHidden":1121},[1118,2454,1120],"Příklad: Odpad materiálu",[1110,3537,3538],{},"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.",[2020,3540,3542],{"className":2022,"code":3541,"language":71,"meta":2024,"style":2024},"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",[2015,3543,3544,3595,3605,3615,3625,3645,3655,3670,3680],{"__ignoreMap":2024},[1115,3545,3546,3549,3551,3553,3555,3557,3559,3561,3563,3565,3567,3569,3571,3573,3575,3577,3579,3581,3583,3585,3587,3589,3591,3593],{"class":2029,"line":10},[1115,3547,3548],{"class":2032},"x4",[1115,3550,2036],{"class":2035},[1115,3552,2040],{"class":2039},[1115,3554,1164],{"class":2043},[1115,3556,2047],{"class":2046},[1115,3558,1199],{"class":2035},[1115,3560,2052],{"class":2046},[1115,3562,1199],{"class":2035},[1115,3564,2057],{"class":2046},[1115,3566,1199],{"class":2035},[1115,3568,2062],{"class":2046},[1115,3570,1199],{"class":2035},[1115,3572,2057],{"class":2046},[1115,3574,1199],{"class":2035},[1115,3576,2057],{"class":2046},[1115,3578,1199],{"class":2035},[1115,3580,2075],{"class":2046},[1115,3582,1199],{"class":2035},[1115,3584,2080],{"class":2046},[1115,3586,1199],{"class":2035},[1115,3588,2052],{"class":2046},[1115,3590,1199],{"class":2035},[1115,3592,2052],{"class":2046},[1115,3594,2185],{"class":2043},[1115,3596,3597,3599,3601,3603],{"class":2029,"line":27},[1115,3598,2190],{"class":2039},[1115,3600,1164],{"class":2043},[1115,3602,3548],{"class":2032},[1115,3604,2185],{"class":2043},[1115,3606,3607,3609,3611,3613],{"class":2029,"line":148},[1115,3608,2201],{"class":2039},[1115,3610,1164],{"class":2043},[1115,3612,3548],{"class":2032},[1115,3614,2185],{"class":2043},[1115,3616,3617,3619,3621,3623],{"class":2029,"line":111},[1115,3618,2223],{"class":2039},[1115,3620,1164],{"class":2043},[1115,3622,3548],{"class":2032},[1115,3624,2185],{"class":2043},[1115,3626,3627,3629,3631,3633,3635,3637,3639,3641,3643],{"class":2029,"line":96},[1115,3628,1758],{"class":2039},[1115,3630,1164],{"class":2043},[1115,3632,3548],{"class":2032},[1115,3634,2257],{"class":2043},[1115,3636,2260],{"class":2035},[1115,3638,2263],{"class":2039},[1115,3640,1164],{"class":2043},[1115,3642,3548],{"class":2032},[1115,3644,2185],{"class":2043},[1115,3646,3647,3649,3651,3653],{"class":2029,"line":89},[1115,3648,2937],{"class":2039},[1115,3650,1164],{"class":2043},[1115,3652,3548],{"class":2032},[1115,3654,2185],{"class":2043},[1115,3656,3657,3660,3662,3664,3666,3668],{"class":2029,"line":82},[1115,3658,3659],{"class":2032},"f4",[1115,3661,2036],{"class":2035},[1115,3663,3117],{"class":2039},[1115,3665,1164],{"class":2043},[1115,3667,3548],{"class":2032},[1115,3669,2185],{"class":2043},[1115,3671,3672,3674,3676,3678],{"class":2029,"line":75},[1115,3673,3128],{"class":2039},[1115,3675,1164],{"class":2043},[1115,3677,3659],{"class":2032},[1115,3679,2185],{"class":2043},[1115,3681,3682,3684,3686,3688,3690,3692],{"class":2029,"line":2322},[1115,3683,3659],{"class":2039},[1115,3685,1164],{"class":2043},[1115,3687,3128],{"class":2039},[1115,3689,1164],{"class":2043},[1115,3691,3659],{"class":2032},[1115,3693,3694],{"class":2043},"))\n",[2020,3696,3699],{"className":3697,"code":3698,"language":2349,"meta":2024},[2347],"[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",[2015,3700,3698],{"__ignoreMap":2024},[1110,3702,3703,3704,3727],{},"Průměrný odpad je 3,86 % se směrodatnou odchylkou 0,18 % a mediánem 3,85 %. Pravý panel obrázku výše ukazuje tvar ",[1115,3705,3707],{"className":3706},[1139],[1141,3708,3709],{"xmlns":1143},[1145,3710,3711,3725],{},[1148,3712,3713,3719,3721,3723],{},[1151,3714,3715,3717],{},[1154,3716,1156],{},[1154,3718,1159],{},[1161,3720,1164],{"stretchy":1163},[1154,3722,1167],{},[1161,3724,1170],{"stretchy":1163},[1172,3726,1175],{"encoding":1174},": hodnota 3,8 se v souboru opakuje třikrát, proto zde funkce skáče o 0,3 najednou, stejně jako hodnota 4,0.",[1232,3729,3731],{"id":3730},"třídění-datového-souboru-do-tříd","Třídění datového souboru do tříd",[1110,3733,3734,3735,3738,3739,3752,3753,3756],{},"Je-li rozsah datového souboru velký (řádově přes 30 až 50 pozorování), hodnoty se před dalším zpracováním ",[1248,3736,3737],{},"roztřídí",": variační rozpětí ",[1115,3740,3742],{"className":3741},[1139],[1141,3743,3744],{"xmlns":1143},[1145,3745,3746,3750],{},[1148,3747,3748],{},[1154,3749,1749],{},[1172,3751,1749],{"encoding":1174}," se rozdělí na určitý počet ",[1248,3754,3755],{},"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.",[1110,3758,3759],{},"Výsledkem je tabulka četností se sloupci:",[1124,3761,3762,3844,3865,3886],{},[1127,3763,3764,3782,3783,3796,3797,3843],{},[1115,3765,3767],{"className":3766},[1139],[1141,3768,3769],{"xmlns":1143},[1145,3770,3771,3779],{},[1148,3772,3773],{},[1151,3774,3775,3777],{},[1154,3776,1193],{},[1154,3778,1196],{},[1172,3780,3781],{"encoding":1174},"I_j"," — ",[1115,3784,3786],{"className":3785},[1139],[1141,3787,3788],{"xmlns":1143},[1145,3789,3790,3794],{},[1148,3791,3792],{},[1154,3793,1196],{},[1172,3795,1196],{"encoding":1174},"-tý interval (v této kapitole vždy zleva uzavřený a zprava otevřený, ",[1115,3798,3800],{"className":3799},[1139],[1141,3801,3802],{"xmlns":1143},[1145,3803,3804,3840],{},[1148,3805,3806,3812,3814,3817,3823,3825,3838],{},[1151,3807,3808,3810],{},[1154,3809,1193],{},[1154,3811,1196],{},[1161,3813,1483],{},[1161,3815,3816],{"stretchy":1163},"⟨",[1151,3818,3819,3821],{},[1154,3820,1784],{},[1154,3822,1196],{},[1161,3824,3288],{"separator":1121},[1151,3826,3827,3829],{},[1154,3828,1784],{},[1148,3830,3831,3833,3836],{},[1154,3832,1196],{},[1161,3834,3835],{},"+",[1312,3837,1489],{},[1161,3839,1170],{"stretchy":1163},[1172,3841,3842],{"encoding":1174},"I_j = \\langle c_j; c_{j+1})","),",[1127,3845,3846,3864],{},[1115,3847,3849],{"className":3848},[1139],[1141,3850,3851],{"xmlns":1143},[1145,3852,3853,3861],{},[1148,3854,3855],{},[1151,3856,3857,3859],{},[1154,3858,1204],{},[1154,3860,1196],{},[1172,3862,3863],{"encoding":1174},"Z_j"," — střed (reprezentant) intervalu,",[1127,3866,3867,3885],{},[1115,3868,3870],{"className":3869},[1139],[1141,3871,3872],{"xmlns":1143},[1145,3873,3874,3882],{},[1148,3875,3876],{},[1151,3877,3878,3880],{},[1154,3879,1213],{},[1154,3881,1196],{},[1172,3883,3884],{"encoding":1174},"f_j"," — četnost, počet hodnot v intervalu,",[1127,3887,3888,3918,3919,1385,3947,1176],{},[1115,3889,3891],{"className":3890},[1139],[1141,3892,3893],{"xmlns":1143},[1145,3894,3895,3915],{},[1148,3896,3897,3903,3905,3911,3913],{},[1151,3898,3899,3901],{},[1154,3900,1110],{},[1154,3902,1196],{},[1161,3904,1483],{},[1151,3906,3907,3909],{},[1154,3908,1213],{},[1154,3910,1196],{},[1154,3912,3245],{"mathvariant":1869},[1154,3914,1159],{},[1172,3916,3917],{"encoding":1174},"p_j = f_j\u002Fn"," — relativní četnost, přičemž ",[1115,3920,3922],{"className":3921},[1139],[1141,3923,3924],{"xmlns":1143},[1145,3925,3926,3944],{},[1148,3927,3928,3934,3940,3942],{},[1151,3929,3930,3932],{},[1161,3931,1497],{},[1154,3933,1196],{},[1151,3935,3936,3938],{},[1154,3937,1213],{},[1154,3939,1196],{},[1161,3941,1483],{},[1154,3943,1159],{},[1172,3945,3946],{"encoding":1174},"\\sum_j f_j = n",[1115,3948,3950],{"className":3949},[1139],[1141,3951,3952],{"xmlns":1143},[1145,3953,3954,3972],{},[1148,3955,3956,3962,3968,3970],{},[1151,3957,3958,3960],{},[1161,3959,1497],{},[1154,3961,1196],{},[1151,3963,3964,3966],{},[1154,3965,1110],{},[1154,3967,1196],{},[1161,3969,1483],{},[1312,3971,1489],{},[1172,3973,3974],{"encoding":1174},"\\sum_j p_j = 1",[1110,3976,3977,3978,3981,3982,3985,3986,3989,3990,3993,3994,3997,3998,4015,4016,4019,4020,3997,4023,4040,4041,4044],{},"V R se třídění provádí příkazem ",[2015,3979,3980],{},"hist()"," — buď necháme R zvolit třídy samo (",[2015,3983,3984],{},"hist(x)","), nebo zadáme hranice přímo (",[2015,3987,3988],{},"hist(x, br = seq(0, 550, by = 50))","). Uložením výsledku do proměnné (",[2015,3991,3992],{},"y \u003C- hist(...)",") získáme jednotlivé sloupce tabulky: ",[2015,3995,3996],{},"y$counts"," (",[1115,3999,4001],{"className":4000},[1139],[1141,4002,4003],{"xmlns":1143},[1145,4004,4005,4013],{},[1148,4006,4007],{},[1151,4008,4009,4011],{},[1154,4010,1213],{},[1154,4012,1196],{},[1172,4014,3884],{"encoding":1174},"), ",[2015,4017,4018],{},"y$breaks"," (hranice tříd), ",[2015,4021,4022],{},"y$mids",[1115,4024,4026],{"className":4025},[1139],[1141,4027,4028],{"xmlns":1143},[1145,4029,4030,4038],{},[1148,4031,4032],{},[1151,4033,4034,4036],{},[1154,4035,1204],{},[1154,4037,1196],{},[1172,4039,3863],{"encoding":1174},") a ",[2015,4042,4043],{},"y$density"," (relativní četnosti na škále hustoty).",[1110,4046,4047,4048,4065,4066,4068,4069,4106,4107,4110,4111,1176],{},"Interval ",[1115,4049,4051],{"className":4050},[1139],[1141,4052,4053],{"xmlns":1143},[1145,4054,4055,4063],{},[1148,4056,4057],{},[1151,4058,4059,4061],{},[1154,4060,1193],{},[1154,4062,1196],{},[1172,4064,3781],{"encoding":1174}," je ve výchozím nastavení ",[2015,4067,3980],{}," zleva otevřený a zprava uzavřený, ",[1115,4070,4072],{"className":4071},[1139],[1141,4073,4074],{"xmlns":1143},[1145,4075,4076,4103],{},[1148,4077,4078,4080,4086,4088,4100],{},[1161,4079,1164],{"stretchy":1163},[1151,4081,4082,4084],{},[1154,4083,1784],{},[1154,4085,1196],{},[1161,4087,3288],{"separator":1121},[1151,4089,4090,4092],{},[1154,4091,1784],{},[1148,4093,4094,4096,4098],{},[1154,4095,1196],{},[1161,4097,3835],{},[1312,4099,1489],{},[1161,4101,4102],{"stretchy":1163},"⟩",[1172,4104,4105],{"encoding":1174},"(c_j; c_{j+1}\\rangle"," — opačně, než jak třídy zapisujeme v této kapitole. Parametr ",[2015,4108,4109],{},"right = FALSE"," třídy obrátí na ",[1115,4112,4114],{"className":4113},[1139],[1141,4115,4116],{"xmlns":1143},[1145,4117,4118,4144],{},[1148,4119,4120,4122,4128,4130,4142],{},[1161,4121,3816],{"stretchy":1163},[1151,4123,4124,4126],{},[1154,4125,1784],{},[1154,4127,1196],{},[1161,4129,3288],{"separator":1121},[1151,4131,4132,4134],{},[1154,4133,1784],{},[1148,4135,4136,4138,4140],{},[1154,4137,1196],{},[1161,4139,3835],{},[1312,4141,1489],{},[1161,4143,1170],{"stretchy":1163},[1172,4145,4146],{"encoding":1174},"\\langle c_j; c_{j+1})",[1110,4148,4149],{},[1393,4150],{"alt":4151,"className":4152,"src":4153},"mask-ps-histogram-trideni",[1242,1397],"\u002Fwiki-assets\u002Fmask-ps-histogram-trideni.png",[1103,4155,4157,4164],{"className":4156,"dataCallout":2447},[1106,2446],[1110,4158,4160,4163],{"className":4159},[1113],[1115,4161],{"className":4162,"ariaHidden":1121},[1118,2454,1120],"Příklad: Třídění datového souboru",[1110,4165,4166],{},"Byly provedeny zkoušky životnosti nového výrobku. Datový soubor obsahuje 68 hodnot doby do poruchy (v minutách). Určete odhady charakteristik a zákona rozdělení.",[2020,4168,4170],{"className":2022,"code":4169,"language":71,"meta":2024,"style":2024},"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",[2015,4171,4172,4233,4285,4335,4386,4437,4486,4527,4537,4557,4624,4634,4666],{"__ignoreMap":2024},[1115,4173,4174,4177,4179,4181,4183,4186,4188,4191,4193,4196,4198,4201,4203,4206,4208,4211,4213,4216,4218,4221,4223,4226,4228,4231],{"class":2029,"line":10},[1115,4175,4176],{"class":2032},"x9",[1115,4178,2036],{"class":2035},[1115,4180,2040],{"class":2039},[1115,4182,1164],{"class":2043},[1115,4184,4185],{"class":2046},"101",[1115,4187,1199],{"class":2035},[1115,4189,4190],{"class":2046}," 338",[1115,4192,1199],{"class":2035},[1115,4194,4195],{"class":2046}," 150",[1115,4197,1199],{"class":2035},[1115,4199,4200],{"class":2046}," 47",[1115,4202,1199],{"class":2035},[1115,4204,4205],{"class":2046}," 10",[1115,4207,1199],{"class":2035},[1115,4209,4210],{"class":2046}," 2",[1115,4212,1199],{"class":2035},[1115,4214,4215],{"class":2046}," 12",[1115,4217,1199],{"class":2035},[1115,4219,4220],{"class":2046}," 392",[1115,4222,1199],{"class":2035},[1115,4224,4225],{"class":2046}," 5",[1115,4227,1199],{"class":2035},[1115,4229,4230],{"class":2046}," 73",[1115,4232,2688],{"class":2035},[1115,4234,4235,4238,4240,4243,4245,4248,4250,4253,4255,4258,4260,4263,4265,4268,4270,4273,4275,4278,4280,4283],{"class":2029,"line":27},[1115,4236,4237],{"class":2046},"        367",[1115,4239,1199],{"class":2035},[1115,4241,4242],{"class":2046}," 54",[1115,4244,1199],{"class":2035},[1115,4246,4247],{"class":2046}," 114",[1115,4249,1199],{"class":2035},[1115,4251,4252],{"class":2046}," 213",[1115,4254,1199],{"class":2035},[1115,4256,4257],{"class":2046}," 71",[1115,4259,1199],{"class":2035},[1115,4261,4262],{"class":2046}," 341",[1115,4264,1199],{"class":2035},[1115,4266,4267],{"class":2046}," 313",[1115,4269,1199],{"class":2035},[1115,4271,4272],{"class":2046}," 112",[1115,4274,1199],{"class":2035},[1115,4276,4277],{"class":2046}," 343",[1115,4279,1199],{"class":2035},[1115,4281,4282],{"class":2046}," 151",[1115,4284,2688],{"class":2035},[1115,4286,4287,4290,4292,4295,4297,4300,4302,4305,4307,4310,4312,4314,4316,4319,4321,4323,4325,4328,4330,4333],{"class":2029,"line":148},[1115,4288,4289],{"class":2046},"        9",[1115,4291,1199],{"class":2035},[1115,4293,4294],{"class":2046}," 160",[1115,4296,1199],{"class":2035},[1115,4298,4299],{"class":2046}," 18",[1115,4301,1199],{"class":2035},[1115,4303,4304],{"class":2046}," 113",[1115,4306,1199],{"class":2035},[1115,4308,4309],{"class":2046}," 77",[1115,4311,1199],{"class":2035},[1115,4313,4257],{"class":2046},[1115,4315,1199],{"class":2035},[1115,4317,4318],{"class":2046}," 159",[1115,4320,1199],{"class":2035},[1115,4322,4215],{"class":2046},[1115,4324,1199],{"class":2035},[1115,4326,4327],{"class":2046}," 119",[1115,4329,1199],{"class":2035},[1115,4331,4332],{"class":2046}," 130",[1115,4334,2688],{"class":2035},[1115,4336,4337,4340,4342,4345,4347,4350,4352,4354,4356,4359,4361,4364,4366,4369,4371,4374,4376,4379,4381,4384],{"class":2029,"line":111},[1115,4338,4339],{"class":2046},"        140",[1115,4341,1199],{"class":2035},[1115,4343,4344],{"class":2046}," 161",[1115,4346,1199],{"class":2035},[1115,4348,4349],{"class":2046}," 379",[1115,4351,1199],{"class":2035},[1115,4353,4242],{"class":2046},[1115,4355,1199],{"class":2035},[1115,4357,4358],{"class":2046}," 373",[1115,4360,1199],{"class":2035},[1115,4362,4363],{"class":2046}," 168",[1115,4365,1199],{"class":2035},[1115,4367,4368],{"class":2046}," 365",[1115,4370,1199],{"class":2035},[1115,4372,4373],{"class":2046}," 110",[1115,4375,1199],{"class":2035},[1115,4377,4378],{"class":2046}," 145",[1115,4380,1199],{"class":2035},[1115,4382,4383],{"class":2046}," 88",[1115,4385,2688],{"class":2035},[1115,4387,4388,4391,4393,4396,4398,4401,4403,4406,4408,4411,4413,4415,4417,4420,4422,4425,4427,4430,4432,4435],{"class":2029,"line":96},[1115,4389,4390],{"class":2046},"        74",[1115,4392,1199],{"class":2035},[1115,4394,4395],{"class":2046}," 46",[1115,4397,1199],{"class":2035},[1115,4399,4400],{"class":2046}," 246",[1115,4402,1199],{"class":2035},[1115,4404,4405],{"class":2046}," 259",[1115,4407,1199],{"class":2035},[1115,4409,4410],{"class":2046}," 19",[1115,4412,1199],{"class":2035},[1115,4414,4327],{"class":2046},[1115,4416,1199],{"class":2035},[1115,4418,4419],{"class":2046}," 48",[1115,4421,1199],{"class":2035},[1115,4423,4424],{"class":2046}," 3",[1115,4426,1199],{"class":2035},[1115,4428,4429],{"class":2046}," 163",[1115,4431,1199],{"class":2035},[1115,4433,4434],{"class":2046}," 179",[1115,4436,2688],{"class":2035},[1115,4438,4439,4442,4444,4447,4449,4452,4454,4457,4459,4462,4464,4466,4468,4470,4472,4474,4476,4479,4481,4484],{"class":2029,"line":89},[1115,4440,4441],{"class":2046},"        194",[1115,4443,1199],{"class":2035},[1115,4445,4446],{"class":2046}," 33",[1115,4448,1199],{"class":2035},[1115,4450,4451],{"class":2046}," 49",[1115,4453,1199],{"class":2035},[1115,4455,4456],{"class":2046}," 501",[1115,4458,1199],{"class":2035},[1115,4460,4461],{"class":2046}," 193",[1115,4463,1199],{"class":2035},[1115,4465,4410],{"class":2046},[1115,4467,1199],{"class":2035},[1115,4469,4225],{"class":2046},[1115,4471,1199],{"class":2035},[1115,4473,4210],{"class":2046},[1115,4475,1199],{"class":2035},[1115,4477,4478],{"class":2046}," 221",[1115,4480,1199],{"class":2035},[1115,4482,4483],{"class":2046}," 300",[1115,4485,2688],{"class":2035},[1115,4487,4488,4491,4493,4496,4498,4501,4503,4506,4508,4511,4513,4516,4518,4520,4522,4525],{"class":2029,"line":82},[1115,4489,4490],{"class":2046},"        88",[1115,4492,1199],{"class":2035},[1115,4494,4495],{"class":2046}," 13",[1115,4497,1199],{"class":2035},[1115,4499,4500],{"class":2046}," 428",[1115,4502,1199],{"class":2035},[1115,4504,4505],{"class":2046}," 249",[1115,4507,1199],{"class":2035},[1115,4509,4510],{"class":2046}," 25",[1115,4512,1199],{"class":2035},[1115,4514,4515],{"class":2046}," 209",[1115,4517,1199],{"class":2035},[1115,4519,4242],{"class":2046},[1115,4521,1199],{"class":2035},[1115,4523,4524],{"class":2046}," 91",[1115,4526,2185],{"class":2043},[1115,4528,4529,4531,4533,4535],{"class":2029,"line":75},[1115,4530,2190],{"class":2039},[1115,4532,1164],{"class":2043},[1115,4534,4176],{"class":2032},[1115,4536,2185],{"class":2043},[1115,4538,4539,4541,4543,4545,4547,4549,4551,4553,4555],{"class":2029,"line":2322},[1115,4540,1758],{"class":2039},[1115,4542,1164],{"class":2043},[1115,4544,4176],{"class":2032},[1115,4546,2257],{"class":2043},[1115,4548,2260],{"class":2035},[1115,4550,2263],{"class":2039},[1115,4552,1164],{"class":2043},[1115,4554,4176],{"class":2032},[1115,4556,2185],{"class":2043},[1115,4558,4559,4562,4564,4567,4569,4571,4573,4576,4578,4581,4583,4586,4588,4591,4593,4596,4598,4601,4603,4605,4608,4610,4613,4615,4618,4620,4622],{"class":2029,"line":72},[1115,4560,4561],{"class":2032},"y9",[1115,4563,2036],{"class":2035},[1115,4565,4566],{"class":2039}," hist",[1115,4568,1164],{"class":2043},[1115,4570,4176],{"class":2032},[1115,4572,1199],{"class":2035},[1115,4574,4575],{"class":2032}," br",[1115,4577,2291],{"class":2035},[1115,4579,4580],{"class":2039}," seq",[1115,4582,1164],{"class":2043},[1115,4584,4585],{"class":2046},"0",[1115,4587,1199],{"class":2035},[1115,4589,4590],{"class":2046}," 550",[1115,4592,1199],{"class":2035},[1115,4594,4595],{"class":2032}," by",[1115,4597,2291],{"class":2035},[1115,4599,4600],{"class":2046}," 50",[1115,4602,1170],{"class":2043},[1115,4604,1199],{"class":2035},[1115,4606,4607],{"class":2032}," right",[1115,4609,2291],{"class":2035},[1115,4611,4612],{"class":2046}," FALSE",[1115,4614,1199],{"class":2035},[1115,4616,4617],{"class":2032}," plot",[1115,4619,2291],{"class":2035},[1115,4621,4612],{"class":2046},[1115,4623,2185],{"class":2043},[1115,4625,4626,4628,4631],{"class":2029,"line":25},[1115,4627,4561],{"class":2032},[1115,4629,4630],{"class":2035},"$",[1115,4632,4633],{"class":2032},"counts\n",[1115,4635,4636,4639,4641,4643,4645,4648,4651,4654,4656,4658,4660,4662,4664],{"class":2029,"line":65},[1115,4637,4638],{"class":2039},"round",[1115,4640,1164],{"class":2043},[1115,4642,4561],{"class":2032},[1115,4644,4630],{"class":2035},[1115,4646,4647],{"class":2032},"counts",[1115,4649,4650],{"class":2035}," \u002F",[1115,4652,4653],{"class":2039}," length",[1115,4655,1164],{"class":2043},[1115,4657,4176],{"class":2032},[1115,4659,1170],{"class":2043},[1115,4661,1199],{"class":2035},[1115,4663,4424],{"class":2046},[1115,4665,2185],{"class":2043},[1115,4667,4668,4670,4672,4674,4676,4678,4680,4682],{"class":2029,"line":63},[1115,4669,2201],{"class":2039},[1115,4671,1164],{"class":2043},[1115,4673,4176],{"class":2032},[1115,4675,2240],{"class":2043},[1115,4677,2223],{"class":2039},[1115,4679,1164],{"class":2043},[1115,4681,4176],{"class":2032},[1115,4683,2185],{"class":2043},[2020,4685,4688],{"className":4686,"code":4687,"language":2349,"meta":2024},[2347],"[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",[2015,4689,4687],{"__ignoreMap":2024},[1110,4691,4692,4693,4721],{},"Variační rozpětí je ",[1115,4694,4696],{"className":4695},[1139],[1141,4697,4698],{"xmlns":1143},[1145,4699,4700,4718],{},[1148,4701,4702,4704,4706,4709,4711,4713,4715],{},[1154,4703,1749],{},[1161,4705,1483],{},[1312,4707,4708],{},"501",[1161,4710,1623],{},[1312,4712,1610],{},[1161,4714,1483],{},[1312,4716,4717],{},"499",[1172,4719,4720],{"encoding":1174},"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:",[3350,4723,4724,4820],{},[3353,4725,4726],{},[3356,4727,4728,4743,4762,4781,4800],{},[3359,4729,4730],{},[1115,4731,4733],{"className":4732},[1139],[1141,4734,4735],{"xmlns":1143},[1145,4736,4737,4741],{},[1148,4738,4739],{},[1154,4740,1196],{},[1172,4742,1196],{"encoding":1174},[3359,4744,4745],{},[1115,4746,4748],{"className":4747},[1139],[1141,4749,4750],{"xmlns":1143},[1145,4751,4752,4760],{},[1148,4753,4754],{},[1151,4755,4756,4758],{},[1154,4757,1193],{},[1154,4759,1196],{},[1172,4761,3781],{"encoding":1174},[3359,4763,4764],{},[1115,4765,4767],{"className":4766},[1139],[1141,4768,4769],{"xmlns":1143},[1145,4770,4771,4779],{},[1148,4772,4773],{},[1151,4774,4775,4777],{},[1154,4776,1204],{},[1154,4778,1196],{},[1172,4780,3863],{"encoding":1174},[3359,4782,4783],{},[1115,4784,4786],{"className":4785},[1139],[1141,4787,4788],{"xmlns":1143},[1145,4789,4790,4798],{},[1148,4791,4792],{},[1151,4793,4794,4796],{},[1154,4795,1213],{},[1154,4797,1196],{},[1172,4799,3884],{"encoding":1174},[3359,4801,4802],{},[1115,4803,4805],{"className":4804},[1139],[1141,4806,4807],{"xmlns":1143},[1145,4808,4809,4817],{},[1148,4810,4811],{},[1151,4812,4813,4815],{},[1154,4814,1110],{},[1154,4816,1196],{},[1172,4818,4819],{"encoding":1174},"p_j",[3389,4821,4822,4838,4854,4869,4884,4899,4914,4928,4943,4957,4972],{},[3356,4823,4824,4826,4829,4832,4835],{},[3394,4825,1489],{},[3394,4827,4828],{},"⟨0; 50)",[3394,4830,4831],{},"25",[3394,4833,4834],{},"19",[3394,4836,4837],{},"0,279",[3356,4839,4840,4842,4845,4848,4851],{},[3394,4841,1610],{},[3394,4843,4844],{},"⟨50; 100)",[3394,4846,4847],{},"75",[3394,4849,4850],{},"11",[3394,4852,4853],{},"0,162",[3356,4855,4856,4858,4861,4864,4866],{},[3394,4857,3512],{},[3394,4859,4860],{},"⟨100; 150)",[3394,4862,4863],{},"125",[3394,4865,3427],{},[3394,4867,4868],{},"0,147",[3356,4870,4871,4874,4877,4880,4882],{},[3394,4872,4873],{},"4",[3394,4875,4876],{},"⟨150; 200)",[3394,4878,4879],{},"175",[3394,4881,3427],{},[3394,4883,4868],{},[3356,4885,4886,4888,4891,4894,4896],{},[3394,4887,3415],{},[3394,4889,4890],{},"⟨200; 250)",[3394,4892,4893],{},"225",[3394,4895,3415],{},[3394,4897,4898],{},"0,074",[3356,4900,4901,4903,4906,4909,4911],{},[3394,4902,3418],{},[3394,4904,4905],{},"⟨250; 300)",[3394,4907,4908],{},"275",[3394,4910,1489],{},[3394,4912,4913],{},"0,015",[3356,4915,4916,4918,4921,4924,4926],{},[3394,4917,3421],{},[3394,4919,4920],{},"⟨300; 350)",[3394,4922,4923],{},"325",[3394,4925,3415],{},[3394,4927,4898],{},[3356,4929,4930,4933,4936,4939,4941],{},[3394,4931,4932],{},"8",[3394,4934,4935],{},"⟨350; 400)",[3394,4937,4938],{},"375",[3394,4940,3415],{},[3394,4942,4898],{},[3356,4944,4945,4947,4950,4953,4955],{},[3394,4946,3424],{},[3394,4948,4949],{},"⟨400; 450)",[3394,4951,4952],{},"425",[3394,4954,1489],{},[3394,4956,4913],{},[3356,4958,4959,4961,4964,4967,4969],{},[3394,4960,3427],{},[3394,4962,4963],{},"⟨450; 500)",[3394,4965,4966],{},"475",[3394,4968,4585],{},[3394,4970,4971],{},"0,000",[3356,4973,4974,4976,4979,4982,4984],{},[3394,4975,4850],{},[3394,4977,4978],{},"⟨500; ∞)",[3394,4980,4981],{},"525",[3394,4983,1489],{},[3394,4985,4913],{},[1110,4987,4988,4989,5006,5007,5024,5025,1381,5049,1381,5077,5096,5097,1381,5120,5139],{},"Asi 27,9 % výrobků vydrželo méně než 50 minut, jen asi 1,5 % mezi 250 a 300 minutami. Charakteristiky spočtené ze středů tříd ",[1115,4990,4992],{"className":4991},[1139],[1141,4993,4994],{"xmlns":1143},[1145,4995,4996,5004],{},[1148,4997,4998],{},[1151,4999,5000,5002],{},[1154,5001,1204],{},[1154,5003,1196],{},[1172,5005,3863],{"encoding":1174}," (vážený průměr a rozptyl se střední hodnotou nahrazenou ",[1115,5008,5010],{"className":5009},[1139],[1141,5011,5012],{"xmlns":1143},[1145,5013,5014,5022],{},[1148,5015,5016],{},[1151,5017,5018,5020],{},[1154,5019,1204],{},[1154,5021,1196],{},[1172,5023,3863],{"encoding":1174},") vycházejí ",[1115,5026,5028],{"className":5027},[1139],[1141,5029,5030],{"xmlns":1143},[1145,5031,5032,5046],{},[1148,5033,5034,5040,5043],{},[1474,5035,5036,5038],{"accent":1121},[1154,5037,1167],{},[1161,5039,1480],{},[1161,5041,5042],{},"≈",[1312,5044,5045],{},"149,26",[1172,5047,5048],{"encoding":1174},"\\bar{x} \\approx 149{,}26",[1115,5050,5052],{"className":5051},[1139],[1141,5053,5054],{"xmlns":1143},[1145,5055,5056,5074],{},[1148,5057,5058,5064,5066,5069,5071],{},[1603,5059,5060,5062],{},[1154,5061,1607],{},[1312,5063,1610],{},[1161,5065,5042],{},[1312,5067,5068],{},"15",[1316,5070,1318],{},[1312,5072,5073],{},"484,5",[1172,5075,5076],{"encoding":1174},"s^2 \\approx 15\\,484{,}5",[1115,5078,5080],{"className":5079},[1139],[1141,5081,5082],{"xmlns":1143},[1145,5083,5084,5093],{},[1148,5085,5086,5088,5090],{},[1154,5087,1607],{},[1161,5089,5042],{},[1312,5091,5092],{},"124,44",[1172,5094,5095],{"encoding":1174},"s \\approx 124{,}44"," — blízko hodnotám ",[1115,5098,5100],{"className":5099},[1139],[1141,5101,5102],{"xmlns":1143},[1145,5103,5104,5117],{},[1148,5105,5106,5112,5114],{},[1474,5107,5108,5110],{"accent":1121},[1154,5109,1167],{},[1161,5111,1480],{},[1161,5113,1483],{},[1312,5115,5116],{},"145,44",[1172,5118,5119],{"encoding":1174},"\\bar{x}=145{,}44",[1115,5121,5123],{"className":5122},[1139],[1141,5124,5125],{"xmlns":1143},[1145,5126,5127,5136],{},[1148,5128,5129,5131,5133],{},[1154,5130,1607],{},[1161,5132,1483],{},[1312,5134,5135],{},"126,13",[1172,5137,5138],{"encoding":1174},"s=126{,}13"," spočteným přímo z nerozdělených dat; malý rozdíl vzniká tím, že třídění nahrazuje skutečné hodnoty středy tříd.",[1110,5141,5142,5143,5146,5147,5184,5185,5204,5205,5219,5220,5246,5247,5250,5251,5254],{},"Tvar histogramu — vysoká četnost u krátkých dob, rychlý pokles — odpovídá ",[1248,5144,5145],{},"exponenciálnímu rozdělení",", které se pro dobu do poruchy používá nejčastěji. Jeho hustota je ",[1115,5148,5150],{"className":5149},[1139],[1141,5151,5152],{"xmlns":1143},[1145,5153,5154,5181],{},[1148,5155,5156,5158,5160,5162,5164,5166,5169],{},[1154,5157,1213],{},[1161,5159,1164],{"stretchy":1163},[1154,5161,1167],{},[1161,5163,1170],{"stretchy":1163},[1161,5165,1483],{},[1154,5167,5168],{},"λ",[1603,5170,5171,5173],{},[1154,5172,1539],{},[1148,5174,5175,5177,5179],{},[1161,5176,1623],{},[1154,5178,5168],{},[1154,5180,1167],{},[1172,5182,5183],{"encoding":1174},"f(x) = \\lambda e^{-\\lambda x}"," pro ",[1115,5186,5188],{"className":5187},[1139],[1141,5189,5190],{"xmlns":1143},[1145,5191,5192,5201],{},[1148,5193,5194,5196,5199],{},[1154,5195,1167],{},[1161,5197,5198],{},"≥",[1312,5200,4585],{},[1172,5202,5203],{"encoding":1174},"x \\ge 0",", s parametrem ",[1115,5206,5208],{"className":5207},[1139],[1141,5209,5210],{"xmlns":1143},[1145,5211,5212,5216],{},[1148,5213,5214],{},[1154,5215,5168],{},[1172,5217,5218],{"encoding":1174},"\\lambda"," odhadnutým jako ",[1115,5221,5223],{"className":5222},[1139],[1141,5224,5225],{"xmlns":1143},[1145,5226,5227,5243],{},[1148,5228,5229,5231,5233,5235,5237],{},[1154,5230,5168],{},[1161,5232,1483],{},[1312,5234,1489],{},[1154,5236,3245],{"mathvariant":1869},[1474,5238,5239,5241],{"accent":1121},[1154,5240,1167],{},[1161,5242,1480],{},[1172,5244,5245],{"encoding":1174},"\\lambda = 1\u002F\\bar{x}"," (v R je ",[2015,5248,5249],{},"rate"," parametrem ",[2015,5252,5253],{},"dexp()","):",[2020,5256,5258],{"className":2022,"code":5257,"language":71,"meta":2024,"style":2024},"rate9 \u003C- 1 \u002F mean(x9)\nrate9\n",[2015,5259,5260,5281],{"__ignoreMap":2024},[1115,5261,5262,5265,5267,5270,5272,5275,5277,5279],{"class":2029,"line":10},[1115,5263,5264],{"class":2032},"rate9",[1115,5266,2036],{"class":2035},[1115,5268,5269],{"class":2046}," 1",[1115,5271,4650],{"class":2035},[1115,5273,5274],{"class":2039}," mean",[1115,5276,1164],{"class":2043},[1115,5278,4176],{"class":2032},[1115,5280,2185],{"class":2043},[1115,5282,5283],{"class":2029,"line":27},[1115,5284,5285],{"class":2032},"rate9\n",[2020,5287,5290],{"className":5288,"code":5289,"language":2349,"meta":2024},[2347],"[1] 0.006875632\n",[2015,5291,5289],{"__ignoreMap":2024},[1110,5293,5294],{},[1393,5295],{"alt":5296,"className":5297,"src":5298},"mask-ps-hustota-fit",[1242,1397],"\u002Fwiki-assets\u002Fmask-ps-hustota-fit.png",[1110,5300,5301,5302,1176],{},"Proložená křivka dobře sleduje tvar sloupců. Zda data odpovídají exponenciálnímu rozdělení formálně, posuzuje test dobré shody popsaný v ",[1239,5303,5307],{"className":5304,"dataFsResolvedFilePath":5305,"href":5306},[1242],"topics\u002Ftestovani-hypotez.md","\u002Fwiki\u002Ftestovani-hypotez","Testování statistických hypotéz",[1103,5309,5311,5318],{"className":5310,"dataCallout":2447},[1106,2446],[1110,5312,5314,5317],{"className":5313},[1113],[1115,5315],{"className":5316,"ariaHidden":1121},[1118,2454,1120],"Příklad: Doba života výrobku",[1110,5319,5320],{},"Sledováním doby života výrobku bylo naměřeno 50 hodnot (v minutách). Určete empirické charakteristiky, roztřiďte datový soubor a nakreslete histogram četností.",[2020,5322,5324],{"className":2022,"code":5323,"language":71,"meta":2024,"style":2024},"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",[2015,5325,5326,5387,5438,5489,5540,5592,5602,5628,5648,5706,5715,5723],{"__ignoreMap":2024},[1115,5327,5328,5331,5333,5335,5337,5340,5342,5345,5347,5350,5352,5355,5357,5360,5362,5365,5367,5370,5372,5375,5377,5380,5382,5385],{"class":2029,"line":10},[1115,5329,5330],{"class":2032},"x5",[1115,5332,2036],{"class":2035},[1115,5334,2040],{"class":2039},[1115,5336,1164],{"class":2043},[1115,5338,5339],{"class":2046},"63",[1115,5341,1199],{"class":2035},[1115,5343,5344],{"class":2046}," 156",[1115,5346,1199],{"class":2035},[1115,5348,5349],{"class":2046}," 184",[1115,5351,1199],{"class":2035},[1115,5353,5354],{"class":2046}," 786",[1115,5356,1199],{"class":2035},[1115,5358,5359],{"class":2046}," 822",[1115,5361,1199],{"class":2035},[1115,5363,5364],{"class":2046}," 278",[1115,5366,1199],{"class":2035},[1115,5368,5369],{"class":2046}," 15",[1115,5371,1199],{"class":2035},[1115,5373,5374],{"class":2046}," 561",[1115,5376,1199],{"class":2035},[1115,5378,5379],{"class":2046}," 229",[1115,5381,1199],{"class":2035},[1115,5383,5384],{"class":2046}," 8",[1115,5386,2688],{"class":2035},[1115,5388,5389,5392,5394,5397,5399,5401,5403,5406,5408,5411,5413,5416,5418,5421,5423,5426,5428,5431,5433,5436],{"class":2029,"line":27},[1115,5390,5391],{"class":2046},"        4",[1115,5393,1199],{"class":2035},[1115,5395,5396],{"class":2046}," 35",[1115,5398,1199],{"class":2035},[1115,5400,4230],{"class":2046},[1115,5402,1199],{"class":2035},[1115,5404,5405],{"class":2046}," 203",[1115,5407,1199],{"class":2035},[1115,5409,5410],{"class":2046}," 178",[1115,5412,1199],{"class":2035},[1115,5414,5415],{"class":2046}," 323",[1115,5417,1199],{"class":2035},[1115,5419,5420],{"class":2046}," 275",[1115,5422,1199],{"class":2035},[1115,5424,5425],{"class":2046}," 176",[1115,5427,1199],{"class":2035},[1115,5429,5430],{"class":2046}," 427",[1115,5432,1199],{"class":2035},[1115,5434,5435],{"class":2046}," 196",[1115,5437,2688],{"class":2035},[1115,5439,5440,5443,5445,5448,5450,5453,5455,5458,5460,5463,5465,5468,5470,5473,5475,5477,5479,5482,5484,5487],{"class":2029,"line":148},[1115,5441,5442],{"class":2046},"        415",[1115,5444,1199],{"class":2035},[1115,5446,5447],{"class":2046}," 140",[1115,5449,1199],{"class":2035},[1115,5451,5452],{"class":2046}," 17",[1115,5454,1199],{"class":2035},[1115,5456,5457],{"class":2046}," 293",[1115,5459,1199],{"class":2035},[1115,5461,5462],{"class":2046}," 991",[1115,5464,1199],{"class":2035},[1115,5466,5467],{"class":2046}," 100",[1115,5469,1199],{"class":2035},[1115,5471,5472],{"class":2046}," 189",[1115,5474,1199],{"class":2035},[1115,5476,5425],{"class":2046},[1115,5478,1199],{"class":2035},[1115,5480,5481],{"class":2046}," 672",[1115,5483,1199],{"class":2035},[1115,5485,5486],{"class":2046}," 134",[1115,5488,2688],{"class":2035},[1115,5490,5491,5494,5496,5499,5501,5504,5506,5509,5511,5513,5515,5518,5520,5523,5525,5528,5530,5533,5535,5538],{"class":2029,"line":111},[1115,5492,5493],{"class":2046},"        529",[1115,5495,1199],{"class":2035},[1115,5497,5498],{"class":2046}," 310",[1115,5500,1199],{"class":2035},[1115,5502,5503],{"class":2046}," 22",[1115,5505,1199],{"class":2035},[1115,5507,5508],{"class":2046}," 69",[1115,5510,1199],{"class":2035},[1115,5512,4332],{"class":2046},[1115,5514,1199],{"class":2035},[1115,5516,5517],{"class":2046}," 272",[1115,5519,1199],{"class":2035},[1115,5521,5522],{"class":2046}," 117",[1115,5524,1199],{"class":2035},[1115,5526,5527],{"class":2046}," 169",[1115,5529,1199],{"class":2035},[1115,5531,5532],{"class":2046}," 466",[1115,5534,1199],{"class":2035},[1115,5536,5537],{"class":2046}," 286",[1115,5539,2688],{"class":2035},[1115,5541,5542,5545,5547,5550,5552,5555,5557,5560,5562,5565,5567,5570,5572,5575,5577,5580,5582,5585,5587,5590],{"class":2029,"line":96},[1115,5543,5544],{"class":2046},"        46",[1115,5546,1199],{"class":2035},[1115,5548,5549],{"class":2046}," 236",[1115,5551,1199],{"class":2035},[1115,5553,5554],{"class":2046}," 387",[1115,5556,1199],{"class":2035},[1115,5558,5559],{"class":2046}," 92",[1115,5561,1199],{"class":2035},[1115,5563,5564],{"class":2046}," 177",[1115,5566,1199],{"class":2035},[1115,5568,5569],{"class":2046}," 188",[1115,5571,1199],{"class":2035},[1115,5573,5574],{"class":2046}," 124",[1115,5576,1199],{"class":2035},[1115,5578,5579],{"class":2046}," 385",[1115,5581,1199],{"class":2035},[1115,5583,5584],{"class":2046}," 174",[1115,5586,1199],{"class":2035},[1115,5588,5589],{"class":2046}," 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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",[2015,5756,5754],{"__ignoreMap":2024},[1110,5758,5759],{},"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.",[1232,5761,5763],{"id":5762},"časté-chyby","Časté chyby",[1124,5765,5766,5784,5885,5954],{},[1127,5767,5768,1932,5771,5774,5775,5778,5779,5781,5782,1176],{},[1248,5769,5770],{},"Výchozí typ kvantilu v R.",[2015,5772,5773],{},"quantile()"," bez argumentu ",[2015,5776,5777],{},"type"," používá jiný výpočetní vzorec (",[2015,5780,2360],{},") než ruční postup v této kapitole — u některých souborů se hodnoty liší. Pro shodu s ručním výpočtem zadávejte ",[2015,5783,2356],{},[1127,5785,5786,5791,5792,5794,5795,5830,5831,5866,5867,5884],{},[1248,5787,5788,5789,1176],{},"Výchozí ohraničení tříd v ",[2015,5790,3980],{}," Bez ",[2015,5793,4109],{}," jsou třídy zprava uzavřené, ",[1115,5796,5798],{"className":5797},[1139],[1141,5799,5800],{"xmlns":1143},[1145,5801,5802,5828],{},[1148,5803,5804,5806,5812,5814,5826],{},[1161,5805,1164],{"stretchy":1163},[1151,5807,5808,5810],{},[1154,5809,1784],{},[1154,5811,1196],{},[1161,5813,3288],{"separator":1121},[1151,5815,5816,5818],{},[1154,5817,1784],{},[1148,5819,5820,5822,5824],{},[1154,5821,1196],{},[1161,5823,3835],{},[1312,5825,1489],{},[1161,5827,4102],{"stretchy":1163},[1172,5829,4105],{"encoding":1174}," — opačně než konvence ",[1115,5832,5834],{"className":5833},[1139],[1141,5835,5836],{"xmlns":1143},[1145,5837,5838,5864],{},[1148,5839,5840,5842,5848,5850,5862],{},[1161,5841,3816],{"stretchy":1163},[1151,5843,5844,5846],{},[1154,5845,1784],{},[1154,5847,1196],{},[1161,5849,3288],{"separator":1121},[1151,5851,5852,5854],{},[1154,5853,1784],{},[1148,5855,5856,5858,5860],{},[1154,5857,1196],{},[1161,5859,3835],{},[1312,5861,1489],{},[1161,5863,1170],{"stretchy":1163},[1172,5865,4146],{"encoding":1174}," použitá v tabulkách výše. Hodnota ležící přesně na hranici pak spadne do jiné třídy a četnosti ",[1115,5868,5870],{"className":5869},[1139],[1141,5871,5872],{"xmlns":1143},[1145,5873,5874,5882],{},[1148,5875,5876],{},[1151,5877,5878,5880],{},[1154,5879,1213],{},[1154,5881,1196],{},[1172,5883,3884],{"encoding":1174}," vyjdou jinak.",[1127,5886,5887,1932,5890,5908,5909,5922,5923,5936,5937,1176],{},[1248,5888,5889],{},"Rozptyl vs. směrodatná odchylka.",[1115,5891,5893],{"className":5892},[1139],[1141,5894,5895],{"xmlns":1143},[1145,5896,5897,5905],{},[1148,5898,5899],{},[1603,5900,5901,5903],{},[1154,5902,1607],{},[1312,5904,1610],{},[1172,5906,5907],{"encoding":1174},"s^2"," se udává v jednotkách znaku na druhou, ",[1115,5910,5912],{"className":5911},[1139],[1141,5913,5914],{"xmlns":1143},[1145,5915,5916,5920],{},[1148,5917,5918],{},[1154,5919,1607],{},[1172,5921,1607],{"encoding":1174}," ve stejných jednotkách jako data — pro interpretaci (např. „kolísání kolem průměru\") patří vždy ",[1115,5924,5926],{"className":5925},[1139],[1141,5927,5928],{"xmlns":1143},[1145,5929,5930,5934],{},[1148,5931,5932],{},[1154,5933,1607],{},[1172,5935,1607],{"encoding":1174},", ne ",[1115,5938,5940],{"className":5939},[1139],[1141,5941,5942],{"xmlns":1143},[1145,5943,5944,5952],{},[1148,5945,5946],{},[1603,5947,5948,5950],{},[1154,5949,1607],{},[1312,5951,1610],{},[1172,5953,5907],{"encoding":1174},[1127,5955,5956,5959],{},[1248,5957,5958],{},"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.",[1232,5961,5963],{"id":5962},"související-stránky","Související stránky",[1124,5965,5966,5971,5979,5984,5992,6000,6008],{},[1127,5967,5968],{},[1239,5969,1245],{"className":5970,"dataFsResolvedFilePath":1243,"href":1244},[1242],[1127,5972,5973],{},[1239,5974,5978],{"className":5975,"dataFsResolvedFilePath":5976,"href":5977},[1242],"topics\u002Fnahodne-veliciny-a-rozdeleni.md","\u002Fwiki\u002Fnahodne-veliciny-a-rozdeleni","Náhodné veličiny a rozdělení pravděpodobnosti",[1127,5980,5981],{},[1239,5982,5307],{"className":5983,"dataFsResolvedFilePath":5305,"href":5306},[1242],[1127,5985,5986],{},[1239,5987,5991],{"className":5988,"dataFsResolvedFilePath":5989,"href":5990},[1242],"topics\u002Fregresni-a-korelacni-analyza.md","\u002Fwiki\u002Fregresni-a-korelacni-analyza","Regresní a korelační analýza",[1127,5993,5994],{},[1239,5995,5999],{"className":5996,"dataFsResolvedFilePath":5997,"href":5998},[1242],"topics\u002Fkontingencni-tabulky.md","\u002Fwiki\u002Fkontingencni-tabulky","Kontingenční tabulky",[1127,6001,6002],{},[1239,6003,6007],{"className":6004,"dataFsResolvedFilePath":6005,"href":6006},[1242],"topics\u002Fregulacni-diagramy-a-indexy-zpusobilosti.md","\u002Fwiki\u002Fregulacni-diagramy-a-indexy-zpusobilosti","Regulační diagramy a indexy způsobilosti",[1127,6009,6010],{},[1239,6011,6015],{"className":6012,"dataFsResolvedFilePath":6013,"href":6014},[1242],"outputs\u002Fmask-r-tahak.md","\u002Fwiki\u002Fmask-r-tahak","Tahák pro R",[1232,6017,6018],{"id":934},"Reference",[1110,6020,6021,6022,6026],{},"KROPÁČ, J. ",[6023,6024,6025],"em",{},"Statistika A",". 4. vyd. Brno: Fakulta podnikatelská VUT, 2011.",[6028,6029,6030],"style",{},"html pre.shiki code .sP4rz, html code.shiki .sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sCsY4, html code.shiki .sCsY4{--shiki-light:#6A737D;--shiki-default:#6A737D;--shiki-dark:#6A737D}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":2024,"searchDepth":27,"depth":27,"links":6032},[6033,6034,6035,6036,6037,6038,6039],{"id":1234,"depth":27,"text":1235},{"id":1412,"depth":27,"text":1413},{"id":2955,"depth":27,"text":2956},{"id":3730,"depth":27,"text":3731},{"id":5762,"depth":27,"text":5763},{"id":5962,"depth":27,"text":5963},{"id":934,"depth":27,"text":6018},null,"2026-10-02","md",{},true,"\u002Ftopics\u002Fpopisna-statistika",{"title":1094,"description":2024},[6048,6049,6050,6051,6052,6053,6054],"raw\u002Fmask\u002F02 datové soubory.pdf","raw\u002Fmask\u002F02 datové soubory - návod R.pdf","raw\u002Fmask\u002Fpříklady 01 a 02.docx","raw\u002Fmask\u002Fdata k příkladům\u002F4.txt","raw\u002Fmask\u002Fdata k příkladům\u002F5.txt","raw\u002Fmask\u002Fdata k příkladům\u002F6.txt","raw\u002Fmask\u002Fdata k příkladům\u002F9.txt","topics\u002Fpopisna-statistika",[23,67,886,624,732,71],"topic","S7Mr0W_asypsa_HGrO-Qlzv4HzQm_pC2nyjSomTKbnk","topics",[6061,11116,15544,19751,24454,29909],{"id":6062,"title":5999,"body":6063,"course":23,"courses":6040,"created":6041,"description":2024,"extension":6042,"meta":11107,"navigation":6044,"path":11108,"seo":11109,"sources":11110,"stem":11113,"tags":11114,"type":6057,"updated":6041,"__hash__":11115},"topics\u002Ftopics\u002Fkontingencni-tabulky.md",{"type":1096,"value":6064,"toc":11097},[6065,6068,6243,6247,6262,6279,6482,6617,7210,7227,7338,7342,7373,7378,7975,7981,8191,8397,8403,8483,8594,8745,8751,8832,8853,8860,8894,8901,8904,8910,8972,9030,9178,9184,9191,9269,9272,9327,9665,9686,9790,9899,9902,9923,9926,10180,10261,10268,10272,10502,10516,10665,10797,10803,10861,10863,10882,10897,10903,10948,10967,10982,10988,11047,11049,11088,11090,11094],[1099,6066,5999],{"id":6067},"kontingenční-tabulky",[1103,6069,6071,6077],{"className":6070,"dataCallout":1108},[1106,1107],[1110,6072,6074,1122],{"className":6073},[1113],[1115,6075],{"className":6076,"ariaHidden":1121},[1118,1119,1120],[1124,6078,6079,6086,6147,6168,6206,6232],{},[1127,6080,6081,6082,6085],{},"Kontingenční tabulka zaznamenává ",[1248,6083,6084],{},"simultánní četnosti"," dvou kvalitativních znaků naměřených na stejném souboru.",[1127,6087,6088,6091,6092,6111,6112,6131,6132,6146],{},[1248,6089,6090],{},"Test nezávislosti"," srovnává pozorované četnosti s očekávanými za platnosti ",[1115,6093,6095],{"className":6094},[1139],[1141,6096,6097],{"xmlns":1143},[1145,6098,6099,6108],{},[1148,6100,6101],{},[1151,6102,6103,6106],{},[1154,6104,6105],{},"H",[1312,6107,4585],{},[1172,6109,6110],{"encoding":1174},"H_0"," pomocí statistiky ",[1115,6113,6115],{"className":6114},[1139],[1141,6116,6117],{"xmlns":1143},[1145,6118,6119,6128],{},[1148,6120,6121],{},[1603,6122,6123,6126],{},[1154,6124,6125],{},"χ",[1312,6127,1610],{},[1172,6129,6130],{"encoding":1174},"\\chi^2","; rozhoduje kritický obor ",[1115,6133,6135],{"className":6134},[1139],[1141,6136,6137],{"xmlns":1143},[1145,6138,6139,6144],{},[1148,6140,6141],{},[1154,6142,6143],{},"W",[1172,6145,6143],{"encoding":1174},", prakticky p-hodnota.",[1127,6148,6149,6150,6167],{},"Aproximace ",[1115,6151,6153],{"className":6152},[1139],[1141,6154,6155],{"xmlns":1143},[1145,6156,6157,6165],{},[1148,6158,6159],{},[1603,6160,6161,6163],{},[1154,6162,6125],{},[1312,6164,1610],{},[1172,6166,6130],{"encoding":1174}," rozdělením platí jen tehdy, když jsou očekávané četnosti dostatečně velké — proto se vždy kontrolují.",[1127,6169,6170,6171,6188,6189,1932,6192,1176],{},"Zamítnutí ",[1115,6172,6174],{"className":6173},[1139],[1141,6175,6176],{"xmlns":1143},[1145,6177,6178,6186],{},[1148,6179,6180],{},[1151,6181,6182,6184],{},[1154,6183,6105],{},[1312,6185,4585],{},[1172,6187,6110],{"encoding":1174}," samo o sobě neříká, jak silná závislost je — na to slouží ",[1248,6190,6191],{},"Cramérův koeficient kontingence",[1115,6193,6195],{"className":6194},[1139],[1141,6196,6197],{"xmlns":1143},[1145,6198,6199,6204],{},[1148,6200,6201],{},[1154,6202,6203],{},"V",[1172,6205,6203],{"encoding":1174},[1127,6207,6208,6211,6212,1176],{},[1248,6209,6210],{},"Čtyřpolní tabulka"," (2×2) je speciální případ s vlastním zjednodušeným vzorcem pro ",[1115,6213,6215],{"className":6214},[1139],[1141,6216,6217],{"xmlns":1143},[1145,6218,6219,6229],{},[1148,6220,6221,6223,6226],{},[1154,6222,1159],{},[1161,6224,6225],{},">",[1312,6227,6228],{},"40",[1172,6230,6231],{"encoding":1174},"n>40",[1127,6233,6234,6235,6238,6239,6242],{},"Pro ",[1248,6236,6237],{},"párová data"," (stejné prvky měřené dvakrát, např. před\u002Fpo zásahu) se používá ",[1248,6240,6241],{},"McNemarův test",", ne obyčejný test nezávislosti.",[1232,6244,6246],{"id":6245},"kontingenční-tabulka","Kontingenční tabulka",[1110,6248,6249,6250,6253,6254,6258,6259,6261],{},"V rámci ",[1239,6251,1245],{"className":6252,"dataFsResolvedFilePath":1243,"href":1244},[1242]," navazují kontingenční tabulky na\n",[1239,6255,6257],{"className":6256,"dataFsResolvedFilePath":5305,"href":5306},[1242],"testování statistických hypotéz",": místo jedné náhodné veličiny teď sledujeme dva\n",[1248,6260,1286],{}," (kategoriální) znaky současně a ptáme se, zda spolu souvisí.",[1110,6263,6264,6265,6267,6268,6270,6271,6274,6275,6278],{},"Znak je ",[1248,6266,1272],{},", pokud nabývá číselných hodnot (stáří, stav tachometru), a ",[1248,6269,1286],{},"\n(kategoriální), pokud nabývá slovních variant (vzdělání, kuřák\u002Fnekuřák). Kvalitativní znaky dále dělíme na\n",[1248,6272,6273],{},"alternativní"," (dvě varianty, např. vada ano\u002Fne) a ",[1248,6276,6277],{},"množné"," (více než dvě varianty, např. svobodný\u002Frozvedený\u002Fženatý).",[1110,6280,6281,6282,6295,6296,6310,6311,4040,6341,6355,6356,6386,6387,6390,6391,6413,6414,1932,6417,6439,6440,6458,6459,6477,6478,6481],{},"Mějme ",[1115,6283,6285],{"className":6284},[1139],[1141,6286,6287],{"xmlns":1143},[1145,6288,6289,6293],{},[1148,6290,6291],{},[1154,6292,1159],{},[1172,6294,1159],{"encoding":1174}," opakování pokusu, při nichž sledujeme dva kvalitativní znaky ",[1115,6297,6299],{"className":6298},[1139],[1141,6300,6301],{"xmlns":1143},[1145,6302,6303,6308],{},[1148,6304,6305],{},[1154,6306,6307],{},"A",[1172,6309,6307],{"encoding":1174}," (varianty ",[1115,6312,6314],{"className":6313},[1139],[1141,6315,6316],{"xmlns":1143},[1145,6317,6318,6338],{},[1148,6319,6320,6326,6328,6330,6332],{},[1151,6321,6322,6324],{},[1154,6323,6307],{},[1312,6325,1489],{},[1161,6327,1199],{"separator":1121},[1161,6329,3022],{},[1161,6331,1199],{"separator":1121},[1151,6333,6334,6336],{},[1154,6335,6307],{},[1154,6337,71],{},[1172,6339,6340],{"encoding":1174},"A_1,\\dots,A_r",[1115,6342,6344],{"className":6343},[1139],[1141,6345,6346],{"xmlns":1143},[1145,6347,6348,6353],{},[1148,6349,6350],{},[1154,6351,6352],{},"B",[1172,6354,6352],{"encoding":1174},"\n(varianty ",[1115,6357,6359],{"className":6358},[1139],[1141,6360,6361],{"xmlns":1143},[1145,6362,6363,6383],{},[1148,6364,6365,6371,6373,6375,6377],{},[1151,6366,6367,6369],{},[1154,6368,6352],{},[1312,6370,1489],{},[1161,6372,1199],{"separator":1121},[1161,6374,3022],{},[1161,6376,1199],{"separator":1121},[1151,6378,6379,6381],{},[1154,6380,6352],{},[1154,6382,1607],{},[1172,6384,6385],{"encoding":1174},"B_1,\\dots,B_s","). Výsledky zapíšeme do ",[1248,6388,6389],{},"kontingenční tabulky",": v políčku ",[1115,6392,6394],{"className":6393},[1139],[1141,6395,6396],{"xmlns":1143},[1145,6397,6398,6410],{},[1148,6399,6400,6402,6404,6406,6408],{},[1161,6401,1164],{"stretchy":1163},[1154,6403,1502],{},[1161,6405,1199],{"separator":1121},[1154,6407,1196],{},[1161,6409,1170],{"stretchy":1163},[1172,6411,6412],{"encoding":1174},"(i,j)"," je ",[1248,6415,6416],{},"simultánní\nčetnost",[1115,6418,6420],{"className":6419},[1139],[1141,6421,6422],{"xmlns":1143},[1145,6423,6424,6436],{},[1148,6425,6426],{},[1151,6427,6428,6430],{},[1154,6429,1159],{},[1148,6431,6432,6434],{},[1154,6433,1502],{},[1154,6435,1196],{},[1172,6437,6438],{"encoding":1174},"n_{ij}",", tedy počet pokusů s variantou ",[1115,6441,6443],{"className":6442},[1139],[1141,6444,6445],{"xmlns":1143},[1145,6446,6447,6455],{},[1148,6448,6449],{},[1151,6450,6451,6453],{},[1154,6452,6307],{},[1154,6454,1502],{},[1172,6456,6457],{"encoding":1174},"A_i"," zároveň s variantou ",[1115,6460,6462],{"className":6461},[1139],[1141,6463,6464],{"xmlns":1143},[1145,6465,6466,6474],{},[1148,6467,6468],{},[1151,6469,6470,6472],{},[1154,6471,6352],{},[1154,6473,1196],{},[1172,6475,6476],{"encoding":1174},"B_j",". Řádkové a sloupcové součty\njsou ",[1248,6479,6480],{},"marginální četnosti",":",[1115,6483,6485],{"className":6484},[1139],[1141,6486,6487],{"xmlns":1143,"display":1468},[1145,6488,6489,6614],{},[1148,6490,6491,6502,6504,6518,6528,6530,6532,6542,6544,6558,6568,6570,6572,6574,6576,6590,6604],{},[1151,6492,6493,6495],{},[1154,6494,1159],{},[1148,6496,6497,6499],{},[1154,6498,1502],{},[1161,6500,6501],{},"∙",[1161,6503,1483],{},[1493,6505,6506,6508,6516],{},[1161,6507,1497],{},[1148,6509,6510,6512,6514],{},[1154,6511,1196],{},[1161,6513,1483],{},[1312,6515,1489],{},[1154,6517,1607],{},[1151,6519,6520,6522],{},[1154,6521,1159],{},[1148,6523,6524,6526],{},[1154,6525,1502],{},[1154,6527,1196],{},[1161,6529,1199],{"separator":1121},[1516,6531],{"width":1518},[1151,6533,6534,6536],{},[1154,6535,1159],{},[1148,6537,6538,6540],{},[1161,6539,6501],{},[1154,6541,1196],{},[1161,6543,1483],{},[1493,6545,6546,6548,6556],{},[1161,6547,1497],{},[1148,6549,6550,6552,6554],{},[1154,6551,1502],{},[1161,6553,1483],{},[1312,6555,1489],{},[1154,6557,71],{},[1151,6559,6560,6562],{},[1154,6561,1159],{},[1148,6563,6564,6566],{},[1154,6565,1502],{},[1154,6567,1196],{},[1161,6569,1199],{"separator":1121},[1516,6571],{"width":1518},[1154,6573,1159],{},[1161,6575,1483],{},[1493,6577,6578,6580,6588],{},[1161,6579,1497],{},[1148,6581,6582,6584,6586],{},[1154,6583,1502],{},[1161,6585,1483],{},[1312,6587,1489],{},[1154,6589,71],{},[1493,6591,6592,6594,6602],{},[1161,6593,1497],{},[1148,6595,6596,6598,6600],{},[1154,6597,1196],{},[1161,6599,1483],{},[1312,6601,1489],{},[1154,6603,1607],{},[1151,6605,6606,6608],{},[1154,6607,1159],{},[1148,6609,6610,6612],{},[1154,6611,1502],{},[1154,6613,1196],{},[1172,6615,6616],{"encoding":1174},"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}",[3350,6618,6619,6730],{},[3353,6620,6621],{},[3356,6622,6623,6644,6664,6684,6686,6706],{},[3359,6624,6625],{},[1115,6626,6628],{"className":6627},[1139],[1141,6629,6630],{"xmlns":1143},[1145,6631,6632,6641],{},[1148,6633,6634,6636,6639],{},[1154,6635,6307],{},[1154,6637,6638],{"mathvariant":1869},"\\",[1154,6640,6352],{},[1172,6642,6643],{"encoding":1174},"A \\backslash B",[3359,6645,6646],{},[1115,6647,6649],{"className":6648},[1139],[1141,6650,6651],{"xmlns":1143},[1145,6652,6653,6661],{},[1148,6654,6655],{},[1151,6656,6657,6659],{},[1154,6658,6352],{},[1312,6660,1489],{},[1172,6662,6663],{"encoding":1174},"B_1",[3359,6665,6666],{},[1115,6667,6669],{"className":6668},[1139],[1141,6670,6671],{"xmlns":1143},[1145,6672,6673,6681],{},[1148,6674,6675],{},[1151,6676,6677,6679],{},[1154,6678,6352],{},[1312,6680,1610],{},[1172,6682,6683],{"encoding":1174},"B_2",[3359,6685,3022],{},[3359,6687,6688],{},[1115,6689,6691],{"className":6690},[1139],[1141,6692,6693],{"xmlns":1143},[1145,6694,6695,6703],{},[1148,6696,6697],{},[1151,6698,6699,6701],{},[1154,6700,6352],{},[1154,6702,1607],{},[1172,6704,6705],{"encoding":1174},"B_s",[3359,6707,6708],{},[1115,6709,6711],{"className":6710},[1139],[1141,6712,6713],{"xmlns":1143},[1145,6714,6715,6727],{},[1148,6716,6717],{},[1151,6718,6719,6721],{},[1154,6720,1159],{},[1148,6722,6723,6725],{},[1154,6724,1502],{},[1161,6726,6501],{},[1172,6728,6729],{"encoding":1174},"n_{i\\bullet}",[3389,6731,6732,6845,6959,6975,7095],{},[3356,6733,6734,6754,6774,6795,6797,6821],{},[3394,6735,6736],{},[1115,6737,6739],{"className":6738},[1139],[1141,6740,6741],{"xmlns":1143},[1145,6742,6743,6751],{},[1148,6744,6745],{},[1151,6746,6747,6749],{},[1154,6748,6307],{},[1312,6750,1489],{},[1172,6752,6753],{"encoding":1174},"A_1",[3394,6755,6756],{},[1115,6757,6759],{"className":6758},[1139],[1141,6760,6761],{"xmlns":1143},[1145,6762,6763,6771],{},[1148,6764,6765],{},[1151,6766,6767,6769],{},[1154,6768,1159],{},[1312,6770,4850],{},[1172,6772,6773],{"encoding":1174},"n_{11}",[3394,6775,6776],{},[1115,6777,6779],{"className":6778},[1139],[1141,6780,6781],{"xmlns":1143},[1145,6782,6783,6792],{},[1148,6784,6785],{},[1151,6786,6787,6789],{},[1154,6788,1159],{},[1312,6790,6791],{},"12",[1172,6793,6794],{"encoding":1174},"n_{12}",[3394,6796,3022],{},[3394,6798,6799],{},[1115,6800,6802],{"className":6801},[1139],[1141,6803,6804],{"xmlns":1143},[1145,6805,6806,6818],{},[1148,6807,6808],{},[1151,6809,6810,6812],{},[1154,6811,1159],{},[1148,6813,6814,6816],{},[1312,6815,1489],{},[1154,6817,1607],{},[1172,6819,6820],{"encoding":1174},"n_{1s}",[3394,6822,6823],{},[1115,6824,6826],{"className":6825},[1139],[1141,6827,6828],{"xmlns":1143},[1145,6829,6830,6842],{},[1148,6831,6832],{},[1151,6833,6834,6836],{},[1154,6835,1159],{},[1148,6837,6838,6840],{},[1312,6839,1489],{},[1161,6841,6501],{},[1172,6843,6844],{"encoding":1174},"n_{1\\bullet}",[3356,6846,6847,6867,6888,6909,6911,6935],{},[3394,6848,6849],{},[1115,6850,6852],{"className":6851},[1139],[1141,6853,6854],{"xmlns":1143},[1145,6855,6856,6864],{},[1148,6857,6858],{},[1151,6859,6860,6862],{},[1154,6861,6307],{},[1312,6863,1610],{},[1172,6865,6866],{"encoding":1174},"A_2",[3394,6868,6869],{},[1115,6870,6872],{"className":6871},[1139],[1141,6873,6874],{"xmlns":1143},[1145,6875,6876,6885],{},[1148,6877,6878],{},[1151,6879,6880,6882],{},[1154,6881,1159],{},[1312,6883,6884],{},"21",[1172,6886,6887],{"encoding":1174},"n_{21}",[3394,6889,6890],{},[1115,6891,6893],{"className":6892},[1139],[1141,6894,6895],{"xmlns":1143},[1145,6896,6897,6906],{},[1148,6898,6899],{},[1151,6900,6901,6903],{},[1154,6902,1159],{},[1312,6904,6905],{},"22",[1172,6907,6908],{"encoding":1174},"n_{22}",[3394,6910,3022],{},[3394,6912,6913],{},[1115,6914,6916],{"className":6915},[1139],[1141,6917,6918],{"xmlns":1143},[1145,6919,6920,6932],{},[1148,6921,6922],{},[1151,6923,6924,6926],{},[1154,6925,1159],{},[1148,6927,6928,6930],{},[1312,6929,1610],{},[1154,6931,1607],{},[1172,6933,6934],{"encoding":1174},"n_{2s}",[3394,6936,6937],{},[1115,6938,6940],{"className":6939},[1139],[1141,6941,6942],{"xmlns":1143},[1145,6943,6944,6956],{},[1148,6945,6946],{},[1151,6947,6948,6950],{},[1154,6949,1159],{},[1148,6951,6952,6954],{},[1312,6953,1610],{},[1161,6955,6501],{},[1172,6957,6958],{"encoding":1174},"n_{2\\bullet}",[3356,6960,6961,6964,6966,6968,6971,6973],{},[3394,6962,6963],{},"⋮",[3394,6965,6963],{},[3394,6967,6963],{},[3394,6969,6970],{},"⋱",[3394,6972,6963],{},[3394,6974,6963],{},[3356,6976,6977,6997,7021,7045,7047,7071],{},[3394,6978,6979],{},[1115,6980,6982],{"className":6981},[1139],[1141,6983,6984],{"xmlns":1143},[1145,6985,6986,6994],{},[1148,6987,6988],{},[1151,6989,6990,6992],{},[1154,6991,6307],{},[1154,6993,71],{},[1172,6995,6996],{"encoding":1174},"A_r",[3394,6998,6999],{},[1115,7000,7002],{"className":7001},[1139],[1141,7003,7004],{"xmlns":1143},[1145,7005,7006,7018],{},[1148,7007,7008],{},[1151,7009,7010,7012],{},[1154,7011,1159],{},[1148,7013,7014,7016],{},[1154,7015,71],{},[1312,7017,1489],{},[1172,7019,7020],{"encoding":1174},"n_{r1}",[3394,7022,7023],{},[1115,7024,7026],{"className":7025},[1139],[1141,7027,7028],{"xmlns":1143},[1145,7029,7030,7042],{},[1148,7031,7032],{},[1151,7033,7034,7036],{},[1154,7035,1159],{},[1148,7037,7038,7040],{},[1154,7039,71],{},[1312,7041,1610],{},[1172,7043,7044],{"encoding":1174},"n_{r2}",[3394,7046,3022],{},[3394,7048,7049],{},[1115,7050,7052],{"className":7051},[1139],[1141,7053,7054],{"xmlns":1143},[1145,7055,7056,7068],{},[1148,7057,7058],{},[1151,7059,7060,7062],{},[1154,7061,1159],{},[1148,7063,7064,7066],{},[1154,7065,71],{},[1154,7067,1607],{},[1172,7069,7070],{"encoding":1174},"n_{rs}",[3394,7072,7073],{},[1115,7074,7076],{"className":7075},[1139],[1141,7077,7078],{"xmlns":1143},[1145,7079,7080,7092],{},[1148,7081,7082],{},[1151,7083,7084,7086],{},[1154,7085,1159],{},[1148,7087,7088,7090],{},[1154,7089,71],{},[1161,7091,6501],{},[1172,7093,7094],{"encoding":1174},"n_{r\\bullet}",[3356,7096,7097,7121,7145,7169,7171,7195],{},[3394,7098,7099],{},[1115,7100,7102],{"className":7101},[1139],[1141,7103,7104],{"xmlns":1143},[1145,7105,7106,7118],{},[1148,7107,7108],{},[1151,7109,7110,7112],{},[1154,7111,1159],{},[1148,7113,7114,7116],{},[1161,7115,6501],{},[1154,7117,1196],{},[1172,7119,7120],{"encoding":1174},"n_{\\bullet j}",[3394,7122,7123],{},[1115,7124,7126],{"className":7125},[1139],[1141,7127,7128],{"xmlns":1143},[1145,7129,7130,7142],{},[1148,7131,7132],{},[1151,7133,7134,7136],{},[1154,7135,1159],{},[1148,7137,7138,7140],{},[1161,7139,6501],{},[1312,7141,1489],{},[1172,7143,7144],{"encoding":1174},"n_{\\bullet 1}",[3394,7146,7147],{},[1115,7148,7150],{"className":7149},[1139],[1141,7151,7152],{"xmlns":1143},[1145,7153,7154,7166],{},[1148,7155,7156],{},[1151,7157,7158,7160],{},[1154,7159,1159],{},[1148,7161,7162,7164],{},[1161,7163,6501],{},[1312,7165,1610],{},[1172,7167,7168],{"encoding":1174},"n_{\\bullet 2}",[3394,7170,3022],{},[3394,7172,7173],{},[1115,7174,7176],{"className":7175},[1139],[1141,7177,7178],{"xmlns":1143},[1145,7179,7180,7192],{},[1148,7181,7182],{},[1151,7183,7184,7186],{},[1154,7185,1159],{},[1148,7187,7188,7190],{},[1161,7189,6501],{},[1154,7191,1607],{},[1172,7193,7194],{"encoding":1174},"n_{\\bullet s}",[3394,7196,7197],{},[1115,7198,7200],{"className":7199},[1139],[1141,7201,7202],{"xmlns":1143},[1145,7203,7204,7208],{},[1148,7205,7206],{},[1154,7207,1159],{},[1172,7209,1159],{"encoding":1174},[1110,7211,7212,7213,7226],{},"Vydělením četností počtem opakování ",[1115,7214,7216],{"className":7215},[1139],[1141,7217,7218],{"xmlns":1143},[1145,7219,7220,7224],{},[1148,7221,7222],{},[1154,7223,1159],{},[1172,7225,1159],{"encoding":1174}," dostaneme odhady pravděpodobností:",[1115,7228,7230],{"className":7229},[1139],[1141,7231,7232],{"xmlns":1143,"display":1468},[1145,7233,7234,7335],{},[1148,7235,7236,7251,7253,7267,7269,7271,7285,7287,7301,7303,7305,7319,7321],{},[1151,7237,7238,7245],{},[1474,7239,7240,7242],{"accent":1121},[1154,7241,1110],{},[1161,7243,7244],{},"^",[1148,7246,7247,7249],{},[1154,7248,1502],{},[1154,7250,1196],{},[1161,7252,1483],{},[1485,7254,7255,7265],{},[1151,7256,7257,7259],{},[1154,7258,1159],{},[1148,7260,7261,7263],{},[1154,7262,1502],{},[1154,7264,1196],{},[1154,7266,1159],{},[1161,7268,1199],{"separator":1121},[1516,7270],{"width":1518},[1151,7272,7273,7279],{},[1474,7274,7275,7277],{"accent":1121},[1154,7276,1110],{},[1161,7278,7244],{},[1148,7280,7281,7283],{},[1154,7282,1502],{},[1161,7284,6501],{},[1161,7286,1483],{},[1485,7288,7289,7299],{},[1151,7290,7291,7293],{},[1154,7292,1159],{},[1148,7294,7295,7297],{},[1154,7296,1502],{},[1161,7298,6501],{},[1154,7300,1159],{},[1161,7302,1199],{"separator":1121},[1516,7304],{"width":1518},[1151,7306,7307,7313],{},[1474,7308,7309,7311],{"accent":1121},[1154,7310,1110],{},[1161,7312,7244],{},[1148,7314,7315,7317],{},[1161,7316,6501],{},[1154,7318,1196],{},[1161,7320,1483],{},[1485,7322,7323,7333],{},[1151,7324,7325,7327],{},[1154,7326,1159],{},[1148,7328,7329,7331],{},[1161,7330,6501],{},[1154,7332,1196],{},[1154,7334,1159],{},[1172,7336,7337],{"encoding":1174},"\\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}",[1232,7339,7341],{"id":7340},"test-nezávislosti-dvou-kvalitativních-znaků","Test nezávislosti dvou kvalitativních znaků",[1110,7343,7344,7345,7358,7359,7372],{},"Test ověřuje, zda varianty znaku ",[1115,7346,7348],{"className":7347},[1139],[1141,7349,7350],{"xmlns":1143},[1145,7351,7352,7356],{},[1148,7353,7354],{},[1154,7355,6307],{},[1172,7357,6307],{"encoding":1174}," a varianty znaku ",[1115,7360,7362],{"className":7361},[1139],[1141,7363,7364],{"xmlns":1143},[1145,7365,7366,7370],{},[1148,7367,7368],{},[1154,7369,6352],{},[1172,7371,6352],{"encoding":1174}," jsou na sobě nezávislé, tedy zda simultánní\npravděpodobnost je součinem marginálních pravděpodobností.",[1110,7374,7375],{},[1248,7376,7377],{},"Postup testu:",[7379,7380,7381,7510,7827,7907],"ol",{},[1127,7382,7383,7437,7438,1381,7464,7490,7491,7509],{},[1115,7384,7386],{"className":7385},[1139],[1141,7387,7388],{"xmlns":1143},[1145,7389,7390,7434],{},[1148,7391,7392,7398,7400,7410,7412,7422,7424],{},[1151,7393,7394,7396],{},[1154,7395,6105],{},[1312,7397,4585],{},[1161,7399,6481],{},[1151,7401,7402,7404],{},[1154,7403,1110],{},[1148,7405,7406,7408],{},[1154,7407,1502],{},[1154,7409,1196],{},[1161,7411,1483],{},[1151,7413,7414,7416],{},[1154,7415,1110],{},[1148,7417,7418,7420],{},[1154,7419,1502],{},[1161,7421,6501],{},[1316,7423,1318],{},[1151,7425,7426,7428],{},[1154,7427,1110],{},[1148,7429,7430,7432],{},[1161,7431,6501],{},[1154,7433,1196],{},[1172,7435,7436],{"encoding":1174},"H_0: p_{ij} = p_{i\\bullet}\\,p_{\\bullet j}"," pro všechna ",[1115,7439,7441],{"className":7440},[1139],[1141,7442,7443],{"xmlns":1143},[1145,7444,7445,7461],{},[1148,7446,7447,7449,7451,7453,7455,7457,7459],{},[1154,7448,1502],{},[1161,7450,1483],{},[1312,7452,1489],{},[1161,7454,1199],{"separator":1121},[1161,7456,3022],{},[1161,7458,1199],{"separator":1121},[1154,7460,71],{},[1172,7462,7463],{"encoding":1174},"i = 1,\\dots,r",[1115,7465,7467],{"className":7466},[1139],[1141,7468,7469],{"xmlns":1143},[1145,7470,7471,7487],{},[1148,7472,7473,7475,7477,7479,7481,7483,7485],{},[1154,7474,1196],{},[1161,7476,1483],{},[1312,7478,1489],{},[1161,7480,1199],{"separator":1121},[1161,7482,3022],{},[1161,7484,1199],{"separator":1121},[1154,7486,1607],{},[1172,7488,7489],{"encoding":1174},"j = 1,\\dots,s"," (znaky jsou na sobě\nnezávislé) proti ",[1115,7492,7494],{"className":7493},[1139],[1141,7495,7496],{"xmlns":1143},[1145,7497,7498,7506],{},[1148,7499,7500],{},[1151,7501,7502,7504],{},[1154,7503,6105],{},[1312,7505,1489],{},[1172,7507,7508],{"encoding":1174},"H_1",": znaky jsou závislé.",[1127,7511,7512,7513,7669,7672,7673,7690,7691,7723,7724,6413,7783,7786,7787,7808,7809,7826],{},"Testové kritérium",[1115,7514,7516],{"className":7515},[1139],[1141,7517,7518],{"xmlns":1143,"display":1468},[1145,7519,7520,7666],{},[1148,7521,7522,7528,7530,7544,7558,7616,7618,7620,7634,7636,7650,7652],{},[1603,7523,7524,7526],{},[1154,7525,6125],{},[1312,7527,1610],{},[1161,7529,1483],{},[1493,7531,7532,7534,7542],{},[1161,7533,1497],{},[1148,7535,7536,7538,7540],{},[1154,7537,1502],{},[1161,7539,1483],{},[1312,7541,1489],{},[1154,7543,71],{},[1493,7545,7546,7548,7556],{},[1161,7547,1497],{},[1148,7549,7550,7552,7554],{},[1154,7551,1196],{},[1161,7553,1483],{},[1312,7555,1489],{},[1154,7557,1607],{},[1485,7559,7560,7598],{},[1148,7561,7562,7564,7574,7576,7578,7592],{},[1161,7563,1164],{"stretchy":1163},[1151,7565,7566,7568],{},[1154,7567,1159],{},[1148,7569,7570,7572],{},[1154,7571,1502],{},[1154,7573,1196],{},[1161,7575,1623],{},[1154,7577,1159],{},[1151,7579,7580,7586],{},[1474,7581,7582,7584],{"accent":1121},[1154,7583,1110],{},[1161,7585,7244],{},[1148,7587,7588,7590],{},[1154,7589,1502],{},[1154,7591,1196],{},[1603,7593,7594,7596],{},[1161,7595,1170],{"stretchy":1163},[1312,7597,1610],{},[1148,7599,7600,7602],{},[1154,7601,1159],{},[1151,7603,7604,7610],{},[1474,7605,7606,7608],{"accent":1121},[1154,7607,1110],{},[1161,7609,7244],{},[1148,7611,7612,7614],{},[1154,7613,1502],{},[1154,7615,1196],{},[1161,7617,1199],{"separator":1121},[1516,7619],{"width":1518},[1151,7621,7622,7628],{},[1474,7623,7624,7626],{"accent":1121},[1154,7625,1110],{},[1161,7627,7244],{},[1148,7629,7630,7632],{},[1154,7631,1502],{},[1154,7633,1196],{},[1161,7635,1483],{},[1151,7637,7638,7644],{},[1474,7639,7640,7642],{"accent":1121},[1154,7641,1110],{},[1161,7643,7244],{},[1148,7645,7646,7648],{},[1154,7647,1502],{},[1161,7649,6501],{},[1316,7651,1318],{},[1151,7653,7654,7660],{},[1474,7655,7656,7658],{"accent":1121},[1154,7657,1110],{},[1161,7659,7244],{},[1148,7661,7662,7664],{},[1161,7663,6501],{},[1154,7665,1196],{},[1172,7667,7668],{"encoding":1174},"\\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}",[7670,7671],"br",{},"má asymptoticky Pearsonovo (",[1115,7674,7676],{"className":7675},[1139],[1141,7677,7678],{"xmlns":1143},[1145,7679,7680,7688],{},[1148,7681,7682],{},[1603,7683,7684,7686],{},[1154,7685,6125],{},[1312,7687,1610],{},[1172,7689,6130],{"encoding":1174},") rozdělení o ",[1115,7692,7694],{"className":7693},[1139],[1141,7695,7696],{"xmlns":1143},[1145,7697,7698,7720],{},[1148,7699,7700,7702,7704,7706,7708,7710,7712,7714,7716,7718],{},[1161,7701,1164],{"stretchy":1163},[1154,7703,71],{},[1161,7705,1623],{},[1312,7707,1489],{},[1161,7709,1170],{"stretchy":1163},[1161,7711,1164],{"stretchy":1163},[1154,7713,1607],{},[1161,7715,1623],{},[1312,7717,1489],{},[1161,7719,1170],{"stretchy":1163},[1172,7721,7722],{"encoding":1174},"(r-1)(s-1)"," stupních volnosti. Hodnota ",[1115,7725,7727],{"className":7726},[1139],[1141,7728,7729],{"xmlns":1143},[1145,7730,7731,7780],{},[1148,7732,7733,7735,7749,7751],{},[1154,7734,1159],{},[1151,7736,7737,7743],{},[1474,7738,7739,7741],{"accent":1121},[1154,7740,1110],{},[1161,7742,7244],{},[1148,7744,7745,7747],{},[1154,7746,1502],{},[1154,7748,1196],{},[1161,7750,1483],{},[7752,7753,7754],"mstyle",{"scriptlevel":4585,"displaystyle":1121},[1485,7755,7756,7778],{},[1148,7757,7758,7768],{},[1151,7759,7760,7762],{},[1154,7761,1159],{},[1148,7763,7764,7766],{},[1154,7765,1502],{},[1161,7767,6501],{},[1151,7769,7770,7772],{},[1154,7771,1159],{},[1148,7773,7774,7776],{},[1161,7775,6501],{},[1154,7777,1196],{},[1154,7779,1159],{},[1172,7781,7782],{"encoding":1174},"n\\hat p_{ij} = \\dfrac{n_{i\\bullet}n_{\\bullet j}}{n}",[1248,7784,7785],{},"očekávaná četnost"," políčka ",[1115,7788,7790],{"className":7789},[1139],[1141,7791,7792],{"xmlns":1143},[1145,7793,7794,7806],{},[1148,7795,7796,7798,7800,7802,7804],{},[1161,7797,1164],{"stretchy":1163},[1154,7799,1502],{},[1161,7801,1199],{"separator":1121},[1154,7803,1196],{},[1161,7805,1170],{"stretchy":1163},[1172,7807,6412],{"encoding":1174}," — četnost, kterou bychom čekali, kdyby ",[1115,7810,7812],{"className":7811},[1139],[1141,7813,7814],{"xmlns":1143},[1145,7815,7816,7824],{},[1148,7817,7818],{},[1151,7819,7820,7822],{},[1154,7821,6105],{},[1312,7823,4585],{},[1172,7825,6110],{"encoding":1174}," platila.",[1127,7828,7829,7830,1176],{},"Kritický obor: ",[1115,7831,7833],{"className":7832},[1139],[1141,7834,7835],{"xmlns":1143},[1145,7836,7837,7904],{},[1148,7838,7839,7841,7843,7846,7852,7854,7860,7862,7877,7879,7881,7883,7885,7887,7889,7891,7893,7895,7897,7899,7901],{},[1154,7840,6143],{},[1161,7842,1483],{},[1161,7844,7845],{"stretchy":1163},"{",[1603,7847,7848,7850],{},[1154,7849,6125],{},[1312,7851,1610],{},[1161,7853,6481],{},[1603,7855,7856,7858],{},[1154,7857,6125],{},[1312,7859,1610],{},[1161,7861,5198],{},[1645,7863,7864,7866,7875],{},[1154,7865,6125],{},[1148,7867,7868,7870,7872],{},[1312,7869,1489],{},[1161,7871,1623],{},[1154,7873,7874],{},"α",[1312,7876,1610],{},[1161,7878,1164],{"stretchy":1163},[1161,7880,1164],{"stretchy":1163},[1154,7882,71],{},[1161,7884,1623],{},[1312,7886,1489],{},[1161,7888,1170],{"stretchy":1163},[1161,7890,1164],{"stretchy":1163},[1154,7892,1607],{},[1161,7894,1623],{},[1312,7896,1489],{},[1161,7898,1170],{"stretchy":1163},[1161,7900,1170],{"stretchy":1163},[1161,7902,7903],{"stretchy":1163},"}",[1172,7905,7906],{"encoding":1174},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}((r-1)(s-1))\\}",[1127,7908,7909,7910,7923,7924,7938,7939,7956,7957,7974],{},"Padne-li testové kritérium do ",[1115,7911,7913],{"className":7912},[1139],[1141,7914,7915],{"xmlns":1143},[1145,7916,7917,7921],{},[1148,7918,7919],{},[1154,7920,6143],{},[1172,7922,6143],{"encoding":1174},", zamítáme na hladině ",[1115,7925,7927],{"className":7926},[1139],[1141,7928,7929],{"xmlns":1143},[1145,7930,7931,7935],{},[1148,7932,7933],{},[1154,7934,7874],{},[1172,7936,7937],{"encoding":1174},"\\alpha"," nulovou hypotézu o nezávislosti a přijímáme\n",[1115,7940,7942],{"className":7941},[1139],[1141,7943,7944],{"xmlns":1143},[1145,7945,7946,7954],{},[1148,7947,7948],{},[1151,7949,7950,7952],{},[1154,7951,6105],{},[1312,7953,1489],{},[1172,7955,7508],{"encoding":1174},"; jinak nemáme důvod ",[1115,7958,7960],{"className":7959},[1139],[1141,7961,7962],{"xmlns":1143},[1145,7963,7964,7972],{},[1148,7965,7966],{},[1151,7967,7968,7970],{},[1154,7969,6105],{},[1312,7971,4585],{},[1172,7973,6110],{"encoding":1174}," zamítnout.",[1110,7976,7977,7978,1176],{},"V R počítá test i očekávané četnosti funkce ",[2015,7979,7980],{},"chisq.test()",[1103,7982,7984,7991,7994,7997,8136],{"className":7983,"dataCallout":2447},[1106,2446],[1110,7985,7987,7990],{"className":7986},[1113],[1115,7988],{"className":7989,"ariaHidden":1121},[1118,2454,1120],"Příklad: nákup potravin na internetu a vzdělání",[1110,7992,7993],{},"Testujte hypotézu, zda se vzájemně ovlivňuje zkušenost s nákupem potravin na internetu a vzdělání respondenta\n(n = 385 respondentů).",[1110,7995,7996],{},"Základní soubor: respondenti; výběrový soubor: respondenti, kteří odpověděli; měřený znak A: vzdělání, měřený\nznak B: způsob nákupu.",[3350,7998,7999,8038],{},[3353,8000,8001],{},[3356,8002,8003,8006,8009,8012,8015],{},[3359,8004,8005],{},"vzdělání \\ nákup",[3359,8007,8008],{},"ano",[3359,8010,8011],{},"ne, ale plánuji",[3359,8013,8014],{},"ne, neplánuji",[3359,8016,8017],{},[1115,8018,8020],{"className":8019},[1139],[1141,8021,8022],{"xmlns":1143},[1145,8023,8024,8036],{},[1148,8025,8026],{},[1151,8027,8028,8030],{},[1154,8029,1159],{},[1148,8031,8032,8034],{},[1154,8033,1502],{},[1161,8035,6501],{},[1172,8037,6729],{"encoding":1174},[3389,8039,8040,8053,8069,8085,8099],{},[3356,8041,8042,8045,8047,8049,8051],{},[3394,8043,8044],{},"SŠ bez maturity",[3394,8046,4873],{},[3394,8048,3165],{},[3394,8050,6791],{},[3394,8052,1314],{},[3356,8054,8055,8058,8060,8063,8066],{},[3394,8056,8057],{},"SŠ s maturitou, VOŠ",[3394,8059,1364],{},[3394,8061,8062],{},"62",[3394,8064,8065],{},"71",[3394,8067,8068],{},"164",[3356,8070,8071,8074,8076,8079,8082],{},[3394,8072,8073],{},"VŠ",[3394,8075,2640],{},[3394,8077,8078],{},"58",[3394,8080,8081],{},"66",[3394,8083,8084],{},"168",[3356,8086,8087,8090,8092,8094,8096],{},[3394,8088,8089],{},"ZŠ",[3394,8091,3512],{},[3394,8093,3424],{},[3394,8095,6791],{},[3394,8097,8098],{},"24",[3356,8100,8101,8124,8127,8130,8133],{},[3394,8102,8103],{},[1115,8104,8106],{"className":8105},[1139],[1141,8107,8108],{"xmlns":1143},[1145,8109,8110,8122],{},[1148,8111,8112],{},[1151,8113,8114,8116],{},[1154,8115,1159],{},[1148,8117,8118,8120],{},[1161,8119,6501],{},[1154,8121,1196],{},[1172,8123,7120],{"encoding":1174},[3394,8125,8126],{},"82",[3394,8128,8129],{},"142",[3394,8131,8132],{},"161",[3394,8134,8135],{},"385",[1110,8137,8138,8190],{},[1115,8139,8141],{"className":8140},[1139],[1141,8142,8143],{"xmlns":1143},[1145,8144,8145,8187],{},[1148,8146,8147,8153,8155,8165,8167,8177],{},[1151,8148,8149,8151],{},[1154,8150,6105],{},[1312,8152,4585],{},[1161,8154,6481],{},[1151,8156,8157,8159],{},[1154,8158,1110],{},[1148,8160,8161,8163],{},[1154,8162,1502],{},[1154,8164,1196],{},[1161,8166,1483],{},[1151,8168,8169,8171],{},[1154,8170,1110],{},[1148,8172,8173,8175],{},[1154,8174,1502],{},[1161,8176,6501],{},[1151,8178,8179,8181],{},[1154,8180,1110],{},[1148,8182,8183,8185],{},[1161,8184,6501],{},[1154,8186,1196],{},[1172,8188,8189],{"encoding":1174},"H_0: p_{ij} = p_{i\\bullet}p_{\\bullet j}"," — vzdělání a způsob nákupu jsou na sobě nezávislé.",[2020,8192,8194],{"className":2022,"code":8193,"language":71,"meta":2024,"style":2024},"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",[2015,8195,8196,8224,8240,8257,8275,8296,8309,8343,8371,8382],{"__ignoreMap":2024},[1115,8197,8198,8201,8203,8206,8208,8210,8212,8214,8216,8218,8220,8222],{"class":2029,"line":10},[1115,8199,8200],{"class":2032},"tab1",[1115,8202,2036],{"class":2035},[1115,8204,8205],{"class":2039}," matrix",[1115,8207,1164],{"class":2043},[1115,8209,1784],{"class":2039},[1115,8211,1164],{"class":2043},[1115,8213,4873],{"class":2046},[1115,8215,1199],{"class":2035},[1115,8217,4495],{"class":2046},[1115,8219,1199],{"class":2035},[1115,8221,4215],{"class":2046},[1115,8223,2688],{"class":2035},[1115,8225,8226,8229,8231,8234,8236,8238],{"class":2029,"line":27},[1115,8227,8228],{"class":2046},"                 31",[1115,8230,1199],{"class":2035},[1115,8232,8233],{"class":2046}," 62",[1115,8235,1199],{"class":2035},[1115,8237,4257],{"class":2046},[1115,8239,2688],{"class":2035},[1115,8241,8242,8245,8247,8250,8252,8255],{"class":2029,"line":148},[1115,8243,8244],{"class":2046},"                 44",[1115,8246,1199],{"class":2035},[1115,8248,8249],{"class":2046}," 58",[1115,8251,1199],{"class":2035},[1115,8253,8254],{"class":2046}," 66",[1115,8256,2688],{"class":2035},[1115,8258,8259,8262,8264,8267,8269,8271,8273],{"class":2029,"line":111},[1115,8260,8261],{"class":2046},"                 3",[1115,8263,1199],{"class":2035},[1115,8265,8266],{"class":2046},"  9",[1115,8268,1199],{"class":2035},[1115,8270,4215],{"class":2046},[1115,8272,1170],{"class":2043},[1115,8274,2688],{"class":2035},[1115,8276,8277,8280,8282,8285,8287,8290,8292,8294],{"class":2029,"line":96},[1115,8278,8279],{"class":2032},"               nrow",[1115,8281,2291],{"class":2035},[1115,8283,8284],{"class":2046}," 4",[1115,8286,1199],{"class":2035},[1115,8288,8289],{"class":2032}," byrow",[1115,8291,2291],{"class":2035},[1115,8293,2409],{"class":2046},[1115,8295,2688],{"class":2035},[1115,8297,8298,8301,8303,8306],{"class":2029,"line":89},[1115,8299,8300],{"class":2032},"               dimnames",[1115,8302,2291],{"class":2035},[1115,8304,8305],{"class":2039}," list",[1115,8307,8308],{"class":2043},"(\n",[1115,8310,8311,8314,8316,8318,8320,8324,8326,8329,8331,8334,8336,8339,8341],{"class":2029,"line":82},[1115,8312,8313],{"class":2032},"                 vzdelani",[1115,8315,2291],{"class":2035},[1115,8317,2040],{"class":2039},[1115,8319,1164],{"class":2043},[1115,8321,8323],{"class":8322},"sIIMD","\"SS bez maturity\"",[1115,8325,1199],{"class":2035},[1115,8327,8328],{"class":8322}," \"SS s maturitou nebo VOS\"",[1115,8330,1199],{"class":2035},[1115,8332,8333],{"class":8322}," \"VS\"",[1115,8335,1199],{"class":2035},[1115,8337,8338],{"class":8322}," \"ZS\"",[1115,8340,1170],{"class":2043},[1115,8342,2688],{"class":2035},[1115,8344,8345,8348,8351,8353,8355,8358,8360,8363,8365,8368],{"class":2029,"line":75},[1115,8346,8347],{"class":2032},"                 nakup",[1115,8349,8350],{"class":2035},"    =",[1115,8352,2040],{"class":2039},[1115,8354,1164],{"class":2043},[1115,8356,8357],{"class":8322},"\"ano\"",[1115,8359,1199],{"class":2035},[1115,8361,8362],{"class":8322}," \"ne, ale planuji\"",[1115,8364,1199],{"class":2035},[1115,8366,8367],{"class":8322}," \"ne, neplanuji\"",[1115,8369,8370],{"class":2043},")))\n",[1115,8372,8373,8376,8378,8380],{"class":2029,"line":2322},[1115,8374,8375],{"class":2039},"chisq.test",[1115,8377,1164],{"class":2043},[1115,8379,8200],{"class":2032},[1115,8381,2185],{"class":2043},[1115,8383,8384,8386,8388,8390,8392,8394],{"class":2029,"line":72},[1115,8385,8375],{"class":2039},[1115,8387,1164],{"class":2043},[1115,8389,8200],{"class":2032},[1115,8391,1170],{"class":2043},[1115,8393,4630],{"class":2035},[1115,8395,8396],{"class":2032},"expected\n",[2020,8398,8401],{"className":8399,"code":8400,"language":2349,"meta":2024},[2347],"    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",[2015,8402,8400],{"__ignoreMap":2024},[1110,8404,8405,8406,8429,8430,8443,8444,8464,8465,8482],{},"Všechny očekávané četnosti jsou nad 5, aproximace je v pořádku. Testové kritérium ",[1115,8407,8409],{"className":8408},[1139],[1141,8410,8411],{"xmlns":1143},[1145,8412,8413,8426],{},[1148,8414,8415,8421,8423],{},[1603,8416,8417,8419],{},[1154,8418,6125],{},[1312,8420,1610],{},[1161,8422,1483],{},[1312,8424,8425],{},"5,49",[1172,8427,8428],{"encoding":1174},"\\chi^2 = 5{,}49"," s ",[1115,8431,8433],{"className":8432},[1139],[1141,8434,8435],{"xmlns":1143},[1145,8436,8437,8441],{},[1148,8438,8439],{},[1312,8440,3418],{},[1172,8442,3418],{"encoding":1174}," stupni\nvolnosti dává p-hodnotu ",[1115,8445,8447],{"className":8446},[1139],[1141,8448,8449],{"xmlns":1143},[1145,8450,8451,8461],{},[1148,8452,8453,8456,8458],{},[1312,8454,8455],{},"0,483",[1161,8457,6225],{},[1312,8459,8460],{},"0,05",[1172,8462,8463],{"encoding":1174},"0{,}483 > 0{,}05",": ",[1115,8466,8468],{"className":8467},[1139],[1141,8469,8470],{"xmlns":1143},[1145,8471,8472,8480],{},[1148,8473,8474],{},[1151,8475,8476,8478],{},[1154,8477,6105],{},[1312,8479,4585],{},[1172,8481,6110],{"encoding":1174}," nezamítáme, závislost mezi zkušeností s nákupem potravin na\ninternetu a vzděláním respondenta se neprokázala.",[1103,8484,8486,8493,8496,8540],{"className":8485,"dataCallout":2447},[1106,2446],[1110,8487,8489,8492],{"className":8488},[1113],[1115,8490],{"className":8491,"ariaHidden":1121},[1118,2454,1120],"Příklad: vzdělání a zveřejňování citlivých údajů na Facebooku",[1110,8494,8495],{},"Mezi 221 osobami bylo zaznamenáno vzdělání a zda zveřejňují na Facebooku citlivé údaje. Proveďte test\nnezávislosti.",[3350,8497,8498,8512],{},[3353,8499,8500],{},[3356,8501,8502,8505,8508,8510],{},[3359,8503,8504],{},"zveřejňuje \\ vzdělání",[3359,8506,8507],{},"SŠ",[3359,8509,8073],{},[3359,8511,8089],{},[3389,8513,8514,8528],{},[3356,8515,8516,8519,8522,8525],{},[3394,8517,8518],{},"ne",[3394,8520,8521],{},"20",[3394,8523,8524],{},"33",[3394,8526,8527],{},"39",[3356,8529,8530,8532,8534,8537],{},[3394,8531,8008],{},[3394,8533,4831],{},[3394,8535,8536],{},"28",[3394,8538,8539],{},"76",[1110,8541,8542,8593],{},[1115,8543,8545],{"className":8544},[1139],[1141,8546,8547],{"xmlns":1143},[1145,8548,8549,8591],{},[1148,8550,8551,8557,8559,8569,8571,8581],{},[1151,8552,8553,8555],{},[1154,8554,6105],{},[1312,8556,4585],{},[1161,8558,6481],{},[1151,8560,8561,8563],{},[1154,8562,1110],{},[1148,8564,8565,8567],{},[1154,8566,1502],{},[1154,8568,1196],{},[1161,8570,1483],{},[1151,8572,8573,8575],{},[1154,8574,1110],{},[1148,8576,8577,8579],{},[1154,8578,1502],{},[1161,8580,6501],{},[1151,8582,8583,8585],{},[1154,8584,1110],{},[1148,8586,8587,8589],{},[1161,8588,6501],{},[1154,8590,1196],{},[1172,8592,8189],{"encoding":1174}," — vzdělání a zveřejňování citlivých údajů jsou na sobě nezávislé.",[2020,8595,8597],{"className":2022,"code":8596,"language":71,"meta":2024,"style":2024},"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",[2015,8598,8599,8627,8646,8664,8674,8697,8721,8731],{"__ignoreMap":2024},[1115,8600,8601,8604,8606,8608,8610,8612,8614,8616,8618,8620,8622,8625],{"class":2029,"line":10},[1115,8602,8603],{"class":2032},"tab2",[1115,8605,2036],{"class":2035},[1115,8607,8205],{"class":2039},[1115,8609,1164],{"class":2043},[1115,8611,1784],{"class":2039},[1115,8613,1164],{"class":2043},[1115,8615,8521],{"class":2046},[1115,8617,1199],{"class":2035},[1115,8619,4446],{"class":2046},[1115,8621,1199],{"class":2035},[1115,8623,8624],{"class":2046}," 39",[1115,8626,2688],{"class":2035},[1115,8628,8629,8632,8634,8637,8639,8642,8644],{"class":2029,"line":27},[1115,8630,8631],{"class":2046},"                 25",[1115,8633,1199],{"class":2035},[1115,8635,8636],{"class":2046}," 28",[1115,8638,1199],{"class":2035},[1115,8640,8641],{"class":2046}," 76",[1115,8643,1170],{"class":2043},[1115,8645,2688],{"class":2035},[1115,8647,8648,8650,8652,8654,8656,8658,8660,8662],{"class":2029,"line":148},[1115,8649,8279],{"class":2032},[1115,8651,2291],{"class":2035},[1115,8653,4210],{"class":2046},[1115,8655,1199],{"class":2035},[1115,8657,8289],{"class":2032},[1115,8659,2291],{"class":2035},[1115,8661,2409],{"class":2046},[1115,8663,2688],{"class":2035},[1115,8665,8666,8668,8670,8672],{"class":2029,"line":111},[1115,8667,8300],{"class":2032},[1115,8669,2291],{"class":2035},[1115,8671,8305],{"class":2039},[1115,8673,8308],{"class":2043},[1115,8675,8676,8679,8681,8683,8685,8688,8690,8693,8695],{"class":2029,"line":96},[1115,8677,8678],{"class":2032},"                 zverejnuje",[1115,8680,2291],{"class":2035},[1115,8682,2040],{"class":2039},[1115,8684,1164],{"class":2043},[1115,8686,8687],{"class":8322},"\"ne\"",[1115,8689,1199],{"class":2035},[1115,8691,8692],{"class":8322}," \"ano\"",[1115,8694,1170],{"class":2043},[1115,8696,2688],{"class":2035},[1115,8698,8699,8701,8704,8706,8708,8711,8713,8715,8717,8719],{"class":2029,"line":89},[1115,8700,8313],{"class":2032},[1115,8702,8703],{"class":2035},"   =",[1115,8705,2040],{"class":2039},[1115,8707,1164],{"class":2043},[1115,8709,8710],{"class":8322},"\"SS\"",[1115,8712,1199],{"class":2035},[1115,8714,8333],{"class":8322},[1115,8716,1199],{"class":2035},[1115,8718,8338],{"class":8322},[1115,8720,8370],{"class":2043},[1115,8722,8723,8725,8727,8729],{"class":2029,"line":82},[1115,8724,8375],{"class":2039},[1115,8726,1164],{"class":2043},[1115,8728,8603],{"class":2032},[1115,8730,2185],{"class":2043},[1115,8732,8733,8735,8737,8739,8741,8743],{"class":2029,"line":75},[1115,8734,8375],{"class":2039},[1115,8736,1164],{"class":2043},[1115,8738,8603],{"class":2032},[1115,8740,1170],{"class":2043},[1115,8742,4630],{"class":2035},[1115,8744,8396],{"class":2032},[2020,8746,8749],{"className":8747,"code":8748,"language":2349,"meta":2024},[2347],"    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",[2015,8750,8748],{"__ignoreMap":2024},[1110,8752,8753,8754,8429,8777,8790,8791,8464,8811,8828,8829,1176],{},"I zde jsou všechny očekávané četnosti nad 5. Testové kritérium ",[1115,8755,8757],{"className":8756},[1139],[1141,8758,8759],{"xmlns":1143},[1145,8760,8761,8774],{},[1148,8762,8763,8769,8771],{},[1603,8764,8765,8767],{},[1154,8766,6125],{},[1312,8768,1610],{},[1161,8770,1483],{},[1312,8772,8773],{},"6,87",[1172,8775,8776],{"encoding":1174},"\\chi^2 = 6{,}87",[1115,8778,8780],{"className":8779},[1139],[1141,8781,8782],{"xmlns":1143},[1145,8783,8784,8788],{},[1148,8785,8786],{},[1312,8787,1610],{},[1172,8789,1610],{"encoding":1174}," stupni volnosti dává\np-hodnotu ",[1115,8792,8794],{"className":8793},[1139],[1141,8795,8796],{"xmlns":1143},[1145,8797,8798,8808],{},[1148,8799,8800,8803,8806],{},[1312,8801,8802],{},"0,032",[1161,8804,8805],{},"\u003C",[1312,8807,8460],{},[1172,8809,8810],{"encoding":1174},"0{,}032 \u003C 0{,}05",[1115,8812,8814],{"className":8813},[1139],[1141,8815,8816],{"xmlns":1143},[1145,8817,8818,8826],{},[1148,8819,8820],{},[1151,8821,8822,8824],{},[1154,8823,6105],{},[1312,8825,4585],{},[1172,8827,6110],{"encoding":1174}," zamítáme — na rozdíl od předchozího příkladu tady vzdělání a zveřejňování\ncitlivých údajů na Facebooku na sobě ",[1248,8830,8831],{},"závisí",[1110,8833,8834,8835,8852],{},"Srovnání pozorovaných a očekávaných četností ukazuje, proč jeden příklad ",[1115,8836,8838],{"className":8837},[1139],[1141,8839,8840],{"xmlns":1143},[1145,8841,8842,8850],{},[1148,8843,8844],{},[1151,8845,8846,8848],{},[1154,8847,6105],{},[1312,8849,4585],{},[1172,8851,6110],{"encoding":1174}," nezamítá a druhý ano — ve druhém\nse pozorované sloupce (zejména u ZŠ) systematicky odchylují od očekávaných, v prvním kolísají jen náhodně kolem nich:",[1110,8854,8855],{},[1393,8856],{"alt":8857,"className":8858,"src":8859},"mask-kt-observed-expected",[1242,1397],"\u002Fwiki-assets\u002Fmask-kt-observed-expected.png",[1110,8861,8862,8863,8880,8881,6481],{},"Totéž je vidět na rozdělení testového kritéria: u prvního příkladu leží ",[1115,8864,8866],{"className":8865},[1139],[1141,8867,8868],{"xmlns":1143},[1145,8869,8870,8878],{},[1148,8871,8872],{},[1603,8873,8874,8876],{},[1154,8875,6125],{},[1312,8877,1610],{},[1172,8879,6130],{"encoding":1174}," hluboko pod kritickou hodnotou,\nu druhého uvnitř kritického oboru ",[1115,8882,8884],{"className":8883},[1139],[1141,8885,8886],{"xmlns":1143},[1145,8887,8888,8892],{},[1148,8889,8890],{},[1154,8891,6143],{},[1172,8893,6143],{"encoding":1174},[1110,8895,8896],{},[1393,8897],{"alt":8898,"className":8899,"src":8900},"mask-kt-chi2-kriticky-obor",[1242,1397],"\u002Fwiki-assets\u002Fmask-kt-chi2-kriticky-obor.png",[1232,8902,6191],{"id":8903},"cramérův-koeficient-kontingence",[1110,8905,8906,8907,6481],{},"Test nezávislosti pouze rozhodne, zda jsou znaky závislé, nebo ne. Sílu závislosti měří ",[1248,8908,8909],{},"Cramérův koeficient\nkontingence",[1115,8911,8913],{"className":8912},[1139],[1141,8914,8915],{"xmlns":1143,"display":1468},[1145,8916,8917,8969],{},[1148,8918,8919,8921,8923,8947,8949,8951,8953,8955,8957,8959,8961,8963,8965,8967],{},[1154,8920,6203],{},[1161,8922,1483],{},[1678,8924,8925],{},[1485,8926,8927,8933],{},[1603,8928,8929,8931],{},[1154,8930,6125],{},[1312,8932,1610],{},[1148,8934,8935,8937,8939,8941,8943,8945],{},[1154,8936,1159],{},[1161,8938,1164],{"stretchy":1163},[1154,8940,1565],{},[1161,8942,1623],{},[1312,8944,1489],{},[1161,8946,1170],{"stretchy":1163},[1161,8948,1199],{"separator":1121},[1516,8950],{"width":1518},[1154,8952,1565],{},[1161,8954,1483],{},[1154,8956,1770],{},[1161,8958,1761],{},[1161,8960,1164],{"stretchy":1163},[1154,8962,71],{},[1161,8964,1199],{"separator":1121},[1154,8966,1607],{},[1161,8968,1170],{"stretchy":1163},[1172,8970,8971],{"encoding":1174},"V = \\sqrt{\\frac{\\chi^2}{n(m-1)}}, \\qquad m = \\min(r, s)",[1110,8973,3074,8974,8991,8992,9010,9011,9029],{},[1115,8975,8977],{"className":8976},[1139],[1141,8978,8979],{"xmlns":1143},[1145,8980,8981,8989],{},[1148,8982,8983],{},[1603,8984,8985,8987],{},[1154,8986,6125],{},[1312,8988,1610],{},[1172,8990,6130],{"encoding":1174}," je hodnota testového kritéria z testu nezávislosti. ",[1115,8993,8995],{"className":8994},[1139],[1141,8996,8997],{"xmlns":1143},[1145,8998,8999,9007],{},[1148,9000,9001,9003,9005],{},[1154,9002,6203],{},[1161,9004,1483],{},[1312,9006,4585],{},[1172,9008,9009],{"encoding":1174},"V = 0"," odpovídá úplné nezávislosti znaků,\n",[1115,9012,9014],{"className":9013},[1139],[1141,9015,9016],{"xmlns":1143},[1145,9017,9018,9026],{},[1148,9019,9020,9022,9024],{},[1154,9021,6203],{},[1161,9023,1483],{},[1312,9025,1489],{},[1172,9027,9028],{"encoding":1174},"V = 1"," jejich úplné závislosti.",[2020,9031,9033],{"className":2022,"code":9032,"language":71,"meta":2024,"style":2024},"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",[2015,9034,9035,9105,9168,9173],{"__ignoreMap":2024},[1115,9036,9037,9040,9042,9045,9047,9050,9052,9054,9056,9058,9060,9062,9065,9067,9069,9071,9074,9076,9078,9080,9083,9085,9087,9089,9092,9094,9096,9099,9101,9103],{"class":2029,"line":10},[1115,9038,9039],{"class":2032},"V1",[1115,9041,2036],{"class":2035},[1115,9043,9044],{"class":2039}," sqrt",[1115,9046,1164],{"class":2043},[1115,9048,9049],{"class":2039},"as.numeric",[1115,9051,1164],{"class":2043},[1115,9053,8375],{"class":2039},[1115,9055,1164],{"class":2043},[1115,9057,8200],{"class":2032},[1115,9059,1170],{"class":2043},[1115,9061,4630],{"class":2035},[1115,9063,9064],{"class":2032},"statistic",[1115,9066,2257],{"class":2043},[1115,9068,3245],{"class":2035},[1115,9070,3997],{"class":2043},[1115,9072,9073],{"class":2039},"sum",[1115,9075,1164],{"class":2043},[1115,9077,8200],{"class":2032},[1115,9079,2257],{"class":2043},[1115,9081,9082],{"class":2035},"*",[1115,9084,3997],{"class":2043},[1115,9086,1770],{"class":2039},[1115,9088,1164],{"class":2043},[1115,9090,9091],{"class":2039},"dim",[1115,9093,1164],{"class":2043},[1115,9095,8200],{"class":2032},[1115,9097,9098],{"class":2043},")) ",[1115,9100,2260],{"class":2035},[1115,9102,5269],{"class":2046},[1115,9104,8370],{"class":2043},[1115,9106,9107,9110,9112,9114,9116,9118,9120,9122,9124,9126,9128,9130,9132,9134,9136,9138,9140,9142,9144,9146,9148,9150,9152,9154,9156,9158,9160,9162,9164,9166],{"class":2029,"line":27},[1115,9108,9109],{"class":2032},"V2",[1115,9111,2036],{"class":2035},[1115,9113,9044],{"class":2039},[1115,9115,1164],{"class":2043},[1115,9117,9049],{"class":2039},[1115,9119,1164],{"class":2043},[1115,9121,8375],{"class":2039},[1115,9123,1164],{"class":2043},[1115,9125,8603],{"class":2032},[1115,9127,1170],{"class":2043},[1115,9129,4630],{"class":2035},[1115,9131,9064],{"class":2032},[1115,9133,2257],{"class":2043},[1115,9135,3245],{"class":2035},[1115,9137,3997],{"class":2043},[1115,9139,9073],{"class":2039},[1115,9141,1164],{"class":2043},[1115,9143,8603],{"class":2032},[1115,9145,2257],{"class":2043},[1115,9147,9082],{"class":2035},[1115,9149,3997],{"class":2043},[1115,9151,1770],{"class":2039},[1115,9153,1164],{"class":2043},[1115,9155,9091],{"class":2039},[1115,9157,1164],{"class":2043},[1115,9159,8603],{"class":2032},[1115,9161,9098],{"class":2043},[1115,9163,2260],{"class":2035},[1115,9165,5269],{"class":2046},[1115,9167,8370],{"class":2043},[1115,9169,9170],{"class":2029,"line":148},[1115,9171,9172],{"class":2032},"V1\n",[1115,9174,9175],{"class":2029,"line":111},[1115,9176,9177],{"class":2032},"V2\n",[2020,9179,9182],{"className":9180,"code":9181,"language":2349,"meta":2024},[2347],"[1] 0.08441958\n[1] 0.1762822\n",[2015,9183,9181],{"__ignoreMap":2024},[1110,9185,9186],{},[1393,9187],{"alt":9188,"className":9189,"src":9190},"mask-kt-cramerovo-v",[1242,1397],"\u002Fwiki-assets\u002Fmask-kt-cramerovo-v.png",[1110,9192,9193,9194,9213,9214,9231,9232,8464,9251,9268],{},"U nákupu potravin je ",[1115,9195,9197],{"className":9196},[1139],[1141,9198,9199],{"xmlns":1143},[1145,9200,9201,9210],{},[1148,9202,9203,9205,9207],{},[1154,9204,6203],{},[1161,9206,1483],{},[1312,9208,9209],{},"0,084",[1172,9211,9212],{"encoding":1174},"V = 0{,}084"," zanedbatelné — ostatně ",[1115,9215,9217],{"className":9216},[1139],[1141,9218,9219],{"xmlns":1143},[1145,9220,9221,9229],{},[1148,9222,9223],{},[1151,9224,9225,9227],{},[1154,9226,6105],{},[1312,9228,4585],{},[1172,9230,6110],{"encoding":1174}," jsme ani nezamítli. U zveřejňování údajů je ",[1115,9233,9235],{"className":9234},[1139],[1141,9236,9237],{"xmlns":1143},[1145,9238,9239,9248],{},[1148,9240,9241,9243,9245],{},[1154,9242,6203],{},[1161,9244,1483],{},[1312,9246,9247],{},"0,176",[1172,9249,9250],{"encoding":1174},"V = 0{,}176",[1115,9252,9254],{"className":9253},[1139],[1141,9255,9256],{"xmlns":1143},[1145,9257,9258,9266],{},[1148,9259,9260],{},[1151,9261,9262,9264],{},[1154,9263,6105],{},[1312,9265,4585],{},[1172,9267,6110],{"encoding":1174},"\njsme zamítli, ale samotná závislost je stále slabá.",[1232,9270,6210],{"id":9271},"čtyřpolní-tabulka",[1110,9273,9274,9276,9277,9290,9291,9304,9305,5254],{},[1248,9275,6210],{}," je speciální případ kontingenční tabulky, kdy oba znaky ",[1115,9278,9280],{"className":9279},[1139],[1141,9281,9282],{"xmlns":1143},[1145,9283,9284,9288],{},[1148,9285,9286],{},[1154,9287,6307],{},[1172,9289,6307],{"encoding":1174}," i ",[1115,9292,9294],{"className":9293},[1139],[1141,9295,9296],{"xmlns":1143},[1145,9297,9298,9302],{},[1148,9299,9300],{},[1154,9301,6352],{},[1172,9303,6352],{"encoding":1174}," mají jen dvě varianty\n(",[1115,9306,9308],{"className":9307},[1139],[1141,9309,9310],{"xmlns":1143},[1145,9311,9312,9324],{},[1148,9313,9314,9316,9318,9320,9322],{},[1154,9315,71],{},[1161,9317,1483],{},[1154,9319,1607],{},[1161,9321,1483],{},[1312,9323,1610],{},[1172,9325,9326],{"encoding":1174},"r = s = 2",[3350,9328,9329,9413],{},[3353,9330,9331],{},[3356,9332,9333,9352,9371,9390],{},[3359,9334,9335],{},[1115,9336,9338],{"className":9337},[1139],[1141,9339,9340],{"xmlns":1143},[1145,9341,9342,9350],{},[1148,9343,9344,9346,9348],{},[1154,9345,6307],{},[1154,9347,6638],{"mathvariant":1869},[1154,9349,6352],{},[1172,9351,6643],{"encoding":1174},[3359,9353,9354],{},[1115,9355,9357],{"className":9356},[1139],[1141,9358,9359],{"xmlns":1143},[1145,9360,9361,9369],{},[1148,9362,9363],{},[1151,9364,9365,9367],{},[1154,9366,6352],{},[1312,9368,1489],{},[1172,9370,6663],{"encoding":1174},[3359,9372,9373],{},[1115,9374,9376],{"className":9375},[1139],[1141,9377,9378],{"xmlns":1143},[1145,9379,9380,9388],{},[1148,9381,9382],{},[1151,9383,9384,9386],{},[1154,9385,6352],{},[1312,9387,1610],{},[1172,9389,6683],{"encoding":1174},[3359,9391,9392],{},[1115,9393,9395],{"className":9394},[1139],[1141,9396,9397],{"xmlns":1143},[1145,9398,9399,9411],{},[1148,9400,9401],{},[1151,9402,9403,9405],{},[1154,9404,1159],{},[1148,9406,9407,9409],{},[1154,9408,1502],{},[1161,9410,6501],{},[1172,9412,6729],{"encoding":1174},[3389,9414,9415,9497,9579],{},[3356,9416,9417,9436,9455,9474],{},[3394,9418,9419],{},[1115,9420,9422],{"className":9421},[1139],[1141,9423,9424],{"xmlns":1143},[1145,9425,9426,9434],{},[1148,9427,9428],{},[1151,9429,9430,9432],{},[1154,9431,6307],{},[1312,9433,1489],{},[1172,9435,6753],{"encoding":1174},[3394,9437,9438],{},[1115,9439,9441],{"className":9440},[1139],[1141,9442,9443],{"xmlns":1143},[1145,9444,9445,9453],{},[1148,9446,9447],{},[1151,9448,9449,9451],{},[1154,9450,1159],{},[1312,9452,4850],{},[1172,9454,6773],{"encoding":1174},[3394,9456,9457],{},[1115,9458,9460],{"className":9459},[1139],[1141,9461,9462],{"xmlns":1143},[1145,9463,9464,9472],{},[1148,9465,9466],{},[1151,9467,9468,9470],{},[1154,9469,1159],{},[1312,9471,6791],{},[1172,9473,6794],{"encoding":1174},[3394,9475,9476],{},[1115,9477,9479],{"className":9478},[1139],[1141,9480,9481],{"xmlns":1143},[1145,9482,9483,9495],{},[1148,9484,9485],{},[1151,9486,9487,9489],{},[1154,9488,1159],{},[1148,9490,9491,9493],{},[1312,9492,1489],{},[1161,9494,6501],{},[1172,9496,6844],{"encoding":1174},[3356,9498,9499,9518,9537,9556],{},[3394,9500,9501],{},[1115,9502,9504],{"className":9503},[1139],[1141,9505,9506],{"xmlns":1143},[1145,9507,9508,9516],{},[1148,9509,9510],{},[1151,9511,9512,9514],{},[1154,9513,6307],{},[1312,9515,1610],{},[1172,9517,6866],{"encoding":1174},[3394,9519,9520],{},[1115,9521,9523],{"className":9522},[1139],[1141,9524,9525],{"xmlns":1143},[1145,9526,9527,9535],{},[1148,9528,9529],{},[1151,9530,9531,9533],{},[1154,9532,1159],{},[1312,9534,6884],{},[1172,9536,6887],{"encoding":1174},[3394,9538,9539],{},[1115,9540,9542],{"className":9541},[1139],[1141,9543,9544],{"xmlns":1143},[1145,9545,9546,9554],{},[1148,9547,9548],{},[1151,9549,9550,9552],{},[1154,9551,1159],{},[1312,9553,6905],{},[1172,9555,6908],{"encoding":1174},[3394,9557,9558],{},[1115,9559,9561],{"className":9560},[1139],[1141,9562,9563],{"xmlns":1143},[1145,9564,9565,9577],{},[1148,9566,9567],{},[1151,9568,9569,9571],{},[1154,9570,1159],{},[1148,9572,9573,9575],{},[1312,9574,1610],{},[1161,9576,6501],{},[1172,9578,6958],{"encoding":1174},[3356,9580,9581,9604,9627,9650],{},[3394,9582,9583],{},[1115,9584,9586],{"className":9585},[1139],[1141,9587,9588],{"xmlns":1143},[1145,9589,9590,9602],{},[1148,9591,9592],{},[1151,9593,9594,9596],{},[1154,9595,1159],{},[1148,9597,9598,9600],{},[1161,9599,6501],{},[1154,9601,1196],{},[1172,9603,7120],{"encoding":1174},[3394,9605,9606],{},[1115,9607,9609],{"className":9608},[1139],[1141,9610,9611],{"xmlns":1143},[1145,9612,9613,9625],{},[1148,9614,9615],{},[1151,9616,9617,9619],{},[1154,9618,1159],{},[1148,9620,9621,9623],{},[1161,9622,6501],{},[1312,9624,1489],{},[1172,9626,7144],{"encoding":1174},[3394,9628,9629],{},[1115,9630,9632],{"className":9631},[1139],[1141,9633,9634],{"xmlns":1143},[1145,9635,9636,9648],{},[1148,9637,9638],{},[1151,9639,9640,9642],{},[1154,9641,1159],{},[1148,9643,9644,9646],{},[1161,9645,6501],{},[1312,9647,1610],{},[1172,9649,7168],{"encoding":1174},[3394,9651,9652],{},[1115,9653,9655],{"className":9654},[1139],[1141,9656,9657],{"xmlns":1143},[1145,9658,9659,9663],{},[1148,9660,9661],{},[1154,9662,1159],{},[1172,9664,1159],{"encoding":1174},[1110,9666,6234,9667,9685],{},[1115,9668,9670],{"className":9669},[1139],[1141,9671,9672],{"xmlns":1143},[1145,9673,9674,9682],{},[1148,9675,9676,9678,9680],{},[1154,9677,1159],{},[1161,9679,6225],{},[1312,9681,6228],{},[1172,9683,9684],{"encoding":1174},"n > 40"," se místo obecného vzorce používá zjednodušená varianta testového kritéria:",[1115,9687,9689],{"className":9688},[1139],[1141,9690,9691],{"xmlns":1143,"display":1468},[1145,9692,9693,9787],{},[1148,9694,9695,9701,9703,9705,9707],{},[1603,9696,9697,9699],{},[1154,9698,6125],{},[1312,9700,1610],{},[1161,9702,1483],{},[1154,9704,1159],{},[1316,9706,1318],{},[1485,9708,9709,9745],{},[1148,9710,9711,9713,9719,9725,9727,9733,9739],{},[1161,9712,1164],{"stretchy":1163},[1151,9714,9715,9717],{},[1154,9716,1159],{},[1312,9718,4850],{},[1151,9720,9721,9723],{},[1154,9722,1159],{},[1312,9724,6905],{},[1161,9726,1623],{},[1151,9728,9729,9731],{},[1154,9730,1159],{},[1312,9732,6791],{},[1151,9734,9735,9737],{},[1154,9736,1159],{},[1312,9738,6884],{},[1603,9740,9741,9743],{},[1161,9742,1170],{"stretchy":1163},[1312,9744,1610],{},[1148,9746,9747,9757,9767,9777],{},[1151,9748,9749,9751],{},[1154,9750,1159],{},[1148,9752,9753,9755],{},[1312,9754,1489],{},[1161,9756,6501],{},[1151,9758,9759,9761],{},[1154,9760,1159],{},[1148,9762,9763,9765],{},[1312,9764,1610],{},[1161,9766,6501],{},[1151,9768,9769,9771],{},[1154,9770,1159],{},[1148,9772,9773,9775],{},[1161,9774,6501],{},[1312,9776,1489],{},[1151,9778,9779,9781],{},[1154,9780,1159],{},[1148,9782,9783,9785],{},[1161,9784,6501],{},[1312,9786,1610],{},[1172,9788,9789],{"encoding":1174},"\\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}}",[1110,9791,9792,9793,9853,9854,9890,9891,9894,9895,9898],{},"s kritickým oborem ",[1115,9794,9796],{"className":9795},[1139],[1141,9797,9798],{"xmlns":1143},[1145,9799,9800,9850],{},[1148,9801,9802,9808,9810,9812,9818,9820,9826,9828,9842,9844,9846,9848],{},[1151,9803,9804,9806],{},[1154,9805,6143],{},[1154,9807,7874],{},[1161,9809,1483],{},[1161,9811,7845],{"stretchy":1163},[1603,9813,9814,9816],{},[1154,9815,6125],{},[1312,9817,1610],{},[1161,9819,6481],{},[1603,9821,9822,9824],{},[1154,9823,6125],{},[1312,9825,1610],{},[1161,9827,5198],{},[1645,9829,9830,9832,9840],{},[1154,9831,6125],{},[1148,9833,9834,9836,9838],{},[1312,9835,1489],{},[1161,9837,1623],{},[1154,9839,7874],{},[1312,9841,1610],{},[1161,9843,1164],{"stretchy":1163},[1312,9845,1489],{},[1161,9847,1170],{"stretchy":1163},[1161,9849,7903],{"stretchy":1163},[1172,9851,9852],{"encoding":1174},"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 ",[1115,9855,9857],{"className":9856},[1139],[1141,9858,9859],{"xmlns":1143},[1145,9860,9861,9887],{},[1148,9862,9863,9865,9867,9869,9871,9873,9875,9877,9879,9881,9883,9885],{},[1161,9864,1164],{"stretchy":1163},[1154,9866,71],{},[1161,9868,1623],{},[1312,9870,1489],{},[1161,9872,1170],{"stretchy":1163},[1161,9874,1164],{"stretchy":1163},[1154,9876,1607],{},[1161,9878,1623],{},[1312,9880,1489],{},[1161,9882,1170],{"stretchy":1163},[1161,9884,1483],{},[1312,9886,1489],{},[1172,9888,9889],{"encoding":1174},"(r-1)(s-1) = 1"," stupeň volnosti. V R dává tuto hodnotu ",[2015,9892,9893],{},"chisq.test(tab, correct = FALSE)",". Bez ",[2015,9896,9897],{},"correct = FALSE"," R u tabulky 2 × 2 použije Yatesovu korekci na kontinuitu a testové kritérium vyjde menší.",[1232,9900,6241],{"id":9901},"mcnemarův-test",[1110,9903,9904,9905,9908,9909,9911,9912,9915,9916,9919,9920,9922],{},"Čtyřpolní tabulka z předchozí sekce porovnává dva ",[1248,9906,9907],{},"různé"," znaky na stejném souboru. ",[1248,9910,6241],{}," řeší\njinou situaci: na prvcích základního souboru se měří ",[1248,9913,9914],{},"jeden"," alternativní znak, a to ",[1248,9917,9918],{},"dvakrát"," — před a po\nnějakém zásahu. Cílem je zjistit, zda zásah změnil pravděpodobnostní rozdělení variant tohoto znaku. Jde tedy o\n",[1248,9921,6237],{}," (stejné prvky měřené opakovaně), ne o dva nezávisle naměřené znaky.",[1110,9924,9925],{},"Kontingenční tabulka před\u002Fpo má tvar:",[3350,9927,9928,9962],{},[3353,9929,9930],{},[3356,9931,9932,9935,9937,9939],{},[3359,9933,9934],{},"před \\ po",[3359,9936,3835],{},[3359,9938,1623],{},[3359,9940,9941],{},[1115,9942,9944],{"className":9943},[1139],[1141,9945,9946],{"xmlns":1143},[1145,9947,9948,9960],{},[1148,9949,9950],{},[1151,9951,9952,9954],{},[1154,9953,1159],{},[1148,9955,9956,9958],{},[1154,9957,1502],{},[1161,9959,6501],{},[1172,9961,6729],{"encoding":1174},[3389,9963,9964,10029,10094],{},[3356,9965,9966,9968,9987,10006],{},[3394,9967,3835],{},[3394,9969,9970],{},[1115,9971,9973],{"className":9972},[1139],[1141,9974,9975],{"xmlns":1143},[1145,9976,9977,9985],{},[1148,9978,9979],{},[1151,9980,9981,9983],{},[1154,9982,1159],{},[1312,9984,4850],{},[1172,9986,6773],{"encoding":1174},[3394,9988,9989],{},[1115,9990,9992],{"className":9991},[1139],[1141,9993,9994],{"xmlns":1143},[1145,9995,9996,10004],{},[1148,9997,9998],{},[1151,9999,10000,10002],{},[1154,10001,1159],{},[1312,10003,6791],{},[1172,10005,6794],{"encoding":1174},[3394,10007,10008],{},[1115,10009,10011],{"className":10010},[1139],[1141,10012,10013],{"xmlns":1143},[1145,10014,10015,10027],{},[1148,10016,10017],{},[1151,10018,10019,10021],{},[1154,10020,1159],{},[1148,10022,10023,10025],{},[1312,10024,1489],{},[1161,10026,6501],{},[1172,10028,6844],{"encoding":1174},[3356,10030,10031,10033,10052,10071],{},[3394,10032,1623],{},[3394,10034,10035],{},[1115,10036,10038],{"className":10037},[1139],[1141,10039,10040],{"xmlns":1143},[1145,10041,10042,10050],{},[1148,10043,10044],{},[1151,10045,10046,10048],{},[1154,10047,1159],{},[1312,10049,6884],{},[1172,10051,6887],{"encoding":1174},[3394,10053,10054],{},[1115,10055,10057],{"className":10056},[1139],[1141,10058,10059],{"xmlns":1143},[1145,10060,10061,10069],{},[1148,10062,10063],{},[1151,10064,10065,10067],{},[1154,10066,1159],{},[1312,10068,6905],{},[1172,10070,6908],{"encoding":1174},[3394,10072,10073],{},[1115,10074,10076],{"className":10075},[1139],[1141,10077,10078],{"xmlns":1143},[1145,10079,10080,10092],{},[1148,10081,10082],{},[1151,10083,10084,10086],{},[1154,10085,1159],{},[1148,10087,10088,10090],{},[1312,10089,1610],{},[1161,10091,6501],{},[1172,10093,6958],{"encoding":1174},[3356,10095,10096,10119,10142,10165],{},[3394,10097,10098],{},[1115,10099,10101],{"className":10100},[1139],[1141,10102,10103],{"xmlns":1143},[1145,10104,10105,10117],{},[1148,10106,10107],{},[1151,10108,10109,10111],{},[1154,10110,1159],{},[1148,10112,10113,10115],{},[1161,10114,6501],{},[1154,10116,1196],{},[1172,10118,7120],{"encoding":1174},[3394,10120,10121],{},[1115,10122,10124],{"className":10123},[1139],[1141,10125,10126],{"xmlns":1143},[1145,10127,10128,10140],{},[1148,10129,10130],{},[1151,10131,10132,10134],{},[1154,10133,1159],{},[1148,10135,10136,10138],{},[1161,10137,6501],{},[1312,10139,1489],{},[1172,10141,7144],{"encoding":1174},[3394,10143,10144],{},[1115,10145,10147],{"className":10146},[1139],[1141,10148,10149],{"xmlns":1143},[1145,10150,10151,10163],{},[1148,10152,10153],{},[1151,10154,10155,10157],{},[1154,10156,1159],{},[1148,10158,10159,10161],{},[1161,10160,6501],{},[1312,10162,1610],{},[1172,10164,7168],{"encoding":1174},[3394,10166,10167],{},[1115,10168,10170],{"className":10169},[1139],[1141,10171,10172],{"xmlns":1143},[1145,10173,10174,10178],{},[1148,10175,10176],{},[1154,10177,1159],{},[1172,10179,1159],{"encoding":1174},[1110,10181,10182,10183,1385,10200,10217,10218,10221,10222,1385,10239,10256,10257,10260],{},"Pole ",[1115,10184,10186],{"className":10185},[1139],[1141,10187,10188],{"xmlns":1143},[1145,10189,10190,10198],{},[1148,10191,10192],{},[1151,10193,10194,10196],{},[1154,10195,1159],{},[1312,10197,4850],{},[1172,10199,6773],{"encoding":1174},[1115,10201,10203],{"className":10202},[1139],[1141,10204,10205],{"xmlns":1143},[1145,10206,10207,10215],{},[1148,10208,10209],{},[1151,10210,10211,10213],{},[1154,10212,1159],{},[1312,10214,6905],{},[1172,10216,6908],{"encoding":1174}," jsou ",[1248,10219,10220],{},"shodná"," (prvek zůstal ve stejné variantě), pole ",[1115,10223,10225],{"className":10224},[1139],[1141,10226,10227],{"xmlns":1143},[1145,10228,10229,10237],{},[1148,10230,10231],{},[1151,10232,10233,10235],{},[1154,10234,1159],{},[1312,10236,6791],{},[1172,10238,6794],{"encoding":1174},[1115,10240,10242],{"className":10241},[1139],[1141,10243,10244],{"xmlns":1143},[1145,10245,10246,10254],{},[1148,10247,10248],{},[1151,10249,10250,10252],{},[1154,10251,1159],{},[1312,10253,6884],{},[1172,10255,6887],{"encoding":1174}," jsou\n",[1248,10258,10259],{},"diskordantní"," (prvek mezi měřeními variantu změnil) — jen ta rozhodují o výsledku testu:",[1110,10262,10263],{},[1393,10264],{"alt":10265,"className":10266,"src":10267},"mask-kt-mcnemar-tabulka",[1242,1397],"\u002Fwiki-assets\u002Fmask-kt-mcnemar-tabulka.png",[1110,10269,10270],{},[1248,10271,7377],{},[7379,10273,10274,10311,10392,10450],{},[1127,10275,10276,10310],{},[1115,10277,10279],{"className":10278},[1139],[1141,10280,10281],{"xmlns":1143},[1145,10282,10283,10307],{},[1148,10284,10285,10291,10293,10299,10301],{},[1151,10286,10287,10289],{},[1154,10288,6105],{},[1312,10290,4585],{},[1161,10292,6481],{},[1151,10294,10295,10297],{},[1154,10296,1110],{},[1312,10298,6791],{},[1161,10300,1483],{},[1151,10302,10303,10305],{},[1154,10304,1110],{},[1312,10306,6884],{},[1172,10308,10309],{"encoding":1174},"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.",[1127,10312,7512,10313,10375,10377,10378,10391],{},[1115,10314,10316],{"className":10315},[1139],[1141,10317,10318],{"xmlns":1143,"display":1468},[1145,10319,10320,10372],{},[1148,10321,10322,10328,10330],{},[1603,10323,10324,10326],{},[1154,10325,6125],{},[1312,10327,1610],{},[1161,10329,1483],{},[1485,10331,10332,10356],{},[1148,10333,10334,10336,10342,10344,10350],{},[1161,10335,1164],{"stretchy":1163},[1151,10337,10338,10340],{},[1154,10339,1159],{},[1312,10341,6791],{},[1161,10343,1623],{},[1151,10345,10346,10348],{},[1154,10347,1159],{},[1312,10349,6884],{},[1603,10351,10352,10354],{},[1161,10353,1170],{"stretchy":1163},[1312,10355,1610],{},[1148,10357,10358,10364,10366],{},[1151,10359,10360,10362],{},[1154,10361,1159],{},[1312,10363,6791],{},[1161,10365,3835],{},[1151,10367,10368,10370],{},[1154,10369,1159],{},[1312,10371,6884],{},[1172,10373,10374],{"encoding":1174},"\\chi^2 = \\frac{(n_{12} - n_{21})^2}{n_{12} + n_{21}}",[7670,10376],{},"má asymptoticky Pearsonovo rozdělení o ",[1115,10379,10381],{"className":10380},[1139],[1141,10382,10383],{"xmlns":1143},[1145,10384,10385,10389],{},[1148,10386,10387],{},[1312,10388,1489],{},[1172,10390,1489],{"encoding":1174}," stupni volnosti.",[1127,10393,7829,10394,1176],{},[1115,10395,10397],{"className":10396},[1139],[1141,10398,10399],{"xmlns":1143},[1145,10400,10401,10447],{},[1148,10402,10403,10405,10407,10409,10415,10417,10423,10425,10439,10441,10443,10445],{},[1154,10404,6143],{},[1161,10406,1483],{},[1161,10408,7845],{"stretchy":1163},[1603,10410,10411,10413],{},[1154,10412,6125],{},[1312,10414,1610],{},[1161,10416,6481],{},[1603,10418,10419,10421],{},[1154,10420,6125],{},[1312,10422,1610],{},[1161,10424,5198],{},[1645,10426,10427,10429,10437],{},[1154,10428,6125],{},[1148,10430,10431,10433,10435],{},[1312,10432,1489],{},[1161,10434,1623],{},[1154,10436,7874],{},[1312,10438,1610],{},[1161,10440,1164],{"stretchy":1163},[1312,10442,1489],{},[1161,10444,1170],{"stretchy":1163},[1161,10446,7903],{"stretchy":1163},[1172,10448,10449],{"encoding":1174},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}(1)\\}",[1127,10451,7909,10452,10465,10466,10483,10484,10501],{},[1115,10453,10455],{"className":10454},[1139],[1141,10456,10457],{"xmlns":1143},[1145,10458,10459,10463],{},[1148,10460,10461],{},[1154,10462,6143],{},[1172,10464,6143],{"encoding":1174},", zamítáme ",[1115,10467,10469],{"className":10468},[1139],[1141,10470,10471],{"xmlns":1143},[1145,10472,10473,10481],{},[1148,10474,10475],{},[1151,10476,10477,10479],{},[1154,10478,6105],{},[1312,10480,4585],{},[1172,10482,6110],{"encoding":1174}," a přijímáme ",[1115,10485,10487],{"className":10486},[1139],[1141,10488,10489],{"xmlns":1143},[1145,10490,10491,10499],{},[1148,10492,10493],{},[1151,10494,10495,10497],{},[1154,10496,6105],{},[1312,10498,1489],{},[1172,10500,7508],{"encoding":1174},": zásah rozdělení variant změnil.",[1110,10503,10504,10505,10508,10509,10512,10513,10515],{},"V R počítá tento test funkce ",[2015,10506,10507],{},"mcnemar.test()",". Vzorec výše ",[1248,10510,10511],{},"neobsahuje korekci na kontinuitu"," — aby R vrátilo\npřesně tuto hodnotu, musí se volat s ",[2015,10514,9897],{}," (viz Časté chyby níže).",[1103,10517,10519,10526,10529,10532,10629],{"className":10518,"dataCallout":2447},[1106,2446],[1110,10520,10522,10525],{"className":10521},[1113],[1115,10523],{"className":10524,"ariaHidden":1121},[1118,2454,1120],"Příklad: informační kampaň a zveřejňování na Facebooku",[1110,10527,10528],{},"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.",[1110,10530,10531],{},"Základní soubor: všichni studenti; výběrový soubor: vybraní studenti; měřený znak: zveřejňování (ano \u002F ne).",[3350,10533,10534,10569],{},[3353,10535,10536],{},[3356,10537,10538,10540,10543,10546],{},[3359,10539,9934],{},[3359,10541,10542],{},"nezveřejňuje",[3359,10544,10545],{},"zveřejňuje",[3359,10547,10548],{},[1115,10549,10551],{"className":10550},[1139],[1141,10552,10553],{"xmlns":1143},[1145,10554,10555,10567],{},[1148,10556,10557],{},[1151,10558,10559,10561],{},[1154,10560,1159],{},[1148,10562,10563,10565],{},[1154,10564,1502],{},[1161,10566,6501],{},[1172,10568,6729],{"encoding":1174},[3389,10570,10571,10583,10595],{},[3356,10572,10573,10575,10577,10580],{},[3394,10574,10542],{},[3394,10576,8098],{},[3394,10578,10579],{},"68",[3394,10581,10582],{},"92",[3356,10584,10585,10587,10589,10592],{},[3394,10586,10545],{},[3394,10588,8536],{},[3394,10590,10591],{},"50",[3394,10593,10594],{},"78",[3356,10596,10597,10620,10623,10626],{},[3394,10598,10599],{},[1115,10600,10602],{"className":10601},[1139],[1141,10603,10604],{"xmlns":1143},[1145,10605,10606,10618],{},[1148,10607,10608],{},[1151,10609,10610,10612],{},[1154,10611,1159],{},[1148,10613,10614,10616],{},[1161,10615,6501],{},[1154,10617,1196],{},[1172,10619,7120],{"encoding":1174},[3394,10621,10622],{},"52",[3394,10624,10625],{},"118",[3394,10627,10628],{},"170",[1110,10630,10631,10664],{},[1115,10632,10634],{"className":10633},[1139],[1141,10635,10636],{"xmlns":1143},[1145,10637,10638,10662],{},[1148,10639,10640,10646,10648,10654,10656],{},[1151,10641,10642,10644],{},[1154,10643,6105],{},[1312,10645,4585],{},[1161,10647,6481],{},[1151,10649,10650,10652],{},[1154,10651,1110],{},[1312,10653,6791],{},[1161,10655,1483],{},[1151,10657,10658,10660],{},[1154,10659,1110],{},[1312,10661,6884],{},[1172,10663,10309],{"encoding":1174}," — informační kampaň nemá na chování vliv.",[2020,10666,10668],{"className":2022,"code":10667,"language":71,"meta":2024,"style":2024},"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",[2015,10669,10670,10694,10707,10725,10735,10758,10777],{"__ignoreMap":2024},[1115,10671,10672,10675,10677,10679,10681,10683,10685,10687,10689,10692],{"class":2029,"line":10},[1115,10673,10674],{"class":2032},"tab3",[1115,10676,2036],{"class":2035},[1115,10678,8205],{"class":2039},[1115,10680,1164],{"class":2043},[1115,10682,1784],{"class":2039},[1115,10684,1164],{"class":2043},[1115,10686,8098],{"class":2046},[1115,10688,1199],{"class":2035},[1115,10690,10691],{"class":2046}," 68",[1115,10693,2688],{"class":2035},[1115,10695,10696,10699,10701,10703,10705],{"class":2029,"line":27},[1115,10697,10698],{"class":2046},"                 28",[1115,10700,1199],{"class":2035},[1115,10702,4600],{"class":2046},[1115,10704,1170],{"class":2043},[1115,10706,2688],{"class":2035},[1115,10708,10709,10711,10713,10715,10717,10719,10721,10723],{"class":2029,"line":148},[1115,10710,8279],{"class":2032},[1115,10712,2291],{"class":2035},[1115,10714,4210],{"class":2046},[1115,10716,1199],{"class":2035},[1115,10718,8289],{"class":2032},[1115,10720,2291],{"class":2035},[1115,10722,2409],{"class":2046},[1115,10724,2688],{"class":2035},[1115,10726,10727,10729,10731,10733],{"class":2029,"line":111},[1115,10728,8300],{"class":2032},[1115,10730,2291],{"class":2035},[1115,10732,8305],{"class":2039},[1115,10734,8308],{"class":2043},[1115,10736,10737,10740,10742,10744,10746,10749,10751,10754,10756],{"class":2029,"line":96},[1115,10738,10739],{"class":2032},"                 pred",[1115,10741,2291],{"class":2035},[1115,10743,2040],{"class":2039},[1115,10745,1164],{"class":2043},[1115,10747,10748],{"class":8322},"\"nezverejnuje\"",[1115,10750,1199],{"class":2035},[1115,10752,10753],{"class":8322}," \"zverejnuje\"",[1115,10755,1170],{"class":2043},[1115,10757,2688],{"class":2035},[1115,10759,10760,10763,10765,10767,10769,10771,10773,10775],{"class":2029,"line":89},[1115,10761,10762],{"class":2032},"                 po",[1115,10764,8703],{"class":2035},[1115,10766,2040],{"class":2039},[1115,10768,1164],{"class":2043},[1115,10770,10748],{"class":8322},[1115,10772,1199],{"class":2035},[1115,10774,10753],{"class":8322},[1115,10776,8370],{"class":2043},[1115,10778,10779,10782,10784,10786,10788,10791,10793,10795],{"class":2029,"line":82},[1115,10780,10781],{"class":2039},"mcnemar.test",[1115,10783,1164],{"class":2043},[1115,10785,10674],{"class":2032},[1115,10787,1199],{"class":2035},[1115,10789,10790],{"class":2032}," correct",[1115,10792,2291],{"class":2035},[1115,10794,4612],{"class":2046},[1115,10796,2185],{"class":2043},[2020,10798,10801],{"className":10799,"code":10800,"language":2349,"meta":2024},[2347],"    McNemar's Chi-squared test\n\ndata:  tab3\nMcNemar's chi-squared = 16.667, df = 1, p-value = 4.456e-05\n",[2015,10802,10800],{"__ignoreMap":2024},[1110,10804,10805,10806,8464,10825,10842,10843,10860],{},"P-hodnota ",[1115,10807,10809],{"className":10808},[1139],[1141,10810,10811],{"xmlns":1143},[1145,10812,10813,10822],{},[1148,10814,10815,10818,10820],{},[1312,10816,10817],{},"0,00004456",[1161,10819,8805],{},[1312,10821,8460],{},[1172,10823,10824],{"encoding":1174},"0{,}00004456 \u003C 0{,}05",[1115,10826,10828],{"className":10827},[1139],[1141,10829,10830],{"xmlns":1143},[1145,10831,10832,10840],{},[1148,10833,10834],{},[1151,10835,10836,10838],{},[1154,10837,6105],{},[1312,10839,4585],{},[1172,10841,6110],{"encoding":1174}," zamítáme, přijímáme ",[1115,10844,10846],{"className":10845},[1139],[1141,10847,10848],{"xmlns":1143},[1145,10849,10850,10858],{},[1148,10851,10852],{},[1151,10853,10854,10856],{},[1154,10855,6105],{},[1312,10857,1489],{},[1172,10859,7508],{"encoding":1174}," — informační kampaň měla vliv na změnu\nchování studentů ve zveřejňování údajů na Facebooku.",[1232,10862,5763],{"id":5762},[1103,10864,10868,10876],{"className":10865,"dataCallout":10867},[1106,10866],"callout-warning","warning",[1110,10869,10871,10875],{"className":10870},[1113],[1115,10872],{"className":10873,"ariaHidden":1121},[1118,10874,1120],"i-lucide:triangle-alert","Test nezávislosti na párovaných datech",[1110,10877,10878,10879,10881],{},"Tabulka před\u002Fpo vypadá jako obyčejná kontingenční tabulka, ale ",[2015,10880,7980],{}," 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.",[2020,10883,10885],{"className":2022,"code":10884,"language":71,"meta":2024,"style":2024},"chisq.test(tab3)\n",[2015,10886,10887],{"__ignoreMap":2024},[1115,10888,10889,10891,10893,10895],{"class":2029,"line":10},[1115,10890,8375],{"class":2039},[1115,10892,1164],{"class":2043},[1115,10894,10674],{"class":2032},[1115,10896,2185],{"class":2043},[2020,10898,10901],{"className":10899,"code":10900,"language":2349,"meta":2024},[2347],"    Pearson's Chi-squared test with Yates' continuity correction\n\ndata:  tab3\nX-squared = 1.4793, df = 1, p-value = 0.2239\n",[2015,10902,10900],{"__ignoreMap":2024},[1110,10904,10805,10905,10924,10925,10942,10943,10945,10946,1176],{},[1115,10906,10908],{"className":10907},[1139],[1141,10909,10910],{"xmlns":1143},[1145,10911,10912,10921],{},[1148,10913,10914,10917,10919],{},[1312,10915,10916],{},"0,224",[1161,10918,6225],{},[1312,10920,8460],{},[1172,10922,10923],{"encoding":1174},"0{,}224 > 0{,}05"," by vedla k nezamítnutí ",[1115,10926,10928],{"className":10927},[1139],[1141,10929,10930],{"xmlns":1143},[1145,10931,10932,10940],{},[1148,10933,10934],{},[1151,10935,10936,10938],{},[1154,10937,6105],{},[1312,10939,4585],{},[1172,10941,6110],{"encoding":1174}," — opačný závěr než správný McNemarův test. Na\npárovaná data (stejné prvky měřené dvakrát) vždy patří ",[2015,10944,10507],{},", nikdy ",[2015,10947,7980],{},[1103,10949,10951,10960],{"className":10950,"dataCallout":10867},[1106,10866],[1110,10952,10954,10957,10958],{"className":10953},[1113],[1115,10955],{"className":10956,"ariaHidden":1121},[1118,10874,1120],"Výchozí korekce na kontinuitu v ",[2015,10959,10507],{},[1110,10961,10962,10963,10966],{},"Bez argumentu ",[2015,10964,10965],{},"correct"," R ve výchozím nastavení použije Yatesovu korekci na kontinuitu, která dá jinou\np-hodnotu než nekorigovaný vzorec uvedený výše.",[2020,10968,10970],{"className":2022,"code":10969,"language":71,"meta":2024,"style":2024},"mcnemar.test(tab3)\n",[2015,10971,10972],{"__ignoreMap":2024},[1115,10973,10974,10976,10978,10980],{"class":2029,"line":10},[1115,10975,10781],{"class":2039},[1115,10977,1164],{"class":2043},[1115,10979,10674],{"class":2032},[1115,10981,2185],{"class":2043},[2020,10983,10986],{"className":10984,"code":10985,"language":2349,"meta":2024},[2347],"    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",[2015,10987,10985],{"__ignoreMap":2024},[1110,10989,10990,10991,11009,11010,11029,11030,11043,11044,1176],{},"Oproti nekorigované hodnotě ",[1115,10992,10994],{"className":10993},[1139],[1141,10995,10996],{"xmlns":1143},[1145,10997,10998,11006],{},[1148,10999,11000,11002,11004],{},[1154,11001,1110],{},[1161,11003,1483],{},[1312,11005,10817],{},[1172,11007,11008],{"encoding":1174},"p = 0{,}00004456"," vyjde ",[1115,11011,11013],{"className":11012},[1139],[1141,11014,11015],{"xmlns":1143},[1145,11016,11017,11026],{},[1148,11018,11019,11021,11023],{},[1154,11020,1110],{},[1161,11022,1483],{},[1312,11024,11025],{},"0,00006879",[1172,11027,11028],{"encoding":1174},"p = 0{,}00006879"," — v tomto příkladu obě vedou ke\nstejnému rozhodnutí, ale u hodnot blíž hranici ",[1115,11031,11033],{"className":11032},[1139],[1141,11034,11035],{"xmlns":1143},[1145,11036,11037,11041],{},[1148,11038,11039],{},[1154,11040,7874],{},[1172,11042,7937],{"encoding":1174}," by korekce mohla rozhodnutí změnit. Aby R reprodukovalo\nnekorigovaný vzorec, je třeba vždy volat ",[2015,11045,11046],{},"mcnemar.test(x, correct = FALSE)",[1232,11048,5963],{"id":5962},[1124,11050,11051,11056,11061,11068,11073,11078,11083],{},[1127,11052,11053],{},[1239,11054,1245],{"className":11055,"dataFsResolvedFilePath":1243,"href":1244},[1242],[1127,11057,11058],{},[1239,11059,5307],{"className":11060,"dataFsResolvedFilePath":5305,"href":5306},[1242],[1127,11062,11063],{},[1239,11064,1094],{"className":11065,"dataFsResolvedFilePath":11066,"href":11067},[1242],"topics\u002Fpopisna-statistika.md","\u002Fwiki\u002Fpopisna-statistika",[1127,11069,11070],{},[1239,11071,5978],{"className":11072,"dataFsResolvedFilePath":5976,"href":5977},[1242],[1127,11074,11075],{},[1239,11076,5991],{"className":11077,"dataFsResolvedFilePath":5989,"href":5990},[1242],[1127,11079,11080],{},[1239,11081,6007],{"className":11082,"dataFsResolvedFilePath":6005,"href":6006},[1242],[1127,11084,11085],{},[1239,11086,6015],{"className":11087,"dataFsResolvedFilePath":6013,"href":6014},[1242],[1232,11089,6018],{"id":934},[1110,11091,6021,11092,6026],{},[6023,11093,6025],{},[6028,11095,11096],{},"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":2024,"searchDepth":27,"depth":27,"links":11098},[11099,11100,11101,11102,11103,11104,11105,11106],{"id":6245,"depth":27,"text":6246},{"id":7340,"depth":27,"text":7341},{"id":8903,"depth":27,"text":6191},{"id":9271,"depth":27,"text":6210},{"id":9901,"depth":27,"text":6241},{"id":5762,"depth":27,"text":5763},{"id":5962,"depth":27,"text":5963},{"id":934,"depth":27,"text":6018},{},"\u002Ftopics\u002Fkontingencni-tabulky",{"title":5999,"description":2024},[11111,11112],"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":11117,"title":5978,"body":11118,"course":23,"courses":6040,"created":6041,"description":2024,"extension":6042,"meta":15535,"navigation":6044,"path":15536,"seo":15537,"sources":15538,"stem":15541,"tags":15542,"type":6057,"updated":6041,"__hash__":15543},"topics\u002Ftopics\u002Fnahodne-veliciny-a-rozdeleni.md",{"type":1096,"value":11119,"toc":15523},[11120,11123,11403,11407,11638,11641,11708,11712,11719,11726,11884,11922,11925,12159,12162,12240,12294,12392,12396,12498,12501,12505,12511,12567,12570,12578,12729,12736,12788,12818,12932,12935,12983,13144,13199,13206,13313,13374,13378,13479,13481,13518,13524,13583,13632,13639,13674,13680,13683,13731,13738,13798,13804,13807,13870,13877,13914,13920,13923,13927,13953,14283,14320,14374,14501,14507,14511,14518,14537,14642,14686,14705,14800,14817,14859,15034,15041,15044,15047,15201,15204,15279,15285,15287,15473,15475,15514,15516,15520],[1099,11121,5978],{"id":11122},"náhodné-veličiny-a-rozdělení-pravděpodobnosti",[1103,11124,11126,11132],{"className":11125,"dataCallout":1108},[1106,1107],[1110,11127,11129,1122],{"className":11128},[1113],[1115,11130],{"className":11131,"ariaHidden":1121},[1118,1119,1120],[1124,11133,11134,11143,11244,11311,11391],{},[1127,11135,11136,11137,11139,11140,11142],{},"Náhodná veličina je funkce, která výsledkům pokusu přiřazuje reálná čísla; rozlišujeme ",[1248,11138,1276],{}," (izolované hodnoty s nenulovou pravděpodobností) a ",[1248,11141,1280],{}," (hodnoty z intervalu, každý bod má nulovou pravděpodobnost).",[1127,11144,11145,11146,1932,11149,11185,11186,11222,11223,11243],{},"Každou náhodnou veličinu popisuje ",[1248,11147,11148],{},"distribuční funkce",[1115,11150,11152],{"className":11151},[1139],[1141,11153,11154],{"xmlns":1143},[1145,11155,11156,11182],{},[1148,11157,11158,11160,11162,11164,11166,11168,11171,11173,11175,11178,11180],{},[1154,11159,1156],{},[1161,11161,1164],{"stretchy":1163},[1154,11163,1167],{},[1161,11165,1170],{"stretchy":1163},[1161,11167,1483],{},[1154,11169,11170],{},"P",[1161,11172,1164],{"stretchy":1163},[1154,11174,1436],{},[1161,11176,11177],{},"≤",[1154,11179,1167],{},[1161,11181,1170],{"stretchy":1163},[1172,11183,11184],{"encoding":1174},"F(x) = P(X \\le x)","; u spojité veličiny platí ",[1115,11187,11189],{"className":11188},[1139],[1141,11190,11191],{"xmlns":1143},[1145,11192,11193,11219],{},[1148,11194,11195,11203,11205,11207,11209,11211,11213,11215,11217],{},[1603,11196,11197,11199],{},[1154,11198,1156],{},[1161,11200,11202],{"mathvariant":1869,"lspace":11201,"rspace":11201},"0em","′",[1161,11204,1164],{"stretchy":1163},[1154,11206,1167],{},[1161,11208,1170],{"stretchy":1163},[1161,11210,1483],{},[1154,11212,1213],{},[1161,11214,1164],{"stretchy":1163},[1154,11216,1167],{},[1161,11218,1170],{"stretchy":1163},[1172,11220,11221],{"encoding":1174},"F'(x) = f(x)",", kde ",[1115,11224,11226],{"className":11225},[1139],[1141,11227,11228],{"xmlns":1143},[1145,11229,11230,11240],{},[1148,11231,11232,11234,11236,11238],{},[1154,11233,1213],{},[1161,11235,1164],{"stretchy":1163},[1154,11237,1167],{},[1161,11239,1170],{"stretchy":1163},[1172,11241,11242],{"encoding":1174},"f(x)"," je hustota pravděpodobnosti.",[1127,11245,11246,11247,1176],{},"Pravděpodobnost na intervalu se počítá jako ",[1115,11248,11250],{"className":11249},[1139],[1141,11251,11252],{"xmlns":1143},[1145,11253,11254,11308],{},[1148,11255,11256,11258,11260,11266,11268,11270,11272,11278,11280,11282,11284,11286,11292,11294,11296,11298,11300,11306],{},[1154,11257,11170],{},[1161,11259,1164],{"stretchy":1163},[1151,11261,11262,11264],{},[1154,11263,1167],{},[1312,11265,1489],{},[1161,11267,8805],{},[1154,11269,1436],{},[1161,11271,8805],{},[1151,11273,11274,11276],{},[1154,11275,1167],{},[1312,11277,1610],{},[1161,11279,1170],{"stretchy":1163},[1161,11281,1483],{},[1154,11283,1156],{},[1161,11285,1164],{"stretchy":1163},[1151,11287,11288,11290],{},[1154,11289,1167],{},[1312,11291,1610],{},[1161,11293,1170],{"stretchy":1163},[1161,11295,1623],{},[1154,11297,1156],{},[1161,11299,1164],{"stretchy":1163},[1151,11301,11302,11304],{},[1154,11303,1167],{},[1312,11305,1489],{},[1161,11307,1170],{"stretchy":1163},[1172,11309,11310],{"encoding":1174},"P(x_1 \u003C X \u003C x_2) = F(x_2) - F(x_1)",[1127,11312,11313,1932,11316,11347,11348,1381,11351,1381,11354,11357,11358,11372,11373,1176],{},[1248,11314,11315],{},"Normální rozdělení",[1115,11317,11319],{"className":11318},[1139],[1141,11320,11321],{"xmlns":1143},[1145,11322,11323,11344],{},[1148,11324,11325,11328,11330,11333,11335,11342],{},[1154,11326,11327],{},"N",[1161,11329,1164],{"stretchy":1163},[1154,11331,11332],{},"μ",[1161,11334,3288],{"separator":1121},[1603,11336,11337,11340],{},[1154,11338,11339],{},"σ",[1312,11341,1610],{},[1161,11343,1170],{"stretchy":1163},[1172,11345,11346],{"encoding":1174},"N(\\mu; \\sigma^2)"," je nejdůležitější spojité rozdělení; v R ho počítáme funkcemi ",[2015,11349,11350],{},"dnorm",[2015,11352,11353],{},"pnorm",[2015,11355,11356],{},"qnorm"," — R jako parametr očekává směrodatnou odchylku ",[1115,11359,11361],{"className":11360},[1139],[1141,11362,11363],{"xmlns":1143},[1145,11364,11365,11369],{},[1148,11366,11367],{},[1154,11368,11339],{},[1172,11370,11371],{"encoding":1174},"\\sigma",", ne rozptyl ",[1115,11374,11376],{"className":11375},[1139],[1141,11377,11378],{"xmlns":1143},[1145,11379,11380,11388],{},[1148,11381,11382],{},[1603,11383,11384,11386],{},[1154,11385,11339],{},[1312,11387,1610],{},[1172,11389,11390],{"encoding":1174},"\\sigma^2",[1127,11392,11393,1381,11396,1385,11399,11402],{},[1248,11394,11395],{},"Studentovo",[1248,11397,11398],{},"Pearsonovo (χ²)",[1248,11400,11401],{},"Fisherovo-Snedecorovo"," rozdělení slouží jako nástroj pro pozdější konstrukci intervalů spolehlivosti a testování hypotéz.",[1232,11404,11406],{"id":11405},"náhodná-veličina","Náhodná veličina",[1110,11408,11409,11412,11413,11428,11429,1932,11431,11444,11445,11465,11466,11222,11479,11503,11504,1381,11517,1381,11531,11545,11546,1381,11559,1381,11572,11585,11586,11599,11600,11613,11614,1176],{},[1239,11410,1245],{"className":11411,"dataFsResolvedFilePath":1243,"href":1244},[1242]," pracuje s veličinami, jejichž hodnota závisí na náhodě. Formálně: uvažujeme základní prostor ",[1115,11414,11416],{"className":11415},[1139],[1141,11417,11418],{"xmlns":1143},[1145,11419,11420,11425],{},[1148,11421,11422],{},[1154,11423,11424],{"mathvariant":1869},"Ω",[1172,11426,11427],{"encoding":1174},"\\Omega"," přiřazený výsledkům pokusu. ",[1248,11430,11406],{},[1115,11432,11434],{"className":11433},[1139],[1141,11435,11436],{"xmlns":1143},[1145,11437,11438,11442],{},[1148,11439,11440],{},[1154,11441,1436],{},[1172,11443,1436],{"encoding":1174}," je funkce, která prvkům ",[1115,11446,11448],{"className":11447},[1139],[1141,11449,11450],{"xmlns":1143},[1145,11451,11452,11462],{},[1148,11453,11454,11457,11460],{},[1154,11455,11456],{},"ω",[1161,11458,11459],{},"∈",[1154,11461,11424],{"mathvariant":1869},[1172,11463,11464],{"encoding":1174},"\\omega \\in \\Omega"," přiřazuje reálná čísla ",[1115,11467,11469],{"className":11468},[1139],[1141,11470,11471],{"xmlns":1143},[1145,11472,11473,11477],{},[1148,11474,11475],{},[1154,11476,1167],{},[1172,11478,1167],{"encoding":1174},[1115,11480,11482],{"className":11481},[1139],[1141,11483,11484],{"xmlns":1143},[1145,11485,11486,11500],{},[1148,11487,11488,11490,11492,11494,11496,11498],{},[1154,11489,1167],{},[1161,11491,1483],{},[1154,11493,1436],{},[1161,11495,1164],{"stretchy":1163},[1154,11497,11456],{},[1161,11499,1170],{"stretchy":1163},[1172,11501,11502],{"encoding":1174},"x = X(\\omega)",". Náhodné veličiny značíme velkými písmeny (",[1115,11505,11507],{"className":11506},[1139],[1141,11508,11509],{"xmlns":1143},[1145,11510,11511,11515],{},[1148,11512,11513],{},[1154,11514,1436],{},[1172,11516,1436],{"encoding":1174},[1115,11518,11520],{"className":11519},[1139],[1141,11521,11522],{"xmlns":1143},[1145,11523,11524,11529],{},[1148,11525,11526],{},[1154,11527,11528],{},"Y",[1172,11530,11528],{"encoding":1174},[1115,11532,11534],{"className":11533},[1139],[1141,11535,11536],{"xmlns":1143},[1145,11537,11538,11543],{},[1148,11539,11540],{},[1154,11541,11542],{},"T",[1172,11544,11542],{"encoding":1174},"), jejich konkrétní hodnoty odpovídajícími malými písmeny (",[1115,11547,11549],{"className":11548},[1139],[1141,11550,11551],{"xmlns":1143},[1145,11552,11553,11557],{},[1148,11554,11555],{},[1154,11556,1167],{},[1172,11558,1167],{"encoding":1174},[1115,11560,11562],{"className":11561},[1139],[1141,11563,11564],{"xmlns":1143},[1145,11565,11566,11570],{},[1148,11567,11568],{},[1154,11569,1528],{},[1172,11571,1528],{"encoding":1174},[1115,11573,11575],{"className":11574},[1139],[1141,11576,11577],{"xmlns":1143},[1145,11578,11579,11583],{},[1148,11580,11581],{},[1154,11582,1807],{},[1172,11584,1807],{"encoding":1174},"); pravděpodobnost, že ",[1115,11587,11589],{"className":11588},[1139],[1141,11590,11591],{"xmlns":1143},[1145,11592,11593,11597],{},[1148,11594,11595],{},[1154,11596,1436],{},[1172,11598,1436],{"encoding":1174}," nabyla hodnoty ",[1115,11601,11603],{"className":11602},[1139],[1141,11604,11605],{"xmlns":1143},[1145,11606,11607,11611],{},[1148,11608,11609],{},[1154,11610,1167],{},[1172,11612,1167],{"encoding":1174},", zapisujeme ",[1115,11615,11617],{"className":11616},[1139],[1141,11618,11619],{"xmlns":1143},[1145,11620,11621,11635],{},[1148,11622,11623,11625,11627,11629,11631,11633],{},[1154,11624,11170],{},[1161,11626,1164],{"stretchy":1163},[1154,11628,1436],{},[1161,11630,1483],{},[1154,11632,1167],{},[1161,11634,1170],{"stretchy":1163},[1172,11636,11637],{"encoding":1174},"P(X = x)",[1110,11639,11640],{},"Podle typu hodnot, kterých náhodná veličina nabývá, rozlišujeme dva typy:",[1124,11642,11643,11702],{},[1127,11644,11645,11648,11649,11662,11663,11701],{},[1248,11646,11647],{},"Diskrétní náhodná veličina"," — prvky ",[1115,11650,11652],{"className":11651},[1139],[1141,11653,11654],{"xmlns":1143},[1145,11655,11656,11660],{},[1148,11657,11658],{},[1154,11659,11424],{"mathvariant":1869},[1172,11661,11427],{"encoding":1174}," se zobrazí na osu reálných čísel jako izolované body ",[1115,11664,11666],{"className":11665},[1139],[1141,11667,11668],{"xmlns":1143},[1145,11669,11670,11698],{},[1148,11671,11672,11678,11680,11686,11688,11690,11692],{},[1151,11673,11674,11676],{},[1154,11675,1167],{},[1312,11677,1489],{},[1161,11679,1199],{"separator":1121},[1151,11681,11682,11684],{},[1154,11683,1167],{},[1312,11685,1610],{},[1161,11687,1199],{"separator":1121},[1161,11689,3022],{},[1161,11691,1199],{"separator":1121},[1151,11693,11694,11696],{},[1154,11695,1167],{},[1154,11697,3064],{},[1172,11699,11700],{"encoding":1174},"x_1, x_2, \\dots, x_k",", přičemž každý z nich má nenulovou pravděpodobnost. Příklad: počet bodů při hodu kostkou, počet studentů na cvičení.",[1127,11703,11704,11707],{},[1248,11705,11706],{},"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.",[1232,11709,11711],{"id":11710},"distribuční-funkce","Distribuční funkce",[1110,11713,11714,11715,11718],{},"Náhodná veličina nabývá při pokusu určité hodnoty, aniž bychom předem věděli, které. Při opakování pokusu se ale projevují zákonitosti, které popisují ",[1248,11716,11717],{},"zákony rozdělení",". Nejobecnějším z nich je distribuční funkce.",[1110,11720,11721],{},[1393,11722],{"alt":11723,"className":11724,"src":11725},"mask-nv-distribucni-funkce",[1242,1397],"\u002Fwiki-assets\u002Fmask-nv-distribucni-funkce.png",[1103,11727,11730,11737],{"className":11728,"dataCallout":654},[1106,11729],"callout-info",[1110,11731,11733,11736],{"className":11732},[1113],[1115,11734],{"className":11735,"ariaHidden":1121},[1118,1119,1120],"Definice",[1110,11738,11739,11740,11753,11754,11774,11775,11788,11789,11825,11844,11845,11858,11859,1176],{},"Distribuční funkcí náhodné veličiny ",[1115,11741,11743],{"className":11742},[1139],[1141,11744,11745],{"xmlns":1143},[1145,11746,11747,11751],{},[1148,11748,11749],{},[1154,11750,1436],{},[1172,11752,1436],{"encoding":1174}," nazýváme reálnou funkci ",[1115,11755,11757],{"className":11756},[1139],[1141,11758,11759],{"xmlns":1143},[1145,11760,11761,11771],{},[1148,11762,11763,11765,11767,11769],{},[1154,11764,1156],{},[1161,11766,1164],{"stretchy":1163},[1154,11768,1167],{},[1161,11770,1170],{"stretchy":1163},[1172,11772,11773],{"encoding":1174},"F(x)"," definovanou pro každé reálné číslo ",[1115,11776,11778],{"className":11777},[1139],[1141,11779,11780],{"xmlns":1143},[1145,11781,11782,11786],{},[1148,11783,11784],{},[1154,11785,1167],{},[1172,11787,1167],{"encoding":1174}," jako\n",[1115,11790,11792],{"className":11791},[1139],[1141,11793,11794],{"xmlns":1143},[1145,11795,11796,11822],{},[1148,11797,11798,11800,11802,11804,11806,11808,11810,11812,11814,11816,11818,11820],{},[1154,11799,1156],{},[1161,11801,1164],{"stretchy":1163},[1154,11803,1167],{},[1161,11805,1170],{"stretchy":1163},[1161,11807,1483],{},[1154,11809,11170],{},[1161,11811,1164],{"stretchy":1163},[1154,11813,1436],{},[1161,11815,11177],{},[1154,11817,1167],{},[1161,11819,1170],{"stretchy":1163},[1154,11821,1176],{"mathvariant":1869},[1172,11823,11824],{"encoding":1174},"F(x) = P(X \\le x).",[1115,11826,11828],{"className":11827},[1139],[1141,11829,11830],{"xmlns":1143},[1145,11831,11832,11842],{},[1148,11833,11834,11836,11838,11840],{},[1154,11835,1156],{},[1161,11837,1164],{"stretchy":1163},[1154,11839,1167],{},[1161,11841,1170],{"stretchy":1163},[1172,11843,11773],{"encoding":1174}," tedy vyjadřuje pravděpodobnost, s jakou ",[1115,11846,11848],{"className":11847},[1139],[1141,11849,11850],{"xmlns":1143},[1145,11851,11852,11856],{},[1148,11853,11854],{},[1154,11855,1436],{},[1172,11857,1436],{"encoding":1174}," nabude hodnoty z intervalu ",[1115,11860,11862],{"className":11861},[1139],[1141,11863,11864],{"xmlns":1143},[1145,11865,11866,11881],{},[1148,11867,11868,11870,11872,11875,11877,11879],{},[1161,11869,1164],{"stretchy":1163},[1161,11871,1623],{},[1154,11873,11874],{"mathvariant":1869},"∞",[1161,11876,1199],{"separator":1121},[1154,11878,1167],{},[1161,11880,4102],{"stretchy":1163},[1172,11882,11883],{"encoding":1174},"(-\\infty, x\\rangle",[1110,11885,11886,11887,11900,11901,11921],{},"Značí-li například ",[1115,11888,11890],{"className":11889},[1139],[1141,11891,11892],{"xmlns":1143},[1145,11893,11894,11898],{},[1148,11895,11896],{},[1154,11897,1436],{},[1172,11899,1436],{"encoding":1174}," výšku mužů v populaci, pak ",[1115,11902,11904],{"className":11903},[1139],[1141,11905,11906],{"xmlns":1143},[1145,11907,11908,11918],{},[1148,11909,11910,11912,11914,11916],{},[1154,11911,1156],{},[1161,11913,1164],{"stretchy":1163},[1312,11915,4879],{},[1161,11917,1170],{"stretchy":1163},[1172,11919,11920],{"encoding":1174},"F(175)"," je pravděpodobnost, že muž měří nejvýše 175 cm.",[1110,11923,11924],{},"Pro distribuční funkci vždy platí:",[1124,11926,11927,11957,12015,12075],{},[1127,11928,11929,1199],{},[1115,11930,11932],{"className":11931},[1139],[1141,11933,11934],{"xmlns":1143},[1145,11935,11936,11954],{},[1148,11937,11938,11940,11942,11944,11946,11948,11950,11952],{},[1312,11939,4585],{},[1161,11941,11177],{},[1154,11943,1156],{},[1161,11945,1164],{"stretchy":1163},[1154,11947,1167],{},[1161,11949,1170],{"stretchy":1163},[1161,11951,11177],{},[1312,11953,1489],{},[1172,11955,11956],{"encoding":1174},"0 \\le F(x) \\le 1",[1127,11958,11959,11960,1199],{},"je neklesající: ",[1115,11961,11963],{"className":11962},[1139],[1141,11964,11965],{"xmlns":1143},[1145,11966,11967,12012],{},[1148,11968,11969,11975,11977,11983,11986,11988,11990,11996,11998,12000,12002,12004,12010],{},[1151,11970,11971,11973],{},[1154,11972,1167],{},[1312,11974,1489],{},[1161,11976,11177],{},[1151,11978,11979,11981],{},[1154,11980,1167],{},[1312,11982,1610],{},[1161,11984,11985],{},"⇒",[1154,11987,1156],{},[1161,11989,1164],{"stretchy":1163},[1151,11991,11992,11994],{},[1154,11993,1167],{},[1312,11995,1489],{},[1161,11997,1170],{"stretchy":1163},[1161,11999,11177],{},[1154,12001,1156],{},[1161,12003,1164],{"stretchy":1163},[1151,12005,12006,12008],{},[1154,12007,1167],{},[1312,12009,1610],{},[1161,12011,1170],{"stretchy":1163},[1172,12013,12014],{"encoding":1174},"x_1 \\le x_2 \\Rightarrow F(x_1) \\le F(x_2)",[1127,12016,12017,12018,1199],{},"je spojitá zprava: ",[1115,12019,12021],{"className":12020},[1139],[1141,12022,12023],{"xmlns":1143},[1145,12024,12025,12072],{},[1148,12026,12027,12050,12052,12054,12056,12058,12060,12062,12064,12066,12068,12070],{},[1151,12028,12029,12036],{},[1148,12030,12031,12034],{},[1154,12032,12033],{},"lim",[1161,12035,1761],{},[1148,12037,12038,12041,12044],{},[1154,12039,12040],{},"h",[1161,12042,12043],{},"→",[1603,12045,12046,12048],{},[1312,12047,4585],{},[1161,12049,3835],{},[1154,12051,1156],{},[1161,12053,1164],{"stretchy":1163},[1154,12055,1167],{},[1161,12057,3835],{},[1154,12059,12040],{},[1161,12061,1170],{"stretchy":1163},[1161,12063,1483],{},[1154,12065,1156],{},[1161,12067,1164],{"stretchy":1163},[1154,12069,1167],{},[1161,12071,1170],{"stretchy":1163},[1172,12073,12074],{"encoding":1174},"\\lim_{h \\to 0^+} F(x+h) = F(x)",[1127,12076,12077,1381,12119,1176],{},[1115,12078,12080],{"className":12079},[1139],[1141,12081,12082],{"xmlns":1143},[1145,12083,12084,12116],{},[1148,12085,12086,12104,12106,12108,12110,12112,12114],{},[1151,12087,12088,12094],{},[1148,12089,12090,12092],{},[1154,12091,12033],{},[1161,12093,1761],{},[1148,12095,12096,12098,12100,12102],{},[1154,12097,1167],{},[1161,12099,12043],{},[1161,12101,1623],{},[1154,12103,11874],{"mathvariant":1869},[1154,12105,1156],{},[1161,12107,1164],{"stretchy":1163},[1154,12109,1167],{},[1161,12111,1170],{"stretchy":1163},[1161,12113,1483],{},[1312,12115,4585],{},[1172,12117,12118],{"encoding":1174},"\\lim_{x \\to -\\infty} F(x) = 0",[1115,12120,12122],{"className":12121},[1139],[1141,12123,12124],{"xmlns":1143},[1145,12125,12126,12156],{},[1148,12127,12128,12144,12146,12148,12150,12152,12154],{},[1151,12129,12130,12136],{},[1148,12131,12132,12134],{},[1154,12133,12033],{},[1161,12135,1761],{},[1148,12137,12138,12140,12142],{},[1154,12139,1167],{},[1161,12141,12043],{},[1154,12143,11874],{"mathvariant":1869},[1154,12145,1156],{},[1161,12147,1164],{"stretchy":1163},[1154,12149,1167],{},[1161,12151,1170],{"stretchy":1163},[1161,12153,1483],{},[1312,12155,1489],{},[1172,12157,12158],{"encoding":1174},"\\lim_{x \\to \\infty} F(x) = 1",[1110,12160,12161],{},"U spojité náhodné veličiny je distribuční funkce svázaná s hustotou pravděpodobnosti vztahem",[1115,12163,12165],{"className":12164},[1139],[1141,12166,12167],{"xmlns":1143,"display":1468},[1145,12168,12169,12237],{},[1148,12170,12171,12177,12179,12181,12183,12185,12187,12189,12191,12193,12195,12197,12199,12201,12203,12205,12207,12220,12222,12224,12226,12228,12230,12233,12235],{},[1603,12172,12173,12175],{},[1154,12174,1156],{},[1161,12176,11202],{"mathvariant":1869,"lspace":11201,"rspace":11201},[1161,12178,1164],{"stretchy":1163},[1154,12180,1167],{},[1161,12182,1170],{"stretchy":1163},[1161,12184,1483],{},[1154,12186,1213],{},[1161,12188,1164],{"stretchy":1163},[1154,12190,1167],{},[1161,12192,1170],{"stretchy":1163},[1161,12194,1199],{"separator":1121},[1516,12196],{"width":1518},[1154,12198,1156],{},[1161,12200,1164],{"stretchy":1163},[1154,12202,1167],{},[1161,12204,1170],{"stretchy":1163},[1161,12206,1483],{},[1645,12208,12209,12212,12218],{},[1161,12210,12211],{},"∫",[1148,12213,12214,12216],{},[1161,12215,1623],{},[1154,12217,11874],{"mathvariant":1869},[1154,12219,1167],{},[1154,12221,1213],{},[1161,12223,1164],{"stretchy":1163},[1154,12225,1807],{},[1161,12227,1170],{"stretchy":1163},[1316,12229,1318],{},[1154,12231,12232],{},"d",[1154,12234,1807],{},[1154,12236,1176],{"mathvariant":1869},[1172,12238,12239],{"encoding":1174},"F'(x) = f(x), \\qquad F(x) = \\int_{-\\infty}^{x} f(t)\\,dt.",[1110,12241,12242,12243,12256,12257,1385,12275,12293],{},"Pravděpodobnost, že ",[1115,12244,12246],{"className":12245},[1139],[1141,12247,12248],{"xmlns":1143},[1145,12249,12250,12254],{},[1148,12251,12252],{},[1154,12253,1436],{},[1172,12255,1436],{"encoding":1174}," padne mezi body ",[1115,12258,12260],{"className":12259},[1139],[1141,12261,12262],{"xmlns":1143},[1145,12263,12264,12272],{},[1148,12265,12266],{},[1151,12267,12268,12270],{},[1154,12269,1167],{},[1312,12271,1489],{},[1172,12273,12274],{"encoding":1174},"x_1",[1115,12276,12278],{"className":12277},[1139],[1141,12279,12280],{"xmlns":1143},[1145,12281,12282,12290],{},[1148,12283,12284],{},[1151,12285,12286,12288],{},[1154,12287,1167],{},[1312,12289,1610],{},[1172,12291,12292],{"encoding":1174},"x_2",", se pak počítá jako",[1115,12295,12297],{"className":12296},[1139],[1141,12298,12299],{"xmlns":1143,"display":1468},[1145,12300,12301,12389],{},[1148,12302,12303,12305,12307,12313,12315,12317,12319,12325,12327,12329,12345,12347,12349,12351,12353,12355,12357,12359,12361,12363,12365,12371,12373,12375,12377,12379,12385,12387],{},[1154,12304,11170],{},[1161,12306,1164],{"stretchy":1163},[1151,12308,12309,12311],{},[1154,12310,1167],{},[1312,12312,1489],{},[1161,12314,8805],{},[1154,12316,1436],{},[1161,12318,8805],{},[1151,12320,12321,12323],{},[1154,12322,1167],{},[1312,12324,1610],{},[1161,12326,1170],{"stretchy":1163},[1161,12328,1483],{},[1645,12330,12331,12333,12339],{},[1161,12332,12211],{},[1151,12334,12335,12337],{},[1154,12336,1167],{},[1312,12338,1489],{},[1151,12340,12341,12343],{},[1154,12342,1167],{},[1312,12344,1610],{},[1154,12346,1213],{},[1161,12348,1164],{"stretchy":1163},[1154,12350,1807],{},[1161,12352,1170],{"stretchy":1163},[1316,12354,1318],{},[1154,12356,12232],{},[1154,12358,1807],{},[1161,12360,1483],{},[1154,12362,1156],{},[1161,12364,1164],{"stretchy":1163},[1151,12366,12367,12369],{},[1154,12368,1167],{},[1312,12370,1610],{},[1161,12372,1170],{"stretchy":1163},[1161,12374,1623],{},[1154,12376,1156],{},[1161,12378,1164],{"stretchy":1163},[1151,12380,12381,12383],{},[1154,12382,1167],{},[1312,12384,1489],{},[1161,12386,1170],{"stretchy":1163},[1154,12388,1176],{"mathvariant":1869},[1172,12390,12391],{"encoding":1174},"P(x_1 \u003C X \u003C x_2) = \\int_{x_1}^{x_2} f(t)\\,dt = F(x_2) - F(x_1).",[1232,12393,12395],{"id":12394},"hustota-pravděpodobnosti","Hustota pravděpodobnosti",[1103,12397,12399,12405],{"className":12398,"dataCallout":654},[1106,11729],[1110,12400,12402,11736],{"className":12401},[1113],[1115,12403],{"className":12404,"ariaHidden":1121},[1118,1119,1120],[1110,12406,12407,12408,12427,12428,12441,12442,12455,12456,1176],{},"Hustota pravděpodobnosti ",[1115,12409,12411],{"className":12410},[1139],[1141,12412,12413],{"xmlns":1143},[1145,12414,12415,12425],{},[1148,12416,12417,12419,12421,12423],{},[1154,12418,1213],{},[1161,12420,1164],{"stretchy":1163},[1154,12422,1167],{},[1161,12424,1170],{"stretchy":1163},[1172,12426,11242],{"encoding":1174}," určuje, jak jsou hodnoty spojité náhodné veličiny ",[1115,12429,12431],{"className":12430},[1139],[1141,12432,12433],{"xmlns":1143},[1145,12434,12435,12439],{},[1148,12436,12437],{},[1154,12438,1436],{},[1172,12440,1436],{"encoding":1174}," nahuštěny v okolí bodu ",[1115,12443,12445],{"className":12444},[1139],[1141,12446,12447],{"xmlns":1143},[1145,12448,12449,12453],{},[1148,12450,12451],{},[1154,12452,1167],{},[1172,12454,1167],{"encoding":1174},". Je vždy nezáporná a platí pro ni ",[1115,12457,12459],{"className":12458},[1139],[1141,12460,12461],{"xmlns":1143},[1145,12462,12463,12495],{},[1148,12464,12465,12477,12479,12481,12483,12485,12487,12489,12491,12493],{},[1645,12466,12467,12469,12475],{},[1161,12468,12211],{},[1148,12470,12471,12473],{},[1161,12472,1623],{},[1154,12474,11874],{"mathvariant":1869},[1154,12476,11874],{"mathvariant":1869},[1154,12478,1213],{},[1161,12480,1164],{"stretchy":1163},[1154,12482,1167],{},[1161,12484,1170],{"stretchy":1163},[1316,12486,1318],{},[1154,12488,12232],{},[1154,12490,1167],{},[1161,12492,1483],{},[1312,12494,1489],{},[1172,12496,12497],{"encoding":1174},"\\int_{-\\infty}^{\\infty} f(x)\\,dx = 1",[1110,12499,12500],{},"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.",[1232,12502,12504],{"id":12503},"charakteristiky-spojité-náhodné-veličiny","Charakteristiky spojité náhodné veličiny",[1110,12506,12507,12510],{},[1248,12508,12509],{},"Střední hodnota"," je nejdůležitější charakteristika náhodné veličiny:",[1115,12512,12514],{"className":12513},[1139],[1141,12515,12516],{"xmlns":1143,"display":1468},[1145,12517,12518,12564],{},[1148,12519,12520,12523,12525,12527,12529,12531,12543,12545,12548,12550,12552,12554,12556,12558,12560,12562],{},[1154,12521,12522],{},"E",[1161,12524,1164],{"stretchy":1163},[1154,12526,1436],{},[1161,12528,1170],{"stretchy":1163},[1161,12530,1483],{},[1645,12532,12533,12535,12541],{},[1161,12534,12211],{},[1148,12536,12537,12539],{},[1161,12538,1623],{},[1154,12540,11874],{"mathvariant":1869},[1154,12542,11874],{"mathvariant":1869},[1154,12544,1167],{},[1161,12546,12547],{},"⋅",[1154,12549,1213],{},[1161,12551,1164],{"stretchy":1163},[1154,12553,1167],{},[1161,12555,1170],{"stretchy":1163},[1316,12557,1318],{},[1154,12559,12232],{},[1154,12561,1167],{},[1154,12563,1176],{"mathvariant":1869},[1172,12565,12566],{"encoding":1174},"E(X) = \\int_{-\\infty}^{\\infty} x \\cdot f(x)\\,dx.",[1110,12568,12569],{},"Je to číslo, kolem něhož kolísají výběrové průměry vypočtené ze sérií pozorovaných hodnot náhodné veličiny.",[1110,12571,12572,1385,12575,6481],{},[1248,12573,12574],{},"Rozptyl",[1248,12576,12577],{},"směrodatná odchylka",[1115,12579,12581],{"className":12580},[1139],[1141,12582,12583],{"xmlns":1143,"display":1468},[1145,12584,12585,12726],{},[1148,12586,12587,12590,12592,12594,12596,12598,12610,12613,12615,12617,12619,12621,12623,12625,12632,12634,12636,12638,12640,12642,12644,12646,12648,12660,12666,12668,12670,12672,12674,12676,12678,12680,12682,12684,12686,12688,12690,12692,12698,12700,12702,12704,12706,12708,12710,12712,12724],{},[1154,12588,12589],{},"D",[1161,12591,1164],{"stretchy":1163},[1154,12593,1436],{},[1161,12595,1170],{"stretchy":1163},[1161,12597,1483],{},[1645,12599,12600,12602,12608],{},[1161,12601,12211],{},[1148,12603,12604,12606],{},[1161,12605,1623],{},[1154,12607,11874],{"mathvariant":1869},[1154,12609,11874],{"mathvariant":1869},[1161,12611,12612],{"stretchy":1163},"[",[1154,12614,1167],{},[1161,12616,1623],{},[1154,12618,12522],{},[1161,12620,1164],{"stretchy":1163},[1154,12622,1436],{},[1161,12624,1170],{"stretchy":1163},[1603,12626,12627,12630],{},[1161,12628,12629],{"stretchy":1163},"]",[1312,12631,1610],{},[1154,12633,1213],{},[1161,12635,1164],{"stretchy":1163},[1154,12637,1167],{},[1161,12639,1170],{"stretchy":1163},[1316,12641,1318],{},[1154,12643,12232],{},[1154,12645,1167],{},[1161,12647,1483],{},[1645,12649,12650,12652,12658],{},[1161,12651,12211],{},[1148,12653,12654,12656],{},[1161,12655,1623],{},[1154,12657,11874],{"mathvariant":1869},[1154,12659,11874],{"mathvariant":1869},[1603,12661,12662,12664],{},[1154,12663,1167],{},[1312,12665,1610],{},[1154,12667,1213],{},[1161,12669,1164],{"stretchy":1163},[1154,12671,1167],{},[1161,12673,1170],{"stretchy":1163},[1316,12675,1318],{},[1154,12677,12232],{},[1154,12679,1167],{},[1161,12681,1623],{},[1161,12683,12612],{"stretchy":1163},[1154,12685,12522],{},[1161,12687,1164],{"stretchy":1163},[1154,12689,1436],{},[1161,12691,1170],{"stretchy":1163},[1603,12693,12694,12696],{},[1161,12695,12629],{"stretchy":1163},[1312,12697,1610],{},[1161,12699,1199],{"separator":1121},[1516,12701],{"width":1518},[1154,12703,11339],{},[1161,12705,1164],{"stretchy":1163},[1154,12707,1436],{},[1161,12709,1170],{"stretchy":1163},[1161,12711,1483],{},[1678,12713,12714],{},[1148,12715,12716,12718,12720,12722],{},[1154,12717,12589],{},[1161,12719,1164],{"stretchy":1163},[1154,12721,1436],{},[1161,12723,1170],{"stretchy":1163},[1154,12725,1176],{"mathvariant":1869},[1172,12727,12728],{"encoding":1174},"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)}.",[1110,12730,12731,12732,12735],{},"Směrodatná odchylka udává, jak moc jsou hodnoty náhodné veličiny rozptýlené kolem střední hodnoty. (Pro odhad těchto charakteristik z naměřených dat viz empirické protějšky v ",[1239,12733,886],{"className":12734,"dataFsResolvedFilePath":11066,"href":11067},[1242],".)",[1110,12737,12738,12740,12741,12754,12755,12773,12774,12787],{},[1248,12739,1823],{}," udávají, jak jsou hodnoty náhodné veličiny ",[1115,12742,12744],{"className":12743},[1139],[1141,12745,12746],{"xmlns":1143},[1145,12747,12748,12752],{},[1148,12749,12750],{},[1154,12751,1436],{},[1172,12753,1436],{"encoding":1174}," rozděleny na ose reálných čísel v určitém pravděpodobnostním poměru. 100p%-ní kvantil ",[1115,12756,12758],{"className":12757},[1139],[1141,12759,12760],{"xmlns":1143},[1145,12761,12762,12770],{},[1148,12763,12764],{},[1151,12765,12766,12768],{},[1154,12767,1167],{},[1154,12769,1110],{},[1172,12771,12772],{"encoding":1174},"x_p"," je číslo, pro které při zvolené pravděpodobnosti ",[1115,12775,12777],{"className":12776},[1139],[1141,12778,12779],{"xmlns":1143},[1145,12780,12781,12785],{},[1148,12782,12783],{},[1154,12784,1110],{},[1172,12786,1110],{"encoding":1174}," platí",[1115,12789,12791],{"className":12790},[1139],[1141,12792,12793],{"xmlns":1143,"display":1468},[1145,12794,12795,12815],{},[1148,12796,12797,12799,12801,12807,12809,12811,12813],{},[1154,12798,1156],{},[1161,12800,1164],{"stretchy":1163},[1151,12802,12803,12805],{},[1154,12804,1167],{},[1154,12806,1110],{},[1161,12808,1170],{"stretchy":1163},[1161,12810,1483],{},[1154,12812,1110],{},[1154,12814,1176],{"mathvariant":1869},[1172,12816,12817],{"encoding":1174},"F(x_p) = p.",[1110,12819,12820,12821,12849,12850,12876,12877,2574,12895,12913,12914,1176],{},"V intervalu ",[1115,12822,12824],{"className":12823},[1139],[1141,12825,12826],{"xmlns":1143},[1145,12827,12828,12846],{},[1148,12829,12830,12832,12834,12836,12838,12844],{},[1161,12831,1164],{"stretchy":1163},[1161,12833,1623],{},[1154,12835,11874],{"mathvariant":1869},[1161,12837,3288],{"separator":1121},[1151,12839,12840,12842],{},[1154,12841,1167],{},[1154,12843,1110],{},[1161,12845,1170],{"stretchy":1163},[1172,12847,12848],{"encoding":1174},"(-\\infty; x_p)"," leží 100p % hodnot, v intervalu ",[1115,12851,12853],{"className":12852},[1139],[1141,12854,12855],{"xmlns":1143},[1145,12856,12857,12873],{},[1148,12858,12859,12861,12867,12869,12871],{},[1161,12860,3816],{"stretchy":1163},[1151,12862,12863,12865],{},[1154,12864,1167],{},[1154,12866,1110],{},[1161,12868,3288],{"separator":1121},[1154,12870,11874],{"mathvariant":1869},[1161,12872,1170],{"stretchy":1163},[1172,12874,12875],{"encoding":1174},"\\langle x_p; \\infty)"," leží 100(1-p) % hodnot. Nejdůležitější kvantily jsou medián ",[1115,12878,12880],{"className":12879},[1139],[1141,12881,12882],{"xmlns":1143},[1145,12883,12884,12892],{},[1148,12885,12886],{},[1151,12887,12888,12890],{},[1154,12889,1167],{},[1312,12891,1952],{},[1172,12893,12894],{"encoding":1174},"x_{0{,}5}",[1115,12896,12898],{"className":12897},[1139],[1141,12899,12900],{"xmlns":1143},[1145,12901,12902,12910],{},[1148,12903,12904],{},[1151,12905,12906,12908],{},[1154,12907,1167],{},[1312,12909,1981],{},[1172,12911,12912],{"encoding":1174},"x_{0{,}25}"," a horní kvartil ",[1115,12915,12917],{"className":12916},[1139],[1141,12918,12919],{"xmlns":1143},[1145,12920,12921,12929],{},[1148,12922,12923],{},[1151,12924,12925,12927],{},[1154,12926,1167],{},[1312,12928,2007],{},[1172,12930,12931],{"encoding":1174},"x_{0{,}75}",[1232,12933,11315],{"id":12934},"normální-rozdělení",[1110,12936,12937,12938,12951,12952,1932,12955,12982],{},"Spojitá náhodná veličina ",[1115,12939,12941],{"className":12940},[1139],[1141,12942,12943],{"xmlns":1143},[1145,12944,12945,12949],{},[1148,12946,12947],{},[1154,12948,1436],{},[1172,12950,1436],{"encoding":1174}," má ",[1248,12953,12954],{},"normální rozdělení",[1115,12956,12958],{"className":12957},[1139],[1141,12959,12960],{"xmlns":1143},[1145,12961,12962,12980],{},[1148,12963,12964,12966,12968,12970,12972,12978],{},[1154,12965,11327],{},[1161,12967,1164],{"stretchy":1163},[1154,12969,11332],{},[1161,12971,3288],{"separator":1121},[1603,12973,12974,12976],{},[1154,12975,11339],{},[1312,12977,1610],{},[1161,12979,1170],{"stretchy":1163},[1172,12981,11346],{"encoding":1174},", jestliže její hustota pravděpodobnosti a distribuční funkce jsou dány předpisy",[1115,12984,12986],{"className":12985},[1139],[1141,12987,12988],{"xmlns":1143,"display":1468},[1145,12989,12990,13141],{},[1148,12991,12992,12994,12996,12998,13000,13002,13019,13055,13057,13059,13061,13063,13065,13067,13069,13085,13097,13133,13135,13137,13139],{},[1154,12993,1213],{},[1161,12995,1164],{"stretchy":1163},[1154,12997,1167],{},[1161,12999,1170],{"stretchy":1163},[1161,13001,1483],{},[1485,13003,13004,13006],{},[1312,13005,1489],{},[1148,13007,13008,13010],{},[1154,13009,11339],{},[1678,13011,13012],{},[1148,13013,13014,13016],{},[1312,13015,1610],{},[1154,13017,13018],{},"π",[1603,13020,13021,13023],{},[1154,13022,1539],{},[1148,13024,13025,13027],{},[1161,13026,1623],{},[1485,13028,13029,13045],{},[1148,13030,13031,13033,13035,13037,13039],{},[1161,13032,1164],{"stretchy":1163},[1154,13034,1167],{},[1161,13036,1623],{},[1154,13038,11332],{},[1603,13040,13041,13043],{},[1161,13042,1170],{"stretchy":1163},[1312,13044,1610],{},[1148,13046,13047,13049],{},[1312,13048,1610],{},[1603,13050,13051,13053],{},[1154,13052,11339],{},[1312,13054,1610],{},[1161,13056,1199],{"separator":1121},[1516,13058],{"width":1518},[1154,13060,1156],{},[1161,13062,1164],{"stretchy":1163},[1154,13064,1167],{},[1161,13066,1170],{"stretchy":1163},[1161,13068,1483],{},[1485,13070,13071,13073],{},[1312,13072,1489],{},[1148,13074,13075,13077],{},[1154,13076,11339],{},[1678,13078,13079],{},[1148,13080,13081,13083],{},[1312,13082,1610],{},[1154,13084,13018],{},[1645,13086,13087,13089,13095],{},[1161,13088,12211],{},[1148,13090,13091,13093],{},[1161,13092,1623],{},[1154,13094,11874],{"mathvariant":1869},[1154,13096,1167],{},[1603,13098,13099,13101],{},[1154,13100,1539],{},[1148,13102,13103,13105],{},[1161,13104,1623],{},[1485,13106,13107,13123],{},[1148,13108,13109,13111,13113,13115,13117],{},[1161,13110,1164],{"stretchy":1163},[1154,13112,1807],{},[1161,13114,1623],{},[1154,13116,11332],{},[1603,13118,13119,13121],{},[1161,13120,1170],{"stretchy":1163},[1312,13122,1610],{},[1148,13124,13125,13127],{},[1312,13126,1610],{},[1603,13128,13129,13131],{},[1154,13130,11339],{},[1312,13132,1610],{},[1316,13134,1318],{},[1154,13136,12232],{},[1154,13138,1807],{},[1161,13140,1199],{"separator":1121},[1172,13142,13143],{"encoding":1174},"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,",[1110,13145,13146,13147,1381,13171,1176],{},"přičemž ",[1115,13148,13150],{"className":13149},[1139],[1141,13151,13152],{"xmlns":1143},[1145,13153,13154,13168],{},[1148,13155,13156,13158,13160,13162,13164,13166],{},[1154,13157,12522],{},[1161,13159,1164],{"stretchy":1163},[1154,13161,1436],{},[1161,13163,1170],{"stretchy":1163},[1161,13165,1483],{},[1154,13167,11332],{},[1172,13169,13170],{"encoding":1174},"E(X) = \\mu",[1115,13172,13174],{"className":13173},[1139],[1141,13175,13176],{"xmlns":1143},[1145,13177,13178,13196],{},[1148,13179,13180,13182,13184,13186,13188,13190],{},[1154,13181,12589],{},[1161,13183,1164],{"stretchy":1163},[1154,13185,1436],{},[1161,13187,1170],{"stretchy":1163},[1161,13189,1483],{},[1603,13191,13192,13194],{},[1154,13193,11339],{},[1312,13195,1610],{},[1172,13197,13198],{"encoding":1174},"D(X) = \\sigma^2",[1110,13200,13201],{},[1393,13202],{"alt":13203,"className":13204,"src":13205},"mask-nv-normalni",[1242,1397],"\u002Fwiki-assets\u002Fmask-nv-normalni.png",[1110,13207,13208,13209,13212,13213,13227,13228,13247,13248,13264,13265,13278,13279,1176],{},"Křivka hustoty se nazývá ",[1248,13210,13211],{},"Gaussova křivka",": je symetrická kolem svislé přímky procházející ",[1115,13214,13216],{"className":13215},[1139],[1141,13217,13218],{"xmlns":1143},[1145,13219,13220,13224],{},[1148,13221,13222],{},[1154,13223,11332],{},[1172,13225,13226],{"encoding":1174},"\\mu",", kde má ",[1115,13229,13231],{"className":13230},[1139],[1141,13232,13233],{"xmlns":1143},[1145,13234,13235,13245],{},[1148,13236,13237,13239,13241,13243],{},[1154,13238,1213],{},[1161,13240,1164],{"stretchy":1163},[1154,13242,1167],{},[1161,13244,1170],{"stretchy":1163},[1172,13246,11242],{"encoding":1174}," globální maximum, a ve vzdálenosti ",[1115,13249,13251],{"className":13250},[1139],[1141,13252,13253],{"xmlns":1143},[1145,13254,13255,13261],{},[1148,13256,13257,13259],{},[1312,13258,3512],{},[1154,13260,11339],{},[1172,13262,13263],{"encoding":1174},"3\\sigma"," od ",[1115,13266,13268],{"className":13267},[1139],[1141,13269,13270],{"xmlns":1143},[1145,13271,13272,13276],{},[1148,13273,13274],{},[1154,13275,11332],{},[1172,13277,13226],{"encoding":1174}," se téměř dotýká osy x — zhruba 99,73 % hodnot leží v intervalu ",[1115,13280,13282],{"className":13281},[1139],[1141,13283,13284],{"xmlns":1143},[1145,13285,13286,13310],{},[1148,13287,13288,13290,13292,13294,13296,13298,13300,13302,13304,13306,13308],{},[1161,13289,1164],{"stretchy":1163},[1154,13291,11332],{},[1161,13293,1623],{},[1312,13295,3512],{},[1154,13297,11339],{},[1161,13299,3288],{"separator":1121},[1154,13301,11332],{},[1161,13303,3835],{},[1312,13305,3512],{},[1154,13307,11339],{},[1161,13309,1170],{"stretchy":1163},[1172,13311,13312],{"encoding":1174},"(\\mu - 3\\sigma; \\mu + 3\\sigma)",[1110,13314,13315,13316,1932,13319,13343,13344,1176],{},"Zvláštní postavení má ",[1248,13317,13318],{},"normované normální rozdělení",[1115,13320,13322],{"className":13321},[1139],[1141,13323,13324],{"xmlns":1143},[1145,13325,13326,13340],{},[1148,13327,13328,13330,13332,13334,13336,13338],{},[1154,13329,11327],{},[1161,13331,1164],{"stretchy":1163},[1312,13333,4585],{},[1161,13335,3288],{"separator":1121},[1312,13337,1489],{},[1161,13339,1170],{"stretchy":1163},[1172,13341,13342],{"encoding":1174},"N(0; 1)",", na které se dá libovolné normální rozdělení převést standardizací ",[1115,13345,13347],{"className":13346},[1139],[1141,13348,13349],{"xmlns":1143},[1145,13350,13351,13371],{},[1148,13352,13353,13355,13357,13359,13361,13363,13365,13367,13369],{},[1154,13354,1204],{},[1161,13356,1483],{},[1161,13358,1164],{"stretchy":1163},[1154,13360,1436],{},[1161,13362,1623],{},[1154,13364,11332],{},[1161,13366,1170],{"stretchy":1163},[1154,13368,3245],{"mathvariant":1869},[1154,13370,11339],{},[1172,13372,13373],{"encoding":1174},"Z = (X-\\mu)\u002F\\sigma",[13375,13376],"graph-mount",{"spec":13377},"{\"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\"}]}",[1103,13379,13381,13388],{"className":13380,"dataCallout":10867},[1106,10866],[1110,13382,13384,13387],{"className":13383},[1113],[1115,13385],{"className":13386,"ariaHidden":1121},[1118,10874,1120],"R očekává směrodatnou odchylku, ne rozptyl",[1110,13389,13390,13391,13418,13419,13422,13423,1381,13425,1385,13427,13429,13430,1932,13433,13446,13447,13472,13473,5936,13476,1176],{},"Zápis ",[1115,13392,13394],{"className":13393},[1139],[1141,13395,13396],{"xmlns":1143},[1145,13397,13398,13416],{},[1148,13399,13400,13402,13404,13406,13408,13414],{},[1154,13401,11327],{},[1161,13403,1164],{"stretchy":1163},[1154,13405,11332],{},[1161,13407,3288],{"separator":1121},[1603,13409,13410,13412],{},[1154,13411,11339],{},[1312,13413,1610],{},[1161,13415,1170],{"stretchy":1163},[1172,13417,11346],{"encoding":1174}," v definici používá ",[1248,13420,13421],{},"rozptyl",". Funkce ",[2015,13424,11350],{},[2015,13426,11353],{},[2015,13428,11356],{}," v R ale jako třetí argument berou ",[1248,13431,13432],{},"směrodatnou odchylku",[1115,13434,13436],{"className":13435},[1139],[1141,13437,13438],{"xmlns":1143},[1145,13439,13440,13444],{},[1148,13441,13442],{},[1154,13443,11339],{},[1172,13445,11371],{"encoding":1174},". Má-li náhodná veličina rozdělení ",[1115,13448,13450],{"className":13449},[1139],[1141,13451,13452],{"xmlns":1143},[1145,13453,13454,13469],{},[1148,13455,13456,13458,13460,13462,13464,13467],{},[1154,13457,11327],{},[1161,13459,1164],{"stretchy":1163},[1312,13461,3427],{},[1161,13463,3288],{"separator":1121},[1312,13465,13466],{},"0,12",[1161,13468,1170],{"stretchy":1163},[1172,13470,13471],{"encoding":1174},"N(10; 0{,}12)",", je ",[2015,13474,13475],{},"sd = sqrt(0.12)",[2015,13477,13478],{},"sd = 0.12",[1110,13480,2122],{},[2020,13482,13484],{"className":2022,"code":13483,"language":71,"meta":2024,"style":2024},"dnorm(0)\npnorm(1.96)\nqnorm(0.975)\n",[2015,13485,13486,13496,13507],{"__ignoreMap":2024},[1115,13487,13488,13490,13492,13494],{"class":2029,"line":10},[1115,13489,11350],{"class":2039},[1115,13491,1164],{"class":2043},[1115,13493,4585],{"class":2046},[1115,13495,2185],{"class":2043},[1115,13497,13498,13500,13502,13505],{"class":2029,"line":27},[1115,13499,11353],{"class":2039},[1115,13501,1164],{"class":2043},[1115,13503,13504],{"class":2046},"1.96",[1115,13506,2185],{"class":2043},[1115,13508,13509,13511,13513,13516],{"class":2029,"line":148},[1115,13510,11356],{"class":2039},[1115,13512,1164],{"class":2043},[1115,13514,13515],{"class":2046},"0.975",[1115,13517,2185],{"class":2043},[2020,13519,13522],{"className":13520,"code":13521,"language":2349,"meta":2024},[2347],"[1] 0.3989423\n[1] 0.9750021\n[1] 1.959964\n",[2015,13523,13521],{"__ignoreMap":2024},[1110,13525,13526,13529,13530,13554,13555,6413,13558,1385,13579,13582],{},[2015,13527,13528],{},"dnorm(0)"," je hodnota hustoty ",[1115,13531,13533],{"className":13532},[1139],[1141,13534,13535],{"xmlns":1143},[1145,13536,13537,13551],{},[1148,13538,13539,13541,13543,13545,13547,13549],{},[1154,13540,11327],{},[1161,13542,1164],{"stretchy":1163},[1312,13544,4585],{},[1161,13546,3288],{"separator":1121},[1312,13548,1489],{},[1161,13550,1170],{"stretchy":1163},[1172,13552,13553],{"encoding":1174},"N(0;1)"," v bodě 0, ",[2015,13556,13557],{},"pnorm(1.96)",[1115,13559,13561],{"className":13560},[1139],[1141,13562,13563],{"xmlns":1143},[1145,13564,13565,13576],{},[1148,13566,13567,13569,13571,13574],{},[1154,13568,1156],{},[1161,13570,1164],{"stretchy":1163},[1312,13572,13573],{},"1,96",[1161,13575,1170],{"stretchy":1163},[1172,13577,13578],{"encoding":1174},"F(1{,}96)",[2015,13580,13581],{},"qnorm(0.975)"," je 97,5%-ní kvantil — hodnota, pod kterou leží 97,5 % pravděpodobnosti.",[1103,13584,13586,13593],{"className":13585,"dataCallout":2447},[1106,2446],[1110,13587,13589,13592],{"className":13588},[1113],[1115,13590],{"className":13591,"ariaHidden":1121},[1118,2454,1120],"Příklad: Návštěvnost zábavního parku",[1110,13594,13595,13596,13631],{},"Denní návštěvnost zábavního parku je náhodná veličina s normálním rozdělením, průměrnou hodnotou 230 a směrodatnou odchylkou 27,5 návštěvníků: ",[1115,13597,13599],{"className":13598},[1139],[1141,13600,13601],{"xmlns":1143},[1145,13602,13603,13628],{},[1148,13604,13605,13607,13610,13612,13614,13617,13619,13626],{},[1154,13606,1436],{},[1161,13608,13609],{},"∼",[1154,13611,11327],{},[1161,13613,1164],{"stretchy":1163},[1312,13615,13616],{},"230",[1161,13618,3288],{"separator":1121},[1603,13620,13621,13624],{},[1312,13622,13623],{},"27,5",[1312,13625,1610],{},[1161,13627,1170],{"stretchy":1163},[1172,13629,13630],{"encoding":1174},"X \\sim N(230; 27{,}5^2)",". Přijde-li za den méně než 180 návštěvníků, je park ztrátový. Kolik procent dní je ztrátových?",[1110,13633,13634],{},[1393,13635],{"alt":13636,"className":13637,"src":13638},"mask-nv-priklad-park",[1242,1397],"\u002Fwiki-assets\u002Fmask-nv-priklad-park.png",[2020,13640,13642],{"className":2022,"code":13641,"language":71,"meta":2024,"style":2024},"pnorm(180, mean = 230, sd = 27.5)\n",[2015,13643,13644],{"__ignoreMap":2024},[1115,13645,13646,13648,13650,13653,13655,13657,13659,13662,13664,13667,13669,13672],{"class":2029,"line":10},[1115,13647,11353],{"class":2039},[1115,13649,1164],{"class":2043},[1115,13651,13652],{"class":2046},"180",[1115,13654,1199],{"class":2035},[1115,13656,5274],{"class":2032},[1115,13658,2291],{"class":2035},[1115,13660,13661],{"class":2046}," 230",[1115,13663,1199],{"class":2035},[1115,13665,13666],{"class":2032}," sd",[1115,13668,2291],{"class":2035},[1115,13670,13671],{"class":2046}," 27.5",[1115,13673,2185],{"class":2043},[2020,13675,13678],{"className":13676,"code":13677,"language":2349,"meta":2024},[2347],"[1] 0.03451817\n",[2015,13679,13677],{"__ignoreMap":2024},[1110,13681,13682],{},"Park je ztrátový přibližně v 3,45 % dní.",[1103,13684,13686,13693],{"className":13685,"dataCallout":2447},[1106,2446],[1110,13687,13689,13692],{"className":13688},[1113],[1115,13690],{"className":13691,"ariaHidden":1121},[1118,2454,1120],"Příklad: Délka výrobku",[1110,13694,13695,13696,13730],{},"Automat je seřízen tak, aby střední hodnota délky výrobku byla 42 mm, s přesností charakterizovanou směrodatnou odchylkou 1,2 mm: ",[1115,13697,13699],{"className":13698},[1139],[1141,13700,13701],{"xmlns":1143},[1145,13702,13703,13727],{},[1148,13704,13705,13707,13709,13711,13713,13716,13718,13725],{},[1154,13706,1436],{},[1161,13708,13609],{},[1154,13710,11327],{},[1161,13712,1164],{"stretchy":1163},[1312,13714,13715],{},"42",[1161,13717,3288],{"separator":1121},[1603,13719,13720,13723],{},[1312,13721,13722],{},"1,2",[1312,13724,1610],{},[1161,13726,1170],{"stretchy":1163},[1172,13728,13729],{"encoding":1174},"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?",[1110,13732,13733],{},[1393,13734],{"alt":13735,"className":13736,"src":13737},"mask-nv-priklad-delka",[1242,1397],"\u002Fwiki-assets\u002Fmask-nv-priklad-delka.png",[2020,13739,13741],{"className":2022,"code":13740,"language":71,"meta":2024,"style":2024},"pnorm(43, mean = 42, sd = 1.2) - pnorm(41, mean = 42, sd = 1.2)\n",[2015,13742,13743],{"__ignoreMap":2024},[1115,13744,13745,13747,13749,13752,13754,13756,13758,13760,13762,13764,13766,13769,13771,13773,13776,13778,13780,13782,13784,13786,13788,13790,13792,13794,13796],{"class":2029,"line":10},[1115,13746,11353],{"class":2039},[1115,13748,1164],{"class":2043},[1115,13750,13751],{"class":2046},"43",[1115,13753,1199],{"class":2035},[1115,13755,5274],{"class":2032},[1115,13757,2291],{"class":2035},[1115,13759,2733],{"class":2046},[1115,13761,1199],{"class":2035},[1115,13763,13666],{"class":2032},[1115,13765,2291],{"class":2035},[1115,13767,13768],{"class":2046}," 1.2",[1115,13770,2257],{"class":2043},[1115,13772,2260],{"class":2035},[1115,13774,13775],{"class":2039}," pnorm",[1115,13777,1164],{"class":2043},[1115,13779,1353],{"class":2046},[1115,13781,1199],{"class":2035},[1115,13783,5274],{"class":2032},[1115,13785,2291],{"class":2035},[1115,13787,2733],{"class":2046},[1115,13789,1199],{"class":2035},[1115,13791,13666],{"class":2032},[1115,13793,2291],{"class":2035},[1115,13795,13768],{"class":2046},[1115,13797,2185],{"class":2043},[2020,13799,13802],{"className":13800,"code":13801,"language":2349,"meta":2024},[2347],"[1] 0.5953432\n",[2015,13803,13801],{"__ignoreMap":2024},[1110,13805,13806],{},"Do 1. jakostní třídy spadá přibližně 59,53 % výrobků.",[1103,13808,13810,13817],{"className":13809,"dataCallout":2447},[1106,2446],[1110,13811,13813,13816],{"className":13812},[1113],[1115,13814],{"className":13815,"ariaHidden":1121},[1118,2454,1120],"Příklad: Obsah ampulky",[1110,13818,13819,13820,13843,13844,13869],{},"Obsah ampulky s lékem (v cm³) má rozdělení ",[1115,13821,13823],{"className":13822},[1139],[1141,13824,13825],{"xmlns":1143},[1145,13826,13827,13841],{},[1148,13828,13829,13831,13833,13835,13837,13839],{},[1154,13830,11327],{},[1161,13832,1164],{"stretchy":1163},[1312,13834,3427],{},[1161,13836,3288],{"separator":1121},[1312,13838,13466],{},[1161,13840,1170],{"stretchy":1163},[1172,13842,13471],{"encoding":1174},", tedy střední hodnota 10 a rozptyl 0,12 (",[1115,13845,13847],{"className":13846},[1139],[1141,13848,13849],{"xmlns":1143},[1145,13850,13851,13866],{},[1148,13852,13853,13855,13857,13861,13863],{},[1154,13854,11339],{},[1161,13856,1483],{},[1678,13858,13859],{},[1312,13860,13466],{},[1161,13862,5042],{},[1312,13864,13865],{},"0,346",[1172,13867,13868],{"encoding":1174},"\\sigma = \\sqrt{0{,}12} \\approx 0{,}346","). Kolik procent ampulek má obsah menší než 9,8 cm³?",[1110,13871,13872],{},[1393,13873],{"alt":13874,"className":13875,"src":13876},"mask-nv-priklad-ampulka",[1242,1397],"\u002Fwiki-assets\u002Fmask-nv-priklad-ampulka.png",[2020,13878,13880],{"className":2022,"code":13879,"language":71,"meta":2024,"style":2024},"pnorm(9.8, mean = 10, sd = sqrt(0.12))\n",[2015,13881,13882],{"__ignoreMap":2024},[1115,13883,13884,13886,13888,13891,13893,13895,13897,13899,13901,13903,13905,13907,13909,13912],{"class":2029,"line":10},[1115,13885,11353],{"class":2039},[1115,13887,1164],{"class":2043},[1115,13889,13890],{"class":2046},"9.8",[1115,13892,1199],{"class":2035},[1115,13894,5274],{"class":2032},[1115,13896,2291],{"class":2035},[1115,13898,4205],{"class":2046},[1115,13900,1199],{"class":2035},[1115,13902,13666],{"class":2032},[1115,13904,2291],{"class":2035},[1115,13906,9044],{"class":2039},[1115,13908,1164],{"class":2043},[1115,13910,13911],{"class":2046},"0.12",[1115,13913,3694],{"class":2043},[2020,13915,13918],{"className":13916,"code":13917,"language":2349,"meta":2024},[2347],"[1] 0.2818514\n",[2015,13919,13917],{"__ignoreMap":2024},[1110,13921,13922],{},"Obsah menší než 9,8 cm³ má přibližně 28,19 % ampulek.",[1232,13924,13926],{"id":13925},"další-rozdělení-dostupná-v-r","Další rozdělení dostupná v R",[1110,13928,13929,13930,13933,13934,13937,13938,13941,13942,3245,13945,13948,13949,13952],{},"Vedle normálního rozdělení R přímo nabízí hustotu, distribuční funkci a kvantilovou funkci i pro další běžná rozdělení. Pojmenování funkcí je jednotné: ",[2015,13931,13932],{},"d*"," je hustota\u002Fpravděpodobnostní funkce, ",[2015,13935,13936],{},"p*"," distribuční funkce (s ",[2015,13939,13940],{},"lower.tail = FALSE",", případně čtvrtým argumentem ",[2015,13943,13944],{},"TRUE",[2015,13946,13947],{},"FALSE",", pro horní chvost) a ",[2015,13950,13951],{},"q*"," kvantilová funkce.",[3350,13954,13955,14061],{},[3353,13956,13957],{},[3356,13958,13959,13962,14008,14034],{},[3359,13960,13961],{},"Rozdělení",[3359,13963,13964,13988,13989],{},[1115,13965,13967],{"className":13966},[1139],[1141,13968,13969],{"xmlns":1143},[1145,13970,13971,13985],{},[1148,13972,13973,13975,13977,13979,13981,13983],{},[1154,13974,11170],{},[1161,13976,1164],{"stretchy":1163},[1154,13978,1436],{},[1161,13980,1483],{},[1154,13982,3064],{},[1161,13984,1170],{"stretchy":1163},[1172,13986,13987],{"encoding":1174},"P(X=k)"," \u002F ",[1115,13990,13992],{"className":13991},[1139],[1141,13993,13994],{"xmlns":1143},[1145,13995,13996,14006],{},[1148,13997,13998,14000,14002,14004],{},[1154,13999,1213],{},[1161,14001,1164],{"stretchy":1163},[1154,14003,1167],{},[1161,14005,1170],{"stretchy":1163},[1172,14007,11242],{"encoding":1174},[3359,14009,14010],{},[1115,14011,14013],{"className":14012},[1139],[1141,14014,14015],{"xmlns":1143},[1145,14016,14017,14031],{},[1148,14018,14019,14021,14023,14025,14027,14029],{},[1154,14020,11170],{},[1161,14022,1164],{"stretchy":1163},[1154,14024,1436],{},[1161,14026,11177],{},[1154,14028,3064],{},[1161,14030,1170],{"stretchy":1163},[1172,14032,14033],{"encoding":1174},"P(X \\le k)",[3359,14035,14036,14037],{},"horní chvost ",[1115,14038,14040],{"className":14039},[1139],[1141,14041,14042],{"xmlns":1143},[1145,14043,14044,14058],{},[1148,14045,14046,14048,14050,14052,14054,14056],{},[1154,14047,11170],{},[1161,14049,1164],{"stretchy":1163},[1154,14051,1436],{},[1161,14053,6225],{},[1154,14055,3064],{},[1161,14057,1170],{"stretchy":1163},[1172,14059,14060],{"encoding":1174},"P(X>k)",[3389,14062,14063,14109,14152,14193,14242],{},[3356,14064,14065,14094,14099,14104],{},[3394,14066,14067,14068],{},"Binomické ",[1115,14069,14071],{"className":14070},[1139],[1141,14072,14073],{"xmlns":1143},[1145,14074,14075,14091],{},[1148,14076,14077,14079,14081,14083,14085,14087,14089],{},[1154,14078,6352],{},[1154,14080,1502],{},[1161,14082,1164],{"stretchy":1163},[1154,14084,1159],{},[1161,14086,1199],{"separator":1121},[1154,14088,1110],{},[1161,14090,1170],{"stretchy":1163},[1172,14092,14093],{"encoding":1174},"Bi(n,p)",[3394,14095,14096],{},[2015,14097,14098],{},"dbinom(k, n, p)",[3394,14100,14101],{},[2015,14102,14103],{},"pbinom(k, n, p)",[3394,14105,14106],{},[2015,14107,14108],{},"pbinom(k, n, p, FALSE)",[3356,14110,14111,14137,14142,14147],{},[3394,14112,14113,14114],{},"Poissonovo ",[1115,14115,14117],{"className":14116},[1139],[1141,14118,14119],{"xmlns":1143},[1145,14120,14121,14134],{},[1148,14122,14123,14125,14128,14130,14132],{},[1154,14124,11170],{},[1154,14126,14127],{},"o",[1161,14129,1164],{"stretchy":1163},[1154,14131,5168],{},[1161,14133,1170],{"stretchy":1163},[1172,14135,14136],{"encoding":1174},"Po(\\lambda)",[3394,14138,14139],{},[2015,14140,14141],{},"dpois(k, lambda)",[3394,14143,14144],{},[2015,14145,14146],{},"ppois(k, lambda)",[3394,14148,14149],{},[2015,14150,14151],{},"ppois(k, lambda, FALSE)",[3356,14153,14154,14178,14183,14188],{},[3394,14155,14156,14157],{},"Geometrické ",[1115,14158,14160],{"className":14159},[1139],[1141,14161,14162],{"xmlns":1143},[1145,14163,14164,14175],{},[1148,14165,14166,14169,14171,14173],{},[1154,14167,14168],{},"G",[1161,14170,1164],{"stretchy":1163},[1154,14172,1110],{},[1161,14174,1170],{"stretchy":1163},[1172,14176,14177],{"encoding":1174},"G(p)",[3394,14179,14180],{},[2015,14181,14182],{},"dgeom(k, p)",[3394,14184,14185],{},[2015,14186,14187],{},"pgeom(k, p)",[3394,14189,14190],{},[2015,14191,14192],{},"pgeom(k, p, FALSE)",[3356,14194,14195,14227,14232,14237],{},[3394,14196,14197,14198],{},"Hypergeometrické ",[1115,14199,14201],{"className":14200},[1139],[1141,14202,14203],{"xmlns":1143},[1145,14204,14205,14224],{},[1148,14206,14207,14209,14211,14213,14215,14218,14220,14222],{},[1154,14208,6105],{},[1161,14210,1164],{"stretchy":1163},[1154,14212,11327],{},[1161,14214,1199],{"separator":1121},[1154,14216,14217],{},"M",[1161,14219,1199],{"separator":1121},[1154,14221,1159],{},[1161,14223,1170],{"stretchy":1163},[1172,14225,14226],{"encoding":1174},"H(N,M,n)",[3394,14228,14229],{},[2015,14230,14231],{},"dhyper(k, M, N-M, n)",[3394,14233,14234],{},[2015,14235,14236],{},"phyper(k, M, N-M, n)",[3394,14238,14239],{},[2015,14240,14241],{},"phyper(k, M, N-M, n, FALSE)",[3356,14243,14244,14268,14273,14278],{},[3394,14245,14246,14247],{},"Exponenciální ",[1115,14248,14250],{"className":14249},[1139],[1141,14251,14252],{"xmlns":1143},[1145,14253,14254,14265],{},[1148,14255,14256,14258,14260,14263],{},[1154,14257,12522],{},[1161,14259,1164],{"stretchy":1163},[1154,14261,14262],{},"δ",[1161,14264,1170],{"stretchy":1163},[1172,14266,14267],{"encoding":1174},"E(\\delta)",[3394,14269,14270],{},[2015,14271,14272],{},"dexp(k, 1\u002Fdelta)",[3394,14274,14275],{},[2015,14276,14277],{},"pexp(k, 1\u002Fdelta)",[3394,14279,14280],{},[2015,14281,14282],{},"pexp(k, 1\u002Fdelta, FALSE)",[1103,14284,14286,14293],{"className":14285,"dataCallout":10867},[1106,10866],[1110,14287,14289,14292],{"className":14288},[1113],[1115,14290],{"className":14291,"ariaHidden":1121},[1118,10874,1120],"Exponenciální rozdělení: R bere intenzitu, ne střední hodnotu",[1110,14294,14295,14296,14298,14299,14313,14314,5936,14317,1176],{},"R parametrizuje exponenciální rozdělení intenzitou (",[2015,14297,5249],{},"). Je-li ",[1115,14300,14302],{"className":14301},[1139],[1141,14303,14304],{"xmlns":1143},[1145,14305,14306,14310],{},[1148,14307,14308],{},[1154,14309,14262],{},[1172,14311,14312],{"encoding":1174},"\\delta"," střední doba do události, do R se dosazuje ",[2015,14315,14316],{},"1\u002Fdelta",[2015,14318,14319],{},"delta",[1110,14321,14322,14323,14354,14355,14373],{},"V R (pravděpodobnostní a distribuční funkce diskrétní náhodné veličiny ",[1115,14324,14326],{"className":14325},[1139],[1141,14327,14328],{"xmlns":1143},[1145,14329,14330,14351],{},[1148,14331,14332,14334,14336,14338,14340,14342,14344,14346,14349],{},[1154,14333,1436],{},[1161,14335,13609],{},[1154,14337,6352],{},[1154,14339,1502],{},[1161,14341,1164],{"stretchy":1163},[1312,14343,3415],{},[1161,14345,3288],{"separator":1121},[1312,14347,14348],{},"0,95",[1161,14350,1170],{"stretchy":1163},[1172,14352,14353],{"encoding":1174},"X \\sim Bi(5; 0{,}95)",", a pravděpodobnost, že u exponenciálního rozdělení se střední hodnotou ",[1115,14356,14358],{"className":14357},[1139],[1141,14359,14360],{"xmlns":1143},[1145,14361,14362,14370],{},[1148,14363,14364,14366,14368],{},[1154,14365,14262],{},[1161,14367,1483],{},[1312,14369,3415],{},[1172,14371,14372],{"encoding":1174},"\\delta = 5"," nastane událost do 3 jednotek času):",[2020,14375,14377],{"className":2022,"code":14376,"language":71,"meta":2024,"style":2024},"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",[2015,14378,14379,14393,14423,14452,14457,14466],{"__ignoreMap":2024},[1115,14380,14381,14383,14385,14388,14390],{"class":2029,"line":10},[1115,14382,1167],{"class":2032},[1115,14384,2036],{"class":2035},[1115,14386,14387],{"class":2046}," 0",[1115,14389,6481],{"class":2035},[1115,14391,14392],{"class":2046},"5\n",[1115,14394,14395,14397,14399,14402,14404,14406,14408,14410,14412,14415,14417,14419,14421],{"class":2029,"line":27},[1115,14396,4638],{"class":2039},[1115,14398,1164],{"class":2043},[1115,14400,14401],{"class":2039},"dbinom",[1115,14403,1164],{"class":2043},[1115,14405,1167],{"class":2032},[1115,14407,1199],{"class":2035},[1115,14409,4225],{"class":2046},[1115,14411,1199],{"class":2035},[1115,14413,14414],{"class":2046}," 0.95",[1115,14416,1170],{"class":2043},[1115,14418,1199],{"class":2035},[1115,14420,8284],{"class":2046},[1115,14422,2185],{"class":2043},[1115,14424,14425,14427,14429,14432,14434,14436,14438,14440,14442,14444,14446,14448,14450],{"class":2029,"line":148},[1115,14426,4638],{"class":2039},[1115,14428,1164],{"class":2043},[1115,14430,14431],{"class":2039},"pbinom",[1115,14433,1164],{"class":2043},[1115,14435,1167],{"class":2032},[1115,14437,1199],{"class":2035},[1115,14439,4225],{"class":2046},[1115,14441,1199],{"class":2035},[1115,14443,14414],{"class":2046},[1115,14445,1170],{"class":2043},[1115,14447,1199],{"class":2035},[1115,14449,8284],{"class":2046},[1115,14451,2185],{"class":2043},[1115,14453,14454],{"class":2029,"line":111},[1115,14455,14456],{"emptyLinePlaceholder":6044},"\n",[1115,14458,14459,14461,14463],{"class":2029,"line":96},[1115,14460,14319],{"class":2032},[1115,14462,2036],{"class":2035},[1115,14464,14465],{"class":2046}," 5\n",[1115,14467,14468,14470,14472,14475,14477,14479,14481,14484,14486,14488,14490,14493,14495,14497,14499],{"class":2029,"line":89},[1115,14469,4638],{"class":2039},[1115,14471,1164],{"class":2043},[1115,14473,14474],{"class":2039},"pexp",[1115,14476,1164],{"class":2043},[1115,14478,3512],{"class":2046},[1115,14480,1199],{"class":2035},[1115,14482,14483],{"class":2032}," rate",[1115,14485,2291],{"class":2035},[1115,14487,5269],{"class":2046},[1115,14489,4650],{"class":2035},[1115,14491,14492],{"class":2032}," delta",[1115,14494,1170],{"class":2043},[1115,14496,1199],{"class":2035},[1115,14498,8284],{"class":2046},[1115,14500,2185],{"class":2043},[2020,14502,14505],{"className":14503,"code":14504,"language":2349,"meta":2024},[2347],"[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",[2015,14506,14504],{"__ignoreMap":2024},[1232,14508,14510],{"id":14509},"studentovo-pearsonovo-a-fisherovo-snedecorovo-rozdělení","Studentovo, Pearsonovo a Fisherovo-Snedecorovo rozdělení",[1110,14512,14513,14514,14517],{},"Tato tři rozdělení mají statistiky, které se dále používají při konstrukci intervalů spolehlivosti a testování hypotéz (viz ",[1239,14515,141],{"className":14516,"dataFsResolvedFilePath":5305,"href":5306},[1242],") — na rozdíl od normálního rozdělení se v příkladech této kapitoly samostatně nepočítají, jsou to nástroje pro další kapitoly.",[1110,14519,14520,8429,14523,14536],{},[1248,14521,14522],{},"Studentovo rozdělení",[1115,14524,14526],{"className":14525},[1139],[1141,14527,14528],{"xmlns":1143},[1145,14529,14530,14534],{},[1148,14531,14532],{},[1154,14533,3064],{},[1172,14535,3064],{"encoding":1174}," stupni volnosti má hustotu pravděpodobnosti",[1115,14538,14540],{"className":14539},[1139],[1141,14541,14542],{"xmlns":1143,"display":1468},[1145,14543,14544,14639],{},[1148,14545,14546,14548,14550,14552,14554,14556,14588,14626,14628,14630,14632,14634,14637],{},[1154,14547,1213],{},[1161,14549,1164],{"stretchy":1163},[1154,14551,1167],{},[1161,14553,1170],{"stretchy":1163},[1161,14555,1483],{},[1485,14557,14558,14560],{},[1312,14559,1489],{},[1148,14561,14562,14564,14584],{},[1154,14563,6352],{},[1148,14565,14566,14568,14574,14576,14582],{},[1161,14567,1164],{"fence":1121},[1485,14569,14570,14572],{},[1312,14571,1489],{},[1312,14573,1610],{},[1161,14575,1199],{"separator":1121},[1485,14577,14578,14580],{},[1154,14579,3064],{},[1312,14581,1610],{},[1161,14583,1170],{"fence":1121},[1678,14585,14586],{},[1154,14587,3064],{},[1603,14589,14590,14610],{},[1148,14591,14592,14594,14596,14598,14608],{},[1161,14593,1164],{"fence":1121},[1312,14595,1489],{},[1161,14597,3835],{},[1485,14599,14600,14606],{},[1603,14601,14602,14604],{},[1154,14603,1167],{},[1312,14605,1610],{},[1154,14607,3064],{},[1161,14609,1170],{"fence":1121},[1148,14611,14612,14614],{},[1161,14613,1623],{},[1485,14615,14616,14624],{},[1148,14617,14618,14620,14622],{},[1154,14619,3064],{},[1161,14621,3835],{},[1312,14623,1489],{},[1312,14625,1610],{},[1161,14627,1199],{"separator":1121},[1516,14629],{"width":1518},[1154,14631,1167],{},[1161,14633,11459],{},[1154,14635,1749],{"mathvariant":14636},"double-struck",[1161,14638,1199],{"separator":1121},[1172,14640,14641],{"encoding":1174},"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},",[1110,14643,3074,14644,14657,14658,14671,14672,14685],{},[1115,14645,14647],{"className":14646},[1139],[1141,14648,14649],{"xmlns":1143},[1145,14650,14651,14655],{},[1148,14652,14653],{},[1154,14654,6352],{},[1172,14656,6352],{"encoding":1174}," je funkce beta. Je symetrické kolem nuly; číslo ",[1115,14659,14661],{"className":14660},[1139],[1141,14662,14663],{"xmlns":1143},[1145,14664,14665,14669],{},[1148,14666,14667],{},[1154,14668,3064],{},[1172,14670,3064],{"encoding":1174}," určuje tvar křivky — s rostoucím ",[1115,14673,14675],{"className":14674},[1139],[1141,14676,14677],{"xmlns":1143},[1145,14678,14679,14683],{},[1148,14680,14681],{},[1154,14682,3064],{},[1172,14684,3064],{"encoding":1174}," se rozdělení blíží normálnímu.",[1110,14687,14688,8429,14691,14704],{},[1248,14689,14690],{},"Pearsonovo (chí-kvadrát) rozdělení",[1115,14692,14694],{"className":14693},[1139],[1141,14695,14696],{"xmlns":1143},[1145,14697,14698,14702],{},[1148,14699,14700],{},[1154,14701,3064],{},[1172,14703,3064],{"encoding":1174}," stupni volnosti:",[1115,14706,14708],{"className":14707},[1139],[1141,14709,14710],{"xmlns":1143,"display":1468},[1145,14711,14712,14797],{},[1148,14713,14714,14716,14718,14720,14722,14724,14755,14771,14785,14787,14789,14791,14793,14795],{},[1154,14715,1213],{},[1161,14717,1164],{"stretchy":1163},[1154,14719,1167],{},[1161,14721,1170],{"stretchy":1163},[1161,14723,1483],{},[1485,14725,14726,14728],{},[1312,14727,1489],{},[1148,14729,14730,14742,14745,14747,14749,14751,14753],{},[1603,14731,14732,14734],{},[1312,14733,1610],{},[1148,14735,14736,14738,14740],{},[1154,14737,3064],{},[1154,14739,3245],{"mathvariant":1869},[1312,14741,1610],{},[1154,14743,14744],{"mathvariant":1869},"Γ",[1161,14746,1164],{"stretchy":1163},[1154,14748,3064],{},[1154,14750,3245],{"mathvariant":1869},[1312,14752,1610],{},[1161,14754,1170],{"stretchy":1163},[1603,14756,14757,14759],{},[1154,14758,1167],{},[1148,14760,14761,14763,14765,14767,14769],{},[1154,14762,3064],{},[1154,14764,3245],{"mathvariant":1869},[1312,14766,1610],{},[1161,14768,1623],{},[1312,14770,1489],{},[1603,14772,14773,14775],{},[1154,14774,1539],{},[1148,14776,14777,14779,14781,14783],{},[1161,14778,1623],{},[1154,14780,1167],{},[1154,14782,3245],{"mathvariant":1869},[1312,14784,1610],{},[1161,14786,1199],{"separator":1121},[1516,14788],{"width":1518},[1154,14790,1167],{},[1161,14792,6225],{},[1312,14794,4585],{},[1161,14796,1199],{"separator":1121},[1172,14798,14799],{"encoding":1174},"f(x) = \\frac{1}{2^{k\u002F2}\\Gamma(k\u002F2)} x^{k\u002F2-1} e^{-x\u002F2}, \\qquad x > 0,",[1110,14801,3074,14802,14816],{},[1115,14803,14805],{"className":14804},[1139],[1141,14806,14807],{"xmlns":1143},[1145,14808,14809,14813],{},[1148,14810,14811],{},[1154,14812,14744],{"mathvariant":1869},[1172,14814,14815],{"encoding":1174},"\\Gamma"," je funkce gama.",[1110,14818,14819,14822,14823,1385,14841,6481],{},[1248,14820,14821],{},"Fisherovo-Snedecorovo rozdělení"," se stupni volnosti ",[1115,14824,14826],{"className":14825},[1139],[1141,14827,14828],{"xmlns":1143},[1145,14829,14830,14838],{},[1148,14831,14832],{},[1151,14833,14834,14836],{},[1154,14835,3064],{},[1312,14837,1489],{},[1172,14839,14840],{"encoding":1174},"k_1",[1115,14842,14844],{"className":14843},[1139],[1141,14845,14846],{"xmlns":1143},[1145,14847,14848,14856],{},[1148,14849,14850],{},[1151,14851,14852,14854],{},[1154,14853,3064],{},[1312,14855,1610],{},[1172,14857,14858],{"encoding":1174},"k_2",[1115,14860,14862],{"className":14861},[1139],[1141,14863,14864],{"xmlns":1143,"display":1468},[1145,14865,14866,15031],{},[1148,14867,14868,14870,14872,14874,14876,14878,14914,14948,14968,15020,15022,15024,15026,15028],{},[1154,14869,1213],{},[1161,14871,1164],{"stretchy":1163},[1154,14873,1167],{},[1161,14875,1170],{"stretchy":1163},[1161,14877,1483],{},[1485,14879,14880,14882],{},[1312,14881,1489],{},[1148,14883,14884,14886],{},[1154,14885,6352],{},[1148,14887,14888,14890,14900,14902,14912],{},[1161,14889,1164],{"fence":1121},[1485,14891,14892,14898],{},[1151,14893,14894,14896],{},[1154,14895,3064],{},[1312,14897,1489],{},[1312,14899,1610],{},[1161,14901,1199],{"separator":1121},[1485,14903,14904,14910],{},[1151,14905,14906,14908],{},[1154,14907,3064],{},[1312,14909,1610],{},[1312,14911,1610],{},[1161,14913,1170],{"fence":1121},[1603,14915,14916,14936],{},[1148,14917,14918,14920,14934],{},[1161,14919,1164],{"fence":1121},[1485,14921,14922,14928],{},[1151,14923,14924,14926],{},[1154,14925,3064],{},[1312,14927,1489],{},[1151,14929,14930,14932],{},[1154,14931,3064],{},[1312,14933,1610],{},[1161,14935,1170],{"fence":1121},[1148,14937,14938,14944,14946],{},[1151,14939,14940,14942],{},[1154,14941,3064],{},[1312,14943,1489],{},[1154,14945,3245],{"mathvariant":1869},[1312,14947,1610],{},[1603,14949,14950,14952],{},[1154,14951,1167],{},[1148,14953,14954,14960,14962,14964,14966],{},[1151,14955,14956,14958],{},[1154,14957,3064],{},[1312,14959,1489],{},[1154,14961,3245],{"mathvariant":1869},[1312,14963,1610],{},[1161,14965,1623],{},[1312,14967,1489],{},[1603,14969,14970,14996],{},[1148,14971,14972,14974,14976,14978,14992,14994],{},[1161,14973,1164],{"fence":1121},[1312,14975,1489],{},[1161,14977,3835],{},[1485,14979,14980,14986],{},[1151,14981,14982,14984],{},[1154,14983,3064],{},[1312,14985,1489],{},[1151,14987,14988,14990],{},[1154,14989,3064],{},[1312,14991,1610],{},[1154,14993,1167],{},[1161,14995,1170],{"fence":1121},[1148,14997,14998,15000],{},[1161,14999,1623],{},[1485,15001,15002,15018],{},[1148,15003,15004,15010,15012],{},[1151,15005,15006,15008],{},[1154,15007,3064],{},[1312,15009,1489],{},[1161,15011,3835],{},[1151,15013,15014,15016],{},[1154,15015,3064],{},[1312,15017,1610],{},[1312,15019,1610],{},[1161,15021,1199],{"separator":1121},[1516,15023],{"width":1518},[1154,15025,1167],{},[1161,15027,6225],{},[1312,15029,15030],{},"0.",[1172,15032,15033],{"encoding":1174},"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.",[1110,15035,15036],{},[1393,15037],{"alt":15038,"className":15039,"src":15040},"mask-nv-specialni-rozdeleni",[1242,1397],"\u002Fwiki-assets\u002Fmask-nv-specialni-rozdeleni.png",[13375,15042],{"spec":15043},"{\"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\":[]}",[1110,15045,15046],{},"R funkce pro tato tři rozdělení:",[3350,15048,15049,15063],{},[3353,15050,15051],{},[3356,15052,15053,15055,15058,15060],{},[3359,15054,13961],{},[3359,15056,15057],{},"hustota",[3359,15059,11148],{},[3359,15061,15062],{},"kvantil",[3389,15064,15065,15105,15149],{},[3356,15066,15067,15090,15095,15100],{},[3394,15068,15069,15070],{},"Studentovo ",[1115,15071,15073],{"className":15072},[1139],[1141,15074,15075],{"xmlns":1143},[1145,15076,15077,15087],{},[1148,15078,15079,15081,15083,15085],{},[1154,15080,1807],{},[1161,15082,1164],{"stretchy":1163},[1154,15084,3064],{},[1161,15086,1170],{"stretchy":1163},[1172,15088,15089],{"encoding":1174},"t(k)",[3394,15091,15092],{},[2015,15093,15094],{},"dt(x, df = k)",[3394,15096,15097],{},[2015,15098,15099],{},"pt(x, df = k)",[3394,15101,15102],{},[2015,15103,15104],{},"qt(p, df = k)",[3356,15106,15107,15134,15139,15144],{},[3394,15108,15109,15110],{},"Pearsonovo ",[1115,15111,15113],{"className":15112},[1139],[1141,15114,15115],{"xmlns":1143},[1145,15116,15117,15131],{},[1148,15118,15119,15125,15127,15129],{},[1603,15120,15121,15123],{},[1154,15122,6125],{},[1312,15124,1610],{},[1161,15126,1164],{"stretchy":1163},[1154,15128,3064],{},[1161,15130,1170],{"stretchy":1163},[1172,15132,15133],{"encoding":1174},"\\chi^2(k)",[3394,15135,15136],{},[2015,15137,15138],{},"dchisq(x, df = k)",[3394,15140,15141],{},[2015,15142,15143],{},"pchisq(x, df = k)",[3394,15145,15146],{},[2015,15147,15148],{},"qchisq(p, df = k)",[3356,15150,15151,15186,15191,15196],{},[3394,15152,15153,15154],{},"Fisherovo-Snedecorovo ",[1115,15155,15157],{"className":15156},[1139],[1141,15158,15159],{"xmlns":1143},[1145,15160,15161,15183],{},[1148,15162,15163,15165,15167,15173,15175,15181],{},[1154,15164,1156],{},[1161,15166,1164],{"stretchy":1163},[1151,15168,15169,15171],{},[1154,15170,3064],{},[1312,15172,1489],{},[1161,15174,1199],{"separator":1121},[1151,15176,15177,15179],{},[1154,15178,3064],{},[1312,15180,1610],{},[1161,15182,1170],{"stretchy":1163},[1172,15184,15185],{"encoding":1174},"F(k_1, k_2)",[3394,15187,15188],{},[2015,15189,15190],{},"df(x, df1 = k1, df2 = k2)",[3394,15192,15193],{},[2015,15194,15195],{},"pf(x, df1 = k1, df2 = k2)",[3394,15197,15198],{},[2015,15199,15200],{},"qf(p, df1 = k1, df2 = k2)",[1110,15202,15203],{},"V R (97,5%-ní kvantil Studentova rozdělení s 9 stupni volnosti, 95%-ní kvantily Pearsonova a Fisherova-Snedecorova rozdělení):",[2020,15205,15207],{"className":2022,"code":15206,"language":71,"meta":2024,"style":2024},"qt(0.975, df = 9)\nqchisq(0.95, df = 9)\nqf(0.95, df1 = 3, df2 = 10)\n",[2015,15208,15209,15230,15250],{"__ignoreMap":2024},[1115,15210,15211,15214,15216,15218,15220,15223,15225,15228],{"class":2029,"line":10},[1115,15212,15213],{"class":2039},"qt",[1115,15215,1164],{"class":2043},[1115,15217,13515],{"class":2046},[1115,15219,1199],{"class":2035},[1115,15221,15222],{"class":2032}," df",[1115,15224,2291],{"class":2035},[1115,15226,15227],{"class":2046}," 9",[1115,15229,2185],{"class":2043},[1115,15231,15232,15235,15237,15240,15242,15244,15246,15248],{"class":2029,"line":27},[1115,15233,15234],{"class":2039},"qchisq",[1115,15236,1164],{"class":2043},[1115,15238,15239],{"class":2046},"0.95",[1115,15241,1199],{"class":2035},[1115,15243,15222],{"class":2032},[1115,15245,2291],{"class":2035},[1115,15247,15227],{"class":2046},[1115,15249,2185],{"class":2043},[1115,15251,15252,15255,15257,15259,15261,15264,15266,15268,15270,15273,15275,15277],{"class":2029,"line":148},[1115,15253,15254],{"class":2039},"qf",[1115,15256,1164],{"class":2043},[1115,15258,15239],{"class":2046},[1115,15260,1199],{"class":2035},[1115,15262,15263],{"class":2032}," df1",[1115,15265,2291],{"class":2035},[1115,15267,4424],{"class":2046},[1115,15269,1199],{"class":2035},[1115,15271,15272],{"class":2032}," df2",[1115,15274,2291],{"class":2035},[1115,15276,4205],{"class":2046},[1115,15278,2185],{"class":2043},[2020,15280,15283],{"className":15281,"code":15282,"language":2349,"meta":2024},[2347],"[1] 2.262157\n[1] 16.91898\n[1] 3.708265\n",[2015,15284,15282],{"__ignoreMap":2024},[1232,15286,5763],{"id":5762},[1124,15288,15289,15375,15425],{},[1127,15290,15291,15294,15295,15322,15323,3245,15325,3245,15327,15329,15330,15350,15351,15374],{},[1248,15292,15293],{},"Rozptyl vs. směrodatná odchylka v R."," Zápis ",[1115,15296,15298],{"className":15297},[1139],[1141,15299,15300],{"xmlns":1143},[1145,15301,15302,15320],{},[1148,15303,15304,15306,15308,15310,15312,15318],{},[1154,15305,11327],{},[1161,15307,1164],{"stretchy":1163},[1154,15309,11332],{},[1161,15311,3288],{"separator":1121},[1603,15313,15314,15316],{},[1154,15315,11339],{},[1312,15317,1610],{},[1161,15319,1170],{"stretchy":1163},[1172,15321,11346],{"encoding":1174}," používá rozptyl, ale ",[2015,15324,11350],{},[2015,15326,11353],{},[2015,15328,11356],{}," očekávají směrodatnou odchylku. Dosazení rozptylu místo ",[1115,15331,15333],{"className":15332},[1139],[1141,15334,15335],{"xmlns":1143},[1145,15336,15337,15347],{},[1148,15338,15339],{},[1678,15340,15341],{},[1603,15342,15343,15345],{},[1154,15344,11339],{},[1312,15346,1610],{},[1172,15348,15349],{"encoding":1174},"\\sqrt{\\sigma^2}"," dává jiný — a pro ",[1115,15352,15354],{"className":15353},[1139],[1141,15355,15356],{"xmlns":1143},[1145,15357,15358,15371],{},[1148,15359,15360,15366,15369],{},[1603,15361,15362,15364],{},[1154,15363,11339],{},[1312,15365,1610],{},[1161,15367,15368],{"mathvariant":1869},"≠",[1312,15370,1489],{},[1172,15372,15373],{"encoding":1174},"\\sigma^2 \\ne 1"," výrazně odlišný — výsledek (viz příklad s ampulkou).",[1127,15376,15377,15404,15405,15424],{},[1248,15378,15379,15403],{},[1115,15380,15382],{"className":15381},[1139],[1141,15383,15384],{"xmlns":1143},[1145,15385,15386,15400],{},[1148,15387,15388,15390,15392,15394,15396,15398],{},[1154,15389,11170],{},[1161,15391,1164],{"stretchy":1163},[1154,15393,1436],{},[1161,15395,1483],{},[1154,15397,1167],{},[1161,15399,1170],{"stretchy":1163},[1172,15401,15402],{"encoding":1174},"P(X=x)"," u spojité veličiny je vždy 0."," Hustota ",[1115,15406,15408],{"className":15407},[1139],[1141,15409,15410],{"xmlns":1143},[1145,15411,15412,15422],{},[1148,15413,15414,15416,15418,15420],{},[1154,15415,1213],{},[1161,15417,1164],{"stretchy":1163},[1154,15419,1167],{},[1161,15421,1170],{"stretchy":1163},[1172,15423,11242],{"encoding":1174}," sama o sobě pravděpodobnost neudává — pravděpodobnost dává až plocha pod křivkou na intervalu.",[1127,15426,15427,1932,15430,15447,15448,15465,15466,15469,15470,1176],{},[1248,15428,15429],{},"Záměna stupňů volnosti u Fisherova-Snedecorova rozdělení.",[1115,15431,15433],{"className":15432},[1139],[1141,15434,15435],{"xmlns":1143},[1145,15436,15437,15445],{},[1148,15438,15439],{},[1151,15440,15441,15443],{},[1154,15442,3064],{},[1312,15444,1489],{},[1172,15446,14840],{"encoding":1174}," (čitatel) a ",[1115,15449,15451],{"className":15450},[1139],[1141,15452,15453],{"xmlns":1143},[1145,15454,15455,15463],{},[1148,15456,15457],{},[1151,15458,15459,15461],{},[1154,15460,3064],{},[1312,15462,1610],{},[1172,15464,14858],{"encoding":1174}," (jmenovatel) nejsou zaměnitelné — ",[2015,15467,15468],{},"qf(p, df1, df2)"," dá jiný výsledek než ",[2015,15471,15472],{},"qf(p, df2, df1)",[1232,15474,5963],{"id":5962},[1124,15476,15477,15482,15487,15492,15498,15503,15509],{},[1127,15478,15479],{},[1239,15480,1245],{"className":15481,"dataFsResolvedFilePath":1243,"href":1244},[1242],[1127,15483,15484],{},[1239,15485,886],{"className":15486,"dataFsResolvedFilePath":11066,"href":11067},[1242],[1127,15488,15489],{},[1239,15490,141],{"className":15491,"dataFsResolvedFilePath":5305,"href":5306},[1242],[1127,15493,15494],{},[1239,15495,15497],{"className":15496,"dataFsResolvedFilePath":5989,"href":5990},[1242],"regresni-a-korelacni-analyza",[1127,15499,15500],{},[1239,15501,716],{"className":15502,"dataFsResolvedFilePath":5997,"href":5998},[1242],[1127,15504,15505],{},[1239,15506,15508],{"className":15507,"dataFsResolvedFilePath":6005,"href":6006},[1242],"regulacni-diagramy-a-indexy-zpusobilosti",[1127,15510,15511],{},[1239,15512,6015],{"className":15513,"dataFsResolvedFilePath":6013,"href":6014},[1242],[1232,15515,6018],{"id":934},[1110,15517,6021,15518,6026],{},[6023,15519,6025],{},[6028,15521,15522],{},"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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analýza"," zkoumá jednostrannou závislost vysvětlované proměnné ",[1115,19776,19778],{"className":19777},[1139],[1141,19779,19780],{"xmlns":1143},[1145,19781,19782,19786],{},[1148,19783,19784],{},[1154,19785,1528],{},[1172,19787,1528],{"encoding":1174}," na vysvětlujících proměnných ",[1115,19790,19792],{"className":19791},[1139],[1141,19793,19794],{"xmlns":1143},[1145,19795,19796,19800],{},[1148,19797,19798],{},[1154,19799,1167],{},[1172,19801,1167],{"encoding":1174}," (příčina → následek); ",[1248,19804,19805],{},"korelační analýza"," měří intenzitu (těsnost) vzájemné závislosti.",[1127,19808,19809,19810,19813,19814,1176],{},"Parametry regresní funkce se odhadují ",[1248,19811,19812],{},"metodou nejmenších čtverců"," — minimalizací součtu čtverců reziduí ",[1115,19815,19817],{"className":19816},[1139],[1141,19818,19819],{"xmlns":1143},[1145,19820,19821,19851],{},[1148,19822,19823,19825,19827,19833,19835,19845],{},[1161,19824,1497],{},[1161,19826,1164],{"stretchy":1163},[1151,19828,19829,19831],{},[1154,19830,1528],{},[1154,19832,1502],{},[1161,19834,1623],{},[1151,19836,19837,19843],{},[1474,19838,19839,19841],{"accent":1121},[1154,19840,1528],{},[1161,19842,7244],{},[1154,19844,1502],{},[1603,19846,19847,19849],{},[1161,19848,1170],{"stretchy":1163},[1312,19850,1610],{},[1172,19852,19853],{"encoding":1174},"\\sum(y_i-\\hat y_i)^2",[1127,19855,19856,19857,1932,19860,19878,19879,1932,19882,19906,19907,1932,19910,1176],{},"Kvalitu fitu měří ",[1248,19858,19859],{},"index determinace",[1115,19861,19863],{"className":19862},[1139],[1141,19864,19865],{"xmlns":1143},[1145,19866,19867,19875],{},[1148,19868,19869],{},[1603,19870,19871,19873],{},[1154,19872,1749],{},[1312,19874,1610],{},[1172,19876,19877],{"encoding":1174},"R^2","; obecnou těsnost závislosti ",[1248,19880,19881],{},"index korelace",[1115,19883,19885],{"className":19884},[1139],[1141,19886,19887],{"xmlns":1143},[1145,19888,19889,19903],{},[1148,19890,19891,19893,19895],{},[1154,19892,1193],{},[1161,19894,1483],{},[1678,19896,19897],{},[1603,19898,19899,19901],{},[1154,19900,1749],{},[1312,19902,1610],{},[1172,19904,19905],{"encoding":1174},"I=\\sqrt{R^2}",", který je pro regresní přímku roven ",[1248,19908,19909],{},"koeficientu korelace",[1115,19911,19913],{"className":19912},[1139],[1141,19914,19915],{"xmlns":1143},[1145,19916,19917,19929],{},[1148,19918,19919],{},[1151,19920,19921,19923],{},[1154,19922,71],{},[1148,19924,19925,19927],{},[1154,19926,1167],{},[1154,19928,1528],{},[1172,19930,19931],{"encoding":1174},"r_{xy}",[1127,19933,19934,19935,19938,19939,19942,19943,19946],{},"Když přímka nestačí, volí se ",[1248,19936,19937],{},"parabolická, polynomická, hyperbolická nebo logaritmická"," regrese (stále lineární v parametrech, odhad metodou nejmenších čtverců) nebo ",[1248,19940,19941],{},"exponenciální"," regrese (nelineární v parametrech, odhad přes ",[2015,19944,19945],{},"nls2",").",[1127,19948,19949,19952],{},[1248,19950,19951],{},"Vícenásobná regrese"," rozšiřuje model o více regresorů; vyžaduje výběr proměnných (ENTER\u002Fstepwise), ověření šesti předpokladů modelu a kontrolu multikolinearity přes VIF.",[1127,19954,19955,19956,1381,19959,1381,19962,1381,19965,1381,19968,1381,19971,1381,19974,1381,19977,1381,19980,1381,19983,1176],{},"V R: ",[2015,19957,19958],{},"lm()",[2015,19960,19961],{},"nls2()",[2015,19963,19964],{},"summary()",[2015,19966,19967],{},"confint()",[2015,19969,19970],{},"predict()",[2015,19972,19973],{},"step()",[2015,19975,19976],{},"car::vif()",[2015,19978,19979],{},"lmtest::dwtest()",[2015,19981,19982],{},"whitestrap::white_test()",[2015,19984,19985],{},"shapiro.test()",[1232,19987,1235],{"id":1234},[1110,19989,19990,19993,19994,1385,20007,20020,20021,20023,20024,20037,20038,20051,20052,20055],{},[1239,19991,1245],{"className":19992,"dataFsResolvedFilePath":1243,"href":1244},[1242]," pracuje se dvěma znaky ",[1115,19995,19997],{"className":19996},[1139],[1141,19998,19999],{"xmlns":1143},[1145,20000,20001,20005],{},[1148,20002,20003],{},[1154,20004,1167],{},[1172,20006,1167],{"encoding":1174},[1115,20008,20010],{"className":20009},[1139],[1141,20011,20012],{"xmlns":1143},[1145,20013,20014,20018],{},[1148,20015,20016],{},[1154,20017,1528],{},[1172,20019,1528],{"encoding":1174}," zjištěnými na stejných jednotkách. ",[1248,20022,19773],{}," se zabývá jednostrannými závislostmi, kdy proti sobě stojí vysvětlující (nezávisle) proměnná ",[1115,20025,20027],{"className":20026},[1139],[1141,20028,20029],{"xmlns":1143},[1145,20030,20031,20035],{},[1148,20032,20033],{},[1154,20034,1167],{},[1172,20036,1167],{"encoding":1174}," v úloze příčiny a vysvětlovaná (závisle) proměnná ",[1115,20039,20041],{"className":20040},[1139],[1141,20042,20043],{"xmlns":1143},[1145,20044,20045,20049],{},[1148,20046,20047],{},[1154,20048,1528],{},[1172,20050,1528],{"encoding":1174}," v úloze následku. ",[1248,20053,20054],{},"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.",[1110,20057,20058,20059,19946],{},"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 (",[1248,20060,20061],{},"regresní funkce",[1110,20063,20064],{},"Druh regresní analýzy určuje struktura datového souboru:",[1124,20066,20067,20104],{},[1127,20068,20069,20072,20073,20086,20087,20100,20101,1199],{},[1248,20070,20071],{},"dvourozměrný datový soubor"," (jedna ",[1115,20074,20076],{"className":20075},[1139],[1141,20077,20078],{"xmlns":1143},[1145,20079,20080,20084],{},[1148,20081,20082],{},[1154,20083,1167],{},[1172,20085,1167],{"encoding":1174},", jedna ",[1115,20088,20090],{"className":20089},[1139],[1141,20091,20092],{"xmlns":1143},[1145,20093,20094,20098],{},[1148,20095,20096],{},[1154,20097,1528],{},[1172,20099,1528],{"encoding":1174},") → ",[1248,20102,20103],{},"regresní analýza dvou proměnných",[1127,20105,20106,20109,20110,20100,20140,1176],{},[1248,20107,20108],{},"vícerozměrný datový soubor"," (více ",[1115,20111,20113],{"className":20112},[1139],[1141,20114,20115],{"xmlns":1143},[1145,20116,20117,20137],{},[1148,20118,20119,20125,20127,20129,20131],{},[1151,20120,20121,20123],{},[1154,20122,1167],{},[1312,20124,1489],{},[1161,20126,1199],{"separator":1121},[1161,20128,3022],{},[1161,20130,1199],{"separator":1121},[1151,20132,20133,20135],{},[1154,20134,1167],{},[1154,20136,1110],{},[1172,20138,20139],{"encoding":1174},"x_1,\\dots,x_p",[1248,20141,20142],{},"vícenásobná regresní analýza",[1110,20144,20145,20146,20149,20150,20153],{},"Volba konkrétní regresní funkce by měla vycházet jak z ",[1248,20147,20148],{},"ekonomické teorie"," (ta napovídá, zda závislost roste, nebo klesá, zda je přímková, nebo zakřivená), tak z ",[1248,20151,20152],{},"grafické a matematicko-statistické analýzy"," dat — oba přístupy je vhodné kombinovat.",[1232,20155,20157],{"id":20156},"metoda-nejmenších-čtverců","Metoda nejmenších čtverců",[1110,20159,20160,20161,1932,20164,20218,20219,20237,20238,1932,20241,20297,20298,20316,20317,20334,20335,20373,20374,1176],{},"Rozlišují se ",[1248,20162,20163],{},"teoretická regresní funkce",[1115,20165,20167],{"className":20166},[1139],[1141,20168,20169],{"xmlns":1143},[1145,20170,20171,20215],{},[1148,20172,20173,20176,20178,20180,20182,20184,20186,20193,20195,20201,20203,20205,20207,20213],{},[1154,20174,20175],{},"η",[1161,20177,1483],{},[1154,20179,1213],{},[1161,20181,1164],{"stretchy":1163},[1154,20183,1167],{},[1161,20185,3288],{"separator":1121},[1151,20187,20188,20191],{},[1154,20189,20190],{},"β",[1312,20192,4585],{},[1161,20194,1199],{"separator":1121},[1151,20196,20197,20199],{},[1154,20198,20190],{},[1312,20200,1489],{},[1161,20202,1199],{"separator":1121},[1161,20204,3022],{},[1161,20206,1199],{"separator":1121},[1151,20208,20209,20211],{},[1154,20210,20190],{},[1154,20212,1110],{},[1161,20214,1170],{"stretchy":1163},[1172,20216,20217],{"encoding":1174},"\\eta = f(x;\\beta_0,\\beta_1,\\dots,\\beta_p)"," — neznámá, populační, daná neznámými parametry ",[1115,20220,20222],{"className":20221},[1139],[1141,20223,20224],{"xmlns":1143},[1145,20225,20226,20234],{},[1148,20227,20228],{},[1151,20229,20230,20232],{},[1154,20231,20190],{},[1154,20233,1502],{},[1172,20235,20236],{"encoding":1174},"\\beta_i"," — a ",[1248,20239,20240],{},"empirická regresní funkce",[1115,20242,20244],{"className":20243},[1139],[1141,20245,20246],{"xmlns":1143},[1145,20247,20248,20294],{},[1148,20249,20250,20256,20258,20260,20262,20264,20266,20272,20274,20280,20282,20284,20286,20292],{},[1474,20251,20252,20254],{"accent":1121},[1154,20253,1528],{},[1161,20255,7244],{},[1161,20257,1483],{},[1154,20259,1213],{},[1161,20261,1164],{"stretchy":1163},[1154,20263,1167],{},[1161,20265,3288],{"separator":1121},[1151,20267,20268,20270],{},[1154,20269,1534],{},[1312,20271,4585],{},[1161,20273,1199],{"separator":1121},[1151,20275,20276,20278],{},[1154,20277,1534],{},[1312,20279,1489],{},[1161,20281,1199],{"separator":1121},[1161,20283,3022],{},[1161,20285,1199],{"separator":1121},[1151,20287,20288,20290],{},[1154,20289,1534],{},[1154,20291,1110],{},[1161,20293,1170],{"stretchy":1163},[1172,20295,20296],{"encoding":1174},"\\hat y = f(x; b_0,b_1,\\dots,b_p)",", jejíž odhadnuté parametry ",[1115,20299,20301],{"className":20300},[1139],[1141,20302,20303],{"xmlns":1143},[1145,20304,20305,20313],{},[1148,20306,20307],{},[1151,20308,20309,20311],{},[1154,20310,1534],{},[1154,20312,1502],{},[1172,20314,20315],{"encoding":1174},"b_i"," jsou odhadem ",[1115,20318,20320],{"className":20319},[1139],[1141,20321,20322],{"xmlns":1143},[1145,20323,20324,20332],{},[1148,20325,20326],{},[1151,20327,20328,20330],{},[1154,20329,20190],{},[1154,20331,1502],{},[1172,20333,20236],{"encoding":1174}," vypočteným z konkrétních dat. Odchylky skutečných hodnot od empirické funkce, ",[1115,20336,20338],{"className":20337},[1139],[1141,20339,20340],{"xmlns":1143},[1145,20341,20342,20370],{},[1148,20343,20344,20350,20352,20358,20360],{},[1151,20345,20346,20348],{},[1154,20347,1539],{},[1154,20349,1502],{},[1161,20351,1483],{},[1151,20353,20354,20356],{},[1154,20355,1528],{},[1154,20357,1502],{},[1161,20359,1623],{},[1151,20361,20362,20368],{},[1474,20363,20364,20366],{"accent":1121},[1154,20365,1528],{},[1161,20367,7244],{},[1154,20369,1502],{},[1172,20371,20372],{"encoding":1174},"e_i=y_i-\\hat y_i",", se nazývají ",[1248,20375,20376],{},"rezidua",[1110,20378,20379,20380,20383],{},"Nejpoužívanější metodou odhadu parametrů je ",[1248,20381,20382],{},"metoda nejmenších čtverců (OLS)",": hledají se takové parametry, pro které je součet čtverců reziduí minimální,",[1115,20385,20387],{"className":20386},[1139],[1141,20388,20389],{"xmlns":1143,"display":1468},[1145,20390,20391,20441],{},[1148,20392,20393,20407,20409,20415,20417,20427,20433,20435,20437,20439],{},[1493,20394,20395,20397,20405],{},[1161,20396,1497],{},[1148,20398,20399,20401,20403],{},[1154,20400,1502],{},[1161,20402,1483],{},[1312,20404,1489],{},[1154,20406,1159],{},[1161,20408,1164],{"stretchy":1163},[1151,20410,20411,20413],{},[1154,20412,1528],{},[1154,20414,1502],{},[1161,20416,1623],{},[1151,20418,20419,20425],{},[1474,20420,20421,20423],{"accent":1121},[1154,20422,1528],{},[1161,20424,7244],{},[1154,20426,1502],{},[1603,20428,20429,20431],{},[1161,20430,1170],{"stretchy":1163},[1312,20432,1610],{},[1161,20434,12043],{},[1154,20436,1770],{},[1161,20438,1761],{},[1154,20440,1176],{"mathvariant":1869},[1172,20442,20443],{"encoding":1174},"\\sum_{i=1}^n (y_i - \\hat y_i)^2 \\to \\min.",[1110,20445,20446],{},"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.",[1110,20448,20449],{},[1393,20450],{"alt":20451,"className":20452,"src":20453},"mask-ra-primka-rezidua",[1242,1397],"\u002Fwiki-assets\u002Fmask-ra-primka-rezidua.png",[1110,20455,20456,20457,20475],{},"Obrázek ukazuje přesně to, co metoda minimalizuje: délky červených úseček jsou rezidua ",[1115,20458,20460],{"className":20459},[1139],[1141,20461,20462],{"xmlns":1143},[1145,20463,20464,20472],{},[1148,20465,20466],{},[1151,20467,20468,20470],{},[1154,20469,1539],{},[1154,20471,1502],{},[1172,20473,20474],{"encoding":1174},"e_i",", metoda nejmenších čtverců volí přímku tak, aby součet jejich čtverců byl nejmenší možný.",[1232,20477,20479],{"id":20478},"regresní-přímka","Regresní přímka",[1110,20481,20482,20483,6481],{},"Nejjednodušší regresní funkcí je ",[1248,20484,20485],{},"regresní přímka",[1115,20487,20489],{"className":20488},[1139],[1141,20490,20491],{"xmlns":1143,"display":1468},[1145,20492,20493,20545],{},[1148,20494,20495,20497,20499,20505,20507,20513,20515,20517,20519,20525,20527,20533,20535,20541,20543],{},[1154,20496,20175],{},[1161,20498,1483],{},[1151,20500,20501,20503],{},[1154,20502,20190],{},[1312,20504,4585],{},[1161,20506,3835],{},[1151,20508,20509,20511],{},[1154,20510,20190],{},[1312,20512,1489],{},[1154,20514,1167],{},[1161,20516,1199],{"separator":1121},[1516,20518],{"width":1518},[1474,20520,20521,20523],{"accent":1121},[1154,20522,1528],{},[1161,20524,7244],{},[1161,20526,1483],{},[1151,20528,20529,20531],{},[1154,20530,1534],{},[1312,20532,4585],{},[1161,20534,3835],{},[1151,20536,20537,20539],{},[1154,20538,1534],{},[1312,20540,1489],{},[1154,20542,1167],{},[1154,20544,1176],{"mathvariant":1869},[1172,20546,20547],{"encoding":1174},"\\eta = \\beta_0 + \\beta_1 x, \\qquad \\hat y = b_0 + b_1 x.",[1110,20549,20550,20551,20569,20570,20583,20584,20597],{},"Koeficient ",[1115,20552,20554],{"className":20553},[1139],[1141,20555,20556],{"xmlns":1143},[1145,20557,20558,20566],{},[1148,20559,20560],{},[1151,20561,20562,20564],{},[1154,20563,1534],{},[1312,20565,1489],{},[1172,20567,20568],{"encoding":1174},"b_1"," udává změnu průměru ",[1115,20571,20573],{"className":20572},[1139],[1141,20574,20575],{"xmlns":1143},[1145,20576,20577,20581],{},[1148,20578,20579],{},[1154,20580,1528],{},[1172,20582,1528],{"encoding":1174}," při jednotkové změně ",[1115,20585,20587],{"className":20586},[1139],[1141,20588,20589],{"xmlns":1143},[1145,20590,20591,20595],{},[1148,20592,20593],{},[1154,20594,1167],{},[1172,20596,1167],{"encoding":1174},"; jeho znaménko určuje, zda je závislost přímá, nebo nepřímá.",[20599,20600,20602],"h3",{"id":20601},"v-r","V R",[1110,20604,20605,20606,20609,20610,20613],{},"Vstupní data se nahrají buď ze souboru (",[2015,20607,20608],{},"d \u003C- read.table(\"data.txt\")",", případně ",[2015,20611,20612],{},"d \u003C- read.table(file.choose())","), nebo zapíší přímo jako vektory. Na šesti domácnostech sledujeme počet členů domácnosti a jejich týdenní výdaje:",[2020,20615,20617],{"className":2022,"code":20616,"language":71,"meta":2024,"style":2024},"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",[2015,20618,20619,20654,20695,20716],{"__ignoreMap":2024},[1115,20620,20621,20624,20626,20628,20630,20632,20634,20636,20638,20640,20642,20644,20646,20648,20650,20652],{"class":2029,"line":10},[1115,20622,20623],{"class":2032},"pocet_clenu",[1115,20625,2036],{"class":2035},[1115,20627,2040],{"class":2039},[1115,20629,1164],{"class":2043},[1115,20631,1489],{"class":2046},[1115,20633,1199],{"class":2035},[1115,20635,4210],{"class":2046},[1115,20637,1199],{"class":2035},[1115,20639,4424],{"class":2046},[1115,20641,1199],{"class":2035},[1115,20643,8284],{"class":2046},[1115,20645,1199],{"class":2035},[1115,20647,4225],{"class":2046},[1115,20649,1199],{"class":2035},[1115,20651,2294],{"class":2046},[1115,20653,2185],{"class":2043},[1115,20655,20656,20659,20661,20663,20665,20668,20670,20673,20675,20678,20680,20683,20685,20688,20690,20693],{"class":2029,"line":27},[1115,20657,20658],{"class":2032},"tydenni_vydaje",[1115,20660,2036],{"class":2035},[1115,20662,2040],{"class":2039},[1115,20664,1164],{"class":2043},[1115,20666,20667],{"class":2046},"490",[1115,20669,1199],{"class":2035},[1115,20671,20672],{"class":2046}," 820",[1115,20674,1199],{"class":2035},[1115,20676,20677],{"class":2046}," 1230",[1115,20679,1199],{"class":2035},[1115,20681,20682],{"class":2046}," 1570",[1115,20684,1199],{"class":2035},[1115,20686,20687],{"class":2046}," 1950",[1115,20689,1199],{"class":2035},[1115,20691,20692],{"class":2046}," 2320",[1115,20694,2185],{"class":2043},[1115,20696,20697,20699,20701,20704,20706,20708,20711,20714],{"class":2029,"line":148},[1115,20698,786],{"class":2032},[1115,20700,2036],{"class":2035},[1115,20702,20703],{"class":2039}," lm",[1115,20705,1164],{"class":2043},[1115,20707,20658],{"class":2032},[1115,20709,20710],{"class":2035}," ~",[1115,20712,20713],{"class":2032}," pocet_clenu",[1115,20715,2185],{"class":2043},[1115,20717,20718,20721,20723,20725],{"class":2029,"line":111},[1115,20719,20720],{"class":2039},"summary",[1115,20722,1164],{"class":2043},[1115,20724,786],{"class":2032},[1115,20726,2185],{"class":2043},[2020,20728,20731],{"className":20729,"code":20730,"language":2349,"meta":2024},[2347],"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",[2015,20732,20730],{"__ignoreMap":2024},[1110,20734,20735,20736,20768,20769,20772,20773,20803,20804,20834,20835,20838,20839,20862],{},"Odhadnutý model je ",[1115,20737,20739],{"className":20738},[1139],[1141,20740,20741],{"xmlns":1143},[1145,20742,20743,20765],{},[1148,20744,20745,20751,20753,20756,20758,20761,20763],{},[1474,20746,20747,20749],{"accent":1121},[1154,20748,1528],{},[1161,20750,7244],{},[1161,20752,1483],{},[1312,20754,20755],{},"108,7",[1161,20757,3835],{},[1312,20759,20760],{},"368,0",[1316,20762,1318],{},[1154,20764,1167],{},[1172,20766,20767],{"encoding":1174},"\\hat y = 108{,}7 + 368{,}0\\,x",". Sloupec ",[2015,20770,20771],{},"Pr(>|t|)"," je p-hodnota t-testu ",[1115,20774,20776],{"className":20775},[1139],[1141,20777,20778],{"xmlns":1143},[1145,20779,20780,20800],{},[1148,20781,20782,20788,20790,20796,20798],{},[1151,20783,20784,20786],{},[1154,20785,6105],{},[1312,20787,4585],{},[1161,20789,6481],{},[1151,20791,20792,20794],{},[1154,20793,20190],{},[1154,20795,1502],{},[1161,20797,1483],{},[1312,20799,4585],{},[1172,20801,20802],{"encoding":1174},"H_0:\\beta_i=0"," proti ",[1115,20805,20807],{"className":20806},[1139],[1141,20808,20809],{"xmlns":1143},[1145,20810,20811,20831],{},[1148,20812,20813,20819,20821,20827,20829],{},[1151,20814,20815,20817],{},[1154,20816,6105],{},[1312,20818,1489],{},[1161,20820,6481],{},[1151,20822,20823,20825],{},[1154,20824,20190],{},[1154,20826,1502],{},[1161,20828,15368],{"mathvariant":1869},[1312,20830,4585],{},[1172,20832,20833],{"encoding":1174},"H_1:\\beta_i\\neq0"," pro každý parametr — obě p-hodnoty jsou hluboko pod 0,05, oba parametry jsou tedy statisticky významné. ",[2015,20836,20837],{},"Multiple R-squared"," je index determinace ",[1115,20840,20842],{"className":20841},[1139],[1141,20843,20844],{"xmlns":1143},[1145,20845,20846,20859],{},[1148,20847,20848,20854,20856],{},[1603,20849,20850,20852],{},[1154,20851,1749],{},[1312,20853,1610],{},[1161,20855,1483],{},[1312,20857,20858],{},"0,9995",[1172,20860,20861],{"encoding":1174},"R^2=0{,}9995",": model vysvětluje 99,95 % rozptylu výdajů.",[1110,20864,20865],{},"Pro doplňkový přehled slouží přímé přístupové funkce:",[2020,20867,20869],{"className":2022,"code":20868,"language":71,"meta":2024,"style":2024},"coef(model)\nfitted(model)\nresiduals(model)\n",[2015,20870,20871,20882,20893],{"__ignoreMap":2024},[1115,20872,20873,20876,20878,20880],{"class":2029,"line":10},[1115,20874,20875],{"class":2039},"coef",[1115,20877,1164],{"class":2043},[1115,20879,786],{"class":2032},[1115,20881,2185],{"class":2043},[1115,20883,20884,20887,20889,20891],{"class":2029,"line":27},[1115,20885,20886],{"class":2039},"fitted",[1115,20888,1164],{"class":2043},[1115,20890,786],{"class":2032},[1115,20892,2185],{"class":2043},[1115,20894,20895,20898,20900,20902],{"class":2029,"line":148},[1115,20896,20897],{"class":2039},"residuals",[1115,20899,1164],{"class":2043},[1115,20901,786],{"class":2032},[1115,20903,2185],{"class":2043},[2020,20905,20908],{"className":20906,"code":20907,"language":2349,"meta":2024},[2347],"(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",[2015,20909,20907],{"__ignoreMap":2024},[1110,20911,20912,20915,20916,1381,20942,20945,20946,20968,20969,1381,20987,20990,20991,21028],{},[2015,20913,20914],{},"coef()"," vrací odhadnuté parametry ",[1115,20917,20919],{"className":20918},[1139],[1141,20920,20921],{"xmlns":1143},[1145,20922,20923,20939],{},[1148,20924,20925,20931,20933],{},[1151,20926,20927,20929],{},[1154,20928,1534],{},[1312,20930,4585],{},[1161,20932,1199],{"separator":1121},[1151,20934,20935,20937],{},[1154,20936,1534],{},[1312,20938,1489],{},[1172,20940,20941],{"encoding":1174},"b_0,b_1",[2015,20943,20944],{},"fitted()"," predikce ",[1115,20947,20949],{"className":20948},[1139],[1141,20950,20951],{"xmlns":1143},[1145,20952,20953,20965],{},[1148,20954,20955],{},[1151,20956,20957,20963],{},[1474,20958,20959,20961],{"accent":1121},[1154,20960,1528],{},[1161,20962,7244],{},[1154,20964,1502],{},[1172,20966,20967],{"encoding":1174},"\\hat y_i"," pro pozorované ",[1115,20970,20972],{"className":20971},[1139],[1141,20973,20974],{"xmlns":1143},[1145,20975,20976,20984],{},[1148,20977,20978],{},[1151,20979,20980,20982],{},[1154,20981,1167],{},[1154,20983,1502],{},[1172,20985,20986],{"encoding":1174},"x_i",[2015,20988,20989],{},"residuals()"," rezidua ",[1115,20992,20994],{"className":20993},[1139],[1141,20995,20996],{"xmlns":1143},[1145,20997,20998,21026],{},[1148,20999,21000,21006,21008,21014,21016],{},[1151,21001,21002,21004],{},[1154,21003,1539],{},[1154,21005,1502],{},[1161,21007,1483],{},[1151,21009,21010,21012],{},[1154,21011,1528],{},[1154,21013,1502],{},[1161,21015,1623],{},[1151,21017,21018,21024],{},[1474,21019,21020,21022],{"accent":1121},[1154,21021,1528],{},[1161,21023,7244],{},[1154,21025,1502],{},[1172,21027,20372],{"encoding":1174}," — stejná čísla, která na obrázku výše tvoří délky červených úseček.",[1110,21030,21031,21032,21045],{},"Intervaly spolehlivosti pro parametry a pro predikci v nových bodech ",[1115,21033,21035],{"className":21034},[1139],[1141,21036,21037],{"xmlns":1143},[1145,21038,21039,21043],{},[1148,21040,21041],{},[1154,21042,1167],{},[1172,21044,1167],{"encoding":1174}," (zde 7 a 8 členů domácnosti):",[2020,21047,21049],{"className":2022,"code":21048,"language":71,"meta":2024,"style":2024},"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",[2015,21050,21051,21071,21099,21138],{"__ignoreMap":2024},[1115,21052,21053,21056,21058,21060,21062,21065,21067,21069],{"class":2029,"line":10},[1115,21054,21055],{"class":2039},"confint",[1115,21057,1164],{"class":2043},[1115,21059,786],{"class":2032},[1115,21061,1199],{"class":2035},[1115,21063,21064],{"class":2032}," level",[1115,21066,2291],{"class":2035},[1115,21068,14414],{"class":2046},[1115,21070,2185],{"class":2043},[1115,21072,21073,21076,21078,21081,21083,21085,21087,21089,21091,21093,21095,21097],{"class":2029,"line":27},[1115,21074,21075],{"class":2032},"nove",[1115,21077,2036],{"class":2035},[1115,21079,21080],{"class":2039}," data.frame",[1115,21082,1164],{"class":2043},[1115,21084,20623],{"class":2032},[1115,21086,2291],{"class":2035},[1115,21088,2040],{"class":2039},[1115,21090,1164],{"class":2043},[1115,21092,3421],{"class":2046},[1115,21094,1199],{"class":2035},[1115,21096,5384],{"class":2046},[1115,21098,3694],{"class":2043},[1115,21100,21101,21104,21106,21108,21110,21113,21115,21118,21120,21123,21125,21128,21130,21132,21134,21136],{"class":2029,"line":148},[1115,21102,21103],{"class":2039},"predict",[1115,21105,1164],{"class":2043},[1115,21107,786],{"class":2032},[1115,21109,1199],{"class":2035},[1115,21111,21112],{"class":2032}," newdata",[1115,21114,2291],{"class":2035},[1115,21116,21117],{"class":2032}," nove",[1115,21119,1199],{"class":2035},[1115,21121,21122],{"class":2032}," interval",[1115,21124,2291],{"class":2035},[1115,21126,21127],{"class":8322}," \"confidence\"",[1115,21129,1199],{"class":2035},[1115,21131,21064],{"class":2032},[1115,21133,2291],{"class":2035},[1115,21135,14414],{"class":2046},[1115,21137,2185],{"class":2043},[1115,21139,21140,21142,21144,21146,21148,21150,21152,21154,21156,21158,21160,21163,21165,21167,21169,21171],{"class":2029,"line":111},[1115,21141,21103],{"class":2039},[1115,21143,1164],{"class":2043},[1115,21145,786],{"class":2032},[1115,21147,1199],{"class":2035},[1115,21149,21112],{"class":2032},[1115,21151,2291],{"class":2035},[1115,21153,21117],{"class":2032},[1115,21155,1199],{"class":2035},[1115,21157,21122],{"class":2032},[1115,21159,2291],{"class":2035},[1115,21161,21162],{"class":8322}," \"prediction\"",[1115,21164,1199],{"class":2035},[1115,21166,21064],{"class":2032},[1115,21168,2291],{"class":2035},[1115,21170,14414],{"class":2046},[1115,21172,2185],{"class":2043},[2020,21174,21177],{"className":21175,"code":21176,"language":2349,"meta":2024},[2347],"                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",[2015,21178,21176],{"__ignoreMap":2024},[1110,21180,21181,21184,21185,1932,21188,21201,21202,1381,21215,21218,21219,21222],{},[2015,21182,21183],{},"interval = \"confidence\""," dává interval spolehlivosti pro ",[1248,21186,21187],{},"střední hodnotu",[1115,21189,21191],{"className":21190},[1139],[1141,21192,21193],{"xmlns":1143},[1145,21194,21195,21199],{},[1148,21196,21197],{},[1154,21198,1528],{},[1172,21200,1528],{"encoding":1174}," při daném ",[1115,21203,21205],{"className":21204},[1139],[1141,21206,21207],{"xmlns":1143},[1145,21208,21209,21213],{},[1148,21210,21211],{},[1154,21212,1167],{},[1172,21214,1167],{"encoding":1174},[2015,21216,21217],{},"interval = \"prediction\""," širší interval pro ",[1248,21220,21221],{},"jednotlivé budoucí pozorování"," — ten musí zahrnout i rozptyl kolem regresní přímky, proto je vždy širší.",[20599,21224,21226],{"id":21225},"diagnostika-modelu","Diagnostika modelu",[1110,21228,21229,21230,1381,21233,1385,21236,21239],{},"Platnost závěrů z regresní přímky stojí na předpokladech o reziduích: ",[1248,21231,21232],{},"absenci autokorelace",[1248,21234,21235],{},"stálosti rozptylu (homoskedasticitě)",[1248,21237,21238],{},"normalitě",". V R se ověřují takto:",[2020,21241,21243],{"className":2022,"code":21242,"language":71,"meta":2024,"style":2024},"library(lmtest)\ndwtest(model)\n",[2015,21244,21245,21257],{"__ignoreMap":2024},[1115,21246,21247,21250,21252,21255],{"class":2029,"line":10},[1115,21248,21249],{"class":2035},"library",[1115,21251,1164],{"class":2043},[1115,21253,21254],{"class":2032},"lmtest",[1115,21256,2185],{"class":2043},[1115,21258,21259,21262,21264,21266],{"class":2029,"line":27},[1115,21260,21261],{"class":2039},"dwtest",[1115,21263,1164],{"class":2043},[1115,21265,786],{"class":2032},[1115,21267,2185],{"class":2043},[2020,21269,21272],{"className":21270,"code":21271,"language":2349,"meta":2024},[2347],"    Durbin-Watson test\n\ndata:  model\nDW = 3.4121, p-value = 0.9555\nalternative hypothesis: true autocorrelation is greater than 0\n",[2015,21273,21271],{"__ignoreMap":2024},[1110,21275,21276,21277,21294,21295,21312,21313,21330],{},"Durbinův–Watsonův test má ",[1115,21278,21280],{"className":21279},[1139],[1141,21281,21282],{"xmlns":1143},[1145,21283,21284,21292],{},[1148,21285,21286],{},[1151,21287,21288,21290],{},[1154,21289,6105],{},[1312,21291,4585],{},[1172,21293,6110],{"encoding":1174},": v modelu není problém s autokorelací, proti ",[1115,21296,21298],{"className":21297},[1139],[1141,21299,21300],{"xmlns":1143},[1145,21301,21302,21310],{},[1148,21303,21304],{},[1151,21305,21306,21308],{},[1154,21307,6105],{},[1312,21309,1489],{},[1172,21311,7508],{"encoding":1174},": 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, ",[1115,21314,21316],{"className":21315},[1139],[1141,21317,21318],{"xmlns":1143},[1145,21319,21320,21328],{},[1148,21321,21322],{},[1151,21323,21324,21326],{},[1154,21325,6105],{},[1312,21327,4585],{},[1172,21329,6110],{"encoding":1174}," se nezamítá.",[2020,21332,21334],{"className":2022,"code":21333,"language":71,"meta":2024,"style":2024},"library(whitestrap)\nwhite_test(model)\n",[2015,21335,21336,21347],{"__ignoreMap":2024},[1115,21337,21338,21340,21342,21345],{"class":2029,"line":10},[1115,21339,21249],{"class":2035},[1115,21341,1164],{"class":2043},[1115,21343,21344],{"class":2032},"whitestrap",[1115,21346,2185],{"class":2043},[1115,21348,21349,21352,21354,21356],{"class":2029,"line":27},[1115,21350,21351],{"class":2039},"white_test",[1115,21353,1164],{"class":2043},[1115,21355,786],{"class":2032},[1115,21357,2185],{"class":2043},[2020,21359,21362],{"className":21360,"code":21361,"language":2349,"meta":2024},[2347],"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",[2015,21363,21361],{"__ignoreMap":2024},[1110,21365,21366,21367,21384,21385,21402,21403,21330],{},"Whiteův test má ",[1115,21368,21370],{"className":21369},[1139],[1141,21371,21372],{"xmlns":1143},[1145,21373,21374,21382],{},[1148,21375,21376],{},[1151,21377,21378,21380],{},[1154,21379,6105],{},[1312,21381,4585],{},[1172,21383,6110],{"encoding":1174},": rozptyl reziduí je stálý (homoskedasticita), proti ",[1115,21386,21388],{"className":21387},[1139],[1141,21389,21390],{"xmlns":1143},[1145,21391,21392,21400],{},[1148,21393,21394],{},[1151,21395,21396,21398],{},[1154,21397,6105],{},[1312,21399,1489],{},[1172,21401,7508],{"encoding":1174},": rozptyl není stálý (heteroskedasticita). P-hodnota 0,21 je nad 0,05, ",[1115,21404,21406],{"className":21405},[1139],[1141,21407,21408],{"xmlns":1143},[1145,21409,21410,21418],{},[1148,21411,21412],{},[1151,21413,21414,21416],{},[1154,21415,6105],{},[1312,21417,4585],{},[1172,21419,6110],{"encoding":1174},[2020,21421,21423],{"className":2022,"code":21422,"language":71,"meta":2024,"style":2024},"shapiro.test(residuals(model))\n",[2015,21424,21425],{"__ignoreMap":2024},[1115,21426,21427,21430,21432,21434,21436,21438],{"class":2029,"line":10},[1115,21428,21429],{"class":2039},"shapiro.test",[1115,21431,1164],{"class":2043},[1115,21433,20897],{"class":2039},[1115,21435,1164],{"class":2043},[1115,21437,786],{"class":2032},[1115,21439,3694],{"class":2043},[2020,21441,21444],{"className":21442,"code":21443,"language":2349,"meta":2024},[2347],"    Shapiro-Wilk normality test\n\ndata:  residuals(model)\nW = 0.94818, p-value = 0.7255\n",[2015,21445,21443],{"__ignoreMap":2024},[1110,21447,21448,21449,21466],{},"Shapiro–Wilkův test má ",[1115,21450,21452],{"className":21451},[1139],[1141,21453,21454],{"xmlns":1143},[1145,21455,21456,21464],{},[1148,21457,21458],{},[1151,21459,21460,21462],{},[1154,21461,6105],{},[1312,21463,4585],{},[1172,21465,6110],{"encoding":1174},": rezidua pocházejí z normálního rozdělení. P-hodnota 0,73 opět nevede k zamítnutí — všechny tři předpoklady model splňuje.",[1110,21468,21469],{},[1393,21470],{"alt":21471,"className":21472,"src":21473},"mask-ra-diagnostika-rezidui",[1242,1397],"\u002Fwiki-assets\u002Fmask-ra-diagnostika-rezidui.png",[1110,21475,21476],{},"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.",[1103,21478,21480,21487,21518,21553,21618],{"className":21479,"dataCallout":2447},[1106,2446],[1110,21481,21483,21486],{"className":21482},[1113],[1115,21484],{"className":21485,"ariaHidden":1121},[1118,2454,1120],"Příklad: Regresní přímka",[1110,21488,21489,21490,21503,21504,21517],{},"V souboru s údaji o hodnotě produkce (v milionech Kč, proměnná ",[1115,21491,21493],{"className":21492},[1139],[1141,21494,21495],{"xmlns":1143},[1145,21496,21497,21501],{},[1148,21498,21499],{},[1154,21500,1528],{},[1172,21502,1528],{"encoding":1174},") a výši investic (ve stovkách tisíc Kč, proměnná ",[1115,21505,21507],{"className":21506},[1139],[1141,21508,21509],{"xmlns":1143},[1145,21510,21511,21515],{},[1148,21512,21513],{},[1154,21514,1167],{},[1172,21516,1167],{"encoding":1174},") 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.",[1110,21519,21520,21521,1176],{},"Výsledek: ",[1115,21522,21524],{"className":21523},[1139],[1141,21525,21526],{"xmlns":1143},[1145,21527,21528,21550],{},[1148,21529,21530,21536,21538,21541,21543,21546,21548],{},[1474,21531,21532,21534],{"accent":1121},[1154,21533,1528],{},[1161,21535,7244],{},[1161,21537,1483],{},[1312,21539,21540],{},"32,74",[1161,21542,3835],{},[1312,21544,21545],{},"2,15",[1316,21547,1318],{},[1154,21549,1167],{},[1172,21551,21552],{"encoding":1174},"\\hat y = 32{,}74 + 2{,}15\\,x",[1110,21554,20550,21555,21577,21578,21617],{},[1115,21556,21558],{"className":21557},[1139],[1141,21559,21560],{"xmlns":1143},[1145,21561,21562,21574],{},[1148,21563,21564,21570,21572],{},[1151,21565,21566,21568],{},[1154,21567,1534],{},[1312,21569,1489],{},[1161,21571,1483],{},[1312,21573,21545],{},[1172,21575,21576],{"encoding":1174},"b_1=2{,}15"," říká, že se zvýšením investic o 100 000 Kč vzroste produkce v průměru o ",[1115,21579,21581],{"className":21580},[1139],[1141,21582,21583],{"xmlns":1143},[1145,21584,21585,21614],{},[1148,21586,21587,21589,21591,21593,21595,21597,21599,21601,21603,21605,21607,21610,21612],{},[1312,21588,21545],{},[1161,21590,12547],{},[1312,21592,1489],{},[1316,21594,1318],{},[1312,21596,1334],{},[1316,21598,1318],{},[1312,21600,1334],{},[1161,21602,1483],{},[1312,21604,1610],{},[1316,21606,1318],{},[1312,21608,21609],{},"150",[1316,21611,1318],{},[1312,21613,1334],{},[1172,21615,21616],{"encoding":1174},"2{,}15\\cdot 1\\,000\\,000=2\\,150\\,000"," Kč.",[1110,21619,21620,21621,8464,21640,21688,21689,19946],{},"Dosazením libovolné hodnoty investic do empirické regresní funkce dostaneme predikci produkce, například pro třináctou firmu s investicemi ",[1115,21622,21624],{"className":21623},[1139],[1141,21625,21626],{"xmlns":1143},[1145,21627,21628,21637],{},[1148,21629,21630,21632,21634],{},[1154,21631,1167],{},[1161,21633,1483],{},[1312,21635,21636],{},"34",[1172,21638,21639],{"encoding":1174},"x=34",[1115,21641,21643],{"className":21642},[1139],[1141,21644,21645],{"xmlns":1143},[1145,21646,21647,21685],{},[1148,21648,21649,21659,21661,21667,21669,21675,21677,21679,21682],{},[1151,21650,21651,21657],{},[1474,21652,21653,21655],{"accent":1121},[1154,21654,1528],{},[1161,21656,7244],{},[1312,21658,3165],{},[1161,21660,1483],{},[1151,21662,21663,21665],{},[1154,21664,1534],{},[1312,21666,4585],{},[1161,21668,3835],{},[1151,21670,21671,21673],{},[1154,21672,1534],{},[1312,21674,1489],{},[1161,21676,12547],{},[1312,21678,21636],{},[1161,21680,21681],{},"≐",[1312,21683,21684],{},"105,81",[1172,21686,21687],{"encoding":1174},"\\hat y_{13} = b_0 + b_1\\cdot 34 \\doteq 105{,}81"," milionu Kč (se zaokrouhlenými koeficienty ",[1115,21690,21692],{"className":21691},[1139],[1141,21693,21694],{"xmlns":1143},[1145,21695,21696,21713],{},[1148,21697,21698,21700,21702,21704,21706,21708,21710],{},[1312,21699,21540],{},[1161,21701,3835],{},[1312,21703,21545],{},[1161,21705,12547],{},[1312,21707,21636],{},[1161,21709,21681],{},[1312,21711,21712],{},"105,8",[1172,21714,21715],{"encoding":1174},"32{,}74 + 2{,}15\\cdot 34 \\doteq 105{,}8",[1232,21717,21719],{"id":21718},"nelineární-a-vyšší-řády-regresních-funkcí","Nelineární a vyšší řády regresních funkcí",[1110,21721,21722,21723,21726,21727,21794,21795,21813,21814,21831],{},"Když přímka závislost nevystihuje, nabízí se další ",[1248,21724,21725],{},"lineární funkce"," — tedy funkce lineární ve svých parametrech, zapsatelné ve tvaru ",[1115,21728,21730],{"className":21729},[1139],[1141,21731,21732],{"xmlns":1143},[1145,21733,21734,21791],{},[1148,21735,21736,21738,21740,21746,21748,21754,21760,21762,21764,21766,21768,21771,21773,21779,21785,21787,21789],{},[1154,21737,20175],{},[1161,21739,1483],{},[1151,21741,21742,21744],{},[1154,21743,20190],{},[1312,21745,4585],{},[1161,21747,3835],{},[1151,21749,21750,21752],{},[1154,21751,20190],{},[1312,21753,1489],{},[1151,21755,21756,21758],{},[1154,21757,1213],{},[1312,21759,1489],{},[1161,21761,1164],{"stretchy":1163},[1154,21763,1167],{},[1161,21765,1170],{"stretchy":1163},[1161,21767,3835],{},[1161,21769,21770],{},"⋯",[1161,21772,3835],{},[1151,21774,21775,21777],{},[1154,21776,20190],{},[1154,21778,1110],{},[1151,21780,21781,21783],{},[1154,21782,1213],{},[1154,21784,1110],{},[1161,21786,1164],{"stretchy":1163},[1154,21788,1167],{},[1161,21790,1170],{"stretchy":1163},[1172,21792,21793],{"encoding":1174},"\\eta=\\beta_0+\\beta_1 f_1(x)+\\dots+\\beta_p f_p(x)"," se známými funkcemi ",[1115,21796,21798],{"className":21797},[1139],[1141,21799,21800],{"xmlns":1143},[1145,21801,21802,21810],{},[1148,21803,21804],{},[1151,21805,21806,21808],{},[1154,21807,1213],{},[1154,21809,1502],{},[1172,21811,21812],{"encoding":1174},"f_i"," a neznámými parametry ",[1115,21815,21817],{"className":21816},[1139],[1141,21818,21819],{"xmlns":1143},[1145,21820,21821,21829],{},[1148,21822,21823],{},[1151,21824,21825,21827],{},[1154,21826,20190],{},[1154,21828,1502],{},[1172,21830,20236],{"encoding":1174},". I tyto parametry se odhadují metodou nejmenších čtverců, stejně jako u přímky:",[1115,21833,21835],{"className":21834},[1139],[1141,21836,21837],{"xmlns":1143,"display":1468},[1145,21838,21839,22149],{},[21840,21841,21844,21917,22030,22089],"mtable",{"rowspacing":21842,"columnalign":21843,"columnspacing":11201},"0.25em","right left",[21845,21846,21847,21871],"mtr",{},[21848,21849,21850],"mtd",{},[7752,21851,21852],{"scriptlevel":4585,"displaystyle":1121},[1148,21853,21854,21868],{},[1148,21855,21856,21859,21865],{},[1316,21857,21858],{},"parabolick",[1474,21860,21861,21863],{"accent":1121},[1316,21862,1239],{},[1161,21864,1531],{},[1316,21866,21867],{}," regrese: ",[1516,21869],{"width":21870},"1em",[21848,21872,21873],{},[7752,21874,21875],{"scriptlevel":4585,"displaystyle":1121},[1148,21876,21877,21879,21885,21887,21893,21895,21901,21903,21905,21911],{},[1148,21878],{},[1474,21880,21881,21883],{"accent":1121},[1154,21882,1528],{},[1161,21884,7244],{},[1161,21886,1483],{},[1151,21888,21889,21891],{},[1154,21890,1534],{},[1312,21892,4585],{},[1161,21894,3835],{},[1151,21896,21897,21899],{},[1154,21898,1534],{},[1312,21900,1489],{},[1154,21902,1167],{},[1161,21904,3835],{},[1151,21906,21907,21909],{},[1154,21908,1534],{},[1312,21910,1610],{},[1603,21912,21913,21915],{},[1154,21914,1167],{},[1312,21916,1610],{},[21845,21918,21919,21966],{},[21848,21920,21921],{},[7752,21922,21923],{"scriptlevel":4585,"displaystyle":1121},[1148,21924,21925,21964],{},[1148,21926,21927,21930,21936,21939,21943,21946,21952,21955,21961],{},[1316,21928,21929],{},"polynomick",[1474,21931,21932,21934],{"accent":1121},[1316,21933,1239],{},[1161,21935,1531],{},[1316,21937,21938],{}," regrese ",[7752,21940,21941],{"scriptlevel":4585,"displaystyle":1163},[1154,21942,1110],{},[1316,21944,21945],{},"-t",[1474,21947,21948,21950],{"accent":1121},[1316,21949,1539],{},[1161,21951,1531],{},[1316,21953,21954],{},"ho stupn",[1474,21956,21957,21959],{"accent":1121},[1316,21958,1539],{},[1161,21960,1542],{},[1316,21962,21963],{},": ",[1516,21965],{"width":21870},[21848,21967,21968],{},[7752,21969,21970],{"scriptlevel":4585,"displaystyle":1121},[1148,21971,21972,21974,21980,21982,21988,21990,21996,21998,22000,22006,22012,22014,22016,22018,22024],{},[1148,21973],{},[1474,21975,21976,21978],{"accent":1121},[1154,21977,1528],{},[1161,21979,7244],{},[1161,21981,1483],{},[1151,21983,21984,21986],{},[1154,21985,1534],{},[1312,21987,4585],{},[1161,21989,3835],{},[1151,21991,21992,21994],{},[1154,21993,1534],{},[1312,21995,1489],{},[1154,21997,1167],{},[1161,21999,3835],{},[1151,22001,22002,22004],{},[1154,22003,1534],{},[1312,22005,1610],{},[1603,22007,22008,22010],{},[1154,22009,1167],{},[1312,22011,1610],{},[1161,22013,3835],{},[1161,22015,21770],{},[1161,22017,3835],{},[1151,22019,22020,22022],{},[1154,22021,1534],{},[1154,22023,1110],{},[1603,22025,22026,22028],{},[1154,22027,1167],{},[1154,22029,1110],{},[21845,22031,22032,22053],{},[21848,22033,22034],{},[7752,22035,22036],{"scriptlevel":4585,"displaystyle":1121},[1148,22037,22038,22051],{},[1148,22039,22040,22043,22049],{},[1316,22041,22042],{},"hyperbolick",[1474,22044,22045,22047],{"accent":1121},[1316,22046,1239],{},[1161,22048,1531],{},[1316,22050,21867],{},[1516,22052],{"width":21870},[21848,22054,22055],{},[7752,22056,22057],{"scriptlevel":4585,"displaystyle":1121},[1148,22058,22059,22061,22067,22069,22075,22077,22083],{},[1148,22060],{},[1474,22062,22063,22065],{"accent":1121},[1154,22064,1528],{},[1161,22066,7244],{},[1161,22068,1483],{},[1151,22070,22071,22073],{},[1154,22072,1534],{},[1312,22074,4585],{},[1161,22076,3835],{},[1151,22078,22079,22081],{},[1154,22080,1534],{},[1312,22082,1489],{},[1485,22084,22085,22087],{},[1312,22086,1489],{},[1154,22088,1167],{},[21845,22090,22091,22112],{},[21848,22092,22093],{},[7752,22094,22095],{"scriptlevel":4585,"displaystyle":1121},[1148,22096,22097,22110],{},[1148,22098,22099,22102,22108],{},[1316,22100,22101],{},"logaritmick",[1474,22103,22104,22106],{"accent":1121},[1316,22105,1239],{},[1161,22107,1531],{},[1316,22109,21867],{},[1516,22111],{"width":21870},[21848,22113,22114],{},[7752,22115,22116],{"scriptlevel":4585,"displaystyle":1121},[1148,22117,22118,22120,22126,22128,22134,22136,22142,22145,22147],{},[1148,22119],{},[1474,22121,22122,22124],{"accent":1121},[1154,22123,1528],{},[1161,22125,7244],{},[1161,22127,1483],{},[1151,22129,22130,22132],{},[1154,22131,1534],{},[1312,22133,4585],{},[1161,22135,3835],{},[1151,22137,22138,22140],{},[1154,22139,1534],{},[1312,22141,1489],{},[1154,22143,22144],{},"ln",[1161,22146,1761],{},[1154,22148,1167],{},[1172,22150,22151],{"encoding":1174},"\\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}",[1110,22153,22154,22155,22158,22159,22205,22206,6481],{},"Naproti tomu ",[1248,22156,22157],{},"nelineární funkce"," nelze do tvaru ",[1115,22160,22162],{"className":22161},[1139],[1141,22163,22164],{"xmlns":1143},[1145,22165,22166,22202],{},[1148,22167,22168,22170,22172,22178,22180,22186,22192,22194,22196,22198,22200],{},[1154,22169,20175],{},[1161,22171,1483],{},[1151,22173,22174,22176],{},[1154,22175,20190],{},[1312,22177,4585],{},[1161,22179,3835],{},[1151,22181,22182,22184],{},[1154,22183,20190],{},[1312,22185,1489],{},[1151,22187,22188,22190],{},[1154,22189,1213],{},[1312,22191,1489],{},[1161,22193,1164],{"stretchy":1163},[1154,22195,1167],{},[1161,22197,1170],{"stretchy":1163},[1161,22199,3835],{},[1161,22201,3022],{},[1172,22203,22204],{"encoding":1174},"\\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 ",[1248,22207,22208],{},"exponenciální regrese",[1115,22210,22212],{"className":22211},[1139],[1141,22213,22214],{"xmlns":1143,"display":1468},[1145,22215,22216,22248],{},[1148,22217,22218,22224,22226,22232,22234,22246],{},[1474,22219,22220,22222],{"accent":1121},[1154,22221,1528],{},[1161,22223,7244],{},[1161,22225,1483],{},[1151,22227,22228,22230],{},[1154,22229,1534],{},[1312,22231,4585],{},[1161,22233,12547],{},[1645,22235,22236,22238,22240],{},[1154,22237,1534],{},[1312,22239,1489],{},[1148,22241,22242,22244],{},[1316,22243,1318],{},[1154,22245,1167],{},[1154,22247,1176],{"mathvariant":1869},[1172,22249,22250],{"encoding":1174},"\\hat y = b_0 \\cdot b_1^{\\,x}.",[1110,22252,22253],{},[1393,22254],{"alt":22255,"className":22256,"src":22257},"mask-ra-nelinearni-krivky",[1242,1397],"\u002Fwiki-assets\u002Fmask-ra-nelinearni-krivky.png",[20599,22259,22261],{"id":22260},"v-r-parabolická-regrese","V R — parabolická regrese",[1110,22263,22264,22265,6481],{},"Na ročních ziscích firmy (šest let) se parabolická regrese odhadne přidáním kvadratického členu ",[2015,22266,22267],{},"I(x^2)",[2020,22269,22271],{"className":2022,"code":22270,"language":71,"meta":2024,"style":2024},"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",[2015,22272,22273,22308,22348,22382],{"__ignoreMap":2024},[1115,22274,22275,22278,22280,22282,22284,22286,22288,22290,22292,22294,22296,22298,22300,22302,22304,22306],{"class":2029,"line":10},[1115,22276,22277],{"class":2032},"rok",[1115,22279,2036],{"class":2035},[1115,22281,2040],{"class":2039},[1115,22283,1164],{"class":2043},[1115,22285,1489],{"class":2046},[1115,22287,1199],{"class":2035},[1115,22289,4210],{"class":2046},[1115,22291,1199],{"class":2035},[1115,22293,4424],{"class":2046},[1115,22295,1199],{"class":2035},[1115,22297,8284],{"class":2046},[1115,22299,1199],{"class":2035},[1115,22301,4225],{"class":2046},[1115,22303,1199],{"class":2035},[1115,22305,2294],{"class":2046},[1115,22307,2185],{"class":2043},[1115,22309,22310,22312,22314,22316,22318,22321,22323,22326,22328,22331,22333,22336,22338,22341,22343,22346],{"class":2029,"line":27},[1115,22311,1088],{"class":2032},[1115,22313,2036],{"class":2035},[1115,22315,2040],{"class":2039},[1115,22317,1164],{"class":2043},[1115,22319,22320],{"class":2046},"112",[1115,22322,1199],{"class":2035},[1115,22324,22325],{"class":2046}," 149",[1115,22327,1199],{"class":2035},[1115,22329,22330],{"class":2046}," 238",[1115,22332,1199],{"class":2035},[1115,22334,22335],{"class":2046}," 354",[1115,22337,1199],{"class":2035},[1115,22339,22340],{"class":2046}," 580",[1115,22342,1199],{"class":2035},[1115,22344,22345],{"class":2046}," 867",[1115,22347,2185],{"class":2043},[1115,22349,22350,22353,22355,22357,22359,22361,22363,22366,22369,22372,22374,22376,22378,22380],{"class":2029,"line":148},[1115,22351,22352],{"class":2032},"model_parabola",[1115,22354,2036],{"class":2035},[1115,22356,20703],{"class":2039},[1115,22358,1164],{"class":2043},[1115,22360,1088],{"class":2032},[1115,22362,20710],{"class":2035},[1115,22364,22365],{"class":2032}," rok",[1115,22367,22368],{"class":2035}," +",[1115,22370,22371],{"class":2039}," I",[1115,22373,1164],{"class":2043},[1115,22375,22277],{"class":2032},[1115,22377,7244],{"class":2035},[1115,22379,1610],{"class":2046},[1115,22381,3694],{"class":2043},[1115,22383,22384,22386,22388,22390],{"class":2029,"line":111},[1115,22385,20720],{"class":2039},[1115,22387,1164],{"class":2043},[1115,22389,22352],{"class":2032},[1115,22391,2185],{"class":2043},[2020,22393,22396],{"className":22394,"code":22395,"language":2349,"meta":2024},[2347],"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",[2015,22397,22395],{"__ignoreMap":2024},[1110,22399,22400,22401,22446],{},"Odhadnutá parabola ",[1115,22402,22404],{"className":22403},[1139],[1141,22405,22406],{"xmlns":1143},[1145,22407,22408,22443],{},[1148,22409,22410,22416,22418,22421,22423,22426,22428,22430,22432,22435,22437],{},[1474,22411,22412,22414],{"accent":1121},[1154,22413,1528],{},[1161,22415,7244],{},[1161,22417,1483],{},[1312,22419,22420],{},"164,6",[1161,22422,1623],{},[1312,22424,22425],{},"76,6",[1316,22427,1318],{},[1154,22429,1167],{},[1161,22431,3835],{},[1312,22433,22434],{},"32,1",[1316,22436,1318],{},[1603,22438,22439,22441],{},[1154,22440,1167],{},[1312,22442,1610],{},[1172,22444,22445],{"encoding":1174},"\\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.",[20599,22448,22450],{"id":22449},"v-r-exponenciální-regrese","V R — exponenciální regrese",[1110,22452,22453,22454,22456],{},"Nelineární funkce se v R odhadují funkcí ",[2015,22455,19961],{}," ze stejnojmenného balíčku. Bez zadaných počátečních hodnot R upozorní, že parametry nastavil na 1, a odhad dopočítá iteračně:",[2020,22458,22460],{"className":2022,"code":22459,"language":71,"meta":2024,"style":2024},"library(nls2)\nmodel_exp \u003C- nls2(zisk ~ b1 * exp(b2 * rok))\nsummary(model_exp)\n",[2015,22461,22462,22472,22508],{"__ignoreMap":2024},[1115,22463,22464,22466,22468,22470],{"class":2029,"line":10},[1115,22465,21249],{"class":2035},[1115,22467,1164],{"class":2043},[1115,22469,19945],{"class":2032},[1115,22471,2185],{"class":2043},[1115,22473,22474,22477,22479,22482,22484,22486,22488,22491,22494,22497,22499,22502,22504,22506],{"class":2029,"line":27},[1115,22475,22476],{"class":2032},"model_exp",[1115,22478,2036],{"class":2035},[1115,22480,22481],{"class":2039}," nls2",[1115,22483,1164],{"class":2043},[1115,22485,1088],{"class":2032},[1115,22487,20710],{"class":2035},[1115,22489,22490],{"class":2032}," b1",[1115,22492,22493],{"class":2035}," *",[1115,22495,22496],{"class":2039}," exp",[1115,22498,1164],{"class":2043},[1115,22500,22501],{"class":2032},"b2",[1115,22503,22493],{"class":2035},[1115,22505,22365],{"class":2032},[1115,22507,3694],{"class":2043},[1115,22509,22510,22512,22514,22516],{"class":2029,"line":148},[1115,22511,20720],{"class":2039},[1115,22513,1164],{"class":2043},[1115,22515,22476],{"class":2032},[1115,22517,2185],{"class":2043},[2020,22519,22522],{"className":22520,"code":22521,"language":2349,"meta":2024},[2347],"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",[2015,22523,22521],{"__ignoreMap":2024},[1110,22525,22526,22527,6481],{},"Stejnou křivku lze zapsat i v mocninném tvaru ",[1115,22528,22530],{"className":22529},[1139],[1141,22531,22532],{"xmlns":1143},[1145,22533,22534,22560],{},[1148,22535,22536,22542,22544,22550,22552],{},[1474,22537,22538,22540],{"accent":1121},[1154,22539,1528],{},[1161,22541,7244],{},[1161,22543,1483],{},[1151,22545,22546,22548],{},[1154,22547,1534],{},[1312,22549,1489],{},[1161,22551,12547],{},[1645,22553,22554,22556,22558],{},[1154,22555,1534],{},[1312,22557,1610],{},[1154,22559,1167],{},[1172,22561,22562],{"encoding":1174},"\\hat y=b_1\\cdot b_2^{x}",[2020,22564,22566],{"className":2022,"code":22565,"language":71,"meta":2024,"style":2024},"model_pow \u003C- nls2(zisk ~ b1 * (b2^rok))\nsummary(model_pow)\n",[2015,22567,22568,22597],{"__ignoreMap":2024},[1115,22569,22570,22573,22575,22577,22579,22581,22583,22585,22587,22589,22591,22593,22595],{"class":2029,"line":10},[1115,22571,22572],{"class":2032},"model_pow",[1115,22574,2036],{"class":2035},[1115,22576,22481],{"class":2039},[1115,22578,1164],{"class":2043},[1115,22580,1088],{"class":2032},[1115,22582,20710],{"class":2035},[1115,22584,22490],{"class":2032},[1115,22586,22493],{"class":2035},[1115,22588,3997],{"class":2043},[1115,22590,22501],{"class":2032},[1115,22592,7244],{"class":2035},[1115,22594,22277],{"class":2032},[1115,22596,3694],{"class":2043},[1115,22598,22599,22601,22603,22605],{"class":2029,"line":27},[1115,22600,20720],{"class":2039},[1115,22602,1164],{"class":2043},[1115,22604,22572],{"class":2032},[1115,22606,2185],{"class":2043},[2020,22608,22611],{"className":22609,"code":22610,"language":2349,"meta":2024},[2347],"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",[2015,22612,22610],{"__ignoreMap":2024},[1110,22614,22615,22616,22680,22681,22705],{},"Obě varianty popisují stejnou křivku (",[1115,22617,22619],{"className":22618},[1139],[1141,22620,22621],{"xmlns":1143},[1145,22622,22623,22677],{},[1148,22624,22625,22642,22644],{},[1645,22626,22627,22629,22631],{},[1154,22628,1534],{},[1312,22630,1610],{},[1148,22632,22633,22636],{},[1316,22634,22635],{},"mocninn",[1474,22637,22638,22640],{"accent":1121},[1316,22639,1528],{},[1161,22641,1531],{},[1161,22643,1483],{},[1603,22645,22646,22648],{},[1154,22647,1539],{},[1148,22649,22650,22652],{},[1316,22651,1318],{},[1645,22653,22654,22656,22658],{},[1154,22655,1534],{},[1312,22657,1610],{},[1148,22659,22660,22663,22669,22671],{},[1316,22661,22662],{},"exponenci",[1474,22664,22665,22667],{"accent":1121},[1316,22666,1239],{},[1161,22668,1531],{},[1316,22670,22144],{},[1474,22672,22673,22675],{"accent":1121},[1316,22674,1793],{},[1161,22676,1531],{},[1172,22678,22679],{"encoding":1174},"b_2^{\\text{mocninný}} = e^{\\,b_2^{\\text{exponenciální}}}",", zde ",[1115,22682,22684],{"className":22683},[1139],[1141,22685,22686],{"xmlns":1143},[1145,22687,22688,22702],{},[1148,22689,22690,22697,22699],{},[1603,22691,22692,22694],{},[1154,22693,1539],{},[1312,22695,22696],{},"0,4316",[1161,22698,5042],{},[1312,22700,22701],{},"1,540",[1172,22703,22704],{"encoding":1174},"e^{0{,}4316}\\approx 1{,}540",") a mají totožnou reziduální chybu — je to jen otázka parametrizace.",[20599,22707,22709],{"id":22708},"v-r-hyperbolická-regrese","V R — hyperbolická regrese",[1110,22711,22712,22713,6481],{},"Hyperbolická regrese se odhadne jako obyčejná lineární regrese na transformované proměnné ",[2015,22714,22715],{},"I(1\u002Fx)",[2020,22717,22719],{"className":2022,"code":22718,"language":71,"meta":2024,"style":2024},"model_hyperbola \u003C- lm(tydenni_vydaje ~ I(1 \u002F pocet_clenu))\nsummary(model_hyperbola)\n",[2015,22720,22721,22748],{"__ignoreMap":2024},[1115,22722,22723,22726,22728,22730,22732,22734,22736,22738,22740,22742,22744,22746],{"class":2029,"line":10},[1115,22724,22725],{"class":2032},"model_hyperbola",[1115,22727,2036],{"class":2035},[1115,22729,20703],{"class":2039},[1115,22731,1164],{"class":2043},[1115,22733,20658],{"class":2032},[1115,22735,20710],{"class":2035},[1115,22737,22371],{"class":2039},[1115,22739,1164],{"class":2043},[1115,22741,1489],{"class":2046},[1115,22743,4650],{"class":2035},[1115,22745,20713],{"class":2032},[1115,22747,3694],{"class":2043},[1115,22749,22750,22752,22754,22756],{"class":2029,"line":27},[1115,22751,20720],{"class":2039},[1115,22753,1164],{"class":2043},[1115,22755,22725],{"class":2032},[1115,22757,2185],{"class":2043},[2020,22759,22762],{"className":22760,"code":22761,"language":2349,"meta":2024},[2347],"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",[2015,22763,22761],{"__ignoreMap":2024},[1110,22765,22766,22767,22801,22802,22823],{},"Model ",[1115,22768,22770],{"className":22769},[1139],[1141,22771,22772],{"xmlns":1143},[1145,22773,22774,22798],{},[1148,22775,22776,22782,22784,22787,22789],{},[1474,22777,22778,22780],{"accent":1121},[1154,22779,1528],{},[1161,22781,7244],{},[1161,22783,1483],{},[1312,22785,22786],{},"2180,7",[1161,22788,1623],{},[7752,22790,22791],{"scriptlevel":4585,"displaystyle":1121},[1485,22792,22793,22796],{},[1312,22794,22795],{},"1920,0",[1154,22797,1167],{},[1172,22799,22800],{"encoding":1174},"\\hat y = 2180{,}7 - \\dfrac{1920{,}0}{x}"," vysvětluje jen 76,3 % rozptylu — u těchto dat je hyperbola podstatně horší volbou než přímka (",[1115,22803,22805],{"className":22804},[1139],[1141,22806,22807],{"xmlns":1143},[1145,22808,22809,22821],{},[1148,22810,22811,22817,22819],{},[1603,22812,22813,22815],{},[1154,22814,1749],{},[1312,22816,1610],{},[1161,22818,1483],{},[1312,22820,20858],{},[1172,22822,20861],{"encoding":1174},"). Právě k takovému porovnání slouží index determinace: nízká hodnota signalizuje, že zvolený typ funkce k datům nesedí.",[1103,22825,22827,22834,22865,22913],{"className":22826,"dataCallout":2447},[1106,2446],[1110,22828,22830,22833],{"className":22829},[1113],[1115,22831],{"className":22832,"ariaHidden":1121},[1118,2454,1120],"Příklad: Parabolická regrese",[1110,22835,22836,22837,22850,22851,22864],{},"Prodejna počítačových her nechala prodavače absolvovat kurz prodejních dovedností. Při dvaceti měřeních sledovala, kolik zákazníků navštíví prodejnu během prodejní doby (proměnná ",[1115,22838,22840],{"className":22839},[1139],[1141,22841,22842],{"xmlns":1143},[1145,22843,22844,22848],{},[1148,22845,22846],{},[1154,22847,1167],{},[1172,22849,1167],{"encoding":1174},") a jaká je toho dne tržba v tisících Kč (proměnná ",[1115,22852,22854],{"className":22853},[1139],[1141,22855,22856],{"xmlns":1143},[1145,22857,22858,22862],{},[1148,22859,22860],{},[1154,22861,1528],{},[1172,22863,1528],{"encoding":1174},"). Zároveň chtěla zjistit, zda při rostoucím počtu zákazníků stačí stávající počet prodavačů.",[1110,22866,21520,22867,1176],{},[1115,22868,22870],{"className":22869},[1139],[1141,22871,22872],{"xmlns":1143},[1145,22873,22874,22910],{},[1148,22875,22876,22882,22884,22886,22889,22891,22894,22896,22898,22900,22902,22904],{},[1474,22877,22878,22880],{"accent":1121},[1154,22879,1528],{},[1161,22881,7244],{},[1161,22883,1483],{},[1161,22885,1623],{},[1312,22887,22888],{},"60,3",[1161,22890,3835],{},[1312,22892,22893],{},"4,55",[1316,22895,1318],{},[1154,22897,1167],{},[1161,22899,1623],{},[1312,22901,8460],{},[1316,22903,1318],{},[1603,22905,22906,22908],{},[1154,22907,1167],{},[1312,22909,1610],{},[1172,22911,22912],{"encoding":1174},"\\hat y = -60{,}3 + 4{,}55\\,x - 0{,}05\\,x^2",[1110,22914,22915,22916,22934],{},"Záporný koeficient ",[1115,22917,22919],{"className":22918},[1139],[1141,22920,22921],{"xmlns":1143},[1145,22922,22923,22931],{},[1148,22924,22925],{},[1151,22926,22927,22929],{},[1154,22928,1534],{},[1312,22930,1610],{},[1172,22932,22933],{"encoding":1174},"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.",[1103,22936,22938,22945,22975,23020],{"className":22937,"dataCallout":2447},[1106,2446],[1110,22939,22941,22944],{"className":22940},[1113],[1115,22942],{"className":22943,"ariaHidden":1121},[1118,2454,1120],"Příklad: Hyperbolická regrese",[1110,22946,22947,22948,22961,22962,19946],{},"V podniku se podle interního účetnictví sledovala závislost vlastních nákladů na jednotku produkce v Kč (proměnná ",[1115,22949,22951],{"className":22950},[1139],[1141,22952,22953],{"xmlns":1143},[1145,22954,22955,22959],{},[1148,22956,22957],{},[1154,22958,1528],{},[1172,22960,1528],{"encoding":1174},") na objemu produkce v tisících kusů (proměnná ",[1115,22963,22965],{"className":22964},[1139],[1141,22966,22967],{"xmlns":1143},[1145,22968,22969,22973],{},[1148,22970,22971],{},[1154,22972,1167],{},[1172,22974,1167],{"encoding":1174},[1110,22976,21520,22977,1176],{},[1115,22978,22980],{"className":22979},[1139],[1141,22981,22982],{"xmlns":1143},[1145,22983,22984,23017],{},[1148,22985,22986,22992,22994,22996,22999,23001],{},[1474,22987,22988,22990],{"accent":1121},[1154,22989,1528],{},[1161,22991,7244],{},[1161,22993,1483],{},[1161,22995,1623],{},[1312,22997,22998],{},"96,78",[1161,23000,3835],{},[7752,23002,23003],{"scriptlevel":4585,"displaystyle":1121},[1485,23004,23005,23015],{},[1148,23006,23007,23010,23012],{},[1312,23008,23009],{},"250",[1316,23011,1318],{},[1312,23013,23014],{},"528,88",[1154,23016,1167],{},[1172,23018,23019],{"encoding":1174},"\\hat y = -96{,}78 + \\dfrac{250\\,528{,}88}{x}",[1110,23021,23022,23023,23040],{},"Záporná hodnota ",[1115,23024,23026],{"className":23025},[1139],[1141,23027,23028],{"xmlns":1143},[1145,23029,23030,23038],{},[1148,23031,23032],{},[1151,23033,23034,23036],{},[1154,23035,1534],{},[1312,23037,1489],{},[1172,23039,20568],{"encoding":1174}," v čitateli ukazuje klesající náklady na jednotku s rostoucím objemem produkce — typický projev úspor z rozsahu, který hyperbola dobře zachycuje.",[1232,23042,23044],{"id":23043},"kvalita-regresní-funkce-a-korelační-analýza","Kvalita regresní funkce a korelační analýza",[1110,23046,23047,23048,6481],{},"Kvalitu odhadnuté regresní funkce vyjadřuje ",[1248,23049,19859],{},[1115,23051,23053],{"className":23052},[1139],[1141,23054,23055],{"xmlns":1143,"display":1468},[1145,23056,23057,23125],{},[1148,23058,23059,23065,23067,23089,23091,23093,23095,23123],{},[1603,23060,23061,23063],{},[1154,23062,1749],{},[1312,23064,1610],{},[1161,23066,1483],{},[1485,23068,23069,23081],{},[1645,23070,23071,23073,23079],{},[1154,23072,1607],{},[1474,23074,23075,23077],{"accent":1121},[1154,23076,1528],{},[1161,23078,7244],{},[1312,23080,1610],{},[1645,23082,23083,23085,23087],{},[1154,23084,1607],{},[1154,23086,1528],{},[1312,23088,1610],{},[1161,23090,1483],{},[1312,23092,1489],{},[1161,23094,1623],{},[1485,23096,23097,23115],{},[1645,23098,23099,23101,23113],{},[1154,23100,1607],{},[1148,23102,23103,23105,23107],{},[1154,23104,1528],{},[1161,23106,1623],{},[1474,23108,23109,23111],{"accent":1121},[1154,23110,1528],{},[1161,23112,7244],{},[1312,23114,1610],{},[1645,23116,23117,23119,23121],{},[1154,23118,1607],{},[1154,23120,1528],{},[1312,23122,1610],{},[1154,23124,1176],{"mathvariant":1869},[1172,23126,23127],{"encoding":1174},"R^2 = \\frac{s^2_{\\hat y}}{s^2_y} = 1 - \\frac{s^2_{y-\\hat y}}{s^2_y}.",[1110,23129,23130,23131,23148,23149,23162],{},"Čím blíž je ",[1115,23132,23134],{"className":23133},[1139],[1141,23135,23136],{"xmlns":1143},[1145,23137,23138,23146],{},[1148,23139,23140],{},[1603,23141,23142,23144],{},[1154,23143,1749],{},[1312,23145,1610],{},[1172,23147,19877],{"encoding":1174}," k 1, tím silnější je závislost; v procentech udává, jakou část rozptylu závisle proměnné ",[1115,23150,23152],{"className":23151},[1139],[1141,23153,23154],{"xmlns":1143},[1145,23155,23156,23160],{},[1148,23157,23158],{},[1154,23159,1528],{},[1172,23161,1528],{"encoding":1174}," se podařilo vysvětlit zvolenou regresní funkcí. Nízký index determinace může signalizovat špatně zvolený typ regresní funkce, ne nutně absenci závislosti.",[1110,23164,23165,23166,1932,23168,23191,23192,6481],{},"Obecnou mírou těsnosti závislosti — platnou pro libovolný typ regresní funkce — je ",[1248,23167,19881],{},[1115,23169,23171],{"className":23170},[1139],[1141,23172,23173],{"xmlns":1143},[1145,23174,23175,23189],{},[1148,23176,23177,23179,23181],{},[1154,23178,1193],{},[1161,23180,1483],{},[1678,23182,23183],{},[1603,23184,23185,23187],{},[1154,23186,1749],{},[1312,23188,1610],{},[1172,23190,19905],{"encoding":1174},". Je-li zvolenou funkcí regresní přímka, index korelace je roven (až na znaménko) ",[1248,23193,19909],{},[1115,23195,23197],{"className":23196},[1139],[1141,23198,23199],{"xmlns":1143,"display":1468},[1145,23200,23201,23251],{},[1148,23202,23203,23213,23215,23249],{},[1151,23204,23205,23207],{},[1154,23206,71],{},[1148,23208,23209,23211],{},[1154,23210,1167],{},[1154,23212,1528],{},[1161,23214,1483],{},[1485,23216,23217,23227],{},[1151,23218,23219,23221],{},[1154,23220,1607],{},[1148,23222,23223,23225],{},[1154,23224,1167],{},[1154,23226,1528],{},[1678,23228,23229],{},[1148,23230,23231,23239,23241],{},[1645,23232,23233,23235,23237],{},[1154,23234,1607],{},[1154,23236,1167],{},[1312,23238,1610],{},[1161,23240,12547],{},[1645,23242,23243,23245,23247],{},[1154,23244,1607],{},[1154,23246,1528],{},[1312,23248,1610],{},[1154,23250,1176],{"mathvariant":1869},[1172,23252,23253],{"encoding":1174},"r_{xy} = \\frac{s_{xy}}{\\sqrt{s^2_x\\cdot s^2_y}}.",[1110,23255,23256,23257,23273,23274,23290],{},"Koeficient korelace nabývá hodnot od ",[1115,23258,23260],{"className":23259},[1139],[1141,23261,23262],{"xmlns":1143},[1145,23263,23264,23270],{},[1148,23265,23266,23268],{},[1161,23267,1623],{},[1312,23269,1489],{},[1172,23271,23272],{"encoding":1174},"-1"," do ",[1115,23275,23277],{"className":23276},[1139],[1141,23278,23279],{"xmlns":1143},[1145,23280,23281,23287],{},[1148,23282,23283,23285],{},[1161,23284,3835],{},[1312,23286,1489],{},[1172,23288,23289],{"encoding":1174},"+1",": znaménko určuje typ závislosti (pozitivní, nebo negativní), absolutní hodnota její sílu — čím blíž k 0, tím je závislost slabší.",[1110,23292,23293],{},[1393,23294],{"alt":23295,"className":23296,"src":23297},"mask-ra-korelace-sila",[1242,1397],"\u002Fwiki-assets\u002Fmask-ra-korelace-sila.png",[1110,23299,23300,23301,23314,23315,23333,23334,1385,23347,23360],{},"S rostoucí absolutní hodnotou ",[1115,23302,23304],{"className":23303},[1139],[1141,23305,23306],{"xmlns":1143},[1145,23307,23308,23312],{},[1148,23309,23310],{},[1154,23311,71],{},[1172,23313,71],{"encoding":1174}," se body v rozptylovém grafu víc blíží přímce; kolem ",[1115,23316,23318],{"className":23317},[1139],[1141,23319,23320],{"xmlns":1143},[1145,23321,23322,23330],{},[1148,23323,23324,23326,23328],{},[1154,23325,71],{},[1161,23327,5042],{},[1312,23329,4585],{},[1172,23331,23332],{"encoding":1174},"r\\approx 0"," je mezi ",[1115,23335,23337],{"className":23336},[1139],[1141,23338,23339],{"xmlns":1143},[1145,23340,23341,23345],{},[1148,23342,23343],{},[1154,23344,1167],{},[1172,23346,1167],{"encoding":1174},[1115,23348,23350],{"className":23349},[1139],[1141,23351,23352],{"xmlns":1143},[1145,23353,23354,23358],{},[1148,23355,23356],{},[1154,23357,1528],{},[1172,23359,1528],{"encoding":1174}," patrná jen náhodná rozptýlenost bez lineárního trendu.",[20599,23362,20602],{"id":23363},"v-r-1",[2020,23365,23367],{"className":2022,"code":23366,"language":71,"meta":2024,"style":2024},"cor(pocet_clenu, tydenni_vydaje)\n",[2015,23368,23369],{"__ignoreMap":2024},[1115,23370,23371,23374,23376,23378,23380,23383],{"class":2029,"line":10},[1115,23372,23373],{"class":2039},"cor",[1115,23375,1164],{"class":2043},[1115,23377,20623],{"class":2032},[1115,23379,1199],{"class":2035},[1115,23381,23382],{"class":2032}," tydenni_vydaje",[1115,23384,2185],{"class":2043},[2020,23386,23389],{"className":23387,"code":23388,"language":2349,"meta":2024},[2347],"[1] 0.9997441\n",[2015,23390,23388],{"__ignoreMap":2024},[1110,23392,23393,23394,23420],{},"Hodnota 0,9997 odpovídá ",[1115,23395,23397],{"className":23396},[1139],[1141,23398,23399],{"xmlns":1143},[1145,23400,23401,23417],{},[1148,23402,23403,23411,23413],{},[1678,23404,23405],{},[1603,23406,23407,23409],{},[1154,23408,1749],{},[1312,23410,1610],{},[1161,23412,1483],{},[1678,23414,23415],{},[1312,23416,20858],{},[1172,23418,23419],{"encoding":1174},"\\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.",[1103,23422,23424,23431,23434],{"className":23423,"dataCallout":2447},[1106,2446],[1110,23425,23427,23430],{"className":23426},[1113],[1115,23428],{"className":23429,"ariaHidden":1121},[1118,2454,1120],"Příklad: Koeficient korelace",[1110,23432,23433],{},"Pro stejná data o hodnotě produkce a výši investic dvanácti firem jako u regresní přímky byl spočten koeficient korelace mezi oběma proměnnými.",[1110,23435,21520,23436,23463],{},[1115,23437,23439],{"className":23438},[1139],[1141,23440,23441],{"xmlns":1143},[1145,23442,23443,23460],{},[1148,23444,23445,23455,23457],{},[1151,23446,23447,23449],{},[1154,23448,71],{},[1148,23450,23451,23453],{},[1154,23452,1167],{},[1154,23454,1528],{},[1161,23456,1483],{},[1312,23458,23459],{},"0,739",[1172,23461,23462],{"encoding":1174},"r_{xy} = 0{,}739"," — silná kladná závislost hodnoty produkce na výši investic.",[1232,23465,23467],{"id":23466},"vícenásobná-regrese-a-korelace","Vícenásobná regrese a korelace",[1110,23469,23470,23471,23484],{},"Pokud na závisle proměnnou ",[1115,23472,23474],{"className":23473},[1139],[1141,23475,23476],{"xmlns":1143},[1145,23477,23478,23482],{},[1148,23479,23480],{},[1154,23481,1528],{},[1172,23483,1528],{"encoding":1174}," působí víc vysvětlujících proměnných současně, analyzuje se zvlášť vliv každé z nich a výsledná regresní funkce se konstruuje jako součet jednoduchých regresních funkcí:",[1115,23486,23488],{"className":23487},[1139],[1141,23489,23490],{"xmlns":1143,"display":1468},[1145,23491,23492,23602],{},[1148,23493,23494,23496,23498,23504,23506,23512,23518,23520,23526,23532,23534,23536,23538,23544,23550,23552,23554,23560,23562,23568,23570,23576,23582,23584,23586,23588,23594,23600],{},[1154,23495,20175],{},[1161,23497,1483],{},[1151,23499,23500,23502],{},[1154,23501,20190],{},[1312,23503,4585],{},[1161,23505,3835],{},[1151,23507,23508,23510],{},[1154,23509,20190],{},[1312,23511,1489],{},[1151,23513,23514,23516],{},[1154,23515,1167],{},[1312,23517,1489],{},[1161,23519,3835],{},[1151,23521,23522,23524],{},[1154,23523,20190],{},[1312,23525,1610],{},[1151,23527,23528,23530],{},[1154,23529,1167],{},[1312,23531,1610],{},[1161,23533,3835],{},[1161,23535,21770],{},[1161,23537,3835],{},[1151,23539,23540,23542],{},[1154,23541,20190],{},[1154,23543,1110],{},[1151,23545,23546,23548],{},[1154,23547,1167],{},[1154,23549,1110],{},[1161,23551,1199],{"separator":1121},[1516,23553],{"width":1518},[1474,23555,23556,23558],{"accent":1121},[1154,23557,1528],{},[1161,23559,7244],{},[1161,23561,1483],{},[1151,23563,23564,23566],{},[1154,23565,1534],{},[1312,23567,4585],{},[1161,23569,3835],{},[1151,23571,23572,23574],{},[1154,23573,1534],{},[1312,23575,1489],{},[1151,23577,23578,23580],{},[1154,23579,1167],{},[1312,23581,1489],{},[1161,23583,3835],{},[1161,23585,21770],{},[1161,23587,3835],{},[1151,23589,23590,23592],{},[1154,23591,1534],{},[1154,23593,1110],{},[1151,23595,23596,23598],{},[1154,23597,1167],{},[1154,23599,1110],{},[1154,23601,1176],{"mathvariant":1869},[1172,23603,23604],{"encoding":1174},"\\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.",[20599,23606,23608],{"id":23607},"výběr-proměnných","Výběr proměnných",[1124,23610,23611,23617],{},[1127,23612,23613,23616],{},[1248,23614,23615],{},"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.",[1127,23618,23619,23622,23623,23626,23627,23630],{},[1248,23620,23621],{},"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 ",[1248,23624,23625],{},"forward"," proměnné postupně přidává, varianta ",[1248,23628,23629],{},"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.",[20599,23632,23634],{"id":23633},"postup-odhadu","Postup odhadu",[7379,23636,23637,23640,23643],{},[1127,23638,23639],{},"ověření předpokladů regresního modelu,",[1127,23641,23642],{},"samotný odhad parametrů,",[1127,23644,23645],{},"reziduální analýza výsledného modelu.",[1110,23647,23648,23649,23666,23667,8464,23669,23698,23699,23728,23729,23746],{},"Důležitost každého parametru ",[1115,23650,23652],{"className":23651},[1139],[1141,23653,23654],{"xmlns":1143},[1145,23655,23656,23664],{},[1148,23657,23658],{},[1151,23659,23660,23662],{},[1154,23661,1534],{},[1154,23663,1502],{},[1172,23665,20315],{"encoding":1174}," v modelu ověřuje ",[1248,23668,992],{},[1115,23670,23672],{"className":23671},[1139],[1141,23673,23674],{"xmlns":1143},[1145,23675,23676,23696],{},[1148,23677,23678,23684,23686,23692,23694],{},[1151,23679,23680,23682],{},[1154,23681,6105],{},[1312,23683,4585],{},[1161,23685,6481],{},[1151,23687,23688,23690],{},[1154,23689,20190],{},[1154,23691,1502],{},[1161,23693,1483],{},[1312,23695,4585],{},[1172,23697,20802],{"encoding":1174}," (proměnná je v modelu nevýznamná) proti ",[1115,23700,23702],{"className":23701},[1139],[1141,23703,23704],{"xmlns":1143},[1145,23705,23706,23726],{},[1148,23707,23708,23714,23716,23722,23724],{},[1151,23709,23710,23712],{},[1154,23711,6105],{},[1312,23713,1489],{},[1161,23715,6481],{},[1151,23717,23718,23720],{},[1154,23719,20190],{},[1154,23721,1502],{},[1161,23723,15368],{"mathvariant":1869},[1312,23725,4585],{},[1172,23727,20833],{"encoding":1174}," (proměnná je významná). Při nezamítnutí ",[1115,23730,23732],{"className":23731},[1139],[1141,23733,23734],{"xmlns":1143},[1145,23735,23736,23744],{},[1148,23737,23738],{},[1151,23739,23740,23742],{},[1154,23741,6105],{},[1312,23743,4585],{},[1172,23745,6110],{"encoding":1174}," by proměnná — a s ní spojený regresor — v modelu neměla zůstat.",[20599,23748,23750],{"id":23749},"předpoklady-modelu","Předpoklady modelu",[7379,23752,23753,23770,23803,23809,23812,23815],{},[1127,23754,23755,23756,23769],{},"Závisle proměnná ",[1115,23757,23759],{"className":23758},[1139],[1141,23760,23761],{"xmlns":1143},[1145,23762,23763,23767],{},[1148,23764,23765],{},[1154,23766,1528],{},[1172,23768,1528],{"encoding":1174}," musí být aspoň intervalového typu (ne binární, diskrétní s málo hodnotami apod.) — jinak je na místě logistická regrese.",[1127,23771,23772,23773,23802],{},"Nezávislé proměnné ",[1115,23774,23776],{"className":23775},[1139],[1141,23777,23778],{"xmlns":1143},[1145,23779,23780,23800],{},[1148,23781,23782,23788,23790,23792,23794],{},[1151,23783,23784,23786],{},[1154,23785,1167],{},[1312,23787,1489],{},[1161,23789,1199],{"separator":1121},[1161,23791,3022],{},[1161,23793,1199],{"separator":1121},[1151,23795,23796,23798],{},[1154,23797,1167],{},[1154,23799,1110],{},[1172,23801,20139],{"encoding":1174}," jsou rovněž aspoň intervalového typu, mohou být i alternativní.",[1127,23804,23805,23806,1176],{},"Nezávislé proměnné by mezi sebou neměly být příliš vysoce korelované — ",[1248,23807,23808],{},"multikolinearita",[1127,23810,23811],{},"V datech nesmí být odlehlé či extrémní hodnoty; regresní analýza je na ně citlivá a mohou vážně narušit kvalitu odhadů.",[1127,23813,23814],{},"Proměnné musí být ve vzájemně lineárním vztahu — vícenásobná lineární regrese je založená na Pearsonově koeficientu korelace, takže nelineární vztahy mezi proměnnými zůstanou neodhalené.",[1127,23816,23817,23818,23822],{},"Proměnné mají mít ",[1239,23819,23821],{"className":23820,"dataFsResolvedFilePath":5976,"href":5977},[1242],"normální rozložení","; význam tohoto předpokladu ustupuje do pozadí u dostatečně velkého datového souboru díky centrální limitní větě.",[1110,23824,23825,23826,23829],{},"Normalita se u menšího počtu pozorování ověřuje stejnými testy jako u jiných znaků (viz ",[1239,23827,6257],{"className":23828,"dataFsResolvedFilePath":5305,"href":5306},[1242],") — 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.",[20599,23831,23832],{"id":23808},"Multikolinearita",[1110,23834,23835],{},"Multikolinearita vzniká, když vysvětlující proměnné silně závisejí jedna na druhé. Je nežádoucí, protože:",[1124,23837,23838,23841,23844],{},[1127,23839,23840],{},"výsledky regrese jsou pak nespolehlivé,",[1127,23842,23843],{},"zvyšuje pravděpodobnost, že se důležitá proměnná jeví jako statisticky nevýznamná a bude z modelu vyřazena,",[1127,23845,23846],{},"směrodatné odchylky odhadnutých parametrů jsou vysoké, testová kritéria t-testů nízká, p-hodnoty vysoké.",[1110,23848,23849,23850,23853,23854,23877,23878,23896,23897,23913],{},"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 ",[1248,23851,23852],{},"VIF (Variance Inflation Factor)",": hodnoty ",[1115,23855,23857],{"className":23856},[1139],[1141,23858,23859],{"xmlns":1143},[1145,23860,23861,23874],{},[1148,23862,23863,23865,23867,23870,23872],{},[1312,23864,1489],{},[1161,23866,8805],{},[1316,23868,23869],{},"VIF",[1161,23871,8805],{},[1312,23873,3415],{},[1172,23875,23876],{"encoding":1174},"1\u003C\\text{VIF}\u003C5"," jsou varující, ",[1115,23879,23881],{"className":23880},[1139],[1141,23882,23883],{"xmlns":1143},[1145,23884,23885,23893],{},[1148,23886,23887,23889,23891],{},[1316,23888,23869],{},[1161,23890,6225],{},[1312,23892,3415],{},[1172,23894,23895],{"encoding":1174},"\\text{VIF}>5"," (přísněji ",[1115,23898,23900],{"className":23899},[1139],[1141,23901,23902],{"xmlns":1143},[1145,23903,23904,23910],{},[1148,23905,23906,23908],{},[1161,23907,6225],{},[1312,23909,3427],{},[1172,23911,23912],{"encoding":1174},">10",") značí vysokou multikolinearitu.",[1110,23915,23916],{},"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.",[20599,23918,23920],{"id":23919},"další-ukazatele-kvality-modelu","Další ukazatele kvality modelu",[1124,23922,23923,23929,23935],{},[1127,23924,23925,23928],{},[1248,23926,23927],{},"F-test"," — testuje hypotézu, že všechny regresní koeficienty jsou rovny nule, proti alternativě, že aspoň jeden v modelu být má (celková významnost modelu).",[1127,23930,23931,23934],{},[1248,23932,23933],{},"RMSE"," (odmocnina z reziduálního rozptylu) — absolutní měřítko vhodnosti funkce (na rozdíl od indexu determinace, který je relativní); nižší hodnota znamená lepší fit.",[1127,23936,23937,23940,23941,23944],{},[1248,23938,23939],{},"AIC"," (Akaikeho informační kritérium) a ",[1248,23942,23943],{},"BIC"," (Bayesovo informační kritérium) — čím nižší hodnoty obou kritérií, tím lepší model; používají se hlavně při stepwise výběru proměnných.",[20599,23946,20602],{"id":23947},"v-r-2",[1110,23949,23950],{},"Pro vícenásobnou regresi je postup v R rozšířením postupu pro regresní přímku — přibývá výběr proměnných a kontrola multikolinearity:",[2020,23952,23954],{"className":2022,"code":23953,"language":71,"meta":2024,"style":2024},"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",[2015,23955,23956,23982,24026,24052,24062,24066,24077,24088,24092,24102,24112,24116,24126,24136,24141],{"__ignoreMap":2024},[1115,23957,23958,23961,23963,23966,23968,23971,23973,23976,23978,23980],{"class":2029,"line":10},[1115,23959,23960],{"class":2032},"data",[1115,23962,2036],{"class":2035},[1115,23964,23965],{"class":2039}," read.table",[1115,23967,1164],{"class":2043},[1115,23969,23970],{"class":8322},"\"4_4.txt\"",[1115,23972,1199],{"class":2035},[1115,23974,23975],{"class":2032}," header",[1115,23977,2291],{"class":2035},[1115,23979,2409],{"class":2046},[1115,23981,2185],{"class":2043},[1115,23983,23984,23987,23989,23991,23993,23995,23997,24000,24002,24005,24007,24010,24012,24015,24017,24020,24022,24024],{"class":2029,"line":27},[1115,23985,23986],{"class":2032},"model_plny",[1115,23988,2036],{"class":2035},[1115,23990,20703],{"class":2039},[1115,23992,1164],{"class":2043},[1115,23994,1528],{"class":2032},[1115,23996,20710],{"class":2035},[1115,23998,23999],{"class":2032}," x1",[1115,24001,22368],{"class":2035},[1115,24003,24004],{"class":2032}," x2",[1115,24006,22368],{"class":2035},[1115,24008,24009],{"class":2032}," x3",[1115,24011,22368],{"class":2035},[1115,24013,24014],{"class":2032}," x4",[1115,24016,1199],{"class":2035},[1115,24018,24019],{"class":2032}," data",[1115,24021,2291],{"class":2035},[1115,24023,24019],{"class":2032},[1115,24025,2185],{"class":2043},[1115,24027,24028,24031,24033,24036,24038,24040,24042,24045,24047,24050],{"class":2029,"line":148},[1115,24029,24030],{"class":2032},"model_krok",[1115,24032,2036],{"class":2035},[1115,24034,24035],{"class":2039}," step",[1115,24037,1164],{"class":2043},[1115,24039,23986],{"class":2032},[1115,24041,1199],{"class":2035},[1115,24043,24044],{"class":2032}," direction",[1115,24046,2291],{"class":2035},[1115,24048,24049],{"class":8322}," \"both\"",[1115,24051,2185],{"class":2043},[1115,24053,24054,24056,24058,24060],{"class":2029,"line":111},[1115,24055,20720],{"class":2039},[1115,24057,1164],{"class":2043},[1115,24059,24030],{"class":2032},[1115,24061,2185],{"class":2043},[1115,24063,24064],{"class":2029,"line":96},[1115,24065,14456],{"emptyLinePlaceholder":6044},[1115,24067,24068,24070,24072,24075],{"class":2029,"line":89},[1115,24069,21249],{"class":2035},[1115,24071,1164],{"class":2043},[1115,24073,24074],{"class":2032},"car",[1115,24076,2185],{"class":2043},[1115,24078,24079,24082,24084,24086],{"class":2029,"line":82},[1115,24080,24081],{"class":2039},"vif",[1115,24083,1164],{"class":2043},[1115,24085,24030],{"class":2032},[1115,24087,2185],{"class":2043},[1115,24089,24090],{"class":2029,"line":75},[1115,24091,14456],{"emptyLinePlaceholder":6044},[1115,24093,24094,24096,24098,24100],{"class":2029,"line":2322},[1115,24095,21249],{"class":2035},[1115,24097,1164],{"class":2043},[1115,24099,21254],{"class":2032},[1115,24101,2185],{"class":2043},[1115,24103,24104,24106,24108,24110],{"class":2029,"line":72},[1115,24105,21261],{"class":2039},[1115,24107,1164],{"class":2043},[1115,24109,24030],{"class":2032},[1115,24111,2185],{"class":2043},[1115,24113,24114],{"class":2029,"line":25},[1115,24115,14456],{"emptyLinePlaceholder":6044},[1115,24117,24118,24120,24122,24124],{"class":2029,"line":65},[1115,24119,21249],{"class":2035},[1115,24121,1164],{"class":2043},[1115,24123,21344],{"class":2032},[1115,24125,2185],{"class":2043},[1115,24127,24128,24130,24132,24134],{"class":2029,"line":63},[1115,24129,21351],{"class":2039},[1115,24131,1164],{"class":2043},[1115,24133,24030],{"class":2032},[1115,24135,2185],{"class":2043},[1115,24137,24139],{"class":2029,"line":24138},14,[1115,24140,14456],{"emptyLinePlaceholder":6044},[1115,24142,24143,24145,24147,24149,24151,24153],{"class":2029,"line":60},[1115,24144,21429],{"class":2039},[1115,24146,1164],{"class":2043},[1115,24148,20897],{"class":2039},[1115,24150,1164],{"class":2043},[1115,24152,24030],{"class":2032},[1115,24154,3694],{"class":2043},[1110,24156,24157,24159,24160,24163],{},[2015,24158,19973],{}," provádí stepwise výběr podle AIC, ",[2015,24161,24162],{},"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.",[1103,24165,24167,24174,24177,24180],{"className":24166,"dataCallout":2447},[1106,2446],[1110,24168,24170,24173],{"className":24169},[1113],[1115,24171],{"className":24172,"ariaHidden":1121},[1118,2454,1120],"Příklad: Vícenásobná regrese",[1110,24175,24176],{},"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.",[1110,24178,24179],{},"Postup: odhad plného modelu → stepwise analýza podle AIC → ověření předpokladů.",[1110,24181,24182,24183,24186,24187,24189,24190,24193],{},"Diagnostika odhaleného modelu ukázala tři problémy: (1) ",[1248,24184,24185],{},"nelinearita"," — mezi některými vysvětlujícími proměnnými a cenou je zjevně jiný než lineární vztah, řešením je zkusit u nich druhou mocninu; (2) ",[1248,24188,23808],{}," mezi dvojicí proměnných popisujících vzdálenost (k silnici a ke spalovně) — doporučeno jednu z nich vynechat; (3) ",[1248,24191,24192],{},"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.",[1232,24195,5763],{"id":5762},[1103,24197,24199,24206],{"className":24198,"dataCallout":10867},[1106,10866],[1110,24200,24202,24205],{"className":24201},[1113],[1115,24203],{"className":24204,"ariaHidden":1121},[1118,10874,1120],"Koeficient korelace jen pro přímku",[1110,24207,24208,24209,24265,24266,24283,24284,24304,24305,1385,24318,1176],{},"Vzorec ",[1115,24210,24212],{"className":24211},[1139],[1141,24213,24214],{"xmlns":1143},[1145,24215,24216,24262],{},[1148,24217,24218,24228,24230,24240,24242],{},[1151,24219,24220,24222],{},[1154,24221,71],{},[1148,24223,24224,24226],{},[1154,24225,1167],{},[1154,24227,1528],{},[1161,24229,1483],{},[1151,24231,24232,24234],{},[1154,24233,1607],{},[1148,24235,24236,24238],{},[1154,24237,1167],{},[1154,24239,1528],{},[1154,24241,3245],{"mathvariant":1869},[1678,24243,24244],{},[1148,24245,24246,24254],{},[1645,24247,24248,24250,24252],{},[1154,24249,1607],{},[1154,24251,1167],{},[1312,24253,1610],{},[1645,24255,24256,24258,24260],{},[1154,24257,1607],{},[1154,24259,1528],{},[1312,24261,1610],{},[1172,24263,24264],{"encoding":1174},"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 ",[1115,24267,24269],{"className":24268},[1139],[1141,24270,24271],{"xmlns":1143},[1145,24272,24273,24281],{},[1148,24274,24275],{},[1603,24276,24277,24279],{},[1154,24278,1749],{},[1312,24280,1610],{},[1172,24282,19877],{"encoding":1174},", případně obecným indexem korelace ",[1115,24285,24287],{"className":24286},[1139],[1141,24288,24289],{"xmlns":1143},[1145,24290,24291,24301],{},[1148,24292,24293],{},[1678,24294,24295],{},[1603,24296,24297,24299],{},[1154,24298,1749],{},[1312,24300,1610],{},[1172,24302,24303],{"encoding":1174},"\\sqrt{R^2}"," — ne koeficientem korelace mezi ",[1115,24306,24308],{"className":24307},[1139],[1141,24309,24310],{"xmlns":1143},[1145,24311,24312,24316],{},[1148,24313,24314],{},[1154,24315,1167],{},[1172,24317,1167],{"encoding":1174},[1115,24319,24321],{"className":24320},[1139],[1141,24322,24323],{"xmlns":1143},[1145,24324,24325,24329],{},[1148,24326,24327],{},[1154,24328,1528],{},[1172,24330,1528],{"encoding":1174},[1103,24332,24334,24341],{"className":24333,"dataCallout":10867},[1106,10866],[1110,24335,24337,24340],{"className":24336},[1113],[1115,24338],{"className":24339,"ariaHidden":1121},[1118,10874,1120],"Významný F-test, nevýznamné t-testy",[1110,24342,24343],{},"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.",[1103,24345,24347,24354],{"className":24346,"dataCallout":10867},[1106,10866],[1110,24348,24350,24353],{"className":24349},[1113],[1115,24351],{"className":24352,"ariaHidden":1121},[1118,10874,1120],"Durbin-Watsonova statistika mimo okolí 2",[1110,24355,24356],{},"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.",[1103,24358,24360,24367],{"className":24359,"dataCallout":10867},[1106,10866],[1110,24361,24363,24366],{"className":24362},[1113],[1115,24364],{"className":24365,"ariaHidden":1121},[1118,10874,1120],"Nízký počet pozorování při stepwise výběru",[1110,24368,24369],{},"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.",[1232,24371,5963],{"id":5962},[1124,24373,24374,24379,24384,24389,24394,24399,24404],{},[1127,24375,24376],{},[1239,24377,1245],{"className":24378,"dataFsResolvedFilePath":1243,"href":1244},[1242],[1127,24380,24381],{},[1239,24382,5978],{"className":24383,"dataFsResolvedFilePath":5976,"href":5977},[1242],[1127,24385,24386],{},[1239,24387,1094],{"className":24388,"dataFsResolvedFilePath":11066,"href":11067},[1242],[1127,24390,24391],{},[1239,24392,5307],{"className":24393,"dataFsResolvedFilePath":5305,"href":5306},[1242],[1127,24395,24396],{},[1239,24397,5999],{"className":24398,"dataFsResolvedFilePath":5997,"href":5998},[1242],[1127,24400,24401],{},[1239,24402,6007],{"className":24403,"dataFsResolvedFilePath":6005,"href":6006},[1242],[1127,24405,24406],{},[1239,24407,6015],{"className":24408,"dataFsResolvedFilePath":6013,"href":6014},[1242],[1232,24410,6018],{"id":934},[1110,24412,6021,24413,6026],{},[6023,24414,6025],{},[6028,24416,24417],{},"html pre.shiki code .sP4rz, html 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diagram zobrazuje vývoj variability procesu v čase a dává signál, že na proces začala působit vymezitelná příčina: bod mimo akční meze UCL a LCL.",[1127,24476,24477,24478,1381,24504,1385,24530,1176],{},"Regulace měřením (spojitá veličina s normálním rozdělením): diagramy ",[1115,24479,24481],{"className":24480},[1139],[1141,24482,24483],{"xmlns":1143},[1145,24484,24485,24501],{},[1148,24486,24487,24489,24495,24497,24499],{},[1161,24488,1164],{"stretchy":1163},[1474,24490,24491,24493],{"accent":1121},[1154,24492,1167],{},[1161,24494,1480],{},[1161,24496,1199],{"separator":1121},[1154,24498,1749],{},[1161,24500,1170],{"stretchy":1163},[1172,24502,24503],{"encoding":1174},"(\\bar{x}, R)",[1115,24505,24507],{"className":24506},[1139],[1141,24508,24509],{"xmlns":1143},[1145,24510,24511,24527],{},[1148,24512,24513,24515,24521,24523,24525],{},[1161,24514,1164],{"stretchy":1163},[1474,24516,24517,24519],{"accent":1121},[1154,24518,1167],{},[1161,24520,1480],{},[1161,24522,1199],{"separator":1121},[1154,24524,1607],{},[1161,24526,1170],{"stretchy":1163},[1172,24528,24529],{"encoding":1174},"(\\bar{x}, s)",[1115,24531,24533],{"className":24532},[1139],[1141,24534,24535],{"xmlns":1143},[1145,24536,24537,24566],{},[1148,24538,24539,24541,24547,24549,24564],{},[1161,24540,1164],{"stretchy":1163},[1151,24542,24543,24545],{},[1154,24544,1167],{},[1154,24546,1502],{},[1161,24548,1199],{"separator":1121},[1151,24550,24551,24553],{},[1154,24552,1749],{},[1148,24554,24555,24557,24560,24562],{},[1154,24556,3064],{},[1154,24558,24559],{},"l",[1161,24561,1199],{"separator":1121},[1154,24563,1502],{},[1161,24565,1170],{"stretchy":1163},[1172,24567,24568],{"encoding":1174},"(x_i, R_{kl,i})",[1127,24570,24571,24572,24585,24586,24599,24600,24616,24617,24630],{},"Regulace srovnáváním (diskrétní veličina): počet neshod ",[1115,24573,24575],{"className":24574},[1139],[1141,24576,24577],{"xmlns":1143},[1145,24578,24579,24583],{},[1148,24580,24581],{},[1154,24582,1784],{},[1172,24584,1784],{"encoding":1174}," (konstantní rozsah) a ",[1115,24587,24589],{"className":24588},[1139],[1141,24590,24591],{"xmlns":1143},[1145,24592,24593,24597],{},[1148,24594,24595],{},[1154,24596,1559],{},[1172,24598,1559],{"encoding":1174}," (nekonstantní rozsah), počet neshodných produktů ",[1115,24601,24603],{"className":24602},[1139],[1141,24604,24605],{"xmlns":1143},[1145,24606,24607,24613],{},[1148,24608,24609,24611],{},[1154,24610,1159],{},[1154,24612,1110],{},[1172,24614,24615],{"encoding":1174},"np"," (konstantní rozsah) a jejich podíl ",[1115,24618,24620],{"className":24619},[1139],[1141,24621,24622],{"xmlns":1143},[1145,24623,24624,24628],{},[1148,24625,24626],{},[1154,24627,1110],{},[1172,24629,1110],{"encoding":1174}," (nekonstantní rozsah).",[1127,24632,24633],{},"Podskupiny s vymezitelnou příčinou se po jejím odstranění z výpočtu vyřadí a meze se přepočítají, dokud jsou všechny body uvnitř mezí.",[1127,24635,24636,24637,1381,24656,1381,24678,1381,24700,24724,24725,24746],{},"Indexy způsobilosti ",[1115,24638,24640],{"className":24639},[1139],[1141,24641,24642],{"xmlns":1143},[1145,24643,24644,24653],{},[1148,24645,24646],{},[1151,24647,24648,24651],{},[1154,24649,24650],{},"C",[1154,24652,1110],{},[1172,24654,24655],{"encoding":1174},"C_p",[1115,24657,24659],{"className":24658},[1139],[1141,24660,24661],{"xmlns":1143},[1145,24662,24663,24675],{},[1148,24664,24665],{},[1151,24666,24667,24669],{},[1154,24668,24650],{},[1148,24670,24671,24673],{},[1154,24672,1110],{},[1154,24674,3064],{},[1172,24676,24677],{"encoding":1174},"C_{pk}",[1115,24679,24681],{"className":24680},[1139],[1141,24682,24683],{"xmlns":1143},[1145,24684,24685,24697],{},[1148,24686,24687],{},[1151,24688,24689,24691],{},[1154,24690,24650],{},[1148,24692,24693,24695],{},[1154,24694,1110],{},[1154,24696,1565],{},[1172,24698,24699],{"encoding":1174},"C_{pm}",[1115,24701,24703],{"className":24702},[1139],[1141,24704,24705],{"xmlns":1143},[1145,24706,24707,24721],{},[1148,24708,24709],{},[1151,24710,24711,24713],{},[1154,24712,24650],{},[1148,24714,24715,24717,24719],{},[1154,24716,1110],{},[1154,24718,1565],{},[1154,24720,3064],{},[1172,24722,24723],{"encoding":1174},"C_{pmk}"," posuzují, zda statisticky zvládnutý proces vyhovuje tolerančním mezím; ",[1115,24726,24728],{"className":24727},[1139],[1141,24729,24730],{"xmlns":1143},[1145,24731,24732,24744],{},[1148,24733,24734],{},[1151,24735,24736,24738],{},[1154,24737,24650],{},[1148,24739,24740,24742],{},[1154,24741,1110],{},[1154,24743,3064],{},[1172,24745,24677],{"encoding":1174}," navíc zohledňuje vychýlení střední hodnoty.",[1127,24748,24749,24750,1176],{},"V R diagramy i indexy počítá balíček ",[2015,24751,360],{},[1232,24753,24755],{"id":24754},"statistická-regulace-procesu","Statistická regulace procesu",[1110,24757,24758,24759,24761,24762,1176],{},"Tradiční zabezpečování jakosti kontroluje výrobky až po jejich vyrobení, což je neekonomické. ",[1248,24760,24755],{}," 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 ",[1248,24763,24764],{},"statisticky zvládnutém stavu",[1110,24766,24767,24768,24771],{},"Teorie regulace vychází z ",[1248,24769,24770],{},"variability"," procesu, kterou způsobují dva druhy příčin:",[3350,24773,24774,24786],{},[3353,24775,24776],{},[3356,24777,24778,24780,24783],{},[3359,24779],{},[3359,24781,24782],{},"Náhodné příčiny",[3359,24784,24785],{},"Vymezitelné příčiny",[3389,24787,24788,24799,24810],{},[3356,24789,24790,24793,24796],{},[3394,24791,24792],{},"Povaha",[3394,24794,24795],{},"široká skupina neidentifikovatelných vlivů, každý přispívá k variabilitě malou měrou",[3394,24797,24798],{},"vlivy, které za běžných podmínek na proces nepůsobí; vyvolají nepřirozené kolísání údajů",[3356,24800,24801,24804,24807],{},[3394,24802,24803],{},"Stav procesu",[3394,24805,24806],{},"ustálený, jakost výstupů je předvídatelná, není nutné zasahovat — statisticky zvládnutý",[3394,24808,24809],{},"jakost výstupů není předvídatelná, je nutné zasáhnout — proces není statisticky zvládnutý",[3356,24811,24812,24815,24818],{},[3394,24813,24814],{},"Příklady",[3394,24816,24817],{},"psychický stav pracovníka, chvění stroje, teplota ovzduší",[3394,24819,24820],{},"změna materiálu, nezaškolená obsluha",[1110,24822,24823,24824,24827,24828,24831],{},"Vymezitelné příčiny jsou ",[1248,24825,24826],{},"sporadické"," (vznikají náhle, změny trvají krátce) nebo ",[1248,24829,24830],{},"přetrvávající"," (trvají stále nebo se mění).",[1110,24833,24834],{},[1393,24835],{"alt":24836,"className":24837,"src":24838},"mask-ilu-pricin-variability",[1242,1397],"\u002Fwiki-assets\u002Fmask-ilu-pricin-variability.png",[1110,24840,24841],{},"Regulace probíhá ve třech fázích:",[7379,24843,24844,24854,24860],{},[1127,24845,24846,24849,24850,24853],{},[1248,24847,24848],{},"Fáze přípravná"," — stanoví se sledované znaky jakosti (rozměr, hmotnost, počet vad…), délka časového intervalu mezi měřeními, ",[1248,24851,24852],{},"logická podskupina"," (skupina měření, v níž se předpokládá působení pouze náhodných příčin), typ regulačního diagramu a místa kontroly v procesu.",[1127,24855,24856,24859],{},[1248,24857,24858],{},"Fáze zabezpečování statistické zvládnutosti"," — pomocí regulačních diagramů se identifikují vymezitelné příčiny a odstraní se jejich působení.",[1127,24861,24862,24865],{},[1248,24863,24864],{},"Fáze analýzy a zabezpečení způsobilosti"," — zkoumá se, zda statisticky zvládnutý proces vyhovuje požadavkům zákazníka; k tomu slouží indexy způsobilosti (níže).",[1232,24867,24869],{"id":24868},"princip-regulačního-diagramu","Princip regulačního diagramu",[1110,24871,24872,24875],{},[1248,24873,24874],{},"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.",[1124,24877,24878,24884,24890],{},[1127,24879,24880,24883],{},[1248,24881,24882],{},"CL"," — střední přímka, odpovídá požadované (referenční) hodnotě použité charakteristiky,",[1127,24885,24886,24889],{},[1248,24887,24888],{},"UCL"," — horní akční regulační mez,",[1127,24891,24892,24895],{},[1248,24893,24894],{},"LCL"," — dolní akční regulační mez.",[1110,24897,24898],{},"Akční meze vymezují pásmo působení pouze náhodných příčin variability.",[1110,24900,24901],{},[1393,24902],{"alt":24903,"className":24904,"src":24905},"mask-rd-schema",[1242,1397],"\u002Fwiki-assets\u002Fmask-rd-schema.png",[1110,24907,24908,24911],{},[1248,24909,24910],{},"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.",[1110,24913,24914,24915,24918,24919,24922],{},"Podle charakteru regulované veličiny se diagramy dělí na diagramy pro ",[1248,24916,24917],{},"regulaci měřením"," (regulovaná veličina je spojitá náhodná veličina) a pro ",[1248,24920,24921],{},"regulaci srovnáváním"," (diskrétní náhodná veličina).",[1110,24924,24925],{},"Postup při konstrukci regulačního diagramu:",[7379,24927,24928,24931,24934,24937,24940,24943,24946,24949,24952],{},[1127,24929,24930],{},"volba regulované veličiny,",[1127,24932,24933],{},"sběr a záznam dat,",[1127,24935,24936],{},"ověření požadovaných předpokladů o datech,",[1127,24938,24939],{},"volba rozsahu logických podskupin,",[1127,24941,24942],{},"volba vhodného regulačního diagramu,",[1127,24944,24945],{},"výpočet hodnot zvoleného testového kritéria pro jednotlivé výběry,",[1127,24947,24948],{},"ověření a zajištění statistické zvládnutosti procesu,",[1127,24950,24951],{},"ověření způsobilosti procesu,",[1127,24953,24954],{},"vlastní regulace procesu.",[1232,24956,24958],{"id":24957},"regulace-měřením","Regulace měřením",[1110,24960,24961],{},"Diagramy pro regulaci měřením se používají, když je regulovaná veličina měřitelná. Požaduje se, aby:",[1124,24963,24964,24967],{},[1127,24965,24966],{},"jednotlivá měření byla vzájemně nezávislá,",[1127,24968,24969,24970,24983,24984,24997,24998,25011,25012,25025],{},"regulovaná veličina byla spojitá náhodná veličina s normálním rozdělením se střední hodnotou ",[1115,24971,24973],{"className":24972},[1139],[1141,24974,24975],{"xmlns":1143},[1145,24976,24977,24981],{},[1148,24978,24979],{},[1154,24980,11332],{},[1172,24982,13226],{"encoding":1174}," a směrodatnou odchylkou ",[1115,24985,24987],{"className":24986},[1139],[1141,24988,24989],{"xmlns":1143},[1145,24990,24991,24995],{},[1148,24992,24993],{},[1154,24994,11339],{},[1172,24996,11371],{"encoding":1174}," — tyto dva parametry charakterizují statistickou stabilitu procesu; ",[1115,24999,25001],{"className":25000},[1139],[1141,25002,25003],{"xmlns":1143},[1145,25004,25005,25009],{},[1148,25006,25007],{},[1154,25008,11332],{},[1172,25010,13226],{"encoding":1174}," je hodnota, na niž je proces nastaven, ",[1115,25013,25015],{"className":25014},[1139],[1141,25016,25017],{"xmlns":1143},[1145,25018,25019,25023],{},[1148,25020,25021],{},[1154,25022,11339],{},[1172,25024,11371],{"encoding":1174}," charakterizuje jeho přesnost.",[1110,25027,25028,25029,1381,25054,1385,25079,25116],{},"Jsou-li předpoklady splněny, volí se diagramy, které současně sledují stabilitu polohy i stabilitu rozptylu: ",[1115,25030,25032],{"className":25031},[1139],[1141,25033,25034],{"xmlns":1143},[1145,25035,25036,25052],{},[1148,25037,25038,25040,25046,25048,25050],{},[1161,25039,1164],{"stretchy":1163},[1474,25041,25042,25044],{"accent":1121},[1154,25043,1167],{},[1161,25045,1480],{},[1161,25047,1199],{"separator":1121},[1154,25049,1749],{},[1161,25051,1170],{"stretchy":1163},[1172,25053,24503],{"encoding":1174},[1115,25055,25057],{"className":25056},[1139],[1141,25058,25059],{"xmlns":1143},[1145,25060,25061,25077],{},[1148,25062,25063,25065,25071,25073,25075],{},[1161,25064,1164],{"stretchy":1163},[1474,25066,25067,25069],{"accent":1121},[1154,25068,1167],{},[1161,25070,1480],{},[1161,25072,1199],{"separator":1121},[1154,25074,1607],{},[1161,25076,1170],{"stretchy":1163},[1172,25078,24529],{"encoding":1174},[1115,25080,25082],{"className":25081},[1139],[1141,25083,25084],{"xmlns":1143},[1145,25085,25086,25114],{},[1148,25087,25088,25090,25096,25098,25112],{},[1161,25089,1164],{"stretchy":1163},[1151,25091,25092,25094],{},[1154,25093,1167],{},[1154,25095,1502],{},[1161,25097,1199],{"separator":1121},[1151,25099,25100,25102],{},[1154,25101,1749],{},[1148,25103,25104,25106,25108,25110],{},[1154,25105,3064],{},[1154,25107,24559],{},[1161,25109,1199],{"separator":1121},[1154,25111,1502],{},[1161,25113,1170],{"stretchy":1163},[1172,25115,24568],{"encoding":1174},". Výsledkem jsou vždy dva diagramy.",[20599,25118,25120,25121],{"id":25119},"diagram-xˉrbarx-r","Diagram ",[1115,25122,25124],{"className":25123},[1139],[1141,25125,25126],{"xmlns":1143},[1145,25127,25128,25144],{},[1148,25129,25130,25132,25138,25140,25142],{},[1161,25131,1164],{"stretchy":1163},[1474,25133,25134,25136],{"accent":1121},[1154,25135,1167],{},[1161,25137,1480],{},[1161,25139,1199],{"separator":1121},[1154,25141,1749],{},[1161,25143,1170],{"stretchy":1163},[1172,25145,24503],{"encoding":1174},[1110,25147,25148,25149,25171,25172,25190],{},"Regulované veličiny jsou výběrové průměry ",[1115,25150,25152],{"className":25151},[1139],[1141,25153,25154],{"xmlns":1143},[1145,25155,25156,25168],{},[1148,25157,25158],{},[1151,25159,25160,25166],{},[1474,25161,25162,25164],{"accent":1121},[1154,25163,1167],{},[1161,25165,1480],{},[1154,25167,1502],{},[1172,25169,25170],{"encoding":1174},"\\bar{x}_i"," a výběrová rozpětí ",[1115,25173,25175],{"className":25174},[1139],[1141,25176,25177],{"xmlns":1143},[1145,25178,25179,25187],{},[1148,25180,25181],{},[1151,25182,25183,25185],{},[1154,25184,1749],{},[1154,25186,1502],{},[1172,25188,25189],{"encoding":1174},"R_i"," v logických podskupinách:",[1115,25192,25194],{"className":25193},[1139],[1141,25195,25196],{"xmlns":1143,"display":1468},[1145,25197,25198,25299],{},[1148,25199,25200,25210,25212,25218,25232,25242,25244,25246,25252,25254,25265,25275,25277,25287,25297],{},[1151,25201,25202,25208],{},[1474,25203,25204,25206],{"accent":1121},[1154,25205,1167],{},[1161,25207,1480],{},[1154,25209,1502],{},[1161,25211,1483],{},[1485,25213,25214,25216],{},[1312,25215,1489],{},[1154,25217,1159],{},[1493,25219,25220,25222,25230],{},[1161,25221,1497],{},[1148,25223,25224,25226,25228],{},[1154,25225,1196],{},[1161,25227,1483],{},[1312,25229,1489],{},[1154,25231,1159],{},[1151,25233,25234,25236],{},[1154,25235,1167],{},[1148,25237,25238,25240],{},[1154,25239,1502],{},[1154,25241,1196],{},[1161,25243,1199],{"separator":1121},[1516,25245],{"width":1518},[1151,25247,25248,25250],{},[1154,25249,1749],{},[1154,25251,1502],{},[1161,25253,1483],{},[25255,25256,25257,25263],"munder",{},[1148,25258,25259,25261],{},[1154,25260,1758],{},[1161,25262,1761],{},[1154,25264,1196],{},[1151,25266,25267,25269],{},[1154,25268,1167],{},[1148,25270,25271,25273],{},[1154,25272,1502],{},[1154,25274,1196],{},[1161,25276,1623],{},[25255,25278,25279,25285],{},[1148,25280,25281,25283],{},[1154,25282,1770],{},[1161,25284,1761],{},[1154,25286,1196],{},[1151,25288,25289,25291],{},[1154,25290,1167],{},[1148,25292,25293,25295],{},[1154,25294,1502],{},[1154,25296,1196],{},[1154,25298,1176],{"mathvariant":1869},[1172,25300,25301],{"encoding":1174},"\\bar{x}_i = \\frac{1}{n}\\sum_{j=1}^n x_{ij}, \\qquad R_i = \\max_j x_{ij} - \\min_j x_{ij}.",[1110,25303,25304],{},"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.",[1110,25306,25307,25308,25334,25335,25348,25349,1385,25370,25387,25388,25401,25402,25420,25421,1176],{},"Data se zapisují do tabulky: řádek ",[1115,25309,25311],{"className":25310},[1139],[1141,25312,25313],{"xmlns":1143},[1145,25314,25315,25331],{},[1148,25316,25317,25319,25321,25323,25325,25327,25329],{},[1154,25318,1502],{},[1161,25320,1483],{},[1312,25322,1489],{},[1161,25324,1199],{"separator":1121},[1161,25326,3022],{},[1161,25328,1199],{"separator":1121},[1154,25330,3064],{},[1172,25332,25333],{"encoding":1174},"i = 1, \\dots, k"," je logická podskupina v pořadí, v jakém byla získána, sloupce obsahují ",[1115,25336,25338],{"className":25337},[1139],[1141,25339,25340],{"xmlns":1143},[1145,25341,25342,25346],{},[1148,25343,25344],{},[1154,25345,1159],{},[1172,25347,1159],{"encoding":1174}," naměřených hodnot a poslední dva sloupce ",[1115,25350,25352],{"className":25351},[1139],[1141,25353,25354],{"xmlns":1143},[1145,25355,25356,25368],{},[1148,25357,25358],{},[1151,25359,25360,25366],{},[1474,25361,25362,25364],{"accent":1121},[1154,25363,1167],{},[1161,25365,1480],{},[1154,25367,1502],{},[1172,25369,25170],{"encoding":1174},[1115,25371,25373],{"className":25372},[1139],[1141,25374,25375],{"xmlns":1143},[1145,25376,25377,25385],{},[1148,25378,25379],{},[1151,25380,25381,25383],{},[1154,25382,1749],{},[1154,25384,1502],{},[1172,25386,25189],{"encoding":1174},". Pro sestrojení diagramu je potřeba aspoň 20 podskupin. Nejprve se určí diagram ",[1115,25389,25391],{"className":25390},[1139],[1141,25392,25393],{"xmlns":1143},[1145,25394,25395,25399],{},[1148,25396,25397],{},[1154,25398,1749],{},[1172,25400,1749],{"encoding":1174},", potom diagram ",[1115,25403,25405],{"className":25404},[1139],[1141,25406,25407],{"xmlns":1143},[1145,25408,25409,25417],{},[1148,25410,25411],{},[1474,25412,25413,25415],{"accent":1121},[1154,25414,1167],{},[1161,25416,1480],{},[1172,25418,25419],{"encoding":1174},"\\bar{x}"," — u obou střední přímka a akční meze. V R se diagramy konstruují funkcí ",[2015,25422,25423],{},"qcc()",[1103,25425,25427,25434],{"className":25426,"dataCallout":2447},[1106,2446],[1110,25428,25430,25433],{"className":25429},[1113],[1115,25431],{"className":25432,"ariaHidden":1121},[1118,2454,1120],"Příklad: kontrola rozměru dílu ve 20 logických podskupinách",[1110,25435,25436,25437,25450,25451,1381,25469,25487,25488,1176],{},"Naměřená data znaku jakosti ",[1115,25438,25440],{"className":25439},[1139],[1141,25441,25442],{"xmlns":1143},[1145,25443,25444,25448],{},[1148,25445,25446],{},[1154,25447,1436],{},[1172,25449,1436],{"encoding":1174}," byla získána ve 20 logických podskupinách po 4 měřeních (",[1115,25452,25454],{"className":25453},[1139],[1141,25455,25456],{"xmlns":1143},[1145,25457,25458,25466],{},[1148,25459,25460,25462,25464],{},[1154,25461,3064],{},[1161,25463,1483],{},[1312,25465,8521],{},[1172,25467,25468],{"encoding":1174},"k=20",[1115,25470,25472],{"className":25471},[1139],[1141,25473,25474],{"xmlns":1143},[1145,25475,25476,25484],{},[1148,25477,25478,25480,25482],{},[1154,25479,1159],{},[1161,25481,1483],{},[1312,25483,4873],{},[1172,25485,25486],{"encoding":1174},"n=4","); znak je měřitelný a má normální rozdělení. Sestrojte regulační diagram ",[1115,25489,25491],{"className":25490},[1139],[1141,25492,25493],{"xmlns":1143},[1145,25494,25495,25511],{},[1148,25496,25497,25499,25505,25507,25509],{},[1161,25498,1164],{"stretchy":1163},[1474,25500,25501,25503],{"accent":1121},[1154,25502,1167],{},[1161,25504,1480],{},[1161,25506,1199],{"separator":1121},[1154,25508,1749],{},[1161,25510,1170],{"stretchy":1163},[1172,25512,24503],{"encoding":1174},[3350,25514,25515,25630],{},[3353,25516,25517],{},[3356,25518,25519,25534,25558,25582,25606],{},[3359,25520,25521],{},[1115,25522,25524],{"className":25523},[1139],[1141,25525,25526],{"xmlns":1143},[1145,25527,25528,25532],{},[1148,25529,25530],{},[1154,25531,1502],{},[1172,25533,1502],{"encoding":1174},[3359,25535,25536],{},[1115,25537,25539],{"className":25538},[1139],[1141,25540,25541],{"xmlns":1143},[1145,25542,25543,25555],{},[1148,25544,25545],{},[1151,25546,25547,25549],{},[1154,25548,1167],{},[1148,25550,25551,25553],{},[1154,25552,1502],{},[1312,25554,1489],{},[1172,25556,25557],{"encoding":1174},"x_{i1}",[3359,25559,25560],{},[1115,25561,25563],{"className":25562},[1139],[1141,25564,25565],{"xmlns":1143},[1145,25566,25567,25579],{},[1148,25568,25569],{},[1151,25570,25571,25573],{},[1154,25572,1167],{},[1148,25574,25575,25577],{},[1154,25576,1502],{},[1312,25578,1610],{},[1172,25580,25581],{"encoding":1174},"x_{i2}",[3359,25583,25584],{},[1115,25585,25587],{"className":25586},[1139],[1141,25588,25589],{"xmlns":1143},[1145,25590,25591,25603],{},[1148,25592,25593],{},[1151,25594,25595,25597],{},[1154,25596,1167],{},[1148,25598,25599,25601],{},[1154,25600,1502],{},[1312,25602,3512],{},[1172,25604,25605],{"encoding":1174},"x_{i3}",[3359,25607,25608],{},[1115,25609,25611],{"className":25610},[1139],[1141,25612,25613],{"xmlns":1143},[1145,25614,25615,25627],{},[1148,25616,25617],{},[1151,25618,25619,25621],{},[1154,25620,1167],{},[1148,25622,25623,25625],{},[1154,25624,1502],{},[1312,25626,4873],{},[1172,25628,25629],{"encoding":1174},"x_{i4}",[3389,25631,25632,25646,25661,25677,25692,25704,25718,25730,25743],{},[3356,25633,25634,25636,25639,25642,25644],{},[3394,25635,1489],{},[3394,25637,25638],{},"106",[3394,25640,25641],{},"98",[3394,25643,4185],{},[3394,25645,4185],{},[3356,25647,25648,25650,25653,25656,25659],{},[3394,25649,1610],{},[3394,25651,25652],{},"95",[3394,25654,25655],{},"94",[3394,25657,25658],{},"108",[3394,25660,10582],{},[3356,25662,25663,25665,25668,25671,25674],{},[3394,25664,3512],{},[3394,25666,25667],{},"122",[3394,25669,25670],{},"105",[3394,25672,25673],{},"103",[3394,25675,25676],{},"133",[3356,25678,25679,25681,25684,25686,25689],{},[3394,25680,4873],{},[3394,25682,25683],{},"113",[3394,25685,8065],{},[3394,25687,25688],{},"128",[3394,25690,25691],{},"135",[3356,25693,25694,25696,25698,25700,25702],{},[3394,25695,3415],{},[3394,25697,4185],{},[3394,25699,10582],{},[3394,25701,25673],{},[3394,25703,10582],{},[3356,25705,25706,25708,25710,25712,25715],{},[3394,25707,3418],{},[3394,25709,25641],{},[3394,25711,25673],{},[3394,25713,25714],{},"97",[3394,25716,25717],{},"99",[3356,25719,25720,25722,25724,25726,25728],{},[3394,25721,3022],{},[3394,25723,3022],{},[3394,25725,3022],{},[3394,25727,3022],{},[3394,25729,3022],{},[3356,25731,25732,25734,25736,25738,25741],{},[3394,25733,4834],{},[3394,25735,25688],{},[3394,25737,25676],{},[3394,25739,25740],{},"120",[3394,25742,4863],{},[3356,25744,25745,25747,25749,25751,25753],{},[3394,25746,8521],{},[3394,25748,25641],{},[3394,25750,25673],{},[3394,25752,25714],{},[3394,25754,25717],{},[1110,25756,25757,25758,25779,25780,6481],{},"Pro každou podskupinu se dopočítá výběrový průměr ",[1115,25759,25761],{"className":25760},[1139],[1141,25762,25763],{"xmlns":1143},[1145,25764,25765,25777],{},[1148,25766,25767],{},[1151,25768,25769,25775],{},[1474,25770,25771,25773],{"accent":1121},[1154,25772,1167],{},[1161,25774,1480],{},[1154,25776,1502],{},[1172,25778,25170],{"encoding":1174}," a rozpětí ",[1115,25781,25783],{"className":25782},[1139],[1141,25784,25785],{"xmlns":1143},[1145,25786,25787,25795],{},[1148,25788,25789],{},[1151,25790,25791,25793],{},[1154,25792,1749],{},[1154,25794,1502],{},[1172,25796,25189],{"encoding":1174},[3350,25798,25799,25860],{},[3353,25800,25801],{},[3356,25802,25803,25818,25841],{},[3359,25804,25805],{},[1115,25806,25808],{"className":25807},[1139],[1141,25809,25810],{"xmlns":1143},[1145,25811,25812,25816],{},[1148,25813,25814],{},[1154,25815,1502],{},[1172,25817,1502],{"encoding":1174},[3359,25819,25820],{},[1115,25821,25823],{"className":25822},[1139],[1141,25824,25825],{"xmlns":1143},[1145,25826,25827,25839],{},[1148,25828,25829],{},[1151,25830,25831,25837],{},[1474,25832,25833,25835],{"accent":1121},[1154,25834,1167],{},[1161,25836,1480],{},[1154,25838,1502],{},[1172,25840,25170],{"encoding":1174},[3359,25842,25843],{},[1115,25844,25846],{"className":25845},[1139],[1141,25847,25848],{"xmlns":1143},[1145,25849,25850,25858],{},[1148,25851,25852],{},[1151,25853,25854,25856],{},[1154,25855,1749],{},[1154,25857,1502],{},[1172,25859,25189],{"encoding":1174},[3389,25861,25862,25871,25881,25891,25901,25910,25919,25927,25936],{},[3356,25863,25864,25866,25869],{},[3394,25865,1489],{},[3394,25867,25868],{},"101,50",[3394,25870,4932],{},[3356,25872,25873,25875,25878],{},[3394,25874,1610],{},[3394,25876,25877],{},"97,25",[3394,25879,25880],{},"16",[3356,25882,25883,25885,25888],{},[3394,25884,3512],{},[3394,25886,25887],{},"115,75",[3394,25889,25890],{},"30",[3356,25892,25893,25895,25898],{},[3394,25894,4873],{},[3394,25896,25897],{},"111,75",[3394,25899,25900],{},"64",[3356,25902,25903,25905,25908],{},[3394,25904,3415],{},[3394,25906,25907],{},"97,00",[3394,25909,4850],{},[3356,25911,25912,25914,25917],{},[3394,25913,3418],{},[3394,25915,25916],{},"99,25",[3394,25918,3418],{},[3356,25920,25921,25923,25925],{},[3394,25922,3022],{},[3394,25924,3022],{},[3394,25926,3022],{},[3356,25928,25929,25931,25934],{},[3394,25930,4834],{},[3394,25932,25933],{},"126,50",[3394,25935,3165],{},[3356,25937,25938,25940,25942],{},[3394,25939,8521],{},[3394,25941,25916],{},[3394,25943,3418],{},[1110,25945,25946,25947,25960,25961,1381,25989,1381,26019,26047,26048,26070,26071,1381,26098,1381,26127,26154,26155,1176],{},"Nejprve se posoudí diagram ",[1115,25948,25950],{"className":25949},[1139],[1141,25951,25952],{"xmlns":1143},[1145,25953,25954,25958],{},[1148,25955,25956],{},[1154,25957,1749],{},[1172,25959,1749],{"encoding":1174}," na všech 20 podskupinách: ",[1115,25962,25964],{"className":25963},[1139],[1141,25965,25966],{"xmlns":1143},[1145,25967,25968,25986],{},[1148,25969,25970,25972,25975,25977,25979,25981,25983],{},[1154,25971,24650],{},[1154,25973,25974],{},"L",[1161,25976,1164],{"stretchy":1163},[1154,25978,1749],{},[1161,25980,1170],{"stretchy":1163},[1161,25982,1483],{},[1312,25984,25985],{},"15,8",[1172,25987,25988],{"encoding":1174},"CL(R)=15{,}8",[1115,25990,25992],{"className":25991},[1139],[1141,25993,25994],{"xmlns":1143},[1145,25995,25996,26016],{},[1148,25997,25998,26001,26003,26005,26007,26009,26011,26013],{},[1154,25999,26000],{},"U",[1154,26002,24650],{},[1154,26004,25974],{},[1161,26006,1164],{"stretchy":1163},[1154,26008,1749],{},[1161,26010,1170],{"stretchy":1163},[1161,26012,1483],{},[1312,26014,26015],{},"36,06",[1172,26017,26018],{"encoding":1174},"UCL(R)=36{,}06",[1115,26020,26022],{"className":26021},[1139],[1141,26023,26024],{"xmlns":1143},[1145,26025,26026,26044],{},[1148,26027,26028,26030,26032,26034,26036,26038,26040,26042],{},[1154,26029,25974],{},[1154,26031,24650],{},[1154,26033,25974],{},[1161,26035,1164],{"stretchy":1163},[1154,26037,1749],{},[1161,26039,1170],{"stretchy":1163},[1161,26041,1483],{},[1312,26043,4585],{},[1172,26045,26046],{"encoding":1174},"LCL(R)=0",". Rozpětí čtvrté podskupiny (",[1115,26049,26051],{"className":26050},[1139],[1141,26052,26053],{"xmlns":1143},[1145,26054,26055,26067],{},[1148,26056,26057,26063,26065],{},[1151,26058,26059,26061],{},[1154,26060,1749],{},[1312,26062,4873],{},[1161,26064,1483],{},[1312,26066,25900],{},[1172,26068,26069],{"encoding":1174},"R_4=64",") mez překračuje; po potvrzení vymezitelné příčiny se podskupina 4 z výpočtu vyřadí a meze se přepočítají — ",[1115,26072,26074],{"className":26073},[1139],[1141,26075,26076],{"xmlns":1143},[1145,26077,26078,26095],{},[1148,26079,26080,26082,26084,26086,26088,26090,26092],{},[1154,26081,24650],{},[1154,26083,25974],{},[1161,26085,1164],{"stretchy":1163},[1154,26087,1749],{},[1161,26089,1170],{"stretchy":1163},[1161,26091,1483],{},[1312,26093,26094],{},"13,26",[1172,26096,26097],{"encoding":1174},"CL(R)=13{,}26",[1115,26099,26101],{"className":26100},[1139],[1141,26102,26103],{"xmlns":1143},[1145,26104,26105,26124],{},[1148,26106,26107,26109,26111,26113,26115,26117,26119,26121],{},[1154,26108,26000],{},[1154,26110,24650],{},[1154,26112,25974],{},[1161,26114,1164],{"stretchy":1163},[1154,26116,1749],{},[1161,26118,1170],{"stretchy":1163},[1161,26120,1483],{},[1312,26122,26123],{},"30,27",[1172,26125,26126],{"encoding":1174},"UCL(R)=30{,}27",[1115,26128,26130],{"className":26129},[1139],[1141,26131,26132],{"xmlns":1143},[1145,26133,26134,26152],{},[1148,26135,26136,26138,26140,26142,26144,26146,26148,26150],{},[1154,26137,25974],{},[1154,26139,24650],{},[1154,26141,25974],{},[1161,26143,1164],{"stretchy":1163},[1154,26145,1749],{},[1161,26147,1170],{"stretchy":1163},[1161,26149,1483],{},[1312,26151,4585],{},[1172,26153,26046],{"encoding":1174},". Diagram rozpětí je teď zvládnutý, lze tedy posoudit diagram ",[1115,26156,26158],{"className":26157},[1139],[1141,26159,26160],{"xmlns":1143},[1145,26161,26162,26170],{},[1148,26163,26164],{},[1474,26165,26166,26168],{"accent":1121},[1154,26167,1167],{},[1161,26169,1480],{},[1172,26171,25419],{"encoding":1174},[1110,26173,25120,26174,26191,26192,1381,26223,1381,26256,26289,26290,26303,26304,1381,26331,1381,26360,26387],{},[1115,26175,26177],{"className":26176},[1139],[1141,26178,26179],{"xmlns":1143},[1145,26180,26181,26189],{},[1148,26182,26183],{},[1474,26184,26185,26187],{"accent":1121},[1154,26186,1167],{},[1161,26188,1480],{},[1172,26190,25419],{"encoding":1174}," bez čtvrté podskupiny dává ",[1115,26193,26195],{"className":26194},[1139],[1141,26196,26197],{"xmlns":1143},[1145,26198,26199,26220],{},[1148,26200,26201,26203,26205,26207,26213,26215,26217],{},[1154,26202,24650],{},[1154,26204,25974],{},[1161,26206,1164],{"stretchy":1163},[1474,26208,26209,26211],{"accent":1121},[1154,26210,1167],{},[1161,26212,1480],{},[1161,26214,1170],{"stretchy":1163},[1161,26216,1483],{},[1312,26218,26219],{},"102,01",[1172,26221,26222],{"encoding":1174},"CL(\\bar{x})=102{,}01",[1115,26224,26226],{"className":26225},[1139],[1141,26227,26228],{"xmlns":1143},[1145,26229,26230,26253],{},[1148,26231,26232,26234,26236,26238,26240,26246,26248,26250],{},[1154,26233,26000],{},[1154,26235,24650],{},[1154,26237,25974],{},[1161,26239,1164],{"stretchy":1163},[1474,26241,26242,26244],{"accent":1121},[1154,26243,1167],{},[1161,26245,1480],{},[1161,26247,1170],{"stretchy":1163},[1161,26249,1483],{},[1312,26251,26252],{},"111,68",[1172,26254,26255],{"encoding":1174},"UCL(\\bar{x})=111{,}68",[1115,26257,26259],{"className":26258},[1139],[1141,26260,26261],{"xmlns":1143},[1145,26262,26263,26286],{},[1148,26264,26265,26267,26269,26271,26273,26279,26281,26283],{},[1154,26266,25974],{},[1154,26268,24650],{},[1154,26270,25974],{},[1161,26272,1164],{"stretchy":1163},[1474,26274,26275,26277],{"accent":1121},[1154,26276,1167],{},[1161,26278,1480],{},[1161,26280,1170],{"stretchy":1163},[1161,26282,1483],{},[1312,26284,26285],{},"92,34",[1172,26287,26288],{"encoding":1174},"LCL(\\bar{x})=92{,}34",". Mez teď překračují průměry podskupin 3 a 19. Po potvrzení vymezitelné příčiny se vyřadí obě najednou a meze diagramu ",[1115,26291,26293],{"className":26292},[1139],[1141,26294,26295],{"xmlns":1143},[1145,26296,26297,26301],{},[1148,26298,26299],{},[1154,26300,1749],{},[1172,26302,1749],{"encoding":1174}," se přepočítají bez podskupin 3, 4 a 19: ",[1115,26305,26307],{"className":26306},[1139],[1141,26308,26309],{"xmlns":1143},[1145,26310,26311,26328],{},[1148,26312,26313,26315,26317,26319,26321,26323,26325],{},[1154,26314,24650],{},[1154,26316,25974],{},[1161,26318,1164],{"stretchy":1163},[1154,26320,1749],{},[1161,26322,1170],{"stretchy":1163},[1161,26324,1483],{},[1312,26326,26327],{},"12,29",[1172,26329,26330],{"encoding":1174},"CL(R)=12{,}29",[1115,26332,26334],{"className":26333},[1139],[1141,26335,26336],{"xmlns":1143},[1145,26337,26338,26357],{},[1148,26339,26340,26342,26344,26346,26348,26350,26352,26354],{},[1154,26341,26000],{},[1154,26343,24650],{},[1154,26345,25974],{},[1161,26347,1164],{"stretchy":1163},[1154,26349,1749],{},[1161,26351,1170],{"stretchy":1163},[1161,26353,1483],{},[1312,26355,26356],{},"28,06",[1172,26358,26359],{"encoding":1174},"UCL(R)=28{,}06",[1115,26361,26363],{"className":26362},[1139],[1141,26364,26365],{"xmlns":1143},[1145,26366,26367,26385],{},[1148,26368,26369,26371,26373,26375,26377,26379,26381,26383],{},[1154,26370,25974],{},[1154,26372,24650],{},[1154,26374,25974],{},[1161,26376,1164],{"stretchy":1163},[1154,26378,1749],{},[1161,26380,1170],{"stretchy":1163},[1161,26382,1483],{},[1312,26384,4585],{},[1172,26386,26046],{"encoding":1174}," — žádná z 17 zbývajících podskupin mez nepřekračuje.",[1110,26389,26390,26391,26408,26409,1381,26440,1381,26473,26506],{},"Konečný diagram ",[1115,26392,26394],{"className":26393},[1139],[1141,26395,26396],{"xmlns":1143},[1145,26397,26398,26406],{},[1148,26399,26400],{},[1474,26401,26402,26404],{"accent":1121},[1154,26403,1167],{},[1161,26405,1480],{},[1172,26407,25419],{"encoding":1174}," na stejných 17 podskupinách má ",[1115,26410,26412],{"className":26411},[1139],[1141,26413,26414],{"xmlns":1143},[1145,26415,26416,26437],{},[1148,26417,26418,26420,26422,26424,26430,26432,26434],{},[1154,26419,24650],{},[1154,26421,25974],{},[1161,26423,1164],{"stretchy":1163},[1474,26425,26426,26428],{"accent":1121},[1154,26427,1167],{},[1161,26429,1480],{},[1161,26431,1170],{"stretchy":1163},[1161,26433,1483],{},[1312,26435,26436],{},"99,76",[1172,26438,26439],{"encoding":1174},"CL(\\bar{x})=99{,}76",[1115,26441,26443],{"className":26442},[1139],[1141,26444,26445],{"xmlns":1143},[1145,26446,26447,26470],{},[1148,26448,26449,26451,26453,26455,26457,26463,26465,26467],{},[1154,26450,26000],{},[1154,26452,24650],{},[1154,26454,25974],{},[1161,26456,1164],{"stretchy":1163},[1474,26458,26459,26461],{"accent":1121},[1154,26460,1167],{},[1161,26462,1480],{},[1161,26464,1170],{"stretchy":1163},[1161,26466,1483],{},[1312,26468,26469],{},"108,73",[1172,26471,26472],{"encoding":1174},"UCL(\\bar{x})=108{,}73",[1115,26474,26476],{"className":26475},[1139],[1141,26477,26478],{"xmlns":1143},[1145,26479,26480,26503],{},[1148,26481,26482,26484,26486,26488,26490,26496,26498,26500],{},[1154,26483,25974],{},[1154,26485,24650],{},[1154,26487,25974],{},[1161,26489,1164],{"stretchy":1163},[1474,26491,26492,26494],{"accent":1121},[1154,26493,1167],{},[1161,26495,1480],{},[1161,26497,1170],{"stretchy":1163},[1161,26499,1483],{},[1312,26501,26502],{},"90,80",[1172,26504,26505],{"encoding":1174},"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.",[1110,26508,26509],{},[1393,26510],{"alt":26511,"className":26512,"src":26513},"mask-rd-priklad1-meze",[1242,1397],"\u002Fwiki-assets\u002Fmask-rd-priklad1-meze.png",[1110,26515,26516,26517,26519,26520,26522],{},"V R se diagramy sestrojí funkcí ",[2015,26518,25423],{}," z balíčku ",[2015,26521,360],{},". Data jsou tabulka, v níž řádek odpovídá logické podskupině a sloupce jednotlivým měřením:",[2020,26524,26526],{"className":2022,"code":26525,"language":71,"meta":2024,"style":2024},"library(qcc)\ndata \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"R\")      # diagram R\nqcc(data, type = \"xbar\")   # diagram x̄\n",[2015,26527,26528,26538,26561,26584],{"__ignoreMap":2024},[1115,26529,26530,26532,26534,26536],{"class":2029,"line":10},[1115,26531,21249],{"class":2035},[1115,26533,1164],{"class":2043},[1115,26535,360],{"class":2032},[1115,26537,2185],{"class":2043},[1115,26539,26540,26542,26544,26546,26548,26551,26553,26555,26557,26559],{"class":2029,"line":27},[1115,26541,23960],{"class":2032},[1115,26543,2036],{"class":2035},[1115,26545,23965],{"class":2039},[1115,26547,1164],{"class":2043},[1115,26549,26550],{"class":8322},"\"3_2.txt\"",[1115,26552,1199],{"class":2035},[1115,26554,23975],{"class":2032},[1115,26556,2291],{"class":2035},[1115,26558,2409],{"class":2046},[1115,26560,2185],{"class":2043},[1115,26562,26563,26565,26567,26569,26571,26573,26575,26578,26581],{"class":2029,"line":148},[1115,26564,360],{"class":2039},[1115,26566,1164],{"class":2043},[1115,26568,23960],{"class":2032},[1115,26570,1199],{"class":2035},[1115,26572,2288],{"class":2032},[1115,26574,2291],{"class":2035},[1115,26576,26577],{"class":8322}," \"R\"",[1115,26579,26580],{"class":2043},")      ",[1115,26582,26583],{"class":2094},"# diagram R\n",[1115,26585,26586,26588,26590,26592,26594,26596,26598,26601,26603],{"class":2029,"line":111},[1115,26587,360],{"class":2039},[1115,26589,1164],{"class":2043},[1115,26591,23960],{"class":2032},[1115,26593,1199],{"class":2035},[1115,26595,2288],{"class":2032},[1115,26597,2291],{"class":2035},[1115,26599,26600],{"class":8322}," \"xbar\"",[1115,26602,2091],{"class":2043},[1115,26604,26605],{"class":2094},"# diagram x̄\n",[1110,26607,26608,26609,26612],{},"Funkce vykreslí diagram se střední přímkou a akčními mezemi a body mimo meze zvýrazní. Podskupina s potvrzenou vymezitelnou příčinou se vyřadí z dat (například ",[2015,26610,26611],{},"data[-4, ]",") a diagram se sestrojí znovu.",[20599,26614,25120,26616],{"id":26615},"diagram-xˉsbarx-s",[1115,26617,26619],{"className":26618},[1139],[1141,26620,26621],{"xmlns":1143},[1145,26622,26623,26639],{},[1148,26624,26625,26627,26633,26635,26637],{},[1161,26626,1164],{"stretchy":1163},[1474,26628,26629,26631],{"accent":1121},[1154,26630,1167],{},[1161,26632,1480],{},[1161,26634,1199],{"separator":1121},[1154,26636,1607],{},[1161,26638,1170],{"stretchy":1163},[1172,26640,24529],{"encoding":1174},[1110,26642,25148,26643,26664,26665,26683,26684,26709],{},[1115,26644,26646],{"className":26645},[1139],[1141,26647,26648],{"xmlns":1143},[1145,26649,26650,26662],{},[1148,26651,26652],{},[1151,26653,26654,26660],{},[1474,26655,26656,26658],{"accent":1121},[1154,26657,1167],{},[1161,26659,1480],{},[1154,26661,1502],{},[1172,26663,25170],{"encoding":1174}," a výběrové směrodatné odchylky ",[1115,26666,26668],{"className":26667},[1139],[1141,26669,26670],{"xmlns":1143},[1145,26671,26672,26680],{},[1148,26673,26674],{},[1151,26675,26676,26678],{},[1154,26677,1607],{},[1154,26679,1502],{},[1172,26681,26682],{"encoding":1174},"s_i"," v logických podskupinách. Podmínky použití jsou stejné jako u ",[1115,26685,26687],{"className":26686},[1139],[1141,26688,26689],{"xmlns":1143},[1145,26690,26691,26707],{},[1148,26692,26693,26695,26701,26703,26705],{},[1161,26694,1164],{"stretchy":1163},[1474,26696,26697,26699],{"accent":1121},[1154,26698,1167],{},[1161,26700,1480],{},[1161,26702,1199],{"separator":1121},[1154,26704,1749],{},[1161,26706,1170],{"stretchy":1163},[1172,26708,24503],{"encoding":1174},", logické podskupiny ale sestávají z většího počtu měření. Data se zapisují do obdobné tabulky.",[2020,26711,26713],{"className":2022,"code":26712,"language":71,"meta":2024,"style":2024},"data \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"S\")      # diagram s\nqcc(data, type = \"xbar\")   # diagram x̄\n",[2015,26714,26715,26737,26759],{"__ignoreMap":2024},[1115,26716,26717,26719,26721,26723,26725,26727,26729,26731,26733,26735],{"class":2029,"line":10},[1115,26718,23960],{"class":2032},[1115,26720,2036],{"class":2035},[1115,26722,23965],{"class":2039},[1115,26724,1164],{"class":2043},[1115,26726,26550],{"class":8322},[1115,26728,1199],{"class":2035},[1115,26730,23975],{"class":2032},[1115,26732,2291],{"class":2035},[1115,26734,2409],{"class":2046},[1115,26736,2185],{"class":2043},[1115,26738,26739,26741,26743,26745,26747,26749,26751,26754,26756],{"class":2029,"line":27},[1115,26740,360],{"class":2039},[1115,26742,1164],{"class":2043},[1115,26744,23960],{"class":2032},[1115,26746,1199],{"class":2035},[1115,26748,2288],{"class":2032},[1115,26750,2291],{"class":2035},[1115,26752,26753],{"class":8322}," \"S\"",[1115,26755,26580],{"class":2043},[1115,26757,26758],{"class":2094},"# diagram s\n",[1115,26760,26761,26763,26765,26767,26769,26771,26773,26775,26777],{"class":2029,"line":148},[1115,26762,360],{"class":2039},[1115,26764,1164],{"class":2043},[1115,26766,23960],{"class":2032},[1115,26768,1199],{"class":2035},[1115,26770,2288],{"class":2032},[1115,26772,2291],{"class":2035},[1115,26774,26600],{"class":8322},[1115,26776,2091],{"class":2043},[1115,26778,26605],{"class":2094},[20599,26780,25120,26782],{"id":26781},"diagram-xirklix_i-r_kli",[1115,26783,26785],{"className":26784},[1139],[1141,26786,26787],{"xmlns":1143},[1145,26788,26789,26817],{},[1148,26790,26791,26793,26799,26801,26815],{},[1161,26792,1164],{"stretchy":1163},[1151,26794,26795,26797],{},[1154,26796,1167],{},[1154,26798,1502],{},[1161,26800,1199],{"separator":1121},[1151,26802,26803,26805],{},[1154,26804,1749],{},[1148,26806,26807,26809,26811,26813],{},[1154,26808,3064],{},[1154,26810,24559],{},[1161,26812,1199],{"separator":1121},[1154,26814,1502],{},[1161,26816,1170],{"stretchy":1163},[1172,26818,24568],{"encoding":1174},[1110,26820,26821,26822,26847,26848,6481],{},"Používá se za stejných podmínek jako ",[1115,26823,26825],{"className":26824},[1139],[1141,26826,26827],{"xmlns":1143},[1145,26828,26829,26845],{},[1148,26830,26831,26833,26839,26841,26843],{},[1161,26832,1164],{"stretchy":1163},[1474,26834,26835,26837],{"accent":1121},[1154,26836,1167],{},[1161,26838,1480],{},[1161,26840,1199],{"separator":1121},[1154,26842,1749],{},[1161,26844,1170],{"stretchy":1163},[1172,26846,24503],{"encoding":1174},", 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 ",[1248,26849,26850],{},"klouzavé rozpětí",[1115,26852,26854],{"className":26853},[1139],[1141,26855,26856],{"xmlns":1143,"display":1468},[1145,26857,26858,26985],{},[1148,26859,26860,26874,26876,26879,26885,26887,26899,26901,26903,26905,26907,26909,26911,26913,26915,26917,26919,26921,26923,26925,26927,26941,26943,26955,26969,26983],{},[1151,26861,26862,26864],{},[1154,26863,1749],{},[1148,26865,26866,26868,26870,26872],{},[1154,26867,3064],{},[1154,26869,24559],{},[1161,26871,1199],{"separator":1121},[1154,26873,1502],{},[1161,26875,1483],{},[1154,26877,26878],{"mathvariant":1869},"∣",[1151,26880,26881,26883],{},[1154,26882,1167],{},[1154,26884,1502],{},[1161,26886,1623],{},[1151,26888,26889,26891],{},[1154,26890,1167],{},[1148,26892,26893,26895,26897],{},[1154,26894,1502],{},[1161,26896,1623],{},[1312,26898,1489],{},[1154,26900,26878],{"mathvariant":1869},[1161,26902,1199],{"separator":1121},[1516,26904],{"width":21870},[1154,26906,1502],{},[1161,26908,1483],{},[1312,26910,1610],{},[1161,26912,1199],{"separator":1121},[1312,26914,3512],{},[1161,26916,1199],{"separator":1121},[1161,26918,3022],{},[1161,26920,1199],{"separator":1121},[1154,26922,3064],{},[1161,26924,1199],{"separator":1121},[1516,26926],{"width":1518},[1151,26928,26929,26935],{},[1474,26930,26931,26933],{"accent":1121},[1154,26932,1749],{},[1161,26934,1480],{},[1148,26936,26937,26939],{},[1154,26938,3064],{},[1154,26940,24559],{},[1161,26942,1483],{},[1485,26944,26945,26947],{},[1312,26946,1489],{},[1148,26948,26949,26951,26953],{},[1154,26950,3064],{},[1161,26952,1623],{},[1312,26954,1489],{},[1493,26956,26957,26959,26967],{},[1161,26958,1497],{},[1148,26960,26961,26963,26965],{},[1154,26962,1502],{},[1161,26964,1483],{},[1312,26966,1610],{},[1154,26968,3064],{},[1151,26970,26971,26973],{},[1154,26972,1749],{},[1148,26974,26975,26977,26979,26981],{},[1154,26976,3064],{},[1154,26978,24559],{},[1161,26980,1199],{"separator":1121},[1154,26982,1502],{},[1154,26984,1176],{"mathvariant":1869},[1172,26986,26987],{"encoding":1174},"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}.",[1110,26989,26990,26991,1385,27008,27034,27035,27060,27061,27078],{},"Regulované veličiny jsou hodnoty ",[1115,26992,26994],{"className":26993},[1139],[1141,26995,26996],{"xmlns":1143},[1145,26997,26998,27006],{},[1148,26999,27000],{},[1151,27001,27002,27004],{},[1154,27003,1167],{},[1154,27005,1502],{},[1172,27007,20986],{"encoding":1174},[1115,27009,27011],{"className":27010},[1139],[1141,27012,27013],{"xmlns":1143},[1145,27014,27015,27031],{},[1148,27016,27017],{},[1151,27018,27019,27021],{},[1154,27020,1749],{},[1148,27022,27023,27025,27027,27029],{},[1154,27024,3064],{},[1154,27026,24559],{},[1161,27028,1199],{"separator":1121},[1154,27030,1502],{},[1172,27032,27033],{"encoding":1174},"R_{kl,i}","; nejdříve se určí střední přímka a meze diagramu ",[1115,27036,27038],{"className":27037},[1139],[1141,27039,27040],{"xmlns":1143},[1145,27041,27042,27058],{},[1148,27043,27044],{},[1151,27045,27046,27048],{},[1154,27047,1749],{},[1148,27049,27050,27052,27054,27056],{},[1154,27051,3064],{},[1154,27053,24559],{},[1161,27055,1199],{"separator":1121},[1154,27057,1502],{},[1172,27059,27033],{"encoding":1174},", potom diagramu ",[1115,27062,27064],{"className":27063},[1139],[1141,27065,27066],{"xmlns":1143},[1145,27067,27068,27076],{},[1148,27069,27070],{},[1151,27071,27072,27074],{},[1154,27073,1167],{},[1154,27075,1502],{},[1172,27077,20986],{"encoding":1174},". Data jsou jeden vektor naměřených hodnot:",[2020,27080,27082],{"className":2022,"code":27081,"language":71,"meta":2024,"style":2024},"data \u003C- read.table(\"3_3.txt\", header = TRUE)\nqcc(data[, 1], type = \"xbar.one\")\n",[2015,27083,27084,27107],{"__ignoreMap":2024},[1115,27085,27086,27088,27090,27092,27094,27097,27099,27101,27103,27105],{"class":2029,"line":10},[1115,27087,23960],{"class":2032},[1115,27089,2036],{"class":2035},[1115,27091,23965],{"class":2039},[1115,27093,1164],{"class":2043},[1115,27095,27096],{"class":8322},"\"3_3.txt\"",[1115,27098,1199],{"class":2035},[1115,27100,23975],{"class":2032},[1115,27102,2291],{"class":2035},[1115,27104,2409],{"class":2046},[1115,27106,2185],{"class":2043},[1115,27108,27109,27111,27113,27115,27117,27119,27121,27123,27125,27127,27129,27132],{"class":2029,"line":27},[1115,27110,360],{"class":2039},[1115,27112,1164],{"class":2043},[1115,27114,23960],{"class":2032},[1115,27116,12612],{"class":2043},[1115,27118,1199],{"class":2035},[1115,27120,5269],{"class":2046},[1115,27122,12629],{"class":2043},[1115,27124,1199],{"class":2035},[1115,27126,2288],{"class":2032},[1115,27128,2291],{"class":2035},[1115,27130,27131],{"class":8322}," \"xbar.one\"",[1115,27133,2185],{"class":2043},[1232,27135,27137],{"id":27136},"regulace-srovnáváním","Regulace srovnáváním",[1110,27139,27140],{},"Diagramy pro regulaci srovnáváním se používají, sledují-li se počty neshodných produktů nebo počty neshod na produktech — regulovaná veličina je diskrétní náhodná veličina.",[3350,27142,27143,27156],{},[3353,27144,27145],{},[3356,27146,27147,27150,27153],{},[3359,27148,27149],{},"Sleduje se",[3359,27151,27152],{},"Konstantní rozsah podskupin",[3359,27154,27155],{},"Nekonstantní rozsah podskupin",[3389,27157,27158,27193],{},[3356,27159,27160,27163,27178],{},[3394,27161,27162],{},"počet neshod na produktech (např. vady na stejných tabulích skla)",[3394,27164,27165],{},[1115,27166,27168],{"className":27167},[1139],[1141,27169,27170],{"xmlns":1143},[1145,27171,27172,27176],{},[1148,27173,27174],{},[1154,27175,1784],{},[1172,27177,1784],{"encoding":1174},[3394,27179,27180],{},[1115,27181,27183],{"className":27182},[1139],[1141,27184,27185],{"xmlns":1143},[1145,27186,27187,27191],{},[1148,27188,27189],{},[1154,27190,1559],{},[1172,27192,1559],{"encoding":1174},[3356,27194,27195,27198,27215],{},[3394,27196,27197],{},"počet neshodných produktů ve výběru (např. neshodné kusy ze série na výrobní lince)",[3394,27199,27200],{},[1115,27201,27203],{"className":27202},[1139],[1141,27204,27205],{"xmlns":1143},[1145,27206,27207,27213],{},[1148,27208,27209,27211],{},[1154,27210,1159],{},[1154,27212,1110],{},[1172,27214,24615],{"encoding":1174},[3394,27216,27217],{},[1115,27218,27220],{"className":27219},[1139],[1141,27221,27222],{"xmlns":1143},[1145,27223,27224,27228],{},[1148,27225,27226],{},[1154,27227,1110],{},[1172,27229,1110],{"encoding":1174},[20599,27231,25120,27233],{"id":27232},"diagram-cc",[1115,27234,27236],{"className":27235},[1139],[1141,27237,27238],{"xmlns":1143},[1145,27239,27240,27244],{},[1148,27241,27242],{},[1154,27243,1784],{},[1172,27245,1784],{"encoding":1174},[1110,27247,27248,27249,27267,27268,27281,27282,27307,27308,27321],{},"Regulovanou veličinou ",[1115,27250,27252],{"className":27251},[1139],[1141,27253,27254],{"xmlns":1143},[1145,27255,27256,27264],{},[1148,27257,27258],{},[1151,27259,27260,27262],{},[1154,27261,1784],{},[1154,27263,1502],{},[1172,27265,27266],{"encoding":1174},"c_i"," je počet neshod na produktech v ",[1115,27269,27271],{"className":27270},[1139],[1141,27272,27273],{"xmlns":1143},[1145,27274,27275,27279],{},[1148,27276,27277],{},[1154,27278,1502],{},[1172,27280,1502],{"encoding":1174},"-té logické podskupině, ",[1115,27283,27285],{"className":27284},[1139],[1141,27286,27287],{"xmlns":1143},[1145,27288,27289,27305],{},[1148,27290,27291,27293,27295,27297,27299,27301,27303],{},[1154,27292,1502],{},[1161,27294,1483],{},[1312,27296,1489],{},[1161,27298,1199],{"separator":1121},[1161,27300,3022],{},[1161,27302,1199],{"separator":1121},[1154,27304,3064],{},[1172,27306,25333],{"encoding":1174},"; v každé podskupině je stejný počet ",[1115,27309,27311],{"className":27310},[1139],[1141,27312,27313],{"xmlns":1143},[1145,27314,27315,27319],{},[1148,27316,27317],{},[1154,27318,1159],{},[1172,27320,1159],{"encoding":1174}," 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.",[1103,27323,27325,27332],{"className":27324,"dataCallout":2447},[1106,2446],[1110,27326,27328,27331],{"className":27327},[1113],[1115,27329],{"className":27330,"ariaHidden":1121},[1118,2454,1120],"Příklad: bodové vady na pásech látky",[1110,27333,27334,27335,27352,27353,1176],{},"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 ",[1115,27336,27338],{"className":27337},[1139],[1141,27339,27340],{"xmlns":1143},[1145,27341,27342,27350],{},[1148,27343,27344],{},[1151,27345,27346,27348],{},[1154,27347,1784],{},[1154,27349,1502],{},[1172,27351,27266],{"encoding":1174},". Sestrojte regulační diagram ",[1115,27354,27356],{"className":27355},[1139],[1141,27357,27358],{"xmlns":1143},[1145,27359,27360,27364],{},[1148,27361,27362],{},[1154,27363,1784],{},[1172,27365,1784],{"encoding":1174},[2020,27367,27369],{"className":2022,"code":27368,"language":71,"meta":2024,"style":2024},"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",[2015,27370,27371,27461,27465,27490],{"__ignoreMap":2024},[1115,27372,27373,27375,27377,27379,27381,27383,27385,27387,27389,27391,27393,27395,27397,27399,27401,27403,27405,27407,27409,27411,27413,27415,27417,27419,27421,27423,27425,27427,27429,27431,27433,27435,27437,27439,27441,27443,27445,27447,27449,27451,27453,27455,27457,27459],{"class":2029,"line":10},[1115,27374,27266],{"class":2032},[1115,27376,2036],{"class":2035},[1115,27378,2040],{"class":2039},[1115,27380,1164],{"class":2043},[1115,27382,3421],{"class":2046},[1115,27384,1199],{"class":2035},[1115,27386,5269],{"class":2046},[1115,27388,1199],{"class":2035},[1115,27390,4210],{"class":2046},[1115,27392,1199],{"class":2035},[1115,27394,4225],{"class":2046},[1115,27396,1199],{"class":2035},[1115,27398,14387],{"class":2046},[1115,27400,1199],{"class":2035},[1115,27402,2294],{"class":2046},[1115,27404,1199],{"class":2035},[1115,27406,4210],{"class":2046},[1115,27408,1199],{"class":2035},[1115,27410,14387],{"class":2046},[1115,27412,1199],{"class":2035},[1115,27414,8284],{"class":2046},[1115,27416,1199],{"class":2035},[1115,27418,8284],{"class":2046},[1115,27420,1199],{"class":2035},[1115,27422,2294],{"class":2046},[1115,27424,1199],{"class":2035},[1115,27426,4424],{"class":2046},[1115,27428,1199],{"class":2035},[1115,27430,4424],{"class":2046},[1115,27432,1199],{"class":2035},[1115,27434,4424],{"class":2046},[1115,27436,1199],{"class":2035},[1115,27438,5269],{"class":2046},[1115,27440,1199],{"class":2035},[1115,27442,2294],{"class":2046},[1115,27444,1199],{"class":2035},[1115,27446,4424],{"class":2046},[1115,27448,1199],{"class":2035},[1115,27450,5269],{"class":2046},[1115,27452,1199],{"class":2035},[1115,27454,4225],{"class":2046},[1115,27456,1199],{"class":2035},[1115,27458,2294],{"class":2046},[1115,27460,2185],{"class":2043},[1115,27462,27463],{"class":2029,"line":27},[1115,27464,14456],{"emptyLinePlaceholder":6044},[1115,27466,27467,27470,27472,27475,27477,27479,27481,27483,27485,27488],{"class":2029,"line":148},[1115,27468,27469],{"class":2032},"q_c",[1115,27471,2036],{"class":2035},[1115,27473,27474],{"class":2039}," qcc",[1115,27476,1164],{"class":2043},[1115,27478,27266],{"class":2032},[1115,27480,1199],{"class":2035},[1115,27482,2288],{"class":2032},[1115,27484,2291],{"class":2035},[1115,27486,27487],{"class":8322}," \"c\"",[1115,27489,2185],{"class":2043},[1115,27491,27492,27494,27496,27498],{"class":2029,"line":111},[1115,27493,20720],{"class":2039},[1115,27495,1164],{"class":2043},[1115,27497,27469],{"class":2032},[1115,27499,2185],{"class":2043},[2020,27501,27504],{"className":27502,"code":27503,"language":2349,"meta":2024},[2347],"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",[2015,27505,27503],{"__ignoreMap":2024},[1110,27507,27508,27509,27538,27539,27562,27563,27585],{},"Průměrný počet vad na pás je ",[1115,27510,27512],{"className":27511},[1139],[1141,27513,27514],{"xmlns":1143},[1145,27515,27516,27535],{},[1148,27517,27518,27520,27522,27524,27530,27532],{},[1154,27519,24650],{},[1154,27521,25974],{},[1161,27523,1483],{},[1474,27525,27526,27528],{"accent":1121},[1154,27527,1784],{},[1161,27529,1480],{},[1161,27531,1483],{},[1312,27533,27534],{},"3,4",[1172,27536,27537],{"encoding":1174},"CL = \\bar{c} = 3{,}4",", horní mez ",[1115,27540,27542],{"className":27541},[1139],[1141,27543,27544],{"xmlns":1143},[1145,27545,27546,27559],{},[1148,27547,27548,27550,27552,27554,27556],{},[1154,27549,26000],{},[1154,27551,24650],{},[1154,27553,25974],{},[1161,27555,1483],{},[1312,27557,27558],{},"8,93",[1172,27560,27561],{"encoding":1174},"UCL = 8{,}93"," a dolní mez ",[1115,27564,27566],{"className":27565},[1139],[1141,27567,27568],{"xmlns":1143},[1145,27569,27570,27582],{},[1148,27571,27572,27574,27576,27578,27580],{},[1154,27573,25974],{},[1154,27575,24650],{},[1154,27577,25974],{},[1161,27579,1483],{},[1312,27581,4585],{},[1172,27583,27584],{"encoding":1174},"LCL = 0",". Žádný pás meze nepřekračuje — proces je zvládnutý.",[1110,27587,27588],{},[1393,27589],{"alt":27590,"className":27591,"src":27592},"mask-rd-priklad2-c",[1242,1397],"\u002Fwiki-assets\u002Fmask-rd-priklad2-c.png",[20599,27594,25120,27596],{"id":27595},"diagram-uu",[1115,27597,27599],{"className":27598},[1139],[1141,27600,27601],{"xmlns":1143},[1145,27602,27603,27607],{},[1148,27604,27605],{},[1154,27606,1559],{},[1172,27608,1559],{"encoding":1174},[1110,27610,27248,27611,27645,27646,27664],{},[1115,27612,27614],{"className":27613},[1139],[1141,27615,27616],{"xmlns":1143},[1145,27617,27618,27642],{},[1148,27619,27620,27626,27628,27634,27636],{},[1151,27621,27622,27624],{},[1154,27623,1559],{},[1154,27625,1502],{},[1161,27627,1483],{},[1151,27629,27630,27632],{},[1154,27631,1784],{},[1154,27633,1502],{},[1154,27635,3245],{"mathvariant":1869},[1151,27637,27638,27640],{},[1154,27639,1159],{},[1154,27641,1502],{},[1172,27643,27644],{"encoding":1174},"u_i = c_i\u002Fn_i"," je průměrný počet neshod přepočítaný na jeden produkt z logické podskupiny; rozsah podskupin ",[1115,27647,27649],{"className":27648},[1139],[1141,27650,27651],{"xmlns":1143},[1145,27652,27653,27661],{},[1148,27654,27655],{},[1151,27656,27657,27659],{},[1154,27658,1159],{},[1154,27660,1502],{},[1172,27662,27663],{"encoding":1174},"n_i"," není konstantní, a proto se bod od bodu mění i meze.",[1110,27666,27667,27668,27671],{},"Za ",[2015,27669,27670],{},"sizes"," se dosadí vektor rozsahů jednotlivých logických podskupin, resp. rozměr jejich jednotek:",[2020,27673,27675],{"className":2022,"code":27674,"language":71,"meta":2024,"style":2024},"data \u003C- read.table(\"3_4.txt\", header = TRUE)   # počty suků a rozměry prken\nqcc(data[, 1], type = \"u\", sizes = data[, 2])\n",[2015,27676,27677,27703],{"__ignoreMap":2024},[1115,27678,27679,27681,27683,27685,27687,27690,27692,27694,27696,27698,27700],{"class":2029,"line":10},[1115,27680,23960],{"class":2032},[1115,27682,2036],{"class":2035},[1115,27684,23965],{"class":2039},[1115,27686,1164],{"class":2043},[1115,27688,27689],{"class":8322},"\"3_4.txt\"",[1115,27691,1199],{"class":2035},[1115,27693,23975],{"class":2032},[1115,27695,2291],{"class":2035},[1115,27697,2409],{"class":2046},[1115,27699,2091],{"class":2043},[1115,27701,27702],{"class":2094},"# počty suků a rozměry prken\n",[1115,27704,27705,27707,27709,27711,27713,27715,27717,27719,27721,27723,27725,27728,27730,27733,27735,27737,27739,27741,27743],{"class":2029,"line":27},[1115,27706,360],{"class":2039},[1115,27708,1164],{"class":2043},[1115,27710,23960],{"class":2032},[1115,27712,12612],{"class":2043},[1115,27714,1199],{"class":2035},[1115,27716,5269],{"class":2046},[1115,27718,12629],{"class":2043},[1115,27720,1199],{"class":2035},[1115,27722,2288],{"class":2032},[1115,27724,2291],{"class":2035},[1115,27726,27727],{"class":8322}," \"u\"",[1115,27729,1199],{"class":2035},[1115,27731,27732],{"class":2032}," sizes",[1115,27734,2291],{"class":2035},[1115,27736,24019],{"class":2032},[1115,27738,12612],{"class":2043},[1115,27740,1199],{"class":2035},[1115,27742,4210],{"class":2046},[1115,27744,27745],{"class":2043},"])\n",[20599,27747,25120,27749],{"id":27748},"diagram-npnp",[1115,27750,27752],{"className":27751},[1139],[1141,27753,27754],{"xmlns":1143},[1145,27755,27756,27762],{},[1148,27757,27758,27760],{},[1154,27759,1159],{},[1154,27761,1110],{},[1172,27763,24615],{"encoding":1174},[1110,27765,27766,27767,11222,27782,27795],{},"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 ",[1115,27768,27770],{"className":27769},[1139],[1141,27771,27772],{"xmlns":1143},[1145,27773,27774,27780],{},[1148,27775,27776,27778],{},[1154,27777,1159],{},[1154,27779,1110],{},[1172,27781,24615],{"encoding":1174},[1115,27783,27785],{"className":27784},[1139],[1141,27786,27787],{"xmlns":1143},[1145,27788,27789,27793],{},[1148,27790,27791],{},[1154,27792,1110],{},[1172,27794,1110],{"encoding":1174}," je pravděpodobnost, že vyrobený produkt je neshodný.",[1110,27797,27798,27799,6481],{},"Pro konstantní rozsah ",[1115,27800,27802],{"className":27801},[1139],[1141,27803,27804],{"xmlns":1143},[1145,27805,27806,27810],{},[1148,27807,27808],{},[1154,27809,1159],{},[1172,27811,1159],{"encoding":1174},[2020,27813,27815],{"className":2022,"code":27814,"language":71,"meta":2024,"style":2024},"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",[2015,27816,27817,27843],{"__ignoreMap":2024},[1115,27818,27819,27821,27823,27825,27827,27830,27832,27834,27836,27838,27840],{"class":2029,"line":10},[1115,27820,23960],{"class":2032},[1115,27822,2036],{"class":2035},[1115,27824,23965],{"class":2039},[1115,27826,1164],{"class":2043},[1115,27828,27829],{"class":8322},"\"3_7.txt\"",[1115,27831,1199],{"class":2035},[1115,27833,23975],{"class":2032},[1115,27835,2291],{"class":2035},[1115,27837,2409],{"class":2046},[1115,27839,2091],{"class":2043},[1115,27841,27842],{"class":2094},"# počty vadných tabletů v sériích po 100 kusech\n",[1115,27844,27845,27847,27849,27851,27853,27855,27857,27859,27861,27863,27865,27868,27870,27872,27874,27876],{"class":2029,"line":27},[1115,27846,360],{"class":2039},[1115,27848,1164],{"class":2043},[1115,27850,23960],{"class":2032},[1115,27852,12612],{"class":2043},[1115,27854,1199],{"class":2035},[1115,27856,5269],{"class":2046},[1115,27858,12629],{"class":2043},[1115,27860,1199],{"class":2035},[1115,27862,2288],{"class":2032},[1115,27864,2291],{"class":2035},[1115,27866,27867],{"class":8322}," \"np\"",[1115,27869,1199],{"class":2035},[1115,27871,27732],{"class":2032},[1115,27873,2291],{"class":2035},[1115,27875,5467],{"class":2046},[1115,27877,2185],{"class":2043},[20599,27879,25120,27881],{"id":27880},"diagram-pp",[1115,27882,27884],{"className":27883},[1139],[1141,27885,27886],{"xmlns":1143},[1145,27887,27888,27892],{},[1148,27889,27890],{},[1154,27891,1110],{},[1172,27893,1110],{"encoding":1174},[1110,27895,27896,27897,27933],{},"Regulovanou veličinou je počet neshodných produktů v logické podskupině přepočtený na jednotku, ",[1115,27898,27900],{"className":27899},[1139],[1141,27901,27902],{"xmlns":1143},[1145,27903,27904,27930],{},[1148,27905,27906,27912,27914,27916,27922,27924],{},[1151,27907,27908,27910],{},[1154,27909,1110],{},[1154,27911,1502],{},[1161,27913,1483],{},[1154,27915,1159],{},[1151,27917,27918,27920],{},[1154,27919,1110],{},[1154,27921,1502],{},[1154,27923,3245],{"mathvariant":1869},[1151,27925,27926,27928],{},[1154,27927,1159],{},[1154,27929,1502],{},[1172,27931,27932],{"encoding":1174},"p_i = np_i\u002Fn_i","; rozsahy podskupin nemusí být konstantní.",[1110,27935,27667,27936,27938],{},[2015,27937,27670],{}," se dosadí vektor rozsahů logických podskupin:",[2020,27940,27942],{"className":2022,"code":27941,"language":71,"meta":2024,"style":2024},"data \u003C- read.table(\"3_6.txt\", header = TRUE)   # počty vadných tabletů a rozsahy sérií\nqcc(data[, 1], type = \"p\", sizes = data[, 2])\n",[2015,27943,27944,27970],{"__ignoreMap":2024},[1115,27945,27946,27948,27950,27952,27954,27957,27959,27961,27963,27965,27967],{"class":2029,"line":10},[1115,27947,23960],{"class":2032},[1115,27949,2036],{"class":2035},[1115,27951,23965],{"class":2039},[1115,27953,1164],{"class":2043},[1115,27955,27956],{"class":8322},"\"3_6.txt\"",[1115,27958,1199],{"class":2035},[1115,27960,23975],{"class":2032},[1115,27962,2291],{"class":2035},[1115,27964,2409],{"class":2046},[1115,27966,2091],{"class":2043},[1115,27968,27969],{"class":2094},"# počty vadných tabletů a rozsahy sérií\n",[1115,27971,27972,27974,27976,27978,27980,27982,27984,27986,27988,27990,27992,27995,27997,27999,28001,28003,28005,28007,28009],{"class":2029,"line":27},[1115,27973,360],{"class":2039},[1115,27975,1164],{"class":2043},[1115,27977,23960],{"class":2032},[1115,27979,12612],{"class":2043},[1115,27981,1199],{"class":2035},[1115,27983,5269],{"class":2046},[1115,27985,12629],{"class":2043},[1115,27987,1199],{"class":2035},[1115,27989,2288],{"class":2032},[1115,27991,2291],{"class":2035},[1115,27993,27994],{"class":8322}," \"p\"",[1115,27996,1199],{"class":2035},[1115,27998,27732],{"class":2032},[1115,28000,2291],{"class":2035},[1115,28002,24019],{"class":2032},[1115,28004,12612],{"class":2043},[1115,28006,1199],{"class":2035},[1115,28008,4210],{"class":2046},[1115,28010,27745],{"class":2043},[1232,28012,28014],{"id":28013},"indexy-způsobilosti","Indexy způsobilosti",[1110,28016,28017,28018,28037,28038,28056],{},"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 ",[1115,28019,28021],{"className":28020},[1139],[1141,28022,28023],{"xmlns":1143},[1145,28024,28025,28034],{},[1148,28026,28027,28029,28032],{},[1154,28028,25974],{},[1154,28030,28031],{},"S",[1154,28033,25974],{},[1172,28035,28036],{"encoding":1174},"LSL"," a horní meze ",[1115,28039,28041],{"className":28040},[1139],[1141,28042,28043],{"xmlns":1143},[1145,28044,28045,28053],{},[1148,28046,28047,28049,28051],{},[1154,28048,26000],{},[1154,28050,28031],{},[1154,28052,25974],{},[1172,28054,28055],{"encoding":1174},"USL",". Způsobilost se zkoumá až pro proces, který je podle regulačních diagramů statisticky zvládnutý (třetí fáze regulace).",[20599,28058,28060,28077],{"id":28059},"cpc_p-index-způsobilosti",[1115,28061,28063],{"className":28062},[1139],[1141,28064,28065],{"xmlns":1143},[1145,28066,28067,28075],{},[1148,28068,28069],{},[1151,28070,28071,28073],{},[1154,28072,24650],{},[1154,28074,1110],{},[1172,28076,24655],{"encoding":1174}," — index způsobilosti",[1110,28079,28080,28081,6481],{},"Podíl mezi délkou tolerančního intervalu a délkou intervalu, ve kterém by za normálního rozdělení mělo ležet skoro všech 99,73 % hodnot znaku, tedy ",[1115,28082,28084],{"className":28083},[1139],[1141,28085,28086],{"xmlns":1143},[1145,28087,28088,28094],{},[1148,28089,28090,28092],{},[1312,28091,3418],{},[1154,28093,11339],{},[1172,28095,28096],{"encoding":1174},"6\\sigma",[1115,28098,28100],{"className":28099},[1139],[1141,28101,28102],{"xmlns":1143,"display":1468},[1145,28103,28104,28140],{},[1148,28105,28106,28112,28114,28138],{},[1151,28107,28108,28110],{},[1154,28109,24650],{},[1154,28111,1110],{},[1161,28113,1483],{},[1485,28115,28116,28132],{},[1148,28117,28118,28120,28122,28124,28126,28128,28130],{},[1154,28119,26000],{},[1154,28121,28031],{},[1154,28123,25974],{},[1161,28125,1623],{},[1154,28127,25974],{},[1154,28129,28031],{},[1154,28131,25974],{},[1148,28133,28134,28136],{},[1312,28135,3418],{},[1154,28137,11339],{},[1154,28139,1176],{"mathvariant":1869},[1172,28141,28142],{"encoding":1174},"C_p = \\frac{USL - LSL}{6\\sigma}.",[1110,28144,28145,28162,28163,28176,28177,1176],{},[1115,28146,28148],{"className":28147},[1139],[1141,28149,28150],{"xmlns":1143},[1145,28151,28152,28160],{},[1148,28153,28154],{},[1151,28155,28156,28158],{},[1154,28157,24650],{},[1154,28159,1110],{},[1172,28161,24655],{"encoding":1174}," srovnává jen délky, nevšímá si, kde uprostřed tolerance proces leží — centrovaný i silně vychýlený proces se stejným ",[1115,28164,28166],{"className":28165},[1139],[1141,28167,28168],{"xmlns":1143},[1145,28169,28170,28174],{},[1148,28171,28172],{},[1154,28173,11339],{},[1172,28175,11371],{"encoding":1174}," mají stejné ",[1115,28178,28180],{"className":28179},[1139],[1141,28181,28182],{"xmlns":1143},[1145,28183,28184,28192],{},[1148,28185,28186],{},[1151,28187,28188,28190],{},[1154,28189,24650],{},[1154,28191,1110],{},[1172,28193,24655],{"encoding":1174},[1110,28195,28196],{},"Doplňkové charakteristiky využití tolerančního intervalu:",[1124,28198,28199,28233,28321],{},[1127,28200,28201,8464,28204,28232],{},[1248,28202,28203],{},"míra využití tolerančního intervalu",[1115,28205,28207],{"className":28206},[1139],[1141,28208,28209],{"xmlns":1143},[1145,28210,28211,28229],{},[1148,28212,28213,28225,28227],{},[7752,28214,28215],{"scriptlevel":4585,"displaystyle":1121},[1485,28216,28217,28219],{},[1312,28218,1862],{},[1151,28220,28221,28223],{},[1154,28222,24650],{},[1154,28224,1110],{},[1316,28226,1318],{},[1154,28228,1870],{"mathvariant":1869},[1172,28230,28231],{"encoding":1174},"\\dfrac{100}{C_p}\\,\\%"," — na kolik procent je toleranční interval využíván sledovaným znakem,",[1127,28234,28235,28238,28239,28256,28257,1385,28289,1199],{},[1248,28236,28237],{},"robustnost procesu",": rezerva, kterou máme v tolerančních mezích, než index ",[1115,28240,28242],{"className":28241},[1139],[1141,28243,28244],{"xmlns":1143},[1145,28245,28246,28254],{},[1148,28247,28248],{},[1151,28249,28250,28252],{},[1154,28251,24650],{},[1154,28253,1110],{},[1172,28255,24655],{"encoding":1174}," nabyde hodnotu 1 — rovná se menší hodnotě z výrazů ",[1115,28258,28260],{"className":28259},[1139],[1141,28261,28262],{"xmlns":1143},[1145,28263,28264,28286],{},[1148,28265,28266,28268,28270,28272,28274,28276,28278,28280,28282,28284],{},[1154,28267,26000],{},[1154,28269,28031],{},[1154,28271,25974],{},[1161,28273,1623],{},[1161,28275,1164],{"stretchy":1163},[1154,28277,11332],{},[1161,28279,3835],{},[1312,28281,3512],{},[1154,28283,11339],{},[1161,28285,1170],{"stretchy":1163},[1172,28287,28288],{"encoding":1174},"USL-(\\mu+3\\sigma)",[1115,28290,28292],{"className":28291},[1139],[1141,28293,28294],{"xmlns":1143},[1145,28295,28296,28318],{},[1148,28297,28298,28300,28302,28304,28306,28308,28310,28312,28314,28316],{},[1161,28299,1164],{"stretchy":1163},[1154,28301,11332],{},[1161,28303,1623],{},[1312,28305,3512],{},[1154,28307,11339],{},[1161,28309,1170],{"stretchy":1163},[1161,28311,1623],{},[1154,28313,25974],{},[1154,28315,28031],{},[1154,28317,25974],{},[1172,28319,28320],{"encoding":1174},"(\\mu-3\\sigma)-LSL",[1127,28322,28323,8464,28326,11222,28366,28380],{},[1248,28324,28325],{},"podíl zmetků",[1115,28327,28329],{"className":28328},[1139],[1141,28330,28331],{"xmlns":1143},[1145,28332,28333,28363],{},[1148,28334,28335,28342,28344,28346,28349,28351,28353,28355,28361],{},[1151,28336,28337,28339],{},[1154,28338,11170],{},[1154,28340,28341],{},"z",[1161,28343,1483],{},[1312,28345,1610],{},[1154,28347,28348],{"mathvariant":1869},"Φ",[1161,28350,1164],{"stretchy":1163},[1161,28352,1623],{},[1312,28354,3512],{},[1151,28356,28357,28359],{},[1154,28358,24650],{},[1154,28360,1110],{},[1161,28362,1170],{"stretchy":1163},[1172,28364,28365],{"encoding":1174},"P_z = 2\\Phi(-3C_p)",[1115,28367,28369],{"className":28368},[1139],[1141,28370,28371],{"xmlns":1143},[1145,28372,28373,28377],{},[1148,28374,28375],{},[1154,28376,28348],{"mathvariant":1869},[1172,28378,28379],{"encoding":1174},"\\Phi"," je distribuční funkce normovaného normálního rozdělení.",[20599,28382,28384,28405],{"id":28383},"cpkc_pk-index-způsobilosti-s-ohledem-na-vychýlení",[1115,28385,28387],{"className":28386},[1139],[1141,28388,28389],{"xmlns":1143},[1145,28390,28391,28403],{},[1148,28392,28393],{},[1151,28394,28395,28397],{},[1154,28396,24650],{},[1148,28398,28399,28401],{},[1154,28400,1110],{},[1154,28402,3064],{},[1172,28404,24677],{"encoding":1174}," — index způsobilosti s ohledem na vychýlení",[1110,28407,28408],{},"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:",[1115,28410,28412],{"className":28411},[1139],[1141,28413,28414],{"xmlns":1143,"display":1468},[1145,28415,28416,28486],{},[1148,28417,28418,28428,28430,28432,28434,28484],{},[1151,28419,28420,28422],{},[1154,28421,24650],{},[1148,28423,28424,28426],{},[1154,28425,1110],{},[1154,28427,3064],{},[1161,28429,1483],{},[1154,28431,1770],{},[1161,28433,1761],{},[1148,28435,28436,28438,28458,28460,28462,28482],{},[1161,28437,1164],{"fence":1121},[1485,28439,28440,28452],{},[1148,28441,28442,28444,28446,28448,28450],{},[1154,28443,26000],{},[1154,28445,28031],{},[1154,28447,25974],{},[1161,28449,1623],{},[1154,28451,11332],{},[1148,28453,28454,28456],{},[1312,28455,3512],{},[1154,28457,11339],{},[1161,28459,1199],{"separator":1121},[1316,28461,1326],{},[1485,28463,28464,28476],{},[1148,28465,28466,28468,28470,28472,28474],{},[1154,28467,11332],{},[1161,28469,1623],{},[1154,28471,25974],{},[1154,28473,28031],{},[1154,28475,25974],{},[1148,28477,28478,28480],{},[1312,28479,3512],{},[1154,28481,11339],{},[1161,28483,1170],{"fence":1121},[1154,28485,1176],{"mathvariant":1869},[1172,28487,28488],{"encoding":1174},"C_{pk} = \\min\\left(\\frac{USL-\\mu}{3\\sigma},\\ \\frac{\\mu-LSL}{3\\sigma}\\right).",[1110,28490,28491,28492,28505,28506,28536,28537,28558,28559,1176],{},"Vyjde-li některý z obou podílů záporný, položí se roven nule; to nastane, když střední hodnota ",[1115,28493,28495],{"className":28494},[1139],[1141,28496,28497],{"xmlns":1143},[1145,28498,28499,28503],{},[1148,28500,28501],{},[1154,28502,11332],{},[1172,28504,13226],{"encoding":1174}," leží mimo toleranční interval, a proces pak není pod statistickou kontrolou. U centrovaného procesu jsou oba podíly stejné a ",[1115,28507,28509],{"className":28508},[1139],[1141,28510,28511],{"xmlns":1143},[1145,28512,28513,28533],{},[1148,28514,28515,28525,28527],{},[1151,28516,28517,28519],{},[1154,28518,24650],{},[1148,28520,28521,28523],{},[1154,28522,1110],{},[1154,28524,3064],{},[1161,28526,1483],{},[1151,28528,28529,28531],{},[1154,28530,24650],{},[1154,28532,1110],{},[1172,28534,28535],{"encoding":1174},"C_{pk} = C_p","; čím víc je proces vychýlený, tím víc je ",[1115,28538,28540],{"className":28539},[1139],[1141,28541,28542],{"xmlns":1143},[1145,28543,28544,28556],{},[1148,28545,28546],{},[1151,28547,28548,28550],{},[1154,28549,24650],{},[1148,28551,28552,28554],{},[1154,28553,1110],{},[1154,28555,3064],{},[1172,28557,24677],{"encoding":1174}," menší než ",[1115,28560,28562],{"className":28561},[1139],[1141,28563,28564],{"xmlns":1143},[1145,28565,28566,28574],{},[1148,28567,28568],{},[1151,28569,28570,28572],{},[1154,28571,24650],{},[1154,28573,1110],{},[1172,28575,24655],{"encoding":1174},[20599,28577,28579,1385,28600,28623],{"id":28578},"cpmc_pm-a-cpmkc_pmk-indexy-vztažené-k-cíli",[1115,28580,28582],{"className":28581},[1139],[1141,28583,28584],{"xmlns":1143},[1145,28585,28586,28598],{},[1148,28587,28588],{},[1151,28589,28590,28592],{},[1154,28591,24650],{},[1148,28593,28594,28596],{},[1154,28595,1110],{},[1154,28597,1565],{},[1172,28599,24699],{"encoding":1174},[1115,28601,28603],{"className":28602},[1139],[1141,28604,28605],{"xmlns":1143},[1145,28606,28607,28621],{},[1148,28608,28609],{},[1151,28610,28611,28613],{},[1154,28612,24650],{},[1148,28614,28615,28617,28619],{},[1154,28616,1110],{},[1154,28618,1565],{},[1154,28620,3064],{},[1172,28622,24723],{"encoding":1174}," — indexy vztažené k cíli",[1110,28625,28626,28627,28640,28641,28654,28655,28698,28699,6481],{},"Pokud má proces zadaný cílový střed ",[1115,28628,28630],{"className":28629},[1139],[1141,28631,28632],{"xmlns":1143},[1145,28633,28634,28638],{},[1148,28635,28636],{},[1154,28637,11542],{},[1172,28639,11542],{"encoding":1174}," (ne nutně střed tolerance), nahradí se ",[1115,28642,28644],{"className":28643},[1139],[1141,28645,28646],{"xmlns":1143},[1145,28647,28648,28652],{},[1148,28649,28650],{},[1154,28651,11339],{},[1172,28653,11371],{"encoding":1174}," odmocninou ze střední čtvercové odchylky od cíle ",[1115,28656,28658],{"className":28657},[1139],[1141,28659,28660],{"xmlns":1143},[1145,28661,28662,28695],{},[1148,28663,28664,28667,28669],{},[1154,28665,28666],{},"τ",[1161,28668,1483],{},[1678,28670,28671],{},[1148,28672,28673,28679,28681,28683,28685,28687,28689],{},[1603,28674,28675,28677],{},[1154,28676,11339],{},[1312,28678,1610],{},[1161,28680,3835],{},[1161,28682,1164],{"stretchy":1163},[1154,28684,11332],{},[1161,28686,1623],{},[1154,28688,11542],{},[1603,28690,28691,28693],{},[1161,28692,1170],{"stretchy":1163},[1312,28694,1610],{},[1172,28696,28697],{"encoding":1174},"\\tau = \\sqrt{\\sigma^2+(\\mu-T)^2}",", která trestá i vychýlení od ",[1115,28700,28702],{"className":28701},[1139],[1141,28703,28704],{"xmlns":1143},[1145,28705,28706,28710],{},[1148,28707,28708],{},[1154,28709,11542],{},[1172,28711,11542],{"encoding":1174},[1115,28713,28715],{"className":28714},[1139],[1141,28716,28717],{"xmlns":1143,"display":1468},[1145,28718,28719,28831],{},[1148,28720,28721,28731,28733,28757,28759,28761,28773,28775,28777,28779,28829],{},[1151,28722,28723,28725],{},[1154,28724,24650],{},[1148,28726,28727,28729],{},[1154,28728,1110],{},[1154,28730,1565],{},[1161,28732,1483],{},[1485,28734,28735,28751],{},[1148,28736,28737,28739,28741,28743,28745,28747,28749],{},[1154,28738,26000],{},[1154,28740,28031],{},[1154,28742,25974],{},[1161,28744,1623],{},[1154,28746,25974],{},[1154,28748,28031],{},[1154,28750,25974],{},[1148,28752,28753,28755],{},[1312,28754,3418],{},[1154,28756,28666],{},[1161,28758,1199],{"separator":1121},[1516,28760],{"width":1518},[1151,28762,28763,28765],{},[1154,28764,24650],{},[1148,28766,28767,28769,28771],{},[1154,28768,1110],{},[1154,28770,1565],{},[1154,28772,3064],{},[1161,28774,1483],{},[1154,28776,1770],{},[1161,28778,1761],{},[1148,28780,28781,28783,28803,28805,28807,28827],{},[1161,28782,1164],{"fence":1121},[1485,28784,28785,28797],{},[1148,28786,28787,28789,28791,28793,28795],{},[1154,28788,26000],{},[1154,28790,28031],{},[1154,28792,25974],{},[1161,28794,1623],{},[1154,28796,11332],{},[1148,28798,28799,28801],{},[1312,28800,3512],{},[1154,28802,28666],{},[1161,28804,1199],{"separator":1121},[1316,28806,1326],{},[1485,28808,28809,28821],{},[1148,28810,28811,28813,28815,28817,28819],{},[1154,28812,11332],{},[1161,28814,1623],{},[1154,28816,25974],{},[1154,28818,28031],{},[1154,28820,25974],{},[1148,28822,28823,28825],{},[1312,28824,3512],{},[1154,28826,28666],{},[1161,28828,1170],{"fence":1121},[1154,28830,1176],{"mathvariant":1869},[1172,28832,28833],{"encoding":1174},"C_{pm} = \\frac{USL-LSL}{6\\tau}, \\qquad C_{pmk} = \\min\\left(\\frac{USL-\\mu}{3\\tau},\\ \\frac{\\mu-LSL}{3\\tau}\\right).",[20599,28835,28837],{"id":28836},"interpretace","Interpretace",[3350,28839,28840,28867],{},[3353,28841,28842],{},[3356,28843,28844,28864],{},[3359,28845,28846,28847],{},"Hodnota ",[1115,28848,28850],{"className":28849},[1139],[1141,28851,28852],{"xmlns":1143},[1145,28853,28854,28862],{},[1148,28855,28856],{},[1151,28857,28858,28860],{},[1154,28859,24650],{},[1154,28861,1110],{},[1172,28863,24655],{"encoding":1174},[3359,28865,28866],{},"Způsobilost procesu",[3389,28868,28869,28898,28941],{},[3356,28870,28871,28895],{},[3394,28872,28873],{},[1115,28874,28876],{"className":28875},[1139],[1141,28877,28878],{"xmlns":1143},[1145,28879,28880,28892],{},[1148,28881,28882,28888,28890],{},[1151,28883,28884,28886],{},[1154,28885,24650],{},[1154,28887,1110],{},[1161,28889,8805],{},[1312,28891,1489],{},[1172,28893,28894],{"encoding":1174},"C_p \u003C 1",[3394,28896,28897],{},"dosahovaná přesnost je menší než předepsaná — proces je nezpůsobilý",[3356,28899,28900,28924],{},[3394,28901,28902],{},[1115,28903,28905],{"className":28904},[1139],[1141,28906,28907],{"xmlns":1143},[1145,28908,28909,28921],{},[1148,28910,28911,28917,28919],{},[1151,28912,28913,28915],{},[1154,28914,24650],{},[1154,28916,1110],{},[1161,28918,1483],{},[1312,28920,1489],{},[1172,28922,28923],{"encoding":1174},"C_p = 1",[3394,28925,28926,28927,28940],{},"dosahovaná přesnost je rovna předepsané — proces je způsobilý, ale sebemenší zvětšení ",[1115,28928,28930],{"className":28929},[1139],[1141,28931,28932],{"xmlns":1143},[1145,28933,28934,28938],{},[1148,28935,28936],{},[1154,28937,11339],{},[1172,28939,11371],{"encoding":1174}," jej posune na nezpůsobilý",[3356,28942,28943,28967],{},[3394,28944,28945],{},[1115,28946,28948],{"className":28947},[1139],[1141,28949,28950],{"xmlns":1143},[1145,28951,28952,28964],{},[1148,28953,28954,28960,28962],{},[1151,28955,28956,28958],{},[1154,28957,24650],{},[1154,28959,1110],{},[1161,28961,6225],{},[1312,28963,1489],{},[1172,28965,28966],{"encoding":1174},"C_p > 1",[3394,28968,28969],{},"dosahovaná přesnost je větší než předepsaná — proces je způsobilý",[1110,28971,28972,28973,28994,28995,1176],{},"U indexu ",[1115,28974,28976],{"className":28975},[1139],[1141,28977,28978],{"xmlns":1143},[1145,28979,28980,28992],{},[1148,28981,28982],{},[1151,28983,28984,28986],{},[1154,28985,24650],{},[1148,28987,28988,28990],{},[1154,28989,1110],{},[1154,28991,3064],{},[1172,28993,24677],{"encoding":1174}," se v praxi požaduje víc než jen hodnota nad 1: s rozvojem technologií roste nárok na rezervu, a běžně se dnes vyžaduje hodnota alespoň ",[1115,28996,28998],{"className":28997},[1139],[1141,28999,29000],{"xmlns":1143},[1145,29001,29002,29007],{},[1148,29003,29004],{},[1312,29005,29006],{},"1,5",[1172,29008,29009],{"encoding":1174},"1{,}5",[1110,29011,29012],{},[1393,29013],{"alt":29014,"className":29015,"src":29016},"mask-rd-cp-panely",[1242,1397],"\u002Fwiki-assets\u002Fmask-rd-cp-panely.png",[1110,29018,29019],{},[1393,29020],{"alt":29021,"className":29022,"src":29023},"mask-rd-cpk-off-centre",[1242,1397],"\u002Fwiki-assets\u002Fmask-rd-cpk-off-centre.png",[20599,29025,29027],{"id":29026},"výpočet-v-r","Výpočet v R",[1110,29029,29030,29031,29034,29035,29038,29039,29042,29043,1385,29060,1381,29077,29080,29081,29094],{},"Indexy způsobilosti počítá ",[2015,29032,29033],{},"process.capability()"," z výstupu regulačního diagramu ",[2015,29036,29037],{},"q","; ",[2015,29040,29041],{},"spec.limits"," jsou toleranční meze ",[1115,29044,29046],{"className":29045},[1139],[1141,29047,29048],{"xmlns":1143},[1145,29049,29050,29058],{},[1148,29051,29052,29054,29056],{},[1154,29053,25974],{},[1154,29055,28031],{},[1154,29057,25974],{},[1172,29059,28036],{"encoding":1174},[1115,29061,29063],{"className":29062},[1139],[1141,29064,29065],{"xmlns":1143},[1145,29066,29067,29075],{},[1148,29068,29069,29071,29073],{},[1154,29070,26000],{},[1154,29072,28031],{},[1154,29074,25974],{},[1172,29076,28055],{"encoding":1174},[2015,29078,29079],{},"target"," cílová hodnota ",[1115,29082,29084],{"className":29083},[1139],[1141,29085,29086],{"xmlns":1143},[1145,29087,29088,29092],{},[1148,29089,29090],{},[1154,29091,11542],{},[1172,29093,11542],{"encoding":1174},". Pro velikost výrobku v mm s tolerančními mezemi 100 a 110 mm a cílovou hodnotou 105 mm:",[2020,29096,29098],{"className":2022,"code":29097,"language":71,"meta":2024,"style":2024},"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",[2015,29099,29100,29110,29133,29148,29170],{"__ignoreMap":2024},[1115,29101,29102,29104,29106,29108],{"class":2029,"line":10},[1115,29103,21249],{"class":2035},[1115,29105,1164],{"class":2043},[1115,29107,360],{"class":2032},[1115,29109,2185],{"class":2043},[1115,29111,29112,29114,29116,29118,29120,29123,29125,29127,29129,29131],{"class":2029,"line":27},[1115,29113,23960],{"class":2032},[1115,29115,2036],{"class":2035},[1115,29117,23965],{"class":2039},[1115,29119,1164],{"class":2043},[1115,29121,29122],{"class":8322},"\"3_8.txt\"",[1115,29124,1199],{"class":2035},[1115,29126,23975],{"class":2032},[1115,29128,2291],{"class":2035},[1115,29130,2409],{"class":2046},[1115,29132,2185],{"class":2043},[1115,29134,29135,29137,29139,29142,29144,29146],{"class":2029,"line":148},[1115,29136,1167],{"class":2032},[1115,29138,2036],{"class":2035},[1115,29140,29141],{"class":2039}," as.matrix",[1115,29143,1164],{"class":2043},[1115,29145,23960],{"class":2032},[1115,29147,2185],{"class":2043},[1115,29149,29150,29152,29154,29156,29158,29160,29162,29164,29166,29168],{"class":2029,"line":111},[1115,29151,29037],{"class":2032},[1115,29153,2036],{"class":2035},[1115,29155,27474],{"class":2039},[1115,29157,1164],{"class":2043},[1115,29159,1167],{"class":2032},[1115,29161,1199],{"class":2035},[1115,29163,2288],{"class":2032},[1115,29165,2291],{"class":2035},[1115,29167,26600],{"class":8322},[1115,29169,2185],{"class":2043},[1115,29171,29172,29175,29177,29179,29181,29184,29186,29188,29190,29192,29194,29196,29198,29200,29203,29205,29208,29210,29213,29215,29217,29219,29221],{"class":2029,"line":96},[1115,29173,29174],{"class":2039},"process.capability",[1115,29176,1164],{"class":2043},[1115,29178,29037],{"class":2032},[1115,29180,1199],{"class":2035},[1115,29182,29183],{"class":2032}," spec.limits",[1115,29185,2291],{"class":2035},[1115,29187,2040],{"class":2039},[1115,29189,1164],{"class":2043},[1115,29191,1862],{"class":2046},[1115,29193,1199],{"class":2035},[1115,29195,4373],{"class":2046},[1115,29197,1170],{"class":2043},[1115,29199,1199],{"class":2035},[1115,29201,29202],{"class":2032}," target",[1115,29204,2291],{"class":2035},[1115,29206,29207],{"class":2046}," 105",[1115,29209,1199],{"class":2035},[1115,29211,29212],{"class":2032}," std.dev",[1115,29214,2291],{"class":2035},[1115,29216,13666],{"class":2039},[1115,29218,1164],{"class":2043},[1115,29220,1167],{"class":2032},[1115,29222,3694],{"class":2043},[1110,29224,29225,29226,1381,29229,1381,29232,1381,29235,1385,29238,29241,29242,1385,29244,29246,29247,29268,29269,29292],{},"Výpis obsahuje řádky ",[2015,29227,29228],{},"Cp",[2015,29230,29231],{},"Cp_l",[2015,29233,29234],{},"Cp_u",[2015,29236,29237],{},"Cp_k",[2015,29239,29240],{},"Cpm"," s hodnotou indexu a 95% intervalem spolehlivosti. ",[2015,29243,29231],{},[2015,29245,29234],{}," jsou dílčí poměry k dolní a horní mezi, jejich minimum je ",[1115,29248,29250],{"className":29249},[1139],[1141,29251,29252],{"xmlns":1143},[1145,29253,29254,29266],{},[1148,29255,29256],{},[1151,29257,29258,29260],{},[1154,29259,24650],{},[1148,29261,29262,29264],{},[1154,29263,1110],{},[1154,29265,3064],{},[1172,29267,24677],{"encoding":1174},". Index ",[1115,29270,29272],{"className":29271},[1139],[1141,29273,29274],{"xmlns":1143},[1145,29275,29276,29290],{},[1148,29277,29278],{},[1151,29279,29280,29282],{},[1154,29281,24650],{},[1148,29283,29284,29286,29288],{},[1154,29285,1110],{},[1154,29287,1565],{},[1154,29289,3064],{},[1172,29291,24723],{"encoding":1174}," a doplňkové charakteristiky se dopočítají ze vzorců výše:",[2020,29294,29296],{"className":2022,"code":29295,"language":71,"meta":2024,"style":2024},"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",[2015,29297,29298,29325,29350,29387,29417,29475,29489,29540],{"__ignoreMap":2024},[1115,29299,29300,29303,29305,29307,29309,29311,29313,29315,29317,29319,29321,29323],{"class":2029,"line":10},[1115,29301,29302],{"class":2032},"mu",[1115,29304,2036],{"class":2035},[1115,29306,5274],{"class":2039},[1115,29308,1164],{"class":2043},[1115,29310,1167],{"class":2032},[1115,29312,2240],{"class":2043},[1115,29314,380],{"class":2032},[1115,29316,2036],{"class":2035},[1115,29318,13666],{"class":2039},[1115,29320,1164],{"class":2043},[1115,29322,1167],{"class":2032},[1115,29324,2185],{"class":2043},[1115,29326,29327,29329,29331,29333,29335,29337,29339,29341,29343,29345,29347],{"class":2029,"line":27},[1115,29328,28036],{"class":2032},[1115,29330,2036],{"class":2035},[1115,29332,5467],{"class":2046},[1115,29334,29038],{"class":2043},[1115,29336,28055],{"class":2032},[1115,29338,2036],{"class":2035},[1115,29340,4373],{"class":2046},[1115,29342,29038],{"class":2043},[1115,29344,11542],{"class":2032},[1115,29346,2036],{"class":2035},[1115,29348,29349],{"class":2046}," 105\n",[1115,29351,29352,29355,29357,29359,29361,29363,29365,29367,29369,29371,29373,29376,29379,29381,29383,29385],{"class":2029,"line":148},[1115,29353,29354],{"class":2032},"tau",[1115,29356,2036],{"class":2035},[1115,29358,9044],{"class":2039},[1115,29360,1164],{"class":2043},[1115,29362,380],{"class":2032},[1115,29364,7244],{"class":2035},[1115,29366,1610],{"class":2046},[1115,29368,22368],{"class":2035},[1115,29370,3997],{"class":2043},[1115,29372,29302],{"class":2032},[1115,29374,29375],{"class":2035}," -",[1115,29377,29378],{"class":2032}," T",[1115,29380,1170],{"class":2043},[1115,29382,7244],{"class":2035},[1115,29384,1610],{"class":2046},[1115,29386,2185],{"class":2043},[1115,29388,29389,29391,29393,29395,29397,29399,29402,29404,29406,29408,29410,29412,29415],{"class":2029,"line":111},[1115,29390,29228],{"class":2032},[1115,29392,2036],{"class":2035},[1115,29394,3997],{"class":2043},[1115,29396,28055],{"class":2032},[1115,29398,29375],{"class":2035},[1115,29400,29401],{"class":2032}," LSL",[1115,29403,2257],{"class":2043},[1115,29405,3245],{"class":2035},[1115,29407,3997],{"class":2043},[1115,29409,3418],{"class":2046},[1115,29411,22493],{"class":2035},[1115,29413,29414],{"class":2032}," sigma",[1115,29416,2185],{"class":2043},[1115,29418,29419,29422,29424,29426,29429,29431,29433,29436,29438,29440,29442,29444,29446,29449,29451,29453,29455,29457,29459,29461,29463,29465,29467,29469,29471,29473],{"class":2029,"line":96},[1115,29420,29421],{"class":2032},"Cpmk",[1115,29423,2036],{"class":2035},[1115,29425,2263],{"class":2039},[1115,29427,29428],{"class":2043},"((",[1115,29430,28055],{"class":2032},[1115,29432,29375],{"class":2035},[1115,29434,29435],{"class":2032}," mu",[1115,29437,2257],{"class":2043},[1115,29439,3245],{"class":2035},[1115,29441,3997],{"class":2043},[1115,29443,3512],{"class":2046},[1115,29445,22493],{"class":2035},[1115,29447,29448],{"class":2032}," tau",[1115,29450,1170],{"class":2043},[1115,29452,1199],{"class":2035},[1115,29454,3997],{"class":2043},[1115,29456,29302],{"class":2032},[1115,29458,29375],{"class":2035},[1115,29460,29401],{"class":2032},[1115,29462,2257],{"class":2043},[1115,29464,3245],{"class":2035},[1115,29466,3997],{"class":2043},[1115,29468,3512],{"class":2046},[1115,29470,22493],{"class":2035},[1115,29472,29448],{"class":2032},[1115,29474,3694],{"class":2043},[1115,29476,29477,29480,29482,29484,29486],{"class":2029,"line":89},[1115,29478,29479],{"class":2032},"miravyuziti",[1115,29481,2036],{"class":2035},[1115,29483,5467],{"class":2046},[1115,29485,4650],{"class":2035},[1115,29487,29488],{"class":2032}," Cp\n",[1115,29490,29491,29494,29496,29498,29500,29502,29504,29506,29508,29510,29512,29514,29516,29518,29520,29522,29524,29526,29528,29530,29532,29534,29536,29538],{"class":2029,"line":82},[1115,29492,29493],{"class":2032},"robustnost",[1115,29495,2036],{"class":2035},[1115,29497,2263],{"class":2039},[1115,29499,1164],{"class":2043},[1115,29501,28055],{"class":2032},[1115,29503,29375],{"class":2035},[1115,29505,3997],{"class":2043},[1115,29507,29302],{"class":2032},[1115,29509,22368],{"class":2035},[1115,29511,4424],{"class":2046},[1115,29513,22493],{"class":2035},[1115,29515,29414],{"class":2032},[1115,29517,1170],{"class":2043},[1115,29519,1199],{"class":2035},[1115,29521,3997],{"class":2043},[1115,29523,29302],{"class":2032},[1115,29525,29375],{"class":2035},[1115,29527,4424],{"class":2046},[1115,29529,22493],{"class":2035},[1115,29531,29414],{"class":2032},[1115,29533,2257],{"class":2043},[1115,29535,2260],{"class":2035},[1115,29537,29401],{"class":2032},[1115,29539,2185],{"class":2043},[1115,29541,29542,29545,29547,29549,29551,29553,29555,29557,29559,29561,29564],{"class":2029,"line":75},[1115,29543,29544],{"class":2032},"Pz",[1115,29546,2036],{"class":2035},[1115,29548,4210],{"class":2046},[1115,29550,22493],{"class":2035},[1115,29552,13775],{"class":2039},[1115,29554,1164],{"class":2043},[1115,29556,2260],{"class":2035},[1115,29558,3512],{"class":2046},[1115,29560,22493],{"class":2035},[1115,29562,29563],{"class":2032}," Cp",[1115,29565,2185],{"class":2043},[1232,29567,5763],{"id":5762},[1124,29569,29570,29573,29633,29724,29790],{},[1127,29571,29572],{},"Počítat indexy způsobilosti pro proces, který není statisticky zvládnutý — způsobilost se zkoumá až ve třetí fázi regulace.",[1127,29574,29575,29576,29593,29594,29611,29612,1176],{},"Posuzovat jen ",[1115,29577,29579],{"className":29578},[1139],[1141,29580,29581],{"xmlns":1143},[1145,29582,29583,29591],{},[1148,29584,29585],{},[1151,29586,29587,29589],{},[1154,29588,24650],{},[1154,29590,1110],{},[1172,29592,24655],{"encoding":1174}," u vychýleného procesu — ",[1115,29595,29597],{"className":29596},[1139],[1141,29598,29599],{"xmlns":1143},[1145,29600,29601,29609],{},[1148,29602,29603],{},[1151,29604,29605,29607],{},[1154,29606,24650],{},[1154,29608,1110],{},[1172,29610,24655],{"encoding":1174}," polohu střední hodnoty nezohledňuje, vychýlení zachytí až ",[1115,29613,29615],{"className":29614},[1139],[1141,29616,29617],{"xmlns":1143},[1145,29618,29619,29631],{},[1148,29620,29621],{},[1151,29622,29623,29625],{},[1154,29624,24650],{},[1148,29626,29627,29629],{},[1154,29628,1110],{},[1154,29630,3064],{},[1172,29632,24677],{"encoding":1174},[1127,29634,29635,29636,29649,29650,29663,29664,29649,29679,29692,29693,29706,29707,29720,29721,29723],{},"Zaměnit diagram ",[1115,29637,29639],{"className":29638},[1139],[1141,29640,29641],{"xmlns":1143},[1145,29642,29643,29647],{},[1148,29644,29645],{},[1154,29646,1784],{},[1172,29648,1784],{"encoding":1174}," s diagramem ",[1115,29651,29653],{"className":29652},[1139],[1141,29654,29655],{"xmlns":1143},[1145,29656,29657,29661],{},[1148,29658,29659],{},[1154,29660,1559],{},[1172,29662,1559],{"encoding":1174}," nebo diagram ",[1115,29665,29667],{"className":29666},[1139],[1141,29668,29669],{"xmlns":1143},[1145,29670,29671,29677],{},[1148,29672,29673,29675],{},[1154,29674,1159],{},[1154,29676,1110],{},[1172,29678,24615],{"encoding":1174},[1115,29680,29682],{"className":29681},[1139],[1141,29683,29684],{"xmlns":1143},[1145,29685,29686,29690],{},[1148,29687,29688],{},[1154,29689,1110],{},[1172,29691,1110],{"encoding":1174}," — při nekonstantním rozsahu podskupin se volí ",[1115,29694,29696],{"className":29695},[1139],[1141,29697,29698],{"xmlns":1143},[1145,29699,29700,29704],{},[1148,29701,29702],{},[1154,29703,1559],{},[1172,29705,1559],{"encoding":1174},", resp. ",[1115,29708,29710],{"className":29709},[1139],[1141,29711,29712],{"xmlns":1143},[1145,29713,29714,29718],{},[1148,29715,29716],{},[1154,29717,1110],{},[1172,29719,1110],{"encoding":1174},", a do ",[2015,29722,27670],{}," se zadává vektor rozsahů.",[1127,29725,29726,29727,29744,29745,29758,29759,29772,29773,1176],{},"Posuzovat diagram ",[1115,29728,29730],{"className":29729},[1139],[1141,29731,29732],{"xmlns":1143},[1145,29733,29734,29742],{},[1148,29735,29736],{},[1474,29737,29738,29740],{"accent":1121},[1154,29739,1167],{},[1161,29741,1480],{},[1172,29743,25419],{"encoding":1174}," dřív než diagram rozpětí — nejprve se určí a stabilizuje diagram ",[1115,29746,29748],{"className":29747},[1139],[1141,29749,29750],{"xmlns":1143},[1145,29751,29752,29756],{},[1148,29753,29754],{},[1154,29755,1749],{},[1172,29757,1749],{"encoding":1174}," (resp. ",[1115,29760,29762],{"className":29761},[1139],[1141,29763,29764],{"xmlns":1143},[1145,29765,29766,29770],{},[1148,29767,29768],{},[1154,29769,1607],{},[1172,29771,1607],{"encoding":1174},"), potom diagram ",[1115,29774,29776],{"className":29775},[1139],[1141,29777,29778],{"xmlns":1143},[1145,29779,29780,29788],{},[1148,29781,29782],{},[1474,29783,29784,29786],{"accent":1121},[1154,29785,1167],{},[1161,29787,1480],{},[1172,29789,25419],{"encoding":1174},[1127,29791,29792],{},"Vyřadit podskupinu jen podle polohy bodu — vyřazuje se až po zjištění a odstranění vymezitelné příčiny.",[1232,29794,5963],{"id":5962},[1124,29796,29797,29802,29807,29813,29818,29823,29828],{},[1127,29798,29799],{},[1239,29800,1245],{"className":29801,"dataFsResolvedFilePath":1243,"href":1244},[1242],[1127,29803,29804],{},[1239,29805,886],{"className":29806,"dataFsResolvedFilePath":11066,"href":11067},[1242],[1127,29808,29809],{},[1239,29810,29812],{"className":29811,"dataFsResolvedFilePath":5976,"href":5977},[1242],"nahodne-veliciny-a-rozdeleni",[1127,29814,29815],{},[1239,29816,141],{"className":29817,"dataFsResolvedFilePath":5305,"href":5306},[1242],[1127,29819,29820],{},[1239,29821,15497],{"className":29822,"dataFsResolvedFilePath":5989,"href":5990},[1242],[1127,29824,29825],{},[1239,29826,716],{"className":29827,"dataFsResolvedFilePath":5997,"href":5998},[1242],[1127,29829,29830],{},[1239,29831,6015],{"className":29832,"dataFsResolvedFilePath":6013,"href":6014},[1242],[1232,29834,6018],{"id":934},[1110,29836,6021,29837,6026],{},[6023,29838,6025],{},[1110,29840,29841,29842,29845],{},"MONTGOMERY, D. C. ",[6023,29843,29844],{},"Introduction to Statistical Quality Control",". 6. vyd. John Wiley & Sons, 2005.",[1110,29847,29848,29849,29852],{},"ČSN ISO 8258. ",[6023,29850,29851],{},"Shewhartovy regulační diagramy",". Praha: Český normalizační institut, 1994.",[1110,29854,29855,29856,29859],{},"KUPKA, K. ",[6023,29857,29858],{},"Statistické řízení jakosti",". Pardubice: TriloByte, 1997.",[6028,29861,29862],{},"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":28013,"depth":27,"text":28014,"children":29886},[29887,29889,29891,29893,29894],{"id":28059,"depth":148,"text":29888},"CpC_p — index způsobilosti",{"id":28383,"depth":148,"text":29890},"CpkC_{pk} — index způsobilosti s ohledem na vychýlení",{"id":28578,"depth":148,"text":29892},"CpmC_{pm} a CpmkC_{pmk} — indexy vztažené k cíli",{"id":28836,"depth":148,"text":28837},{"id":29026,"depth":148,"text":29027},{"id":5762,"depth":27,"text":5763},{"id":5962,"depth":27,"text":5963},{"id":934,"depth":27,"text":6018},{},"\u002Ftopics\u002Fregulacni-diagramy-a-indexy-zpusobilosti",{"title":6007,"description":2024},[29902,29903,29904,29905],"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":29910,"title":5307,"body":29911,"course":23,"courses":6040,"created":6041,"description":2024,"extension":6042,"meta":39722,"navigation":6044,"path":39723,"seo":39724,"sources":39725,"stem":39731,"tags":39732,"type":6057,"updated":6041,"__hash__":39733},"topics\u002Ftopics\u002Ftestovani-hypotez.md",{"type":1096,"value":29912,"toc":39695},[29913,29916,30115,30159,30163,30173,30176,30242,30292,30445,30449,30452,30546,30696,30715,30722,30811,30815,30850,30887,30925,30960,30964,30971,31189,31308,31312,31444,31498,31520,31862,31869,31957,31963,32004,32289,32298,32413,32419,32426,32431,32437,32531,32537,32563,32569,32661,32667,32717,32721,32917,32977,33339,33678,33777,33783,34011,34015,34281,34285,34288,34354,34401,34857,34861,34864,35051,35084,35306,35625,35664,35671,36328,36467,36473,36629,36635,36642,36695,36701,36874,36880,36944,36949,37134,37140,37185,37189,37192,37196,37243,37471,37487,37576,37582,37608,37612,37615,37687,37780,37849,37855,37878,38325,38332,38336,38366,38370,38620,38639,38700,38709,38865,38871,38897,39072,39076,39097,39128,39132,39156,39186,39190,39250,39308,39312,39319,39492,39494,39647,39649,39686,39688,39692],[1099,29914,5307],{"id":29915},"testování-statistických-hypotéz",[1103,29917,29919,29925],{"className":29918,"dataCallout":1108},[1106,1107],[1110,29920,29922,1122],{"className":29921},[1113],[1115,29923],{"className":29924,"ariaHidden":1121},[1118,1119,1120],[1124,29926,29927,29997,30079,30082,30085],{},[1127,29928,29929,29930,29947,29948,29965,29966,1381,29979,29996],{},"Test porovnává tvrzení ",[1115,29931,29933],{"className":29932},[1139],[1141,29934,29935],{"xmlns":1143},[1145,29936,29937,29945],{},[1148,29938,29939],{},[1151,29940,29941,29943],{},[1154,29942,6105],{},[1312,29944,4585],{},[1172,29946,6110],{"encoding":1174}," s alternativou ",[1115,29949,29951],{"className":29950},[1139],[1141,29952,29953],{"xmlns":1143},[1145,29954,29955,29963],{},[1148,29956,29957],{},[1151,29958,29959,29961],{},[1154,29960,6105],{},[1312,29962,1489],{},[1172,29964,7508],{"encoding":1174}," pomocí testového kritéria spočteného z výběru; padne-li kritérium do kritického oboru ",[1115,29967,29969],{"className":29968},[1139],[1141,29970,29971],{"xmlns":1143},[1145,29972,29973,29977],{},[1148,29974,29975],{},[1154,29976,6143],{},[1172,29978,6143],{"encoding":1174},[1115,29980,29982],{"className":29981},[1139],[1141,29983,29984],{"xmlns":1143},[1145,29985,29986,29994],{},[1148,29987,29988],{},[1151,29989,29990,29992],{},[1154,29991,6105],{},[1312,29993,4585],{},[1172,29995,6110],{"encoding":1174}," zamítáme.",[1127,29998,29999,30000,30013,30014,30031,30032,30046,30047,30064,30065,30078],{},"Rozhodnutí nese dva typy chyb: chybu I. druhu (",[1115,30001,30003],{"className":30002},[1139],[1141,30004,30005],{"xmlns":1143},[1145,30006,30007,30011],{},[1148,30008,30009],{},[1154,30010,7874],{},[1172,30012,7937],{"encoding":1174},", zamítnutí platné ",[1115,30015,30017],{"className":30016},[1139],[1141,30018,30019],{"xmlns":1143},[1145,30020,30021,30029],{},[1148,30022,30023],{},[1151,30024,30025,30027],{},[1154,30026,6105],{},[1312,30028,4585],{},[1172,30030,6110],{"encoding":1174},") a chybu II. druhu (",[1115,30033,30035],{"className":30034},[1139],[1141,30036,30037],{"xmlns":1143},[1145,30038,30039,30043],{},[1148,30040,30041],{},[1154,30042,20190],{},[1172,30044,30045],{"encoding":1174},"\\beta",", přijetí neplatné ",[1115,30048,30050],{"className":30049},[1139],[1141,30051,30052],{"xmlns":1143},[1145,30053,30054,30062],{},[1148,30055,30056],{},[1151,30057,30058,30060],{},[1154,30059,6105],{},[1312,30061,4585],{},[1172,30063,6110],{"encoding":1174},"). Hladina významnosti ",[1115,30066,30068],{"className":30067},[1139],[1141,30069,30070],{"xmlns":1143},[1145,30071,30072,30076],{},[1148,30073,30074],{},[1154,30075,7874],{},[1172,30077,7937],{"encoding":1174}," se volí předem, obvykle 0,05.",[1127,30080,30081],{},"Pro střední hodnotu normálního rozdělení slouží jednovýběrový a párový t-test; pro srovnání dvou souborů F-test (rozptyly) a dvouvýběrový t-test (střední hodnoty).",[1127,30083,30084],{},"Normalitu ověřuje Shapiro-Wilkův test, shodu s libovolným rozdělením Kolmogorov-Smirnovův test; při porušené normalitě nastupují neparametrické testy (Wilcoxonovy, Kruskalův-Wallisův, mediánový, Friedmanův).",[1127,30086,30087,30088,30101,30102,1176],{},"Rozhodnutí lze číst dvěma rovnocennými způsoby — podle polohy kritéria vůči ",[1115,30089,30091],{"className":30090},[1139],[1141,30092,30093],{"xmlns":1143},[1145,30094,30095,30099],{},[1148,30096,30097],{},[1154,30098,6143],{},[1172,30100,6143],{"encoding":1174},", nebo podle p-hodnoty vůči ",[1115,30103,30105],{"className":30104},[1139],[1141,30106,30107],{"xmlns":1143},[1145,30108,30109,30113],{},[1148,30110,30111],{},[1154,30112,7874],{},[1172,30114,7937],{"encoding":1174},[1110,30116,30117,30118,30122,30123,30127,30128,30132,30133,1381,30146,19946],{},"Testy statistických hypotéz jsou nástroj ",[1239,30119,30121],{"className":30120,"dataFsResolvedFilePath":1243,"href":1244},[1242],"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 ",[1239,30124,30126],{"className":30125,"dataFsResolvedFilePath":11066,"href":11067},[1242],"popisnou statistiku"," výběru, a z rozdělení uvedených u ",[1239,30129,30131],{"className":30130,"dataFsResolvedFilePath":5976,"href":5977},[1242],"náhodných veličin"," (normální, ",[1115,30134,30136],{"className":30135},[1139],[1141,30137,30138],{"xmlns":1143},[1145,30139,30140,30144],{},[1148,30141,30142],{},[1154,30143,1807],{},[1172,30145,1807],{"encoding":1174},[1115,30147,30149],{"className":30148},[1139],[1141,30150,30151],{"xmlns":1143},[1145,30152,30153,30157],{},[1148,30154,30155],{},[1154,30156,1156],{},[1172,30158,1156],{"encoding":1174},[1232,30160,30162],{"id":30161},"statistická-hypotéza-a-její-test","Statistická hypotéza a její test",[1110,30164,30165,30168,30169,30172],{},[1248,30166,30167],{},"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. ",[1248,30170,30171],{},"Testování hypotéz"," je proces ověření správnosti nebo nesprávnosti hypotézy pomocí výsledků získaných náhodným výběrem.",[1110,30174,30175],{},"Proti sobě stojí dvě hypotézy:",[1124,30177,30178,30201],{},[1127,30179,30180,30200],{},[1248,30181,30182,30183],{},"Nulová hypotéza ",[1115,30184,30186],{"className":30185},[1139],[1141,30187,30188],{"xmlns":1143},[1145,30189,30190,30198],{},[1148,30191,30192],{},[1151,30193,30194,30196],{},[1154,30195,6105],{},[1312,30197,4585],{},[1172,30199,6110],{"encoding":1174}," — tvrzení o parametru nebo rozdělení, které chceme ověřit.",[1127,30202,30203,30223,30224,30241],{},[1248,30204,30205,30206],{},"Alternativní hypotéza ",[1115,30207,30209],{"className":30208},[1139],[1141,30210,30211],{"xmlns":1143},[1145,30212,30213,30221],{},[1148,30214,30215],{},[1151,30216,30217,30219],{},[1154,30218,6105],{},[1312,30220,1489],{},[1172,30222,7508],{"encoding":1174}," — staví se proti ",[1115,30225,30227],{"className":30226},[1139],[1141,30228,30229],{"xmlns":1143},[1145,30230,30231,30239],{},[1148,30232,30233],{},[1151,30234,30235,30237],{},[1154,30236,6105],{},[1312,30238,4585],{},[1172,30240,6110],{"encoding":1174}," a určitým způsobem popírá její tvrzení.",[1110,30243,6234,30244,30274,30275,6481],{},[1115,30245,30247],{"className":30246},[1139],[1141,30248,30249],{"xmlns":1143},[1145,30250,30251,30271],{},[1148,30252,30253,30259,30261,30263,30265],{},[1151,30254,30255,30257],{},[1154,30256,6105],{},[1312,30258,4585],{},[1161,30260,6481],{},[1154,30262,11332],{},[1161,30264,1483],{},[1151,30266,30267,30269],{},[1154,30268,11332],{},[1312,30270,4585],{},[1172,30272,30273],{"encoding":1174},"H_0: \\mu = \\mu_0"," existují tři varianty ",[1115,30276,30278],{"className":30277},[1139],[1141,30279,30280],{"xmlns":1143},[1145,30281,30282,30290],{},[1148,30283,30284],{},[1151,30285,30286,30288],{},[1154,30287,6105],{},[1312,30289,1489],{},[1172,30291,7508],{"encoding":1174},[3350,30293,30294,30324],{},[3353,30295,30296],{},[3356,30297,30298,30318,30321],{},[3359,30299,30300,30301],{},"Tvar ",[1115,30302,30304],{"className":30303},[1139],[1141,30305,30306],{"xmlns":1143},[1145,30307,30308,30316],{},[1148,30309,30310],{},[1151,30311,30312,30314],{},[1154,30313,6105],{},[1312,30315,1489],{},[1172,30317,7508],{"encoding":1174},[3359,30319,30320],{},"Zápis",[3359,30322,30323],{},"Typ",[3389,30325,30326,30366,30406],{},[3356,30327,30328,30331,30363],{},[3394,30329,30330],{},"nerovnost",[3394,30332,30333],{},[1115,30334,30336],{"className":30335},[1139],[1141,30337,30338],{"xmlns":1143},[1145,30339,30340,30360],{},[1148,30341,30342,30348,30350,30352,30354],{},[1151,30343,30344,30346],{},[1154,30345,6105],{},[1312,30347,1489],{},[1161,30349,6481],{},[1154,30351,11332],{},[1161,30353,15368],{"mathvariant":1869},[1151,30355,30356,30358],{},[1154,30357,11332],{},[1312,30359,4585],{},[1172,30361,30362],{"encoding":1174},"H_1: \\mu \\neq \\mu_0",[3394,30364,30365],{},"dvoustranná",[3356,30367,30368,30371,30403],{},[3394,30369,30370],{},"větší",[3394,30372,30373],{},[1115,30374,30376],{"className":30375},[1139],[1141,30377,30378],{"xmlns":1143},[1145,30379,30380,30400],{},[1148,30381,30382,30388,30390,30392,30394],{},[1151,30383,30384,30386],{},[1154,30385,6105],{},[1312,30387,1489],{},[1161,30389,6481],{},[1154,30391,11332],{},[1161,30393,6225],{},[1151,30395,30396,30398],{},[1154,30397,11332],{},[1312,30399,4585],{},[1172,30401,30402],{"encoding":1174},"H_1: \\mu > \\mu_0",[3394,30404,30405],{},"jednostranná",[3356,30407,30408,30411,30443],{},[3394,30409,30410],{},"menší",[3394,30412,30413],{},[1115,30414,30416],{"className":30415},[1139],[1141,30417,30418],{"xmlns":1143},[1145,30419,30420,30440],{},[1148,30421,30422,30428,30430,30432,30434],{},[1151,30423,30424,30426],{},[1154,30425,6105],{},[1312,30427,1489],{},[1161,30429,6481],{},[1154,30431,11332],{},[1161,30433,8805],{},[1151,30435,30436,30438],{},[1154,30437,11332],{},[1312,30439,4585],{},[1172,30441,30442],{"encoding":1174},"H_1: \\mu \u003C \\mu_0",[3394,30444,30405],{},[20599,30446,30448],{"id":30447},"chyba-i-a-ii-druhu","Chyba I. a II. druhu",[1110,30450,30451],{},"Protože je úsudek odvozen z náhodného výběru, může vést ke dvěma typům chybného rozhodnutí:",[1124,30453,30454,30491],{},[1127,30455,30456,30459,30460,30477,30478,1176],{},[1248,30457,30458],{},"Chyba I. druhu"," — zamítnutí ",[1115,30461,30463],{"className":30462},[1139],[1141,30464,30465],{"xmlns":1143},[1145,30466,30467,30475],{},[1148,30468,30469],{},[1151,30470,30471,30473],{},[1154,30472,6105],{},[1312,30474,4585],{},[1172,30476,6110],{"encoding":1174},", ačkoliv ve skutečnosti platí. Pravděpodobnost ",[1115,30479,30481],{"className":30480},[1139],[1141,30482,30483],{"xmlns":1143},[1145,30484,30485,30489],{},[1148,30486,30487],{},[1154,30488,7874],{},[1172,30490,7937],{"encoding":1174},[1127,30492,30493,30496,30497,30514,30515,30532,30533,1176],{},[1248,30494,30495],{},"Chyba II. druhu"," — přijetí ",[1115,30498,30500],{"className":30499},[1139],[1141,30501,30502],{"xmlns":1143},[1145,30503,30504,30512],{},[1148,30505,30506],{},[1151,30507,30508,30510],{},[1154,30509,6105],{},[1312,30511,4585],{},[1172,30513,6110],{"encoding":1174},", ačkoliv platí ",[1115,30516,30518],{"className":30517},[1139],[1141,30519,30520],{"xmlns":1143},[1145,30521,30522,30530],{},[1148,30523,30524],{},[1151,30525,30526,30528],{},[1154,30527,6105],{},[1312,30529,1489],{},[1172,30531,7508],{"encoding":1174},". Pravděpodobnost ",[1115,30534,30536],{"className":30535},[1139],[1141,30537,30538],{"xmlns":1143},[1145,30539,30540,30544],{},[1148,30541,30542],{},[1154,30543,20190],{},[1172,30545,30045],{"encoding":1174},[3350,30547,30548,30611],{},[3353,30549,30550],{},[3356,30551,30552,30572,30591],{},[3359,30553,30554,30555],{},"Úsudek o ",[1115,30556,30558],{"className":30557},[1139],[1141,30559,30560],{"xmlns":1143},[1145,30561,30562,30570],{},[1148,30563,30564],{},[1151,30565,30566,30568],{},[1154,30567,6105],{},[1312,30569,4585],{},[1172,30571,6110],{"encoding":1174},[3359,30573,30574,12787],{},[1115,30575,30577],{"className":30576},[1139],[1141,30578,30579],{"xmlns":1143},[1145,30580,30581,30589],{},[1148,30582,30583],{},[1151,30584,30585,30587],{},[1154,30586,6105],{},[1312,30588,4585],{},[1172,30590,6110],{"encoding":1174},[3359,30592,30593,30610],{},[1115,30594,30596],{"className":30595},[1139],[1141,30597,30598],{"xmlns":1143},[1145,30599,30600,30608],{},[1148,30601,30602],{},[1151,30603,30604,30606],{},[1154,30605,6105],{},[1312,30607,4585],{},[1172,30609,6110],{"encoding":1174}," neplatí",[3389,30612,30613,30655],{},[3356,30614,30615,30618,30639],{},[3394,30616,30617],{},"Nezamítá se",[3394,30619,30620,30621],{},"správné rozhodnutí, ",[1115,30622,30624],{"className":30623},[1139],[1141,30625,30626],{"xmlns":1143},[1145,30627,30628,30636],{},[1148,30629,30630,30632,30634],{},[1312,30631,1489],{},[1161,30633,1623],{},[1154,30635,7874],{},[1172,30637,30638],{"encoding":1174},"1-\\alpha",[3394,30640,30641,30642],{},"chyba II. druhu, ",[1115,30643,30645],{"className":30644},[1139],[1141,30646,30647],{"xmlns":1143},[1145,30648,30649,30653],{},[1148,30650,30651],{},[1154,30652,20190],{},[1172,30654,30045],{"encoding":1174},[3356,30656,30657,30660,30676],{},[3394,30658,30659],{},"Zamítá se",[3394,30661,30662,30663],{},"chyba I. druhu, ",[1115,30664,30666],{"className":30665},[1139],[1141,30667,30668],{"xmlns":1143},[1145,30669,30670,30674],{},[1148,30671,30672],{},[1154,30673,7874],{},[1172,30675,7937],{"encoding":1174},[3394,30677,30620,30678],{},[1115,30679,30681],{"className":30680},[1139],[1141,30682,30683],{"xmlns":1143},[1145,30684,30685,30693],{},[1148,30686,30687,30689,30691],{},[1312,30688,1489],{},[1161,30690,1623],{},[1154,30692,20190],{},[1172,30694,30695],{"encoding":1174},"1-\\beta",[1110,30697,30698,1932,30701,30714],{},[1248,30699,30700],{},"Hladina významnosti",[1115,30702,30704],{"className":30703},[1139],[1141,30705,30706],{"xmlns":1143},[1145,30707,30708,30712],{},[1148,30709,30710],{},[1154,30711,7874],{},[1172,30713,7937],{"encoding":1174}," 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.",[1110,30716,30717],{},[1393,30718],{"alt":30719,"className":30720,"src":30721},"mask-th-chyba-i-ii",[1242,1397],"\u002Fwiki-assets\u002Fmask-th-chyba-i-ii.png",[1110,30723,30724,30725,30738,30739,30752,30753,30766,30767,6413,30780,30793,30794,1176],{},"Obrázek ukazuje, proč jde o kompromis: posunutí kritické hodnoty ",[1115,30726,30728],{"className":30727},[1139],[1141,30729,30730],{"xmlns":1143},[1145,30731,30732,30736],{},[1148,30733,30734],{},[1154,30735,1784],{},[1172,30737,1784],{"encoding":1174}," doleva zmenší ",[1115,30740,30742],{"className":30741},[1139],[1141,30743,30744],{"xmlns":1143},[1145,30745,30746,30750],{},[1148,30747,30748],{},[1154,30749,20190],{},[1172,30751,30045],{"encoding":1174},", ale zvětší ",[1115,30754,30756],{"className":30755},[1139],[1141,30757,30758],{"xmlns":1143},[1145,30759,30760,30764],{},[1148,30761,30762],{},[1154,30763,7874],{},[1172,30765,7937],{"encoding":1174},", a naopak. Pro danou hladinu ",[1115,30768,30770],{"className":30769},[1139],[1141,30771,30772],{"xmlns":1143},[1145,30773,30774,30778],{},[1148,30775,30776],{},[1154,30777,7874],{},[1172,30779,7937],{"encoding":1174},[1115,30781,30783],{"className":30782},[1139],[1141,30784,30785],{"xmlns":1143},[1145,30786,30787,30791],{},[1148,30788,30789],{},[1154,30790,1784],{},[1172,30792,1784],{"encoding":1174}," jednoznačně určena rozdělením kritéria za platnosti ",[1115,30795,30797],{"className":30796},[1139],[1141,30798,30799],{"xmlns":1143},[1145,30800,30801,30809],{},[1148,30802,30803],{},[1151,30804,30805,30807],{},[1154,30806,6105],{},[1312,30808,4585],{},[1172,30810,6110],{"encoding":1174},[20599,30812,30814],{"id":30813},"testové-kritérium-a-kritický-obor","Testové kritérium a kritický obor",[1110,30816,30817,1932,30819,30832,30833,1176],{},[1248,30818,7512],{},[1115,30820,30822],{"className":30821},[1139],[1141,30823,30824],{"xmlns":1143},[1145,30825,30826,30830],{},[1148,30827,30828],{},[1154,30829,11542],{},[1172,30831,11542],{"encoding":1174}," je statistika spočtená z výběru; aby bylo možné test provést, musí být známo jeho rozdělení za platnosti ",[1115,30834,30836],{"className":30835},[1139],[1141,30837,30838],{"xmlns":1143},[1145,30839,30840,30848],{},[1148,30841,30842],{},[1151,30843,30844,30846],{},[1154,30845,6105],{},[1312,30847,4585],{},[1172,30849,6110],{"encoding":1174},[1110,30851,30852,1932,30855,30868,30869,30886],{},[1248,30853,30854],{},"Kritický obor",[1115,30856,30858],{"className":30857},[1139],[1141,30859,30860],{"xmlns":1143},[1145,30861,30862,30866],{},[1148,30863,30864],{},[1154,30865,6143],{},[1172,30867,6143],{"encoding":1174}," je množina hodnot svědčících pro ",[1115,30870,30872],{"className":30871},[1139],[1141,30873,30874],{"xmlns":1143},[1145,30875,30876,30884],{},[1148,30877,30878],{},[1151,30879,30880,30882],{},[1154,30881,6105],{},[1312,30883,1489],{},[1172,30885,7508],{"encoding":1174},". Je zkonstruován tak, aby",[1115,30888,30890],{"className":30889},[1139],[1141,30891,30892],{"xmlns":1143,"display":1468},[1145,30893,30894,30922],{},[1148,30895,30896,30898,30900,30902,30904,30906,30908,30914,30916,30918,30920],{},[1154,30897,11170],{},[1161,30899,1164],{"stretchy":1163},[1154,30901,11542],{},[1161,30903,11459],{},[1154,30905,6143],{},[1161,30907,26878],{},[1151,30909,30910,30912],{},[1154,30911,6105],{},[1312,30913,4585],{},[1161,30915,1170],{"stretchy":1163},[1161,30917,1483],{},[1154,30919,7874],{},[1161,30921,1199],{"separator":1121},[1172,30923,30924],{"encoding":1174},"P(T \\in W \\mid H_0) = \\alpha,",[1110,30926,30927,30928,30941,30942,30959],{},"tedy aby pravděpodobnost, že výběr dá hodnotu kritéria v ",[1115,30929,30931],{"className":30930},[1139],[1141,30932,30933],{"xmlns":1143},[1145,30934,30935,30939],{},[1148,30936,30937],{},[1154,30938,6143],{},[1172,30940,6143],{"encoding":1174}," i při platné ",[1115,30943,30945],{"className":30944},[1139],[1141,30946,30947],{"xmlns":1143},[1145,30948,30949,30957],{},[1148,30950,30951],{},[1151,30952,30953,30955],{},[1154,30954,6105],{},[1312,30956,4585],{},[1172,30958,6110],{"encoding":1174},", byla rovna zvolené hladině významnosti.",[20599,30961,30963],{"id":30962},"postup-testování-hypotézy","Postup testování hypotézy",[1110,30965,30966],{},[1393,30967],{"alt":30968,"className":30969,"src":30970},"mask-ilu-postup-testovani",[1242,1397],"\u002Fwiki-assets\u002Fmask-ilu-postup-testovani.png",[7379,30972,30973,31010,31013,31029],{},[1127,30974,30975,30976,1385,30993,1176],{},"Formulace hypotéz ",[1115,30977,30979],{"className":30978},[1139],[1141,30980,30981],{"xmlns":1143},[1145,30982,30983,30991],{},[1148,30984,30985],{},[1151,30986,30987,30989],{},[1154,30988,6105],{},[1312,30990,4585],{},[1172,30992,6110],{"encoding":1174},[1115,30994,30996],{"className":30995},[1139],[1141,30997,30998],{"xmlns":1143},[1145,30999,31000,31008],{},[1148,31001,31002],{},[1151,31003,31004,31006],{},[1154,31005,6105],{},[1312,31007,1489],{},[1172,31009,7508],{"encoding":1174},[1127,31011,31012],{},"Volba testového kritéria a výpočet jeho hodnoty.",[1127,31014,31015,31016,1176],{},"Volba hladiny významnosti a sestrojení příslušného kritického oboru ",[1115,31017,31019],{"className":31018},[1139],[1141,31020,31021],{"xmlns":1143},[1145,31022,31023,31027],{},[1148,31024,31025],{},[1154,31026,6143],{},[1172,31028,6143],{"encoding":1174},[1127,31030,31031,31032],{},"Formulace závěru:\n",[1124,31033,31034,31112],{},[1127,31035,31036,31037,8464,31055,31072,31073,31093,31094,31111],{},"pokud ",[1115,31038,31040],{"className":31039},[1139],[1141,31041,31042],{"xmlns":1143},[1145,31043,31044,31052],{},[1148,31045,31046,31048,31050],{},[1154,31047,11542],{},[1161,31049,11459],{},[1154,31051,6143],{},[1172,31053,31054],{"encoding":1174},"T \\in W",[1115,31056,31058],{"className":31057},[1139],[1141,31059,31060],{"xmlns":1143},[1145,31061,31062,31070],{},[1148,31063,31064],{},[1151,31065,31066,31068],{},[1154,31067,6105],{},[1312,31069,1489],{},[1172,31071,7508],{"encoding":1174}," je testem prokázána na hladině významnosti ",[1115,31074,31076],{"className":31075},[1139],[1141,31077,31078],{"xmlns":1143},[1145,31079,31080,31090],{},[1148,31081,31082,31084,31086,31088],{},[1312,31083,1862],{},[1154,31085,7874],{},[1316,31087,1318],{},[1154,31089,1870],{"mathvariant":1869},[1172,31091,31092],{"encoding":1174},"100\\alpha\\,\\%"," (zamítáme ",[1115,31095,31097],{"className":31096},[1139],[1141,31098,31099],{"xmlns":1143},[1145,31100,31101,31109],{},[1148,31102,31103],{},[1151,31104,31105,31107],{},[1154,31106,6105],{},[1312,31108,4585],{},[1172,31110,6110],{"encoding":1174},");",[1127,31113,31036,31114,8464,31133,31150,31151,31170,31171,31188],{},[1115,31115,31117],{"className":31116},[1139],[1141,31118,31119],{"xmlns":1143},[1145,31120,31121,31130],{},[1148,31122,31123,31125,31128],{},[1154,31124,11542],{},[1161,31126,31127],{"mathvariant":1869},"∉",[1154,31129,6143],{},[1172,31131,31132],{"encoding":1174},"T \\notin W",[1115,31134,31136],{"className":31135},[1139],[1141,31137,31138],{"xmlns":1143},[1145,31139,31140,31148],{},[1148,31141,31142],{},[1151,31143,31144,31146],{},[1154,31145,6105],{},[1312,31147,1489],{},[1172,31149,7508],{"encoding":1174}," není testem prokázána na hladině významnosti ",[1115,31152,31154],{"className":31153},[1139],[1141,31155,31156],{"xmlns":1143},[1145,31157,31158,31168],{},[1148,31159,31160,31162,31164,31166],{},[1312,31161,1862],{},[1154,31163,7874],{},[1316,31165,1318],{},[1154,31167,1870],{"mathvariant":1869},[1172,31169,31092],{"encoding":1174}," ; ",[1115,31172,31174],{"className":31173},[1139],[1141,31175,31176],{"xmlns":1143},[1145,31177,31178,31186],{},[1148,31179,31180],{},[1151,31181,31182,31184],{},[1154,31183,6105],{},[1312,31185,4585],{},[1172,31187,6110],{"encoding":1174}," nezamítáme.",[1110,31190,31191,31192,31195,31196,31213,31214,31231,31232,31252,31253,29038,31270,1932,31290,31307],{},"Rovnocennou alternativou je ",[1248,31193,31194],{},"p-hodnota",": udává, nakolik jsou data slučitelná s ",[1115,31197,31199],{"className":31198},[1139],[1141,31200,31201],{"xmlns":1143},[1145,31202,31203,31211],{},[1148,31204,31205],{},[1151,31206,31207,31209],{},[1154,31208,6105],{},[1312,31210,4585],{},[1172,31212,6110],{"encoding":1174},". Čím menší p-hodnota, tím více data svědčí proti ",[1115,31215,31217],{"className":31216},[1139],[1141,31218,31219],{"xmlns":1143},[1145,31220,31221,31229],{},[1148,31222,31223],{},[1151,31224,31225,31227],{},[1154,31226,6105],{},[1312,31228,4585],{},[1172,31230,6110],{"encoding":1174},". Rozhodovací pravidlo: ",[1115,31233,31235],{"className":31234},[1139],[1141,31236,31237],{"xmlns":1143},[1145,31238,31239,31249],{},[1148,31240,31241,31243,31245,31247],{},[1154,31242,1110],{},[1161,31244,11177],{},[1154,31246,7874],{},[1161,31248,11985],{},[1172,31250,31251],{"encoding":1174},"p \\le \\alpha \\Rightarrow"," zamítáme ",[1115,31254,31256],{"className":31255},[1139],[1141,31257,31258],{"xmlns":1143},[1145,31259,31260,31268],{},[1148,31261,31262],{},[1151,31263,31264,31266],{},[1154,31265,6105],{},[1312,31267,4585],{},[1172,31269,6110],{"encoding":1174},[1115,31271,31273],{"className":31272},[1139],[1141,31274,31275],{"xmlns":1143},[1145,31276,31277,31287],{},[1148,31278,31279,31281,31283,31285],{},[1154,31280,1110],{},[1161,31282,6225],{},[1154,31284,7874],{},[1161,31286,11985],{},[1172,31288,31289],{"encoding":1174},"p > \\alpha \\Rightarrow",[1115,31291,31293],{"className":31292},[1139],[1141,31294,31295],{"xmlns":1143},[1145,31296,31297,31305],{},[1148,31298,31299],{},[1151,31300,31301,31303],{},[1154,31302,6105],{},[1312,31304,4585],{},[1172,31306,6110],{"encoding":1174}," nezamítáme. Obě cesty — kritický obor i p-hodnota — vedou vždy ke stejnému závěru; R u všech testů vrací p-hodnotu přímo.",[1232,31309,31311],{"id":31310},"jednovýběrový-t-test","Jednovýběrový t-test",[1110,31313,31314,31315,31328,31329,31361,31362,31375,31376,1385,31393,31410,31411,31429,31430,31443],{},"Test o střední hodnotě ",[1115,31316,31318],{"className":31317},[1139],[1141,31319,31320],{"xmlns":1143},[1145,31321,31322,31326],{},[1148,31323,31324],{},[1154,31325,11332],{},[1172,31327,13226],{"encoding":1174}," rozdělení ",[1115,31330,31332],{"className":31331},[1139],[1141,31333,31334],{"xmlns":1143},[1145,31335,31336,31358],{},[1148,31337,31338,31340,31342,31344,31346,31348,31350,31356],{},[1154,31339,1436],{},[1161,31341,13609],{},[1154,31343,11327],{},[1161,31345,1164],{"stretchy":1163},[1154,31347,11332],{},[1161,31349,1199],{"separator":1121},[1603,31351,31352,31354],{},[1154,31353,11339],{},[1312,31355,1610],{},[1161,31357,1170],{"stretchy":1163},[1172,31359,31360],{"encoding":1174},"X \\sim N(\\mu, \\sigma^2)",". Z výběru o rozsahu ",[1115,31363,31365],{"className":31364},[1139],[1141,31366,31367],{"xmlns":1143},[1145,31368,31369,31373],{},[1148,31370,31371],{},[1154,31372,1159],{},[1172,31374,1159],{"encoding":1174}," se určí charakteristiky ",[1115,31377,31379],{"className":31378},[1139],[1141,31380,31381],{"xmlns":1143},[1145,31382,31383,31391],{},[1148,31384,31385],{},[1474,31386,31387,31389],{"accent":1121},[1154,31388,1167],{},[1161,31390,1480],{},[1172,31392,25419],{"encoding":1174},[1115,31394,31396],{"className":31395},[1139],[1141,31397,31398],{"xmlns":1143},[1145,31399,31400,31408],{},[1148,31401,31402],{},[1603,31403,31404,31406],{},[1154,31405,1607],{},[1312,31407,1610],{},[1172,31409,5907],{"encoding":1174},"; testem se posuzuje vztah mezi zvoleným číslem ",[1115,31412,31414],{"className":31413},[1139],[1141,31415,31416],{"xmlns":1143},[1145,31417,31418,31426],{},[1148,31419,31420],{},[1151,31421,31422,31424],{},[1154,31423,11332],{},[1312,31425,4585],{},[1172,31427,31428],{"encoding":1174},"\\mu_0"," a neznámou hodnotou ",[1115,31431,31433],{"className":31432},[1139],[1141,31434,31435],{"xmlns":1143},[1145,31436,31437,31441],{},[1148,31438,31439],{},[1154,31440,11332],{},[1172,31442,13226],{"encoding":1174},". Testové kritérium",[1115,31445,31447],{"className":31446},[1139],[1141,31448,31449],{"xmlns":1143,"display":1468},[1145,31450,31451,31495],{},[1148,31452,31453,31455,31457,31477,31481,31483],{},[1154,31454,11542],{},[1161,31456,1483],{},[1485,31458,31459,31475],{},[1148,31460,31461,31467,31469],{},[1474,31462,31463,31465],{"accent":1121},[1154,31464,1167],{},[1161,31466,1480],{},[1161,31468,1623],{},[1151,31470,31471,31473],{},[1154,31472,11332],{},[1312,31474,4585],{},[1154,31476,1607],{},[1678,31478,31479],{},[1154,31480,1159],{},[1161,31482,13609],{},[1151,31484,31485,31487],{},[1154,31486,1807],{},[1148,31488,31489,31491,31493],{},[1154,31490,1159],{},[1161,31492,1623],{},[1312,31494,1489],{},[1172,31496,31497],{"encoding":1174},"T = \\frac{\\bar{x} - \\mu_0}{s}\\sqrt{n} \\sim t_{n-1}",[1110,31499,31500,31501,31519],{},"má Studentovo rozdělení o ",[1115,31502,31504],{"className":31503},[1139],[1141,31505,31506],{"xmlns":1143},[1145,31507,31508,31516],{},[1148,31509,31510,31512,31514],{},[1154,31511,1159],{},[1161,31513,1623],{},[1312,31515,1489],{},[1172,31517,31518],{"encoding":1174},"n-1"," stupních volnosti.",[3350,31521,31522,31580],{},[3353,31523,31524],{},[3356,31525,31526,31545,31564],{},[3359,31527,31528],{},[1115,31529,31531],{"className":31530},[1139],[1141,31532,31533],{"xmlns":1143},[1145,31534,31535,31543],{},[1148,31536,31537],{},[1151,31538,31539,31541],{},[1154,31540,6105],{},[1312,31542,4585],{},[1172,31544,6110],{"encoding":1174},[3359,31546,31547],{},[1115,31548,31550],{"className":31549},[1139],[1141,31551,31552],{"xmlns":1143},[1145,31553,31554,31562],{},[1148,31555,31556],{},[1151,31557,31558,31560],{},[1154,31559,6105],{},[1312,31561,1489],{},[1172,31563,7508],{"encoding":1174},[3359,31565,31566,31567],{},"Kritický obor ",[1115,31568,31570],{"className":31569},[1139],[1141,31571,31572],{"xmlns":1143},[1145,31573,31574,31578],{},[1148,31575,31576],{},[1154,31577,6143],{},[1172,31579,6143],{"encoding":1174},[3389,31581,31582,31672,31770],{},[3356,31583,31584,31608,31632],{},[3394,31585,31586],{},[1115,31587,31589],{"className":31588},[1139],[1141,31590,31591],{"xmlns":1143},[1145,31592,31593,31605],{},[1148,31594,31595,31597,31599],{},[1154,31596,11332],{},[1161,31598,11177],{},[1151,31600,31601,31603],{},[1154,31602,11332],{},[1312,31604,4585],{},[1172,31606,31607],{"encoding":1174},"\\mu \\le \\mu_0",[3394,31609,31610],{},[1115,31611,31613],{"className":31612},[1139],[1141,31614,31615],{"xmlns":1143},[1145,31616,31617,31629],{},[1148,31618,31619,31621,31623],{},[1154,31620,11332],{},[1161,31622,6225],{},[1151,31624,31625,31627],{},[1154,31626,11332],{},[1312,31628,4585],{},[1172,31630,31631],{"encoding":1174},"\\mu > \\mu_0",[3394,31633,31634],{},[1115,31635,31637],{"className":31636},[1139],[1141,31638,31639],{"xmlns":1143},[1145,31640,31641,31669],{},[1148,31642,31643,31645,31647,31659,31661,31663,31665,31667],{},[1154,31644,1807],{},[1161,31646,5198],{},[1151,31648,31649,31651],{},[1154,31650,1807],{},[1148,31652,31653,31655,31657],{},[1312,31654,1489],{},[1161,31656,1623],{},[1154,31658,7874],{},[1161,31660,1164],{"stretchy":1163},[1154,31662,1159],{},[1161,31664,1623],{},[1312,31666,1489],{},[1161,31668,1170],{"stretchy":1163},[1172,31670,31671],{"encoding":1174},"t \\ge t_{1-\\alpha}(n-1)",[3356,31673,31674,31698,31722],{},[3394,31675,31676],{},[1115,31677,31679],{"className":31678},[1139],[1141,31680,31681],{"xmlns":1143},[1145,31682,31683,31695],{},[1148,31684,31685,31687,31689],{},[1154,31686,11332],{},[1161,31688,1483],{},[1151,31690,31691,31693],{},[1154,31692,11332],{},[1312,31694,4585],{},[1172,31696,31697],{"encoding":1174},"\\mu = \\mu_0",[3394,31699,31700],{},[1115,31701,31703],{"className":31702},[1139],[1141,31704,31705],{"xmlns":1143},[1145,31706,31707,31719],{},[1148,31708,31709,31711,31713],{},[1154,31710,11332],{},[1161,31712,15368],{"mathvariant":1869},[1151,31714,31715,31717],{},[1154,31716,11332],{},[1312,31718,4585],{},[1172,31720,31721],{"encoding":1174},"\\mu \\neq \\mu_0",[3394,31723,31724],{},[1115,31725,31727],{"className":31726},[1139],[1141,31728,31729],{"xmlns":1143},[1145,31730,31731,31767],{},[1148,31732,31733,31735,31737,31739,31741,31757,31759,31761,31763,31765],{},[1161,31734,26878],{"stretchy":1163},[1154,31736,1807],{},[1161,31738,26878],{"stretchy":1163},[1161,31740,5198],{},[1151,31742,31743,31745],{},[1154,31744,1807],{},[1148,31746,31747,31749,31751,31753,31755],{},[1312,31748,1489],{},[1161,31750,1623],{},[1154,31752,7874],{},[1154,31754,3245],{"mathvariant":1869},[1312,31756,1610],{},[1161,31758,1164],{"stretchy":1163},[1154,31760,1159],{},[1161,31762,1623],{},[1312,31764,1489],{},[1161,31766,1170],{"stretchy":1163},[1172,31768,31769],{"encoding":1174},"\\lvert t \\rvert \\ge t_{1-\\alpha\u002F2}(n-1)",[3356,31771,31772,31796,31820],{},[3394,31773,31774],{},[1115,31775,31777],{"className":31776},[1139],[1141,31778,31779],{"xmlns":1143},[1145,31780,31781,31793],{},[1148,31782,31783,31785,31787],{},[1154,31784,11332],{},[1161,31786,5198],{},[1151,31788,31789,31791],{},[1154,31790,11332],{},[1312,31792,4585],{},[1172,31794,31795],{"encoding":1174},"\\mu \\ge \\mu_0",[3394,31797,31798],{},[1115,31799,31801],{"className":31800},[1139],[1141,31802,31803],{"xmlns":1143},[1145,31804,31805,31817],{},[1148,31806,31807,31809,31811],{},[1154,31808,11332],{},[1161,31810,8805],{},[1151,31812,31813,31815],{},[1154,31814,11332],{},[1312,31816,4585],{},[1172,31818,31819],{"encoding":1174},"\\mu \u003C \\mu_0",[3394,31821,31822],{},[1115,31823,31825],{"className":31824},[1139],[1141,31826,31827],{"xmlns":1143},[1145,31828,31829,31859],{},[1148,31830,31831,31833,31835,31837,31849,31851,31853,31855,31857],{},[1154,31832,1807],{},[1161,31834,11177],{},[1161,31836,1623],{},[1151,31838,31839,31841],{},[1154,31840,1807],{},[1148,31842,31843,31845,31847],{},[1312,31844,1489],{},[1161,31846,1623],{},[1154,31848,7874],{},[1161,31850,1164],{"stretchy":1163},[1154,31852,1159],{},[1161,31854,1623],{},[1312,31856,1489],{},[1161,31858,1170],{"stretchy":1163},[1172,31860,31861],{"encoding":1174},"t \\le -t_{1-\\alpha}(n-1)",[1110,31863,31864,31865,31868],{},"V R test provádí ",[2015,31866,31867],{},"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?",[2020,31870,31872],{"className":2022,"code":31871,"language":71,"meta":2024,"style":2024},"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",[2015,31873,31874,31928],{"__ignoreMap":2024},[1115,31875,31876,31878,31880,31882,31884,31887,31889,31892,31894,31897,31899,31902,31904,31907,31909,31912,31914,31916,31918,31921,31923,31926],{"class":2029,"line":10},[1115,31877,1167],{"class":2032},[1115,31879,2036],{"class":2035},[1115,31881,2040],{"class":2039},[1115,31883,1164],{"class":2043},[1115,31885,31886],{"class":2046},"12.5",[1115,31888,1199],{"class":2035},[1115,31890,31891],{"class":2046}," 13.5",[1115,31893,1199],{"class":2035},[1115,31895,31896],{"class":2046}," 11.9",[1115,31898,1199],{"class":2035},[1115,31900,31901],{"class":2046}," 12.2",[1115,31903,1199],{"class":2035},[1115,31905,31906],{"class":2046}," 13.0",[1115,31908,1199],{"class":2035},[1115,31910,31911],{"class":2046}," 14.3",[1115,31913,1199],{"class":2035},[1115,31915,31901],{"class":2046},[1115,31917,1199],{"class":2035},[1115,31919,31920],{"class":2046}," 11.8",[1115,31922,1199],{"class":2035},[1115,31924,31925],{"class":2046}," 14.0",[1115,31927,2185],{"class":2043},[1115,31929,31930,31933,31935,31937,31939,31941,31943,31945,31947,31950,31952,31955],{"class":2029,"line":27},[1115,31931,31932],{"class":2039},"t.test",[1115,31934,1164],{"class":2043},[1115,31936,1167],{"class":2032},[1115,31938,1199],{"class":2035},[1115,31940,29435],{"class":2032},[1115,31942,2291],{"class":2035},[1115,31944,4215],{"class":2046},[1115,31946,1199],{"class":2035},[1115,31948,31949],{"class":2032}," alternative",[1115,31951,2291],{"class":2035},[1115,31953,31954],{"class":8322}," \"two.sided\"",[1115,31956,2185],{"class":2043},[2020,31958,31961],{"className":31959,"code":31960,"language":2349,"meta":2024},[2347],"    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",[2015,31962,31960],{"__ignoreMap":2024},[1110,31964,31965,31967,31968,31971,31972,31975,31976,31979,31980,32003],{},[2015,31966,1807],{}," je testové kritérium, ",[2015,31969,31970],{},"df"," stupně volnosti, ",[2015,31973,31974],{},"p-value"," p-hodnota pro zvolenou alternativu a ",[2015,31977,31978],{},"mean of x"," výběrový průměr. Zde ",[1115,31981,31983],{"className":31982},[1139],[1141,31984,31985],{"xmlns":1143},[1145,31986,31987,32000],{},[1148,31988,31989,31991,31993,31996,31998],{},[1154,31990,1110],{},[1161,31992,1483],{},[1312,31994,31995],{},"0,02843",[1161,31997,8805],{},[1312,31999,8460],{},[1172,32001,32002],{"encoding":1174},"p = 0{,}02843 \u003C 0{,}05",": úprava trasy průměrnou dobu jízdy (původně 12 minut) statisticky významně změnila.",[1103,32005,32007,32014,32102,32158,32250],{"className":32006,"dataCallout":2447},[1106,2446],[1110,32008,32010,32013],{"className":32009},[1113],[1115,32011],{"className":32012,"ariaHidden":1121},[1118,2454,1120],"Příklad: Kontrola objemu lahví",[1110,32015,32016,32017,32039,32040,32058,32059,32082,32083,32101],{},"Pivovar plní lahve, deklarovaný objem je ",[1115,32018,32020],{"className":32019},[1139],[1141,32021,32022],{"xmlns":1143},[1145,32023,32024,32036],{},[1148,32025,32026,32032,32034],{},[1151,32027,32028,32030],{},[1154,32029,11332],{},[1312,32031,4585],{},[1161,32033,1483],{},[1312,32035,1952],{},[1172,32037,32038],{"encoding":1174},"\\mu_0 = 0{,}5"," l. Náhodný výběr ",[1115,32041,32043],{"className":32042},[1139],[1141,32044,32045],{"xmlns":1143},[1145,32046,32047,32055],{},[1148,32048,32049,32051,32053],{},[1154,32050,1159],{},[1161,32052,1483],{},[1312,32054,8521],{},[1172,32056,32057],{"encoding":1174},"n = 20"," lahví dal ",[1115,32060,32062],{"className":32061},[1139],[1141,32063,32064],{"xmlns":1143},[1145,32065,32066,32079],{},[1148,32067,32068,32074,32076],{},[1474,32069,32070,32072],{"accent":1121},[1154,32071,1167],{},[1161,32073,1480],{},[1161,32075,1483],{},[1312,32077,32078],{},"0,492",[1172,32080,32081],{"encoding":1174},"\\bar{x} = 0{,}492"," l, ",[1115,32084,32086],{"className":32085},[1139],[1141,32087,32088],{"xmlns":1143},[1145,32089,32090,32098],{},[1148,32091,32092,32094,32096],{},[1154,32093,1607],{},[1161,32095,1483],{},[1312,32097,4913],{},[1172,32099,32100],{"encoding":1174},"s = 0{,}015"," l. Na hladině významnosti 5 % ověřte podezření, že pivovar lahve nedoplňuje.",[1110,32103,32104,32130,32131,32157],{},[1115,32105,32107],{"className":32106},[1139],[1141,32108,32109],{"xmlns":1143},[1145,32110,32111,32127],{},[1148,32112,32113,32119,32121,32123,32125],{},[1151,32114,32115,32117],{},[1154,32116,6105],{},[1312,32118,4585],{},[1161,32120,6481],{},[1154,32122,11332],{},[1161,32124,5198],{},[1312,32126,1952],{},[1172,32128,32129],{"encoding":1174},"H_0: \\mu \\ge 0{,}5"," l (objem je v pořádku nebo větší), ",[1115,32132,32134],{"className":32133},[1139],[1141,32135,32136],{"xmlns":1143},[1145,32137,32138,32154],{},[1148,32139,32140,32146,32148,32150,32152],{},[1151,32141,32142,32144],{},[1154,32143,6105],{},[1312,32145,1489],{},[1161,32147,6481],{},[1154,32149,11332],{},[1161,32151,8805],{},[1312,32153,1952],{},[1172,32155,32156],{"encoding":1174},"H_1: \\mu \u003C 0{,}5"," l (lahve jsou nedoplněné).",[1110,32159,32160],{},[1115,32161,32163],{"className":32162},[1139],[1141,32164,32165],{"xmlns":1143},[1145,32166,32167,32247],{},[1148,32168,32169,32171,32173,32185,32189,32191,32193,32196,32198,32200,32202,32204,32206,32208,32210,32212,32224,32226,32228,32230,32232,32234,32236,32238,32240,32242,32245],{},[1154,32170,1807],{},[1161,32172,1483],{},[1485,32174,32175,32183],{},[1148,32176,32177,32179,32181],{},[1312,32178,32078],{},[1161,32180,1623],{},[1312,32182,1952],{},[1312,32184,4913],{},[1678,32186,32187],{},[1312,32188,8521],{},[1161,32190,1483],{},[1161,32192,1623],{},[1312,32194,32195],{},"2,385",[1161,32197,1199],{"separator":1121},[1516,32199],{"width":1518},[1154,32201,6143],{},[1161,32203,1483],{},[1161,32205,7845],{"stretchy":1163},[1154,32207,1807],{},[1161,32209,11177],{},[1161,32211,1623],{},[1151,32213,32214,32216],{},[1154,32215,1807],{},[1148,32217,32218,32220,32222],{},[1312,32219,4585],{},[1161,32221,1199],{"separator":1121},[1312,32223,25652],{},[1161,32225,1164],{"stretchy":1163},[1312,32227,4834],{},[1161,32229,1170],{"stretchy":1163},[1161,32231,7903],{"stretchy":1163},[1161,32233,1483],{},[1161,32235,7845],{"stretchy":1163},[1154,32237,1807],{},[1161,32239,11177],{},[1161,32241,1623],{},[1312,32243,32244],{},"1,729",[1161,32246,7903],{"stretchy":1163},[1172,32248,32249],{"encoding":1174},"t = \\frac{0{,}492 - 0{,}5}{0{,}015}\\sqrt{20} = -2{,}385, \\qquad W = \\{t \\le -t_{0,95}(19)\\} = \\{t \\le -1{,}729\\}",[1110,32251,32252,32253,10465,32271,32288],{},"Protože ",[1115,32254,32256],{"className":32255},[1139],[1141,32257,32258],{"xmlns":1143},[1145,32259,32260,32268],{},[1148,32261,32262,32264,32266],{},[1154,32263,1807],{},[1161,32265,11459],{},[1154,32267,6143],{},[1172,32269,32270],{"encoding":1174},"t \\in W",[1115,32272,32274],{"className":32273},[1139],[1141,32275,32276],{"xmlns":1143},[1145,32277,32278,32286],{},[1148,32279,32280],{},[1151,32281,32282,32284],{},[1154,32283,6105],{},[1312,32285,4585],{},[1172,32287,6110],{"encoding":1174},": na hladině významnosti 5 % se potvrdilo, že pivovar plní lahve pod deklarovaný objem.",[1110,32290,32291,32292,32294,32295,6481],{},"Ze souhrnných charakteristik bez surových dat ",[2015,32293,31867],{}," spustit nelze — kritérium a kritická hodnota se dopočítají přímo z definice pomocí ",[2015,32296,32297],{},"qt()",[2020,32299,32301],{"className":2022,"code":32300,"language":71,"meta":2024,"style":2024},"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",[2015,32302,32303,32341,32373,32403,32408],{"__ignoreMap":2024},[1115,32304,32305,32308,32310,32313,32315,32317,32319,32322,32324,32326,32328,32331,32333,32336,32338],{"class":2029,"line":10},[1115,32306,32307],{"class":2032},"xbar",[1115,32309,2036],{"class":2035},[1115,32311,32312],{"class":2046}," 0.492",[1115,32314,29038],{"class":2043},[1115,32316,1607],{"class":2032},[1115,32318,2036],{"class":2035},[1115,32320,32321],{"class":2046}," 0.015",[1115,32323,29038],{"class":2043},[1115,32325,1159],{"class":2032},[1115,32327,2036],{"class":2035},[1115,32329,32330],{"class":2046}," 20",[1115,32332,29038],{"class":2043},[1115,32334,32335],{"class":2032},"mu0",[1115,32337,2036],{"class":2035},[1115,32339,32340],{"class":2046}," 0.5\n",[1115,32342,32343,32345,32347,32349,32351,32353,32356,32358,32360,32363,32365,32367,32369,32371],{"class":2029,"line":27},[1115,32344,1807],{"class":2032},[1115,32346,2036],{"class":2035},[1115,32348,3997],{"class":2043},[1115,32350,32307],{"class":2032},[1115,32352,29375],{"class":2035},[1115,32354,32355],{"class":2032}," mu0",[1115,32357,2257],{"class":2043},[1115,32359,3245],{"class":2035},[1115,32361,32362],{"class":2032}," s",[1115,32364,22493],{"class":2035},[1115,32366,9044],{"class":2039},[1115,32368,1164],{"class":2043},[1115,32370,1159],{"class":2032},[1115,32372,2185],{"class":2043},[1115,32374,32375,32378,32380,32383,32385,32388,32390,32392,32394,32397,32399,32401],{"class":2029,"line":148},[1115,32376,32377],{"class":2032},"t_krit",[1115,32379,2036],{"class":2035},[1115,32381,32382],{"class":2039}," qt",[1115,32384,1164],{"class":2043},[1115,32386,32387],{"class":2046},"0.05",[1115,32389,1199],{"class":2035},[1115,32391,15222],{"class":2032},[1115,32393,2291],{"class":2035},[1115,32395,32396],{"class":2032}," n",[1115,32398,29375],{"class":2035},[1115,32400,5269],{"class":2046},[1115,32402,2185],{"class":2043},[1115,32404,32405],{"class":2029,"line":111},[1115,32406,32407],{"class":2032},"t\n",[1115,32409,32410],{"class":2029,"line":96},[1115,32411,32412],{"class":2032},"t_krit\n",[2020,32414,32417],{"className":32415,"code":32416,"language":2349,"meta":2024},[2347],"[1] -2.385139\n[1] -1.729133\n",[2015,32418,32416],{"__ignoreMap":2024},[1110,32420,32421],{},[1393,32422],{"alt":32423,"className":32424,"src":32425},"mask-th-t-jednostranny",[1242,1397],"\u002Fwiki-assets\u002Fmask-th-t-jednostranny.png",[1110,32427,32428,32429,6481],{},"Další dva příklady mají k dispozici surová data, takže je lze otestovat přímo ",[2015,32430,31867],{},[1110,32432,32433,32436],{},[1248,32434,32435],{},"Životnost baterií."," Výrobce udává průměrnou životnost 10 hodin, na 11 bateriích byly naměřeny hodnoty v hodinách.",[2020,32438,32440],{"className":2022,"code":32439,"language":71,"meta":2024,"style":2024},"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",[2015,32441,32442,32505],{"__ignoreMap":2024},[1115,32443,32444,32447,32449,32451,32453,32456,32458,32461,32463,32466,32468,32471,32473,32476,32478,32481,32483,32485,32487,32490,32492,32494,32496,32499,32501,32503],{"class":2029,"line":10},[1115,32445,32446],{"class":2032},"x2",[1115,32448,2036],{"class":2035},[1115,32450,2040],{"class":2039},[1115,32452,1164],{"class":2043},[1115,32454,32455],{"class":2046},"9.5",[1115,32457,1199],{"class":2035},[1115,32459,32460],{"class":2046}," 10.5",[1115,32462,1199],{"class":2035},[1115,32464,32465],{"class":2046}," 8.9",[1115,32467,1199],{"class":2035},[1115,32469,32470],{"class":2046}," 9.2",[1115,32472,1199],{"class":2035},[1115,32474,32475],{"class":2046}," 10.0",[1115,32477,1199],{"class":2035},[1115,32479,32480],{"class":2046}," 8.5",[1115,32482,1199],{"class":2035},[1115,32484,32470],{"class":2046},[1115,32486,1199],{"class":2035},[1115,32488,32489],{"class":2046}," 8.8",[1115,32491,1199],{"class":2035},[1115,32493,32475],{"class":2046},[1115,32495,1199],{"class":2035},[1115,32497,32498],{"class":2046}," 9.5",[1115,32500,1199],{"class":2035},[1115,32502,32470],{"class":2046},[1115,32504,2185],{"class":2043},[1115,32506,32507,32509,32511,32513,32515,32517,32519,32521,32523,32525,32527,32529],{"class":2029,"line":27},[1115,32508,31932],{"class":2039},[1115,32510,1164],{"class":2043},[1115,32512,32446],{"class":2032},[1115,32514,1199],{"class":2035},[1115,32516,29435],{"class":2032},[1115,32518,2291],{"class":2035},[1115,32520,4205],{"class":2046},[1115,32522,1199],{"class":2035},[1115,32524,31949],{"class":2032},[1115,32526,2291],{"class":2035},[1115,32528,31954],{"class":8322},[1115,32530,2185],{"class":2043},[2020,32532,32535],{"className":32533,"code":32534,"language":2349,"meta":2024},[2347],"    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",[2015,32536,32534],{"__ignoreMap":2024},[1110,32538,32539,32562],{},[1115,32540,32542],{"className":32541},[1139],[1141,32543,32544],{"xmlns":1143},[1145,32545,32546,32559],{},[1148,32547,32548,32550,32552,32555,32557],{},[1154,32549,1110],{},[1161,32551,1483],{},[1312,32553,32554],{},"0,006548",[1161,32556,8805],{},[1312,32558,8460],{},[1172,32560,32561],{"encoding":1174},"p = 0{,}006548 \u003C 0{,}05",": skutečná životnost se od deklarovaných 10 hodin statisticky významně liší (baterie vydrží méně).",[1110,32564,32565,32568],{},[1248,32566,32567],{},"Odpad materiálu."," Na deseti obráběných kusech byl naměřen odpad materiálu v procentech; testuje se rozdíl proti 4 % a zároveň normalita dat.",[2020,32570,32572],{"className":2022,"code":32571,"language":71,"meta":2024,"style":2024},"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",[2015,32573,32574,32625,32651],{"__ignoreMap":2024},[1115,32575,32576,32579,32581,32583,32585,32587,32589,32591,32593,32595,32597,32599,32601,32603,32605,32607,32609,32611,32613,32615,32617,32619,32621,32623],{"class":2029,"line":10},[1115,32577,32578],{"class":2032},"x3",[1115,32580,2036],{"class":2035},[1115,32582,2040],{"class":2039},[1115,32584,1164],{"class":2043},[1115,32586,2047],{"class":2046},[1115,32588,1199],{"class":2035},[1115,32590,2052],{"class":2046},[1115,32592,1199],{"class":2035},[1115,32594,2057],{"class":2046},[1115,32596,1199],{"class":2035},[1115,32598,2062],{"class":2046},[1115,32600,1199],{"class":2035},[1115,32602,2057],{"class":2046},[1115,32604,1199],{"class":2035},[1115,32606,2057],{"class":2046},[1115,32608,1199],{"class":2035},[1115,32610,2075],{"class":2046},[1115,32612,1199],{"class":2035},[1115,32614,2080],{"class":2046},[1115,32616,1199],{"class":2035},[1115,32618,2052],{"class":2046},[1115,32620,1199],{"class":2035},[1115,32622,2052],{"class":2046},[1115,32624,2185],{"class":2043},[1115,32626,32627,32629,32631,32633,32635,32637,32639,32641,32643,32645,32647,32649],{"class":2029,"line":27},[1115,32628,31932],{"class":2039},[1115,32630,1164],{"class":2043},[1115,32632,32578],{"class":2032},[1115,32634,1199],{"class":2035},[1115,32636,29435],{"class":2032},[1115,32638,2291],{"class":2035},[1115,32640,8284],{"class":2046},[1115,32642,1199],{"class":2035},[1115,32644,31949],{"class":2032},[1115,32646,2291],{"class":2035},[1115,32648,31954],{"class":8322},[1115,32650,2185],{"class":2043},[1115,32652,32653,32655,32657,32659],{"class":2029,"line":148},[1115,32654,21429],{"class":2039},[1115,32656,1164],{"class":2043},[1115,32658,32578],{"class":2032},[1115,32660,2185],{"class":2043},[2020,32662,32665],{"className":32663,"code":32664,"language":2349,"meta":2024},[2347],"    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",[2015,32666,32664],{"__ignoreMap":2024},[1110,32668,32669,32692,32693,32716],{},[1115,32670,32672],{"className":32671},[1139],[1141,32673,32674],{"xmlns":1143},[1145,32675,32676,32689],{},[1148,32677,32678,32680,32682,32685,32687],{},[1154,32679,1110],{},[1161,32681,1483],{},[1312,32683,32684],{},"0,0343",[1161,32686,8805],{},[1312,32688,8460],{},[1172,32690,32691],{"encoding":1174},"p = 0{,}0343 \u003C 0{,}05",": průměrný odpad se od 4 % statisticky významně liší (výběrový průměr 3,86 %). Shapiro-Wilkův test dává ",[1115,32694,32696],{"className":32695},[1139],[1141,32697,32698],{"xmlns":1143},[1145,32699,32700,32713],{},[1148,32701,32702,32704,32706,32709,32711],{},[1154,32703,1110],{},[1161,32705,1483],{},[1312,32707,32708],{},"0,4634",[1161,32710,6225],{},[1312,32712,8460],{},[1172,32714,32715],{"encoding":1174},"p = 0{,}4634 > 0{,}05",", předpoklad normality pro t-test je v pořádku.",[1232,32718,32720],{"id":32719},"párový-t-test","Párový t-test",[1110,32722,32723,32724,32754,32755,11222,32789,32827,32828,32841,32842,1385,32860,32880,32881,32898,32899,31443],{},"Používá se, když jsou měření závislá — na stejných objektech se měří dvě hodnoty ",[1115,32725,32727],{"className":32726},[1139],[1141,32728,32729],{"xmlns":1143},[1145,32730,32731,32751],{},[1148,32732,32733,32735,32741,32743,32749],{},[1161,32734,1164],{"stretchy":1163},[1151,32736,32737,32739],{},[1154,32738,1436],{},[1154,32740,1502],{},[1161,32742,1199],{"separator":1121},[1151,32744,32745,32747],{},[1154,32746,11528],{},[1154,32748,1502],{},[1161,32750,1170],{"stretchy":1163},[1172,32752,32753],{"encoding":1174},"(X_i, Y_i)"," a vyhodnocují se jejich diference ",[1115,32756,32758],{"className":32757},[1139],[1141,32759,32760],{"xmlns":1143},[1145,32761,32762,32786],{},[1148,32763,32764,32770,32772,32778,32780],{},[1151,32765,32766,32768],{},[1154,32767,12589],{},[1154,32769,1502],{},[1161,32771,1483],{},[1151,32773,32774,32776],{},[1154,32775,1436],{},[1154,32777,1502],{},[1161,32779,1623],{},[1151,32781,32782,32784],{},[1154,32783,11528],{},[1154,32785,1502],{},[1172,32787,32788],{"encoding":1174},"D_i = X_i - Y_i",[1115,32790,32792],{"className":32791},[1139],[1141,32793,32794],{"xmlns":1143},[1145,32795,32796,32824],{},[1148,32797,32798,32800,32802,32804,32806,32812,32814,32822],{},[1154,32799,12589],{},[1161,32801,13609],{},[1154,32803,11327],{},[1161,32805,1164],{"stretchy":1163},[1151,32807,32808,32810],{},[1154,32809,11332],{},[1154,32811,12589],{},[1161,32813,1199],{"separator":1121},[1645,32815,32816,32818,32820],{},[1154,32817,11339],{},[1154,32819,12589],{},[1312,32821,1610],{},[1161,32823,1170],{"stretchy":1163},[1172,32825,32826],{"encoding":1174},"D \\sim N(\\mu_D, \\sigma_D^2)",". Z ",[1115,32829,32831],{"className":32830},[1139],[1141,32832,32833],{"xmlns":1143},[1145,32834,32835,32839],{},[1148,32836,32837],{},[1154,32838,1159],{},[1172,32840,1159],{"encoding":1174}," dvojic se určí ",[1115,32843,32845],{"className":32844},[1139],[1141,32846,32847],{"xmlns":1143},[1145,32848,32849,32857],{},[1148,32850,32851],{},[1474,32852,32853,32855],{"accent":1121},[1154,32854,12232],{},[1161,32856,1480],{},[1172,32858,32859],{"encoding":1174},"\\bar{d}",[1115,32861,32863],{"className":32862},[1139],[1141,32864,32865],{"xmlns":1143},[1145,32866,32867,32877],{},[1148,32868,32869],{},[1645,32870,32871,32873,32875],{},[1154,32872,1607],{},[1154,32874,12232],{},[1312,32876,1610],{},[1172,32878,32879],{"encoding":1174},"s_d^2","; testuje se vztah mezi zvoleným číslem ",[1115,32882,32884],{"className":32883},[1139],[1141,32885,32886],{"xmlns":1143},[1145,32887,32888,32896],{},[1148,32889,32890],{},[1151,32891,32892,32894],{},[1154,32893,11332],{},[1312,32895,4585],{},[1172,32897,31428],{"encoding":1174}," (obvykle 0) a ",[1115,32900,32902],{"className":32901},[1139],[1141,32903,32904],{"xmlns":1143},[1145,32905,32906,32914],{},[1148,32907,32908],{},[1151,32909,32910,32912],{},[1154,32911,11332],{},[1154,32913,12589],{},[1172,32915,32916],{"encoding":1174},"\\mu_D",[1115,32918,32920],{"className":32919},[1139],[1141,32921,32922],{"xmlns":1143,"display":1468},[1145,32923,32924,32974],{},[1148,32925,32926,32928,32930,32954,32958,32960,32972],{},[1154,32927,11542],{},[1161,32929,1483],{},[1485,32931,32932,32948],{},[1148,32933,32934,32940,32942],{},[1474,32935,32936,32938],{"accent":1121},[1154,32937,12232],{},[1161,32939,1480],{},[1161,32941,1623],{},[1151,32943,32944,32946],{},[1154,32945,11332],{},[1312,32947,4585],{},[1151,32949,32950,32952],{},[1154,32951,1607],{},[1154,32953,12232],{},[1678,32955,32956],{},[1154,32957,1159],{},[1161,32959,13609],{},[1151,32961,32962,32964],{},[1154,32963,1807],{},[1148,32965,32966,32968,32970],{},[1154,32967,1159],{},[1161,32969,1623],{},[1312,32971,1489],{},[1154,32973,1176],{"mathvariant":1869},[1172,32975,32976],{"encoding":1174},"T = \\frac{\\bar{d} - \\mu_0}{s_d}\\sqrt{n} \\sim t_{n-1}.",[3350,32978,32979,33036],{},[3353,32980,32981],{},[3356,32982,32983,33002,33021],{},[3359,32984,32985],{},[1115,32986,32988],{"className":32987},[1139],[1141,32989,32990],{"xmlns":1143},[1145,32991,32992,33000],{},[1148,32993,32994],{},[1151,32995,32996,32998],{},[1154,32997,6105],{},[1312,32999,4585],{},[1172,33001,6110],{"encoding":1174},[3359,33003,33004],{},[1115,33005,33007],{"className":33006},[1139],[1141,33008,33009],{"xmlns":1143},[1145,33010,33011,33019],{},[1148,33012,33013],{},[1151,33014,33015,33017],{},[1154,33016,6105],{},[1312,33018,1489],{},[1172,33020,7508],{"encoding":1174},[3359,33022,31566,33023],{},[1115,33024,33026],{"className":33025},[1139],[1141,33027,33028],{"xmlns":1143},[1145,33029,33030,33034],{},[1148,33031,33032],{},[1154,33033,6143],{},[1172,33035,6143],{"encoding":1174},[3389,33037,33038,33135,33240],{},[3356,33039,33040,33068,33096],{},[3394,33041,33042],{},[1115,33043,33045],{"className":33044},[1139],[1141,33046,33047],{"xmlns":1143},[1145,33048,33049,33065],{},[1148,33050,33051,33057,33059],{},[1151,33052,33053,33055],{},[1154,33054,11332],{},[1154,33056,12589],{},[1161,33058,11177],{},[1151,33060,33061,33063],{},[1154,33062,11332],{},[1312,33064,4585],{},[1172,33066,33067],{"encoding":1174},"\\mu_D \\le \\mu_0",[3394,33069,33070],{},[1115,33071,33073],{"className":33072},[1139],[1141,33074,33075],{"xmlns":1143},[1145,33076,33077,33093],{},[1148,33078,33079,33085,33087],{},[1151,33080,33081,33083],{},[1154,33082,11332],{},[1154,33084,12589],{},[1161,33086,6225],{},[1151,33088,33089,33091],{},[1154,33090,11332],{},[1312,33092,4585],{},[1172,33094,33095],{"encoding":1174},"\\mu_D > \\mu_0",[3394,33097,33098],{},[1115,33099,33101],{"className":33100},[1139],[1141,33102,33103],{"xmlns":1143},[1145,33104,33105,33133],{},[1148,33106,33107,33109,33111,33123,33125,33127,33129,33131],{},[1154,33108,1807],{},[1161,33110,5198],{},[1151,33112,33113,33115],{},[1154,33114,1807],{},[1148,33116,33117,33119,33121],{},[1312,33118,1489],{},[1161,33120,1623],{},[1154,33122,7874],{},[1161,33124,1164],{"stretchy":1163},[1154,33126,1159],{},[1161,33128,1623],{},[1312,33130,1489],{},[1161,33132,1170],{"stretchy":1163},[1172,33134,31671],{"encoding":1174},[3356,33136,33137,33165,33193],{},[3394,33138,33139],{},[1115,33140,33142],{"className":33141},[1139],[1141,33143,33144],{"xmlns":1143},[1145,33145,33146,33162],{},[1148,33147,33148,33154,33156],{},[1151,33149,33150,33152],{},[1154,33151,11332],{},[1154,33153,12589],{},[1161,33155,1483],{},[1151,33157,33158,33160],{},[1154,33159,11332],{},[1312,33161,4585],{},[1172,33163,33164],{"encoding":1174},"\\mu_D = \\mu_0",[3394,33166,33167],{},[1115,33168,33170],{"className":33169},[1139],[1141,33171,33172],{"xmlns":1143},[1145,33173,33174,33190],{},[1148,33175,33176,33182,33184],{},[1151,33177,33178,33180],{},[1154,33179,11332],{},[1154,33181,12589],{},[1161,33183,15368],{"mathvariant":1869},[1151,33185,33186,33188],{},[1154,33187,11332],{},[1312,33189,4585],{},[1172,33191,33192],{"encoding":1174},"\\mu_D \\neq \\mu_0",[3394,33194,33195],{},[1115,33196,33198],{"className":33197},[1139],[1141,33199,33200],{"xmlns":1143},[1145,33201,33202,33238],{},[1148,33203,33204,33206,33208,33210,33212,33228,33230,33232,33234,33236],{},[1161,33205,26878],{"stretchy":1163},[1154,33207,1807],{},[1161,33209,26878],{"stretchy":1163},[1161,33211,5198],{},[1151,33213,33214,33216],{},[1154,33215,1807],{},[1148,33217,33218,33220,33222,33224,33226],{},[1312,33219,1489],{},[1161,33221,1623],{},[1154,33223,7874],{},[1154,33225,3245],{"mathvariant":1869},[1312,33227,1610],{},[1161,33229,1164],{"stretchy":1163},[1154,33231,1159],{},[1161,33233,1623],{},[1312,33235,1489],{},[1161,33237,1170],{"stretchy":1163},[1172,33239,31769],{"encoding":1174},[3356,33241,33242,33270,33298],{},[3394,33243,33244],{},[1115,33245,33247],{"className":33246},[1139],[1141,33248,33249],{"xmlns":1143},[1145,33250,33251,33267],{},[1148,33252,33253,33259,33261],{},[1151,33254,33255,33257],{},[1154,33256,11332],{},[1154,33258,12589],{},[1161,33260,5198],{},[1151,33262,33263,33265],{},[1154,33264,11332],{},[1312,33266,4585],{},[1172,33268,33269],{"encoding":1174},"\\mu_D \\ge \\mu_0",[3394,33271,33272],{},[1115,33273,33275],{"className":33274},[1139],[1141,33276,33277],{"xmlns":1143},[1145,33278,33279,33295],{},[1148,33280,33281,33287,33289],{},[1151,33282,33283,33285],{},[1154,33284,11332],{},[1154,33286,12589],{},[1161,33288,8805],{},[1151,33290,33291,33293],{},[1154,33292,11332],{},[1312,33294,4585],{},[1172,33296,33297],{"encoding":1174},"\\mu_D \u003C \\mu_0",[3394,33299,33300],{},[1115,33301,33303],{"className":33302},[1139],[1141,33304,33305],{"xmlns":1143},[1145,33306,33307,33337],{},[1148,33308,33309,33311,33313,33315,33327,33329,33331,33333,33335],{},[1154,33310,1807],{},[1161,33312,11177],{},[1161,33314,1623],{},[1151,33316,33317,33319],{},[1154,33318,1807],{},[1148,33320,33321,33323,33325],{},[1312,33322,1489],{},[1161,33324,1623],{},[1154,33326,7874],{},[1161,33328,1164],{"stretchy":1163},[1154,33330,1159],{},[1161,33332,1623],{},[1312,33334,1489],{},[1161,33336,1170],{"stretchy":1163},[1172,33338,31861],{"encoding":1174},[1103,33340,33342,33349,33491,33555,33641],{"className":33341,"dataCallout":2447},[1106,2446],[1110,33343,33345,33348],{"className":33344},[1113],[1115,33346],{"className":33347,"ariaHidden":1121},[1118,2454,1120],"Příklad: Snížení spotřeby paliva aditivem",[1110,33350,33351,33352,33370,33371,33389,33390,33408,33409,33442,33443,33466,33467,33490],{},"U ",[1115,33353,33355],{"className":33354},[1139],[1141,33356,33357],{"xmlns":1143},[1145,33358,33359,33367],{},[1148,33360,33361,33363,33365],{},[1154,33362,1159],{},[1161,33364,1483],{},[1312,33366,3427],{},[1172,33368,33369],{"encoding":1174},"n = 10"," vozů se změřila spotřeba před přidáním aditiva (",[1115,33372,33374],{"className":33373},[1139],[1141,33375,33376],{"xmlns":1143},[1145,33377,33378,33386],{},[1148,33379,33380],{},[1151,33381,33382,33384],{},[1154,33383,1436],{},[1154,33385,1502],{},[1172,33387,33388],{"encoding":1174},"X_i",") a po něm (",[1115,33391,33393],{"className":33392},[1139],[1141,33394,33395],{"xmlns":1143},[1145,33396,33397,33405],{},[1148,33398,33399],{},[1151,33400,33401,33403],{},[1154,33402,11528],{},[1154,33404,1502],{},[1172,33406,33407],{"encoding":1174},"Y_i","), diference ",[1115,33410,33412],{"className":33411},[1139],[1141,33413,33414],{"xmlns":1143},[1145,33415,33416,33440],{},[1148,33417,33418,33424,33426,33432,33434],{},[1151,33419,33420,33422],{},[1154,33421,12589],{},[1154,33423,1502],{},[1161,33425,1483],{},[1151,33427,33428,33430],{},[1154,33429,1436],{},[1154,33431,1502],{},[1161,33433,1623],{},[1151,33435,33436,33438],{},[1154,33437,11528],{},[1154,33439,1502],{},[1172,33441,32788],{"encoding":1174}," představují úsporu paliva. Z dat vyšla průměrná úspora ",[1115,33444,33446],{"className":33445},[1139],[1141,33447,33448],{"xmlns":1143},[1145,33449,33450,33463],{},[1148,33451,33452,33458,33460],{},[1474,33453,33454,33456],{"accent":1121},[1154,33455,12232],{},[1161,33457,1480],{},[1161,33459,1483],{},[1312,33461,33462],{},"0,4",[1172,33464,33465],{"encoding":1174},"\\bar{d} = 0{,}4"," l\u002F100 km, ",[1115,33468,33470],{"className":33469},[1139],[1141,33471,33472],{"xmlns":1143},[1145,33473,33474,33487],{},[1148,33475,33476,33482,33484],{},[1151,33477,33478,33480],{},[1154,33479,1607],{},[1154,33481,12232],{},[1161,33483,1483],{},[1312,33485,33486],{},"0,35",[1172,33488,33489],{"encoding":1174},"s_d = 0{,}35"," l\u002F100 km. Ověřte, že aditivum spotřebu statisticky významně snižuje.",[1110,33492,33493,33523,33524,33554],{},[1115,33494,33496],{"className":33495},[1139],[1141,33497,33498],{"xmlns":1143},[1145,33499,33500,33520],{},[1148,33501,33502,33508,33510,33516,33518],{},[1151,33503,33504,33506],{},[1154,33505,6105],{},[1312,33507,4585],{},[1161,33509,6481],{},[1151,33511,33512,33514],{},[1154,33513,11332],{},[1154,33515,12589],{},[1161,33517,11177],{},[1312,33519,4585],{},[1172,33521,33522],{"encoding":1174},"H_0: \\mu_D \\le 0"," (aditivum nemá vliv nebo spotřebu zvyšuje), ",[1115,33525,33527],{"className":33526},[1139],[1141,33528,33529],{"xmlns":1143},[1145,33530,33531,33551],{},[1148,33532,33533,33539,33541,33547,33549],{},[1151,33534,33535,33537],{},[1154,33536,6105],{},[1312,33538,1489],{},[1161,33540,6481],{},[1151,33542,33543,33545],{},[1154,33544,11332],{},[1154,33546,12589],{},[1161,33548,6225],{},[1312,33550,4585],{},[1172,33552,33553],{"encoding":1174},"H_1: \\mu_D > 0"," (aditivum spotřebu snižuje).",[1110,33556,33557],{},[1115,33558,33560],{"className":33559},[1139],[1141,33561,33562],{"xmlns":1143},[1145,33563,33564,33638],{},[1148,33565,33566,33568,33570,33582,33586,33588,33591,33593,33595,33597,33599,33601,33603,33605,33617,33619,33621,33623,33625,33627,33629,33631,33633,33636],{},[1154,33567,1807],{},[1161,33569,1483],{},[1485,33571,33572,33580],{},[1148,33573,33574,33576,33578],{},[1312,33575,33462],{},[1161,33577,1623],{},[1312,33579,4585],{},[1312,33581,33486],{},[1678,33583,33584],{},[1312,33585,3427],{},[1161,33587,1483],{},[1312,33589,33590],{},"3,614",[1161,33592,1199],{"separator":1121},[1516,33594],{"width":1518},[1154,33596,6143],{},[1161,33598,1483],{},[1161,33600,7845],{"stretchy":1163},[1154,33602,1807],{},[1161,33604,5198],{},[1151,33606,33607,33609],{},[1154,33608,1807],{},[1148,33610,33611,33613,33615],{},[1312,33612,4585],{},[1161,33614,1199],{"separator":1121},[1312,33616,25652],{},[1161,33618,1164],{"stretchy":1163},[1312,33620,3424],{},[1161,33622,1170],{"stretchy":1163},[1161,33624,7903],{"stretchy":1163},[1161,33626,1483],{},[1161,33628,7845],{"stretchy":1163},[1154,33630,1807],{},[1161,33632,5198],{},[1312,33634,33635],{},"1,833",[1161,33637,7903],{"stretchy":1163},[1172,33639,33640],{"encoding":1174},"t = \\frac{0{,}4 - 0}{0{,}35}\\sqrt{10} = 3{,}614, \\qquad W = \\{t \\ge t_{0,95}(9)\\} = \\{t \\ge 1{,}833\\}",[1110,33642,32252,33643,10465,33660,33677],{},[1115,33644,33646],{"className":33645},[1139],[1141,33647,33648],{"xmlns":1143},[1145,33649,33650,33658],{},[1148,33651,33652,33654,33656],{},[1154,33653,1807],{},[1161,33655,11459],{},[1154,33657,6143],{},[1172,33659,32270],{"encoding":1174},[1115,33661,33663],{"className":33662},[1139],[1141,33664,33665],{"xmlns":1143},[1145,33666,33667,33675],{},[1148,33668,33669],{},[1151,33670,33671,33673],{},[1154,33672,6105],{},[1312,33674,4585],{},[1172,33676,6110],{"encoding":1174},": aditivum prokazatelně snižuje průměrnou spotřebu paliva.",[2020,33679,33681],{"className":2022,"code":33680,"language":71,"meta":2024,"style":2024},"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",[2015,33682,33683,33712,33743,33769,33773],{"__ignoreMap":2024},[1115,33684,33685,33688,33690,33693,33695,33698,33700,33703,33705,33707,33709],{"class":2029,"line":10},[1115,33686,33687],{"class":2032},"dbar",[1115,33689,2036],{"class":2035},[1115,33691,33692],{"class":2046}," 0.4",[1115,33694,29038],{"class":2043},[1115,33696,33697],{"class":2032},"sd_d",[1115,33699,2036],{"class":2035},[1115,33701,33702],{"class":2046}," 0.35",[1115,33704,29038],{"class":2043},[1115,33706,1159],{"class":2032},[1115,33708,2036],{"class":2035},[1115,33710,33711],{"class":2046}," 10\n",[1115,33713,33714,33716,33718,33720,33722,33724,33726,33728,33730,33733,33735,33737,33739,33741],{"class":2029,"line":27},[1115,33715,1807],{"class":2032},[1115,33717,2036],{"class":2035},[1115,33719,3997],{"class":2043},[1115,33721,33687],{"class":2032},[1115,33723,29375],{"class":2035},[1115,33725,14387],{"class":2046},[1115,33727,2257],{"class":2043},[1115,33729,3245],{"class":2035},[1115,33731,33732],{"class":2032}," sd_d",[1115,33734,22493],{"class":2035},[1115,33736,9044],{"class":2039},[1115,33738,1164],{"class":2043},[1115,33740,1159],{"class":2032},[1115,33742,2185],{"class":2043},[1115,33744,33745,33747,33749,33751,33753,33755,33757,33759,33761,33763,33765,33767],{"class":2029,"line":148},[1115,33746,32377],{"class":2032},[1115,33748,2036],{"class":2035},[1115,33750,32382],{"class":2039},[1115,33752,1164],{"class":2043},[1115,33754,15239],{"class":2046},[1115,33756,1199],{"class":2035},[1115,33758,15222],{"class":2032},[1115,33760,2291],{"class":2035},[1115,33762,32396],{"class":2032},[1115,33764,29375],{"class":2035},[1115,33766,5269],{"class":2046},[1115,33768,2185],{"class":2043},[1115,33770,33771],{"class":2029,"line":111},[1115,33772,32407],{"class":2032},[1115,33774,33775],{"class":2029,"line":96},[1115,33776,32412],{"class":2032},[2020,33778,33781],{"className":33779,"code":33780,"language":2349,"meta":2024},[2347],"[1] 3.614032\n[1] 1.833113\n",[2015,33782,33780],{"__ignoreMap":2024},[1103,33784,33786,33793,33796,33941,33947],{"className":33785,"dataCallout":10867},[1106,10866],[1110,33787,33789,33792],{"className":33788},[1113],[1115,33790],{"className":33791,"ariaHidden":1121},[1118,10874,1120],"Ověřte normalitu diferencí, ne jen výsledek testu",[1110,33794,33795],{},"Realitní kancelář nechala dva odhadce ocenit osm nemovitostí (tisíce Kč):",[2020,33797,33799],{"className":2022,"code":33798,"language":71,"meta":2024,"style":2024},"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",[2015,33800,33801,33852,33903,33927],{"__ignoreMap":2024},[1115,33802,33803,33806,33808,33810,33812,33815,33817,33820,33822,33825,33827,33830,33832,33835,33837,33840,33842,33845,33847,33850],{"class":2029,"line":10},[1115,33804,33805],{"class":2032},"estA",[1115,33807,2036],{"class":2035},[1115,33809,2040],{"class":2039},[1115,33811,1164],{"class":2043},[1115,33813,33814],{"class":2046},"3282",[1115,33816,1199],{"class":2035},[1115,33818,33819],{"class":2046}," 2506",[1115,33821,1199],{"class":2035},[1115,33823,33824],{"class":2046}," 2812",[1115,33826,1199],{"class":2035},[1115,33828,33829],{"class":2046}," 5453",[1115,33831,1199],{"class":2035},[1115,33833,33834],{"class":2046}," 3263",[1115,33836,1199],{"class":2035},[1115,33838,33839],{"class":2046}," 4571",[1115,33841,1199],{"class":2035},[1115,33843,33844],{"class":2046}," 3121",[1115,33846,1199],{"class":2035},[1115,33848,33849],{"class":2046}," 2963",[1115,33851,2185],{"class":2043},[1115,33853,33854,33857,33859,33861,33863,33866,33868,33871,33873,33876,33878,33881,33883,33886,33888,33891,33893,33896,33898,33901],{"class":2029,"line":27},[1115,33855,33856],{"class":2032},"estB",[1115,33858,2036],{"class":2035},[1115,33860,2040],{"class":2039},[1115,33862,1164],{"class":2043},[1115,33864,33865],{"class":2046},"3271",[1115,33867,1199],{"class":2035},[1115,33869,33870],{"class":2046}," 2531",[1115,33872,1199],{"class":2035},[1115,33874,33875],{"class":2046}," 2799",[1115,33877,1199],{"class":2035},[1115,33879,33880],{"class":2046}," 5471",[1115,33882,1199],{"class":2035},[1115,33884,33885],{"class":2046}," 3285",[1115,33887,1199],{"class":2035},[1115,33889,33890],{"class":2046}," 4557",[1115,33892,1199],{"class":2035},[1115,33894,33895],{"class":2046}," 3139",[1115,33897,1199],{"class":2035},[1115,33899,33900],{"class":2046}," 2976",[1115,33902,2185],{"class":2043},[1115,33904,33905,33907,33909,33911,33913,33916,33918,33921,33923,33925],{"class":2029,"line":148},[1115,33906,31932],{"class":2039},[1115,33908,1164],{"class":2043},[1115,33910,33805],{"class":2032},[1115,33912,1199],{"class":2035},[1115,33914,33915],{"class":2032}," estB",[1115,33917,1199],{"class":2035},[1115,33919,33920],{"class":2032}," paired",[1115,33922,2291],{"class":2035},[1115,33924,2409],{"class":2046},[1115,33926,2185],{"class":2043},[1115,33928,33929,33931,33933,33935,33937,33939],{"class":2029,"line":111},[1115,33930,21429],{"class":2039},[1115,33932,1164],{"class":2043},[1115,33934,33805],{"class":2032},[1115,33936,29375],{"class":2035},[1115,33938,33915],{"class":2032},[1115,33940,2185],{"class":2043},[2020,33942,33945],{"className":33943,"code":33944,"language":2349,"meta":2024},[2347],"    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",[2015,33946,33944],{"__ignoreMap":2024},[1110,33948,33949,33950,3997,33967,33986,33987,34010],{},"Párový t-test sám nezamítá ",[1115,33951,33953],{"className":33952},[1139],[1141,33954,33955],{"xmlns":1143},[1145,33956,33957,33965],{},[1148,33958,33959],{},[1151,33960,33961,33963],{},[1154,33962,6105],{},[1312,33964,4585],{},[1172,33966,6110],{"encoding":1174},[1115,33968,33970],{"className":33969},[1139],[1141,33971,33972],{"xmlns":1143},[1145,33973,33974,33983],{},[1148,33975,33976,33978,33980],{},[1154,33977,1110],{},[1161,33979,1483],{},[1312,33981,33982],{},"0,2635",[1172,33984,33985],{"encoding":1174},"p = 0{,}2635","): odhadci se podle něj neliší. Shapiro-Wilkův test na diferencích ale dává ",[1115,33988,33990],{"className":33989},[1139],[1141,33991,33992],{"xmlns":1143},[1145,33993,33994,34007],{},[1148,33995,33996,33998,34000,34003,34005],{},[1154,33997,1110],{},[1161,33999,1483],{},[1312,34001,34002],{},"0,03203",[1161,34004,8805],{},[1312,34006,8460],{},[1172,34008,34009],{"encoding":1174},"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).",[1232,34012,34014],{"id":34013},"testy-o-dvou-základních-souborech","Testy o dvou základních souborech",[1110,34016,34017,34018,34044,34045,34083,34084,1385,34102,34083,34140,34158,34159,1385,34191,34223,34224,34250,34251,1176],{},"Uvažují se dva nezávislé základní soubory ",[1115,34019,34021],{"className":34020},[1139],[1141,34022,34023],{"xmlns":1143},[1145,34024,34025,34041],{},[1148,34026,34027,34033,34035],{},[1151,34028,34029,34031],{},[1154,34030,1204],{},[1312,34032,1489],{},[1161,34034,1199],{"separator":1121},[1151,34036,34037,34039],{},[1154,34038,1204],{},[1312,34040,1610],{},[1172,34042,34043],{"encoding":1174},"Z_1, Z_2"," se znakem ",[1115,34046,34048],{"className":34047},[1139],[1141,34049,34050],{"xmlns":1143},[1145,34051,34052,34080],{},[1148,34053,34054,34056,34058,34060,34062,34068,34070,34078],{},[1154,34055,1436],{},[1161,34057,13609],{},[1154,34059,11327],{},[1161,34061,1164],{"stretchy":1163},[1151,34063,34064,34066],{},[1154,34065,11332],{},[1312,34067,1489],{},[1161,34069,1199],{"separator":1121},[1645,34071,34072,34074,34076],{},[1154,34073,11339],{},[1312,34075,1489],{},[1312,34077,1610],{},[1161,34079,1170],{"stretchy":1163},[1172,34081,34082],{"encoding":1174},"X \\sim N(\\mu_1, \\sigma_1^2)"," v ",[1115,34085,34087],{"className":34086},[1139],[1141,34088,34089],{"xmlns":1143},[1145,34090,34091,34099],{},[1148,34092,34093],{},[1151,34094,34095,34097],{},[1154,34096,1204],{},[1312,34098,1489],{},[1172,34100,34101],{"encoding":1174},"Z_1",[1115,34103,34105],{"className":34104},[1139],[1141,34106,34107],{"xmlns":1143},[1145,34108,34109,34137],{},[1148,34110,34111,34113,34115,34117,34119,34125,34127,34135],{},[1154,34112,1436],{},[1161,34114,13609],{},[1154,34116,11327],{},[1161,34118,1164],{"stretchy":1163},[1151,34120,34121,34123],{},[1154,34122,11332],{},[1312,34124,1610],{},[1161,34126,1199],{"separator":1121},[1645,34128,34129,34131,34133],{},[1154,34130,11339],{},[1312,34132,1610],{},[1312,34134,1610],{},[1161,34136,1170],{"stretchy":1163},[1172,34138,34139],{"encoding":1174},"X \\sim N(\\mu_2, \\sigma_2^2)",[1115,34141,34143],{"className":34142},[1139],[1141,34144,34145],{"xmlns":1143},[1145,34146,34147,34155],{},[1148,34148,34149],{},[1151,34150,34151,34153],{},[1154,34152,1204],{},[1312,34154,1610],{},[1172,34156,34157],{"encoding":1174},"Z_2",". Z výběrů se určí ",[1115,34160,34162],{"className":34161},[1139],[1141,34163,34164],{"xmlns":1143},[1145,34165,34166,34188],{},[1148,34167,34168,34178,34180],{},[1151,34169,34170,34176],{},[1474,34171,34172,34174],{"accent":1121},[1154,34173,1167],{},[1161,34175,1480],{},[1312,34177,1489],{},[1161,34179,1199],{"separator":1121},[1645,34181,34182,34184,34186],{},[1154,34183,1607],{},[1312,34185,1489],{},[1312,34187,1610],{},[1172,34189,34190],{"encoding":1174},"\\bar{x}_1, s_1^2",[1115,34192,34194],{"className":34193},[1139],[1141,34195,34196],{"xmlns":1143},[1145,34197,34198,34220],{},[1148,34199,34200,34210,34212],{},[1151,34201,34202,34208],{},[1474,34203,34204,34206],{"accent":1121},[1154,34205,1167],{},[1161,34207,1480],{},[1312,34209,1610],{},[1161,34211,1199],{"separator":1121},[1645,34213,34214,34216,34218],{},[1154,34215,1607],{},[1312,34217,1610],{},[1312,34219,1610],{},[1172,34221,34222],{"encoding":1174},"\\bar{x}_2, s_2^2",". Testují se varianty vztahů mezi ",[1115,34225,34227],{"className":34226},[1139],[1141,34228,34229],{"xmlns":1143},[1145,34230,34231,34247],{},[1148,34232,34233,34239,34241],{},[1151,34234,34235,34237],{},[1154,34236,11332],{},[1312,34238,1489],{},[1161,34240,1199],{"separator":1121},[1151,34242,34243,34245],{},[1154,34244,11332],{},[1312,34246,1610],{},[1172,34248,34249],{"encoding":1174},"\\mu_1, \\mu_2",", resp. mezi ",[1115,34252,34254],{"className":34253},[1139],[1141,34255,34256],{"xmlns":1143},[1145,34257,34258,34278],{},[1148,34259,34260,34268,34270],{},[1645,34261,34262,34264,34266],{},[1154,34263,11339],{},[1312,34265,1489],{},[1312,34267,1610],{},[1161,34269,1199],{"separator":1121},[1645,34271,34272,34274,34276],{},[1154,34273,11339],{},[1312,34275,1610],{},[1312,34277,1610],{},[1172,34279,34280],{"encoding":1174},"\\sigma_1^2, \\sigma_2^2",[20599,34282,34284],{"id":34283},"f-test-o-rozptylech","F-test o rozptylech",[1110,34286,34287],{},"Statistika",[1115,34289,34291],{"className":34290},[1139],[1141,34292,34293],{"xmlns":1143,"display":1468},[1145,34294,34295,34351],{},[1148,34296,34297,34299,34301,34319,34321],{},[1154,34298,1156],{},[1161,34300,1483],{},[1485,34302,34303,34311],{},[1645,34304,34305,34307,34309],{},[1154,34306,1607],{},[1312,34308,1489],{},[1312,34310,1610],{},[1645,34312,34313,34315,34317],{},[1154,34314,1607],{},[1312,34316,1610],{},[1312,34318,1610],{},[1161,34320,13609],{},[1151,34322,34323,34325],{},[1154,34324,1156],{},[1148,34326,34327,34333,34335,34337,34339,34341,34347,34349],{},[1151,34328,34329,34331],{},[1154,34330,1159],{},[1312,34332,1489],{},[1161,34334,1623],{},[1312,34336,1489],{},[1161,34338,1199],{"separator":1121},[1316,34340,1318],{},[1151,34342,34343,34345],{},[1154,34344,1159],{},[1312,34346,1610],{},[1161,34348,1623],{},[1312,34350,1489],{},[1172,34352,34353],{"encoding":1174},"F = \\frac{s_1^2}{s_2^2} \\sim F_{n_1-1,\\,n_2-1}",[1110,34355,34356,34357,1385,34379,31519],{},"má Fisherovo-Snedecorovo rozdělení o ",[1115,34358,34360],{"className":34359},[1139],[1141,34361,34362],{"xmlns":1143},[1145,34363,34364,34376],{},[1148,34365,34366,34372,34374],{},[1151,34367,34368,34370],{},[1154,34369,1159],{},[1312,34371,1489],{},[1161,34373,1623],{},[1312,34375,1489],{},[1172,34377,34378],{"encoding":1174},"n_1-1",[1115,34380,34382],{"className":34381},[1139],[1141,34383,34384],{"xmlns":1143},[1145,34385,34386,34398],{},[1148,34387,34388,34394,34396],{},[1151,34389,34390,34392],{},[1154,34391,1159],{},[1312,34393,1610],{},[1161,34395,1623],{},[1312,34397,1489],{},[1172,34399,34400],{"encoding":1174},"n_2-1",[3350,34402,34403,34460],{},[3353,34404,34405],{},[3356,34406,34407,34426,34445],{},[3359,34408,34409],{},[1115,34410,34412],{"className":34411},[1139],[1141,34413,34414],{"xmlns":1143},[1145,34415,34416,34424],{},[1148,34417,34418],{},[1151,34419,34420,34422],{},[1154,34421,6105],{},[1312,34423,4585],{},[1172,34425,6110],{"encoding":1174},[3359,34427,34428],{},[1115,34429,34431],{"className":34430},[1139],[1141,34432,34433],{"xmlns":1143},[1145,34434,34435,34443],{},[1148,34436,34437],{},[1151,34438,34439,34441],{},[1154,34440,6105],{},[1312,34442,1489],{},[1172,34444,7508],{"encoding":1174},[3359,34446,31566,34447],{},[1115,34448,34450],{"className":34449},[1139],[1141,34451,34452],{"xmlns":1143},[1145,34453,34454,34458],{},[1148,34455,34456],{},[1154,34457,6143],{},[1172,34459,6143],{"encoding":1174},[3389,34461,34462,34576,34749],{},[3356,34463,34464,34492,34520],{},[3394,34465,34466],{},[1115,34467,34469],{"className":34468},[1139],[1141,34470,34471],{"xmlns":1143},[1145,34472,34473,34489],{},[1148,34474,34475,34481,34483],{},[1151,34476,34477,34479],{},[1154,34478,11339],{},[1312,34480,1489],{},[1161,34482,11177],{},[1151,34484,34485,34487],{},[1154,34486,11339],{},[1312,34488,1610],{},[1172,34490,34491],{"encoding":1174},"\\sigma_1 \\le \\sigma_2",[3394,34493,34494],{},[1115,34495,34497],{"className":34496},[1139],[1141,34498,34499],{"xmlns":1143},[1145,34500,34501,34517],{},[1148,34502,34503,34509,34511],{},[1151,34504,34505,34507],{},[1154,34506,11339],{},[1312,34508,1489],{},[1161,34510,6225],{},[1151,34512,34513,34515],{},[1154,34514,11339],{},[1312,34516,1610],{},[1172,34518,34519],{"encoding":1174},"\\sigma_1 > \\sigma_2",[3394,34521,34522],{},[1115,34523,34525],{"className":34524},[1139],[1141,34526,34527],{"xmlns":1143},[1145,34528,34529,34573],{},[1148,34530,34531,34533,34535,34547,34549,34555,34557,34559,34561,34567,34569,34571],{},[1154,34532,1156],{},[1161,34534,5198],{},[1151,34536,34537,34539],{},[1154,34538,1156],{},[1148,34540,34541,34543,34545],{},[1312,34542,1489],{},[1161,34544,1623],{},[1154,34546,7874],{},[1161,34548,1164],{"stretchy":1163},[1151,34550,34551,34553],{},[1154,34552,1159],{},[1312,34554,1489],{},[1161,34556,1623],{},[1312,34558,1489],{},[1161,34560,1199],{"separator":1121},[1151,34562,34563,34565],{},[1154,34564,1159],{},[1312,34566,1610],{},[1161,34568,1623],{},[1312,34570,1489],{},[1161,34572,1170],{"stretchy":1163},[1172,34574,34575],{"encoding":1174},"F \\ge F_{1-\\alpha}(n_1-1, n_2-1)",[3356,34577,34578,34606,34634],{},[3394,34579,34580],{},[1115,34581,34583],{"className":34582},[1139],[1141,34584,34585],{"xmlns":1143},[1145,34586,34587,34603],{},[1148,34588,34589,34595,34597],{},[1151,34590,34591,34593],{},[1154,34592,11339],{},[1312,34594,1489],{},[1161,34596,1483],{},[1151,34598,34599,34601],{},[1154,34600,11339],{},[1312,34602,1610],{},[1172,34604,34605],{"encoding":1174},"\\sigma_1 = \\sigma_2",[3394,34607,34608],{},[1115,34609,34611],{"className":34610},[1139],[1141,34612,34613],{"xmlns":1143},[1145,34614,34615,34631],{},[1148,34616,34617,34623,34625],{},[1151,34618,34619,34621],{},[1154,34620,11339],{},[1312,34622,1489],{},[1161,34624,15368],{"mathvariant":1869},[1151,34626,34627,34629],{},[1154,34628,11339],{},[1312,34630,1610],{},[1172,34632,34633],{"encoding":1174},"\\sigma_1 \\neq \\sigma_2",[3394,34635,34636,34690,34691],{},[1115,34637,34639],{"className":34638},[1139],[1141,34640,34641],{"xmlns":1143},[1145,34642,34643,34687],{},[1148,34644,34645,34647,34649,34661,34663,34669,34671,34673,34675,34681,34683,34685],{},[1154,34646,1156],{},[1161,34648,11177],{},[1151,34650,34651,34653],{},[1154,34652,1156],{},[1148,34654,34655,34657,34659],{},[1154,34656,7874],{},[1154,34658,3245],{"mathvariant":1869},[1312,34660,1610],{},[1161,34662,1164],{"stretchy":1163},[1151,34664,34665,34667],{},[1154,34666,1159],{},[1312,34668,1489],{},[1161,34670,1623],{},[1312,34672,1489],{},[1161,34674,1199],{"separator":1121},[1151,34676,34677,34679],{},[1154,34678,1159],{},[1312,34680,1610],{},[1161,34682,1623],{},[1312,34684,1489],{},[1161,34686,1170],{"stretchy":1163},[1172,34688,34689],{"encoding":1174},"F \\le F_{\\alpha\u002F2}(n_1-1, n_2-1)"," nebo ",[1115,34692,34694],{"className":34693},[1139],[1141,34695,34696],{"xmlns":1143},[1145,34697,34698,34746],{},[1148,34699,34700,34702,34704,34720,34722,34728,34730,34732,34734,34740,34742,34744],{},[1154,34701,1156],{},[1161,34703,5198],{},[1151,34705,34706,34708],{},[1154,34707,1156],{},[1148,34709,34710,34712,34714,34716,34718],{},[1312,34711,1489],{},[1161,34713,1623],{},[1154,34715,7874],{},[1154,34717,3245],{"mathvariant":1869},[1312,34719,1610],{},[1161,34721,1164],{"stretchy":1163},[1151,34723,34724,34726],{},[1154,34725,1159],{},[1312,34727,1489],{},[1161,34729,1623],{},[1312,34731,1489],{},[1161,34733,1199],{"separator":1121},[1151,34735,34736,34738],{},[1154,34737,1159],{},[1312,34739,1610],{},[1161,34741,1623],{},[1312,34743,1489],{},[1161,34745,1170],{"stretchy":1163},[1172,34747,34748],{"encoding":1174},"F \\ge F_{1-\\alpha\u002F2}(n_1-1, n_2-1)",[3356,34750,34751,34779,34807],{},[3394,34752,34753],{},[1115,34754,34756],{"className":34755},[1139],[1141,34757,34758],{"xmlns":1143},[1145,34759,34760,34776],{},[1148,34761,34762,34768,34770],{},[1151,34763,34764,34766],{},[1154,34765,11339],{},[1312,34767,1489],{},[1161,34769,5198],{},[1151,34771,34772,34774],{},[1154,34773,11339],{},[1312,34775,1610],{},[1172,34777,34778],{"encoding":1174},"\\sigma_1 \\ge \\sigma_2",[3394,34780,34781],{},[1115,34782,34784],{"className":34783},[1139],[1141,34785,34786],{"xmlns":1143},[1145,34787,34788,34804],{},[1148,34789,34790,34796,34798],{},[1151,34791,34792,34794],{},[1154,34793,11339],{},[1312,34795,1489],{},[1161,34797,8805],{},[1151,34799,34800,34802],{},[1154,34801,11339],{},[1312,34803,1610],{},[1172,34805,34806],{"encoding":1174},"\\sigma_1 \u003C \\sigma_2",[3394,34808,34809],{},[1115,34810,34812],{"className":34811},[1139],[1141,34813,34814],{"xmlns":1143},[1145,34815,34816,34854],{},[1148,34817,34818,34820,34822,34828,34830,34836,34838,34840,34842,34848,34850,34852],{},[1154,34819,1156],{},[1161,34821,11177],{},[1151,34823,34824,34826],{},[1154,34825,1156],{},[1154,34827,7874],{},[1161,34829,1164],{"stretchy":1163},[1151,34831,34832,34834],{},[1154,34833,1159],{},[1312,34835,1489],{},[1161,34837,1623],{},[1312,34839,1489],{},[1161,34841,1199],{"separator":1121},[1151,34843,34844,34846],{},[1154,34845,1159],{},[1312,34847,1610],{},[1161,34849,1623],{},[1312,34851,1489],{},[1161,34853,1170],{"stretchy":1163},[1172,34855,34856],{"encoding":1174},"F \\le F_{\\alpha}(n_1-1, n_2-1)",[20599,34858,34860],{"id":34859},"dvouvýběrový-t-test-o-středních-hodnotách","Dvouvýběrový t-test o středních hodnotách",[1110,34862,34863],{},"Volba statistiky závisí na tom, zda jsou rozptyly považovány za shodné:",[1115,34865,34867],{"className":34866},[1139],[1141,34868,34869],{"xmlns":1143,"display":1468},[1145,34870,34871,35048],{},[1148,34872,34873,34879,34881,34957,35005,35007,35009,35018,35020,35026,35028,35034,35036,35042,35044,35046],{},[1151,34874,34875,34877],{},[1154,34876,11542],{},[1312,34878,1489],{},[1161,34880,1483],{},[1485,34882,34883,34907],{},[1148,34884,34885,34895,34897],{},[1151,34886,34887,34893],{},[1474,34888,34889,34891],{"accent":1121},[1154,34890,1167],{},[1161,34892,1480],{},[1312,34894,1489],{},[1161,34896,1623],{},[1151,34898,34899,34905],{},[1474,34900,34901,34903],{"accent":1121},[1154,34902,1167],{},[1161,34904,1480],{},[1312,34906,1610],{},[1678,34908,34909],{},[1148,34910,34911,34913,34919,34921,34923,34925,34933,34935,34937,34943,34945,34947,34949],{},[1161,34912,1164],{"stretchy":1163},[1151,34914,34915,34917],{},[1154,34916,1159],{},[1312,34918,1489],{},[1161,34920,1623],{},[1312,34922,1489],{},[1161,34924,1170],{"stretchy":1163},[1645,34926,34927,34929,34931],{},[1154,34928,1607],{},[1312,34930,1489],{},[1312,34932,1610],{},[1161,34934,3835],{},[1161,34936,1164],{"stretchy":1163},[1151,34938,34939,34941],{},[1154,34940,1159],{},[1312,34942,1610],{},[1161,34944,1623],{},[1312,34946,1489],{},[1161,34948,1170],{"stretchy":1163},[1645,34950,34951,34953,34955],{},[1154,34952,1607],{},[1312,34954,1610],{},[1312,34956,1610],{},[1678,34958,34959],{},[1485,34960,34961,34981],{},[1148,34962,34963,34969,34971,34977,34979],{},[1151,34964,34965,34967],{},[1154,34966,1159],{},[1312,34968,1489],{},[1161,34970,3835],{},[1151,34972,34973,34975],{},[1154,34974,1159],{},[1312,34976,1610],{},[1161,34978,1623],{},[1312,34980,1610],{},[1148,34982,34983,34993,34995],{},[1485,34984,34985,34987],{},[1312,34986,1489],{},[1151,34988,34989,34991],{},[1154,34990,1159],{},[1312,34992,1489],{},[1161,34994,3835],{},[1485,34996,34997,34999],{},[1312,34998,1489],{},[1151,35000,35001,35003],{},[1154,35002,1159],{},[1312,35004,1610],{},[1161,35006,1199],{"separator":1121},[1516,35008],{"width":1518},[1645,35010,35011,35013,35015],{},[1154,35012,1807],{},[1154,35014,1110],{},[1161,35016,35017],{},"∗",[1161,35019,1483],{},[1151,35021,35022,35024],{},[1154,35023,1807],{},[1154,35025,1110],{},[1161,35027,1164],{"stretchy":1163},[1151,35029,35030,35032],{},[1154,35031,1159],{},[1312,35033,1489],{},[1161,35035,3835],{},[1151,35037,35038,35040],{},[1154,35039,1159],{},[1312,35041,1610],{},[1161,35043,1623],{},[1312,35045,1610],{},[1161,35047,1170],{"stretchy":1163},[1172,35049,35050],{"encoding":1174},"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)",[1110,35052,35053,35054,35083],{},"se použije, pokud jsou rozptyly ",[1115,35055,35057],{"className":35056},[1139],[1141,35058,35059],{"xmlns":1143},[1145,35060,35061,35081],{},[1148,35062,35063,35071,35073],{},[1645,35064,35065,35067,35069],{},[1154,35066,11339],{},[1312,35068,1489],{},[1312,35070,1610],{},[1161,35072,1199],{"separator":1121},[1645,35074,35075,35077,35079],{},[1154,35076,11339],{},[1312,35078,1610],{},[1312,35080,1610],{},[1172,35082,34280],{"encoding":1174}," alespoň přibližně shodné; při rozdílných rozptylech",[1115,35085,35087],{"className":35086},[1139],[1141,35088,35089],{"xmlns":1143,"display":1468},[1145,35090,35091,35303],{},[1148,35092,35093,35099,35101,35165,35167,35169,35177,35179,35301],{},[1151,35094,35095,35097],{},[1154,35096,11542],{},[1312,35098,1610],{},[1161,35100,1483],{},[1485,35102,35103,35127],{},[1148,35104,35105,35115,35117],{},[1151,35106,35107,35113],{},[1474,35108,35109,35111],{"accent":1121},[1154,35110,1167],{},[1161,35112,1480],{},[1312,35114,1489],{},[1161,35116,1623],{},[1151,35118,35119,35125],{},[1474,35120,35121,35123],{"accent":1121},[1154,35122,1167],{},[1161,35124,1480],{},[1312,35126,1610],{},[1678,35128,35129],{},[1148,35130,35131,35139,35141,35147,35149,35157,35159],{},[1645,35132,35133,35135,35137],{},[1154,35134,1607],{},[1312,35136,1489],{},[1312,35138,1610],{},[1154,35140,3245],{"mathvariant":1869},[1151,35142,35143,35145],{},[1154,35144,1159],{},[1312,35146,1489],{},[1161,35148,3835],{},[1645,35150,35151,35153,35155],{},[1154,35152,1607],{},[1312,35154,1610],{},[1312,35156,1610],{},[1154,35158,3245],{"mathvariant":1869},[1151,35160,35161,35163],{},[1154,35162,1159],{},[1312,35164,1610],{},[1161,35166,1199],{"separator":1121},[1516,35168],{"width":1518},[1645,35170,35171,35173,35175],{},[1154,35172,1807],{},[1154,35174,1110],{},[1161,35176,35017],{},[1161,35178,1483],{},[1485,35180,35181,35261],{},[1148,35182,35183,35201,35207,35209,35215,35217,35219,35221,35223,35241,35247,35249,35255,35257,35259],{},[7752,35184,35185],{"scriptlevel":4585,"displaystyle":1121},[1485,35186,35187,35195],{},[1645,35188,35189,35191,35193],{},[1154,35190,1607],{},[1312,35192,1489],{},[1312,35194,1610],{},[1151,35196,35197,35199],{},[1154,35198,1159],{},[1312,35200,1489],{},[1151,35202,35203,35205],{},[1154,35204,1807],{},[1154,35206,1110],{},[1161,35208,1164],{"stretchy":1163},[1151,35210,35211,35213],{},[1154,35212,1159],{},[1312,35214,1489],{},[1161,35216,1623],{},[1312,35218,1489],{},[1161,35220,1170],{"stretchy":1163},[1161,35222,3835],{},[7752,35224,35225],{"scriptlevel":4585,"displaystyle":1121},[1485,35226,35227,35235],{},[1645,35228,35229,35231,35233],{},[1154,35230,1607],{},[1312,35232,1610],{},[1312,35234,1610],{},[1151,35236,35237,35239],{},[1154,35238,1159],{},[1312,35240,1610],{},[1151,35242,35243,35245],{},[1154,35244,1807],{},[1154,35246,1110],{},[1161,35248,1164],{"stretchy":1163},[1151,35250,35251,35253],{},[1154,35252,1159],{},[1312,35254,1610],{},[1161,35256,1623],{},[1312,35258,1489],{},[1161,35260,1170],{"stretchy":1163},[1148,35262,35263,35281,35283],{},[7752,35264,35265],{"scriptlevel":4585,"displaystyle":1121},[1485,35266,35267,35275],{},[1645,35268,35269,35271,35273],{},[1154,35270,1607],{},[1312,35272,1489],{},[1312,35274,1610],{},[1151,35276,35277,35279],{},[1154,35278,1159],{},[1312,35280,1489],{},[1161,35282,3835],{},[7752,35284,35285],{"scriptlevel":4585,"displaystyle":1121},[1485,35286,35287,35295],{},[1645,35288,35289,35291,35293],{},[1154,35290,1607],{},[1312,35292,1610],{},[1312,35294,1610],{},[1151,35296,35297,35299],{},[1154,35298,1159],{},[1312,35300,1610],{},[1154,35302,1176],{"mathvariant":1869},[1172,35304,35305],{"encoding":1174},"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}}.",[3350,35307,35308,35365],{},[3353,35309,35310],{},[3356,35311,35312,35331,35350],{},[3359,35313,35314],{},[1115,35315,35317],{"className":35316},[1139],[1141,35318,35319],{"xmlns":1143},[1145,35320,35321,35329],{},[1148,35322,35323],{},[1151,35324,35325,35327],{},[1154,35326,6105],{},[1312,35328,4585],{},[1172,35330,6110],{"encoding":1174},[3359,35332,35333],{},[1115,35334,35336],{"className":35335},[1139],[1141,35337,35338],{"xmlns":1143},[1145,35339,35340,35348],{},[1148,35341,35342],{},[1151,35343,35344,35346],{},[1154,35345,6105],{},[1312,35347,1489],{},[1172,35349,7508],{"encoding":1174},[3359,35351,31566,35352],{},[1115,35353,35355],{"className":35354},[1139],[1141,35356,35357],{"xmlns":1143},[1145,35358,35359,35363],{},[1148,35360,35361],{},[1154,35362,6143],{},[1172,35364,6143],{"encoding":1174},[3389,35366,35367,35451,35539],{},[3356,35368,35369,35397,35425],{},[3394,35370,35371],{},[1115,35372,35374],{"className":35373},[1139],[1141,35375,35376],{"xmlns":1143},[1145,35377,35378,35394],{},[1148,35379,35380,35386,35388],{},[1151,35381,35382,35384],{},[1154,35383,11332],{},[1312,35385,1489],{},[1161,35387,11177],{},[1151,35389,35390,35392],{},[1154,35391,11332],{},[1312,35393,1610],{},[1172,35395,35396],{"encoding":1174},"\\mu_1 \\le \\mu_2",[3394,35398,35399],{},[1115,35400,35402],{"className":35401},[1139],[1141,35403,35404],{"xmlns":1143},[1145,35405,35406,35422],{},[1148,35407,35408,35414,35416],{},[1151,35409,35410,35412],{},[1154,35411,11332],{},[1312,35413,1489],{},[1161,35415,6225],{},[1151,35417,35418,35420],{},[1154,35419,11332],{},[1312,35421,1610],{},[1172,35423,35424],{"encoding":1174},"\\mu_1 > \\mu_2",[3394,35426,35427],{},[1115,35428,35430],{"className":35429},[1139],[1141,35431,35432],{"xmlns":1143},[1145,35433,35434,35448],{},[1148,35435,35436,35438,35440],{},[1154,35437,1807],{},[1161,35439,5198],{},[1645,35441,35442,35444,35446],{},[1154,35443,1807],{},[1154,35445,1110],{},[1161,35447,35017],{},[1172,35449,35450],{"encoding":1174},"t \\ge t_p^*",[3356,35452,35453,35481,35509],{},[3394,35454,35455],{},[1115,35456,35458],{"className":35457},[1139],[1141,35459,35460],{"xmlns":1143},[1145,35461,35462,35478],{},[1148,35463,35464,35470,35472],{},[1151,35465,35466,35468],{},[1154,35467,11332],{},[1312,35469,1489],{},[1161,35471,1483],{},[1151,35473,35474,35476],{},[1154,35475,11332],{},[1312,35477,1610],{},[1172,35479,35480],{"encoding":1174},"\\mu_1 = \\mu_2",[3394,35482,35483],{},[1115,35484,35486],{"className":35485},[1139],[1141,35487,35488],{"xmlns":1143},[1145,35489,35490,35506],{},[1148,35491,35492,35498,35500],{},[1151,35493,35494,35496],{},[1154,35495,11332],{},[1312,35497,1489],{},[1161,35499,15368],{"mathvariant":1869},[1151,35501,35502,35504],{},[1154,35503,11332],{},[1312,35505,1610],{},[1172,35507,35508],{"encoding":1174},"\\mu_1 \\neq \\mu_2",[3394,35510,35511],{},[1115,35512,35514],{"className":35513},[1139],[1141,35515,35516],{"xmlns":1143},[1145,35517,35518,35536],{},[1148,35519,35520,35522,35524,35526,35528],{},[1161,35521,26878],{"stretchy":1163},[1154,35523,1807],{},[1161,35525,26878],{"stretchy":1163},[1161,35527,5198],{},[1645,35529,35530,35532,35534],{},[1154,35531,1807],{},[1154,35533,1110],{},[1161,35535,35017],{},[1172,35537,35538],{"encoding":1174},"\\lvert t \\rvert \\ge t_p^*",[3356,35540,35541,35569,35597],{},[3394,35542,35543],{},[1115,35544,35546],{"className":35545},[1139],[1141,35547,35548],{"xmlns":1143},[1145,35549,35550,35566],{},[1148,35551,35552,35558,35560],{},[1151,35553,35554,35556],{},[1154,35555,11332],{},[1312,35557,1489],{},[1161,35559,5198],{},[1151,35561,35562,35564],{},[1154,35563,11332],{},[1312,35565,1610],{},[1172,35567,35568],{"encoding":1174},"\\mu_1 \\ge \\mu_2",[3394,35570,35571],{},[1115,35572,35574],{"className":35573},[1139],[1141,35575,35576],{"xmlns":1143},[1145,35577,35578,35594],{},[1148,35579,35580,35586,35588],{},[1151,35581,35582,35584],{},[1154,35583,11332],{},[1312,35585,1489],{},[1161,35587,8805],{},[1151,35589,35590,35592],{},[1154,35591,11332],{},[1312,35593,1610],{},[1172,35595,35596],{"encoding":1174},"\\mu_1 \u003C \\mu_2",[3394,35598,35599],{},[1115,35600,35602],{"className":35601},[1139],[1141,35603,35604],{"xmlns":1143},[1145,35605,35606,35622],{},[1148,35607,35608,35610,35612,35614],{},[1154,35609,1807],{},[1161,35611,11177],{},[1161,35613,1623],{},[1645,35615,35616,35618,35620],{},[1154,35617,1807],{},[1154,35619,1110],{},[1161,35621,35017],{},[1172,35623,35624],{"encoding":1174},"t \\le -t_p^*",[1110,35626,35627,35628,34690,35646,1176],{},"Postup je dvoukrokový: nejprve F-test rozhodne o shodě rozptylů, pak se podle výsledku zvolí ",[1115,35629,35631],{"className":35630},[1139],[1141,35632,35633],{"xmlns":1143},[1145,35634,35635,35643],{},[1148,35636,35637],{},[1151,35638,35639,35641],{},[1154,35640,11542],{},[1312,35642,1489],{},[1172,35644,35645],{"encoding":1174},"T_1",[1115,35647,35649],{"className":35648},[1139],[1141,35650,35651],{"xmlns":1143},[1145,35652,35653,35661],{},[1148,35654,35655],{},[1151,35656,35657,35659],{},[1154,35658,11542],{},[1312,35660,1610],{},[1172,35662,35663],{"encoding":1174},"T_2",[1110,35665,35666],{},[1393,35667],{"alt":35668,"className":35669,"src":35670},"mask-th-f-kriticky-obor",[1242,1397],"\u002Fwiki-assets\u002Fmask-th-f-kriticky-obor.png",[1103,35672,35674,35681,35831,35912,36041,36079,36152,36291],{"className":35673,"dataCallout":2447},[1106,2446],[1110,35675,35677,35680],{"className":35676},[1113],[1115,35678],{"className":35679,"ariaHidden":1121},[1118,2454,1120],"Příklad: Porovnání dvou dodavatelů součástek",[1110,35682,35683,35684,1381,35706,35732,35733,35757,35758,1381,35780,35732,35806,35830],{},"Pevnost plastových dílů: dodavatel A (",[1115,35685,35687],{"className":35686},[1139],[1141,35688,35689],{"xmlns":1143},[1145,35690,35691,35703],{},[1148,35692,35693,35699,35701],{},[1151,35694,35695,35697],{},[1154,35696,1159],{},[1312,35698,1489],{},[1161,35700,1483],{},[1312,35702,3427],{},[1172,35704,35705],{"encoding":1174},"n_1 = 10",[1115,35707,35709],{"className":35708},[1139],[1141,35710,35711],{"xmlns":1143},[1145,35712,35713,35729],{},[1148,35714,35715,35725,35727],{},[1151,35716,35717,35723],{},[1474,35718,35719,35721],{"accent":1121},[1154,35720,1167],{},[1161,35722,1480],{},[1312,35724,1489],{},[1161,35726,1483],{},[1312,35728,8126],{},[1172,35730,35731],{"encoding":1174},"\\bar{x}_1 = 82"," MPa, ",[1115,35734,35736],{"className":35735},[1139],[1141,35737,35738],{"xmlns":1143},[1145,35739,35740,35754],{},[1148,35741,35742,35750,35752],{},[1645,35743,35744,35746,35748],{},[1154,35745,1607],{},[1312,35747,1489],{},[1312,35749,1610],{},[1161,35751,1483],{},[1312,35753,4831],{},[1172,35755,35756],{"encoding":1174},"s_1^2 = 25","), dodavatel B (",[1115,35759,35761],{"className":35760},[1139],[1141,35762,35763],{"xmlns":1143},[1145,35764,35765,35777],{},[1148,35766,35767,35773,35775],{},[1151,35768,35769,35771],{},[1154,35770,1159],{},[1312,35772,1610],{},[1161,35774,1483],{},[1312,35776,6791],{},[1172,35778,35779],{"encoding":1174},"n_2 = 12",[1115,35781,35783],{"className":35782},[1139],[1141,35784,35785],{"xmlns":1143},[1145,35786,35787,35803],{},[1148,35788,35789,35799,35801],{},[1151,35790,35791,35797],{},[1474,35792,35793,35795],{"accent":1121},[1154,35794,1167],{},[1161,35796,1480],{},[1312,35798,1610],{},[1161,35800,1483],{},[1312,35802,4847],{},[1172,35804,35805],{"encoding":1174},"\\bar{x}_2 = 75",[1115,35807,35809],{"className":35808},[1139],[1141,35810,35811],{"xmlns":1143},[1145,35812,35813,35827],{},[1148,35814,35815,35823,35825],{},[1645,35816,35817,35819,35821],{},[1154,35818,1607],{},[1312,35820,1610],{},[1312,35822,1610],{},[1161,35824,1483],{},[1312,35826,25880],{},[1172,35828,35829],{"encoding":1174},"s_2^2 = 16","). Předpokládá se normalita obou rozdělení.",[1110,35832,35833,1932,35836,1381,35874,1176],{},[1248,35834,35835],{},"Krok 1 — F-test rozptylů.",[1115,35837,35839],{"className":35838},[1139],[1141,35840,35841],{"xmlns":1143},[1145,35842,35843,35871],{},[1148,35844,35845,35851,35853,35861,35863],{},[1151,35846,35847,35849],{},[1154,35848,6105],{},[1312,35850,4585],{},[1161,35852,6481],{},[1645,35854,35855,35857,35859],{},[1154,35856,11339],{},[1312,35858,1489],{},[1312,35860,1610],{},[1161,35862,1483],{},[1645,35864,35865,35867,35869],{},[1154,35866,11339],{},[1312,35868,1610],{},[1312,35870,1610],{},[1172,35872,35873],{"encoding":1174},"H_0: \\sigma_1^2 = \\sigma_2^2",[1115,35875,35877],{"className":35876},[1139],[1141,35878,35879],{"xmlns":1143},[1145,35880,35881,35909],{},[1148,35882,35883,35889,35891,35899,35901],{},[1151,35884,35885,35887],{},[1154,35886,6105],{},[1312,35888,1489],{},[1161,35890,6481],{},[1645,35892,35893,35895,35897],{},[1154,35894,11339],{},[1312,35896,1489],{},[1312,35898,1610],{},[1161,35900,15368],{"mathvariant":1869},[1645,35902,35903,35905,35907],{},[1154,35904,11339],{},[1312,35906,1610],{},[1312,35908,1610],{},[1172,35910,35911],{"encoding":1174},"H_1: \\sigma_1^2 \\neq \\sigma_2^2",[1110,35913,35914],{},[1115,35915,35917],{"className":35916},[1139],[1141,35918,35919],{"xmlns":1143},[1145,35920,35921,36038],{},[1148,35922,35923,35925,35927,35933,35935,35938,35940,35942,35944,35946,35948,35950,35952,35965,35967,35969,35971,35973,35975,35978,35981,35983,35985,35987,36000,36002,36004,36006,36008,36010,36012,36014,36016,36018,36020,36023,36025,36027,36029,36031,36033,36036],{},[1154,35924,1156],{},[1161,35926,1483],{},[1485,35928,35929,35931],{},[1312,35930,4831],{},[1312,35932,25880],{},[1161,35934,1483],{},[1312,35936,35937],{},"1,5625",[1161,35939,1199],{"separator":1121},[1516,35941],{"width":1518},[1154,35943,6143],{},[1161,35945,1483],{},[1161,35947,7845],{"stretchy":1163},[1154,35949,1156],{},[1161,35951,11177],{},[1151,35953,35954,35956],{},[1154,35955,1156],{},[1148,35957,35958,35960,35962],{},[1312,35959,4585],{},[1161,35961,1199],{"separator":1121},[1312,35963,35964],{},"025",[1161,35966,1164],{"stretchy":1163},[1312,35968,3424],{},[1161,35970,1199],{"separator":1121},[1312,35972,4850],{},[1161,35974,1170],{"stretchy":1163},[1316,35976,35977],{},"  ",[1316,35979,35980],{},"nebo",[1316,35982,35977],{},[1154,35984,1156],{},[1161,35986,5198],{},[1151,35988,35989,35991],{},[1154,35990,1156],{},[1148,35992,35993,35995,35997],{},[1312,35994,4585],{},[1161,35996,1199],{"separator":1121},[1312,35998,35999],{},"975",[1161,36001,1164],{"stretchy":1163},[1312,36003,3424],{},[1161,36005,1199],{"separator":1121},[1312,36007,4850],{},[1161,36009,1170],{"stretchy":1163},[1161,36011,7903],{"stretchy":1163},[1161,36013,1483],{},[1161,36015,7845],{"stretchy":1163},[1154,36017,1156],{},[1161,36019,11177],{},[1312,36021,36022],{},"0,256",[1316,36024,35977],{},[1316,36026,35980],{},[1316,36028,35977],{},[1154,36030,1156],{},[1161,36032,5198],{},[1312,36034,36035],{},"3,588",[1161,36037,7903],{"stretchy":1163},[1172,36039,36040],{"encoding":1174},"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\\}",[1110,36042,36043,36061,36062,1176],{},[1115,36044,36046],{"className":36045},[1139],[1141,36047,36048],{"xmlns":1143},[1145,36049,36050,36058],{},[1148,36051,36052,36054,36056],{},[1154,36053,1156],{},[1161,36055,31127],{"mathvariant":1869},[1154,36057,6143],{},[1172,36059,36060],{"encoding":1174},"F \\notin W",", rozptyly nezamítáme jako shodné — pro t-test se použije ",[1115,36063,36065],{"className":36064},[1139],[1141,36066,36067],{"xmlns":1143},[1145,36068,36069,36077],{},[1148,36070,36071],{},[1151,36072,36073,36075],{},[1154,36074,11542],{},[1312,36076,1489],{},[1172,36078,35645],{"encoding":1174},[1110,36080,36081,1932,36084,1381,36118,1176],{},[1248,36082,36083],{},"Krok 2 — dvouvýběrový t-test středních hodnot.",[1115,36085,36087],{"className":36086},[1139],[1141,36088,36089],{"xmlns":1143},[1145,36090,36091,36115],{},[1148,36092,36093,36099,36101,36107,36109],{},[1151,36094,36095,36097],{},[1154,36096,6105],{},[1312,36098,4585],{},[1161,36100,6481],{},[1151,36102,36103,36105],{},[1154,36104,11332],{},[1312,36106,1489],{},[1161,36108,1483],{},[1151,36110,36111,36113],{},[1154,36112,11332],{},[1312,36114,1610],{},[1172,36116,36117],{"encoding":1174},"H_0: \\mu_1 = \\mu_2",[1115,36119,36121],{"className":36120},[1139],[1141,36122,36123],{"xmlns":1143},[1145,36124,36125,36149],{},[1148,36126,36127,36133,36135,36141,36143],{},[1151,36128,36129,36131],{},[1154,36130,6105],{},[1312,36132,1489],{},[1161,36134,6481],{},[1151,36136,36137,36139],{},[1154,36138,11332],{},[1312,36140,1489],{},[1161,36142,15368],{"mathvariant":1869},[1151,36144,36145,36147],{},[1154,36146,11332],{},[1312,36148,1610],{},[1172,36150,36151],{"encoding":1174},"H_1: \\mu_1 \\neq \\mu_2",[1110,36153,36154],{},[1115,36155,36157],{"className":36156},[1139],[1141,36158,36159],{"xmlns":1143},[1145,36160,36161,36288],{},[1148,36162,36163,36171,36173,36193,36195,36198,36200,36202,36204,36206,36220,36228,36230,36233,36235,36237,36239,36241,36243,36245,36247,36249,36251,36263,36265,36267,36269,36271,36273,36275,36277,36279,36281,36283,36286],{},[1645,36164,36165,36167,36169],{},[1154,36166,1607],{},[1154,36168,1110],{},[1312,36170,1610],{},[1161,36172,1483],{},[1485,36174,36175,36191],{},[1148,36176,36177,36179,36181,36183,36185,36187,36189],{},[1312,36178,3424],{},[1161,36180,12547],{},[1312,36182,4831],{},[1161,36184,3835],{},[1312,36186,4850],{},[1161,36188,12547],{},[1312,36190,25880],{},[1312,36192,8521],{},[1161,36194,1483],{},[1312,36196,36197],{},"20,05",[1161,36199,1199],{"separator":1121},[1516,36201],{"width":1518},[1154,36203,1807],{},[1161,36205,1483],{},[1485,36207,36208,36216],{},[1148,36209,36210,36212,36214],{},[1312,36211,8126],{},[1161,36213,1623],{},[1312,36215,4847],{},[1678,36217,36218],{},[1312,36219,36197],{},[1678,36221,36222],{},[1485,36223,36224,36226],{},[1312,36225,25740],{},[1312,36227,6905],{},[1161,36229,5042],{},[1312,36231,36232],{},"3,651",[1161,36234,1199],{"separator":1121},[1516,36236],{"width":1518},[1154,36238,6143],{},[1161,36240,1483],{},[1161,36242,7845],{"stretchy":1163},[1161,36244,26878],{"stretchy":1163},[1154,36246,1807],{},[1161,36248,26878],{"stretchy":1163},[1161,36250,5198],{},[1151,36252,36253,36255],{},[1154,36254,1807],{},[1148,36256,36257,36259,36261],{},[1312,36258,4585],{},[1161,36260,1199],{"separator":1121},[1312,36262,35999],{},[1161,36264,1164],{"stretchy":1163},[1312,36266,8521],{},[1161,36268,1170],{"stretchy":1163},[1161,36270,7903],{"stretchy":1163},[1161,36272,1483],{},[1161,36274,7845],{"stretchy":1163},[1161,36276,26878],{"stretchy":1163},[1154,36278,1807],{},[1161,36280,26878],{"stretchy":1163},[1161,36282,5198],{},[1312,36284,36285],{},"2,086",[1161,36287,7903],{"stretchy":1163},[1172,36289,36290],{"encoding":1174},"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\\}",[1110,36292,36293,10465,36310,36327],{},[1115,36294,36296],{"className":36295},[1139],[1141,36297,36298],{"xmlns":1143},[1145,36299,36300,36308],{},[1148,36301,36302,36304,36306],{},[1154,36303,1807],{},[1161,36305,11459],{},[1154,36307,6143],{},[1172,36309,32270],{"encoding":1174},[1115,36311,36313],{"className":36312},[1139],[1141,36314,36315],{"xmlns":1143},[1145,36316,36317,36325],{},[1148,36318,36319],{},[1151,36320,36321,36323],{},[1154,36322,6105],{},[1312,36324,4585],{},[1172,36326,6110],{"encoding":1174},": pevnost součástek od obou dodavatelů se statisticky významně liší.",[2020,36329,36331],{"className":2022,"code":36330,"language":71,"meta":2024,"style":2024},"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",[2015,36332,36333,36351,36371,36386,36421,36452,36457,36462],{"__ignoreMap":2024},[1115,36334,36335,36338,36340,36342,36344,36347,36349],{"class":2029,"line":10},[1115,36336,36337],{"class":2032},"s1",[1115,36339,2036],{"class":2035},[1115,36341,4510],{"class":2046},[1115,36343,29038],{"class":2043},[1115,36345,36346],{"class":2032},"n1",[1115,36348,2036],{"class":2035},[1115,36350,33711],{"class":2046},[1115,36352,36353,36356,36358,36361,36363,36366,36368],{"class":2029,"line":27},[1115,36354,36355],{"class":2032},"s2",[1115,36357,2036],{"class":2035},[1115,36359,36360],{"class":2046}," 16",[1115,36362,29038],{"class":2043},[1115,36364,36365],{"class":2032},"n2",[1115,36367,2036],{"class":2035},[1115,36369,36370],{"class":2046}," 12\n",[1115,36372,36373,36376,36378,36381,36383],{"class":2029,"line":148},[1115,36374,36375],{"class":2032},"Fstat",[1115,36377,2036],{"class":2035},[1115,36379,36380],{"class":2032}," s1",[1115,36382,4650],{"class":2035},[1115,36384,36385],{"class":2032}," s2\n",[1115,36387,36388,36391,36393,36396,36398,36401,36403,36406,36408,36410,36412,36415,36417,36419],{"class":2029,"line":111},[1115,36389,36390],{"class":2032},"F_dolni",[1115,36392,2036],{"class":2035},[1115,36394,36395],{"class":2039}," qf",[1115,36397,1164],{"class":2043},[1115,36399,36400],{"class":2046},"0.025",[1115,36402,1199],{"class":2035},[1115,36404,36405],{"class":2032}," n1",[1115,36407,29375],{"class":2035},[1115,36409,5269],{"class":2046},[1115,36411,1199],{"class":2035},[1115,36413,36414],{"class":2032}," n2",[1115,36416,29375],{"class":2035},[1115,36418,5269],{"class":2046},[1115,36420,2185],{"class":2043},[1115,36422,36423,36426,36428,36430,36432,36434,36436,36438,36440,36442,36444,36446,36448,36450],{"class":2029,"line":96},[1115,36424,36425],{"class":2032},"F_horni",[1115,36427,2036],{"class":2035},[1115,36429,36395],{"class":2039},[1115,36431,1164],{"class":2043},[1115,36433,13515],{"class":2046},[1115,36435,1199],{"class":2035},[1115,36437,36405],{"class":2032},[1115,36439,29375],{"class":2035},[1115,36441,5269],{"class":2046},[1115,36443,1199],{"class":2035},[1115,36445,36414],{"class":2032},[1115,36447,29375],{"class":2035},[1115,36449,5269],{"class":2046},[1115,36451,2185],{"class":2043},[1115,36453,36454],{"class":2029,"line":89},[1115,36455,36456],{"class":2032},"Fstat\n",[1115,36458,36459],{"class":2029,"line":82},[1115,36460,36461],{"class":2032},"F_dolni\n",[1115,36463,36464],{"class":2029,"line":75},[1115,36465,36466],{"class":2032},"F_horni\n",[2020,36468,36471],{"className":36469,"code":36470,"language":2349,"meta":2024},[2347],"[1] 1.5625\n[1] 0.2556189\n[1] 3.587899\n",[2015,36472,36470],{"__ignoreMap":2024},[2020,36474,36476],{"className":2022,"code":36475,"language":71,"meta":2024,"style":2024},"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",[2015,36477,36478,36535,36586,36616,36621,36625],{"__ignoreMap":2024},[1115,36479,36480,36483,36485,36488,36490,36492,36494,36496,36498,36500,36502,36504,36506,36508,36510,36512,36514,36517,36519,36521,36523,36525,36527,36529,36531,36533],{"class":2029,"line":10},[1115,36481,36482],{"class":2032},"sp2",[1115,36484,2036],{"class":2035},[1115,36486,36487],{"class":2043}," ((",[1115,36489,36346],{"class":2032},[1115,36491,29375],{"class":2035},[1115,36493,5269],{"class":2046},[1115,36495,2257],{"class":2043},[1115,36497,9082],{"class":2035},[1115,36499,36380],{"class":2032},[1115,36501,22368],{"class":2035},[1115,36503,3997],{"class":2043},[1115,36505,36365],{"class":2032},[1115,36507,29375],{"class":2035},[1115,36509,5269],{"class":2046},[1115,36511,2257],{"class":2043},[1115,36513,9082],{"class":2035},[1115,36515,36516],{"class":2032}," s2",[1115,36518,2257],{"class":2043},[1115,36520,3245],{"class":2035},[1115,36522,3997],{"class":2043},[1115,36524,36346],{"class":2032},[1115,36526,22368],{"class":2035},[1115,36528,36414],{"class":2032},[1115,36530,29375],{"class":2035},[1115,36532,4210],{"class":2046},[1115,36534,2185],{"class":2043},[1115,36536,36537,36539,36541,36543,36545,36547,36550,36552,36554,36556,36558,36560,36562,36564,36566,36568,36570,36572,36574,36576,36578,36580,36582,36584],{"class":2029,"line":27},[1115,36538,1807],{"class":2032},[1115,36540,2036],{"class":2035},[1115,36542,3997],{"class":2043},[1115,36544,8126],{"class":2046},[1115,36546,29375],{"class":2035},[1115,36548,36549],{"class":2046}," 75",[1115,36551,2257],{"class":2043},[1115,36553,3245],{"class":2035},[1115,36555,9044],{"class":2039},[1115,36557,1164],{"class":2043},[1115,36559,36482],{"class":2032},[1115,36561,2257],{"class":2043},[1115,36563,9082],{"class":2035},[1115,36565,9044],{"class":2039},[1115,36567,1164],{"class":2043},[1115,36569,36346],{"class":2032},[1115,36571,22493],{"class":2035},[1115,36573,36414],{"class":2032},[1115,36575,4650],{"class":2035},[1115,36577,3997],{"class":2043},[1115,36579,36346],{"class":2032},[1115,36581,22368],{"class":2035},[1115,36583,36414],{"class":2032},[1115,36585,3694],{"class":2043},[1115,36587,36588,36590,36592,36594,36596,36598,36600,36602,36604,36606,36608,36610,36612,36614],{"class":2029,"line":148},[1115,36589,32377],{"class":2032},[1115,36591,2036],{"class":2035},[1115,36593,32382],{"class":2039},[1115,36595,1164],{"class":2043},[1115,36597,13515],{"class":2046},[1115,36599,1199],{"class":2035},[1115,36601,15222],{"class":2032},[1115,36603,2291],{"class":2035},[1115,36605,36405],{"class":2032},[1115,36607,22368],{"class":2035},[1115,36609,36414],{"class":2032},[1115,36611,29375],{"class":2035},[1115,36613,4210],{"class":2046},[1115,36615,2185],{"class":2043},[1115,36617,36618],{"class":2029,"line":111},[1115,36619,36620],{"class":2032},"sp2\n",[1115,36622,36623],{"class":2029,"line":96},[1115,36624,32407],{"class":2032},[1115,36626,36627],{"class":2029,"line":89},[1115,36628,32412],{"class":2032},[2020,36630,36633],{"className":36631,"code":36632,"language":2349,"meta":2024},[2347],"[1] 20.05\n[1] 3.65107\n[1] 2.085963\n",[2015,36634,36632],{"__ignoreMap":2024},[1110,36636,36637],{},[1393,36638],{"alt":36639,"className":36640,"src":36641},"mask-th-t-dvoustranny",[1242,1397],"\u002Fwiki-assets\u002Fmask-th-t-dvoustranny.png",[1110,36643,36644,36645,1385,36648,36650,36651,36654,36655,1385,36672,8464,36689,36691,36692,36694],{},"V R provede obě kroky ",[2015,36646,36647],{},"var.test()",[2015,36649,31867],{},". Parametr ",[2015,36652,36653],{},"var.equal"," nastavuje volbu mezi ",[1115,36656,36658],{"className":36657},[1139],[1141,36659,36660],{"xmlns":1143},[1145,36661,36662,36670],{},[1148,36663,36664],{},[1151,36665,36666,36668],{},[1154,36667,11542],{},[1312,36669,1489],{},[1172,36671,35645],{"encoding":1174},[1115,36673,36675],{"className":36674},[1139],[1141,36676,36677],{"xmlns":1143},[1145,36678,36679,36687],{},[1148,36680,36681],{},[1151,36682,36683,36685],{},[1154,36684,11542],{},[1312,36686,1610],{},[1172,36688,35663],{"encoding":1174},[2015,36690,13944],{}," znamená předpoklad shodných rozptylů (podle výsledku F-testu), ",[2015,36693,13947],{}," předpoklad rozdílných rozptylů.",[1110,36696,36697,36700],{},[1248,36698,36699],{},"Kabely A\u002FB."," Pevnost v tahu dvou výrobců (MPa, 12 kabelů od každého):",[2020,36702,36704],{"className":2022,"code":36703,"language":71,"meta":2024,"style":2024},"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",[2015,36705,36706,36772,36835,36851],{"__ignoreMap":2024},[1115,36707,36708,36710,36712,36714,36716,36719,36721,36724,36726,36729,36731,36734,36736,36738,36740,36743,36745,36748,36750,36752,36754,36757,36759,36761,36763,36766,36768,36770],{"class":2029,"line":10},[1115,36709,6307],{"class":2032},[1115,36711,2036],{"class":2035},[1115,36713,2040],{"class":2039},[1115,36715,1164],{"class":2043},[1115,36717,36718],{"class":2046},"313",[1115,36720,1199],{"class":2035},[1115,36722,36723],{"class":2046}," 299",[1115,36725,1199],{"class":2035},[1115,36727,36728],{"class":2046}," 315",[1115,36730,1199],{"class":2035},[1115,36732,36733],{"class":2046}," 312",[1115,36735,1199],{"class":2035},[1115,36737,5498],{"class":2046},[1115,36739,1199],{"class":2035},[1115,36741,36742],{"class":2046}," 308",[1115,36744,1199],{"class":2035},[1115,36746,36747],{"class":2046}," 314",[1115,36749,1199],{"class":2035},[1115,36751,4267],{"class":2046},[1115,36753,1199],{"class":2035},[1115,36755,36756],{"class":2046}," 305",[1115,36758,1199],{"class":2035},[1115,36760,5498],{"class":2046},[1115,36762,1199],{"class":2035},[1115,36764,36765],{"class":2046}," 309",[1115,36767,1199],{"class":2035},[1115,36769,36747],{"class":2046},[1115,36771,2185],{"class":2043},[1115,36773,36774,36776,36778,36780,36782,36785,36787,36790,36792,36794,36796,36798,36800,36803,36805,36808,36810,36812,36814,36816,36818,36820,36822,36825,36827,36829,36831,36833],{"class":2029,"line":27},[1115,36775,6352],{"class":2032},[1115,36777,2036],{"class":2035},[1115,36779,2040],{"class":2039},[1115,36781,1164],{"class":2043},[1115,36783,36784],{"class":2046},"307",[1115,36786,1199],{"class":2035},[1115,36788,36789],{"class":2046}," 322",[1115,36791,1199],{"class":2035},[1115,36793,4267],{"class":2046},[1115,36795,1199],{"class":2035},[1115,36797,4267],{"class":2046},[1115,36799,1199],{"class":2035},[1115,36801,36802],{"class":2046}," 311",[1115,36804,1199],{"class":2035},[1115,36806,36807],{"class":2046}," 316",[1115,36809,1199],{"class":2035},[1115,36811,36728],{"class":2046},[1115,36813,1199],{"class":2035},[1115,36815,36747],{"class":2046},[1115,36817,1199],{"class":2035},[1115,36819,36742],{"class":2046},[1115,36821,1199],{"class":2035},[1115,36823,36824],{"class":2046}," 319",[1115,36826,1199],{"class":2035},[1115,36828,4267],{"class":2046},[1115,36830,1199],{"class":2035},[1115,36832,36733],{"class":2046},[1115,36834,2185],{"class":2043},[1115,36836,36837,36840,36842,36844,36846,36849],{"class":2029,"line":148},[1115,36838,36839],{"class":2039},"var.test",[1115,36841,1164],{"class":2043},[1115,36843,6307],{"class":2032},[1115,36845,1199],{"class":2035},[1115,36847,36848],{"class":2032}," B",[1115,36850,2185],{"class":2043},[1115,36852,36853,36855,36857,36859,36861,36863,36865,36868,36870,36872],{"class":2029,"line":111},[1115,36854,31932],{"class":2039},[1115,36856,1164],{"class":2043},[1115,36858,6307],{"class":2032},[1115,36860,1199],{"class":2035},[1115,36862,36848],{"class":2032},[1115,36864,1199],{"class":2035},[1115,36866,36867],{"class":2032}," var.equal",[1115,36869,2291],{"class":2035},[1115,36871,2409],{"class":2046},[1115,36873,2185],{"class":2043},[2020,36875,36878],{"className":36876,"code":36877,"language":2349,"meta":2024},[2347],"    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",[2015,36879,36877],{"__ignoreMap":2024},[1110,36881,36882,36883,2115,36902,36905,36906,36925,36926,36943],{},"F-test shodu rozptylů nezamítá (",[1115,36884,36886],{"className":36885},[1139],[1141,36887,36888],{"xmlns":1143},[1145,36889,36890,36899],{},[1148,36891,36892,36894,36896],{},[1154,36893,1110],{},[1161,36895,1483],{},[1312,36897,36898],{},"0,7776",[1172,36900,36901],{"encoding":1174},"p = 0{,}7776",[2015,36903,36904],{},"var.equal = TRUE",". Výsledný t-test dává ",[1115,36907,36909],{"className":36908},[1139],[1141,36910,36911],{"xmlns":1143},[1145,36912,36913,36922],{},[1148,36914,36915,36917,36919],{},[1154,36916,1110],{},[1161,36918,1483],{},[1312,36920,36921],{},"0,06932",[1172,36923,36924],{"encoding":1174},"p = 0{,}06932"," — na hladině 5 % se ",[1115,36927,36929],{"className":36928},[1139],[1141,36930,36931],{"xmlns":1143},[1145,36932,36933,36941],{},[1148,36934,36935],{},[1151,36936,36937,36939],{},[1154,36938,6105],{},[1312,36940,4585],{},[1172,36942,6110],{"encoding":1174}," nezamítá, ale hodnota je těsně nad hranicí.",[1110,36945,36946],{},[1248,36947,36948],{},"Výšky chlapců a dívek v páté třídě:",[2020,36950,36952],{"className":2022,"code":36951,"language":71,"meta":2024,"style":2024},"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",[2015,36953,36954,37034,37097,37112],{"__ignoreMap":2024},[1115,36955,36956,36959,36961,36963,36965,36968,36970,36972,36974,36977,36979,36982,36984,36987,36989,36992,36994,36996,36998,37000,37002,37004,37006,37008,37010,37013,37015,37018,37020,37023,37025,37027,37029,37032],{"class":2029,"line":10},[1115,36957,36958],{"class":2032},"boys",[1115,36960,2036],{"class":2035},[1115,36962,2040],{"class":2039},[1115,36964,1164],{"class":2043},[1115,36966,36967],{"class":2046},"130",[1115,36969,1199],{"class":2035},[1115,36971,5447],{"class":2046},[1115,36973,1199],{"class":2035},[1115,36975,36976],{"class":2046}," 136",[1115,36978,1199],{"class":2035},[1115,36980,36981],{"class":2046}," 141",[1115,36983,1199],{"class":2035},[1115,36985,36986],{"class":2046}," 139",[1115,36988,1199],{"class":2035},[1115,36990,36991],{"class":2046}," 133",[1115,36993,1199],{"class":2035},[1115,36995,22325],{"class":2046},[1115,36997,1199],{"class":2035},[1115,36999,4282],{"class":2046},[1115,37001,1199],{"class":2035},[1115,37003,36986],{"class":2046},[1115,37005,1199],{"class":2035},[1115,37007,36976],{"class":2046},[1115,37009,1199],{"class":2035},[1115,37011,37012],{"class":2046}," 138",[1115,37014,1199],{"class":2035},[1115,37016,37017],{"class":2046}," 142",[1115,37019,1199],{"class":2035},[1115,37021,37022],{"class":2046}," 127",[1115,37024,1199],{"class":2035},[1115,37026,36986],{"class":2046},[1115,37028,1199],{"class":2035},[1115,37030,37031],{"class":2046}," 147",[1115,37033,2185],{"class":2043},[1115,37035,37036,37039,37041,37043,37045,37047,37049,37051,37053,37056,37058,37061,37063,37066,37068,37070,37072,37074,37076,37078,37080,37082,37084,37087,37089,37091,37093,37095],{"class":2029,"line":27},[1115,37037,37038],{"class":2032},"girls",[1115,37040,2036],{"class":2035},[1115,37042,2040],{"class":2039},[1115,37044,1164],{"class":2043},[1115,37046,25691],{"class":2046},[1115,37048,1199],{"class":2035},[1115,37050,36981],{"class":2046},[1115,37052,1199],{"class":2035},[1115,37054,37055],{"class":2046}," 143",[1115,37057,1199],{"class":2035},[1115,37059,37060],{"class":2046}," 132",[1115,37062,1199],{"class":2035},[1115,37064,37065],{"class":2046}," 146",[1115,37067,1199],{"class":2035},[1115,37069,37065],{"class":2046},[1115,37071,1199],{"class":2035},[1115,37073,4282],{"class":2046},[1115,37075,1199],{"class":2035},[1115,37077,36981],{"class":2046},[1115,37079,1199],{"class":2035},[1115,37081,36981],{"class":2046},[1115,37083,1199],{"class":2035},[1115,37085,37086],{"class":2046}," 131",[1115,37088,1199],{"class":2035},[1115,37090,37017],{"class":2046},[1115,37092,1199],{"class":2035},[1115,37094,36981],{"class":2046},[1115,37096,2185],{"class":2043},[1115,37098,37099,37101,37103,37105,37107,37110],{"class":2029,"line":148},[1115,37100,36839],{"class":2039},[1115,37102,1164],{"class":2043},[1115,37104,36958],{"class":2032},[1115,37106,1199],{"class":2035},[1115,37108,37109],{"class":2032}," girls",[1115,37111,2185],{"class":2043},[1115,37113,37114,37116,37118,37120,37122,37124,37126,37128,37130,37132],{"class":2029,"line":111},[1115,37115,31932],{"class":2039},[1115,37117,1164],{"class":2043},[1115,37119,36958],{"class":2032},[1115,37121,1199],{"class":2035},[1115,37123,37109],{"class":2032},[1115,37125,1199],{"class":2035},[1115,37127,36867],{"class":2032},[1115,37129,2291],{"class":2035},[1115,37131,2409],{"class":2046},[1115,37133,2185],{"class":2043},[2020,37135,37138],{"className":37136,"code":37137,"language":2349,"meta":2024},[2347],"    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",[2015,37139,37137],{"__ignoreMap":2024},[1110,37141,36882,37142,37161,37162,37164,37165,37184],{},[1115,37143,37145],{"className":37144},[1139],[1141,37146,37147],{"xmlns":1143},[1145,37148,37149,37158],{},[1148,37150,37151,37153,37155],{},[1154,37152,1110],{},[1161,37154,1483],{},[1312,37156,37157],{},"0,6977",[1172,37159,37160],{"encoding":1174},"p = 0{,}6977","), t-test s ",[2015,37163,36904],{}," dává ",[1115,37166,37168],{"className":37167},[1139],[1141,37169,37170],{"xmlns":1143},[1145,37171,37172,37181],{},[1148,37173,37174,37176,37178],{},[1154,37175,1110],{},[1161,37177,1483],{},[1312,37179,37180],{},"0,4883",[1172,37182,37183],{"encoding":1174},"p = 0{,}4883",": na hladině 5 % se rozdíl průměrných výšek chlapců a dívek neprokázal.",[1232,37186,37188],{"id":37187},"testy-dobré-shody-a-normalita","Testy dobré shody a normalita",[1110,37190,37191],{},"Testy dobré shody ověřují, zda datový soubor pochází ze základního souboru s určitým typem rozdělení (normální, exponenciální apod.).",[20599,37193,37195],{"id":37194},"kolmogorovův-smirnovův-test","Kolmogorovův-Smirnovův test",[1110,37197,37198,37199,37222,37223,37242],{},"Univerzální test pro spojitá rozdělení. Porovnává empirickou distribuční funkci ",[1115,37200,37202],{"className":37201},[1139],[1141,37203,37204],{"xmlns":1143},[1145,37205,37206,37220],{},[1148,37207,37208,37214,37216,37218],{},[1151,37209,37210,37212],{},[1154,37211,1156],{},[1154,37213,1159],{},[1161,37215,1164],{"stretchy":1163},[1154,37217,1167],{},[1161,37219,1170],{"stretchy":1163},[1172,37221,1175],{"encoding":1174}," s teoretickou distribuční funkcí ",[1115,37224,37226],{"className":37225},[1139],[1141,37227,37228],{"xmlns":1143},[1145,37229,37230,37240],{},[1148,37231,37232,37234,37236,37238],{},[1154,37233,1156],{},[1161,37235,1164],{"stretchy":1163},[1154,37237,1167],{},[1161,37239,1170],{"stretchy":1163},[1172,37241,11773],{"encoding":1174}," testovaného rozdělení.",[1124,37244,37245,37308,37328,37384],{},[1127,37246,37247,37264,37265,1385,37288,37307],{},[1115,37248,37250],{"className":37249},[1139],[1141,37251,37252],{"xmlns":1143},[1145,37253,37254,37262],{},[1148,37255,37256],{},[1151,37257,37258,37260],{},[1154,37259,6105],{},[1312,37261,4585],{},[1172,37263,6110],{"encoding":1174},": odchylky mezi ",[1115,37266,37268],{"className":37267},[1139],[1141,37269,37270],{"xmlns":1143},[1145,37271,37272,37286],{},[1148,37273,37274,37280,37282,37284],{},[1151,37275,37276,37278],{},[1154,37277,1156],{},[1154,37279,1159],{},[1161,37281,1164],{"stretchy":1163},[1154,37283,1167],{},[1161,37285,1170],{"stretchy":1163},[1172,37287,1175],{"encoding":1174},[1115,37289,37291],{"className":37290},[1139],[1141,37292,37293],{"xmlns":1143},[1145,37294,37295,37305],{},[1148,37296,37297,37299,37301,37303],{},[1154,37298,1156],{},[1161,37300,1164],{"stretchy":1163},[1154,37302,1167],{},[1161,37304,1170],{"stretchy":1163},[1172,37306,11773],{"encoding":1174}," jsou náhodné (data mají dané rozdělení).",[1127,37309,37310,37327],{},[1115,37311,37313],{"className":37312},[1139],[1141,37314,37315],{"xmlns":1143},[1145,37316,37317,37325],{},[1148,37318,37319],{},[1151,37320,37321,37323],{},[1154,37322,6105],{},[1312,37324,1489],{},[1172,37326,7508],{"encoding":1174},": data nemají dané rozdělení.",[1127,37329,37330,37331,1176],{},"Testové kritérium: ",[1115,37332,37334],{"className":37333},[1139],[1141,37335,37336],{"xmlns":1143},[1145,37337,37338,37381],{},[1148,37339,37340,37342,37344,37355,37357,37363,37365,37367,37369,37371,37373,37375,37377,37379],{},[1154,37341,12589],{},[1161,37343,1483],{},[1151,37345,37346,37353],{},[1148,37347,37348,37351],{},[1154,37349,37350],{},"sup",[1161,37352,1761],{},[1154,37354,1167],{},[1161,37356,26878],{"stretchy":1163},[1151,37358,37359,37361],{},[1154,37360,1156],{},[1154,37362,1159],{},[1161,37364,1164],{"stretchy":1163},[1154,37366,1167],{},[1161,37368,1170],{"stretchy":1163},[1161,37370,1623],{},[1154,37372,1156],{},[1161,37374,1164],{"stretchy":1163},[1154,37376,1167],{},[1161,37378,1170],{"stretchy":1163},[1161,37380,26878],{"stretchy":1163},[1172,37382,37383],{"encoding":1174},"D = \\sup_x \\lvert F_n(x) - F(x) \\rvert",[1127,37385,7829,37386,37430,37431,37449,37450,1176],{},[1115,37387,37389],{"className":37388},[1139],[1141,37390,37391],{"xmlns":1143},[1145,37392,37393,37427],{},[1148,37394,37395,37401,37403,37405,37407,37409,37411,37413,37419,37421,37423,37425],{},[1151,37396,37397,37399],{},[1154,37398,6143],{},[1154,37400,7874],{},[1161,37402,1483],{},[1161,37404,7845],{"stretchy":1163},[1154,37406,12232],{},[1161,37408,6481],{},[1154,37410,12232],{},[1161,37412,6225],{},[1151,37414,37415,37417],{},[1154,37416,12589],{},[1154,37418,7874],{},[1161,37420,1164],{"stretchy":1163},[1154,37422,1159],{},[1161,37424,1170],{"stretchy":1163},[1161,37426,7903],{"stretchy":1163},[1172,37428,37429],{"encoding":1174},"W_\\alpha = \\{d : d > D_\\alpha(n)\\}","; pro ",[1115,37432,37434],{"className":37433},[1139],[1141,37435,37436],{"xmlns":1143},[1145,37437,37438,37446],{},[1148,37439,37440,37442,37444],{},[1154,37441,1159],{},[1161,37443,6225],{},[1312,37445,25890],{},[1172,37447,37448],{"encoding":1174},"n>30"," se kritická hodnota aproximuje zlomkem ",[1115,37451,37453],{"className":37452},[1139],[1141,37454,37455],{"xmlns":1143},[1145,37456,37457,37468],{},[1148,37458,37459,37462,37464],{},[1312,37460,37461],{},"1,36",[1154,37463,3245],{"mathvariant":1869},[1678,37465,37466],{},[1154,37467,1159],{},[1172,37469,37470],{"encoding":1174},"1{,}36\u002F\\sqrt{n}",[1110,37472,31864,37473,37476,37477,37479,37480,1381,37483,37486],{},[2015,37474,37475],{},"ks.test()",", kde se za ",[2015,37478,11773],{}," dosadí příslušná distribuční funkce (",[2015,37481,37482],{},"\"pnorm\"",[2015,37484,37485],{},"\"pexp\"",", …) s jejími parametry:",[2020,37488,37490],{"className":2022,"code":37489,"language":71,"meta":2024,"style":2024},"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",[2015,37491,37492,37542],{"__ignoreMap":2024},[1115,37493,37494,37496,37498,37500,37502,37504,37506,37508,37510,37512,37514,37516,37518,37520,37522,37524,37526,37528,37530,37532,37534,37536,37538,37540],{"class":2029,"line":10},[1115,37495,32578],{"class":2032},[1115,37497,2036],{"class":2035},[1115,37499,2040],{"class":2039},[1115,37501,1164],{"class":2043},[1115,37503,2047],{"class":2046},[1115,37505,1199],{"class":2035},[1115,37507,2052],{"class":2046},[1115,37509,1199],{"class":2035},[1115,37511,2057],{"class":2046},[1115,37513,1199],{"class":2035},[1115,37515,2062],{"class":2046},[1115,37517,1199],{"class":2035},[1115,37519,2057],{"class":2046},[1115,37521,1199],{"class":2035},[1115,37523,2057],{"class":2046},[1115,37525,1199],{"class":2035},[1115,37527,2075],{"class":2046},[1115,37529,1199],{"class":2035},[1115,37531,2080],{"class":2046},[1115,37533,1199],{"class":2035},[1115,37535,2052],{"class":2046},[1115,37537,1199],{"class":2035},[1115,37539,2052],{"class":2046},[1115,37541,2185],{"class":2043},[1115,37543,37544,37547,37549,37551,37553,37556,37558,37560,37562,37564,37566,37568,37570,37572,37574],{"class":2029,"line":27},[1115,37545,37546],{"class":2039},"ks.test",[1115,37548,1164],{"class":2043},[1115,37550,32578],{"class":2032},[1115,37552,1199],{"class":2035},[1115,37554,37555],{"class":8322}," \"pnorm\"",[1115,37557,1199],{"class":2035},[1115,37559,5274],{"class":2039},[1115,37561,1164],{"class":2043},[1115,37563,32578],{"class":2032},[1115,37565,1170],{"class":2043},[1115,37567,1199],{"class":2035},[1115,37569,13666],{"class":2039},[1115,37571,1164],{"class":2043},[1115,37573,32578],{"class":2032},[1115,37575,3694],{"class":2043},[2020,37577,37580],{"className":37578,"code":37579,"language":2349,"meta":2024},[2347],"    Asymptotic one-sample Kolmogorov-Smirnov test\n\ndata:  x3\nD = 0.18469, p-value = 0.8847\nalternative hypothesis: two-sided\n",[2015,37581,37579],{"__ignoreMap":2024},[1110,37583,37584,37607],{},[1115,37585,37587],{"className":37586},[1139],[1141,37588,37589],{"xmlns":1143},[1145,37590,37591,37604],{},[1148,37592,37593,37595,37597,37600,37602],{},[1154,37594,1110],{},[1161,37596,1483],{},[1312,37598,37599],{},"0,8847",[1161,37601,6225],{},[1312,37603,8460],{},[1172,37605,37606],{"encoding":1174},"p = 0{,}8847 > 0{,}05",": odpad materiálu je slučitelný s normálním rozdělením se stejným průměrem a směrodatnou odchylkou.",[20599,37609,37611],{"id":37610},"shapiro-wilkův-test","Shapiro-Wilkův test",[1110,37613,37614],{},"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.",[1124,37616,37617,37637,37657],{},[1127,37618,37619,37636],{},[1115,37620,37622],{"className":37621},[1139],[1141,37623,37624],{"xmlns":1143},[1145,37625,37626,37634],{},[1148,37627,37628],{},[1151,37629,37630,37632],{},[1154,37631,6105],{},[1312,37633,4585],{},[1172,37635,6110],{"encoding":1174},": data mají normální rozdělení.",[1127,37638,37639,37656],{},[1115,37640,37642],{"className":37641},[1139],[1141,37643,37644],{"xmlns":1143},[1145,37645,37646,37654],{},[1148,37647,37648],{},[1151,37649,37650,37652],{},[1154,37651,6105],{},[1312,37653,1489],{},[1172,37655,7508],{"encoding":1174},": data nemají normální rozdělení.",[1127,37658,37659,37660,37686],{},"Testová statistika ",[1115,37661,37663],{"className":37662},[1139],[1141,37664,37665],{"xmlns":1143},[1145,37666,37667,37683],{},[1148,37668,37669,37671,37673,37675,37677,37679,37681],{},[1154,37670,6143],{},[1161,37672,11459],{},[1161,37674,3816],{"stretchy":1163},[1312,37676,4585],{},[1161,37678,1199],{"separator":1121},[1312,37680,1489],{},[1161,37682,4102],{"stretchy":1163},[1172,37684,37685],{"encoding":1174},"W \\in \\langle 0,1 \\rangle","; hodnoty blízké 1 indikují shodu s normalitou.",[1110,37688,37689,37690,37703,37704,1932,37724,37741,37742,1932,37762,37779],{},"Na rozdíl od ostatních testů v této kapitole se Shapiro-Wilkův test v praxi vyhodnocuje pouze přes p-hodnotu (tabulka kritických hodnot pro ",[1115,37691,37693],{"className":37692},[1139],[1141,37694,37695],{"xmlns":1143},[1145,37696,37697,37701],{},[1148,37698,37699],{},[1154,37700,6143],{},[1172,37702,6143],{"encoding":1174}," se běžně neudává): ",[1115,37705,37707],{"className":37706},[1139],[1141,37708,37709],{"xmlns":1143},[1145,37710,37711,37721],{},[1148,37712,37713,37715,37717,37719],{},[1154,37714,1110],{},[1161,37716,5198],{},[1154,37718,7874],{},[1161,37720,11985],{},[1172,37722,37723],{"encoding":1174},"p \\ge \\alpha \\Rightarrow",[1115,37725,37727],{"className":37726},[1139],[1141,37728,37729],{"xmlns":1143},[1145,37730,37731,37739],{},[1148,37732,37733],{},[1151,37734,37735,37737],{},[1154,37736,6105],{},[1312,37738,4585],{},[1172,37740,6110],{"encoding":1174}," nezamítáme (normalitu lze předpokládat); ",[1115,37743,37745],{"className":37744},[1139],[1141,37746,37747],{"xmlns":1143},[1145,37748,37749,37759],{},[1148,37750,37751,37753,37755,37757],{},[1154,37752,1110],{},[1161,37754,8805],{},[1154,37756,7874],{},[1161,37758,11985],{},[1172,37760,37761],{"encoding":1174},"p \u003C \\alpha \\Rightarrow",[1115,37763,37765],{"className":37764},[1139],[1141,37766,37767],{"xmlns":1143},[1145,37768,37769,37777],{},[1148,37770,37771],{},[1151,37772,37773,37775],{},[1154,37774,6105],{},[1312,37776,4585],{},[1172,37778,6110],{"encoding":1174}," zamítáme (předpoklad normality je porušen).",[2020,37781,37783],{"className":2022,"code":37782,"language":71,"meta":2024,"style":2024},"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",[2015,37784,37785,37839],{"__ignoreMap":2024},[1115,37786,37787,37789,37791,37793,37795,37797,37799,37801,37803,37805,37807,37809,37811,37813,37815,37817,37819,37821,37823,37825,37827,37829,37831,37833,37835,37837],{"class":2029,"line":10},[1115,37788,32446],{"class":2032},[1115,37790,2036],{"class":2035},[1115,37792,2040],{"class":2039},[1115,37794,1164],{"class":2043},[1115,37796,32455],{"class":2046},[1115,37798,1199],{"class":2035},[1115,37800,32460],{"class":2046},[1115,37802,1199],{"class":2035},[1115,37804,32465],{"class":2046},[1115,37806,1199],{"class":2035},[1115,37808,32470],{"class":2046},[1115,37810,1199],{"class":2035},[1115,37812,32475],{"class":2046},[1115,37814,1199],{"class":2035},[1115,37816,32480],{"class":2046},[1115,37818,1199],{"class":2035},[1115,37820,32470],{"class":2046},[1115,37822,1199],{"class":2035},[1115,37824,32489],{"class":2046},[1115,37826,1199],{"class":2035},[1115,37828,32475],{"class":2046},[1115,37830,1199],{"class":2035},[1115,37832,32498],{"class":2046},[1115,37834,1199],{"class":2035},[1115,37836,32470],{"class":2046},[1115,37838,2185],{"class":2043},[1115,37840,37841,37843,37845,37847],{"class":2029,"line":27},[1115,37842,21429],{"class":2039},[1115,37844,1164],{"class":2043},[1115,37846,32446],{"class":2032},[1115,37848,2185],{"class":2043},[2020,37850,37853],{"className":37851,"code":37852,"language":2349,"meta":2024},[2347],"    Shapiro-Wilk normality test\n\ndata:  x2\nW = 0.96022, p-value = 0.7744\n",[2015,37854,37852],{"__ignoreMap":2024},[1110,37856,37857,37858,37877],{},"U dat o životnosti baterií se normalita nezamítá (",[1115,37859,37861],{"className":37860},[1139],[1141,37862,37863],{"xmlns":1143},[1145,37864,37865,37874],{},[1148,37866,37867,37869,37871],{},[1154,37868,1110],{},[1161,37870,1483],{},[1312,37872,37873],{},"0,7744",[1172,37875,37876],{"encoding":1174},"p = 0{,}7744","), předpoklad t-testu je tedy splněn.",[1103,37879,37881,37888,37891,38258,38264],{"className":37880,"dataCallout":2447},[1106,2446],[1110,37882,37884,37887],{"className":37883},[1113],[1115,37885],{"className":37886,"ariaHidden":1121},[1118,2454,1120],"Příklad: Doba do poruchy výrobku",[1110,37889,37890],{},"Zkoušky životnosti nového výrobku daly soubor 68 hodnot doby do poruchy (v minutách). Odhadněte charakteristiky a zákon rozdělení.",[2020,37892,37894],{"className":2022,"code":37893,"language":71,"meta":2024,"style":2024},"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",[2015,37895,37896,37987,38065,38153,38187,38197,38207,38217,38227],{"__ignoreMap":2024},[1115,37897,37898,37900,37902,37904,37906,37908,37910,37912,37914,37916,37918,37920,37922,37924,37926,37928,37930,37932,37934,37936,37938,37940,37942,37944,37946,37949,37951,37953,37955,37957,37959,37961,37963,37965,37967,37969,37971,37973,37975,37977,37979,37981,37983,37985],{"class":2029,"line":10},[1115,37899,4176],{"class":2032},[1115,37901,2036],{"class":2035},[1115,37903,2040],{"class":2039},[1115,37905,1164],{"class":2043},[1115,37907,4185],{"class":2046},[1115,37909,1199],{"class":2035},[1115,37911,4190],{"class":2046},[1115,37913,1199],{"class":2035},[1115,37915,4195],{"class":2046},[1115,37917,1199],{"class":2035},[1115,37919,4200],{"class":2046},[1115,37921,1199],{"class":2035},[1115,37923,4205],{"class":2046},[1115,37925,1199],{"class":2035},[1115,37927,4210],{"class":2046},[1115,37929,1199],{"class":2035},[1115,37931,4215],{"class":2046},[1115,37933,1199],{"class":2035},[1115,37935,4220],{"class":2046},[1115,37937,1199],{"class":2035},[1115,37939,4225],{"class":2046},[1115,37941,1199],{"class":2035},[1115,37943,4230],{"class":2046},[1115,37945,1199],{"class":2035},[1115,37947,37948],{"class":2046}," 367",[1115,37950,1199],{"class":2035},[1115,37952,4242],{"class":2046},[1115,37954,1199],{"class":2035},[1115,37956,4247],{"class":2046},[1115,37958,1199],{"class":2035},[1115,37960,4252],{"class":2046},[1115,37962,1199],{"class":2035},[1115,37964,4257],{"class":2046},[1115,37966,1199],{"class":2035},[1115,37968,4262],{"class":2046},[1115,37970,1199],{"class":2035},[1115,37972,4267],{"class":2046},[1115,37974,1199],{"class":2035},[1115,37976,4272],{"class":2046},[1115,37978,1199],{"class":2035},[1115,37980,4277],{"class":2046},[1115,37982,1199],{"class":2035},[1115,37984,4282],{"class":2046},[1115,37986,2688],{"class":2035},[1115,37988,37989,37991,37993,37995,37997,37999,38001,38003,38005,38007,38009,38011,38013,38015,38017,38019,38021,38023,38025,38027,38029,38031,38033,38035,38037,38039,38041,38043,38045,38047,38049,38051,38053,38055,38057,38059,38061,38063],{"class":2029,"line":27},[1115,37990,4289],{"class":2046},[1115,37992,1199],{"class":2035},[1115,37994,4294],{"class":2046},[1115,37996,1199],{"class":2035},[1115,37998,4299],{"class":2046},[1115,38000,1199],{"class":2035},[1115,38002,4304],{"class":2046},[1115,38004,1199],{"class":2035},[1115,38006,4309],{"class":2046},[1115,38008,1199],{"class":2035},[1115,38010,4257],{"class":2046},[1115,38012,1199],{"class":2035},[1115,38014,4318],{"class":2046},[1115,38016,1199],{"class":2035},[1115,38018,4215],{"class":2046},[1115,38020,1199],{"class":2035},[1115,38022,4327],{"class":2046},[1115,38024,1199],{"class":2035},[1115,38026,4332],{"class":2046},[1115,38028,1199],{"class":2035},[1115,38030,5447],{"class":2046},[1115,38032,1199],{"class":2035},[1115,38034,4344],{"class":2046},[1115,38036,1199],{"class":2035},[1115,38038,4349],{"class":2046},[1115,38040,1199],{"class":2035},[1115,38042,4242],{"class":2046},[1115,38044,1199],{"class":2035},[1115,38046,4358],{"class":2046},[1115,38048,1199],{"class":2035},[1115,38050,4363],{"class":2046},[1115,38052,1199],{"class":2035},[1115,38054,4368],{"class":2046},[1115,38056,1199],{"class":2035},[1115,38058,4373],{"class":2046},[1115,38060,1199],{"class":2035},[1115,38062,4378],{"class":2046},[1115,38064,2688],{"class":2035},[1115,38066,38067,38069,38071,38074,38076,38078,38080,38082,38084,38086,38088,38090,38092,38094,38096,38098,38100,38102,38104,38106,38108,38110,38112,38115,38117,38119,38121,38123,38125,38127,38129,38131,38133,38135,38137,38139,38141,38143,38145,38147,38149,38151],{"class":2029,"line":148},[1115,38068,4490],{"class":2046},[1115,38070,1199],{"class":2035},[1115,38072,38073],{"class":2046}," 74",[1115,38075,1199],{"class":2035},[1115,38077,4395],{"class":2046},[1115,38079,1199],{"class":2035},[1115,38081,4400],{"class":2046},[1115,38083,1199],{"class":2035},[1115,38085,4405],{"class":2046},[1115,38087,1199],{"class":2035},[1115,38089,4410],{"class":2046},[1115,38091,1199],{"class":2035},[1115,38093,4327],{"class":2046},[1115,38095,1199],{"class":2035},[1115,38097,4419],{"class":2046},[1115,38099,1199],{"class":2035},[1115,38101,4424],{"class":2046},[1115,38103,1199],{"class":2035},[1115,38105,4429],{"class":2046},[1115,38107,1199],{"class":2035},[1115,38109,4434],{"class":2046},[1115,38111,1199],{"class":2035},[1115,38113,38114],{"class":2046}," 194",[1115,38116,1199],{"class":2035},[1115,38118,4446],{"class":2046},[1115,38120,1199],{"class":2035},[1115,38122,4451],{"class":2046},[1115,38124,1199],{"class":2035},[1115,38126,4456],{"class":2046},[1115,38128,1199],{"class":2035},[1115,38130,4461],{"class":2046},[1115,38132,1199],{"class":2035},[1115,38134,4410],{"class":2046},[1115,38136,1199],{"class":2035},[1115,38138,4225],{"class":2046},[1115,38140,1199],{"class":2035},[1115,38142,4210],{"class":2046},[1115,38144,1199],{"class":2035},[1115,38146,4478],{"class":2046},[1115,38148,1199],{"class":2035},[1115,38150,4483],{"class":2046},[1115,38152,2688],{"class":2035},[1115,38154,38155,38157,38159,38161,38163,38165,38167,38169,38171,38173,38175,38177,38179,38181,38183,38185],{"class":2029,"line":111},[1115,38156,4490],{"class":2046},[1115,38158,1199],{"class":2035},[1115,38160,4495],{"class":2046},[1115,38162,1199],{"class":2035},[1115,38164,4500],{"class":2046},[1115,38166,1199],{"class":2035},[1115,38168,4505],{"class":2046},[1115,38170,1199],{"class":2035},[1115,38172,4510],{"class":2046},[1115,38174,1199],{"class":2035},[1115,38176,4515],{"class":2046},[1115,38178,1199],{"class":2035},[1115,38180,4242],{"class":2046},[1115,38182,1199],{"class":2035},[1115,38184,4524],{"class":2046},[1115,38186,2185],{"class":2043},[1115,38188,38189,38191,38193,38195],{"class":2029,"line":96},[1115,38190,2201],{"class":2039},[1115,38192,1164],{"class":2043},[1115,38194,4176],{"class":2032},[1115,38196,2185],{"class":2043},[1115,38198,38199,38201,38203,38205],{"class":2029,"line":89},[1115,38200,2223],{"class":2039},[1115,38202,1164],{"class":2043},[1115,38204,4176],{"class":2032},[1115,38206,2185],{"class":2043},[1115,38208,38209,38211,38213,38215],{"class":2029,"line":82},[1115,38210,2937],{"class":2039},[1115,38212,1164],{"class":2043},[1115,38214,4176],{"class":2032},[1115,38216,2185],{"class":2043},[1115,38218,38219,38221,38223,38225],{"class":2029,"line":75},[1115,38220,21429],{"class":2039},[1115,38222,1164],{"class":2043},[1115,38224,4176],{"class":2032},[1115,38226,2185],{"class":2043},[1115,38228,38229,38231,38233,38235,38237,38240,38242,38244,38246,38248,38250,38252,38254,38256],{"class":2029,"line":2322},[1115,38230,37546],{"class":2039},[1115,38232,1164],{"class":2043},[1115,38234,4176],{"class":2032},[1115,38236,1199],{"class":2035},[1115,38238,38239],{"class":8322}," \"pexp\"",[1115,38241,1199],{"class":2035},[1115,38243,14483],{"class":2032},[1115,38245,2291],{"class":2035},[1115,38247,5269],{"class":2046},[1115,38249,4650],{"class":2035},[1115,38251,5274],{"class":2039},[1115,38253,1164],{"class":2043},[1115,38255,4176],{"class":2032},[1115,38257,3694],{"class":2043},[2020,38259,38262],{"className":38260,"code":38261,"language":2349,"meta":2024},[2347],"[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",[2015,38263,38261],{"__ignoreMap":2024},[1110,38265,38266,38267,38286,38287,38304,38305,38324],{},"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 (",[1115,38268,38270],{"className":38269},[1139],[1141,38271,38272],{"xmlns":1143},[1145,38273,38274,38283],{},[1148,38275,38276,38278,38280],{},[1154,38277,1110],{},[1161,38279,8805],{},[1312,38281,38282],{},"0,0001",[1172,38284,38285],{"encoding":1174},"p \u003C 0{,}0001","), zatímco Kolmogorov-Smirnovův test proti exponenciálnímu rozdělení se střední hodnotou ",[1115,38288,38290],{"className":38289},[1139],[1141,38291,38292],{"xmlns":1143},[1145,38293,38294,38302],{},[1148,38295,38296],{},[1474,38297,38298,38300],{"accent":1121},[1154,38299,1167],{},[1161,38301,1480],{},[1172,38303,25419],{"encoding":1174}," shodu nezamítá (",[1115,38306,38308],{"className":38307},[1139],[1141,38309,38310],{"xmlns":1143},[1145,38311,38312,38321],{},[1148,38313,38314,38316,38318],{},[1154,38315,1110],{},[1161,38317,1483],{},[1312,38319,38320],{},"0,8421",[1172,38322,38323],{"encoding":1174},"p = 0{,}8421","): data odpovídají spíše exponenciálnímu rozdělení než normálnímu.",[1110,38326,38327],{},[1393,38328],{"alt":38329,"className":38330,"src":38331},"mask-th-exponencialni-shoda",[1242,1397],"\u002Fwiki-assets\u002Fmask-th-exponencialni-shoda.png",[1232,38333,38335],{"id":38334},"neparametrické-testy","Neparametrické testy",[1110,38337,38338,38339,3997,38341,38365],{},"Když předpoklad normality neplatí, nahrazují t-testy jejich neparametrické obdoby — Wilcoxonovy testy posuzují ",[1248,38340,1583],{},[1115,38342,38344],{"className":38343},[1139],[1141,38345,38346],{"xmlns":1143},[1145,38347,38348,38362],{},[1148,38349,38350],{},[1151,38351,38352,38354],{},[1154,38353,1167],{},[1148,38355,38356,38358,38360],{},[1312,38357,4585],{},[1161,38359,1199],{"separator":1121},[1312,38361,3415],{},[1172,38363,38364],{"encoding":1174},"x_{0,5}",") místo střední hodnoty a nevyžadují normalitu dat.",[20599,38367,38369],{"id":38368},"wilcoxonovy-testy","Wilcoxonovy testy",[3350,38371,38372,38417],{},[3353,38373,38374],{},[3356,38375,38376,38395,38414],{},[3359,38377,38378],{},[1115,38379,38381],{"className":38380},[1139],[1141,38382,38383],{"xmlns":1143},[1145,38384,38385,38393],{},[1148,38386,38387],{},[1151,38388,38389,38391],{},[1154,38390,6105],{},[1312,38392,4585],{},[1172,38394,6110],{"encoding":1174},[3359,38396,38397],{},[1115,38398,38400],{"className":38399},[1139],[1141,38401,38402],{"xmlns":1143},[1145,38403,38404,38412],{},[1148,38405,38406],{},[1151,38407,38408,38410],{},[1154,38409,6105],{},[1312,38411,1489],{},[1172,38413,7508],{"encoding":1174},[3359,38415,38416],{},"Příkaz v R",[3389,38418,38419,38486,38553],{},[3356,38420,38421,38451,38481],{},[3394,38422,38423],{},[1115,38424,38426],{"className":38425},[1139],[1141,38427,38428],{"xmlns":1143},[1145,38429,38430,38448],{},[1148,38431,38432,38444,38446],{},[1151,38433,38434,38436],{},[1154,38435,1167],{},[1148,38437,38438,38440,38442],{},[1312,38439,4585],{},[1161,38441,1199],{"separator":1121},[1312,38443,3415],{},[1161,38445,11177],{},[1154,38447,1784],{},[1172,38449,38450],{"encoding":1174},"x_{0,5} \\le c",[3394,38452,38453],{},[1115,38454,38456],{"className":38455},[1139],[1141,38457,38458],{"xmlns":1143},[1145,38459,38460,38478],{},[1148,38461,38462,38474,38476],{},[1151,38463,38464,38466],{},[1154,38465,1167],{},[1148,38467,38468,38470,38472],{},[1312,38469,4585],{},[1161,38471,1199],{"separator":1121},[1312,38473,3415],{},[1161,38475,6225],{},[1154,38477,1784],{},[1172,38479,38480],{"encoding":1174},"x_{0,5} > c",[3394,38482,38483],{},[2015,38484,38485],{},"wilcox.test(x, alternative = \"greater\", mu = c)",[3356,38487,38488,38518,38548],{},[3394,38489,38490],{},[1115,38491,38493],{"className":38492},[1139],[1141,38494,38495],{"xmlns":1143},[1145,38496,38497,38515],{},[1148,38498,38499,38511,38513],{},[1151,38500,38501,38503],{},[1154,38502,1167],{},[1148,38504,38505,38507,38509],{},[1312,38506,4585],{},[1161,38508,1199],{"separator":1121},[1312,38510,3415],{},[1161,38512,1483],{},[1154,38514,1784],{},[1172,38516,38517],{"encoding":1174},"x_{0,5} = c",[3394,38519,38520],{},[1115,38521,38523],{"className":38522},[1139],[1141,38524,38525],{"xmlns":1143},[1145,38526,38527,38545],{},[1148,38528,38529,38541,38543],{},[1151,38530,38531,38533],{},[1154,38532,1167],{},[1148,38534,38535,38537,38539],{},[1312,38536,4585],{},[1161,38538,1199],{"separator":1121},[1312,38540,3415],{},[1161,38542,15368],{"mathvariant":1869},[1154,38544,1784],{},[1172,38546,38547],{"encoding":1174},"x_{0,5} \\neq c",[3394,38549,38550],{},[2015,38551,38552],{},"wilcox.test(x, alternative = \"two.sided\", mu = c)",[3356,38554,38555,38585,38615],{},[3394,38556,38557],{},[1115,38558,38560],{"className":38559},[1139],[1141,38561,38562],{"xmlns":1143},[1145,38563,38564,38582],{},[1148,38565,38566,38578,38580],{},[1151,38567,38568,38570],{},[1154,38569,1167],{},[1148,38571,38572,38574,38576],{},[1312,38573,4585],{},[1161,38575,1199],{"separator":1121},[1312,38577,3415],{},[1161,38579,5198],{},[1154,38581,1784],{},[1172,38583,38584],{"encoding":1174},"x_{0,5} \\ge c",[3394,38586,38587],{},[1115,38588,38590],{"className":38589},[1139],[1141,38591,38592],{"xmlns":1143},[1145,38593,38594,38612],{},[1148,38595,38596,38608,38610],{},[1151,38597,38598,38600],{},[1154,38599,1167],{},[1148,38601,38602,38604,38606],{},[1312,38603,4585],{},[1161,38605,1199],{"separator":1121},[1312,38607,3415],{},[1161,38609,8805],{},[1154,38611,1784],{},[1172,38613,38614],{"encoding":1174},"x_{0,5} \u003C c",[3394,38616,38617],{},[2015,38618,38619],{},"wilcox.test(x, alternative = \"less\", mu = c)",[1110,38621,38622,38625,38626,1176],{},[6023,38623,38624],{},"Jednovýběrový Wilcoxonův test"," (obdoba t-testu) posuzuje odchylku mediánu od konstanty ",[1115,38627,38629],{"className":38628},[1139],[1141,38630,38631],{"xmlns":1143},[1145,38632,38633,38637],{},[1148,38634,38635],{},[1154,38636,1784],{},[1172,38638,1784],{"encoding":1174},[1110,38640,38641,38644,38645,13264,38683,38696,38697,1176],{},[6023,38642,38643],{},"Jednovýběrový Wilcoxonův test na diferencích"," (obdoba párového t-testu) posuzuje odchylku mediánu rozdílu ",[1115,38646,38648],{"className":38647},[1139],[1141,38649,38650],{"xmlns":1143},[1145,38651,38652,38680],{},[1148,38653,38654,38666,38668],{},[1151,38655,38656,38658],{},[1154,38657,1167],{},[1148,38659,38660,38662,38664],{},[1312,38661,4585],{},[1161,38663,1199],{"separator":1121},[1312,38665,3415],{},[1161,38667,1623],{},[1151,38669,38670,38672],{},[1154,38671,1528],{},[1148,38673,38674,38676,38678],{},[1312,38675,4585],{},[1161,38677,1199],{"separator":1121},[1312,38679,3415],{},[1172,38681,38682],{"encoding":1174},"x_{0,5}-y_{0,5}",[1115,38684,38686],{"className":38685},[1139],[1141,38687,38688],{"xmlns":1143},[1145,38689,38690,38694],{},[1148,38691,38692],{},[1154,38693,1784],{},[1172,38695,1784],{"encoding":1174},"; v R se volá se stejnými argumenty jako výše a navíc ",[2015,38698,38699],{},"paired = TRUE",[1110,38701,38702,38705,38706,38708],{},[6023,38703,38704],{},"Dvouvýběrový Wilcoxonův test"," (obdoba dvouvýběrového t-testu) posuzuje odchylku mediánů dvou nezávislých výběrů; argument ",[2015,38707,29302],{}," odpadá. Pro výšky chlapců a dívek z příkladu výše:",[2020,38710,38712],{"className":2022,"code":38711,"language":71,"meta":2024,"style":2024},"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",[2015,38713,38714,38784,38842],{"__ignoreMap":2024},[1115,38715,38716,38718,38720,38722,38724,38726,38728,38730,38732,38734,38736,38738,38740,38742,38744,38746,38748,38750,38752,38754,38756,38758,38760,38762,38764,38766,38768,38770,38772,38774,38776,38778,38780,38782],{"class":2029,"line":10},[1115,38717,36958],{"class":2032},[1115,38719,2036],{"class":2035},[1115,38721,2040],{"class":2039},[1115,38723,1164],{"class":2043},[1115,38725,36967],{"class":2046},[1115,38727,1199],{"class":2035},[1115,38729,5447],{"class":2046},[1115,38731,1199],{"class":2035},[1115,38733,36976],{"class":2046},[1115,38735,1199],{"class":2035},[1115,38737,36981],{"class":2046},[1115,38739,1199],{"class":2035},[1115,38741,36986],{"class":2046},[1115,38743,1199],{"class":2035},[1115,38745,36991],{"class":2046},[1115,38747,1199],{"class":2035},[1115,38749,22325],{"class":2046},[1115,38751,1199],{"class":2035},[1115,38753,4282],{"class":2046},[1115,38755,1199],{"class":2035},[1115,38757,36986],{"class":2046},[1115,38759,1199],{"class":2035},[1115,38761,36976],{"class":2046},[1115,38763,1199],{"class":2035},[1115,38765,37012],{"class":2046},[1115,38767,1199],{"class":2035},[1115,38769,37017],{"class":2046},[1115,38771,1199],{"class":2035},[1115,38773,37022],{"class":2046},[1115,38775,1199],{"class":2035},[1115,38777,36986],{"class":2046},[1115,38779,1199],{"class":2035},[1115,38781,37031],{"class":2046},[1115,38783,2185],{"class":2043},[1115,38785,38786,38788,38790,38792,38794,38796,38798,38800,38802,38804,38806,38808,38810,38812,38814,38816,38818,38820,38822,38824,38826,38828,38830,38832,38834,38836,38838,38840],{"class":2029,"line":27},[1115,38787,37038],{"class":2032},[1115,38789,2036],{"class":2035},[1115,38791,2040],{"class":2039},[1115,38793,1164],{"class":2043},[1115,38795,25691],{"class":2046},[1115,38797,1199],{"class":2035},[1115,38799,36981],{"class":2046},[1115,38801,1199],{"class":2035},[1115,38803,37055],{"class":2046},[1115,38805,1199],{"class":2035},[1115,38807,37060],{"class":2046},[1115,38809,1199],{"class":2035},[1115,38811,37065],{"class":2046},[1115,38813,1199],{"class":2035},[1115,38815,37065],{"class":2046},[1115,38817,1199],{"class":2035},[1115,38819,4282],{"class":2046},[1115,38821,1199],{"class":2035},[1115,38823,36981],{"class":2046},[1115,38825,1199],{"class":2035},[1115,38827,36981],{"class":2046},[1115,38829,1199],{"class":2035},[1115,38831,37086],{"class":2046},[1115,38833,1199],{"class":2035},[1115,38835,37017],{"class":2046},[1115,38837,1199],{"class":2035},[1115,38839,36981],{"class":2046},[1115,38841,2185],{"class":2043},[1115,38843,38844,38847,38849,38851,38853,38855,38857,38859,38861,38863],{"class":2029,"line":148},[1115,38845,38846],{"class":2039},"wilcox.test",[1115,38848,1164],{"class":2043},[1115,38850,36958],{"class":2032},[1115,38852,1199],{"class":2035},[1115,38854,37109],{"class":2032},[1115,38856,1199],{"class":2035},[1115,38858,31949],{"class":2032},[1115,38860,2291],{"class":2035},[1115,38862,31954],{"class":8322},[1115,38864,2185],{"class":2043},[2020,38866,38869],{"className":38867,"code":38868,"language":2349,"meta":2024},[2347],"    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",[2015,38870,38868],{"__ignoreMap":2024},[1110,38872,38873,38896],{},[1115,38874,38876],{"className":38875},[1139],[1141,38877,38878],{"xmlns":1143},[1145,38879,38880,38893],{},[1148,38881,38882,38884,38886,38889,38891],{},[1154,38883,1110],{},[1161,38885,1483],{},[1312,38887,38888],{},"0,315",[1161,38890,6225],{},[1312,38892,8460],{},[1172,38894,38895],{"encoding":1174},"p = 0{,}315 > 0{,}05",": mediány výšek chlapců a dívek se statisticky významně neliší — stejný závěr jako u dvouvýběrového t-testu.",[1103,38898,38900,38907,38929,39040,39046],{"className":38899,"dataCallout":2447},[1106,2446],[1110,38901,38903,38906],{"className":38902},[1113],[1115,38904],{"className":38905,"ariaHidden":1121},[1118,2454,1120],"Příklad: Realitní odhadci — neparametrická alternativa",[1110,38908,38909,38910,38928],{},"U odhadů cen z párového t-testu výše normalita diferencí neplatí (",[1115,38911,38913],{"className":38912},[1139],[1141,38914,38915],{"xmlns":1143},[1145,38916,38917,38925],{},[1148,38918,38919,38921,38923],{},[1154,38920,1110],{},[1161,38922,1483],{},[1312,38924,34002],{},[1172,38926,38927],{"encoding":1174},"p = 0{,}03203","). Správnou volbou je párový Wilcoxonův test:",[2020,38930,38932],{"className":2022,"code":38931,"language":71,"meta":2024,"style":2024},"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",[2015,38933,38934,38976,39018],{"__ignoreMap":2024},[1115,38935,38936,38938,38940,38942,38944,38946,38948,38950,38952,38954,38956,38958,38960,38962,38964,38966,38968,38970,38972,38974],{"class":2029,"line":10},[1115,38937,33805],{"class":2032},[1115,38939,2036],{"class":2035},[1115,38941,2040],{"class":2039},[1115,38943,1164],{"class":2043},[1115,38945,33814],{"class":2046},[1115,38947,1199],{"class":2035},[1115,38949,33819],{"class":2046},[1115,38951,1199],{"class":2035},[1115,38953,33824],{"class":2046},[1115,38955,1199],{"class":2035},[1115,38957,33829],{"class":2046},[1115,38959,1199],{"class":2035},[1115,38961,33834],{"class":2046},[1115,38963,1199],{"class":2035},[1115,38965,33839],{"class":2046},[1115,38967,1199],{"class":2035},[1115,38969,33844],{"class":2046},[1115,38971,1199],{"class":2035},[1115,38973,33849],{"class":2046},[1115,38975,2185],{"class":2043},[1115,38977,38978,38980,38982,38984,38986,38988,38990,38992,38994,38996,38998,39000,39002,39004,39006,39008,39010,39012,39014,39016],{"class":2029,"line":27},[1115,38979,33856],{"class":2032},[1115,38981,2036],{"class":2035},[1115,38983,2040],{"class":2039},[1115,38985,1164],{"class":2043},[1115,38987,33865],{"class":2046},[1115,38989,1199],{"class":2035},[1115,38991,33870],{"class":2046},[1115,38993,1199],{"class":2035},[1115,38995,33875],{"class":2046},[1115,38997,1199],{"class":2035},[1115,38999,33880],{"class":2046},[1115,39001,1199],{"class":2035},[1115,39003,33885],{"class":2046},[1115,39005,1199],{"class":2035},[1115,39007,33890],{"class":2046},[1115,39009,1199],{"class":2035},[1115,39011,33895],{"class":2046},[1115,39013,1199],{"class":2035},[1115,39015,33900],{"class":2046},[1115,39017,2185],{"class":2043},[1115,39019,39020,39022,39024,39026,39028,39030,39032,39034,39036,39038],{"class":2029,"line":148},[1115,39021,38846],{"class":2039},[1115,39023,1164],{"class":2043},[1115,39025,33805],{"class":2032},[1115,39027,1199],{"class":2035},[1115,39029,33915],{"class":2032},[1115,39031,1199],{"class":2035},[1115,39033,33920],{"class":2032},[1115,39035,2291],{"class":2035},[1115,39037,2409],{"class":2046},[1115,39039,2185],{"class":2043},[2020,39041,39044],{"className":39042,"code":39043,"language":2349,"meta":2024},[2347],"    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",[2015,39045,39043],{"__ignoreMap":2024},[1110,39047,39048,39071],{},[1115,39049,39051],{"className":39050},[1139],[1141,39052,39053],{"xmlns":1143},[1145,39054,39055,39068],{},[1148,39056,39057,39059,39061,39064,39066],{},[1154,39058,1110],{},[1161,39060,1483],{},[1312,39062,39063],{},"0,1484",[1161,39065,6225],{},[1312,39067,8460],{},[1172,39069,39070],{"encoding":1174},"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.",[20599,39073,39075],{"id":39074},"kruskalův-wallisův-test","Kruskalův-Wallisův test",[1110,39077,39078,39079,39096],{},"Zobecnění dvouvýběrového Wilcoxonova testu, neparametrická obdoba analýzy rozptylu jednoduchého třídění. ",[1115,39080,39082],{"className":39081},[1139],[1141,39083,39084],{"xmlns":1143},[1145,39085,39086,39094],{},[1148,39087,39088],{},[1151,39089,39090,39092],{},[1154,39091,6105],{},[1312,39093,4585],{},[1172,39095,6110],{"encoding":1174},": všechny výběry pocházejí ze stejného rozdělení.",[2020,39098,39100],{"className":2022,"code":39099,"language":71,"meta":2024,"style":2024},"kruskal.test(kvantitativní_proměnná ~ faktor, data = soubor)\n",[2015,39101,39102],{"__ignoreMap":2024},[1115,39103,39104,39107,39109,39112,39114,39117,39119,39121,39123,39126],{"class":2029,"line":10},[1115,39105,39106],{"class":2039},"kruskal.test",[1115,39108,1164],{"class":2043},[1115,39110,39111],{"class":2032},"kvantitativní_proměnná",[1115,39113,20710],{"class":2035},[1115,39115,39116],{"class":2032}," faktor",[1115,39118,1199],{"class":2035},[1115,39120,24019],{"class":2032},[1115,39122,2291],{"class":2035},[1115,39124,39125],{"class":2032}," soubor",[1115,39127,2185],{"class":2043},[20599,39129,39131],{"id":39130},"mediánový-test","Mediánový test",[1110,39133,39134,39135,39152,39153,6481],{},"Má stejný účel jako Kruskalův-Wallisův test (obdoba analýzy rozptylu jednoduchého třídění, ",[1115,39136,39138],{"className":39137},[1139],[1141,39139,39140],{"xmlns":1143},[1145,39141,39142,39150],{},[1148,39143,39144],{},[1151,39145,39146,39148],{},[1154,39147,6105],{},[1312,39149,4585],{},[1172,39151,6110],{"encoding":1174},": všechny výběry pocházejí ze stejného rozdělení) a je součástí balíčku ",[2015,39154,39155],{},"agricolae",[2020,39157,39159],{"className":2022,"code":39158,"language":71,"meta":2024,"style":2024},"library(agricolae)\nMedian.test(kvantitativní_proměnná, faktor)\n",[2015,39160,39161,39171],{"__ignoreMap":2024},[1115,39162,39163,39165,39167,39169],{"class":2029,"line":10},[1115,39164,21249],{"class":2035},[1115,39166,1164],{"class":2043},[1115,39168,39155],{"class":2032},[1115,39170,2185],{"class":2043},[1115,39172,39173,39176,39178,39180,39182,39184],{"class":2029,"line":27},[1115,39174,39175],{"class":2039},"Median.test",[1115,39177,1164],{"class":2043},[1115,39179,39111],{"class":2032},[1115,39181,1199],{"class":2035},[1115,39183,39116],{"class":2032},[1115,39185,2185],{"class":2043},[20599,39187,39189],{"id":39188},"friedmanův-test","Friedmanův test",[1110,39191,39192,39193,39210,39211,39249],{},"Neparametrická obdoba analýzy rozptylu dvojného třídění s jedním pozorováním v každé podtřídě. ",[1115,39194,39196],{"className":39195},[1139],[1141,39197,39198],{"xmlns":1143},[1145,39199,39200,39208],{},[1148,39201,39202],{},[1151,39203,39204,39206],{},[1154,39205,6105],{},[1312,39207,4585],{},[1172,39209,6110],{"encoding":1174},": distribuční funkce veličin ",[1115,39212,39214],{"className":39213},[1139],[1141,39215,39216],{"xmlns":1143},[1145,39217,39218,39246],{},[1148,39219,39220,39230,39232,39234,39236],{},[1151,39221,39222,39224],{},[1154,39223,1436],{},[1148,39225,39226,39228],{},[1154,39227,1502],{},[1312,39229,1489],{},[1161,39231,1199],{"separator":1121},[1161,39233,3022],{},[1161,39235,1199],{"separator":1121},[1151,39237,39238,39240],{},[1154,39239,1436],{},[1148,39241,39242,39244],{},[1154,39243,1502],{},[1154,39245,3064],{},[1172,39247,39248],{"encoding":1174},"X_{i1}, \\dots, X_{ik}"," jsou totožné.",[2020,39251,39253],{"className":2022,"code":39252,"language":71,"meta":2024,"style":2024},"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",[2015,39254,39255,39285,39290],{"__ignoreMap":2024},[1115,39256,39257,39260,39262,39264,39266,39269,39272,39275,39277,39279,39281,39283],{"class":2029,"line":10},[1115,39258,39259],{"class":2039},"friedman.test",[1115,39261,1164],{"class":2043},[1115,39263,39111],{"class":2032},[1115,39265,20710],{"class":2035},[1115,39267,39268],{"class":2032}," faktor_A",[1115,39270,39271],{"class":2035}," |",[1115,39273,39274],{"class":2032}," faktor_B",[1115,39276,1199],{"class":2035},[1115,39278,24019],{"class":2032},[1115,39280,2291],{"class":2035},[1115,39282,39125],{"class":2032},[1115,39284,2185],{"class":2043},[1115,39286,39287],{"class":2029,"line":27},[1115,39288,39289],{"class":2094},"# jsou-li proměnné samostatné vektory (bez argumentu data):\n",[1115,39291,39292,39294,39296,39298,39300,39302,39304,39306],{"class":2029,"line":148},[1115,39293,39259],{"class":2039},[1115,39295,1164],{"class":2043},[1115,39297,39111],{"class":2032},[1115,39299,1199],{"class":2035},[1115,39301,39268],{"class":2032},[1115,39303,1199],{"class":2035},[1115,39305,39274],{"class":2032},[1115,39307,2185],{"class":2043},[1232,39309,39311],{"id":39310},"přehled-testů","Přehled testů",[1110,39313,39314],{},[1393,39315],{"alt":39316,"className":39317,"src":39318},"mask-ilu-volba-testu",[1242,1397],"\u002Fwiki-assets\u002Fmask-ilu-volba-testu.png",[3350,39320,39321,39334],{},[3353,39322,39323],{},[3356,39324,39325,39328,39331],{},[3359,39326,39327],{},"Situace",[3359,39329,39330],{},"Test",[3359,39332,39333],{},"R funkce",[3389,39335,39336,39349,39362,39374,39387,39402,39414,39427,39440,39453,39465,39480],{},[3356,39337,39338,39341,39344],{},[3394,39339,39340],{},"Jedna střední hodnota vs. zadané číslo, normální data",[3394,39342,39343],{},"jednovýběrový t-test",[3394,39345,39346],{},[2015,39347,39348],{},"t.test(x, mu = ..., alternative = ...)",[3356,39350,39351,39354,39357],{},[3394,39352,39353],{},"Rozdíl dvou závislých měření, diference normální",[3394,39355,39356],{},"párový t-test",[3394,39358,39359],{},[2015,39360,39361],{},"t.test(x, y, paired = TRUE)",[3356,39363,39364,39367,39369],{},[3394,39365,39366],{},"Shoda rozptylů dvou nezávislých normálních výběrů",[3394,39368,23927],{},[3394,39370,39371],{},[2015,39372,39373],{},"var.test(x, y)",[3356,39375,39376,39379,39382],{},[3394,39377,39378],{},"Shoda středních hodnot dvou nezávislých normálních výběrů",[3394,39380,39381],{},"dvouvýběrový t-test",[3394,39383,39384],{},[2015,39385,39386],{},"t.test(x, y, var.equal = TRUE\u002FFALSE)",[3356,39388,39389,39392,39394],{},[3394,39390,39391],{},"Shoda dat se zadaným typem rozdělení (normální, exponenciální, …)",[3394,39393,37195],{},[3394,39395,39396,1381,39399],{},[2015,39397,39398],{},"ks.test(x, \"pnorm\", mu, sigma)",[2015,39400,39401],{},"ks.test(x, \"pexp\", 1\u002Fdelta)",[3356,39403,39404,39407,39409],{},[3394,39405,39406],{},"Normalita dat",[3394,39408,37611],{},[3394,39410,39411],{},[2015,39412,39413],{},"shapiro.test(x)",[3356,39415,39416,39419,39422],{},[3394,39417,39418],{},"Medián jednoho výběru vs. konstanta, data nejsou normální",[3394,39420,39421],{},"jednovýběrový Wilcoxonův test",[3394,39423,39424],{},[2015,39425,39426],{},"wilcox.test(x, mu = c, alternative = ...)",[3356,39428,39429,39432,39435],{},[3394,39430,39431],{},"Medián diferencí dvou závislých měření, data nejsou normální",[3394,39433,39434],{},"párový Wilcoxonův test",[3394,39436,39437],{},[2015,39438,39439],{},"wilcox.test(x, y, paired = TRUE, mu = c)",[3356,39441,39442,39445,39448],{},[3394,39443,39444],{},"Mediány dvou nezávislých výběrů, data nejsou normální",[3394,39446,39447],{},"dvouvýběrový Wilcoxonův test",[3394,39449,39450],{},[2015,39451,39452],{},"wilcox.test(x, y)",[3356,39454,39455,39458,39460],{},[3394,39456,39457],{},"Více než dva nezávislé výběry, data nejsou normální",[3394,39459,39075],{},[3394,39461,39462],{},[2015,39463,39464],{},"kruskal.test(y ~ faktor, data)",[3356,39466,39467,39470,39473],{},[3394,39468,39469],{},"Více než dva nezávislé výběry, data nejsou normální (alternativa)",[3394,39471,39472],{},"mediánový test",[3394,39474,39475,26519,39478],{},[2015,39476,39477],{},"Median.test(y, faktor)",[2015,39479,39155],{},[3356,39481,39482,39485,39487],{},[3394,39483,39484],{},"Více než dva závislé výběry (dvojné třídění, jedno pozorování na podtřídu)",[3394,39486,39189],{},[3394,39488,39489],{},[2015,39490,39491],{},"friedman.test(y ~ A | B, data)",[1232,39493,5763],{"id":5762},[1124,39495,39496,39573,39579,39596,39627],{},[1127,39497,39498,39537,39538,36925,39555,39572],{},[1248,39499,39500,39501,39518,39519,39536],{},"Nezamítnutí ",[1115,39502,39504],{"className":39503},[1139],[1141,39505,39506],{"xmlns":1143},[1145,39507,39508,39516],{},[1148,39509,39510],{},[1151,39511,39512,39514],{},[1154,39513,6105],{},[1312,39515,4585],{},[1172,39517,6110],{"encoding":1174}," není důkaz, že ",[1115,39520,39522],{"className":39521},[1139],[1141,39523,39524],{"xmlns":1143},[1145,39525,39526,39534],{},[1148,39527,39528],{},[1151,39529,39530,39532],{},[1154,39531,6105],{},[1312,39533,4585],{},[1172,39535,6110],{"encoding":1174}," platí."," U kabelů A\u002FB vyšlo ",[1115,39539,39541],{"className":39540},[1139],[1141,39542,39543],{"xmlns":1143},[1145,39544,39545,39553],{},[1148,39546,39547,39549,39551],{},[1154,39548,1110],{},[1161,39550,1483],{},[1312,39552,36921],{},[1172,39554,36924],{"encoding":1174},[1115,39556,39558],{"className":39557},[1139],[1141,39559,39560],{"xmlns":1143},[1145,39561,39562,39570],{},[1148,39563,39564],{},[1151,39565,39566,39568],{},[1154,39567,6105],{},[1312,39569,4585],{},[1172,39571,6110],{"encoding":1174}," nezamítá, ale hodnota je blízko hranice; správná interpretace je „data rovnost průměrů nevyvracejí“, ne „rovnost je prokázána“.",[1127,39574,39575,39578],{},[1248,39576,39577],{},"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.",[1127,39580,39581,39588,39589,39592,39593,39595],{},[1248,39582,39583,34083,39585,39587],{},[2015,39584,36653],{},[2015,39586,31867],{}," se volí podle F-testu, ne podle výchozí hodnoty."," Výchozí nastavení R je ",[2015,39590,39591],{},"var.equal = FALSE"," (Welchova varianta); pokud F-test potvrdí shodné rozptyly, je třeba explicitně napsat ",[2015,39594,36904],{},", jinak se použije jiná statistika a jiné stupně volnosti.",[1127,39597,39598,39601,39602,39605,39606,39623,39624,1176],{},[1248,39599,39600],{},"Jednostranná vs. dvoustranná alternativa mění kritický obor i závěr."," Volba ",[2015,39603,39604],{},"alternative = \"greater\"\u002F\"less\"\u002F\"two.sided\""," musí odpovídat formulaci ",[1115,39607,39609],{"className":39608},[1139],[1141,39610,39611],{"xmlns":1143},[1145,39612,39613,39621],{},[1148,39614,39615],{},[1151,39616,39617,39619],{},[1154,39618,6105],{},[1312,39620,1489],{},[1172,39622,7508],{"encoding":1174}," v zadání, ne být ponechána na výchozí hodnotě ",[2015,39625,39626],{},"\"two.sided\"",[1127,39628,39629,39632,39633,39646],{},[1248,39630,39631],{},"Shapiro-Wilkův test se vyhodnocuje jen přes p-hodnotu",", ne porovnáním ",[1115,39634,39636],{"className":39635},[1139],[1141,39637,39638],{"xmlns":1143},[1145,39639,39640,39644],{},[1148,39641,39642],{},[1154,39643,6143],{},[1172,39645,6143],{"encoding":1174}," s tabulkovou kritickou hodnotou jako u ostatních testů v této kapitole.",[1232,39648,5963],{"id":5962},[1124,39650,39651,39656,39661,39666,39671,39676,39681],{},[1127,39652,39653],{},[1239,39654,1245],{"className":39655,"dataFsResolvedFilePath":1243,"href":1244},[1242],[1127,39657,39658],{},[1239,39659,5978],{"className":39660,"dataFsResolvedFilePath":5976,"href":5977},[1242],[1127,39662,39663],{},[1239,39664,1094],{"className":39665,"dataFsResolvedFilePath":11066,"href":11067},[1242],[1127,39667,39668],{},[1239,39669,5991],{"className":39670,"dataFsResolvedFilePath":5989,"href":5990},[1242],[1127,39672,39673],{},[1239,39674,5999],{"className":39675,"dataFsResolvedFilePath":5997,"href":5998},[1242],[1127,39677,39678],{},[1239,39679,6007],{"className":39680,"dataFsResolvedFilePath":6005,"href":6006},[1242],[1127,39682,39683],{},[1239,39684,6015],{"className":39685,"dataFsResolvedFilePath":6013,"href":6014},[1242],[1232,39687,6018],{"id":934},[1110,39689,6021,39690,6026],{},[6023,39691,6025],{},[6028,39693,39694],{},"html pre.shiki code .sP4rz, 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