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i neparametricky, vždy s výpočtem v R.",[1136,1137,1139],"h2",{"id":1138},"co-tato-část-pokrývá","Co tato část pokrývá",[1141,1142,1143,1156],"table",{},[1144,1145,1146],"thead",{},[1147,1148,1149,1153],"tr",{},[1150,1151,1152],"th",{},"Kapitola",[1150,1154,1155],{},"Obsah",[1157,1158,1159,1173,1186],"tbody",{},[1147,1160,1161,1170],{},[1162,1163,1164],"td",{},[1127,1165,1169],{"className":1166,"dataFsResolvedFilePath":1167,"href":1168},[1130],"topics\u002Fnahodne-veliciny-a-rozdeleni.md","\u002Fwiki\u002Fnahodne-veliciny-a-rozdeleni","Náhodné veličiny a rozdělení pravděpodobnosti",[1162,1171,1172],{},"distribuční funkce, hustota pravděpodobnosti, normální rozdělení, kvantily normálního rozdělení, rozdělení t, χ² a F",[1147,1174,1175,1183],{},[1162,1176,1177],{},[1127,1178,1182],{"className":1179,"dataFsResolvedFilePath":1180,"href":1181},[1130],"topics\u002Fpopisna-statistika.md","\u002Fwiki\u002Fpopisna-statistika","Popisná statistika a datové soubory",[1162,1184,1185],{},"výběrový 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stránky",[1204,1205,1206,1212,1217,1222,1227],"ul",{},[1207,1208,1209],"li",{},[1127,1210,1133],{"className":1211,"dataFsResolvedFilePath":1131,"href":1132},[1130],[1207,1213,1214],{},[1127,1215,1169],{"className":1216,"dataFsResolvedFilePath":1167,"href":1168},[1130],[1207,1218,1219],{},[1127,1220,1182],{"className":1221,"dataFsResolvedFilePath":1180,"href":1181},[1130],[1207,1223,1224],{},[1127,1225,1195],{"className":1226,"dataFsResolvedFilePath":1193,"href":1194},[1130],[1207,1228,1229],{},[1127,1230,1234],{"className":1231,"dataFsResolvedFilePath":1232,"href":1233},[1130],"outputs\u002Fmask-r-tahak.md","\u002Fwiki\u002Fmask-r-tahak","masK — Tahák pro R",[1136,1236,1237],{"id":934},"Reference",[1110,1239,1240,1241,1245],{},"KROPÁČ, J. ",[1242,1243,1244],"em",{},"Statistika A",". 4. vyd. Brno: Fakulta podnikatelská VUT, 2011.",{"title":1247,"searchDepth":27,"depth":27,"links":1248},"",[1249,1250,1251],{"id":1138,"depth":27,"text":1139},{"id":1201,"depth":27,"text":1202},{"id":934,"depth":27,"text":1237},null,"2026-10-02","md",{},true,"\u002Fsummaries\u002Fmask-prednasky-veliciny-data-testy",{"title":1094,"description":1247},[1260,1261,1262,1263,1264,1265,1266,1267,1268],"raw\u002Fmask\u002F01 náhodné veličiny.pdf","raw\u002Fmask\u002F01 náhodné veličiny - návod R.pdf","raw\u002Fmask\u002F02 datové soubory.pdf","raw\u002Fmask\u002F02 datové soubory - návod R.pdf","raw\u002Fmask\u002F03 testy hypotéz.pdf","raw\u002Fmask\u002F03 testování hypotéz - návod R 01.pdf","raw\u002Fmask\u002F03 testování hypotéz - návod R 02.pdf","raw\u002Fmask\u002Fpříklady 01 a 02.docx","raw\u002Fmask\u002Fpříklady 03.docx","summaries\u002Fmask-prednasky-veliciny-data-testy",[23,67,332,141,71],"summary","smiY-h6Q1bqxi7gCaS-UY2aGzQvcih4pLe2N5zV_qGg","summaries",[1275,6444,10909,15673,20375,25830],{"id":1276,"title":1277,"body":1278,"course":23,"courses":1252,"created":1253,"description":1247,"extension":1254,"meta":6434,"navigation":1256,"path":6435,"seo":6436,"sources":6437,"stem":6440,"tags":6441,"type":6442,"updated":1253,"__hash__":6443},"topics\u002Ftopics\u002Fkontingencni-tabulky.md","Kontingenční tabulky",{"type":1096,"value":1279,"toc":6424},[1280,1283,1480,1484,1500,1518,1731,1872,2467,2484,2597,2601,2632,2637,3240,3247,3467,3693,3701,3782,3894,4047,4053,4134,4155,4164,4198,4205,4208,4214,4280,4339,4492,4498,4505,4583,4586,4642,4980,5001,5105,5214,5217,5238,5241,5496,5578,5585,5589,5819,5833,5982,6116,6122,6180,6184,6203,6218,6224,6269,6288,6303,6309,6368,6370,6414,6416,6420],[1099,1281,1277],{"id":1282},"kontingenční-tabulky",[1103,1284,1288,1296],{"className":1285,"dataCallout":1287},[1106,1286],"callout-default","tldr",[1110,1289,1291,1295],{"className":1290},[1113],[1115,1292],{"className":1293,"ariaHidden":1121},[1118,1294,1120],"i-lucide:info","V kostce",[1204,1297,1298,1306,1380,1401,1441,1469],{},[1207,1299,1300,1301,1305],{},"Kontingenční tabulka zaznamenává ",[1302,1303,1304],"strong",{},"simultánní četnosti"," dvou kvalitativních znaků naměřených na stejném souboru.",[1207,1307,1308,1311,1312,1342,1343,1364,1365,1379],{},[1302,1309,1310],{},"Test nezávislosti"," srovnává pozorované četnosti s očekávanými za platnosti ",[1115,1313,1316],{"className":1314},[1315],"katex",[1317,1318,1320],"math",{"xmlns":1319},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1321,1322,1323,1337],"semantics",{},[1324,1325,1326],"mrow",{},[1327,1328,1329,1333],"msub",{},[1330,1331,1332],"mi",{},"H",[1334,1335,1336],"mn",{},"0",[1338,1339,1341],"annotation",{"encoding":1340},"application\u002Fx-tex","H_0"," pomocí statistiky ",[1115,1344,1346],{"className":1345},[1315],[1317,1347,1348],{"xmlns":1319},[1321,1349,1350,1361],{},[1324,1351,1352],{},[1353,1354,1355,1358],"msup",{},[1330,1356,1357],{},"χ",[1334,1359,1360],{},"2",[1338,1362,1363],{"encoding":1340},"\\chi^2","; rozhoduje kritický obor ",[1115,1366,1368],{"className":1367},[1315],[1317,1369,1370],{"xmlns":1319},[1321,1371,1372,1377],{},[1324,1373,1374],{},[1330,1375,1376],{},"W",[1338,1378,1376],{"encoding":1340},", prakticky p-hodnota.",[1207,1381,1382,1383,1400],{},"Aproximace ",[1115,1384,1386],{"className":1385},[1315],[1317,1387,1388],{"xmlns":1319},[1321,1389,1390,1398],{},[1324,1391,1392],{},[1353,1393,1394,1396],{},[1330,1395,1357],{},[1334,1397,1360],{},[1338,1399,1363],{"encoding":1340}," rozdělením platí jen tehdy, když jsou očekávané četnosti dostatečně velké — proto se vždy kontrolují.",[1207,1402,1403,1404,1421,1422,1425,1426,1440],{},"Zamítnutí ",[1115,1405,1407],{"className":1406},[1315],[1317,1408,1409],{"xmlns":1319},[1321,1410,1411,1419],{},[1324,1412,1413],{},[1327,1414,1415,1417],{},[1330,1416,1332],{},[1334,1418,1336],{},[1338,1420,1341],{"encoding":1340}," samo o sobě neříká, jak silná závislost je — na to slouží ",[1302,1423,1424],{},"Cramérův koeficient kontingence"," ",[1115,1427,1429],{"className":1428},[1315],[1317,1430,1431],{"xmlns":1319},[1321,1432,1433,1438],{},[1324,1434,1435],{},[1330,1436,1437],{},"V",[1338,1439,1437],{"encoding":1340},".",[1207,1442,1443,1446,1447,1440],{},[1302,1444,1445],{},"Čtyřpolní tabulka"," (2×2) je speciální případ s vlastním zjednodušeným vzorcem pro ",[1115,1448,1450],{"className":1449},[1315],[1317,1451,1452],{"xmlns":1319},[1321,1453,1454,1466],{},[1324,1455,1456,1459,1463],{},[1330,1457,1458],{},"n",[1460,1461,1462],"mo",{},">",[1334,1464,1465],{},"40",[1338,1467,1468],{"encoding":1340},"n>40",[1207,1470,1471,1472,1475,1476,1479],{},"Pro ",[1302,1473,1474],{},"párová data"," (stejné prvky měřené dvakrát, např. před\u002Fpo zásahu) se používá ",[1302,1477,1478],{},"McNemarův test",", ne obyčejný test nezávislosti.",[1136,1481,1483],{"id":1482},"kontingenční-tabulka","Kontingenční tabulka",[1110,1485,1486,1487,1490,1491,1495,1496,1499],{},"V rámci ",[1127,1488,1133],{"className":1489,"dataFsResolvedFilePath":1131,"href":1132},[1130]," navazují kontingenční tabulky na\n",[1127,1492,1494],{"className":1493,"dataFsResolvedFilePath":1193,"href":1194},[1130],"testování statistických hypotéz",": místo jedné náhodné veličiny teď sledujeme dva\n",[1302,1497,1498],{},"kvalitativní"," (kategoriální) znaky současně a ptáme se, zda spolu souvisí.",[1110,1501,1502,1503,1506,1507,1509,1510,1513,1514,1517],{},"Znak je ",[1302,1504,1505],{},"kvantitativní",", pokud nabývá číselných hodnot (stáří, stav tachometru), a ",[1302,1508,1498],{},"\n(kategoriální), pokud nabývá slovních variant (vzdělání, kuřák\u002Fnekuřák). Kvalitativní znaky dále dělíme na\n",[1302,1511,1512],{},"alternativní"," (dvě varianty, např. vada ano\u002Fne) a ",[1302,1515,1516],{},"množné"," (více než dvě varianty, např. svobodný\u002Frozvedený\u002Fženatý).",[1110,1519,1520,1521,1534,1535,1549,1550,1583,1584,1598,1599,1630,1631,1634,1635,1662,1663,1425,1666,1688,1689,1707,1708,1726,1727,1730],{},"Mějme ",[1115,1522,1524],{"className":1523},[1315],[1317,1525,1526],{"xmlns":1319},[1321,1527,1528,1532],{},[1324,1529,1530],{},[1330,1531,1458],{},[1338,1533,1458],{"encoding":1340}," opakování pokusu, při nichž sledujeme dva kvalitativní znaky ",[1115,1536,1538],{"className":1537},[1315],[1317,1539,1540],{"xmlns":1319},[1321,1541,1542,1547],{},[1324,1543,1544],{},[1330,1545,1546],{},"A",[1338,1548,1546],{"encoding":1340}," (varianty ",[1115,1551,1553],{"className":1552},[1315],[1317,1554,1555],{"xmlns":1319},[1321,1556,1557,1580],{},[1324,1558,1559,1566,1569,1572,1574],{},[1327,1560,1561,1563],{},[1330,1562,1546],{},[1334,1564,1565],{},"1",[1460,1567,1568],{"separator":1121},",",[1460,1570,1571],{},"…",[1460,1573,1568],{"separator":1121},[1327,1575,1576,1578],{},[1330,1577,1546],{},[1330,1579,71],{},[1338,1581,1582],{"encoding":1340},"A_1,\\dots,A_r",") a ",[1115,1585,1587],{"className":1586},[1315],[1317,1588,1589],{"xmlns":1319},[1321,1590,1591,1596],{},[1324,1592,1593],{},[1330,1594,1595],{},"B",[1338,1597,1595],{"encoding":1340},"\n(varianty ",[1115,1600,1602],{"className":1601},[1315],[1317,1603,1604],{"xmlns":1319},[1321,1605,1606,1627],{},[1324,1607,1608,1614,1616,1618,1620],{},[1327,1609,1610,1612],{},[1330,1611,1595],{},[1334,1613,1565],{},[1460,1615,1568],{"separator":1121},[1460,1617,1571],{},[1460,1619,1568],{"separator":1121},[1327,1621,1622,1624],{},[1330,1623,1595],{},[1330,1625,1626],{},"s",[1338,1628,1629],{"encoding":1340},"B_1,\\dots,B_s","). Výsledky zapíšeme do ",[1302,1632,1633],{},"kontingenční tabulky",": v políčku ",[1115,1636,1638],{"className":1637},[1315],[1317,1639,1640],{"xmlns":1319},[1321,1641,1642,1659],{},[1324,1643,1644,1648,1651,1653,1656],{},[1460,1645,1647],{"stretchy":1646},"false","(",[1330,1649,1650],{},"i",[1460,1652,1568],{"separator":1121},[1330,1654,1655],{},"j",[1460,1657,1658],{"stretchy":1646},")",[1338,1660,1661],{"encoding":1340},"(i,j)"," je ",[1302,1664,1665],{},"simultánní\nčetnost",[1115,1667,1669],{"className":1668},[1315],[1317,1670,1671],{"xmlns":1319},[1321,1672,1673,1685],{},[1324,1674,1675],{},[1327,1676,1677,1679],{},[1330,1678,1458],{},[1324,1680,1681,1683],{},[1330,1682,1650],{},[1330,1684,1655],{},[1338,1686,1687],{"encoding":1340},"n_{ij}",", tedy počet pokusů s variantou ",[1115,1690,1692],{"className":1691},[1315],[1317,1693,1694],{"xmlns":1319},[1321,1695,1696,1704],{},[1324,1697,1698],{},[1327,1699,1700,1702],{},[1330,1701,1546],{},[1330,1703,1650],{},[1338,1705,1706],{"encoding":1340},"A_i"," zároveň s variantou ",[1115,1709,1711],{"className":1710},[1315],[1317,1712,1713],{"xmlns":1319},[1321,1714,1715,1723],{},[1324,1716,1717],{},[1327,1718,1719,1721],{},[1330,1720,1595],{},[1330,1722,1655],{},[1338,1724,1725],{"encoding":1340},"B_j",". Řádkové a sloupcové součty\njsou ",[1302,1728,1729],{},"marginální četnosti",":",[1115,1732,1734],{"className":1733},[1315],[1317,1735,1737],{"xmlns":1319,"display":1736},"block",[1321,1738,1739,1869],{},[1324,1740,1741,1752,1755,1771,1781,1783,1787,1797,1799,1813,1823,1825,1827,1829,1831,1845,1859],{},[1327,1742,1743,1745],{},[1330,1744,1458],{},[1324,1746,1747,1749],{},[1330,1748,1650],{},[1460,1750,1751],{},"∙",[1460,1753,1754],{},"=",[1756,1757,1758,1761,1769],"munderover",{},[1460,1759,1760],{},"∑",[1324,1762,1763,1765,1767],{},[1330,1764,1655],{},[1460,1766,1754],{},[1334,1768,1565],{},[1330,1770,1626],{},[1327,1772,1773,1775],{},[1330,1774,1458],{},[1324,1776,1777,1779],{},[1330,1778,1650],{},[1330,1780,1655],{},[1460,1782,1568],{"separator":1121},[1784,1785],"mspace",{"width":1786},"2em",[1327,1788,1789,1791],{},[1330,1790,1458],{},[1324,1792,1793,1795],{},[1460,1794,1751],{},[1330,1796,1655],{},[1460,1798,1754],{},[1756,1800,1801,1803,1811],{},[1460,1802,1760],{},[1324,1804,1805,1807,1809],{},[1330,1806,1650],{},[1460,1808,1754],{},[1334,1810,1565],{},[1330,1812,71],{},[1327,1814,1815,1817],{},[1330,1816,1458],{},[1324,1818,1819,1821],{},[1330,1820,1650],{},[1330,1822,1655],{},[1460,1824,1568],{"separator":1121},[1784,1826],{"width":1786},[1330,1828,1458],{},[1460,1830,1754],{},[1756,1832,1833,1835,1843],{},[1460,1834,1760],{},[1324,1836,1837,1839,1841],{},[1330,1838,1650],{},[1460,1840,1754],{},[1334,1842,1565],{},[1330,1844,71],{},[1756,1846,1847,1849,1857],{},[1460,1848,1760],{},[1324,1850,1851,1853,1855],{},[1330,1852,1655],{},[1460,1854,1754],{},[1334,1856,1565],{},[1330,1858,1626],{},[1327,1860,1861,1863],{},[1330,1862,1458],{},[1324,1864,1865,1867],{},[1330,1866,1650],{},[1330,1868,1655],{},[1338,1870,1871],{"encoding":1340},"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}",[1141,1873,1874,1986],{},[1144,1875,1876],{},[1147,1877,1878,1900,1920,1940,1942,1962],{},[1150,1879,1880],{},[1115,1881,1883],{"className":1882},[1315],[1317,1884,1885],{"xmlns":1319},[1321,1886,1887,1897],{},[1324,1888,1889,1891,1895],{},[1330,1890,1546],{},[1330,1892,1894],{"mathvariant":1893},"normal","\\",[1330,1896,1595],{},[1338,1898,1899],{"encoding":1340},"A \\backslash B",[1150,1901,1902],{},[1115,1903,1905],{"className":1904},[1315],[1317,1906,1907],{"xmlns":1319},[1321,1908,1909,1917],{},[1324,1910,1911],{},[1327,1912,1913,1915],{},[1330,1914,1595],{},[1334,1916,1565],{},[1338,1918,1919],{"encoding":1340},"B_1",[1150,1921,1922],{},[1115,1923,1925],{"className":1924},[1315],[1317,1926,1927],{"xmlns":1319},[1321,1928,1929,1937],{},[1324,1930,1931],{},[1327,1932,1933,1935],{},[1330,1934,1595],{},[1334,1936,1360],{},[1338,1938,1939],{"encoding":1340},"B_2",[1150,1941,1571],{},[1150,1943,1944],{},[1115,1945,1947],{"className":1946},[1315],[1317,1948,1949],{"xmlns":1319},[1321,1950,1951,1959],{},[1324,1952,1953],{},[1327,1954,1955,1957],{},[1330,1956,1595],{},[1330,1958,1626],{},[1338,1960,1961],{"encoding":1340},"B_s",[1150,1963,1964],{},[1115,1965,1967],{"className":1966},[1315],[1317,1968,1969],{"xmlns":1319},[1321,1970,1971,1983],{},[1324,1972,1973],{},[1327,1974,1975,1977],{},[1330,1976,1458],{},[1324,1978,1979,1981],{},[1330,1980,1650],{},[1460,1982,1751],{},[1338,1984,1985],{"encoding":1340},"n_{i\\bullet}",[1157,1987,1988,2102,2216,2232,2352],{},[1147,1989,1990,2010,2031,2052,2054,2078],{},[1162,1991,1992],{},[1115,1993,1995],{"className":1994},[1315],[1317,1996,1997],{"xmlns":1319},[1321,1998,1999,2007],{},[1324,2000,2001],{},[1327,2002,2003,2005],{},[1330,2004,1546],{},[1334,2006,1565],{},[1338,2008,2009],{"encoding":1340},"A_1",[1162,2011,2012],{},[1115,2013,2015],{"className":2014},[1315],[1317,2016,2017],{"xmlns":1319},[1321,2018,2019,2028],{},[1324,2020,2021],{},[1327,2022,2023,2025],{},[1330,2024,1458],{},[1334,2026,2027],{},"11",[1338,2029,2030],{"encoding":1340},"n_{11}",[1162,2032,2033],{},[1115,2034,2036],{"className":2035},[1315],[1317,2037,2038],{"xmlns":1319},[1321,2039,2040,2049],{},[1324,2041,2042],{},[1327,2043,2044,2046],{},[1330,2045,1458],{},[1334,2047,2048],{},"12",[1338,2050,2051],{"encoding":1340},"n_{12}",[1162,2053,1571],{},[1162,2055,2056],{},[1115,2057,2059],{"className":2058},[1315],[1317,2060,2061],{"xmlns":1319},[1321,2062,2063,2075],{},[1324,2064,2065],{},[1327,2066,2067,2069],{},[1330,2068,1458],{},[1324,2070,2071,2073],{},[1334,2072,1565],{},[1330,2074,1626],{},[1338,2076,2077],{"encoding":1340},"n_{1s}",[1162,2079,2080],{},[1115,2081,2083],{"className":2082},[1315],[1317,2084,2085],{"xmlns":1319},[1321,2086,2087,2099],{},[1324,2088,2089],{},[1327,2090,2091,2093],{},[1330,2092,1458],{},[1324,2094,2095,2097],{},[1334,2096,1565],{},[1460,2098,1751],{},[1338,2100,2101],{"encoding":1340},"n_{1\\bullet}",[1147,2103,2104,2124,2145,2166,2168,2192],{},[1162,2105,2106],{},[1115,2107,2109],{"className":2108},[1315],[1317,2110,2111],{"xmlns":1319},[1321,2112,2113,2121],{},[1324,2114,2115],{},[1327,2116,2117,2119],{},[1330,2118,1546],{},[1334,2120,1360],{},[1338,2122,2123],{"encoding":1340},"A_2",[1162,2125,2126],{},[1115,2127,2129],{"className":2128},[1315],[1317,2130,2131],{"xmlns":1319},[1321,2132,2133,2142],{},[1324,2134,2135],{},[1327,2136,2137,2139],{},[1330,2138,1458],{},[1334,2140,2141],{},"21",[1338,2143,2144],{"encoding":1340},"n_{21}",[1162,2146,2147],{},[1115,2148,2150],{"className":2149},[1315],[1317,2151,2152],{"xmlns":1319},[1321,2153,2154,2163],{},[1324,2155,2156],{},[1327,2157,2158,2160],{},[1330,2159,1458],{},[1334,2161,2162],{},"22",[1338,2164,2165],{"encoding":1340},"n_{22}",[1162,2167,1571],{},[1162,2169,2170],{},[1115,2171,2173],{"className":2172},[1315],[1317,2174,2175],{"xmlns":1319},[1321,2176,2177,2189],{},[1324,2178,2179],{},[1327,2180,2181,2183],{},[1330,2182,1458],{},[1324,2184,2185,2187],{},[1334,2186,1360],{},[1330,2188,1626],{},[1338,2190,2191],{"encoding":1340},"n_{2s}",[1162,2193,2194],{},[1115,2195,2197],{"className":2196},[1315],[1317,2198,2199],{"xmlns":1319},[1321,2200,2201,2213],{},[1324,2202,2203],{},[1327,2204,2205,2207],{},[1330,2206,1458],{},[1324,2208,2209,2211],{},[1334,2210,1360],{},[1460,2212,1751],{},[1338,2214,2215],{"encoding":1340},"n_{2\\bullet}",[1147,2217,2218,2221,2223,2225,2228,2230],{},[1162,2219,2220],{},"⋮",[1162,2222,2220],{},[1162,2224,2220],{},[1162,2226,2227],{},"⋱",[1162,2229,2220],{},[1162,2231,2220],{},[1147,2233,2234,2254,2278,2302,2304,2328],{},[1162,2235,2236],{},[1115,2237,2239],{"className":2238},[1315],[1317,2240,2241],{"xmlns":1319},[1321,2242,2243,2251],{},[1324,2244,2245],{},[1327,2246,2247,2249],{},[1330,2248,1546],{},[1330,2250,71],{},[1338,2252,2253],{"encoding":1340},"A_r",[1162,2255,2256],{},[1115,2257,2259],{"className":2258},[1315],[1317,2260,2261],{"xmlns":1319},[1321,2262,2263,2275],{},[1324,2264,2265],{},[1327,2266,2267,2269],{},[1330,2268,1458],{},[1324,2270,2271,2273],{},[1330,2272,71],{},[1334,2274,1565],{},[1338,2276,2277],{"encoding":1340},"n_{r1}",[1162,2279,2280],{},[1115,2281,2283],{"className":2282},[1315],[1317,2284,2285],{"xmlns":1319},[1321,2286,2287,2299],{},[1324,2288,2289],{},[1327,2290,2291,2293],{},[1330,2292,1458],{},[1324,2294,2295,2297],{},[1330,2296,71],{},[1334,2298,1360],{},[1338,2300,2301],{"encoding":1340},"n_{r2}",[1162,2303,1571],{},[1162,2305,2306],{},[1115,2307,2309],{"className":2308},[1315],[1317,2310,2311],{"xmlns":1319},[1321,2312,2313,2325],{},[1324,2314,2315],{},[1327,2316,2317,2319],{},[1330,2318,1458],{},[1324,2320,2321,2323],{},[1330,2322,71],{},[1330,2324,1626],{},[1338,2326,2327],{"encoding":1340},"n_{rs}",[1162,2329,2330],{},[1115,2331,2333],{"className":2332},[1315],[1317,2334,2335],{"xmlns":1319},[1321,2336,2337,2349],{},[1324,2338,2339],{},[1327,2340,2341,2343],{},[1330,2342,1458],{},[1324,2344,2345,2347],{},[1330,2346,71],{},[1460,2348,1751],{},[1338,2350,2351],{"encoding":1340},"n_{r\\bullet}",[1147,2353,2354,2378,2402,2426,2428,2452],{},[1162,2355,2356],{},[1115,2357,2359],{"className":2358},[1315],[1317,2360,2361],{"xmlns":1319},[1321,2362,2363,2375],{},[1324,2364,2365],{},[1327,2366,2367,2369],{},[1330,2368,1458],{},[1324,2370,2371,2373],{},[1460,2372,1751],{},[1330,2374,1655],{},[1338,2376,2377],{"encoding":1340},"n_{\\bullet j}",[1162,2379,2380],{},[1115,2381,2383],{"className":2382},[1315],[1317,2384,2385],{"xmlns":1319},[1321,2386,2387,2399],{},[1324,2388,2389],{},[1327,2390,2391,2393],{},[1330,2392,1458],{},[1324,2394,2395,2397],{},[1460,2396,1751],{},[1334,2398,1565],{},[1338,2400,2401],{"encoding":1340},"n_{\\bullet 1}",[1162,2403,2404],{},[1115,2405,2407],{"className":2406},[1315],[1317,2408,2409],{"xmlns":1319},[1321,2410,2411,2423],{},[1324,2412,2413],{},[1327,2414,2415,2417],{},[1330,2416,1458],{},[1324,2418,2419,2421],{},[1460,2420,1751],{},[1334,2422,1360],{},[1338,2424,2425],{"encoding":1340},"n_{\\bullet 2}",[1162,2427,1571],{},[1162,2429,2430],{},[1115,2431,2433],{"className":2432},[1315],[1317,2434,2435],{"xmlns":1319},[1321,2436,2437,2449],{},[1324,2438,2439],{},[1327,2440,2441,2443],{},[1330,2442,1458],{},[1324,2444,2445,2447],{},[1460,2446,1751],{},[1330,2448,1626],{},[1338,2450,2451],{"encoding":1340},"n_{\\bullet s}",[1162,2453,2454],{},[1115,2455,2457],{"className":2456},[1315],[1317,2458,2459],{"xmlns":1319},[1321,2460,2461,2465],{},[1324,2462,2463],{},[1330,2464,1458],{},[1338,2466,1458],{"encoding":1340},[1110,2468,2469,2470,2483],{},"Vydělením četností počtem opakování ",[1115,2471,2473],{"className":2472},[1315],[1317,2474,2475],{"xmlns":1319},[1321,2476,2477,2481],{},[1324,2478,2479],{},[1330,2480,1458],{},[1338,2482,1458],{"encoding":1340}," dostaneme odhady pravděpodobností:",[1115,2485,2487],{"className":2486},[1315],[1317,2488,2489],{"xmlns":1319,"display":1736},[1321,2490,2491,2594],{},[1324,2492,2493,2509,2511,2526,2528,2530,2544,2546,2560,2562,2564,2578,2580],{},[1327,2494,2495,2503],{},[2496,2497,2498,2500],"mover",{"accent":1121},[1330,2499,1110],{},[1460,2501,2502],{},"^",[1324,2504,2505,2507],{},[1330,2506,1650],{},[1330,2508,1655],{},[1460,2510,1754],{},[2512,2513,2514,2524],"mfrac",{},[1327,2515,2516,2518],{},[1330,2517,1458],{},[1324,2519,2520,2522],{},[1330,2521,1650],{},[1330,2523,1655],{},[1330,2525,1458],{},[1460,2527,1568],{"separator":1121},[1784,2529],{"width":1786},[1327,2531,2532,2538],{},[2496,2533,2534,2536],{"accent":1121},[1330,2535,1110],{},[1460,2537,2502],{},[1324,2539,2540,2542],{},[1330,2541,1650],{},[1460,2543,1751],{},[1460,2545,1754],{},[2512,2547,2548,2558],{},[1327,2549,2550,2552],{},[1330,2551,1458],{},[1324,2553,2554,2556],{},[1330,2555,1650],{},[1460,2557,1751],{},[1330,2559,1458],{},[1460,2561,1568],{"separator":1121},[1784,2563],{"width":1786},[1327,2565,2566,2572],{},[2496,2567,2568,2570],{"accent":1121},[1330,2569,1110],{},[1460,2571,2502],{},[1324,2573,2574,2576],{},[1460,2575,1751],{},[1330,2577,1655],{},[1460,2579,1754],{},[2512,2581,2582,2592],{},[1327,2583,2584,2586],{},[1330,2585,1458],{},[1324,2587,2588,2590],{},[1460,2589,1751],{},[1330,2591,1655],{},[1330,2593,1458],{},[1338,2595,2596],{"encoding":1340},"\\hat p_{ij} = \\frac{n_{ij}}{n}, \\qquad \\hat p_{i\\bullet} = \\frac{n_{i\\bullet}}{n}, \\qquad \\hat p_{\\bullet j} = \\frac{n_{\\bullet j}}{n}",[1136,2598,2600],{"id":2599},"test-nezávislosti-dvou-kvalitativních-znaků","Test nezávislosti dvou kvalitativních znaků",[1110,2602,2603,2604,2617,2618,2631],{},"Test ověřuje, zda varianty znaku ",[1115,2605,2607],{"className":2606},[1315],[1317,2608,2609],{"xmlns":1319},[1321,2610,2611,2615],{},[1324,2612,2613],{},[1330,2614,1546],{},[1338,2616,1546],{"encoding":1340}," a varianty znaku ",[1115,2619,2621],{"className":2620},[1315],[1317,2622,2623],{"xmlns":1319},[1321,2624,2625,2629],{},[1324,2626,2627],{},[1330,2628,1595],{},[1338,2630,1595],{"encoding":1340}," jsou na sobě nezávislé, tedy zda simultánní\npravděpodobnost je součinem marginálních pravděpodobností.",[1110,2633,2634],{},[1302,2635,2636],{},"Postup testu:",[2638,2639,2640,2772,3090,3172],"ol",{},[1207,2641,2642,2698,2699,2725,2726,2752,2753,2771],{},[1115,2643,2645],{"className":2644},[1315],[1317,2646,2647],{"xmlns":1319},[1321,2648,2649,2695],{},[1324,2650,2651,2657,2659,2669,2671,2681,2685],{},[1327,2652,2653,2655],{},[1330,2654,1332],{},[1334,2656,1336],{},[1460,2658,1730],{},[1327,2660,2661,2663],{},[1330,2662,1110],{},[1324,2664,2665,2667],{},[1330,2666,1650],{},[1330,2668,1655],{},[1460,2670,1754],{},[1327,2672,2673,2675],{},[1330,2674,1110],{},[1324,2676,2677,2679],{},[1330,2678,1650],{},[1460,2680,1751],{},[2682,2683,2684],"mtext",{}," ",[1327,2686,2687,2689],{},[1330,2688,1110],{},[1324,2690,2691,2693],{},[1460,2692,1751],{},[1330,2694,1655],{},[1338,2696,2697],{"encoding":1340},"H_0: p_{ij} = p_{i\\bullet}\\,p_{\\bullet j}"," pro všechna ",[1115,2700,2702],{"className":2701},[1315],[1317,2703,2704],{"xmlns":1319},[1321,2705,2706,2722],{},[1324,2707,2708,2710,2712,2714,2716,2718,2720],{},[1330,2709,1650],{},[1460,2711,1754],{},[1334,2713,1565],{},[1460,2715,1568],{"separator":1121},[1460,2717,1571],{},[1460,2719,1568],{"separator":1121},[1330,2721,71],{},[1338,2723,2724],{"encoding":1340},"i = 1,\\dots,r",", ",[1115,2727,2729],{"className":2728},[1315],[1317,2730,2731],{"xmlns":1319},[1321,2732,2733,2749],{},[1324,2734,2735,2737,2739,2741,2743,2745,2747],{},[1330,2736,1655],{},[1460,2738,1754],{},[1334,2740,1565],{},[1460,2742,1568],{"separator":1121},[1460,2744,1571],{},[1460,2746,1568],{"separator":1121},[1330,2748,1626],{},[1338,2750,2751],{"encoding":1340},"j = 1,\\dots,s"," (znaky jsou na sobě\nnezávislé) proti ",[1115,2754,2756],{"className":2755},[1315],[1317,2757,2758],{"xmlns":1319},[1321,2759,2760,2768],{},[1324,2761,2762],{},[1327,2763,2764,2766],{},[1330,2765,1332],{},[1334,2767,1565],{},[1338,2769,2770],{"encoding":1340},"H_1",": znaky jsou závislé.",[1207,2773,2774,2775,2932,2935,2936,2953,2954,2986,2987,1662,3046,3049,3050,3071,3072,3089],{},"Testové kritérium",[1115,2776,2778],{"className":2777},[1315],[1317,2779,2780],{"xmlns":1319,"display":1736},[1321,2781,2782,2929],{},[1324,2783,2784,2790,2792,2806,2820,2879,2881,2883,2897,2899,2913,2915],{},[1353,2785,2786,2788],{},[1330,2787,1357],{},[1334,2789,1360],{},[1460,2791,1754],{},[1756,2793,2794,2796,2804],{},[1460,2795,1760],{},[1324,2797,2798,2800,2802],{},[1330,2799,1650],{},[1460,2801,1754],{},[1334,2803,1565],{},[1330,2805,71],{},[1756,2807,2808,2810,2818],{},[1460,2809,1760],{},[1324,2811,2812,2814,2816],{},[1330,2813,1655],{},[1460,2815,1754],{},[1334,2817,1565],{},[1330,2819,1626],{},[2512,2821,2822,2861],{},[1324,2823,2824,2826,2836,2839,2841,2855],{},[1460,2825,1647],{"stretchy":1646},[1327,2827,2828,2830],{},[1330,2829,1458],{},[1324,2831,2832,2834],{},[1330,2833,1650],{},[1330,2835,1655],{},[1460,2837,2838],{},"−",[1330,2840,1458],{},[1327,2842,2843,2849],{},[2496,2844,2845,2847],{"accent":1121},[1330,2846,1110],{},[1460,2848,2502],{},[1324,2850,2851,2853],{},[1330,2852,1650],{},[1330,2854,1655],{},[1353,2856,2857,2859],{},[1460,2858,1658],{"stretchy":1646},[1334,2860,1360],{},[1324,2862,2863,2865],{},[1330,2864,1458],{},[1327,2866,2867,2873],{},[2496,2868,2869,2871],{"accent":1121},[1330,2870,1110],{},[1460,2872,2502],{},[1324,2874,2875,2877],{},[1330,2876,1650],{},[1330,2878,1655],{},[1460,2880,1568],{"separator":1121},[1784,2882],{"width":1786},[1327,2884,2885,2891],{},[2496,2886,2887,2889],{"accent":1121},[1330,2888,1110],{},[1460,2890,2502],{},[1324,2892,2893,2895],{},[1330,2894,1650],{},[1330,2896,1655],{},[1460,2898,1754],{},[1327,2900,2901,2907],{},[2496,2902,2903,2905],{"accent":1121},[1330,2904,1110],{},[1460,2906,2502],{},[1324,2908,2909,2911],{},[1330,2910,1650],{},[1460,2912,1751],{},[2682,2914,2684],{},[1327,2916,2917,2923],{},[2496,2918,2919,2921],{"accent":1121},[1330,2920,1110],{},[1460,2922,2502],{},[1324,2924,2925,2927],{},[1460,2926,1751],{},[1330,2928,1655],{},[1338,2930,2931],{"encoding":1340},"\\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}",[2933,2934],"br",{},"má asymptoticky Pearsonovo (",[1115,2937,2939],{"className":2938},[1315],[1317,2940,2941],{"xmlns":1319},[1321,2942,2943,2951],{},[1324,2944,2945],{},[1353,2946,2947,2949],{},[1330,2948,1357],{},[1334,2950,1360],{},[1338,2952,1363],{"encoding":1340},") rozdělení o ",[1115,2955,2957],{"className":2956},[1315],[1317,2958,2959],{"xmlns":1319},[1321,2960,2961,2983],{},[1324,2962,2963,2965,2967,2969,2971,2973,2975,2977,2979,2981],{},[1460,2964,1647],{"stretchy":1646},[1330,2966,71],{},[1460,2968,2838],{},[1334,2970,1565],{},[1460,2972,1658],{"stretchy":1646},[1460,2974,1647],{"stretchy":1646},[1330,2976,1626],{},[1460,2978,2838],{},[1334,2980,1565],{},[1460,2982,1658],{"stretchy":1646},[1338,2984,2985],{"encoding":1340},"(r-1)(s-1)"," stupních volnosti. Hodnota ",[1115,2988,2990],{"className":2989},[1315],[1317,2991,2992],{"xmlns":1319},[1321,2993,2994,3043],{},[1324,2995,2996,2998,3012,3014],{},[1330,2997,1458],{},[1327,2999,3000,3006],{},[2496,3001,3002,3004],{"accent":1121},[1330,3003,1110],{},[1460,3005,2502],{},[1324,3007,3008,3010],{},[1330,3009,1650],{},[1330,3011,1655],{},[1460,3013,1754],{},[3015,3016,3017],"mstyle",{"scriptlevel":1336,"displaystyle":1121},[2512,3018,3019,3041],{},[1324,3020,3021,3031],{},[1327,3022,3023,3025],{},[1330,3024,1458],{},[1324,3026,3027,3029],{},[1330,3028,1650],{},[1460,3030,1751],{},[1327,3032,3033,3035],{},[1330,3034,1458],{},[1324,3036,3037,3039],{},[1460,3038,1751],{},[1330,3040,1655],{},[1330,3042,1458],{},[1338,3044,3045],{"encoding":1340},"n\\hat p_{ij} = \\dfrac{n_{i\\bullet}n_{\\bullet j}}{n}",[1302,3047,3048],{},"očekávaná četnost"," políčka ",[1115,3051,3053],{"className":3052},[1315],[1317,3054,3055],{"xmlns":1319},[1321,3056,3057,3069],{},[1324,3058,3059,3061,3063,3065,3067],{},[1460,3060,1647],{"stretchy":1646},[1330,3062,1650],{},[1460,3064,1568],{"separator":1121},[1330,3066,1655],{},[1460,3068,1658],{"stretchy":1646},[1338,3070,1661],{"encoding":1340}," — četnost, kterou bychom čekali, kdyby ",[1115,3073,3075],{"className":3074},[1315],[1317,3076,3077],{"xmlns":1319},[1321,3078,3079,3087],{},[1324,3080,3081],{},[1327,3082,3083,3085],{},[1330,3084,1332],{},[1334,3086,1336],{},[1338,3088,1341],{"encoding":1340}," platila.",[1207,3091,3092,3093,1440],{},"Kritický obor: ",[1115,3094,3096],{"className":3095},[1315],[1317,3097,3098],{"xmlns":1319},[1321,3099,3100,3169],{},[1324,3101,3102,3104,3106,3109,3115,3117,3123,3126,3142,3144,3146,3148,3150,3152,3154,3156,3158,3160,3162,3164,3166],{},[1330,3103,1376],{},[1460,3105,1754],{},[1460,3107,3108],{"stretchy":1646},"{",[1353,3110,3111,3113],{},[1330,3112,1357],{},[1334,3114,1360],{},[1460,3116,1730],{},[1353,3118,3119,3121],{},[1330,3120,1357],{},[1334,3122,1360],{},[1460,3124,3125],{},"≥",[3127,3128,3129,3131,3140],"msubsup",{},[1330,3130,1357],{},[1324,3132,3133,3135,3137],{},[1334,3134,1565],{},[1460,3136,2838],{},[1330,3138,3139],{},"α",[1334,3141,1360],{},[1460,3143,1647],{"stretchy":1646},[1460,3145,1647],{"stretchy":1646},[1330,3147,71],{},[1460,3149,2838],{},[1334,3151,1565],{},[1460,3153,1658],{"stretchy":1646},[1460,3155,1647],{"stretchy":1646},[1330,3157,1626],{},[1460,3159,2838],{},[1334,3161,1565],{},[1460,3163,1658],{"stretchy":1646},[1460,3165,1658],{"stretchy":1646},[1460,3167,3168],{"stretchy":1646},"}",[1338,3170,3171],{"encoding":1340},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}((r-1)(s-1))\\}",[1207,3173,3174,3175,3188,3189,3203,3204,3221,3222,3239],{},"Padne-li testové kritérium do ",[1115,3176,3178],{"className":3177},[1315],[1317,3179,3180],{"xmlns":1319},[1321,3181,3182,3186],{},[1324,3183,3184],{},[1330,3185,1376],{},[1338,3187,1376],{"encoding":1340},", zamítáme na hladině ",[1115,3190,3192],{"className":3191},[1315],[1317,3193,3194],{"xmlns":1319},[1321,3195,3196,3200],{},[1324,3197,3198],{},[1330,3199,3139],{},[1338,3201,3202],{"encoding":1340},"\\alpha"," nulovou hypotézu o nezávislosti a přijímáme\n",[1115,3205,3207],{"className":3206},[1315],[1317,3208,3209],{"xmlns":1319},[1321,3210,3211,3219],{},[1324,3212,3213],{},[1327,3214,3215,3217],{},[1330,3216,1332],{},[1334,3218,1565],{},[1338,3220,2770],{"encoding":1340},"; jinak nemáme důvod ",[1115,3223,3225],{"className":3224},[1315],[1317,3226,3227],{"xmlns":1319},[1321,3228,3229,3237],{},[1324,3230,3231],{},[1327,3232,3233,3235],{},[1330,3234,1332],{},[1334,3236,1336],{},[1338,3238,1341],{"encoding":1340}," zamítnout.",[1110,3241,3242,3243,1440],{},"V R počítá test i očekávané četnosti funkce ",[3244,3245,3246],"code",{},"chisq.test()",[1103,3248,3252,3260,3263,3266,3412],{"className":3249,"dataCallout":3251},[1106,3250],"callout-example","example",[1110,3253,3255,3259],{"className":3254},[1113],[1115,3256],{"className":3257,"ariaHidden":1121},[1118,3258,1120],"i-lucide:flask-conical","Příklad: nákup potravin na internetu a vzdělání",[1110,3261,3262],{},"Testujte hypotézu, zda se vzájemně ovlivňuje zkušenost s nákupem potravin na internetu a vzdělání respondenta\n(n = 385 respondentů).",[1110,3264,3265],{},"Základní soubor: respondenti; výběrový soubor: respondenti, kteří odpověděli; měřený znak A: vzdělání, měřený\nznak B: způsob nákupu.",[1141,3267,3268,3307],{},[1144,3269,3270],{},[1147,3271,3272,3275,3278,3281,3284],{},[1150,3273,3274],{},"vzdělání \\ nákup",[1150,3276,3277],{},"ano",[1150,3279,3280],{},"ne, ale plánuji",[1150,3282,3283],{},"ne, neplánuji",[1150,3285,3286],{},[1115,3287,3289],{"className":3288},[1315],[1317,3290,3291],{"xmlns":1319},[1321,3292,3293,3305],{},[1324,3294,3295],{},[1327,3296,3297,3299],{},[1330,3298,1458],{},[1324,3300,3301,3303],{},[1330,3302,1650],{},[1460,3304,1751],{},[1338,3306,1985],{"encoding":1340},[1157,3308,3309,3325,3342,3359,3375],{},[1147,3310,3311,3314,3317,3320,3322],{},[1162,3312,3313],{},"SŠ bez maturity",[1162,3315,3316],{},"4",[1162,3318,3319],{},"13",[1162,3321,2048],{},[1162,3323,3324],{},"29",[1147,3326,3327,3330,3333,3336,3339],{},[1162,3328,3329],{},"SŠ s maturitou, VOŠ",[1162,3331,3332],{},"31",[1162,3334,3335],{},"62",[1162,3337,3338],{},"71",[1162,3340,3341],{},"164",[1147,3343,3344,3347,3350,3353,3356],{},[1162,3345,3346],{},"VŠ",[1162,3348,3349],{},"44",[1162,3351,3352],{},"58",[1162,3354,3355],{},"66",[1162,3357,3358],{},"168",[1147,3360,3361,3364,3367,3370,3372],{},[1162,3362,3363],{},"ZŠ",[1162,3365,3366],{},"3",[1162,3368,3369],{},"9",[1162,3371,2048],{},[1162,3373,3374],{},"24",[1147,3376,3377,3400,3403,3406,3409],{},[1162,3378,3379],{},[1115,3380,3382],{"className":3381},[1315],[1317,3383,3384],{"xmlns":1319},[1321,3385,3386,3398],{},[1324,3387,3388],{},[1327,3389,3390,3392],{},[1330,3391,1458],{},[1324,3393,3394,3396],{},[1460,3395,1751],{},[1330,3397,1655],{},[1338,3399,2377],{"encoding":1340},[1162,3401,3402],{},"82",[1162,3404,3405],{},"142",[1162,3407,3408],{},"161",[1162,3410,3411],{},"385",[1110,3413,3414,3466],{},[1115,3415,3417],{"className":3416},[1315],[1317,3418,3419],{"xmlns":1319},[1321,3420,3421,3463],{},[1324,3422,3423,3429,3431,3441,3443,3453],{},[1327,3424,3425,3427],{},[1330,3426,1332],{},[1334,3428,1336],{},[1460,3430,1730],{},[1327,3432,3433,3435],{},[1330,3434,1110],{},[1324,3436,3437,3439],{},[1330,3438,1650],{},[1330,3440,1655],{},[1460,3442,1754],{},[1327,3444,3445,3447],{},[1330,3446,1110],{},[1324,3448,3449,3451],{},[1330,3450,1650],{},[1460,3452,1751],{},[1327,3454,3455,3457],{},[1330,3456,1110],{},[1324,3458,3459,3461],{},[1460,3460,1751],{},[1330,3462,1655],{},[1338,3464,3465],{"encoding":1340},"H_0: p_{ij} = p_{i\\bullet}p_{\\bullet j}"," — vzdělání a způsob nákupu jsou na sobě nezávislé.",[3468,3469,3472],"pre",{"className":3470,"code":3471,"language":71,"meta":1247,"style":1247},"language-r shiki shiki-themes github-light github-light github-dark","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",[3244,3473,3474,3513,3530,3547,3565,3588,3601,3636,3664,3677],{"__ignoreMap":1247},[1115,3475,3477,3481,3485,3489,3492,3495,3497,3500,3502,3505,3507,3510],{"class":3476,"line":10},"line",[1115,3478,3480],{"class":3479},"sP4rz","tab1",[1115,3482,3484],{"class":3483},"s8jYJ"," \u003C-",[1115,3486,3488],{"class":3487},"snPdu"," matrix",[1115,3490,1647],{"class":3491},"sxrX7",[1115,3493,3494],{"class":3487},"c",[1115,3496,1647],{"class":3491},[1115,3498,3316],{"class":3499},"sBjJW",[1115,3501,1568],{"class":3483},[1115,3503,3504],{"class":3499}," 13",[1115,3506,1568],{"class":3483},[1115,3508,3509],{"class":3499}," 12",[1115,3511,3512],{"class":3483},",\n",[1115,3514,3515,3518,3520,3523,3525,3528],{"class":3476,"line":27},[1115,3516,3517],{"class":3499},"                 31",[1115,3519,1568],{"class":3483},[1115,3521,3522],{"class":3499}," 62",[1115,3524,1568],{"class":3483},[1115,3526,3527],{"class":3499}," 71",[1115,3529,3512],{"class":3483},[1115,3531,3532,3535,3537,3540,3542,3545],{"class":3476,"line":148},[1115,3533,3534],{"class":3499},"                 44",[1115,3536,1568],{"class":3483},[1115,3538,3539],{"class":3499}," 58",[1115,3541,1568],{"class":3483},[1115,3543,3544],{"class":3499}," 66",[1115,3546,3512],{"class":3483},[1115,3548,3549,3552,3554,3557,3559,3561,3563],{"class":3476,"line":111},[1115,3550,3551],{"class":3499},"                 3",[1115,3553,1568],{"class":3483},[1115,3555,3556],{"class":3499},"  9",[1115,3558,1568],{"class":3483},[1115,3560,3509],{"class":3499},[1115,3562,1658],{"class":3491},[1115,3564,3512],{"class":3483},[1115,3566,3567,3570,3573,3576,3578,3581,3583,3586],{"class":3476,"line":96},[1115,3568,3569],{"class":3479},"               nrow",[1115,3571,3572],{"class":3483}," =",[1115,3574,3575],{"class":3499}," 4",[1115,3577,1568],{"class":3483},[1115,3579,3580],{"class":3479}," byrow",[1115,3582,3572],{"class":3483},[1115,3584,3585],{"class":3499}," TRUE",[1115,3587,3512],{"class":3483},[1115,3589,3590,3593,3595,3598],{"class":3476,"line":89},[1115,3591,3592],{"class":3479},"               dimnames",[1115,3594,3572],{"class":3483},[1115,3596,3597],{"class":3487}," list",[1115,3599,3600],{"class":3491},"(\n",[1115,3602,3603,3606,3608,3611,3613,3617,3619,3622,3624,3627,3629,3632,3634],{"class":3476,"line":82},[1115,3604,3605],{"class":3479},"                 vzdelani",[1115,3607,3572],{"class":3483},[1115,3609,3610],{"class":3487}," c",[1115,3612,1647],{"class":3491},[1115,3614,3616],{"class":3615},"sIIMD","\"SS bez maturity\"",[1115,3618,1568],{"class":3483},[1115,3620,3621],{"class":3615}," \"SS s maturitou nebo VOS\"",[1115,3623,1568],{"class":3483},[1115,3625,3626],{"class":3615}," \"VS\"",[1115,3628,1568],{"class":3483},[1115,3630,3631],{"class":3615}," \"ZS\"",[1115,3633,1658],{"class":3491},[1115,3635,3512],{"class":3483},[1115,3637,3638,3641,3644,3646,3648,3651,3653,3656,3658,3661],{"class":3476,"line":75},[1115,3639,3640],{"class":3479},"                 nakup",[1115,3642,3643],{"class":3483},"    =",[1115,3645,3610],{"class":3487},[1115,3647,1647],{"class":3491},[1115,3649,3650],{"class":3615},"\"ano\"",[1115,3652,1568],{"class":3483},[1115,3654,3655],{"class":3615}," \"ne, ale planuji\"",[1115,3657,1568],{"class":3483},[1115,3659,3660],{"class":3615}," \"ne, neplanuji\"",[1115,3662,3663],{"class":3491},")))\n",[1115,3665,3667,3670,3672,3674],{"class":3476,"line":3666},9,[1115,3668,3669],{"class":3487},"chisq.test",[1115,3671,1647],{"class":3491},[1115,3673,3480],{"class":3479},[1115,3675,3676],{"class":3491},")\n",[1115,3678,3679,3681,3683,3685,3687,3690],{"class":3476,"line":72},[1115,3680,3669],{"class":3487},[1115,3682,1647],{"class":3491},[1115,3684,3480],{"class":3479},[1115,3686,1658],{"class":3491},[1115,3688,3689],{"class":3483},"$",[1115,3691,3692],{"class":3479},"expected\n",[3468,3694,3699],{"className":3695,"code":3697,"language":3698,"meta":1247},[3696],"language-text","    Pearson's Chi-squared test\n\ndata:  tab1\nX-squared = 5.4875, df = 6, p-value = 0.483\n\n                         nakup\nvzdelani                        ano ne, ale planuji ne, neplanuji\n  SS bez maturity          6.176623       10.696104      12.12727\n  SS s maturitou nebo VOS 34.929870       60.488312      68.58182\n  VS                      35.781818       61.963636      70.25455\n  ZS                       5.111688        8.851948      10.03636\n","text",[3244,3700,3697],{"__ignoreMap":1247},[1110,3702,3703,3704,3727,3728,3742,3743,3763,3764,3781],{},"Všechny očekávané četnosti jsou nad 5, aproximace je v pořádku. Testové kritérium ",[1115,3705,3707],{"className":3706},[1315],[1317,3708,3709],{"xmlns":1319},[1321,3710,3711,3724],{},[1324,3712,3713,3719,3721],{},[1353,3714,3715,3717],{},[1330,3716,1357],{},[1334,3718,1360],{},[1460,3720,1754],{},[1334,3722,3723],{},"5,49",[1338,3725,3726],{"encoding":1340},"\\chi^2 = 5{,}49"," s ",[1115,3729,3731],{"className":3730},[1315],[1317,3732,3733],{"xmlns":1319},[1321,3734,3735,3740],{},[1324,3736,3737],{},[1334,3738,3739],{},"6",[1338,3741,3739],{"encoding":1340}," stupni\nvolnosti dává p-hodnotu ",[1115,3744,3746],{"className":3745},[1315],[1317,3747,3748],{"xmlns":1319},[1321,3749,3750,3760],{},[1324,3751,3752,3755,3757],{},[1334,3753,3754],{},"0,483",[1460,3756,1462],{},[1334,3758,3759],{},"0,05",[1338,3761,3762],{"encoding":1340},"0{,}483 > 0{,}05",": ",[1115,3765,3767],{"className":3766},[1315],[1317,3768,3769],{"xmlns":1319},[1321,3770,3771,3779],{},[1324,3772,3773],{},[1327,3774,3775,3777],{},[1330,3776,1332],{},[1334,3778,1336],{},[1338,3780,1341],{"encoding":1340}," nezamítáme, závislost mezi zkušeností s nákupem potravin na\ninternetu a vzděláním respondenta se neprokázala.",[1103,3783,3785,3792,3795,3840],{"className":3784,"dataCallout":3251},[1106,3250],[1110,3786,3788,3791],{"className":3787},[1113],[1115,3789],{"className":3790,"ariaHidden":1121},[1118,3258,1120],"Příklad: vzdělání a zveřejňování citlivých údajů na Facebooku",[1110,3793,3794],{},"Mezi 221 osobami bylo zaznamenáno vzdělání a zda zveřejňují na Facebooku citlivé údaje. Proveďte test\nnezávislosti.",[1141,3796,3797,3811],{},[1144,3798,3799],{},[1147,3800,3801,3804,3807,3809],{},[1150,3802,3803],{},"zveřejňuje \\ vzdělání",[1150,3805,3806],{},"SŠ",[1150,3808,3346],{},[1150,3810,3363],{},[1157,3812,3813,3827],{},[1147,3814,3815,3818,3821,3824],{},[1162,3816,3817],{},"ne",[1162,3819,3820],{},"20",[1162,3822,3823],{},"33",[1162,3825,3826],{},"39",[1147,3828,3829,3831,3834,3837],{},[1162,3830,3277],{},[1162,3832,3833],{},"25",[1162,3835,3836],{},"28",[1162,3838,3839],{},"76",[1110,3841,3842,3893],{},[1115,3843,3845],{"className":3844},[1315],[1317,3846,3847],{"xmlns":1319},[1321,3848,3849,3891],{},[1324,3850,3851,3857,3859,3869,3871,3881],{},[1327,3852,3853,3855],{},[1330,3854,1332],{},[1334,3856,1336],{},[1460,3858,1730],{},[1327,3860,3861,3863],{},[1330,3862,1110],{},[1324,3864,3865,3867],{},[1330,3866,1650],{},[1330,3868,1655],{},[1460,3870,1754],{},[1327,3872,3873,3875],{},[1330,3874,1110],{},[1324,3876,3877,3879],{},[1330,3878,1650],{},[1460,3880,1751],{},[1327,3882,3883,3885],{},[1330,3884,1110],{},[1324,3886,3887,3889],{},[1460,3888,1751],{},[1330,3890,1655],{},[1338,3892,3465],{"encoding":1340}," — vzdělání a zveřejňování citlivých údajů jsou na sobě nezávislé.",[3468,3895,3897],{"className":3470,"code":3896,"language":71,"meta":1247,"style":1247},"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",[3244,3898,3899,3928,3947,3966,3976,3999,4023,4033],{"__ignoreMap":1247},[1115,3900,3901,3904,3906,3908,3910,3912,3914,3916,3918,3921,3923,3926],{"class":3476,"line":10},[1115,3902,3903],{"class":3479},"tab2",[1115,3905,3484],{"class":3483},[1115,3907,3488],{"class":3487},[1115,3909,1647],{"class":3491},[1115,3911,3494],{"class":3487},[1115,3913,1647],{"class":3491},[1115,3915,3820],{"class":3499},[1115,3917,1568],{"class":3483},[1115,3919,3920],{"class":3499}," 33",[1115,3922,1568],{"class":3483},[1115,3924,3925],{"class":3499}," 39",[1115,3927,3512],{"class":3483},[1115,3929,3930,3933,3935,3938,3940,3943,3945],{"class":3476,"line":27},[1115,3931,3932],{"class":3499},"                 25",[1115,3934,1568],{"class":3483},[1115,3936,3937],{"class":3499}," 28",[1115,3939,1568],{"class":3483},[1115,3941,3942],{"class":3499}," 76",[1115,3944,1658],{"class":3491},[1115,3946,3512],{"class":3483},[1115,3948,3949,3951,3953,3956,3958,3960,3962,3964],{"class":3476,"line":148},[1115,3950,3569],{"class":3479},[1115,3952,3572],{"class":3483},[1115,3954,3955],{"class":3499}," 2",[1115,3957,1568],{"class":3483},[1115,3959,3580],{"class":3479},[1115,3961,3572],{"class":3483},[1115,3963,3585],{"class":3499},[1115,3965,3512],{"class":3483},[1115,3967,3968,3970,3972,3974],{"class":3476,"line":111},[1115,3969,3592],{"class":3479},[1115,3971,3572],{"class":3483},[1115,3973,3597],{"class":3487},[1115,3975,3600],{"class":3491},[1115,3977,3978,3981,3983,3985,3987,3990,3992,3995,3997],{"class":3476,"line":96},[1115,3979,3980],{"class":3479},"                 zverejnuje",[1115,3982,3572],{"class":3483},[1115,3984,3610],{"class":3487},[1115,3986,1647],{"class":3491},[1115,3988,3989],{"class":3615},"\"ne\"",[1115,3991,1568],{"class":3483},[1115,3993,3994],{"class":3615}," \"ano\"",[1115,3996,1658],{"class":3491},[1115,3998,3512],{"class":3483},[1115,4000,4001,4003,4006,4008,4010,4013,4015,4017,4019,4021],{"class":3476,"line":89},[1115,4002,3605],{"class":3479},[1115,4004,4005],{"class":3483},"   =",[1115,4007,3610],{"class":3487},[1115,4009,1647],{"class":3491},[1115,4011,4012],{"class":3615},"\"SS\"",[1115,4014,1568],{"class":3483},[1115,4016,3626],{"class":3615},[1115,4018,1568],{"class":3483},[1115,4020,3631],{"class":3615},[1115,4022,3663],{"class":3491},[1115,4024,4025,4027,4029,4031],{"class":3476,"line":82},[1115,4026,3669],{"class":3487},[1115,4028,1647],{"class":3491},[1115,4030,3903],{"class":3479},[1115,4032,3676],{"class":3491},[1115,4034,4035,4037,4039,4041,4043,4045],{"class":3476,"line":75},[1115,4036,3669],{"class":3487},[1115,4038,1647],{"class":3491},[1115,4040,3903],{"class":3479},[1115,4042,1658],{"class":3491},[1115,4044,3689],{"class":3483},[1115,4046,3692],{"class":3479},[3468,4048,4051],{"className":4049,"code":4050,"language":3698,"meta":1247},[3696],"    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",[3244,4052,4050],{"__ignoreMap":1247},[1110,4054,4055,4056,3727,4079,4092,4093,3763,4113,4130,4131,1440],{},"I zde jsou všechny očekávané četnosti nad 5. Testové kritérium ",[1115,4057,4059],{"className":4058},[1315],[1317,4060,4061],{"xmlns":1319},[1321,4062,4063,4076],{},[1324,4064,4065,4071,4073],{},[1353,4066,4067,4069],{},[1330,4068,1357],{},[1334,4070,1360],{},[1460,4072,1754],{},[1334,4074,4075],{},"6,87",[1338,4077,4078],{"encoding":1340},"\\chi^2 = 6{,}87",[1115,4080,4082],{"className":4081},[1315],[1317,4083,4084],{"xmlns":1319},[1321,4085,4086,4090],{},[1324,4087,4088],{},[1334,4089,1360],{},[1338,4091,1360],{"encoding":1340}," stupni volnosti dává\np-hodnotu ",[1115,4094,4096],{"className":4095},[1315],[1317,4097,4098],{"xmlns":1319},[1321,4099,4100,4110],{},[1324,4101,4102,4105,4108],{},[1334,4103,4104],{},"0,032",[1460,4106,4107],{},"\u003C",[1334,4109,3759],{},[1338,4111,4112],{"encoding":1340},"0{,}032 \u003C 0{,}05",[1115,4114,4116],{"className":4115},[1315],[1317,4117,4118],{"xmlns":1319},[1321,4119,4120,4128],{},[1324,4121,4122],{},[1327,4123,4124,4126],{},[1330,4125,1332],{},[1334,4127,1336],{},[1338,4129,1341],{"encoding":1340}," zamítáme — na rozdíl od předchozího příkladu tady vzdělání a zveřejňování\ncitlivých údajů na Facebooku na sobě ",[1302,4132,4133],{},"závisí",[1110,4135,4136,4137,4154],{},"Srovnání pozorovaných a očekávaných četností ukazuje, proč jeden příklad ",[1115,4138,4140],{"className":4139},[1315],[1317,4141,4142],{"xmlns":1319},[1321,4143,4144,4152],{},[1324,4145,4146],{},[1327,4147,4148,4150],{},[1330,4149,1332],{},[1334,4151,1336],{},[1338,4153,1341],{"encoding":1340}," nezamítá a druhý ano — ve druhém\nse pozorované sloupce (zejména u ZŠ) systematicky odchylují od očekávaných, v prvním kolísají jen náhodně kolem nich:",[1110,4156,4157],{},[4158,4159],"img",{"alt":4160,"className":4161,"src":4163},"mask-kt-observed-expected",[1130,4162],"wikilink-broken","\u002Fwiki-assets\u002Fmask-kt-observed-expected.png",[1110,4165,4166,4167,4184,4185,1730],{},"Totéž je vidět na rozdělení testového kritéria: u prvního příkladu leží ",[1115,4168,4170],{"className":4169},[1315],[1317,4171,4172],{"xmlns":1319},[1321,4173,4174,4182],{},[1324,4175,4176],{},[1353,4177,4178,4180],{},[1330,4179,1357],{},[1334,4181,1360],{},[1338,4183,1363],{"encoding":1340}," hluboko pod kritickou hodnotou,\nu druhého uvnitř kritického oboru ",[1115,4186,4188],{"className":4187},[1315],[1317,4189,4190],{"xmlns":1319},[1321,4191,4192,4196],{},[1324,4193,4194],{},[1330,4195,1376],{},[1338,4197,1376],{"encoding":1340},[1110,4199,4200],{},[4158,4201],{"alt":4202,"className":4203,"src":4204},"mask-kt-chi2-kriticky-obor",[1130,4162],"\u002Fwiki-assets\u002Fmask-kt-chi2-kriticky-obor.png",[1136,4206,1424],{"id":4207},"cramérův-koeficient-kontingence",[1110,4209,4210,4211,1730],{},"Test nezávislosti pouze rozhodne, zda jsou znaky závislé, nebo ne. Sílu závislosti měří ",[1302,4212,4213],{},"Cramérův koeficient\nkontingence",[1115,4215,4217],{"className":4216},[1315],[1317,4218,4219],{"xmlns":1319,"display":1736},[1321,4220,4221,4277],{},[1324,4222,4223,4225,4227,4253,4255,4257,4259,4261,4264,4267,4269,4271,4273,4275],{},[1330,4224,1437],{},[1460,4226,1754],{},[4228,4229,4230],"msqrt",{},[2512,4231,4232,4238],{},[1353,4233,4234,4236],{},[1330,4235,1357],{},[1334,4237,1360],{},[1324,4239,4240,4242,4244,4247,4249,4251],{},[1330,4241,1458],{},[1460,4243,1647],{"stretchy":1646},[1330,4245,4246],{},"m",[1460,4248,2838],{},[1334,4250,1565],{},[1460,4252,1658],{"stretchy":1646},[1460,4254,1568],{"separator":1121},[1784,4256],{"width":1786},[1330,4258,4246],{},[1460,4260,1754],{},[1330,4262,4263],{},"min",[1460,4265,4266],{},"⁡",[1460,4268,1647],{"stretchy":1646},[1330,4270,71],{},[1460,4272,1568],{"separator":1121},[1330,4274,1626],{},[1460,4276,1658],{"stretchy":1646},[1338,4278,4279],{"encoding":1340},"V = \\sqrt{\\frac{\\chi^2}{n(m-1)}}, \\qquad m = \\min(r, s)",[1110,4281,4282,4283,4300,4301,4319,4320,4338],{},"kde ",[1115,4284,4286],{"className":4285},[1315],[1317,4287,4288],{"xmlns":1319},[1321,4289,4290,4298],{},[1324,4291,4292],{},[1353,4293,4294,4296],{},[1330,4295,1357],{},[1334,4297,1360],{},[1338,4299,1363],{"encoding":1340}," je hodnota testového kritéria z testu nezávislosti. ",[1115,4302,4304],{"className":4303},[1315],[1317,4305,4306],{"xmlns":1319},[1321,4307,4308,4316],{},[1324,4309,4310,4312,4314],{},[1330,4311,1437],{},[1460,4313,1754],{},[1334,4315,1336],{},[1338,4317,4318],{"encoding":1340},"V = 0"," odpovídá úplné nezávislosti znaků,\n",[1115,4321,4323],{"className":4322},[1315],[1317,4324,4325],{"xmlns":1319},[1321,4326,4327,4335],{},[1324,4328,4329,4331,4333],{},[1330,4330,1437],{},[1460,4332,1754],{},[1334,4334,1565],{},[1338,4336,4337],{"encoding":1340},"V = 1"," jejich úplné závislosti.",[3468,4340,4342],{"className":3470,"code":4341,"language":71,"meta":1247,"style":1247},"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",[3244,4343,4344,4419,4482,4487],{"__ignoreMap":1247},[1115,4345,4346,4349,4351,4354,4356,4359,4361,4363,4365,4367,4369,4371,4374,4377,4380,4383,4386,4388,4390,4392,4395,4397,4399,4401,4404,4406,4408,4411,4414,4417],{"class":3476,"line":10},[1115,4347,4348],{"class":3479},"V1",[1115,4350,3484],{"class":3483},[1115,4352,4353],{"class":3487}," sqrt",[1115,4355,1647],{"class":3491},[1115,4357,4358],{"class":3487},"as.numeric",[1115,4360,1647],{"class":3491},[1115,4362,3669],{"class":3487},[1115,4364,1647],{"class":3491},[1115,4366,3480],{"class":3479},[1115,4368,1658],{"class":3491},[1115,4370,3689],{"class":3483},[1115,4372,4373],{"class":3479},"statistic",[1115,4375,4376],{"class":3491},") ",[1115,4378,4379],{"class":3483},"\u002F",[1115,4381,4382],{"class":3491}," (",[1115,4384,4385],{"class":3487},"sum",[1115,4387,1647],{"class":3491},[1115,4389,3480],{"class":3479},[1115,4391,4376],{"class":3491},[1115,4393,4394],{"class":3483},"*",[1115,4396,4382],{"class":3491},[1115,4398,4263],{"class":3487},[1115,4400,1647],{"class":3491},[1115,4402,4403],{"class":3487},"dim",[1115,4405,1647],{"class":3491},[1115,4407,3480],{"class":3479},[1115,4409,4410],{"class":3491},")) ",[1115,4412,4413],{"class":3483},"-",[1115,4415,4416],{"class":3499}," 1",[1115,4418,3663],{"class":3491},[1115,4420,4421,4424,4426,4428,4430,4432,4434,4436,4438,4440,4442,4444,4446,4448,4450,4452,4454,4456,4458,4460,4462,4464,4466,4468,4470,4472,4474,4476,4478,4480],{"class":3476,"line":27},[1115,4422,4423],{"class":3479},"V2",[1115,4425,3484],{"class":3483},[1115,4427,4353],{"class":3487},[1115,4429,1647],{"class":3491},[1115,4431,4358],{"class":3487},[1115,4433,1647],{"class":3491},[1115,4435,3669],{"class":3487},[1115,4437,1647],{"class":3491},[1115,4439,3903],{"class":3479},[1115,4441,1658],{"class":3491},[1115,4443,3689],{"class":3483},[1115,4445,4373],{"class":3479},[1115,4447,4376],{"class":3491},[1115,4449,4379],{"class":3483},[1115,4451,4382],{"class":3491},[1115,4453,4385],{"class":3487},[1115,4455,1647],{"class":3491},[1115,4457,3903],{"class":3479},[1115,4459,4376],{"class":3491},[1115,4461,4394],{"class":3483},[1115,4463,4382],{"class":3491},[1115,4465,4263],{"class":3487},[1115,4467,1647],{"class":3491},[1115,4469,4403],{"class":3487},[1115,4471,1647],{"class":3491},[1115,4473,3903],{"class":3479},[1115,4475,4410],{"class":3491},[1115,4477,4413],{"class":3483},[1115,4479,4416],{"class":3499},[1115,4481,3663],{"class":3491},[1115,4483,4484],{"class":3476,"line":148},[1115,4485,4486],{"class":3479},"V1\n",[1115,4488,4489],{"class":3476,"line":111},[1115,4490,4491],{"class":3479},"V2\n",[3468,4493,4496],{"className":4494,"code":4495,"language":3698,"meta":1247},[3696],"[1] 0.08441958\n[1] 0.1762822\n",[3244,4497,4495],{"__ignoreMap":1247},[1110,4499,4500],{},[4158,4501],{"alt":4502,"className":4503,"src":4504},"mask-kt-cramerovo-v",[1130,4162],"\u002Fwiki-assets\u002Fmask-kt-cramerovo-v.png",[1110,4506,4507,4508,4527,4528,4545,4546,3763,4565,4582],{},"U nákupu potravin je ",[1115,4509,4511],{"className":4510},[1315],[1317,4512,4513],{"xmlns":1319},[1321,4514,4515,4524],{},[1324,4516,4517,4519,4521],{},[1330,4518,1437],{},[1460,4520,1754],{},[1334,4522,4523],{},"0,084",[1338,4525,4526],{"encoding":1340},"V = 0{,}084"," zanedbatelné — ostatně ",[1115,4529,4531],{"className":4530},[1315],[1317,4532,4533],{"xmlns":1319},[1321,4534,4535,4543],{},[1324,4536,4537],{},[1327,4538,4539,4541],{},[1330,4540,1332],{},[1334,4542,1336],{},[1338,4544,1341],{"encoding":1340}," jsme ani nezamítli. U zveřejňování údajů je ",[1115,4547,4549],{"className":4548},[1315],[1317,4550,4551],{"xmlns":1319},[1321,4552,4553,4562],{},[1324,4554,4555,4557,4559],{},[1330,4556,1437],{},[1460,4558,1754],{},[1334,4560,4561],{},"0,176",[1338,4563,4564],{"encoding":1340},"V = 0{,}176",[1115,4566,4568],{"className":4567},[1315],[1317,4569,4570],{"xmlns":1319},[1321,4571,4572,4580],{},[1324,4573,4574],{},[1327,4575,4576,4578],{},[1330,4577,1332],{},[1334,4579,1336],{},[1338,4581,1341],{"encoding":1340},"\njsme zamítli, ale samotná závislost je stále slabá.",[1136,4584,1445],{"id":4585},"čtyřpolní-tabulka",[1110,4587,4588,4590,4591,4604,4605,4618,4619,4641],{},[1302,4589,1445],{}," je speciální případ kontingenční tabulky, kdy oba znaky ",[1115,4592,4594],{"className":4593},[1315],[1317,4595,4596],{"xmlns":1319},[1321,4597,4598,4602],{},[1324,4599,4600],{},[1330,4601,1546],{},[1338,4603,1546],{"encoding":1340}," i ",[1115,4606,4608],{"className":4607},[1315],[1317,4609,4610],{"xmlns":1319},[1321,4611,4612,4616],{},[1324,4613,4614],{},[1330,4615,1595],{},[1338,4617,1595],{"encoding":1340}," mají jen dvě varianty\n(",[1115,4620,4622],{"className":4621},[1315],[1317,4623,4624],{"xmlns":1319},[1321,4625,4626,4638],{},[1324,4627,4628,4630,4632,4634,4636],{},[1330,4629,71],{},[1460,4631,1754],{},[1330,4633,1626],{},[1460,4635,1754],{},[1334,4637,1360],{},[1338,4639,4640],{"encoding":1340},"r = s = 2","):",[1141,4643,4644,4728],{},[1144,4645,4646],{},[1147,4647,4648,4667,4686,4705],{},[1150,4649,4650],{},[1115,4651,4653],{"className":4652},[1315],[1317,4654,4655],{"xmlns":1319},[1321,4656,4657,4665],{},[1324,4658,4659,4661,4663],{},[1330,4660,1546],{},[1330,4662,1894],{"mathvariant":1893},[1330,4664,1595],{},[1338,4666,1899],{"encoding":1340},[1150,4668,4669],{},[1115,4670,4672],{"className":4671},[1315],[1317,4673,4674],{"xmlns":1319},[1321,4675,4676,4684],{},[1324,4677,4678],{},[1327,4679,4680,4682],{},[1330,4681,1595],{},[1334,4683,1565],{},[1338,4685,1919],{"encoding":1340},[1150,4687,4688],{},[1115,4689,4691],{"className":4690},[1315],[1317,4692,4693],{"xmlns":1319},[1321,4694,4695,4703],{},[1324,4696,4697],{},[1327,4698,4699,4701],{},[1330,4700,1595],{},[1334,4702,1360],{},[1338,4704,1939],{"encoding":1340},[1150,4706,4707],{},[1115,4708,4710],{"className":4709},[1315],[1317,4711,4712],{"xmlns":1319},[1321,4713,4714,4726],{},[1324,4715,4716],{},[1327,4717,4718,4720],{},[1330,4719,1458],{},[1324,4721,4722,4724],{},[1330,4723,1650],{},[1460,4725,1751],{},[1338,4727,1985],{"encoding":1340},[1157,4729,4730,4812,4894],{},[1147,4731,4732,4751,4770,4789],{},[1162,4733,4734],{},[1115,4735,4737],{"className":4736},[1315],[1317,4738,4739],{"xmlns":1319},[1321,4740,4741,4749],{},[1324,4742,4743],{},[1327,4744,4745,4747],{},[1330,4746,1546],{},[1334,4748,1565],{},[1338,4750,2009],{"encoding":1340},[1162,4752,4753],{},[1115,4754,4756],{"className":4755},[1315],[1317,4757,4758],{"xmlns":1319},[1321,4759,4760,4768],{},[1324,4761,4762],{},[1327,4763,4764,4766],{},[1330,4765,1458],{},[1334,4767,2027],{},[1338,4769,2030],{"encoding":1340},[1162,4771,4772],{},[1115,4773,4775],{"className":4774},[1315],[1317,4776,4777],{"xmlns":1319},[1321,4778,4779,4787],{},[1324,4780,4781],{},[1327,4782,4783,4785],{},[1330,4784,1458],{},[1334,4786,2048],{},[1338,4788,2051],{"encoding":1340},[1162,4790,4791],{},[1115,4792,4794],{"className":4793},[1315],[1317,4795,4796],{"xmlns":1319},[1321,4797,4798,4810],{},[1324,4799,4800],{},[1327,4801,4802,4804],{},[1330,4803,1458],{},[1324,4805,4806,4808],{},[1334,4807,1565],{},[1460,4809,1751],{},[1338,4811,2101],{"encoding":1340},[1147,4813,4814,4833,4852,4871],{},[1162,4815,4816],{},[1115,4817,4819],{"className":4818},[1315],[1317,4820,4821],{"xmlns":1319},[1321,4822,4823,4831],{},[1324,4824,4825],{},[1327,4826,4827,4829],{},[1330,4828,1546],{},[1334,4830,1360],{},[1338,4832,2123],{"encoding":1340},[1162,4834,4835],{},[1115,4836,4838],{"className":4837},[1315],[1317,4839,4840],{"xmlns":1319},[1321,4841,4842,4850],{},[1324,4843,4844],{},[1327,4845,4846,4848],{},[1330,4847,1458],{},[1334,4849,2141],{},[1338,4851,2144],{"encoding":1340},[1162,4853,4854],{},[1115,4855,4857],{"className":4856},[1315],[1317,4858,4859],{"xmlns":1319},[1321,4860,4861,4869],{},[1324,4862,4863],{},[1327,4864,4865,4867],{},[1330,4866,1458],{},[1334,4868,2162],{},[1338,4870,2165],{"encoding":1340},[1162,4872,4873],{},[1115,4874,4876],{"className":4875},[1315],[1317,4877,4878],{"xmlns":1319},[1321,4879,4880,4892],{},[1324,4881,4882],{},[1327,4883,4884,4886],{},[1330,4885,1458],{},[1324,4887,4888,4890],{},[1334,4889,1360],{},[1460,4891,1751],{},[1338,4893,2215],{"encoding":1340},[1147,4895,4896,4919,4942,4965],{},[1162,4897,4898],{},[1115,4899,4901],{"className":4900},[1315],[1317,4902,4903],{"xmlns":1319},[1321,4904,4905,4917],{},[1324,4906,4907],{},[1327,4908,4909,4911],{},[1330,4910,1458],{},[1324,4912,4913,4915],{},[1460,4914,1751],{},[1330,4916,1655],{},[1338,4918,2377],{"encoding":1340},[1162,4920,4921],{},[1115,4922,4924],{"className":4923},[1315],[1317,4925,4926],{"xmlns":1319},[1321,4927,4928,4940],{},[1324,4929,4930],{},[1327,4931,4932,4934],{},[1330,4933,1458],{},[1324,4935,4936,4938],{},[1460,4937,1751],{},[1334,4939,1565],{},[1338,4941,2401],{"encoding":1340},[1162,4943,4944],{},[1115,4945,4947],{"className":4946},[1315],[1317,4948,4949],{"xmlns":1319},[1321,4950,4951,4963],{},[1324,4952,4953],{},[1327,4954,4955,4957],{},[1330,4956,1458],{},[1324,4958,4959,4961],{},[1460,4960,1751],{},[1334,4962,1360],{},[1338,4964,2425],{"encoding":1340},[1162,4966,4967],{},[1115,4968,4970],{"className":4969},[1315],[1317,4971,4972],{"xmlns":1319},[1321,4973,4974,4978],{},[1324,4975,4976],{},[1330,4977,1458],{},[1338,4979,1458],{"encoding":1340},[1110,4981,1471,4982,5000],{},[1115,4983,4985],{"className":4984},[1315],[1317,4986,4987],{"xmlns":1319},[1321,4988,4989,4997],{},[1324,4990,4991,4993,4995],{},[1330,4992,1458],{},[1460,4994,1462],{},[1334,4996,1465],{},[1338,4998,4999],{"encoding":1340},"n > 40"," se místo obecného vzorce používá zjednodušená varianta testového kritéria:",[1115,5002,5004],{"className":5003},[1315],[1317,5005,5006],{"xmlns":1319,"display":1736},[1321,5007,5008,5102],{},[1324,5009,5010,5016,5018,5020,5022],{},[1353,5011,5012,5014],{},[1330,5013,1357],{},[1334,5015,1360],{},[1460,5017,1754],{},[1330,5019,1458],{},[2682,5021,2684],{},[2512,5023,5024,5060],{},[1324,5025,5026,5028,5034,5040,5042,5048,5054],{},[1460,5027,1647],{"stretchy":1646},[1327,5029,5030,5032],{},[1330,5031,1458],{},[1334,5033,2027],{},[1327,5035,5036,5038],{},[1330,5037,1458],{},[1334,5039,2162],{},[1460,5041,2838],{},[1327,5043,5044,5046],{},[1330,5045,1458],{},[1334,5047,2048],{},[1327,5049,5050,5052],{},[1330,5051,1458],{},[1334,5053,2141],{},[1353,5055,5056,5058],{},[1460,5057,1658],{"stretchy":1646},[1334,5059,1360],{},[1324,5061,5062,5072,5082,5092],{},[1327,5063,5064,5066],{},[1330,5065,1458],{},[1324,5067,5068,5070],{},[1334,5069,1565],{},[1460,5071,1751],{},[1327,5073,5074,5076],{},[1330,5075,1458],{},[1324,5077,5078,5080],{},[1334,5079,1360],{},[1460,5081,1751],{},[1327,5083,5084,5086],{},[1330,5085,1458],{},[1324,5087,5088,5090],{},[1460,5089,1751],{},[1334,5091,1565],{},[1327,5093,5094,5096],{},[1330,5095,1458],{},[1324,5097,5098,5100],{},[1460,5099,1751],{},[1334,5101,1360],{},[1338,5103,5104],{"encoding":1340},"\\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}}",[1110,5106,5107,5108,5168,5169,5205,5206,5209,5210,5213],{},"s kritickým oborem ",[1115,5109,5111],{"className":5110},[1315],[1317,5112,5113],{"xmlns":1319},[1321,5114,5115,5165],{},[1324,5116,5117,5123,5125,5127,5133,5135,5141,5143,5157,5159,5161,5163],{},[1327,5118,5119,5121],{},[1330,5120,1376],{},[1330,5122,3139],{},[1460,5124,1754],{},[1460,5126,3108],{"stretchy":1646},[1353,5128,5129,5131],{},[1330,5130,1357],{},[1334,5132,1360],{},[1460,5134,1730],{},[1353,5136,5137,5139],{},[1330,5138,1357],{},[1334,5140,1360],{},[1460,5142,3125],{},[3127,5144,5145,5147,5155],{},[1330,5146,1357],{},[1324,5148,5149,5151,5153],{},[1334,5150,1565],{},[1460,5152,2838],{},[1330,5154,3139],{},[1334,5156,1360],{},[1460,5158,1647],{"stretchy":1646},[1334,5160,1565],{},[1460,5162,1658],{"stretchy":1646},[1460,5164,3168],{"stretchy":1646},[1338,5166,5167],{"encoding":1340},"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 ",[1115,5170,5172],{"className":5171},[1315],[1317,5173,5174],{"xmlns":1319},[1321,5175,5176,5202],{},[1324,5177,5178,5180,5182,5184,5186,5188,5190,5192,5194,5196,5198,5200],{},[1460,5179,1647],{"stretchy":1646},[1330,5181,71],{},[1460,5183,2838],{},[1334,5185,1565],{},[1460,5187,1658],{"stretchy":1646},[1460,5189,1647],{"stretchy":1646},[1330,5191,1626],{},[1460,5193,2838],{},[1334,5195,1565],{},[1460,5197,1658],{"stretchy":1646},[1460,5199,1754],{},[1334,5201,1565],{},[1338,5203,5204],{"encoding":1340},"(r-1)(s-1) = 1"," stupeň volnosti. V R dává tuto hodnotu ",[3244,5207,5208],{},"chisq.test(tab, correct = FALSE)",". Bez ",[3244,5211,5212],{},"correct = FALSE"," R u tabulky 2 × 2 použije Yatesovu korekci na kontinuitu a testové kritérium vyjde menší.",[1136,5215,1478],{"id":5216},"mcnemarův-test",[1110,5218,5219,5220,5223,5224,5226,5227,5230,5231,5234,5235,5237],{},"Čtyřpolní tabulka z předchozí sekce porovnává dva ",[1302,5221,5222],{},"různé"," znaky na stejném souboru. ",[1302,5225,1478],{}," řeší\njinou situaci: na prvcích základního souboru se měří ",[1302,5228,5229],{},"jeden"," alternativní znak, a to ",[1302,5232,5233],{},"dvakrát"," — před a po\nnějakém zásahu. Cílem je zjistit, zda zásah změnil pravděpodobnostní rozdělení variant tohoto znaku. Jde tedy o\n",[1302,5236,1474],{}," (stejné prvky měřené opakovaně), ne o dva nezávisle naměřené znaky.",[1110,5239,5240],{},"Kontingenční tabulka před\u002Fpo má tvar:",[1141,5242,5243,5278],{},[1144,5244,5245],{},[1147,5246,5247,5250,5253,5255],{},[1150,5248,5249],{},"před \\ po",[1150,5251,5252],{},"+",[1150,5254,2838],{},[1150,5256,5257],{},[1115,5258,5260],{"className":5259},[1315],[1317,5261,5262],{"xmlns":1319},[1321,5263,5264,5276],{},[1324,5265,5266],{},[1327,5267,5268,5270],{},[1330,5269,1458],{},[1324,5271,5272,5274],{},[1330,5273,1650],{},[1460,5275,1751],{},[1338,5277,1985],{"encoding":1340},[1157,5279,5280,5345,5410],{},[1147,5281,5282,5284,5303,5322],{},[1162,5283,5252],{},[1162,5285,5286],{},[1115,5287,5289],{"className":5288},[1315],[1317,5290,5291],{"xmlns":1319},[1321,5292,5293,5301],{},[1324,5294,5295],{},[1327,5296,5297,5299],{},[1330,5298,1458],{},[1334,5300,2027],{},[1338,5302,2030],{"encoding":1340},[1162,5304,5305],{},[1115,5306,5308],{"className":5307},[1315],[1317,5309,5310],{"xmlns":1319},[1321,5311,5312,5320],{},[1324,5313,5314],{},[1327,5315,5316,5318],{},[1330,5317,1458],{},[1334,5319,2048],{},[1338,5321,2051],{"encoding":1340},[1162,5323,5324],{},[1115,5325,5327],{"className":5326},[1315],[1317,5328,5329],{"xmlns":1319},[1321,5330,5331,5343],{},[1324,5332,5333],{},[1327,5334,5335,5337],{},[1330,5336,1458],{},[1324,5338,5339,5341],{},[1334,5340,1565],{},[1460,5342,1751],{},[1338,5344,2101],{"encoding":1340},[1147,5346,5347,5349,5368,5387],{},[1162,5348,2838],{},[1162,5350,5351],{},[1115,5352,5354],{"className":5353},[1315],[1317,5355,5356],{"xmlns":1319},[1321,5357,5358,5366],{},[1324,5359,5360],{},[1327,5361,5362,5364],{},[1330,5363,1458],{},[1334,5365,2141],{},[1338,5367,2144],{"encoding":1340},[1162,5369,5370],{},[1115,5371,5373],{"className":5372},[1315],[1317,5374,5375],{"xmlns":1319},[1321,5376,5377,5385],{},[1324,5378,5379],{},[1327,5380,5381,5383],{},[1330,5382,1458],{},[1334,5384,2162],{},[1338,5386,2165],{"encoding":1340},[1162,5388,5389],{},[1115,5390,5392],{"className":5391},[1315],[1317,5393,5394],{"xmlns":1319},[1321,5395,5396,5408],{},[1324,5397,5398],{},[1327,5399,5400,5402],{},[1330,5401,1458],{},[1324,5403,5404,5406],{},[1334,5405,1360],{},[1460,5407,1751],{},[1338,5409,2215],{"encoding":1340},[1147,5411,5412,5435,5458,5481],{},[1162,5413,5414],{},[1115,5415,5417],{"className":5416},[1315],[1317,5418,5419],{"xmlns":1319},[1321,5420,5421,5433],{},[1324,5422,5423],{},[1327,5424,5425,5427],{},[1330,5426,1458],{},[1324,5428,5429,5431],{},[1460,5430,1751],{},[1330,5432,1655],{},[1338,5434,2377],{"encoding":1340},[1162,5436,5437],{},[1115,5438,5440],{"className":5439},[1315],[1317,5441,5442],{"xmlns":1319},[1321,5443,5444,5456],{},[1324,5445,5446],{},[1327,5447,5448,5450],{},[1330,5449,1458],{},[1324,5451,5452,5454],{},[1460,5453,1751],{},[1334,5455,1565],{},[1338,5457,2401],{"encoding":1340},[1162,5459,5460],{},[1115,5461,5463],{"className":5462},[1315],[1317,5464,5465],{"xmlns":1319},[1321,5466,5467,5479],{},[1324,5468,5469],{},[1327,5470,5471,5473],{},[1330,5472,1458],{},[1324,5474,5475,5477],{},[1460,5476,1751],{},[1334,5478,1360],{},[1338,5480,2425],{"encoding":1340},[1162,5482,5483],{},[1115,5484,5486],{"className":5485},[1315],[1317,5487,5488],{"xmlns":1319},[1321,5489,5490,5494],{},[1324,5491,5492],{},[1330,5493,1458],{},[1338,5495,1458],{"encoding":1340},[1110,5497,5498,5499,5516,5517,5534,5535,5538,5539,5516,5556,5573,5574,5577],{},"Pole ",[1115,5500,5502],{"className":5501},[1315],[1317,5503,5504],{"xmlns":1319},[1321,5505,5506,5514],{},[1324,5507,5508],{},[1327,5509,5510,5512],{},[1330,5511,1458],{},[1334,5513,2027],{},[1338,5515,2030],{"encoding":1340}," a ",[1115,5518,5520],{"className":5519},[1315],[1317,5521,5522],{"xmlns":1319},[1321,5523,5524,5532],{},[1324,5525,5526],{},[1327,5527,5528,5530],{},[1330,5529,1458],{},[1334,5531,2162],{},[1338,5533,2165],{"encoding":1340}," jsou ",[1302,5536,5537],{},"shodná"," (prvek zůstal ve stejné variantě), pole ",[1115,5540,5542],{"className":5541},[1315],[1317,5543,5544],{"xmlns":1319},[1321,5545,5546,5554],{},[1324,5547,5548],{},[1327,5549,5550,5552],{},[1330,5551,1458],{},[1334,5553,2048],{},[1338,5555,2051],{"encoding":1340},[1115,5557,5559],{"className":5558},[1315],[1317,5560,5561],{"xmlns":1319},[1321,5562,5563,5571],{},[1324,5564,5565],{},[1327,5566,5567,5569],{},[1330,5568,1458],{},[1334,5570,2141],{},[1338,5572,2144],{"encoding":1340}," jsou\n",[1302,5575,5576],{},"diskordantní"," (prvek mezi měřeními variantu změnil) — jen ta rozhodují o výsledku testu:",[1110,5579,5580],{},[4158,5581],{"alt":5582,"className":5583,"src":5584},"mask-kt-mcnemar-tabulka",[1130,4162],"\u002Fwiki-assets\u002Fmask-kt-mcnemar-tabulka.png",[1110,5586,5587],{},[1302,5588,2636],{},[2638,5590,5591,5628,5709,5767],{},[1207,5592,5593,5627],{},[1115,5594,5596],{"className":5595},[1315],[1317,5597,5598],{"xmlns":1319},[1321,5599,5600,5624],{},[1324,5601,5602,5608,5610,5616,5618],{},[1327,5603,5604,5606],{},[1330,5605,1332],{},[1334,5607,1336],{},[1460,5609,1730],{},[1327,5611,5612,5614],{},[1330,5613,1110],{},[1334,5615,2048],{},[1460,5617,1754],{},[1327,5619,5620,5622],{},[1330,5621,1110],{},[1334,5623,2141],{},[1338,5625,5626],{"encoding":1340},"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.",[1207,5629,2774,5630,5692,5694,5695,5708],{},[1115,5631,5633],{"className":5632},[1315],[1317,5634,5635],{"xmlns":1319,"display":1736},[1321,5636,5637,5689],{},[1324,5638,5639,5645,5647],{},[1353,5640,5641,5643],{},[1330,5642,1357],{},[1334,5644,1360],{},[1460,5646,1754],{},[2512,5648,5649,5673],{},[1324,5650,5651,5653,5659,5661,5667],{},[1460,5652,1647],{"stretchy":1646},[1327,5654,5655,5657],{},[1330,5656,1458],{},[1334,5658,2048],{},[1460,5660,2838],{},[1327,5662,5663,5665],{},[1330,5664,1458],{},[1334,5666,2141],{},[1353,5668,5669,5671],{},[1460,5670,1658],{"stretchy":1646},[1334,5672,1360],{},[1324,5674,5675,5681,5683],{},[1327,5676,5677,5679],{},[1330,5678,1458],{},[1334,5680,2048],{},[1460,5682,5252],{},[1327,5684,5685,5687],{},[1330,5686,1458],{},[1334,5688,2141],{},[1338,5690,5691],{"encoding":1340},"\\chi^2 = \\frac{(n_{12} - n_{21})^2}{n_{12} + n_{21}}",[2933,5693],{},"má asymptoticky Pearsonovo rozdělení o ",[1115,5696,5698],{"className":5697},[1315],[1317,5699,5700],{"xmlns":1319},[1321,5701,5702,5706],{},[1324,5703,5704],{},[1334,5705,1565],{},[1338,5707,1565],{"encoding":1340}," stupni volnosti.",[1207,5710,3092,5711,1440],{},[1115,5712,5714],{"className":5713},[1315],[1317,5715,5716],{"xmlns":1319},[1321,5717,5718,5764],{},[1324,5719,5720,5722,5724,5726,5732,5734,5740,5742,5756,5758,5760,5762],{},[1330,5721,1376],{},[1460,5723,1754],{},[1460,5725,3108],{"stretchy":1646},[1353,5727,5728,5730],{},[1330,5729,1357],{},[1334,5731,1360],{},[1460,5733,1730],{},[1353,5735,5736,5738],{},[1330,5737,1357],{},[1334,5739,1360],{},[1460,5741,3125],{},[3127,5743,5744,5746,5754],{},[1330,5745,1357],{},[1324,5747,5748,5750,5752],{},[1334,5749,1565],{},[1460,5751,2838],{},[1330,5753,3139],{},[1334,5755,1360],{},[1460,5757,1647],{"stretchy":1646},[1334,5759,1565],{},[1460,5761,1658],{"stretchy":1646},[1460,5763,3168],{"stretchy":1646},[1338,5765,5766],{"encoding":1340},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}(1)\\}",[1207,5768,3174,5769,5782,5783,5800,5801,5818],{},[1115,5770,5772],{"className":5771},[1315],[1317,5773,5774],{"xmlns":1319},[1321,5775,5776,5780],{},[1324,5777,5778],{},[1330,5779,1376],{},[1338,5781,1376],{"encoding":1340},", zamítáme ",[1115,5784,5786],{"className":5785},[1315],[1317,5787,5788],{"xmlns":1319},[1321,5789,5790,5798],{},[1324,5791,5792],{},[1327,5793,5794,5796],{},[1330,5795,1332],{},[1334,5797,1336],{},[1338,5799,1341],{"encoding":1340}," a přijímáme ",[1115,5802,5804],{"className":5803},[1315],[1317,5805,5806],{"xmlns":1319},[1321,5807,5808,5816],{},[1324,5809,5810],{},[1327,5811,5812,5814],{},[1330,5813,1332],{},[1334,5815,1565],{},[1338,5817,2770],{"encoding":1340},": zásah rozdělení variant změnil.",[1110,5820,5821,5822,5825,5826,5829,5830,5832],{},"V R počítá tento test funkce ",[3244,5823,5824],{},"mcnemar.test()",". Vzorec výše ",[1302,5827,5828],{},"neobsahuje korekci na kontinuitu"," — aby R vrátilo\npřesně tuto hodnotu, musí se volat s ",[3244,5831,5212],{}," (viz Časté chyby níže).",[1103,5834,5836,5843,5846,5849,5946],{"className":5835,"dataCallout":3251},[1106,3250],[1110,5837,5839,5842],{"className":5838},[1113],[1115,5840],{"className":5841,"ariaHidden":1121},[1118,3258,1120],"Příklad: informační kampaň a zveřejňování na Facebooku",[1110,5844,5845],{},"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.",[1110,5847,5848],{},"Základní soubor: všichni studenti; výběrový soubor: vybraní studenti; měřený znak: zveřejňování (ano \u002F ne).",[1141,5850,5851,5886],{},[1144,5852,5853],{},[1147,5854,5855,5857,5860,5863],{},[1150,5856,5249],{},[1150,5858,5859],{},"nezveřejňuje",[1150,5861,5862],{},"zveřejňuje",[1150,5864,5865],{},[1115,5866,5868],{"className":5867},[1315],[1317,5869,5870],{"xmlns":1319},[1321,5871,5872,5884],{},[1324,5873,5874],{},[1327,5875,5876,5878],{},[1330,5877,1458],{},[1324,5879,5880,5882],{},[1330,5881,1650],{},[1460,5883,1751],{},[1338,5885,1985],{"encoding":1340},[1157,5887,5888,5900,5912],{},[1147,5889,5890,5892,5894,5897],{},[1162,5891,5859],{},[1162,5893,3374],{},[1162,5895,5896],{},"68",[1162,5898,5899],{},"92",[1147,5901,5902,5904,5906,5909],{},[1162,5903,5862],{},[1162,5905,3836],{},[1162,5907,5908],{},"50",[1162,5910,5911],{},"78",[1147,5913,5914,5937,5940,5943],{},[1162,5915,5916],{},[1115,5917,5919],{"className":5918},[1315],[1317,5920,5921],{"xmlns":1319},[1321,5922,5923,5935],{},[1324,5924,5925],{},[1327,5926,5927,5929],{},[1330,5928,1458],{},[1324,5930,5931,5933],{},[1460,5932,1751],{},[1330,5934,1655],{},[1338,5936,2377],{"encoding":1340},[1162,5938,5939],{},"52",[1162,5941,5942],{},"118",[1162,5944,5945],{},"170",[1110,5947,5948,5981],{},[1115,5949,5951],{"className":5950},[1315],[1317,5952,5953],{"xmlns":1319},[1321,5954,5955,5979],{},[1324,5956,5957,5963,5965,5971,5973],{},[1327,5958,5959,5961],{},[1330,5960,1332],{},[1334,5962,1336],{},[1460,5964,1730],{},[1327,5966,5967,5969],{},[1330,5968,1110],{},[1334,5970,2048],{},[1460,5972,1754],{},[1327,5974,5975,5977],{},[1330,5976,1110],{},[1334,5978,2141],{},[1338,5980,5626],{"encoding":1340}," — informační kampaň nemá na chování vliv.",[3468,5983,5985],{"className":3470,"code":5984,"language":71,"meta":1247,"style":1247},"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",[3244,5986,5987,6011,6025,6043,6053,6076,6095],{"__ignoreMap":1247},[1115,5988,5989,5992,5994,5996,5998,6000,6002,6004,6006,6009],{"class":3476,"line":10},[1115,5990,5991],{"class":3479},"tab3",[1115,5993,3484],{"class":3483},[1115,5995,3488],{"class":3487},[1115,5997,1647],{"class":3491},[1115,5999,3494],{"class":3487},[1115,6001,1647],{"class":3491},[1115,6003,3374],{"class":3499},[1115,6005,1568],{"class":3483},[1115,6007,6008],{"class":3499}," 68",[1115,6010,3512],{"class":3483},[1115,6012,6013,6016,6018,6021,6023],{"class":3476,"line":27},[1115,6014,6015],{"class":3499},"                 28",[1115,6017,1568],{"class":3483},[1115,6019,6020],{"class":3499}," 50",[1115,6022,1658],{"class":3491},[1115,6024,3512],{"class":3483},[1115,6026,6027,6029,6031,6033,6035,6037,6039,6041],{"class":3476,"line":148},[1115,6028,3569],{"class":3479},[1115,6030,3572],{"class":3483},[1115,6032,3955],{"class":3499},[1115,6034,1568],{"class":3483},[1115,6036,3580],{"class":3479},[1115,6038,3572],{"class":3483},[1115,6040,3585],{"class":3499},[1115,6042,3512],{"class":3483},[1115,6044,6045,6047,6049,6051],{"class":3476,"line":111},[1115,6046,3592],{"class":3479},[1115,6048,3572],{"class":3483},[1115,6050,3597],{"class":3487},[1115,6052,3600],{"class":3491},[1115,6054,6055,6058,6060,6062,6064,6067,6069,6072,6074],{"class":3476,"line":96},[1115,6056,6057],{"class":3479},"                 pred",[1115,6059,3572],{"class":3483},[1115,6061,3610],{"class":3487},[1115,6063,1647],{"class":3491},[1115,6065,6066],{"class":3615},"\"nezverejnuje\"",[1115,6068,1568],{"class":3483},[1115,6070,6071],{"class":3615}," \"zverejnuje\"",[1115,6073,1658],{"class":3491},[1115,6075,3512],{"class":3483},[1115,6077,6078,6081,6083,6085,6087,6089,6091,6093],{"class":3476,"line":89},[1115,6079,6080],{"class":3479},"                 po",[1115,6082,4005],{"class":3483},[1115,6084,3610],{"class":3487},[1115,6086,1647],{"class":3491},[1115,6088,6066],{"class":3615},[1115,6090,1568],{"class":3483},[1115,6092,6071],{"class":3615},[1115,6094,3663],{"class":3491},[1115,6096,6097,6100,6102,6104,6106,6109,6111,6114],{"class":3476,"line":82},[1115,6098,6099],{"class":3487},"mcnemar.test",[1115,6101,1647],{"class":3491},[1115,6103,5991],{"class":3479},[1115,6105,1568],{"class":3483},[1115,6107,6108],{"class":3479}," correct",[1115,6110,3572],{"class":3483},[1115,6112,6113],{"class":3499}," FALSE",[1115,6115,3676],{"class":3491},[3468,6117,6120],{"className":6118,"code":6119,"language":3698,"meta":1247},[3696],"    McNemar's Chi-squared test\n\ndata:  tab3\nMcNemar's chi-squared = 16.667, df = 1, p-value = 4.456e-05\n",[3244,6121,6119],{"__ignoreMap":1247},[1110,6123,6124,6125,3763,6144,6161,6162,6179],{},"P-hodnota ",[1115,6126,6128],{"className":6127},[1315],[1317,6129,6130],{"xmlns":1319},[1321,6131,6132,6141],{},[1324,6133,6134,6137,6139],{},[1334,6135,6136],{},"0,00004456",[1460,6138,4107],{},[1334,6140,3759],{},[1338,6142,6143],{"encoding":1340},"0{,}00004456 \u003C 0{,}05",[1115,6145,6147],{"className":6146},[1315],[1317,6148,6149],{"xmlns":1319},[1321,6150,6151,6159],{},[1324,6152,6153],{},[1327,6154,6155,6157],{},[1330,6156,1332],{},[1334,6158,1336],{},[1338,6160,1341],{"encoding":1340}," zamítáme, přijímáme ",[1115,6163,6165],{"className":6164},[1315],[1317,6166,6167],{"xmlns":1319},[1321,6168,6169,6177],{},[1324,6170,6171],{},[1327,6172,6173,6175],{},[1330,6174,1332],{},[1334,6176,1565],{},[1338,6178,2770],{"encoding":1340}," — informační kampaň měla vliv na změnu\nchování studentů ve zveřejňování údajů na Facebooku.",[1136,6181,6183],{"id":6182},"časté-chyby","Časté chyby",[1103,6185,6189,6197],{"className":6186,"dataCallout":6188},[1106,6187],"callout-warning","warning",[1110,6190,6192,6196],{"className":6191},[1113],[1115,6193],{"className":6194,"ariaHidden":1121},[1118,6195,1120],"i-lucide:triangle-alert","Test nezávislosti na párovaných datech",[1110,6198,6199,6200,6202],{},"Tabulka před\u002Fpo vypadá jako obyčejná kontingenční tabulka, ale ",[3244,6201,3246],{}," 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.",[3468,6204,6206],{"className":3470,"code":6205,"language":71,"meta":1247,"style":1247},"chisq.test(tab3)\n",[3244,6207,6208],{"__ignoreMap":1247},[1115,6209,6210,6212,6214,6216],{"class":3476,"line":10},[1115,6211,3669],{"class":3487},[1115,6213,1647],{"class":3491},[1115,6215,5991],{"class":3479},[1115,6217,3676],{"class":3491},[3468,6219,6222],{"className":6220,"code":6221,"language":3698,"meta":1247},[3696],"    Pearson's Chi-squared test with Yates' continuity correction\n\ndata:  tab3\nX-squared = 1.4793, df = 1, p-value = 0.2239\n",[3244,6223,6221],{"__ignoreMap":1247},[1110,6225,6124,6226,6245,6246,6263,6264,6266,6267,1440],{},[1115,6227,6229],{"className":6228},[1315],[1317,6230,6231],{"xmlns":1319},[1321,6232,6233,6242],{},[1324,6234,6235,6238,6240],{},[1334,6236,6237],{},"0,224",[1460,6239,1462],{},[1334,6241,3759],{},[1338,6243,6244],{"encoding":1340},"0{,}224 > 0{,}05"," by vedla k nezamítnutí ",[1115,6247,6249],{"className":6248},[1315],[1317,6250,6251],{"xmlns":1319},[1321,6252,6253,6261],{},[1324,6254,6255],{},[1327,6256,6257,6259],{},[1330,6258,1332],{},[1334,6260,1336],{},[1338,6262,1341],{"encoding":1340}," — opačný závěr než správný McNemarův test. Na\npárovaná data (stejné prvky měřené dvakrát) vždy patří ",[3244,6265,5824],{},", nikdy ",[3244,6268,3246],{},[1103,6270,6272,6281],{"className":6271,"dataCallout":6188},[1106,6187],[1110,6273,6275,6278,6279],{"className":6274},[1113],[1115,6276],{"className":6277,"ariaHidden":1121},[1118,6195,1120],"Výchozí korekce na kontinuitu v ",[3244,6280,5824],{},[1110,6282,6283,6284,6287],{},"Bez argumentu ",[3244,6285,6286],{},"correct"," R ve výchozím nastavení použije Yatesovu korekci na kontinuitu, která dá jinou\np-hodnotu než nekorigovaný vzorec uvedený výše.",[3468,6289,6291],{"className":3470,"code":6290,"language":71,"meta":1247,"style":1247},"mcnemar.test(tab3)\n",[3244,6292,6293],{"__ignoreMap":1247},[1115,6294,6295,6297,6299,6301],{"class":3476,"line":10},[1115,6296,6099],{"class":3487},[1115,6298,1647],{"class":3491},[1115,6300,5991],{"class":3479},[1115,6302,3676],{"class":3491},[3468,6304,6307],{"className":6305,"code":6306,"language":3698,"meta":1247},[3696],"    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",[3244,6308,6306],{"__ignoreMap":1247},[1110,6310,6311,6312,6330,6331,6350,6351,6364,6365,1440],{},"Oproti nekorigované hodnotě ",[1115,6313,6315],{"className":6314},[1315],[1317,6316,6317],{"xmlns":1319},[1321,6318,6319,6327],{},[1324,6320,6321,6323,6325],{},[1330,6322,1110],{},[1460,6324,1754],{},[1334,6326,6136],{},[1338,6328,6329],{"encoding":1340},"p = 0{,}00004456"," vyjde ",[1115,6332,6334],{"className":6333},[1315],[1317,6335,6336],{"xmlns":1319},[1321,6337,6338,6347],{},[1324,6339,6340,6342,6344],{},[1330,6341,1110],{},[1460,6343,1754],{},[1334,6345,6346],{},"0,00006879",[1338,6348,6349],{"encoding":1340},"p = 0{,}00006879"," — v tomto příkladu obě vedou ke\nstejnému rozhodnutí, ale u hodnot blíž hranici ",[1115,6352,6354],{"className":6353},[1315],[1317,6355,6356],{"xmlns":1319},[1321,6357,6358,6362],{},[1324,6359,6360],{},[1330,6361,3139],{},[1338,6363,3202],{"encoding":1340}," by korekce mohla rozhodnutí změnit. Aby R reprodukovalo\nnekorigovaný vzorec, je třeba vždy volat ",[3244,6366,6367],{},"mcnemar.test(x, correct = FALSE)",[1136,6369,1202],{"id":1201},[1204,6371,6372,6377,6382,6387,6392,6400,6408],{},[1207,6373,6374],{},[1127,6375,1133],{"className":6376,"dataFsResolvedFilePath":1131,"href":1132},[1130],[1207,6378,6379],{},[1127,6380,1195],{"className":6381,"dataFsResolvedFilePath":1193,"href":1194},[1130],[1207,6383,6384],{},[1127,6385,1182],{"className":6386,"dataFsResolvedFilePath":1180,"href":1181},[1130],[1207,6388,6389],{},[1127,6390,1169],{"className":6391,"dataFsResolvedFilePath":1167,"href":1168},[1130],[1207,6393,6394],{},[1127,6395,6399],{"className":6396,"dataFsResolvedFilePath":6397,"href":6398},[1130],"topics\u002Fregresni-a-korelacni-analyza.md","\u002Fwiki\u002Fregresni-a-korelacni-analyza","Regresní a korelační analýza",[1207,6401,6402],{},[1127,6403,6407],{"className":6404,"dataFsResolvedFilePath":6405,"href":6406},[1130],"topics\u002Fregulacni-diagramy-a-indexy-zpusobilosti.md","\u002Fwiki\u002Fregulacni-diagramy-a-indexy-zpusobilosti","Regulační diagramy a indexy způsobilosti",[1207,6409,6410],{},[1127,6411,6413],{"className":6412,"dataFsResolvedFilePath":1232,"href":1233},[1130],"Tahák pro R",[1136,6415,1237],{"id":934},[1110,6417,1240,6418,1245],{},[1242,6419,1244],{},[6421,6422,6423],"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 .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: 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: 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var(--shiki-dark-text-decoration);}",{"title":1247,"searchDepth":27,"depth":27,"links":6425},[6426,6427,6428,6429,6430,6431,6432,6433],{"id":1482,"depth":27,"text":1483},{"id":2599,"depth":27,"text":2600},{"id":4207,"depth":27,"text":1424},{"id":4585,"depth":27,"text":1445},{"id":5216,"depth":27,"text":1478},{"id":6182,"depth":27,"text":6183},{"id":1201,"depth":27,"text":1202},{"id":934,"depth":27,"text":1237},{},"\u002Ftopics\u002Fkontingencni-tabulky",{"title":1277,"description":1247},[6438,6439],"raw\u002Fmask\u002F05 kontingenční tabulky.pdf","raw\u002Fmask\u002Fpříklady 04 a 05.docx","topics\u002Fkontingencni-tabulky",[23,67,714,486,768,71],"topic","E-gDO0c3LOdVy6YB6I-h8KKMQKlrqjomMSQWFmOANZE",{"id":6445,"title":1169,"body":6446,"course":23,"courses":1252,"created":1253,"description":1247,"extension":1254,"meta":10902,"navigation":1256,"path":10903,"seo":10904,"sources":10905,"stem":10906,"tags":10907,"type":6442,"updated":1253,"__hash__":10908},"topics\u002Ftopics\u002Fnahodne-veliciny-a-rozdeleni.md",{"type":1096,"value":6447,"toc":10890},[6448,6451,6738,6742,6975,6978,7046,7050,7057,7064,7223,7262,7265,7499,7502,7580,7634,7732,7736,7838,7841,7845,7851,7907,7910,7918,8069,8076,8129,8159,8278,8281,8329,8491,8546,8553,8660,8722,8726,8829,8832,8869,8875,8934,8983,8990,9026,9032,9035,9083,9090,9152,9158,9161,9225,9232,9271,9277,9280,9284,9310,9641,9679,9734,9864,9870,9874,9881,9900,10006,10050,10069,10164,10181,10223,10398,10405,10408,10411,10565,10568,10644,10650,10652,10838,10840,10881,10883,10887],[1099,6449,1169],{"id":6450},"náhodné-veličiny-a-rozdělení-pravděpodobnosti",[1103,6452,6454,6460],{"className":6453,"dataCallout":1287},[1106,1286],[1110,6455,6457,1295],{"className":6456},[1113],[1115,6458],{"className":6459,"ariaHidden":1121},[1118,1294,1120],[1204,6461,6462,6473,6578,6645,6726],{},[1207,6463,6464,6465,6468,6469,6472],{},"Náhodná veličina je funkce, která výsledkům pokusu přiřazuje reálná čísla; rozlišujeme ",[1302,6466,6467],{},"diskrétní"," (izolované hodnoty s nenulovou pravděpodobností) a ",[1302,6470,6471],{},"spojité"," (hodnoty z intervalu, každý bod má nulovou pravděpodobnost).",[1207,6474,6475,6476,1425,6479,6518,6519,6556,6557,6577],{},"Každou náhodnou veličinu popisuje ",[1302,6477,6478],{},"distribuční funkce",[1115,6480,6482],{"className":6481},[1315],[1317,6483,6484],{"xmlns":1319},[1321,6485,6486,6515],{},[1324,6487,6488,6491,6493,6496,6498,6500,6503,6505,6508,6511,6513],{},[1330,6489,6490],{},"F",[1460,6492,1647],{"stretchy":1646},[1330,6494,6495],{},"x",[1460,6497,1658],{"stretchy":1646},[1460,6499,1754],{},[1330,6501,6502],{},"P",[1460,6504,1647],{"stretchy":1646},[1330,6506,6507],{},"X",[1460,6509,6510],{},"≤",[1330,6512,6495],{},[1460,6514,1658],{"stretchy":1646},[1338,6516,6517],{"encoding":1340},"F(x) = P(X \\le x)","; u spojité veličiny platí ",[1115,6520,6522],{"className":6521},[1315],[1317,6523,6524],{"xmlns":1319},[1321,6525,6526,6553],{},[1324,6527,6528,6536,6538,6540,6542,6544,6547,6549,6551],{},[1353,6529,6530,6532],{},[1330,6531,6490],{},[1460,6533,6535],{"mathvariant":1893,"lspace":6534,"rspace":6534},"0em","′",[1460,6537,1647],{"stretchy":1646},[1330,6539,6495],{},[1460,6541,1658],{"stretchy":1646},[1460,6543,1754],{},[1330,6545,6546],{},"f",[1460,6548,1647],{"stretchy":1646},[1330,6550,6495],{},[1460,6552,1658],{"stretchy":1646},[1338,6554,6555],{"encoding":1340},"F'(x) = f(x)",", kde ",[1115,6558,6560],{"className":6559},[1315],[1317,6561,6562],{"xmlns":1319},[1321,6563,6564,6574],{},[1324,6565,6566,6568,6570,6572],{},[1330,6567,6546],{},[1460,6569,1647],{"stretchy":1646},[1330,6571,6495],{},[1460,6573,1658],{"stretchy":1646},[1338,6575,6576],{"encoding":1340},"f(x)"," je hustota pravděpodobnosti.",[1207,6579,6580,6581,1440],{},"Pravděpodobnost na intervalu se počítá jako ",[1115,6582,6584],{"className":6583},[1315],[1317,6585,6586],{"xmlns":1319},[1321,6587,6588,6642],{},[1324,6589,6590,6592,6594,6600,6602,6604,6606,6612,6614,6616,6618,6620,6626,6628,6630,6632,6634,6640],{},[1330,6591,6502],{},[1460,6593,1647],{"stretchy":1646},[1327,6595,6596,6598],{},[1330,6597,6495],{},[1334,6599,1565],{},[1460,6601,4107],{},[1330,6603,6507],{},[1460,6605,4107],{},[1327,6607,6608,6610],{},[1330,6609,6495],{},[1334,6611,1360],{},[1460,6613,1658],{"stretchy":1646},[1460,6615,1754],{},[1330,6617,6490],{},[1460,6619,1647],{"stretchy":1646},[1327,6621,6622,6624],{},[1330,6623,6495],{},[1334,6625,1360],{},[1460,6627,1658],{"stretchy":1646},[1460,6629,2838],{},[1330,6631,6490],{},[1460,6633,1647],{"stretchy":1646},[1327,6635,6636,6638],{},[1330,6637,6495],{},[1334,6639,1565],{},[1460,6641,1658],{"stretchy":1646},[1338,6643,6644],{"encoding":1340},"P(x_1 \u003C X \u003C x_2) = F(x_2) - F(x_1)",[1207,6646,6647,1425,6650,6682,6683,2725,6686,2725,6689,6692,6693,6707,6708,1440],{},[1302,6648,6649],{},"Normální rozdělení",[1115,6651,6653],{"className":6652},[1315],[1317,6654,6655],{"xmlns":1319},[1321,6656,6657,6679],{},[1324,6658,6659,6662,6664,6667,6670,6677],{},[1330,6660,6661],{},"N",[1460,6663,1647],{"stretchy":1646},[1330,6665,6666],{},"μ",[1460,6668,6669],{"separator":1121},";",[1353,6671,6672,6675],{},[1330,6673,6674],{},"σ",[1334,6676,1360],{},[1460,6678,1658],{"stretchy":1646},[1338,6680,6681],{"encoding":1340},"N(\\mu; \\sigma^2)"," je nejdůležitější spojité rozdělení; v R ho počítáme funkcemi ",[3244,6684,6685],{},"dnorm",[3244,6687,6688],{},"pnorm",[3244,6690,6691],{},"qnorm"," — R jako parametr očekává směrodatnou odchylku ",[1115,6694,6696],{"className":6695},[1315],[1317,6697,6698],{"xmlns":1319},[1321,6699,6700,6704],{},[1324,6701,6702],{},[1330,6703,6674],{},[1338,6705,6706],{"encoding":1340},"\\sigma",", ne rozptyl ",[1115,6709,6711],{"className":6710},[1315],[1317,6712,6713],{"xmlns":1319},[1321,6714,6715,6723],{},[1324,6716,6717],{},[1353,6718,6719,6721],{},[1330,6720,6674],{},[1334,6722,1360],{},[1338,6724,6725],{"encoding":1340},"\\sigma^2",[1207,6727,6728,2725,6731,5516,6734,6737],{},[1302,6729,6730],{},"Studentovo",[1302,6732,6733],{},"Pearsonovo (χ²)",[1302,6735,6736],{},"Fisherovo-Snedecorovo"," rozdělení slouží jako nástroj pro pozdější konstrukci intervalů spolehlivosti a testování hypotéz.",[1136,6739,6741],{"id":6740},"náhodná-veličina","Náhodná veličina",[1110,6743,6744,6747,6748,6763,6764,1425,6766,6779,6780,6800,6801,6556,6814,6838,6839,2725,6852,2725,6866,6880,6881,2725,6894,2725,6908,6922,6923,6936,6937,6950,6951,1440],{},[1127,6745,1133],{"className":6746,"dataFsResolvedFilePath":1131,"href":1132},[1130]," pracuje s veličinami, jejichž hodnota závisí na náhodě. Formálně: uvažujeme základní prostor ",[1115,6749,6751],{"className":6750},[1315],[1317,6752,6753],{"xmlns":1319},[1321,6754,6755,6760],{},[1324,6756,6757],{},[1330,6758,6759],{"mathvariant":1893},"Ω",[1338,6761,6762],{"encoding":1340},"\\Omega"," přiřazený výsledkům pokusu. ",[1302,6765,6741],{},[1115,6767,6769],{"className":6768},[1315],[1317,6770,6771],{"xmlns":1319},[1321,6772,6773,6777],{},[1324,6774,6775],{},[1330,6776,6507],{},[1338,6778,6507],{"encoding":1340}," je funkce, která prvkům ",[1115,6781,6783],{"className":6782},[1315],[1317,6784,6785],{"xmlns":1319},[1321,6786,6787,6797],{},[1324,6788,6789,6792,6795],{},[1330,6790,6791],{},"ω",[1460,6793,6794],{},"∈",[1330,6796,6759],{"mathvariant":1893},[1338,6798,6799],{"encoding":1340},"\\omega \\in \\Omega"," přiřazuje reálná čísla ",[1115,6802,6804],{"className":6803},[1315],[1317,6805,6806],{"xmlns":1319},[1321,6807,6808,6812],{},[1324,6809,6810],{},[1330,6811,6495],{},[1338,6813,6495],{"encoding":1340},[1115,6815,6817],{"className":6816},[1315],[1317,6818,6819],{"xmlns":1319},[1321,6820,6821,6835],{},[1324,6822,6823,6825,6827,6829,6831,6833],{},[1330,6824,6495],{},[1460,6826,1754],{},[1330,6828,6507],{},[1460,6830,1647],{"stretchy":1646},[1330,6832,6791],{},[1460,6834,1658],{"stretchy":1646},[1338,6836,6837],{"encoding":1340},"x = X(\\omega)",". Náhodné veličiny značíme velkými písmeny (",[1115,6840,6842],{"className":6841},[1315],[1317,6843,6844],{"xmlns":1319},[1321,6845,6846,6850],{},[1324,6847,6848],{},[1330,6849,6507],{},[1338,6851,6507],{"encoding":1340},[1115,6853,6855],{"className":6854},[1315],[1317,6856,6857],{"xmlns":1319},[1321,6858,6859,6864],{},[1324,6860,6861],{},[1330,6862,6863],{},"Y",[1338,6865,6863],{"encoding":1340},[1115,6867,6869],{"className":6868},[1315],[1317,6870,6871],{"xmlns":1319},[1321,6872,6873,6878],{},[1324,6874,6875],{},[1330,6876,6877],{},"T",[1338,6879,6877],{"encoding":1340},"), jejich konkrétní hodnoty odpovídajícími malými písmeny (",[1115,6882,6884],{"className":6883},[1315],[1317,6885,6886],{"xmlns":1319},[1321,6887,6888,6892],{},[1324,6889,6890],{},[1330,6891,6495],{},[1338,6893,6495],{"encoding":1340},[1115,6895,6897],{"className":6896},[1315],[1317,6898,6899],{"xmlns":1319},[1321,6900,6901,6906],{},[1324,6902,6903],{},[1330,6904,6905],{},"y",[1338,6907,6905],{"encoding":1340},[1115,6909,6911],{"className":6910},[1315],[1317,6912,6913],{"xmlns":1319},[1321,6914,6915,6920],{},[1324,6916,6917],{},[1330,6918,6919],{},"t",[1338,6921,6919],{"encoding":1340},"); pravděpodobnost, že ",[1115,6924,6926],{"className":6925},[1315],[1317,6927,6928],{"xmlns":1319},[1321,6929,6930,6934],{},[1324,6931,6932],{},[1330,6933,6507],{},[1338,6935,6507],{"encoding":1340}," nabyla hodnoty ",[1115,6938,6940],{"className":6939},[1315],[1317,6941,6942],{"xmlns":1319},[1321,6943,6944,6948],{},[1324,6945,6946],{},[1330,6947,6495],{},[1338,6949,6495],{"encoding":1340},", zapisujeme ",[1115,6952,6954],{"className":6953},[1315],[1317,6955,6956],{"xmlns":1319},[1321,6957,6958,6972],{},[1324,6959,6960,6962,6964,6966,6968,6970],{},[1330,6961,6502],{},[1460,6963,1647],{"stretchy":1646},[1330,6965,6507],{},[1460,6967,1754],{},[1330,6969,6495],{},[1460,6971,1658],{"stretchy":1646},[1338,6973,6974],{"encoding":1340},"P(X = x)",[1110,6976,6977],{},"Podle typu hodnot, kterých náhodná veličina nabývá, rozlišujeme dva typy:",[1204,6979,6980,7040],{},[1207,6981,6982,6985,6986,6999,7000,7039],{},[1302,6983,6984],{},"Diskrétní náhodná veličina"," — prvky ",[1115,6987,6989],{"className":6988},[1315],[1317,6990,6991],{"xmlns":1319},[1321,6992,6993,6997],{},[1324,6994,6995],{},[1330,6996,6759],{"mathvariant":1893},[1338,6998,6762],{"encoding":1340}," se zobrazí na osu reálných čísel jako izolované body ",[1115,7001,7003],{"className":7002},[1315],[1317,7004,7005],{"xmlns":1319},[1321,7006,7007,7036],{},[1324,7008,7009,7015,7017,7023,7025,7027,7029],{},[1327,7010,7011,7013],{},[1330,7012,6495],{},[1334,7014,1565],{},[1460,7016,1568],{"separator":1121},[1327,7018,7019,7021],{},[1330,7020,6495],{},[1334,7022,1360],{},[1460,7024,1568],{"separator":1121},[1460,7026,1571],{},[1460,7028,1568],{"separator":1121},[1327,7030,7031,7033],{},[1330,7032,6495],{},[1330,7034,7035],{},"k",[1338,7037,7038],{"encoding":1340},"x_1, x_2, \\dots, x_k",", přičemž každý z nich má nenulovou pravděpodobnost. Příklad: počet bodů při hodu kostkou, počet studentů na cvičení.",[1207,7041,7042,7045],{},[1302,7043,7044],{},"Spojitá náhodná veličina"," — hodnoty tvoří interval na ose reálných čísel, přičemž každý bod intervalu má nulovou pravděpodobnost. Příklad: velikost výrobku, doba psaní testu, výška dětí v populaci.",[1136,7047,7049],{"id":7048},"distribuční-funkce","Distribuční funkce",[1110,7051,7052,7053,7056],{},"Náhodná veličina nabývá při pokusu určité hodnoty, aniž bychom předem věděli, které. Při opakování pokusu se ale projevují zákonitosti, které popisují ",[1302,7054,7055],{},"zákony rozdělení",". Nejobecnějším z nich je distribuční funkce.",[1110,7058,7059],{},[4158,7060],{"alt":7061,"className":7062,"src":7063},"mask-nv-distribucni-funkce",[1130,4162],"\u002Fwiki-assets\u002Fmask-nv-distribucni-funkce.png",[1103,7065,7068,7075],{"className":7066,"dataCallout":654},[1106,7067],"callout-info",[1110,7069,7071,7074],{"className":7070},[1113],[1115,7072],{"className":7073,"ariaHidden":1121},[1118,1294,1120],"Definice",[1110,7076,7077,7078,7091,7092,7112,7113,7126,7127,7163,7182,7183,7196,7197,1440],{},"Distribuční funkcí náhodné veličiny ",[1115,7079,7081],{"className":7080},[1315],[1317,7082,7083],{"xmlns":1319},[1321,7084,7085,7089],{},[1324,7086,7087],{},[1330,7088,6507],{},[1338,7090,6507],{"encoding":1340}," nazýváme reálnou funkci ",[1115,7093,7095],{"className":7094},[1315],[1317,7096,7097],{"xmlns":1319},[1321,7098,7099,7109],{},[1324,7100,7101,7103,7105,7107],{},[1330,7102,6490],{},[1460,7104,1647],{"stretchy":1646},[1330,7106,6495],{},[1460,7108,1658],{"stretchy":1646},[1338,7110,7111],{"encoding":1340},"F(x)"," definovanou pro každé reálné číslo ",[1115,7114,7116],{"className":7115},[1315],[1317,7117,7118],{"xmlns":1319},[1321,7119,7120,7124],{},[1324,7121,7122],{},[1330,7123,6495],{},[1338,7125,6495],{"encoding":1340}," jako\n",[1115,7128,7130],{"className":7129},[1315],[1317,7131,7132],{"xmlns":1319},[1321,7133,7134,7160],{},[1324,7135,7136,7138,7140,7142,7144,7146,7148,7150,7152,7154,7156,7158],{},[1330,7137,6490],{},[1460,7139,1647],{"stretchy":1646},[1330,7141,6495],{},[1460,7143,1658],{"stretchy":1646},[1460,7145,1754],{},[1330,7147,6502],{},[1460,7149,1647],{"stretchy":1646},[1330,7151,6507],{},[1460,7153,6510],{},[1330,7155,6495],{},[1460,7157,1658],{"stretchy":1646},[1330,7159,1440],{"mathvariant":1893},[1338,7161,7162],{"encoding":1340},"F(x) = P(X \\le x).",[1115,7164,7166],{"className":7165},[1315],[1317,7167,7168],{"xmlns":1319},[1321,7169,7170,7180],{},[1324,7171,7172,7174,7176,7178],{},[1330,7173,6490],{},[1460,7175,1647],{"stretchy":1646},[1330,7177,6495],{},[1460,7179,1658],{"stretchy":1646},[1338,7181,7111],{"encoding":1340}," tedy vyjadřuje pravděpodobnost, s jakou ",[1115,7184,7186],{"className":7185},[1315],[1317,7187,7188],{"xmlns":1319},[1321,7189,7190,7194],{},[1324,7191,7192],{},[1330,7193,6507],{},[1338,7195,6507],{"encoding":1340}," nabude hodnoty z intervalu ",[1115,7198,7200],{"className":7199},[1315],[1317,7201,7202],{"xmlns":1319},[1321,7203,7204,7220],{},[1324,7205,7206,7208,7210,7213,7215,7217],{},[1460,7207,1647],{"stretchy":1646},[1460,7209,2838],{},[1330,7211,7212],{"mathvariant":1893},"∞",[1460,7214,1568],{"separator":1121},[1330,7216,6495],{},[1460,7218,7219],{"stretchy":1646},"⟩",[1338,7221,7222],{"encoding":1340},"(-\\infty, x\\rangle",[1110,7224,7225,7226,7239,7240,7261],{},"Značí-li například ",[1115,7227,7229],{"className":7228},[1315],[1317,7230,7231],{"xmlns":1319},[1321,7232,7233,7237],{},[1324,7234,7235],{},[1330,7236,6507],{},[1338,7238,6507],{"encoding":1340}," výšku mužů v populaci, pak ",[1115,7241,7243],{"className":7242},[1315],[1317,7244,7245],{"xmlns":1319},[1321,7246,7247,7258],{},[1324,7248,7249,7251,7253,7256],{},[1330,7250,6490],{},[1460,7252,1647],{"stretchy":1646},[1334,7254,7255],{},"175",[1460,7257,1658],{"stretchy":1646},[1338,7259,7260],{"encoding":1340},"F(175)"," je pravděpodobnost, že muž měří nejvýše 175 cm.",[1110,7263,7264],{},"Pro distribuční funkci vždy platí:",[1204,7266,7267,7297,7355,7415],{},[1207,7268,7269,1568],{},[1115,7270,7272],{"className":7271},[1315],[1317,7273,7274],{"xmlns":1319},[1321,7275,7276,7294],{},[1324,7277,7278,7280,7282,7284,7286,7288,7290,7292],{},[1334,7279,1336],{},[1460,7281,6510],{},[1330,7283,6490],{},[1460,7285,1647],{"stretchy":1646},[1330,7287,6495],{},[1460,7289,1658],{"stretchy":1646},[1460,7291,6510],{},[1334,7293,1565],{},[1338,7295,7296],{"encoding":1340},"0 \\le F(x) \\le 1",[1207,7298,7299,7300,1568],{},"je neklesající: ",[1115,7301,7303],{"className":7302},[1315],[1317,7304,7305],{"xmlns":1319},[1321,7306,7307,7352],{},[1324,7308,7309,7315,7317,7323,7326,7328,7330,7336,7338,7340,7342,7344,7350],{},[1327,7310,7311,7313],{},[1330,7312,6495],{},[1334,7314,1565],{},[1460,7316,6510],{},[1327,7318,7319,7321],{},[1330,7320,6495],{},[1334,7322,1360],{},[1460,7324,7325],{},"⇒",[1330,7327,6490],{},[1460,7329,1647],{"stretchy":1646},[1327,7331,7332,7334],{},[1330,7333,6495],{},[1334,7335,1565],{},[1460,7337,1658],{"stretchy":1646},[1460,7339,6510],{},[1330,7341,6490],{},[1460,7343,1647],{"stretchy":1646},[1327,7345,7346,7348],{},[1330,7347,6495],{},[1334,7349,1360],{},[1460,7351,1658],{"stretchy":1646},[1338,7353,7354],{"encoding":1340},"x_1 \\le x_2 \\Rightarrow F(x_1) \\le F(x_2)",[1207,7356,7357,7358,1568],{},"je spojitá zprava: ",[1115,7359,7361],{"className":7360},[1315],[1317,7362,7363],{"xmlns":1319},[1321,7364,7365,7412],{},[1324,7366,7367,7390,7392,7394,7396,7398,7400,7402,7404,7406,7408,7410],{},[1327,7368,7369,7376],{},[1324,7370,7371,7374],{},[1330,7372,7373],{},"lim",[1460,7375,4266],{},[1324,7377,7378,7381,7384],{},[1330,7379,7380],{},"h",[1460,7382,7383],{},"→",[1353,7385,7386,7388],{},[1334,7387,1336],{},[1460,7389,5252],{},[1330,7391,6490],{},[1460,7393,1647],{"stretchy":1646},[1330,7395,6495],{},[1460,7397,5252],{},[1330,7399,7380],{},[1460,7401,1658],{"stretchy":1646},[1460,7403,1754],{},[1330,7405,6490],{},[1460,7407,1647],{"stretchy":1646},[1330,7409,6495],{},[1460,7411,1658],{"stretchy":1646},[1338,7413,7414],{"encoding":1340},"\\lim_{h \\to 0^+} F(x+h) = F(x)",[1207,7416,7417,2725,7459,1440],{},[1115,7418,7420],{"className":7419},[1315],[1317,7421,7422],{"xmlns":1319},[1321,7423,7424,7456],{},[1324,7425,7426,7444,7446,7448,7450,7452,7454],{},[1327,7427,7428,7434],{},[1324,7429,7430,7432],{},[1330,7431,7373],{},[1460,7433,4266],{},[1324,7435,7436,7438,7440,7442],{},[1330,7437,6495],{},[1460,7439,7383],{},[1460,7441,2838],{},[1330,7443,7212],{"mathvariant":1893},[1330,7445,6490],{},[1460,7447,1647],{"stretchy":1646},[1330,7449,6495],{},[1460,7451,1658],{"stretchy":1646},[1460,7453,1754],{},[1334,7455,1336],{},[1338,7457,7458],{"encoding":1340},"\\lim_{x \\to -\\infty} F(x) = 0",[1115,7460,7462],{"className":7461},[1315],[1317,7463,7464],{"xmlns":1319},[1321,7465,7466,7496],{},[1324,7467,7468,7484,7486,7488,7490,7492,7494],{},[1327,7469,7470,7476],{},[1324,7471,7472,7474],{},[1330,7473,7373],{},[1460,7475,4266],{},[1324,7477,7478,7480,7482],{},[1330,7479,6495],{},[1460,7481,7383],{},[1330,7483,7212],{"mathvariant":1893},[1330,7485,6490],{},[1460,7487,1647],{"stretchy":1646},[1330,7489,6495],{},[1460,7491,1658],{"stretchy":1646},[1460,7493,1754],{},[1334,7495,1565],{},[1338,7497,7498],{"encoding":1340},"\\lim_{x \\to \\infty} F(x) = 1",[1110,7500,7501],{},"U spojité náhodné veličiny je distribuční funkce svázaná s hustotou pravděpodobnosti vztahem",[1115,7503,7505],{"className":7504},[1315],[1317,7506,7507],{"xmlns":1319,"display":1736},[1321,7508,7509,7577],{},[1324,7510,7511,7517,7519,7521,7523,7525,7527,7529,7531,7533,7535,7537,7539,7541,7543,7545,7547,7560,7562,7564,7566,7568,7570,7573,7575],{},[1353,7512,7513,7515],{},[1330,7514,6490],{},[1460,7516,6535],{"mathvariant":1893,"lspace":6534,"rspace":6534},[1460,7518,1647],{"stretchy":1646},[1330,7520,6495],{},[1460,7522,1658],{"stretchy":1646},[1460,7524,1754],{},[1330,7526,6546],{},[1460,7528,1647],{"stretchy":1646},[1330,7530,6495],{},[1460,7532,1658],{"stretchy":1646},[1460,7534,1568],{"separator":1121},[1784,7536],{"width":1786},[1330,7538,6490],{},[1460,7540,1647],{"stretchy":1646},[1330,7542,6495],{},[1460,7544,1658],{"stretchy":1646},[1460,7546,1754],{},[3127,7548,7549,7552,7558],{},[1460,7550,7551],{},"∫",[1324,7553,7554,7556],{},[1460,7555,2838],{},[1330,7557,7212],{"mathvariant":1893},[1330,7559,6495],{},[1330,7561,6546],{},[1460,7563,1647],{"stretchy":1646},[1330,7565,6919],{},[1460,7567,1658],{"stretchy":1646},[2682,7569,2684],{},[1330,7571,7572],{},"d",[1330,7574,6919],{},[1330,7576,1440],{"mathvariant":1893},[1338,7578,7579],{"encoding":1340},"F'(x) = f(x), \\qquad F(x) = \\int_{-\\infty}^{x} f(t)\\,dt.",[1110,7581,7582,7583,7596,7597,5516,7615,7633],{},"Pravděpodobnost, že ",[1115,7584,7586],{"className":7585},[1315],[1317,7587,7588],{"xmlns":1319},[1321,7589,7590,7594],{},[1324,7591,7592],{},[1330,7593,6507],{},[1338,7595,6507],{"encoding":1340}," padne mezi body ",[1115,7598,7600],{"className":7599},[1315],[1317,7601,7602],{"xmlns":1319},[1321,7603,7604,7612],{},[1324,7605,7606],{},[1327,7607,7608,7610],{},[1330,7609,6495],{},[1334,7611,1565],{},[1338,7613,7614],{"encoding":1340},"x_1",[1115,7616,7618],{"className":7617},[1315],[1317,7619,7620],{"xmlns":1319},[1321,7621,7622,7630],{},[1324,7623,7624],{},[1327,7625,7626,7628],{},[1330,7627,6495],{},[1334,7629,1360],{},[1338,7631,7632],{"encoding":1340},"x_2",", se pak počítá jako",[1115,7635,7637],{"className":7636},[1315],[1317,7638,7639],{"xmlns":1319,"display":1736},[1321,7640,7641,7729],{},[1324,7642,7643,7645,7647,7653,7655,7657,7659,7665,7667,7669,7685,7687,7689,7691,7693,7695,7697,7699,7701,7703,7705,7711,7713,7715,7717,7719,7725,7727],{},[1330,7644,6502],{},[1460,7646,1647],{"stretchy":1646},[1327,7648,7649,7651],{},[1330,7650,6495],{},[1334,7652,1565],{},[1460,7654,4107],{},[1330,7656,6507],{},[1460,7658,4107],{},[1327,7660,7661,7663],{},[1330,7662,6495],{},[1334,7664,1360],{},[1460,7666,1658],{"stretchy":1646},[1460,7668,1754],{},[3127,7670,7671,7673,7679],{},[1460,7672,7551],{},[1327,7674,7675,7677],{},[1330,7676,6495],{},[1334,7678,1565],{},[1327,7680,7681,7683],{},[1330,7682,6495],{},[1334,7684,1360],{},[1330,7686,6546],{},[1460,7688,1647],{"stretchy":1646},[1330,7690,6919],{},[1460,7692,1658],{"stretchy":1646},[2682,7694,2684],{},[1330,7696,7572],{},[1330,7698,6919],{},[1460,7700,1754],{},[1330,7702,6490],{},[1460,7704,1647],{"stretchy":1646},[1327,7706,7707,7709],{},[1330,7708,6495],{},[1334,7710,1360],{},[1460,7712,1658],{"stretchy":1646},[1460,7714,2838],{},[1330,7716,6490],{},[1460,7718,1647],{"stretchy":1646},[1327,7720,7721,7723],{},[1330,7722,6495],{},[1334,7724,1565],{},[1460,7726,1658],{"stretchy":1646},[1330,7728,1440],{"mathvariant":1893},[1338,7730,7731],{"encoding":1340},"P(x_1 \u003C X \u003C x_2) = \\int_{x_1}^{x_2} f(t)\\,dt = F(x_2) - F(x_1).",[1136,7733,7735],{"id":7734},"hustota-pravděpodobnosti","Hustota pravděpodobnosti",[1103,7737,7739,7745],{"className":7738,"dataCallout":654},[1106,7067],[1110,7740,7742,7074],{"className":7741},[1113],[1115,7743],{"className":7744,"ariaHidden":1121},[1118,1294,1120],[1110,7746,7747,7748,7767,7768,7781,7782,7795,7796,1440],{},"Hustota pravděpodobnosti ",[1115,7749,7751],{"className":7750},[1315],[1317,7752,7753],{"xmlns":1319},[1321,7754,7755,7765],{},[1324,7756,7757,7759,7761,7763],{},[1330,7758,6546],{},[1460,7760,1647],{"stretchy":1646},[1330,7762,6495],{},[1460,7764,1658],{"stretchy":1646},[1338,7766,6576],{"encoding":1340}," určuje, jak jsou hodnoty spojité náhodné veličiny ",[1115,7769,7771],{"className":7770},[1315],[1317,7772,7773],{"xmlns":1319},[1321,7774,7775,7779],{},[1324,7776,7777],{},[1330,7778,6507],{},[1338,7780,6507],{"encoding":1340}," nahuštěny v okolí bodu ",[1115,7783,7785],{"className":7784},[1315],[1317,7786,7787],{"xmlns":1319},[1321,7788,7789,7793],{},[1324,7790,7791],{},[1330,7792,6495],{},[1338,7794,6495],{"encoding":1340},". Je vždy nezáporná a platí pro ni ",[1115,7797,7799],{"className":7798},[1315],[1317,7800,7801],{"xmlns":1319},[1321,7802,7803,7835],{},[1324,7804,7805,7817,7819,7821,7823,7825,7827,7829,7831,7833],{},[3127,7806,7807,7809,7815],{},[1460,7808,7551],{},[1324,7810,7811,7813],{},[1460,7812,2838],{},[1330,7814,7212],{"mathvariant":1893},[1330,7816,7212],{"mathvariant":1893},[1330,7818,6546],{},[1460,7820,1647],{"stretchy":1646},[1330,7822,6495],{},[1460,7824,1658],{"stretchy":1646},[2682,7826,2684],{},[1330,7828,7572],{},[1330,7830,6495],{},[1460,7832,1754],{},[1334,7834,1565],{},[1338,7836,7837],{"encoding":1340},"\\int_{-\\infty}^{\\infty} f(x)\\,dx = 1",[1110,7839,7840],{},"Intuitivně: rozdělíme-li hodnoty náhodné veličiny (např. výšku mužů v populaci) do stejně širokých intervalů, bude v intervalech blízko průměru nahuštěno víc pozorování než v krajních intervalech — hustota tam bude vyšší.",[1136,7842,7844],{"id":7843},"charakteristiky-spojité-náhodné-veličiny","Charakteristiky spojité náhodné veličiny",[1110,7846,7847,7850],{},[1302,7848,7849],{},"Střední hodnota"," je nejdůležitější charakteristika náhodné veličiny:",[1115,7852,7854],{"className":7853},[1315],[1317,7855,7856],{"xmlns":1319,"display":1736},[1321,7857,7858,7904],{},[1324,7859,7860,7863,7865,7867,7869,7871,7883,7885,7888,7890,7892,7894,7896,7898,7900,7902],{},[1330,7861,7862],{},"E",[1460,7864,1647],{"stretchy":1646},[1330,7866,6507],{},[1460,7868,1658],{"stretchy":1646},[1460,7870,1754],{},[3127,7872,7873,7875,7881],{},[1460,7874,7551],{},[1324,7876,7877,7879],{},[1460,7878,2838],{},[1330,7880,7212],{"mathvariant":1893},[1330,7882,7212],{"mathvariant":1893},[1330,7884,6495],{},[1460,7886,7887],{},"⋅",[1330,7889,6546],{},[1460,7891,1647],{"stretchy":1646},[1330,7893,6495],{},[1460,7895,1658],{"stretchy":1646},[2682,7897,2684],{},[1330,7899,7572],{},[1330,7901,6495],{},[1330,7903,1440],{"mathvariant":1893},[1338,7905,7906],{"encoding":1340},"E(X) = \\int_{-\\infty}^{\\infty} x \\cdot f(x)\\,dx.",[1110,7908,7909],{},"Je to číslo, kolem něhož kolísají výběrové průměry vypočtené ze sérií pozorovaných hodnot náhodné veličiny.",[1110,7911,7912,5516,7915,1730],{},[1302,7913,7914],{},"Rozptyl",[1302,7916,7917],{},"směrodatná odchylka",[1115,7919,7921],{"className":7920},[1315],[1317,7922,7923],{"xmlns":1319,"display":1736},[1321,7924,7925,8066],{},[1324,7926,7927,7930,7932,7934,7936,7938,7950,7953,7955,7957,7959,7961,7963,7965,7972,7974,7976,7978,7980,7982,7984,7986,7988,8000,8006,8008,8010,8012,8014,8016,8018,8020,8022,8024,8026,8028,8030,8032,8038,8040,8042,8044,8046,8048,8050,8052,8064],{},[1330,7928,7929],{},"D",[1460,7931,1647],{"stretchy":1646},[1330,7933,6507],{},[1460,7935,1658],{"stretchy":1646},[1460,7937,1754],{},[3127,7939,7940,7942,7948],{},[1460,7941,7551],{},[1324,7943,7944,7946],{},[1460,7945,2838],{},[1330,7947,7212],{"mathvariant":1893},[1330,7949,7212],{"mathvariant":1893},[1460,7951,7952],{"stretchy":1646},"[",[1330,7954,6495],{},[1460,7956,2838],{},[1330,7958,7862],{},[1460,7960,1647],{"stretchy":1646},[1330,7962,6507],{},[1460,7964,1658],{"stretchy":1646},[1353,7966,7967,7970],{},[1460,7968,7969],{"stretchy":1646},"]",[1334,7971,1360],{},[1330,7973,6546],{},[1460,7975,1647],{"stretchy":1646},[1330,7977,6495],{},[1460,7979,1658],{"stretchy":1646},[2682,7981,2684],{},[1330,7983,7572],{},[1330,7985,6495],{},[1460,7987,1754],{},[3127,7989,7990,7992,7998],{},[1460,7991,7551],{},[1324,7993,7994,7996],{},[1460,7995,2838],{},[1330,7997,7212],{"mathvariant":1893},[1330,7999,7212],{"mathvariant":1893},[1353,8001,8002,8004],{},[1330,8003,6495],{},[1334,8005,1360],{},[1330,8007,6546],{},[1460,8009,1647],{"stretchy":1646},[1330,8011,6495],{},[1460,8013,1658],{"stretchy":1646},[2682,8015,2684],{},[1330,8017,7572],{},[1330,8019,6495],{},[1460,8021,2838],{},[1460,8023,7952],{"stretchy":1646},[1330,8025,7862],{},[1460,8027,1647],{"stretchy":1646},[1330,8029,6507],{},[1460,8031,1658],{"stretchy":1646},[1353,8033,8034,8036],{},[1460,8035,7969],{"stretchy":1646},[1334,8037,1360],{},[1460,8039,1568],{"separator":1121},[1784,8041],{"width":1786},[1330,8043,6674],{},[1460,8045,1647],{"stretchy":1646},[1330,8047,6507],{},[1460,8049,1658],{"stretchy":1646},[1460,8051,1754],{},[4228,8053,8054],{},[1324,8055,8056,8058,8060,8062],{},[1330,8057,7929],{},[1460,8059,1647],{"stretchy":1646},[1330,8061,6507],{},[1460,8063,1658],{"stretchy":1646},[1330,8065,1440],{"mathvariant":1893},[1338,8067,8068],{"encoding":1340},"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)}.",[1110,8070,8071,8072,8075],{},"Směrodatná odchylka udává, jak moc jsou hodnoty náhodné veličiny rozptýlené kolem střední hodnoty. (Pro odhad těchto charakteristik z naměřených dat viz empirické protějšky v ",[1127,8073,886],{"className":8074,"dataFsResolvedFilePath":1180,"href":1181},[1130],".)",[1110,8077,8078,8081,8082,8095,8096,8114,8115,8128],{},[1302,8079,8080],{},"Kvantily"," udávají, jak jsou hodnoty náhodné veličiny ",[1115,8083,8085],{"className":8084},[1315],[1317,8086,8087],{"xmlns":1319},[1321,8088,8089,8093],{},[1324,8090,8091],{},[1330,8092,6507],{},[1338,8094,6507],{"encoding":1340}," rozděleny na ose reálných čísel v určitém pravděpodobnostním poměru. 100p%-ní kvantil ",[1115,8097,8099],{"className":8098},[1315],[1317,8100,8101],{"xmlns":1319},[1321,8102,8103,8111],{},[1324,8104,8105],{},[1327,8106,8107,8109],{},[1330,8108,6495],{},[1330,8110,1110],{},[1338,8112,8113],{"encoding":1340},"x_p"," je číslo, pro které při zvolené pravděpodobnosti ",[1115,8116,8118],{"className":8117},[1315],[1317,8119,8120],{"xmlns":1319},[1321,8121,8122,8126],{},[1324,8123,8124],{},[1330,8125,1110],{},[1338,8127,1110],{"encoding":1340}," platí",[1115,8130,8132],{"className":8131},[1315],[1317,8133,8134],{"xmlns":1319,"display":1736},[1321,8135,8136,8156],{},[1324,8137,8138,8140,8142,8148,8150,8152,8154],{},[1330,8139,6490],{},[1460,8141,1647],{"stretchy":1646},[1327,8143,8144,8146],{},[1330,8145,6495],{},[1330,8147,1110],{},[1460,8149,1658],{"stretchy":1646},[1460,8151,1754],{},[1330,8153,1110],{},[1330,8155,1440],{"mathvariant":1893},[1338,8157,8158],{"encoding":1340},"F(x_p) = p.",[1110,8160,8161,8162,8190,8191,8218,8219,8238,8239,8258,8259,1440],{},"V intervalu ",[1115,8163,8165],{"className":8164},[1315],[1317,8166,8167],{"xmlns":1319},[1321,8168,8169,8187],{},[1324,8170,8171,8173,8175,8177,8179,8185],{},[1460,8172,1647],{"stretchy":1646},[1460,8174,2838],{},[1330,8176,7212],{"mathvariant":1893},[1460,8178,6669],{"separator":1121},[1327,8180,8181,8183],{},[1330,8182,6495],{},[1330,8184,1110],{},[1460,8186,1658],{"stretchy":1646},[1338,8188,8189],{"encoding":1340},"(-\\infty; x_p)"," leží 100p % hodnot, v intervalu ",[1115,8192,8194],{"className":8193},[1315],[1317,8195,8196],{"xmlns":1319},[1321,8197,8198,8215],{},[1324,8199,8200,8203,8209,8211,8213],{},[1460,8201,8202],{"stretchy":1646},"⟨",[1327,8204,8205,8207],{},[1330,8206,6495],{},[1330,8208,1110],{},[1460,8210,6669],{"separator":1121},[1330,8212,7212],{"mathvariant":1893},[1460,8214,1658],{"stretchy":1646},[1338,8216,8217],{"encoding":1340},"\\langle x_p; \\infty)"," leží 100(1-p) % hodnot. Nejdůležitější kvantily jsou medián ",[1115,8220,8222],{"className":8221},[1315],[1317,8223,8224],{"xmlns":1319},[1321,8225,8226,8235],{},[1324,8227,8228],{},[1327,8229,8230,8232],{},[1330,8231,6495],{},[1334,8233,8234],{},"0,5",[1338,8236,8237],{"encoding":1340},"x_{0{,}5}",", dolní kvartil ",[1115,8240,8242],{"className":8241},[1315],[1317,8243,8244],{"xmlns":1319},[1321,8245,8246,8255],{},[1324,8247,8248],{},[1327,8249,8250,8252],{},[1330,8251,6495],{},[1334,8253,8254],{},"0,25",[1338,8256,8257],{"encoding":1340},"x_{0{,}25}"," a horní kvartil ",[1115,8260,8262],{"className":8261},[1315],[1317,8263,8264],{"xmlns":1319},[1321,8265,8266,8275],{},[1324,8267,8268],{},[1327,8269,8270,8272],{},[1330,8271,6495],{},[1334,8273,8274],{},"0,75",[1338,8276,8277],{"encoding":1340},"x_{0{,}75}",[1136,8279,6649],{"id":8280},"normální-rozdělení",[1110,8282,8283,8284,8297,8298,1425,8301,8328],{},"Spojitá náhodná veličina ",[1115,8285,8287],{"className":8286},[1315],[1317,8288,8289],{"xmlns":1319},[1321,8290,8291,8295],{},[1324,8292,8293],{},[1330,8294,6507],{},[1338,8296,6507],{"encoding":1340}," má ",[1302,8299,8300],{},"normální rozdělení",[1115,8302,8304],{"className":8303},[1315],[1317,8305,8306],{"xmlns":1319},[1321,8307,8308,8326],{},[1324,8309,8310,8312,8314,8316,8318,8324],{},[1330,8311,6661],{},[1460,8313,1647],{"stretchy":1646},[1330,8315,6666],{},[1460,8317,6669],{"separator":1121},[1353,8319,8320,8322],{},[1330,8321,6674],{},[1334,8323,1360],{},[1460,8325,1658],{"stretchy":1646},[1338,8327,6681],{"encoding":1340},", jestliže její hustota pravděpodobnosti a distribuční funkce jsou dány předpisy",[1115,8330,8332],{"className":8331},[1315],[1317,8333,8334],{"xmlns":1319,"display":1736},[1321,8335,8336,8488],{},[1324,8337,8338,8340,8342,8344,8346,8348,8365,8402,8404,8406,8408,8410,8412,8414,8416,8432,8444,8480,8482,8484,8486],{},[1330,8339,6546],{},[1460,8341,1647],{"stretchy":1646},[1330,8343,6495],{},[1460,8345,1658],{"stretchy":1646},[1460,8347,1754],{},[2512,8349,8350,8352],{},[1334,8351,1565],{},[1324,8353,8354,8356],{},[1330,8355,6674],{},[4228,8357,8358],{},[1324,8359,8360,8362],{},[1334,8361,1360],{},[1330,8363,8364],{},"π",[1353,8366,8367,8370],{},[1330,8368,8369],{},"e",[1324,8371,8372,8374],{},[1460,8373,2838],{},[2512,8375,8376,8392],{},[1324,8377,8378,8380,8382,8384,8386],{},[1460,8379,1647],{"stretchy":1646},[1330,8381,6495],{},[1460,8383,2838],{},[1330,8385,6666],{},[1353,8387,8388,8390],{},[1460,8389,1658],{"stretchy":1646},[1334,8391,1360],{},[1324,8393,8394,8396],{},[1334,8395,1360],{},[1353,8397,8398,8400],{},[1330,8399,6674],{},[1334,8401,1360],{},[1460,8403,1568],{"separator":1121},[1784,8405],{"width":1786},[1330,8407,6490],{},[1460,8409,1647],{"stretchy":1646},[1330,8411,6495],{},[1460,8413,1658],{"stretchy":1646},[1460,8415,1754],{},[2512,8417,8418,8420],{},[1334,8419,1565],{},[1324,8421,8422,8424],{},[1330,8423,6674],{},[4228,8425,8426],{},[1324,8427,8428,8430],{},[1334,8429,1360],{},[1330,8431,8364],{},[3127,8433,8434,8436,8442],{},[1460,8435,7551],{},[1324,8437,8438,8440],{},[1460,8439,2838],{},[1330,8441,7212],{"mathvariant":1893},[1330,8443,6495],{},[1353,8445,8446,8448],{},[1330,8447,8369],{},[1324,8449,8450,8452],{},[1460,8451,2838],{},[2512,8453,8454,8470],{},[1324,8455,8456,8458,8460,8462,8464],{},[1460,8457,1647],{"stretchy":1646},[1330,8459,6919],{},[1460,8461,2838],{},[1330,8463,6666],{},[1353,8465,8466,8468],{},[1460,8467,1658],{"stretchy":1646},[1334,8469,1360],{},[1324,8471,8472,8474],{},[1334,8473,1360],{},[1353,8475,8476,8478],{},[1330,8477,6674],{},[1334,8479,1360],{},[2682,8481,2684],{},[1330,8483,7572],{},[1330,8485,6919],{},[1460,8487,1568],{"separator":1121},[1338,8489,8490],{"encoding":1340},"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,",[1110,8492,8493,8494,2725,8518,1440],{},"přičemž ",[1115,8495,8497],{"className":8496},[1315],[1317,8498,8499],{"xmlns":1319},[1321,8500,8501,8515],{},[1324,8502,8503,8505,8507,8509,8511,8513],{},[1330,8504,7862],{},[1460,8506,1647],{"stretchy":1646},[1330,8508,6507],{},[1460,8510,1658],{"stretchy":1646},[1460,8512,1754],{},[1330,8514,6666],{},[1338,8516,8517],{"encoding":1340},"E(X) = \\mu",[1115,8519,8521],{"className":8520},[1315],[1317,8522,8523],{"xmlns":1319},[1321,8524,8525,8543],{},[1324,8526,8527,8529,8531,8533,8535,8537],{},[1330,8528,7929],{},[1460,8530,1647],{"stretchy":1646},[1330,8532,6507],{},[1460,8534,1658],{"stretchy":1646},[1460,8536,1754],{},[1353,8538,8539,8541],{},[1330,8540,6674],{},[1334,8542,1360],{},[1338,8544,8545],{"encoding":1340},"D(X) = \\sigma^2",[1110,8547,8548],{},[4158,8549],{"alt":8550,"className":8551,"src":8552},"mask-nv-normalni",[1130,4162],"\u002Fwiki-assets\u002Fmask-nv-normalni.png",[1110,8554,8555,8556,8559,8560,8574,8575,8594,8595,8611,8612,8625,8626,1440],{},"Křivka hustoty se nazývá ",[1302,8557,8558],{},"Gaussova křivka",": je symetrická kolem svislé přímky procházející ",[1115,8561,8563],{"className":8562},[1315],[1317,8564,8565],{"xmlns":1319},[1321,8566,8567,8571],{},[1324,8568,8569],{},[1330,8570,6666],{},[1338,8572,8573],{"encoding":1340},"\\mu",", kde má ",[1115,8576,8578],{"className":8577},[1315],[1317,8579,8580],{"xmlns":1319},[1321,8581,8582,8592],{},[1324,8583,8584,8586,8588,8590],{},[1330,8585,6546],{},[1460,8587,1647],{"stretchy":1646},[1330,8589,6495],{},[1460,8591,1658],{"stretchy":1646},[1338,8593,6576],{"encoding":1340}," globální maximum, a ve vzdálenosti ",[1115,8596,8598],{"className":8597},[1315],[1317,8599,8600],{"xmlns":1319},[1321,8601,8602,8608],{},[1324,8603,8604,8606],{},[1334,8605,3366],{},[1330,8607,6674],{},[1338,8609,8610],{"encoding":1340},"3\\sigma"," od ",[1115,8613,8615],{"className":8614},[1315],[1317,8616,8617],{"xmlns":1319},[1321,8618,8619,8623],{},[1324,8620,8621],{},[1330,8622,6666],{},[1338,8624,8573],{"encoding":1340}," se téměř dotýká osy x — zhruba 99,73 % hodnot leží v intervalu ",[1115,8627,8629],{"className":8628},[1315],[1317,8630,8631],{"xmlns":1319},[1321,8632,8633,8657],{},[1324,8634,8635,8637,8639,8641,8643,8645,8647,8649,8651,8653,8655],{},[1460,8636,1647],{"stretchy":1646},[1330,8638,6666],{},[1460,8640,2838],{},[1334,8642,3366],{},[1330,8644,6674],{},[1460,8646,6669],{"separator":1121},[1330,8648,6666],{},[1460,8650,5252],{},[1334,8652,3366],{},[1330,8654,6674],{},[1460,8656,1658],{"stretchy":1646},[1338,8658,8659],{"encoding":1340},"(\\mu - 3\\sigma; \\mu + 3\\sigma)",[1110,8661,8662,8663,1425,8666,8690,8691,1440],{},"Zvláštní postavení má ",[1302,8664,8665],{},"normované normální rozdělení",[1115,8667,8669],{"className":8668},[1315],[1317,8670,8671],{"xmlns":1319},[1321,8672,8673,8687],{},[1324,8674,8675,8677,8679,8681,8683,8685],{},[1330,8676,6661],{},[1460,8678,1647],{"stretchy":1646},[1334,8680,1336],{},[1460,8682,6669],{"separator":1121},[1334,8684,1565],{},[1460,8686,1658],{"stretchy":1646},[1338,8688,8689],{"encoding":1340},"N(0; 1)",", na které se dá libovolné normální rozdělení převést standardizací ",[1115,8692,8694],{"className":8693},[1315],[1317,8695,8696],{"xmlns":1319},[1321,8697,8698,8719],{},[1324,8699,8700,8703,8705,8707,8709,8711,8713,8715,8717],{},[1330,8701,8702],{},"Z",[1460,8704,1754],{},[1460,8706,1647],{"stretchy":1646},[1330,8708,6507],{},[1460,8710,2838],{},[1330,8712,6666],{},[1460,8714,1658],{"stretchy":1646},[1330,8716,4379],{"mathvariant":1893},[1330,8718,6674],{},[1338,8720,8721],{"encoding":1340},"Z = (X-\\mu)\u002F\\sigma",[8723,8724],"graph-mount",{"spec":8725},"{\"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\"}]}",[1103,8727,8729,8736],{"className":8728,"dataCallout":6188},[1106,6187],[1110,8730,8732,8735],{"className":8731},[1113],[1115,8733],{"className":8734,"ariaHidden":1121},[1118,6195,1120],"R očekává směrodatnou odchylku, ne rozptyl",[1110,8737,8738,8739,8766,8767,8770,8771,2725,8773,5516,8775,8777,8778,1425,8781,8794,8795,8821,8822,8825,8826,1440],{},"Zápis ",[1115,8740,8742],{"className":8741},[1315],[1317,8743,8744],{"xmlns":1319},[1321,8745,8746,8764],{},[1324,8747,8748,8750,8752,8754,8756,8762],{},[1330,8749,6661],{},[1460,8751,1647],{"stretchy":1646},[1330,8753,6666],{},[1460,8755,6669],{"separator":1121},[1353,8757,8758,8760],{},[1330,8759,6674],{},[1334,8761,1360],{},[1460,8763,1658],{"stretchy":1646},[1338,8765,6681],{"encoding":1340}," v definici používá ",[1302,8768,8769],{},"rozptyl",". Funkce ",[3244,8772,6685],{},[3244,8774,6688],{},[3244,8776,6691],{}," v R ale jako třetí argument berou ",[1302,8779,8780],{},"směrodatnou odchylku",[1115,8782,8784],{"className":8783},[1315],[1317,8785,8786],{"xmlns":1319},[1321,8787,8788,8792],{},[1324,8789,8790],{},[1330,8791,6674],{},[1338,8793,6706],{"encoding":1340},". Má-li náhodná veličina rozdělení ",[1115,8796,8798],{"className":8797},[1315],[1317,8799,8800],{"xmlns":1319},[1321,8801,8802,8818],{},[1324,8803,8804,8806,8808,8811,8813,8816],{},[1330,8805,6661],{},[1460,8807,1647],{"stretchy":1646},[1334,8809,8810],{},"10",[1460,8812,6669],{"separator":1121},[1334,8814,8815],{},"0,12",[1460,8817,1658],{"stretchy":1646},[1338,8819,8820],{"encoding":1340},"N(10; 0{,}12)",", je ",[3244,8823,8824],{},"sd = sqrt(0.12)",", ne ",[3244,8827,8828],{},"sd = 0.12",[1110,8830,8831],{},"V R:",[3468,8833,8835],{"className":3470,"code":8834,"language":71,"meta":1247,"style":1247},"dnorm(0)\npnorm(1.96)\nqnorm(0.975)\n",[3244,8836,8837,8847,8858],{"__ignoreMap":1247},[1115,8838,8839,8841,8843,8845],{"class":3476,"line":10},[1115,8840,6685],{"class":3487},[1115,8842,1647],{"class":3491},[1115,8844,1336],{"class":3499},[1115,8846,3676],{"class":3491},[1115,8848,8849,8851,8853,8856],{"class":3476,"line":27},[1115,8850,6688],{"class":3487},[1115,8852,1647],{"class":3491},[1115,8854,8855],{"class":3499},"1.96",[1115,8857,3676],{"class":3491},[1115,8859,8860,8862,8864,8867],{"class":3476,"line":148},[1115,8861,6691],{"class":3487},[1115,8863,1647],{"class":3491},[1115,8865,8866],{"class":3499},"0.975",[1115,8868,3676],{"class":3491},[3468,8870,8873],{"className":8871,"code":8872,"language":3698,"meta":1247},[3696],"[1] 0.3989423\n[1] 0.9750021\n[1] 1.959964\n",[3244,8874,8872],{"__ignoreMap":1247},[1110,8876,8877,8880,8881,8905,8906,1662,8909,5516,8930,8933],{},[3244,8878,8879],{},"dnorm(0)"," je hodnota hustoty ",[1115,8882,8884],{"className":8883},[1315],[1317,8885,8886],{"xmlns":1319},[1321,8887,8888,8902],{},[1324,8889,8890,8892,8894,8896,8898,8900],{},[1330,8891,6661],{},[1460,8893,1647],{"stretchy":1646},[1334,8895,1336],{},[1460,8897,6669],{"separator":1121},[1334,8899,1565],{},[1460,8901,1658],{"stretchy":1646},[1338,8903,8904],{"encoding":1340},"N(0;1)"," v bodě 0, ",[3244,8907,8908],{},"pnorm(1.96)",[1115,8910,8912],{"className":8911},[1315],[1317,8913,8914],{"xmlns":1319},[1321,8915,8916,8927],{},[1324,8917,8918,8920,8922,8925],{},[1330,8919,6490],{},[1460,8921,1647],{"stretchy":1646},[1334,8923,8924],{},"1,96",[1460,8926,1658],{"stretchy":1646},[1338,8928,8929],{"encoding":1340},"F(1{,}96)",[3244,8931,8932],{},"qnorm(0.975)"," je 97,5%-ní kvantil — hodnota, pod kterou leží 97,5 % pravděpodobnosti.",[1103,8935,8937,8944],{"className":8936,"dataCallout":3251},[1106,3250],[1110,8938,8940,8943],{"className":8939},[1113],[1115,8941],{"className":8942,"ariaHidden":1121},[1118,3258,1120],"Příklad: Návštěvnost zábavního parku",[1110,8945,8946,8947,8982],{},"Denní návštěvnost zábavního parku je náhodná veličina s normálním rozdělením, průměrnou hodnotou 230 a směrodatnou odchylkou 27,5 návštěvníků: ",[1115,8948,8950],{"className":8949},[1315],[1317,8951,8952],{"xmlns":1319},[1321,8953,8954,8979],{},[1324,8955,8956,8958,8961,8963,8965,8968,8970,8977],{},[1330,8957,6507],{},[1460,8959,8960],{},"∼",[1330,8962,6661],{},[1460,8964,1647],{"stretchy":1646},[1334,8966,8967],{},"230",[1460,8969,6669],{"separator":1121},[1353,8971,8972,8975],{},[1334,8973,8974],{},"27,5",[1334,8976,1360],{},[1460,8978,1658],{"stretchy":1646},[1338,8980,8981],{"encoding":1340},"X \\sim N(230; 27{,}5^2)",". Přijde-li za den méně než 180 návštěvníků, je park ztrátový. Kolik procent dní je ztrátových?",[1110,8984,8985],{},[4158,8986],{"alt":8987,"className":8988,"src":8989},"mask-nv-priklad-park",[1130,4162],"\u002Fwiki-assets\u002Fmask-nv-priklad-park.png",[3468,8991,8993],{"className":3470,"code":8992,"language":71,"meta":1247,"style":1247},"pnorm(180, mean = 230, sd = 27.5)\n",[3244,8994,8995],{"__ignoreMap":1247},[1115,8996,8997,8999,9001,9004,9006,9009,9011,9014,9016,9019,9021,9024],{"class":3476,"line":10},[1115,8998,6688],{"class":3487},[1115,9000,1647],{"class":3491},[1115,9002,9003],{"class":3499},"180",[1115,9005,1568],{"class":3483},[1115,9007,9008],{"class":3479}," mean",[1115,9010,3572],{"class":3483},[1115,9012,9013],{"class":3499}," 230",[1115,9015,1568],{"class":3483},[1115,9017,9018],{"class":3479}," sd",[1115,9020,3572],{"class":3483},[1115,9022,9023],{"class":3499}," 27.5",[1115,9025,3676],{"class":3491},[3468,9027,9030],{"className":9028,"code":9029,"language":3698,"meta":1247},[3696],"[1] 0.03451817\n",[3244,9031,9029],{"__ignoreMap":1247},[1110,9033,9034],{},"Park je ztrátový přibližně v 3,45 % dní.",[1103,9036,9038,9045],{"className":9037,"dataCallout":3251},[1106,3250],[1110,9039,9041,9044],{"className":9040},[1113],[1115,9042],{"className":9043,"ariaHidden":1121},[1118,3258,1120],"Příklad: Délka výrobku",[1110,9046,9047,9048,9082],{},"Automat je seřízen tak, aby střední hodnota délky výrobku byla 42 mm, s přesností charakterizovanou směrodatnou odchylkou 1,2 mm: ",[1115,9049,9051],{"className":9050},[1315],[1317,9052,9053],{"xmlns":1319},[1321,9054,9055,9079],{},[1324,9056,9057,9059,9061,9063,9065,9068,9070,9077],{},[1330,9058,6507],{},[1460,9060,8960],{},[1330,9062,6661],{},[1460,9064,1647],{"stretchy":1646},[1334,9066,9067],{},"42",[1460,9069,6669],{"separator":1121},[1353,9071,9072,9075],{},[1334,9073,9074],{},"1,2",[1334,9076,1360],{},[1460,9078,1658],{"stretchy":1646},[1338,9080,9081],{"encoding":1340},"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?",[1110,9084,9085],{},[4158,9086],{"alt":9087,"className":9088,"src":9089},"mask-nv-priklad-delka",[1130,4162],"\u002Fwiki-assets\u002Fmask-nv-priklad-delka.png",[3468,9091,9093],{"className":3470,"code":9092,"language":71,"meta":1247,"style":1247},"pnorm(43, mean = 42, sd = 1.2) - pnorm(41, mean = 42, sd = 1.2)\n",[3244,9094,9095],{"__ignoreMap":1247},[1115,9096,9097,9099,9101,9104,9106,9108,9110,9113,9115,9117,9119,9122,9124,9126,9129,9131,9134,9136,9138,9140,9142,9144,9146,9148,9150],{"class":3476,"line":10},[1115,9098,6688],{"class":3487},[1115,9100,1647],{"class":3491},[1115,9102,9103],{"class":3499},"43",[1115,9105,1568],{"class":3483},[1115,9107,9008],{"class":3479},[1115,9109,3572],{"class":3483},[1115,9111,9112],{"class":3499}," 42",[1115,9114,1568],{"class":3483},[1115,9116,9018],{"class":3479},[1115,9118,3572],{"class":3483},[1115,9120,9121],{"class":3499}," 1.2",[1115,9123,4376],{"class":3491},[1115,9125,4413],{"class":3483},[1115,9127,9128],{"class":3487}," pnorm",[1115,9130,1647],{"class":3491},[1115,9132,9133],{"class":3499},"41",[1115,9135,1568],{"class":3483},[1115,9137,9008],{"class":3479},[1115,9139,3572],{"class":3483},[1115,9141,9112],{"class":3499},[1115,9143,1568],{"class":3483},[1115,9145,9018],{"class":3479},[1115,9147,3572],{"class":3483},[1115,9149,9121],{"class":3499},[1115,9151,3676],{"class":3491},[3468,9153,9156],{"className":9154,"code":9155,"language":3698,"meta":1247},[3696],"[1] 0.5953432\n",[3244,9157,9155],{"__ignoreMap":1247},[1110,9159,9160],{},"Do 1. jakostní třídy spadá přibližně 59,53 % výrobků.",[1103,9162,9164,9171],{"className":9163,"dataCallout":3251},[1106,3250],[1110,9165,9167,9170],{"className":9166},[1113],[1115,9168],{"className":9169,"ariaHidden":1121},[1118,3258,1120],"Příklad: Obsah ampulky",[1110,9172,9173,9174,9197,9198,9224],{},"Obsah ampulky s lékem (v cm³) má rozdělení ",[1115,9175,9177],{"className":9176},[1315],[1317,9178,9179],{"xmlns":1319},[1321,9180,9181,9195],{},[1324,9182,9183,9185,9187,9189,9191,9193],{},[1330,9184,6661],{},[1460,9186,1647],{"stretchy":1646},[1334,9188,8810],{},[1460,9190,6669],{"separator":1121},[1334,9192,8815],{},[1460,9194,1658],{"stretchy":1646},[1338,9196,8820],{"encoding":1340},", tedy střední hodnota 10 a rozptyl 0,12 (",[1115,9199,9201],{"className":9200},[1315],[1317,9202,9203],{"xmlns":1319},[1321,9204,9205,9221],{},[1324,9206,9207,9209,9211,9215,9218],{},[1330,9208,6674],{},[1460,9210,1754],{},[4228,9212,9213],{},[1334,9214,8815],{},[1460,9216,9217],{},"≈",[1334,9219,9220],{},"0,346",[1338,9222,9223],{"encoding":1340},"\\sigma = \\sqrt{0{,}12} \\approx 0{,}346","). Kolik procent ampulek má obsah menší než 9,8 cm³?",[1110,9226,9227],{},[4158,9228],{"alt":9229,"className":9230,"src":9231},"mask-nv-priklad-ampulka",[1130,4162],"\u002Fwiki-assets\u002Fmask-nv-priklad-ampulka.png",[3468,9233,9235],{"className":3470,"code":9234,"language":71,"meta":1247,"style":1247},"pnorm(9.8, mean = 10, sd = sqrt(0.12))\n",[3244,9236,9237],{"__ignoreMap":1247},[1115,9238,9239,9241,9243,9246,9248,9250,9252,9255,9257,9259,9261,9263,9265,9268],{"class":3476,"line":10},[1115,9240,6688],{"class":3487},[1115,9242,1647],{"class":3491},[1115,9244,9245],{"class":3499},"9.8",[1115,9247,1568],{"class":3483},[1115,9249,9008],{"class":3479},[1115,9251,3572],{"class":3483},[1115,9253,9254],{"class":3499}," 10",[1115,9256,1568],{"class":3483},[1115,9258,9018],{"class":3479},[1115,9260,3572],{"class":3483},[1115,9262,4353],{"class":3487},[1115,9264,1647],{"class":3491},[1115,9266,9267],{"class":3499},"0.12",[1115,9269,9270],{"class":3491},"))\n",[3468,9272,9275],{"className":9273,"code":9274,"language":3698,"meta":1247},[3696],"[1] 0.2818514\n",[3244,9276,9274],{"__ignoreMap":1247},[1110,9278,9279],{},"Obsah menší než 9,8 cm³ má přibližně 28,19 % ampulek.",[1136,9281,9283],{"id":9282},"další-rozdělení-dostupná-v-r","Další rozdělení dostupná v R",[1110,9285,9286,9287,9290,9291,9294,9295,9298,9299,4379,9302,9305,9306,9309],{},"Vedle normálního rozdělení R přímo nabízí hustotu, distribuční funkci a kvantilovou funkci i pro další běžná rozdělení. Pojmenování funkcí je jednotné: ",[3244,9288,9289],{},"d*"," je hustota\u002Fpravděpodobnostní funkce, ",[3244,9292,9293],{},"p*"," distribuční funkce (s ",[3244,9296,9297],{},"lower.tail = FALSE",", případně čtvrtým argumentem ",[3244,9300,9301],{},"TRUE",[3244,9303,9304],{},"FALSE",", pro horní chvost) a ",[3244,9307,9308],{},"q*"," kvantilová funkce.",[1141,9311,9312,9418],{},[1144,9313,9314],{},[1147,9315,9316,9319,9365,9391],{},[1150,9317,9318],{},"Rozdělení",[1150,9320,9321,9345,9346],{},[1115,9322,9324],{"className":9323},[1315],[1317,9325,9326],{"xmlns":1319},[1321,9327,9328,9342],{},[1324,9329,9330,9332,9334,9336,9338,9340],{},[1330,9331,6502],{},[1460,9333,1647],{"stretchy":1646},[1330,9335,6507],{},[1460,9337,1754],{},[1330,9339,7035],{},[1460,9341,1658],{"stretchy":1646},[1338,9343,9344],{"encoding":1340},"P(X=k)"," \u002F ",[1115,9347,9349],{"className":9348},[1315],[1317,9350,9351],{"xmlns":1319},[1321,9352,9353,9363],{},[1324,9354,9355,9357,9359,9361],{},[1330,9356,6546],{},[1460,9358,1647],{"stretchy":1646},[1330,9360,6495],{},[1460,9362,1658],{"stretchy":1646},[1338,9364,6576],{"encoding":1340},[1150,9366,9367],{},[1115,9368,9370],{"className":9369},[1315],[1317,9371,9372],{"xmlns":1319},[1321,9373,9374,9388],{},[1324,9375,9376,9378,9380,9382,9384,9386],{},[1330,9377,6502],{},[1460,9379,1647],{"stretchy":1646},[1330,9381,6507],{},[1460,9383,6510],{},[1330,9385,7035],{},[1460,9387,1658],{"stretchy":1646},[1338,9389,9390],{"encoding":1340},"P(X \\le k)",[1150,9392,9393,9394],{},"horní chvost ",[1115,9395,9397],{"className":9396},[1315],[1317,9398,9399],{"xmlns":1319},[1321,9400,9401,9415],{},[1324,9402,9403,9405,9407,9409,9411,9413],{},[1330,9404,6502],{},[1460,9406,1647],{"stretchy":1646},[1330,9408,6507],{},[1460,9410,1462],{},[1330,9412,7035],{},[1460,9414,1658],{"stretchy":1646},[1338,9416,9417],{"encoding":1340},"P(X>k)",[1157,9419,9420,9466,9510,9551,9600],{},[1147,9421,9422,9451,9456,9461],{},[1162,9423,9424,9425],{},"Binomické ",[1115,9426,9428],{"className":9427},[1315],[1317,9429,9430],{"xmlns":1319},[1321,9431,9432,9448],{},[1324,9433,9434,9436,9438,9440,9442,9444,9446],{},[1330,9435,1595],{},[1330,9437,1650],{},[1460,9439,1647],{"stretchy":1646},[1330,9441,1458],{},[1460,9443,1568],{"separator":1121},[1330,9445,1110],{},[1460,9447,1658],{"stretchy":1646},[1338,9449,9450],{"encoding":1340},"Bi(n,p)",[1162,9452,9453],{},[3244,9454,9455],{},"dbinom(k, n, p)",[1162,9457,9458],{},[3244,9459,9460],{},"pbinom(k, n, p)",[1162,9462,9463],{},[3244,9464,9465],{},"pbinom(k, n, p, FALSE)",[1147,9467,9468,9495,9500,9505],{},[1162,9469,9470,9471],{},"Poissonovo ",[1115,9472,9474],{"className":9473},[1315],[1317,9475,9476],{"xmlns":1319},[1321,9477,9478,9492],{},[1324,9479,9480,9482,9485,9487,9490],{},[1330,9481,6502],{},[1330,9483,9484],{},"o",[1460,9486,1647],{"stretchy":1646},[1330,9488,9489],{},"λ",[1460,9491,1658],{"stretchy":1646},[1338,9493,9494],{"encoding":1340},"Po(\\lambda)",[1162,9496,9497],{},[3244,9498,9499],{},"dpois(k, lambda)",[1162,9501,9502],{},[3244,9503,9504],{},"ppois(k, lambda)",[1162,9506,9507],{},[3244,9508,9509],{},"ppois(k, lambda, FALSE)",[1147,9511,9512,9536,9541,9546],{},[1162,9513,9514,9515],{},"Geometrické ",[1115,9516,9518],{"className":9517},[1315],[1317,9519,9520],{"xmlns":1319},[1321,9521,9522,9533],{},[1324,9523,9524,9527,9529,9531],{},[1330,9525,9526],{},"G",[1460,9528,1647],{"stretchy":1646},[1330,9530,1110],{},[1460,9532,1658],{"stretchy":1646},[1338,9534,9535],{"encoding":1340},"G(p)",[1162,9537,9538],{},[3244,9539,9540],{},"dgeom(k, p)",[1162,9542,9543],{},[3244,9544,9545],{},"pgeom(k, p)",[1162,9547,9548],{},[3244,9549,9550],{},"pgeom(k, p, FALSE)",[1147,9552,9553,9585,9590,9595],{},[1162,9554,9555,9556],{},"Hypergeometrické ",[1115,9557,9559],{"className":9558},[1315],[1317,9560,9561],{"xmlns":1319},[1321,9562,9563,9582],{},[1324,9564,9565,9567,9569,9571,9573,9576,9578,9580],{},[1330,9566,1332],{},[1460,9568,1647],{"stretchy":1646},[1330,9570,6661],{},[1460,9572,1568],{"separator":1121},[1330,9574,9575],{},"M",[1460,9577,1568],{"separator":1121},[1330,9579,1458],{},[1460,9581,1658],{"stretchy":1646},[1338,9583,9584],{"encoding":1340},"H(N,M,n)",[1162,9586,9587],{},[3244,9588,9589],{},"dhyper(k, M, N-M, n)",[1162,9591,9592],{},[3244,9593,9594],{},"phyper(k, M, N-M, n)",[1162,9596,9597],{},[3244,9598,9599],{},"phyper(k, M, N-M, n, FALSE)",[1147,9601,9602,9626,9631,9636],{},[1162,9603,9604,9605],{},"Exponenciální ",[1115,9606,9608],{"className":9607},[1315],[1317,9609,9610],{"xmlns":1319},[1321,9611,9612,9623],{},[1324,9613,9614,9616,9618,9621],{},[1330,9615,7862],{},[1460,9617,1647],{"stretchy":1646},[1330,9619,9620],{},"δ",[1460,9622,1658],{"stretchy":1646},[1338,9624,9625],{"encoding":1340},"E(\\delta)",[1162,9627,9628],{},[3244,9629,9630],{},"dexp(k, 1\u002Fdelta)",[1162,9632,9633],{},[3244,9634,9635],{},"pexp(k, 1\u002Fdelta)",[1162,9637,9638],{},[3244,9639,9640],{},"pexp(k, 1\u002Fdelta, FALSE)",[1103,9642,9644,9651],{"className":9643,"dataCallout":6188},[1106,6187],[1110,9645,9647,9650],{"className":9646},[1113],[1115,9648],{"className":9649,"ariaHidden":1121},[1118,6195,1120],"Exponenciální rozdělení: R bere intenzitu, ne střední hodnotu",[1110,9652,9653,9654,9657,9658,9672,9673,8825,9676,1440],{},"R parametrizuje exponenciální rozdělení intenzitou (",[3244,9655,9656],{},"rate","). Je-li ",[1115,9659,9661],{"className":9660},[1315],[1317,9662,9663],{"xmlns":1319},[1321,9664,9665,9669],{},[1324,9666,9667],{},[1330,9668,9620],{},[1338,9670,9671],{"encoding":1340},"\\delta"," střední doba do události, do R se dosazuje ",[3244,9674,9675],{},"1\u002Fdelta",[3244,9677,9678],{},"delta",[1110,9680,9681,9682,9714,9715,9733],{},"V R (pravděpodobnostní a distribuční funkce diskrétní náhodné veličiny ",[1115,9683,9685],{"className":9684},[1315],[1317,9686,9687],{"xmlns":1319},[1321,9688,9689,9711],{},[1324,9690,9691,9693,9695,9697,9699,9701,9704,9706,9709],{},[1330,9692,6507],{},[1460,9694,8960],{},[1330,9696,1595],{},[1330,9698,1650],{},[1460,9700,1647],{"stretchy":1646},[1334,9702,9703],{},"5",[1460,9705,6669],{"separator":1121},[1334,9707,9708],{},"0,95",[1460,9710,1658],{"stretchy":1646},[1338,9712,9713],{"encoding":1340},"X \\sim Bi(5; 0{,}95)",", a pravděpodobnost, že u exponenciálního rozdělení se střední hodnotou ",[1115,9716,9718],{"className":9717},[1315],[1317,9719,9720],{"xmlns":1319},[1321,9721,9722,9730],{},[1324,9723,9724,9726,9728],{},[1330,9725,9620],{},[1460,9727,1754],{},[1334,9729,9703],{},[1338,9731,9732],{"encoding":1340},"\\delta = 5"," nastane událost do 3 jednotek času):",[3468,9735,9737],{"className":3470,"code":9736,"language":71,"meta":1247,"style":1247},"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",[3244,9738,9739,9753,9785,9814,9819,9828],{"__ignoreMap":1247},[1115,9740,9741,9743,9745,9748,9750],{"class":3476,"line":10},[1115,9742,6495],{"class":3479},[1115,9744,3484],{"class":3483},[1115,9746,9747],{"class":3499}," 0",[1115,9749,1730],{"class":3483},[1115,9751,9752],{"class":3499},"5\n",[1115,9754,9755,9758,9760,9763,9765,9767,9769,9772,9774,9777,9779,9781,9783],{"class":3476,"line":27},[1115,9756,9757],{"class":3487},"round",[1115,9759,1647],{"class":3491},[1115,9761,9762],{"class":3487},"dbinom",[1115,9764,1647],{"class":3491},[1115,9766,6495],{"class":3479},[1115,9768,1568],{"class":3483},[1115,9770,9771],{"class":3499}," 5",[1115,9773,1568],{"class":3483},[1115,9775,9776],{"class":3499}," 0.95",[1115,9778,1658],{"class":3491},[1115,9780,1568],{"class":3483},[1115,9782,3575],{"class":3499},[1115,9784,3676],{"class":3491},[1115,9786,9787,9789,9791,9794,9796,9798,9800,9802,9804,9806,9808,9810,9812],{"class":3476,"line":148},[1115,9788,9757],{"class":3487},[1115,9790,1647],{"class":3491},[1115,9792,9793],{"class":3487},"pbinom",[1115,9795,1647],{"class":3491},[1115,9797,6495],{"class":3479},[1115,9799,1568],{"class":3483},[1115,9801,9771],{"class":3499},[1115,9803,1568],{"class":3483},[1115,9805,9776],{"class":3499},[1115,9807,1658],{"class":3491},[1115,9809,1568],{"class":3483},[1115,9811,3575],{"class":3499},[1115,9813,3676],{"class":3491},[1115,9815,9816],{"class":3476,"line":111},[1115,9817,9818],{"emptyLinePlaceholder":1256},"\n",[1115,9820,9821,9823,9825],{"class":3476,"line":96},[1115,9822,9678],{"class":3479},[1115,9824,3484],{"class":3483},[1115,9826,9827],{"class":3499}," 5\n",[1115,9829,9830,9832,9834,9837,9839,9841,9843,9846,9848,9850,9853,9856,9858,9860,9862],{"class":3476,"line":89},[1115,9831,9757],{"class":3487},[1115,9833,1647],{"class":3491},[1115,9835,9836],{"class":3487},"pexp",[1115,9838,1647],{"class":3491},[1115,9840,3366],{"class":3499},[1115,9842,1568],{"class":3483},[1115,9844,9845],{"class":3479}," rate",[1115,9847,3572],{"class":3483},[1115,9849,4416],{"class":3499},[1115,9851,9852],{"class":3483}," \u002F",[1115,9854,9855],{"class":3479}," delta",[1115,9857,1658],{"class":3491},[1115,9859,1568],{"class":3483},[1115,9861,3575],{"class":3499},[1115,9863,3676],{"class":3491},[3468,9865,9868],{"className":9866,"code":9867,"language":3698,"meta":1247},[3696],"[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",[3244,9869,9867],{"__ignoreMap":1247},[1136,9871,9873],{"id":9872},"studentovo-pearsonovo-a-fisherovo-snedecorovo-rozdělení","Studentovo, Pearsonovo a Fisherovo-Snedecorovo rozdělení",[1110,9875,9876,9877,9880],{},"Tato tři rozdělení mají statistiky, které se dále používají při konstrukci intervalů spolehlivosti a testování hypotéz (viz ",[1127,9878,141],{"className":9879,"dataFsResolvedFilePath":1193,"href":1194},[1130],") — na rozdíl od normálního rozdělení se v příkladech této kapitoly samostatně nepočítají, jsou to nástroje pro další kapitoly.",[1110,9882,9883,3727,9886,9899],{},[1302,9884,9885],{},"Studentovo rozdělení",[1115,9887,9889],{"className":9888},[1315],[1317,9890,9891],{"xmlns":1319},[1321,9892,9893,9897],{},[1324,9894,9895],{},[1330,9896,7035],{},[1338,9898,7035],{"encoding":1340}," stupni volnosti má hustotu pravděpodobnosti",[1115,9901,9903],{"className":9902},[1315],[1317,9904,9905],{"xmlns":1319,"display":1736},[1321,9906,9907,10003],{},[1324,9908,9909,9911,9913,9915,9917,9919,9951,9989,9991,9993,9995,9997,10001],{},[1330,9910,6546],{},[1460,9912,1647],{"stretchy":1646},[1330,9914,6495],{},[1460,9916,1658],{"stretchy":1646},[1460,9918,1754],{},[2512,9920,9921,9923],{},[1334,9922,1565],{},[1324,9924,9925,9927,9947],{},[1330,9926,1595],{},[1324,9928,9929,9931,9937,9939,9945],{},[1460,9930,1647],{"fence":1121},[2512,9932,9933,9935],{},[1334,9934,1565],{},[1334,9936,1360],{},[1460,9938,1568],{"separator":1121},[2512,9940,9941,9943],{},[1330,9942,7035],{},[1334,9944,1360],{},[1460,9946,1658],{"fence":1121},[4228,9948,9949],{},[1330,9950,7035],{},[1353,9952,9953,9973],{},[1324,9954,9955,9957,9959,9961,9971],{},[1460,9956,1647],{"fence":1121},[1334,9958,1565],{},[1460,9960,5252],{},[2512,9962,9963,9969],{},[1353,9964,9965,9967],{},[1330,9966,6495],{},[1334,9968,1360],{},[1330,9970,7035],{},[1460,9972,1658],{"fence":1121},[1324,9974,9975,9977],{},[1460,9976,2838],{},[2512,9978,9979,9987],{},[1324,9980,9981,9983,9985],{},[1330,9982,7035],{},[1460,9984,5252],{},[1334,9986,1565],{},[1334,9988,1360],{},[1460,9990,1568],{"separator":1121},[1784,9992],{"width":1786},[1330,9994,6495],{},[1460,9996,6794],{},[1330,9998,10000],{"mathvariant":9999},"double-struck","R",[1460,10002,1568],{"separator":1121},[1338,10004,10005],{"encoding":1340},"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},",[1110,10007,4282,10008,10021,10022,10035,10036,10049],{},[1115,10009,10011],{"className":10010},[1315],[1317,10012,10013],{"xmlns":1319},[1321,10014,10015,10019],{},[1324,10016,10017],{},[1330,10018,1595],{},[1338,10020,1595],{"encoding":1340}," je funkce beta. Je symetrické kolem nuly; číslo ",[1115,10023,10025],{"className":10024},[1315],[1317,10026,10027],{"xmlns":1319},[1321,10028,10029,10033],{},[1324,10030,10031],{},[1330,10032,7035],{},[1338,10034,7035],{"encoding":1340}," určuje tvar křivky — s rostoucím ",[1115,10037,10039],{"className":10038},[1315],[1317,10040,10041],{"xmlns":1319},[1321,10042,10043,10047],{},[1324,10044,10045],{},[1330,10046,7035],{},[1338,10048,7035],{"encoding":1340}," se rozdělení blíží normálnímu.",[1110,10051,10052,3727,10055,10068],{},[1302,10053,10054],{},"Pearsonovo (chí-kvadrát) rozdělení",[1115,10056,10058],{"className":10057},[1315],[1317,10059,10060],{"xmlns":1319},[1321,10061,10062,10066],{},[1324,10063,10064],{},[1330,10065,7035],{},[1338,10067,7035],{"encoding":1340}," stupni volnosti:",[1115,10070,10072],{"className":10071},[1315],[1317,10073,10074],{"xmlns":1319,"display":1736},[1321,10075,10076,10161],{},[1324,10077,10078,10080,10082,10084,10086,10088,10119,10135,10149,10151,10153,10155,10157,10159],{},[1330,10079,6546],{},[1460,10081,1647],{"stretchy":1646},[1330,10083,6495],{},[1460,10085,1658],{"stretchy":1646},[1460,10087,1754],{},[2512,10089,10090,10092],{},[1334,10091,1565],{},[1324,10093,10094,10106,10109,10111,10113,10115,10117],{},[1353,10095,10096,10098],{},[1334,10097,1360],{},[1324,10099,10100,10102,10104],{},[1330,10101,7035],{},[1330,10103,4379],{"mathvariant":1893},[1334,10105,1360],{},[1330,10107,10108],{"mathvariant":1893},"Γ",[1460,10110,1647],{"stretchy":1646},[1330,10112,7035],{},[1330,10114,4379],{"mathvariant":1893},[1334,10116,1360],{},[1460,10118,1658],{"stretchy":1646},[1353,10120,10121,10123],{},[1330,10122,6495],{},[1324,10124,10125,10127,10129,10131,10133],{},[1330,10126,7035],{},[1330,10128,4379],{"mathvariant":1893},[1334,10130,1360],{},[1460,10132,2838],{},[1334,10134,1565],{},[1353,10136,10137,10139],{},[1330,10138,8369],{},[1324,10140,10141,10143,10145,10147],{},[1460,10142,2838],{},[1330,10144,6495],{},[1330,10146,4379],{"mathvariant":1893},[1334,10148,1360],{},[1460,10150,1568],{"separator":1121},[1784,10152],{"width":1786},[1330,10154,6495],{},[1460,10156,1462],{},[1334,10158,1336],{},[1460,10160,1568],{"separator":1121},[1338,10162,10163],{"encoding":1340},"f(x) = \\frac{1}{2^{k\u002F2}\\Gamma(k\u002F2)} x^{k\u002F2-1} e^{-x\u002F2}, \\qquad x > 0,",[1110,10165,4282,10166,10180],{},[1115,10167,10169],{"className":10168},[1315],[1317,10170,10171],{"xmlns":1319},[1321,10172,10173,10177],{},[1324,10174,10175],{},[1330,10176,10108],{"mathvariant":1893},[1338,10178,10179],{"encoding":1340},"\\Gamma"," je funkce gama.",[1110,10182,10183,10186,10187,5516,10205,1730],{},[1302,10184,10185],{},"Fisherovo-Snedecorovo rozdělení"," se stupni volnosti ",[1115,10188,10190],{"className":10189},[1315],[1317,10191,10192],{"xmlns":1319},[1321,10193,10194,10202],{},[1324,10195,10196],{},[1327,10197,10198,10200],{},[1330,10199,7035],{},[1334,10201,1565],{},[1338,10203,10204],{"encoding":1340},"k_1",[1115,10206,10208],{"className":10207},[1315],[1317,10209,10210],{"xmlns":1319},[1321,10211,10212,10220],{},[1324,10213,10214],{},[1327,10215,10216,10218],{},[1330,10217,7035],{},[1334,10219,1360],{},[1338,10221,10222],{"encoding":1340},"k_2",[1115,10224,10226],{"className":10225},[1315],[1317,10227,10228],{"xmlns":1319,"display":1736},[1321,10229,10230,10395],{},[1324,10231,10232,10234,10236,10238,10240,10242,10278,10312,10332,10384,10386,10388,10390,10392],{},[1330,10233,6546],{},[1460,10235,1647],{"stretchy":1646},[1330,10237,6495],{},[1460,10239,1658],{"stretchy":1646},[1460,10241,1754],{},[2512,10243,10244,10246],{},[1334,10245,1565],{},[1324,10247,10248,10250],{},[1330,10249,1595],{},[1324,10251,10252,10254,10264,10266,10276],{},[1460,10253,1647],{"fence":1121},[2512,10255,10256,10262],{},[1327,10257,10258,10260],{},[1330,10259,7035],{},[1334,10261,1565],{},[1334,10263,1360],{},[1460,10265,1568],{"separator":1121},[2512,10267,10268,10274],{},[1327,10269,10270,10272],{},[1330,10271,7035],{},[1334,10273,1360],{},[1334,10275,1360],{},[1460,10277,1658],{"fence":1121},[1353,10279,10280,10300],{},[1324,10281,10282,10284,10298],{},[1460,10283,1647],{"fence":1121},[2512,10285,10286,10292],{},[1327,10287,10288,10290],{},[1330,10289,7035],{},[1334,10291,1565],{},[1327,10293,10294,10296],{},[1330,10295,7035],{},[1334,10297,1360],{},[1460,10299,1658],{"fence":1121},[1324,10301,10302,10308,10310],{},[1327,10303,10304,10306],{},[1330,10305,7035],{},[1334,10307,1565],{},[1330,10309,4379],{"mathvariant":1893},[1334,10311,1360],{},[1353,10313,10314,10316],{},[1330,10315,6495],{},[1324,10317,10318,10324,10326,10328,10330],{},[1327,10319,10320,10322],{},[1330,10321,7035],{},[1334,10323,1565],{},[1330,10325,4379],{"mathvariant":1893},[1334,10327,1360],{},[1460,10329,2838],{},[1334,10331,1565],{},[1353,10333,10334,10360],{},[1324,10335,10336,10338,10340,10342,10356,10358],{},[1460,10337,1647],{"fence":1121},[1334,10339,1565],{},[1460,10341,5252],{},[2512,10343,10344,10350],{},[1327,10345,10346,10348],{},[1330,10347,7035],{},[1334,10349,1565],{},[1327,10351,10352,10354],{},[1330,10353,7035],{},[1334,10355,1360],{},[1330,10357,6495],{},[1460,10359,1658],{"fence":1121},[1324,10361,10362,10364],{},[1460,10363,2838],{},[2512,10365,10366,10382],{},[1324,10367,10368,10374,10376],{},[1327,10369,10370,10372],{},[1330,10371,7035],{},[1334,10373,1565],{},[1460,10375,5252],{},[1327,10377,10378,10380],{},[1330,10379,7035],{},[1334,10381,1360],{},[1334,10383,1360],{},[1460,10385,1568],{"separator":1121},[1784,10387],{"width":1786},[1330,10389,6495],{},[1460,10391,1462],{},[1334,10393,10394],{},"0.",[1338,10396,10397],{"encoding":1340},"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.",[1110,10399,10400],{},[4158,10401],{"alt":10402,"className":10403,"src":10404},"mask-nv-specialni-rozdeleni",[1130,4162],"\u002Fwiki-assets\u002Fmask-nv-specialni-rozdeleni.png",[8723,10406],{"spec":10407},"{\"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\":[]}",[1110,10409,10410],{},"R funkce pro tato tři rozdělení:",[1141,10412,10413,10427],{},[1144,10414,10415],{},[1147,10416,10417,10419,10422,10424],{},[1150,10418,9318],{},[1150,10420,10421],{},"hustota",[1150,10423,6478],{},[1150,10425,10426],{},"kvantil",[1157,10428,10429,10469,10513],{},[1147,10430,10431,10454,10459,10464],{},[1162,10432,10433,10434],{},"Studentovo ",[1115,10435,10437],{"className":10436},[1315],[1317,10438,10439],{"xmlns":1319},[1321,10440,10441,10451],{},[1324,10442,10443,10445,10447,10449],{},[1330,10444,6919],{},[1460,10446,1647],{"stretchy":1646},[1330,10448,7035],{},[1460,10450,1658],{"stretchy":1646},[1338,10452,10453],{"encoding":1340},"t(k)",[1162,10455,10456],{},[3244,10457,10458],{},"dt(x, df = k)",[1162,10460,10461],{},[3244,10462,10463],{},"pt(x, df = k)",[1162,10465,10466],{},[3244,10467,10468],{},"qt(p, df = k)",[1147,10470,10471,10498,10503,10508],{},[1162,10472,10473,10474],{},"Pearsonovo ",[1115,10475,10477],{"className":10476},[1315],[1317,10478,10479],{"xmlns":1319},[1321,10480,10481,10495],{},[1324,10482,10483,10489,10491,10493],{},[1353,10484,10485,10487],{},[1330,10486,1357],{},[1334,10488,1360],{},[1460,10490,1647],{"stretchy":1646},[1330,10492,7035],{},[1460,10494,1658],{"stretchy":1646},[1338,10496,10497],{"encoding":1340},"\\chi^2(k)",[1162,10499,10500],{},[3244,10501,10502],{},"dchisq(x, df = k)",[1162,10504,10505],{},[3244,10506,10507],{},"pchisq(x, df = k)",[1162,10509,10510],{},[3244,10511,10512],{},"qchisq(p, df = k)",[1147,10514,10515,10550,10555,10560],{},[1162,10516,10517,10518],{},"Fisherovo-Snedecorovo ",[1115,10519,10521],{"className":10520},[1315],[1317,10522,10523],{"xmlns":1319},[1321,10524,10525,10547],{},[1324,10526,10527,10529,10531,10537,10539,10545],{},[1330,10528,6490],{},[1460,10530,1647],{"stretchy":1646},[1327,10532,10533,10535],{},[1330,10534,7035],{},[1334,10536,1565],{},[1460,10538,1568],{"separator":1121},[1327,10540,10541,10543],{},[1330,10542,7035],{},[1334,10544,1360],{},[1460,10546,1658],{"stretchy":1646},[1338,10548,10549],{"encoding":1340},"F(k_1, k_2)",[1162,10551,10552],{},[3244,10553,10554],{},"df(x, df1 = k1, df2 = k2)",[1162,10556,10557],{},[3244,10558,10559],{},"pf(x, df1 = k1, df2 = k2)",[1162,10561,10562],{},[3244,10563,10564],{},"qf(p, df1 = k1, df2 = k2)",[1110,10566,10567],{},"V R (97,5%-ní kvantil Studentova rozdělení s 9 stupni volnosti, 95%-ní kvantily Pearsonova a Fisherova-Snedecorova rozdělení):",[3468,10569,10571],{"className":3470,"code":10570,"language":71,"meta":1247,"style":1247},"qt(0.975, df = 9)\nqchisq(0.95, df = 9)\nqf(0.95, df1 = 3, df2 = 10)\n",[3244,10572,10573,10594,10614],{"__ignoreMap":1247},[1115,10574,10575,10578,10580,10582,10584,10587,10589,10592],{"class":3476,"line":10},[1115,10576,10577],{"class":3487},"qt",[1115,10579,1647],{"class":3491},[1115,10581,8866],{"class":3499},[1115,10583,1568],{"class":3483},[1115,10585,10586],{"class":3479}," df",[1115,10588,3572],{"class":3483},[1115,10590,10591],{"class":3499}," 9",[1115,10593,3676],{"class":3491},[1115,10595,10596,10599,10601,10604,10606,10608,10610,10612],{"class":3476,"line":27},[1115,10597,10598],{"class":3487},"qchisq",[1115,10600,1647],{"class":3491},[1115,10602,10603],{"class":3499},"0.95",[1115,10605,1568],{"class":3483},[1115,10607,10586],{"class":3479},[1115,10609,3572],{"class":3483},[1115,10611,10591],{"class":3499},[1115,10613,3676],{"class":3491},[1115,10615,10616,10619,10621,10623,10625,10628,10630,10633,10635,10638,10640,10642],{"class":3476,"line":148},[1115,10617,10618],{"class":3487},"qf",[1115,10620,1647],{"class":3491},[1115,10622,10603],{"class":3499},[1115,10624,1568],{"class":3483},[1115,10626,10627],{"class":3479}," df1",[1115,10629,3572],{"class":3483},[1115,10631,10632],{"class":3499}," 3",[1115,10634,1568],{"class":3483},[1115,10636,10637],{"class":3479}," df2",[1115,10639,3572],{"class":3483},[1115,10641,9254],{"class":3499},[1115,10643,3676],{"class":3491},[3468,10645,10648],{"className":10646,"code":10647,"language":3698,"meta":1247},[3696],"[1] 2.262157\n[1] 16.91898\n[1] 3.708265\n",[3244,10649,10647],{"__ignoreMap":1247},[1136,10651,6183],{"id":6182},[1204,10653,10654,10740,10790],{},[1207,10655,10656,10659,10660,10687,10688,4379,10690,4379,10692,10694,10695,10715,10716,10739],{},[1302,10657,10658],{},"Rozptyl vs. směrodatná odchylka v R."," Zápis ",[1115,10661,10663],{"className":10662},[1315],[1317,10664,10665],{"xmlns":1319},[1321,10666,10667,10685],{},[1324,10668,10669,10671,10673,10675,10677,10683],{},[1330,10670,6661],{},[1460,10672,1647],{"stretchy":1646},[1330,10674,6666],{},[1460,10676,6669],{"separator":1121},[1353,10678,10679,10681],{},[1330,10680,6674],{},[1334,10682,1360],{},[1460,10684,1658],{"stretchy":1646},[1338,10686,6681],{"encoding":1340}," používá rozptyl, ale ",[3244,10689,6685],{},[3244,10691,6688],{},[3244,10693,6691],{}," očekávají směrodatnou odchylku. Dosazení rozptylu místo ",[1115,10696,10698],{"className":10697},[1315],[1317,10699,10700],{"xmlns":1319},[1321,10701,10702,10712],{},[1324,10703,10704],{},[4228,10705,10706],{},[1353,10707,10708,10710],{},[1330,10709,6674],{},[1334,10711,1360],{},[1338,10713,10714],{"encoding":1340},"\\sqrt{\\sigma^2}"," dává jiný — a pro ",[1115,10717,10719],{"className":10718},[1315],[1317,10720,10721],{"xmlns":1319},[1321,10722,10723,10736],{},[1324,10724,10725,10731,10734],{},[1353,10726,10727,10729],{},[1330,10728,6674],{},[1334,10730,1360],{},[1460,10732,10733],{"mathvariant":1893},"≠",[1334,10735,1565],{},[1338,10737,10738],{"encoding":1340},"\\sigma^2 \\ne 1"," výrazně odlišný — výsledek (viz příklad s ampulkou).",[1207,10741,10742,10769,10770,10789],{},[1302,10743,10744,10768],{},[1115,10745,10747],{"className":10746},[1315],[1317,10748,10749],{"xmlns":1319},[1321,10750,10751,10765],{},[1324,10752,10753,10755,10757,10759,10761,10763],{},[1330,10754,6502],{},[1460,10756,1647],{"stretchy":1646},[1330,10758,6507],{},[1460,10760,1754],{},[1330,10762,6495],{},[1460,10764,1658],{"stretchy":1646},[1338,10766,10767],{"encoding":1340},"P(X=x)"," u spojité veličiny je vždy 0."," Hustota ",[1115,10771,10773],{"className":10772},[1315],[1317,10774,10775],{"xmlns":1319},[1321,10776,10777,10787],{},[1324,10778,10779,10781,10783,10785],{},[1330,10780,6546],{},[1460,10782,1647],{"stretchy":1646},[1330,10784,6495],{},[1460,10786,1658],{"stretchy":1646},[1338,10788,6576],{"encoding":1340}," sama o sobě pravděpodobnost neudává — pravděpodobnost dává až plocha pod křivkou na intervalu.",[1207,10791,10792,1425,10795,10812,10813,10830,10831,10834,10835,1440],{},[1302,10793,10794],{},"Záměna stupňů volnosti u Fisherova-Snedecorova rozdělení.",[1115,10796,10798],{"className":10797},[1315],[1317,10799,10800],{"xmlns":1319},[1321,10801,10802,10810],{},[1324,10803,10804],{},[1327,10805,10806,10808],{},[1330,10807,7035],{},[1334,10809,1565],{},[1338,10811,10204],{"encoding":1340}," (čitatel) a ",[1115,10814,10816],{"className":10815},[1315],[1317,10817,10818],{"xmlns":1319},[1321,10819,10820,10828],{},[1324,10821,10822],{},[1327,10823,10824,10826],{},[1330,10825,7035],{},[1334,10827,1360],{},[1338,10829,10222],{"encoding":1340}," (jmenovatel) nejsou zaměnitelné — ",[3244,10832,10833],{},"qf(p, df1, df2)"," dá jiný výsledek než ",[3244,10836,10837],{},"qf(p, df2, df1)",[1136,10839,1202],{"id":1201},[1204,10841,10842,10847,10852,10857,10863,10870,10876],{},[1207,10843,10844],{},[1127,10845,1133],{"className":10846,"dataFsResolvedFilePath":1131,"href":1132},[1130],[1207,10848,10849],{},[1127,10850,886],{"className":10851,"dataFsResolvedFilePath":1180,"href":1181},[1130],[1207,10853,10854],{},[1127,10855,141],{"className":10856,"dataFsResolvedFilePath":1193,"href":1194},[1130],[1207,10858,10859],{},[1127,10860,10862],{"className":10861,"dataFsResolvedFilePath":6397,"href":6398},[1130],"regresni-a-korelacni-analyza",[1207,10864,10865],{},[1127,10866,716],{"className":10867,"dataFsResolvedFilePath":10868,"href":10869},[1130],"topics\u002Fkontingencni-tabulky.md","\u002Fwiki\u002Fkontingencni-tabulky",[1207,10871,10872],{},[1127,10873,10875],{"className":10874,"dataFsResolvedFilePath":6405,"href":6406},[1130],"regulacni-diagramy-a-indexy-zpusobilosti",[1207,10877,10878],{},[1127,10879,6413],{"className":10880,"dataFsResolvedFilePath":1232,"href":1233},[1130],[1136,10882,1237],{"id":934},[1110,10884,1240,10885,1245],{},[1242,10886,1244],{},[6421,10888,10889],{},"html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .sP4rz, html code.shiki .sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}",{"title":1247,"searchDepth":27,"depth":27,"links":10891},[10892,10893,10894,10895,10896,10897,10898,10899,10900,10901],{"id":6740,"depth":27,"text":6741},{"id":7048,"depth":27,"text":7049},{"id":7734,"depth":27,"text":7735},{"id":7843,"depth":27,"text":7844},{"id":8280,"depth":27,"text":6649},{"id":9282,"depth":27,"text":9283},{"id":9872,"depth":27,"text":9873},{"id":6182,"depth":27,"text":6183},{"id":1201,"depth":27,"text":1202},{"id":934,"depth":27,"text":1237},{},"\u002Ftopics\u002Fnahodne-veliciny-a-rozdeleni",{"title":1169,"description":1247},[1260,1261,1267],"topics\u002Fnahodne-veliciny-a-rozdeleni",[23,67,812,332,532,71],"y7MCWBwmskoGgsMoqVPhRRaL6YYTo3Cf-R4Yf-89eMs",{"id":10910,"title":1182,"body":10911,"course":23,"courses":1252,"created":1253,"description":1247,"extension":1254,"meta":15662,"navigation":1256,"path":15663,"seo":15664,"sources":15665,"stem":15670,"tags":15671,"type":6442,"updated":1253,"__hash__":15672},"topics\u002Ftopics\u002Fpopisna-statistika.md",{"type":1096,"value":10912,"toc":15653},[10913,10916,11010,11014,11024,11150,11157,11168,11172,11215,11220,11322,11332,11337,11476,11552,11556,11657,11738,11745,11816,11835,11837,12053,12059,12069,12076,12079,12133,12139,12149,12162,12308,12311,12324,12643,12649,12652,12656,12735,12769,12798,12800,12878,12884,12945,12952,12965,13042,13158,13208,13221,13376,13382,13409,13413,13438,13441,13654,13722,13823,13830,13843,14346,14352,14384,14644,14797,14908,14937,14943,14950,14956,14969,15399,15405,15408,15410,15605,15607,15644,15646,15650],[1099,10914,1182],{"id":10915},"popisná-statistika-a-datové-soubory",[1103,10917,10919,10925],{"className":10918,"dataCallout":1287},[1106,1286],[1110,10920,10922,1295],{"className":10921},[1113],[1115,10923],{"className":10924,"ariaHidden":1121},[1118,1294,1120],[1204,10926,10927,10930,10933,10960,11007],{},[1207,10928,10929],{},"Rozlišit základní a výběrový soubor, typ statistického znaku (kvantitativní\u002Fkvalitativní, diskrétní\u002Fspojitý) a požadavek reprezentativity a nezávislého výběru.",[1207,10931,10932],{},"Spočítat výběrový průměr, rozptyl, směrodatnou odchylku a variační rozpětí; interpretovat je jako bodové odhady charakteristik náhodné veličiny.",[1207,10934,10935,10936,1440],{},"Určit medián a kvartily a číst empirickou distribuční funkci ",[1115,10937,10939],{"className":10938},[1315],[1317,10940,10941],{"xmlns":1319},[1321,10942,10943,10957],{},[1324,10944,10945,10951,10953,10955],{},[1327,10946,10947,10949],{},[1330,10948,6490],{},[1330,10950,1458],{},[1460,10952,1647],{"stretchy":1646},[1330,10954,6495],{},[1460,10956,1658],{"stretchy":1646},[1338,10958,10959],{"encoding":1340},"F_n(x)",[1207,10961,10962,10963,11006],{},"Roztřídit velký datový soubor do tříd (intervalové rozdělení četností), sestavit tabulku ",[1115,10964,10966],{"className":10965},[1315],[1317,10967,10968],{"xmlns":1319},[1321,10969,10970,11003],{},[1324,10971,10972,10979,10981,10987,10989,10995,10997],{},[1327,10973,10974,10977],{},[1330,10975,10976],{},"I",[1330,10978,1655],{},[1460,10980,1568],{"separator":1121},[1327,10982,10983,10985],{},[1330,10984,8702],{},[1330,10986,1655],{},[1460,10988,1568],{"separator":1121},[1327,10990,10991,10993],{},[1330,10992,6546],{},[1330,10994,1655],{},[1460,10996,1568],{"separator":1121},[1327,10998,10999,11001],{},[1330,11000,1110],{},[1330,11002,1655],{},[1338,11004,11005],{"encoding":1340},"I_j, Z_j, f_j, p_j"," a nakreslit histogram.",[1207,11008,11009],{},"Z histogramu odhadnout zákon rozdělení dat; formální test shody patří do testování hypotéz.",[1136,11011,11013],{"id":11012},"základní-pojmy","Základní pojmy",[1110,11015,11016,11019,11020,11023],{},[1127,11017,1133],{"className":11018,"dataFsResolvedFilePath":1131,"href":1132},[1130]," pracuje s ",[1302,11021,11022],{},"datovými soubory"," — konkrétními hodnotami, které popisují vlastnost zkoumaných prvků.",[1204,11025,11026,11032,11056,11062,11137],{},[1207,11027,11028,11031],{},[1302,11029,11030],{},"Základní soubor"," — množina prvků, na nichž provádíme šetření (např. všichni výdělečně činní obyvatelé ČR).",[1207,11033,11034,11037,11038],{},[1302,11035,11036],{},"Statistický znak"," — funkce, která vyjadřuje určitou vlastnost prvku (např. velikost platu). Znaky dělíme na:\n",[1204,11039,11040,11051],{},[1207,11041,11042,11044,11045,11047,11048,11050],{},[1302,11043,1505],{}," (vyjádřitelné číslem) — dále ",[1302,11046,6467],{}," (spočetně mnoho hodnot) nebo ",[1302,11049,6471],{}," (libovolná hodnota v intervalu);",[1207,11052,11053,11055],{},[1302,11054,1498],{}," (vyjádřitelné slovně).",[1207,11057,11058,11061],{},[1302,11059,11060],{},"Výběrový soubor"," — podmnožina prvků základního souboru, na níž znak skutečně zjišťujeme (např. 5 náhodně vybraných obyvatel).",[1207,11063,11064,11067,11068,1440],{},[1302,11065,11066],{},"Datový soubor"," — n-tice naměřených hodnot zkoumaného znaku, např. ",[1115,11069,11071],{"className":11070},[1315],[1317,11072,11073],{"xmlns":1319},[1321,11074,11075,11134],{},[1324,11076,11077,11079,11081,11083,11086,11088,11091,11094,11096,11099,11101,11103,11106,11108,11111,11113,11115,11117,11119,11121,11123,11125,11127,11129,11132],{},[1460,11078,1647],{"stretchy":1646},[1334,11080,3324],{},[2682,11082,2684],{},[1334,11084,11085],{},"500",[1460,11087,1568],{"separator":1121},[2682,11089,11090],{}," ",[1334,11092,11093],{},"38",[2682,11095,2684],{},[1334,11097,11098],{},"000",[1460,11100,1568],{"separator":1121},[2682,11102,11090],{},[1334,11104,11105],{},"37",[2682,11107,2684],{},[1334,11109,11110],{},"800",[1460,11112,1568],{"separator":1121},[2682,11114,11090],{},[1334,11116,9133],{},[2682,11118,2684],{},[1334,11120,11098],{},[1460,11122,1568],{"separator":1121},[2682,11124,11090],{},[1334,11126,3332],{},[2682,11128,2684],{},[1334,11130,11131],{},"200",[1460,11133,1658],{"stretchy":1646},[1338,11135,11136],{"encoding":1340},"(29\\,500,\\ 38\\,000,\\ 37\\,800,\\ 41\\,000,\\ 31\\,200)",[1207,11138,11139,11140,2725,11143,5516,11146,11149],{},"Podle počtu sledovaných znaků rozlišujeme ",[1302,11141,11142],{},"jednorozměrné",[1302,11144,11145],{},"dvourozměrné",[1302,11147,11148],{},"vícerozměrné"," datové soubory.",[1110,11151,11152],{},[4158,11153],{"alt":11154,"className":11155,"src":11156},"mask-ilu-zakladni-soubor-vyber",[1130,4162],"\u002Fwiki-assets\u002Fmask-ilu-zakladni-soubor-vyber.png",[1110,11158,11159,11160,11163,11164,11167],{},"Aby výběrový soubor dobře vypovídal o základním souboru, měl by být ",[1302,11161,11162],{},"reprezentativní"," (podobný základnímu souboru svým složením). Není-li to možné zajistit přímo, volí se prvky do výběru náhodně — ",[1302,11165,11166],{},"nezávislý výběr",". Bez náhodnosti výběru nelze vlastnosti základního souboru správně vystihnout.",[1136,11169,11171],{"id":11170},"empirické-charakteristiky","Empirické charakteristiky",[1110,11173,11174,11175,11178,11179,11182,11183,11196,11197,11200,11201,11214],{},"Zpracováním datového souboru získáme ",[1302,11176,11177],{},"empirické charakteristiky"," a odhad ",[1302,11180,11181],{},"zákona rozdělení"," zkoumané náhodné veličiny ",[1115,11184,11186],{"className":11185},[1315],[1317,11187,11188],{"xmlns":1319},[1321,11189,11190,11194],{},[1324,11191,11192],{},[1330,11193,6507],{},[1338,11195,6507],{"encoding":1340},". Jde o ",[1302,11198,11199],{},"bodové odhady"," charakteristik ",[1115,11202,11204],{"className":11203},[1315],[1317,11205,11206],{"xmlns":1319},[1321,11207,11208,11212],{},[1324,11209,11210],{},[1330,11211,6507],{},[1338,11213,6507],{"encoding":1340},"; ruční výpočet podle vzorců níže je potřeba jen bez dostupného softwaru.",[1110,11216,11217],{},[1302,11218,11219],{},"Míry polohy",[1115,11221,11223],{"className":11222},[1315],[1317,11224,11225],{"xmlns":1319,"display":1736},[1321,11226,11227,11319],{},[1324,11228,11229,11236,11238,11244,11258,11264,11266],{},[2496,11230,11231,11233],{"accent":1121},[1330,11232,6495],{},[1460,11234,11235],{},"ˉ",[1460,11237,1754],{},[2512,11239,11240,11242],{},[1334,11241,1565],{},[1330,11243,1458],{},[1756,11245,11246,11248,11256],{},[1460,11247,1760],{},[1324,11249,11250,11252,11254],{},[1330,11251,1650],{},[1460,11253,1754],{},[1334,11255,1565],{},[1330,11257,1458],{},[1327,11259,11260,11262],{},[1330,11261,6495],{},[1330,11263,1650],{},[1784,11265],{"width":1786},[1324,11267,11268,11271,11278,11281,11288,11291,11297,11300,11308,11310,11316],{},[2682,11269,11270],{},"(v",[2496,11272,11273,11275],{"accent":1121},[2682,11274,6905],{},[1460,11276,11277],{},"ˊ",[2682,11279,11280],{},"b",[2496,11282,11283,11285],{"accent":1121},[2682,11284,8369],{},[1460,11286,11287],{},"ˇ",[2682,11289,11290],{},"rov",[2496,11292,11293,11295],{"accent":1121},[2682,11294,6905],{},[1460,11296,11277],{},[2682,11298,11299],{}," pr",[2496,11301,11302,11305],{"accent":1121},[2682,11303,11304],{},"u",[1460,11306,11307],{},"˚",[2682,11309,4246],{},[2496,11311,11312,11314],{"accent":1121},[2682,11313,8369],{},[1460,11315,11287],{},[2682,11317,11318],{},"r)",[1338,11320,11321],{"encoding":1340},"\\bar{x} = \\frac{1}{n}\\sum_{i=1}^{n} x_i \\qquad \\text{(výběrový průměr)}",[1110,11323,11324,11325,5516,11328,11331],{},"Dalšími mírami polohy jsou ",[1302,11326,11327],{},"medián",[1302,11329,11330],{},"modus"," (nejčetnější hodnota výběru).",[1110,11333,11334],{},[1302,11335,11336],{},"Míry variability",[1115,11338,11340],{"className":11339},[1315],[1317,11341,11342],{"xmlns":1319,"display":1736},[1321,11343,11344,11473],{},[1324,11345,11346,11352,11354,11366,11408,11410,11412,11414,11416,11424,11426],{},[1353,11347,11348,11350],{},[1330,11349,1626],{},[1334,11351,1360],{},[1460,11353,1754],{},[2512,11355,11356,11358],{},[1334,11357,1565],{},[1324,11359,11360,11362,11364],{},[1330,11361,1458],{},[1460,11363,2838],{},[1334,11365,1565],{},[1324,11367,11368,11370,11384,11392,11394,11396,11406],{},[1460,11369,1647],{"fence":1121},[1756,11371,11372,11374,11382],{},[1460,11373,1760],{},[1324,11375,11376,11378,11380],{},[1330,11377,1650],{},[1460,11379,1754],{},[1334,11381,1565],{},[1330,11383,1458],{},[3127,11385,11386,11388,11390],{},[1330,11387,6495],{},[1330,11389,1650],{},[1334,11391,1360],{},[1460,11393,2838],{},[1330,11395,1458],{},[1353,11397,11398,11404],{},[2496,11399,11400,11402],{"accent":1121},[1330,11401,6495],{},[1460,11403,11235],{},[1334,11405,1360],{},[1460,11407,1658],{"fence":1121},[1460,11409,1568],{"separator":1121},[1784,11411],{"width":1786},[1330,11413,1626],{},[1460,11415,1754],{},[4228,11417,11418],{},[1353,11419,11420,11422],{},[1330,11421,1626],{},[1334,11423,1360],{},[1784,11425],{"width":1786},[1324,11427,11428,11430,11436,11438,11444,11446,11452,11455,11461,11464,11470],{},[2682,11429,11270],{},[2496,11431,11432,11434],{"accent":1121},[2682,11433,6905],{},[1460,11435,11277],{},[2682,11437,11280],{},[2496,11439,11440,11442],{"accent":1121},[2682,11441,8369],{},[1460,11443,11287],{},[2682,11445,11290],{},[2496,11447,11448,11450],{"accent":1121},[2682,11449,6905],{},[1460,11451,11277],{},[2682,11453,11454],{}," rozptyl, sm",[2496,11456,11457,11459],{"accent":1121},[2682,11458,8369],{},[1460,11460,11287],{},[2682,11462,11463],{},"rodatn",[2496,11465,11466,11468],{"accent":1121},[2682,11467,1127],{},[1460,11469,11277],{},[2682,11471,11472],{}," odchylka)",[1338,11474,11475],{"encoding":1340},"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)}",[1115,11477,11479],{"className":11478},[1315],[1317,11480,11481],{"xmlns":1319,"display":1736},[1321,11482,11483,11549],{},[1324,11484,11485,11487,11489,11498,11500,11508,11510],{},[1330,11486,10000],{},[1460,11488,1754],{},[1327,11490,11491,11493,11496],{},[1330,11492,6495],{},[1330,11494,11495],{},"max",[1460,11497,4266],{},[1460,11499,2838],{},[1327,11501,11502,11504,11506],{},[1330,11503,6495],{},[1330,11505,4263],{},[1460,11507,4266],{},[1784,11509],{"width":1786},[1324,11511,11512,11515,11521,11523,11530,11533,11539,11541,11547],{},[2682,11513,11514],{},"(varia",[2496,11516,11517,11519],{"accent":1121},[2682,11518,3494],{},[1460,11520,11287],{},[2682,11522,1458],{},[2496,11524,11525,11528],{"accent":1121},[2682,11526,11527],{},"ı",[1460,11529,11277],{},[2682,11531,11532],{}," rozp",[2496,11534,11535,11537],{"accent":1121},[2682,11536,8369],{},[1460,11538,11287],{},[2682,11540,6919],{},[2496,11542,11543,11545],{"accent":1121},[2682,11544,11527],{},[1460,11546,11277],{},[2682,11548,1658],{},[1338,11550,11551],{"encoding":1340},"R = x_{\\max} - x_{\\min} \\qquad \\text{(variační rozpětí)}",[1110,11553,11554],{},[1302,11555,8080],{},[1110,11557,11558,11559,11582,11583,11605,11606,11627,11628,11656],{},"Kvantil ",[1115,11560,11562],{"className":11561},[1315],[1317,11563,11564],{"xmlns":1319},[1321,11565,11566,11579],{},[1324,11567,11568],{},[1327,11569,11570,11577],{},[2496,11571,11572,11574],{"accent":1121},[1330,11573,6495],{},[1460,11575,11576],{},"~",[1330,11578,1110],{},[1338,11580,11581],{"encoding":1340},"\\tilde{x}_p"," dělí hodnoty datového souboru na dvě části: ",[1115,11584,11586],{"className":11585},[1315],[1317,11587,11588],{"xmlns":1319},[1321,11589,11590,11602],{},[1324,11591,11592,11595,11597,11599],{},[1334,11593,11594],{},"100",[1330,11596,1110],{},[2682,11598,2684],{},[1330,11600,11601],{"mathvariant":1893},"%",[1338,11603,11604],{"encoding":1340},"100p\\,\\%"," hodnot je menších nebo rovných ",[1115,11607,11609],{"className":11608},[1315],[1317,11610,11611],{"xmlns":1319},[1321,11612,11613,11625],{},[1324,11614,11615],{},[1327,11616,11617,11623],{},[2496,11618,11619,11621],{"accent":1121},[1330,11620,6495],{},[1460,11622,11576],{},[1330,11624,1110],{},[1338,11626,11581],{"encoding":1340},", zbylých ",[1115,11629,11631],{"className":11630},[1315],[1317,11632,11633],{"xmlns":1319},[1321,11634,11635,11653],{},[1324,11636,11637,11639,11641,11643,11645,11647,11649,11651],{},[1334,11638,11594],{},[1460,11640,1647],{"stretchy":1646},[1334,11642,1565],{},[1460,11644,2838],{},[1330,11646,1110],{},[1460,11648,1658],{"stretchy":1646},[2682,11650,2684],{},[1330,11652,11601],{"mathvariant":1893},[1338,11654,11655],{"encoding":1340},"100(1-p)\\,\\%"," je větších. Nejdůležitější kvantily:",[1204,11658,11659,11686],{},[1207,11660,11661,1425,11663,11685],{},[1302,11662,11327],{},[1115,11664,11666],{"className":11665},[1315],[1317,11667,11668],{"xmlns":1319},[1321,11669,11670,11682],{},[1324,11671,11672],{},[1327,11673,11674,11680],{},[2496,11675,11676,11678],{"accent":1121},[1330,11677,6495],{},[1460,11679,11576],{},[1334,11681,8234],{},[1338,11683,11684],{"encoding":1340},"\\tilde{x}_{0{,}5}"," — pro lichý počet prvků uspořádaného souboru prostřední prvek, pro sudý počet průměr dvou prostředních prvků;",[1207,11687,11688,1425,11691,5516,11713,1425,11716,1440],{},[1302,11689,11690],{},"dolní kvartil",[1115,11692,11694],{"className":11693},[1315],[1317,11695,11696],{"xmlns":1319},[1321,11697,11698,11710],{},[1324,11699,11700],{},[1327,11701,11702,11708],{},[2496,11703,11704,11706],{"accent":1121},[1330,11705,6495],{},[1460,11707,11576],{},[1334,11709,8254],{},[1338,11711,11712],{"encoding":1340},"\\tilde{x}_{0{,}25}",[1302,11714,11715],{},"horní kvartil",[1115,11717,11719],{"className":11718},[1315],[1317,11720,11721],{"xmlns":1319},[1321,11722,11723,11735],{},[1324,11724,11725],{},[1327,11726,11727,11733],{},[2496,11728,11729,11731],{"accent":1121},[1330,11730,6495],{},[1460,11732,11576],{},[1334,11734,8274],{},[1338,11736,11737],{"encoding":1340},"\\tilde{x}_{0{,}75}",[1110,11739,11740,11741,11744],{},"Datový soubor se do R zadává buď přímo (",[3244,11742,11743],{},"x \u003C- c(...)","), nebo načtením ze souboru:",[3468,11746,11748],{"className":3470,"code":11747,"language":71,"meta":1247,"style":1247},"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",[3244,11749,11750,11811],{"__ignoreMap":1247},[1115,11751,11752,11754,11756,11758,11760,11763,11765,11768,11770,11773,11775,11778,11780,11782,11784,11786,11788,11791,11793,11796,11798,11800,11802,11804,11807],{"class":3476,"line":10},[1115,11753,6495],{"class":3479},[1115,11755,3484],{"class":3483},[1115,11757,3610],{"class":3487},[1115,11759,1647],{"class":3491},[1115,11761,11762],{"class":3499},"4.1",[1115,11764,1568],{"class":3483},[1115,11766,11767],{"class":3499}," 4.0",[1115,11769,1568],{"class":3483},[1115,11771,11772],{"class":3499}," 3.8",[1115,11774,1568],{"class":3483},[1115,11776,11777],{"class":3499}," 3.9",[1115,11779,1568],{"class":3483},[1115,11781,11772],{"class":3499},[1115,11783,1568],{"class":3483},[1115,11785,11772],{"class":3499},[1115,11787,1568],{"class":3483},[1115,11789,11790],{"class":3499}," 3.5",[1115,11792,1568],{"class":3483},[1115,11794,11795],{"class":3499}," 3.7",[1115,11797,1568],{"class":3483},[1115,11799,11767],{"class":3499},[1115,11801,1568],{"class":3483},[1115,11803,11767],{"class":3499},[1115,11805,11806],{"class":3491},")   ",[1115,11808,11810],{"class":11809},"sCsY4","# přímé zadání hodnot\n",[1115,11812,11813],{"class":3476,"line":27},[1115,11814,11815],{"class":11809},"# x \u003C- read.table(\"data.txt\")[, 1]                       # načtení prvního sloupce ze souboru\n",[1110,11817,11818,11819,11822,11823,11826,11827,11830,11831,11834],{},"Řádek s načtením ze souboru je zakomentovaný znakem ",[3244,11820,11821],{},"#",": soubor musí ležet v pracovním adresáři R. ",[3244,11824,11825],{},"read.table()"," vrací datovou tabulku (",[3244,11828,11829],{},"data.frame","), proto ",[3244,11832,11833],{},"[, 1]"," vybere její první sloupec jako vektor.",[1110,11836,8831],{},[3468,11838,11840],{"className":3470,"code":11839,"language":71,"meta":1247,"style":1247},"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",[3244,11841,11842,11899,11910,11921,11932,11943,11981,12007,12030],{"__ignoreMap":1247},[1115,11843,11844,11846,11848,11850,11852,11855,11857,11860,11862,11865,11867,11870,11872,11874,11876,11879,11881,11883,11885,11888,11890,11893,11895,11897],{"class":3476,"line":10},[1115,11845,6495],{"class":3479},[1115,11847,3484],{"class":3483},[1115,11849,3610],{"class":3487},[1115,11851,1647],{"class":3491},[1115,11853,11854],{"class":3499},"11.1",[1115,11856,1568],{"class":3483},[1115,11858,11859],{"class":3499}," 12.7",[1115,11861,1568],{"class":3483},[1115,11863,11864],{"class":3499}," 10.8",[1115,11866,1568],{"class":3483},[1115,11868,11869],{"class":3499}," 13.2",[1115,11871,1568],{"class":3483},[1115,11873,11859],{"class":3499},[1115,11875,1568],{"class":3483},[1115,11877,11878],{"class":3499}," 13.4",[1115,11880,1568],{"class":3483},[1115,11882,11859],{"class":3499},[1115,11884,1568],{"class":3483},[1115,11886,11887],{"class":3499}," 14.4",[1115,11889,1568],{"class":3483},[1115,11891,11892],{"class":3499}," 14.7",[1115,11894,1568],{"class":3483},[1115,11896,11887],{"class":3499},[1115,11898,3676],{"class":3491},[1115,11900,11901,11904,11906,11908],{"class":3476,"line":27},[1115,11902,11903],{"class":3487},"length",[1115,11905,1647],{"class":3491},[1115,11907,6495],{"class":3479},[1115,11909,3676],{"class":3491},[1115,11911,11912,11915,11917,11919],{"class":3476,"line":148},[1115,11913,11914],{"class":3487},"mean",[1115,11916,1647],{"class":3491},[1115,11918,6495],{"class":3479},[1115,11920,3676],{"class":3491},[1115,11922,11923,11926,11928,11930],{"class":3476,"line":111},[1115,11924,11925],{"class":3487},"var",[1115,11927,1647],{"class":3491},[1115,11929,6495],{"class":3479},[1115,11931,3676],{"class":3491},[1115,11933,11934,11937,11939,11941],{"class":3476,"line":96},[1115,11935,11936],{"class":3487},"sd",[1115,11938,1647],{"class":3491},[1115,11940,6495],{"class":3479},[1115,11942,3676],{"class":3491},[1115,11944,11945,11947,11949,11951,11954,11956,11958,11960,11962,11964,11966,11968,11970,11972,11975,11977,11979],{"class":3476,"line":89},[1115,11946,4263],{"class":3487},[1115,11948,1647],{"class":3491},[1115,11950,6495],{"class":3479},[1115,11952,11953],{"class":3491},"); ",[1115,11955,11495],{"class":3487},[1115,11957,1647],{"class":3491},[1115,11959,6495],{"class":3479},[1115,11961,11953],{"class":3491},[1115,11963,11495],{"class":3487},[1115,11965,1647],{"class":3491},[1115,11967,6495],{"class":3479},[1115,11969,4376],{"class":3491},[1115,11971,4413],{"class":3483},[1115,11973,11974],{"class":3487}," min",[1115,11976,1647],{"class":3491},[1115,11978,6495],{"class":3479},[1115,11980,3676],{"class":3491},[1115,11982,11983,11986,11988,11990,11992,11995,11997,12000,12002,12005],{"class":3476,"line":82},[1115,11984,11985],{"class":3487},"quantile",[1115,11987,1647],{"class":3491},[1115,11989,6495],{"class":3479},[1115,11991,1568],{"class":3483},[1115,11993,11994],{"class":3499}," 0.5",[1115,11996,1568],{"class":3483},[1115,11998,11999],{"class":3479}," type",[1115,12001,3572],{"class":3483},[1115,12003,12004],{"class":3499}," 6",[1115,12006,3676],{"class":3491},[1115,12008,12009,12011,12013,12015,12017,12020,12022,12024,12026,12028],{"class":3476,"line":75},[1115,12010,11985],{"class":3487},[1115,12012,1647],{"class":3491},[1115,12014,6495],{"class":3479},[1115,12016,1568],{"class":3483},[1115,12018,12019],{"class":3499}," 0.25",[1115,12021,1568],{"class":3483},[1115,12023,11999],{"class":3479},[1115,12025,3572],{"class":3483},[1115,12027,12004],{"class":3499},[1115,12029,3676],{"class":3491},[1115,12031,12032,12034,12036,12038,12040,12043,12045,12047,12049,12051],{"class":3476,"line":3666},[1115,12033,11985],{"class":3487},[1115,12035,1647],{"class":3491},[1115,12037,6495],{"class":3479},[1115,12039,1568],{"class":3483},[1115,12041,12042],{"class":3499}," 0.75",[1115,12044,1568],{"class":3483},[1115,12046,11999],{"class":3479},[1115,12048,3572],{"class":3483},[1115,12050,12004],{"class":3499},[1115,12052,3676],{"class":3491},[3468,12054,12057],{"className":12055,"code":12056,"language":3698,"meta":1247},[3696],"[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",[3244,12058,12056],{"__ignoreMap":1247},[1110,12060,12061,12064,12065,12068],{},[3244,12062,12063],{},"quantile(x, p, type = 6)"," je potřeba zadat explicitně — výchozí typ v R (",[3244,12066,12067],{},"type = 7",") by u některých souborů dal mírně odlišné hodnoty kvantilů než ruční výpočet použitý v této kapitole.",[1110,12070,12071],{},[4158,12072],{"alt":12073,"className":12074,"src":12075},"mask-ps-kvantily",[1130,4162],"\u002Fwiki-assets\u002Fmask-ps-kvantily.png",[1110,12077,12078],{},"Seřazení souboru a krabicový graf:",[3468,12080,12082],{"className":3470,"code":12081,"language":71,"meta":1247,"style":1247},"sort(x)                     # vzestupně\nsort(x, decreasing = TRUE)  # sestupně\nboxplot(x)\n",[3244,12083,12084,12099,12122],{"__ignoreMap":1247},[1115,12085,12086,12089,12091,12093,12096],{"class":3476,"line":10},[1115,12087,12088],{"class":3487},"sort",[1115,12090,1647],{"class":3491},[1115,12092,6495],{"class":3479},[1115,12094,12095],{"class":3491},")                     ",[1115,12097,12098],{"class":11809},"# vzestupně\n",[1115,12100,12101,12103,12105,12107,12109,12112,12114,12116,12119],{"class":3476,"line":27},[1115,12102,12088],{"class":3487},[1115,12104,1647],{"class":3491},[1115,12106,6495],{"class":3479},[1115,12108,1568],{"class":3483},[1115,12110,12111],{"class":3479}," decreasing",[1115,12113,3572],{"class":3483},[1115,12115,3585],{"class":3499},[1115,12117,12118],{"class":3491},")  ",[1115,12120,12121],{"class":11809},"# sestupně\n",[1115,12123,12124,12127,12129,12131],{"class":3476,"line":148},[1115,12125,12126],{"class":3487},"boxplot",[1115,12128,1647],{"class":3491},[1115,12130,6495],{"class":3479},[1115,12132,3676],{"class":3491},[3468,12134,12137],{"className":12135,"code":12136,"language":3698,"meta":1247},[3696]," [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",[3244,12138,12136],{"__ignoreMap":1247},[1110,12140,12141,12144,12145,12148],{},[3244,12142,12143],{},"boxplot()"," kreslí krabici mezi hodnotami ",[3244,12146,12147],{},"fivenum(x)"," (zde 12,7 a 14,4), které se od kvartilů typu 6 mohou mírně lišit.",[1103,12150,12152,12159],{"className":12151,"dataCallout":3251},[1106,3250],[1110,12153,12155,12158],{"className":12154},[1113],[1115,12156],{"className":12157,"ariaHidden":1121},[1118,3258,1120],"Příklad: Empirické charakteristiky",[1110,12160,12161],{},"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.",[1110,12163,12164,12165,2725,12188,2725,12211,2725,12230,12249,12250,8238,12277,12292,12293,1440],{},"Výstup R kódu výše dává ",[1115,12166,12168],{"className":12167},[1315],[1317,12169,12170],{"xmlns":1319},[1321,12171,12172,12185],{},[1324,12173,12174,12180,12182],{},[2496,12175,12176,12178],{"accent":1121},[1330,12177,6495],{},[1460,12179,11235],{},[1460,12181,1754],{},[1334,12183,12184],{},"13,01",[1338,12186,12187],{"encoding":1340},"\\bar{x}=13{,}01",[1115,12189,12191],{"className":12190},[1315],[1317,12192,12193],{"xmlns":1319},[1321,12194,12195,12208],{},[1324,12196,12197,12203,12205],{},[1353,12198,12199,12201],{},[1330,12200,1626],{},[1334,12202,1360],{},[1460,12204,1754],{},[1334,12206,12207],{},"1,75",[1338,12209,12210],{"encoding":1340},"s^2=1{,}75",[1115,12212,12214],{"className":12213},[1315],[1317,12215,12216],{"xmlns":1319},[1321,12217,12218,12227],{},[1324,12219,12220,12222,12224],{},[1330,12221,1626],{},[1460,12223,1754],{},[1334,12225,12226],{},"1,32",[1338,12228,12229],{"encoding":1340},"s=1{,}32",[1115,12231,12233],{"className":12232},[1315],[1317,12234,12235],{"xmlns":1319},[1321,12236,12237,12246],{},[1324,12238,12239,12241,12243],{},[1330,12240,10000],{},[1460,12242,1754],{},[1334,12244,12245],{},"3,9",[1338,12247,12248],{"encoding":1340},"R=3{,}9",", medián ",[1115,12251,12253],{"className":12252},[1315],[1317,12254,12255],{"xmlns":1319},[1321,12256,12257,12274],{},[1324,12258,12259,12269,12271],{},[1327,12260,12261,12267],{},[2496,12262,12263,12265],{"accent":1121},[1330,12264,6495],{},[1460,12266,11576],{},[1334,12268,8234],{},[1460,12270,1754],{},[1334,12272,12273],{},"12,95",[1338,12275,12276],{"encoding":1340},"\\tilde{x}_{0{,}5}=12{,}95",[1115,12278,12280],{"className":12279},[1315],[1317,12281,12282],{"xmlns":1319},[1321,12283,12284,12289],{},[1324,12285,12286],{},[1334,12287,12288],{},"12,3",[1338,12290,12291],{"encoding":1340},"12{,}3",", horní kvartil ",[1115,12294,12296],{"className":12295},[1315],[1317,12297,12298],{"xmlns":1319},[1321,12299,12300,12305],{},[1324,12301,12302],{},[1334,12303,12304],{},"14,4",[1338,12306,12307],{"encoding":1340},"14{,}4",[1110,12309,12310],{},"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.",[1103,12312,12314,12321],{"className":12313,"dataCallout":3251},[1106,3250],[1110,12315,12317,12320],{"className":12316},[1113],[1115,12318],{"className":12319,"ariaHidden":1121},[1118,3258,1120],"Příklad: Doba oprav televizorů",[1110,12322,12323],{},"Při 50 opravách určité závady televizoru byly naměřeny časy (v minutách). Určete empirické charakteristiky.",[3468,12325,12327],{"className":3470,"code":12326,"language":71,"meta":1247,"style":1247},"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",[3244,12328,12329,12389,12440,12487,12534,12582,12592,12602,12612,12632],{"__ignoreMap":1247},[1115,12330,12331,12334,12336,12338,12340,12342,12344,12347,12349,12352,12354,12357,12359,12362,12364,12367,12369,12372,12374,12377,12379,12382,12384,12387],{"class":3476,"line":10},[1115,12332,12333],{"class":3479},"x6",[1115,12335,3484],{"class":3483},[1115,12337,3610],{"class":3487},[1115,12339,1647],{"class":3491},[1115,12341,3349],{"class":3499},[1115,12343,1568],{"class":3483},[1115,12345,12346],{"class":3499}," 40.2",[1115,12348,1568],{"class":3483},[1115,12350,12351],{"class":3499}," 41.9",[1115,12353,1568],{"class":3483},[1115,12355,12356],{"class":3499}," 43.4",[1115,12358,1568],{"class":3483},[1115,12360,12361],{"class":3499}," 42.8",[1115,12363,1568],{"class":3483},[1115,12365,12366],{"class":3499}," 42.3",[1115,12368,1568],{"class":3483},[1115,12370,12371],{"class":3499}," 43.2",[1115,12373,1568],{"class":3483},[1115,12375,12376],{"class":3499}," 45",[1115,12378,1568],{"class":3483},[1115,12380,12381],{"class":3499}," 41.5",[1115,12383,1568],{"class":3483},[1115,12385,12386],{"class":3499}," 42.7",[1115,12388,3512],{"class":3483},[1115,12390,12391,12394,12396,12399,12401,12404,12406,12409,12411,12414,12416,12419,12421,12424,12426,12429,12431,12433,12435,12438],{"class":3476,"line":27},[1115,12392,12393],{"class":3499},"        43.9",[1115,12395,1568],{"class":3483},[1115,12397,12398],{"class":3499}," 40.1",[1115,12400,1568],{"class":3483},[1115,12402,12403],{"class":3499}," 43.3",[1115,12405,1568],{"class":3483},[1115,12407,12408],{"class":3499}," 41.1",[1115,12410,1568],{"class":3483},[1115,12412,12413],{"class":3499}," 42.5",[1115,12415,1568],{"class":3483},[1115,12417,12418],{"class":3499}," 42.4",[1115,12420,1568],{"class":3483},[1115,12422,12423],{"class":3499}," 41.4",[1115,12425,1568],{"class":3483},[1115,12427,12428],{"class":3499}," 40.8",[1115,12430,1568],{"class":3483},[1115,12432,9112],{"class":3499},[1115,12434,1568],{"class":3483},[1115,12436,12437],{"class":3499}," 44.7",[1115,12439,3512],{"class":3483},[1115,12441,12442,12445,12447,12449,12451,12453,12455,12458,12460,12463,12465,12468,12470,12472,12474,12477,12479,12481,12483,12485],{"class":3476,"line":148},[1115,12443,12444],{"class":3499},"        41.2",[1115,12446,1568],{"class":3483},[1115,12448,12351],{"class":3499},[1115,12450,1568],{"class":3483},[1115,12452,12418],{"class":3499},[1115,12454,1568],{"class":3483},[1115,12456,12457],{"class":3499}," 44.4",[1115,12459,1568],{"class":3483},[1115,12461,12462],{"class":3499}," 40.5",[1115,12464,1568],{"class":3483},[1115,12466,12467],{"class":3499}," 39.7",[1115,12469,1568],{"class":3483},[1115,12471,12408],{"class":3499},[1115,12473,1568],{"class":3483},[1115,12475,12476],{"class":3499}," 41",[1115,12478,1568],{"class":3483},[1115,12480,12351],{"class":3499},[1115,12482,1568],{"class":3483},[1115,12484,12428],{"class":3499},[1115,12486,3512],{"class":3483},[1115,12488,12489,12492,12494,12496,12498,12501,12503,12505,12507,12509,12511,12514,12516,12519,12521,12523,12525,12528,12530,12532],{"class":3476,"line":111},[1115,12490,12491],{"class":3499},"        43",[1115,12493,1568],{"class":3483},[1115,12495,12361],{"class":3499},[1115,12497,1568],{"class":3483},[1115,12499,12500],{"class":3499}," 42.9",[1115,12502,1568],{"class":3483},[1115,12504,12386],{"class":3499},[1115,12506,1568],{"class":3483},[1115,12508,12403],{"class":3499},[1115,12510,1568],{"class":3483},[1115,12512,12513],{"class":3499}," 42.2",[1115,12515,1568],{"class":3483},[1115,12517,12518],{"class":3499}," 39.2",[1115,12520,1568],{"class":3483},[1115,12522,12381],{"class":3499},[1115,12524,1568],{"class":3483},[1115,12526,12527],{"class":3499}," 41.6",[1115,12529,1568],{"class":3483},[1115,12531,12386],{"class":3499},[1115,12533,3512],{"class":3483},[1115,12535,12536,12539,12541,12543,12545,12548,12550,12552,12554,12557,12559,12562,12564,12567,12569,12571,12573,12576,12578,12580],{"class":3476,"line":96},[1115,12537,12538],{"class":3499},"        45",[1115,12540,1568],{"class":3483},[1115,12542,12366],{"class":3499},[1115,12544,1568],{"class":3483},[1115,12546,12547],{"class":3499}," 43.6",[1115,12549,1568],{"class":3483},[1115,12551,12371],{"class":3499},[1115,12553,1568],{"class":3483},[1115,12555,12556],{"class":3499}," 38.8",[1115,12558,1568],{"class":3483},[1115,12560,12561],{"class":3499}," 43",[1115,12563,1568],{"class":3483},[1115,12565,12566],{"class":3499}," 44.2",[1115,12568,1568],{"class":3483},[1115,12570,12561],{"class":3499},[1115,12572,1568],{"class":3483},[1115,12574,12575],{"class":3499}," 40",[1115,12577,1568],{"class":3483},[1115,12579,12457],{"class":3499},[1115,12581,3676],{"class":3491},[1115,12583,12584,12586,12588,12590],{"class":3476,"line":89},[1115,12585,11903],{"class":3487},[1115,12587,1647],{"class":3491},[1115,12589,12333],{"class":3479},[1115,12591,3676],{"class":3491},[1115,12593,12594,12596,12598,12600],{"class":3476,"line":82},[1115,12595,11914],{"class":3487},[1115,12597,1647],{"class":3491},[1115,12599,12333],{"class":3479},[1115,12601,3676],{"class":3491},[1115,12603,12604,12606,12608,12610],{"class":3476,"line":75},[1115,12605,11936],{"class":3487},[1115,12607,1647],{"class":3491},[1115,12609,12333],{"class":3479},[1115,12611,3676],{"class":3491},[1115,12613,12614,12616,12618,12620,12622,12624,12626,12628,12630],{"class":3476,"line":3666},[1115,12615,11495],{"class":3487},[1115,12617,1647],{"class":3491},[1115,12619,12333],{"class":3479},[1115,12621,4376],{"class":3491},[1115,12623,4413],{"class":3483},[1115,12625,11974],{"class":3487},[1115,12627,1647],{"class":3491},[1115,12629,12333],{"class":3479},[1115,12631,3676],{"class":3491},[1115,12633,12634,12637,12639,12641],{"class":3476,"line":72},[1115,12635,12636],{"class":3487},"median",[1115,12638,1647],{"class":3491},[1115,12640,12333],{"class":3479},[1115,12642,3676],{"class":3491},[3468,12644,12647],{"className":12645,"code":12646,"language":3698,"meta":1247},[3696],"[1] 50\n[1] 42.27\n[1] 1.48052\n[1] 6.2\n[1] 42.4\n",[3244,12648,12646],{"__ignoreMap":1247},[1110,12650,12651],{},"Průměrná doba opravy je 42,27 minuty se směrodatnou odchylkou 1,48 minuty a mediánem 42,4 minuty; průměr a medián téměř splývají, data jsou kolem středu rozložena souměrně.",[1136,12653,12655],{"id":12654},"empirická-distribuční-funkce","Empirická distribuční funkce",[1110,12657,12658,12659,12672,12673,1425,12676,12699,12700,12734],{},"Pro libovolný rozsah datového souboru, diskrétní i spojitou náhodnou veličinu ",[1115,12660,12662],{"className":12661},[1315],[1317,12663,12664],{"xmlns":1319},[1321,12665,12666,12670],{},[1324,12667,12668],{},[1330,12669,6507],{},[1338,12671,6507],{"encoding":1340},", lze sestrojit ",[1302,12674,12675],{},"empirickou distribuční funkci",[1115,12677,12679],{"className":12678},[1315],[1317,12680,12681],{"xmlns":1319},[1321,12682,12683,12697],{},[1324,12684,12685,12691,12693,12695],{},[1327,12686,12687,12689],{},[1330,12688,6490],{},[1330,12690,1458],{},[1460,12692,1647],{"stretchy":1646},[1330,12694,6495],{},[1460,12696,1658],{"stretchy":1646},[1338,12698,10959],{"encoding":1340},". Pro datový soubor ",[1115,12701,12703],{"className":12702},[1315],[1317,12704,12705],{"xmlns":1319},[1321,12706,12707,12731],{},[1324,12708,12709,12711,12717,12719,12721,12723,12729],{},[1460,12710,1647],{"stretchy":1646},[1327,12712,12713,12715],{},[1330,12714,6495],{},[1334,12716,1565],{},[1460,12718,1568],{"separator":1121},[1460,12720,1571],{},[1460,12722,1568],{"separator":1121},[1327,12724,12725,12727],{},[1330,12726,6495],{},[1330,12728,1458],{},[1460,12730,1658],{"stretchy":1646},[1338,12732,12733],{"encoding":1340},"(x_1,\\dots,x_n)"," je",[1115,12736,12738],{"className":12737},[1315],[1317,12739,12740],{"xmlns":1319,"display":1736},[1321,12741,12742,12766],{},[1324,12743,12744,12750,12752,12754,12756,12758,12764],{},[1327,12745,12746,12748],{},[1330,12747,6490],{},[1330,12749,1458],{},[1460,12751,1647],{"stretchy":1646},[1330,12753,6495],{},[1460,12755,1658],{"stretchy":1646},[1460,12757,1754],{},[2512,12759,12760,12762],{},[1330,12761,7035],{},[1330,12763,1458],{},[1460,12765,1568],{"separator":1121},[1338,12767,12768],{"encoding":1340},"F_n(x) = \\frac{k}{n},",[1110,12770,4282,12771,12784,12785,1440],{},[1115,12772,12774],{"className":12773},[1315],[1317,12775,12776],{"xmlns":1319},[1321,12777,12778,12782],{},[1324,12779,12780],{},[1330,12781,7035],{},[1338,12783,7035],{"encoding":1340}," je počet prvků datového souboru menších nebo rovných číslu ",[1115,12786,12788],{"className":12787},[1315],[1317,12789,12790],{"xmlns":1319},[1321,12791,12792,12796],{},[1324,12793,12794],{},[1330,12795,6495],{},[1338,12797,6495],{"encoding":1340},[1110,12799,8831],{},[3468,12801,12803],{"className":3470,"code":12802,"language":71,"meta":1247,"style":1247},"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",[3244,12804,12805,12820,12835,12853,12867],{"__ignoreMap":1247},[1115,12806,12807,12809,12811,12814,12816,12818],{"class":3476,"line":10},[1115,12808,6546],{"class":3479},[1115,12810,3484],{"class":3483},[1115,12812,12813],{"class":3487}," ecdf",[1115,12815,1647],{"class":3491},[1115,12817,6495],{"class":3479},[1115,12819,3676],{"class":3491},[1115,12821,12822,12825,12827,12829,12832],{"class":3476,"line":27},[1115,12823,12824],{"class":3487},"knots",[1115,12826,1647],{"class":3491},[1115,12828,6546],{"class":3479},[1115,12830,12831],{"class":3491},")        ",[1115,12833,12834],{"class":11809},"# vzestupně seřazené různé hodnoty datového souboru\n",[1115,12836,12837,12839,12841,12843,12845,12847,12850],{"class":3476,"line":148},[1115,12838,6546],{"class":3487},[1115,12840,1647],{"class":3491},[1115,12842,12824],{"class":3487},[1115,12844,1647],{"class":3491},[1115,12846,6546],{"class":3479},[1115,12848,12849],{"class":3491},"))      ",[1115,12851,12852],{"class":11809},"# hodnoty Fn(x) v těchto bodech\n",[1115,12854,12855,12857,12859,12861,12864],{"class":3476,"line":111},[1115,12856,6546],{"class":3487},[1115,12858,1647],{"class":3491},[1115,12860,3319],{"class":3499},[1115,12862,12863],{"class":3491},")            ",[1115,12865,12866],{"class":11809},"# Fn v libovolném bodě\n",[1115,12868,12869,12872,12874,12876],{"class":3476,"line":96},[1115,12870,12871],{"class":3487},"plot",[1115,12873,1647],{"class":3491},[1115,12875,6546],{"class":3479},[1115,12877,3676],{"class":3491},[3468,12879,12882],{"className":12880,"code":12881,"language":3698,"meta":1247},[3696],"[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",[3244,12883,12881],{"__ignoreMap":1247},[1110,12885,12886,12889,12890,12908,12909,12912,12913,12926,12927,1440],{},[3244,12887,12888],{},"knots()"," vrací jen různé hodnoty (opakující se hodnota 12,7 je ve výpočtu ",[1115,12891,12893],{"className":12892},[1315],[1317,12894,12895],{"xmlns":1319},[1321,12896,12897,12905],{},[1324,12898,12899],{},[1327,12900,12901,12903],{},[1330,12902,6490],{},[1330,12904,1458],{},[1338,12906,12907],{"encoding":1340},"F_n"," započtena třikrát, v seznamu uzlů je ale jen jednou); ",[3244,12910,12911],{},"plot(f)"," nakreslí schodovitý graf, který v každém uzlu skáče o ",[1115,12914,12916],{"className":12915},[1315],[1317,12917,12918],{"xmlns":1319},[1321,12919,12920,12924],{},[1324,12921,12922],{},[1330,12923,7035],{},[1338,12925,7035],{"encoding":1340},"-násobek ",[1115,12928,12930],{"className":12929},[1315],[1317,12931,12932],{"xmlns":1319},[1321,12933,12934,12942],{},[1324,12935,12936,12938,12940],{},[1334,12937,1565],{},[1330,12939,4379],{"mathvariant":1893},[1330,12941,1458],{},[1338,12943,12944],{"encoding":1340},"1\u002Fn",[1110,12946,12947],{},[4158,12948],{"alt":12949,"className":12950,"src":12951},"mask-ps-ecdf",[1130,4162],"\u002Fwiki-assets\u002Fmask-ps-ecdf.png",[1103,12953,12955,12962],{"className":12954,"dataCallout":3251},[1106,3250],[1110,12956,12958,12961],{"className":12957},[1113],[1115,12959],{"className":12960,"ariaHidden":1121},[1118,3258,1120],"Příklad: Empirická distribuční funkce",[1110,12963,12964],{},"Pro předchozí datový soubor (doba opravy součástky) určete empirickou distribuční funkci.",[1110,12966,12967,12968,1440],{},"Uspořádaný soubor je ",[1115,12969,12971],{"className":12970},[1315],[1317,12972,12973],{"xmlns":1319},[1321,12974,12975,13039],{},[1324,12976,12977,12980,12982,12984,12987,12989,12991,12994,12996,12998,13000,13002,13004,13006,13008,13010,13013,13015,13017,13020,13022,13024,13026,13028,13030,13032,13034,13036],{},[1334,12978,12979],{},"10,8",[1460,12981,6669],{"separator":1121},[2682,12983,11090],{},[1334,12985,12986],{},"11,1",[1460,12988,6669],{"separator":1121},[2682,12990,11090],{},[1334,12992,12993],{},"12,7",[1460,12995,6669],{"separator":1121},[2682,12997,11090],{},[1334,12999,12993],{},[1460,13001,6669],{"separator":1121},[2682,13003,11090],{},[1334,13005,12993],{},[1460,13007,6669],{"separator":1121},[2682,13009,11090],{},[1334,13011,13012],{},"13,2",[1460,13014,6669],{"separator":1121},[2682,13016,11090],{},[1334,13018,13019],{},"13,4",[1460,13021,6669],{"separator":1121},[2682,13023,11090],{},[1334,13025,12304],{},[1460,13027,6669],{"separator":1121},[2682,13029,11090],{},[1334,13031,12304],{},[1460,13033,6669],{"separator":1121},[2682,13035,11090],{},[1334,13037,13038],{},"14,7",[1338,13040,13041],{"encoding":1340},"10{,}8;\\ 11{,}1;\\ 12{,}7;\\ 12{,}7;\\ 12{,}7;\\ 13{,}2;\\ 13{,}4;\\ 14{,}4;\\ 14{,}4;\\ 14{,}7",[1141,13043,13044,13077],{},[1144,13045,13046],{},[1147,13047,13048,13063,13065,13067,13069,13071,13073,13075],{},[1150,13049,13050],{},[1115,13051,13053],{"className":13052},[1315],[1317,13054,13055],{"xmlns":1319},[1321,13056,13057,13061],{},[1324,13058,13059],{},[1330,13060,6495],{},[1338,13062,6495],{"encoding":1340},[1150,13064,12979],{},[1150,13066,12986],{},[1150,13068,12993],{},[1150,13070,13012],{},[1150,13072,13019],{},[1150,13074,12304],{},[1150,13076,13038],{},[1157,13078,13079,13111],{},[1147,13080,13081,13096,13098,13100,13102,13104,13107,13109],{},[1162,13082,13083],{},[1115,13084,13086],{"className":13085},[1315],[1317,13087,13088],{"xmlns":1319},[1321,13089,13090,13094],{},[1324,13091,13092],{},[1330,13093,7035],{},[1338,13095,7035],{"encoding":1340},[1162,13097,1565],{},[1162,13099,1360],{},[1162,13101,9703],{},[1162,13103,3739],{},[1162,13105,13106],{},"7",[1162,13108,3369],{},[1162,13110,8810],{},[1147,13112,13113,13138,13141,13144,13146,13149,13152,13155],{},[1162,13114,13115],{},[1115,13116,13118],{"className":13117},[1315],[1317,13119,13120],{"xmlns":1319},[1321,13121,13122,13136],{},[1324,13123,13124,13130,13132,13134],{},[1327,13125,13126,13128],{},[1330,13127,6490],{},[1330,13129,1458],{},[1460,13131,1647],{"stretchy":1646},[1330,13133,6495],{},[1460,13135,1658],{"stretchy":1646},[1338,13137,10959],{"encoding":1340},[1162,13139,13140],{},"0,1",[1162,13142,13143],{},"0,2",[1162,13145,8234],{},[1162,13147,13148],{},"0,6",[1162,13150,13151],{},"0,7",[1162,13153,13154],{},"0,9",[1162,13156,13157],{},"1,0",[1110,13159,13160,13161,13183,13184,13207],{},"Graf (levý panel výše) odpovídá tabulce: funkce je nulová pod 10,8, skáče o ",[1115,13162,13164],{"className":13163},[1315],[1317,13165,13166],{"xmlns":1319},[1321,13167,13168,13180],{},[1324,13169,13170,13172,13174,13176,13178],{},[1334,13171,1565],{},[1330,13173,4379],{"mathvariant":1893},[1330,13175,1458],{},[1460,13177,1754],{},[1334,13179,13140],{},[1338,13181,13182],{"encoding":1340},"1\u002Fn = 0{,}1"," v každé jednoduché hodnotě a o ",[1115,13185,13187],{"className":13186},[1315],[1317,13188,13189],{"xmlns":1319},[1321,13190,13191,13204],{},[1324,13192,13193,13195,13197,13199,13201],{},[1334,13194,3366],{},[1330,13196,4379],{"mathvariant":1893},[1330,13198,1458],{},[1460,13200,1754],{},[1334,13202,13203],{},"0,3",[1338,13205,13206],{"encoding":1340},"3\u002Fn = 0{,}3"," v bodě 12,7, kde se hodnota opakuje třikrát.",[1103,13209,13211,13218],{"className":13210,"dataCallout":3251},[1106,3250],[1110,13212,13214,13217],{"className":13213},[1113],[1115,13215],{"className":13216,"ariaHidden":1121},[1118,3258,1120],"Příklad: Odpad materiálu",[1110,13219,13220],{},"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.",[3468,13222,13224],{"className":3470,"code":13223,"language":71,"meta":1247,"style":1247},"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",[3244,13225,13226,13277,13287,13297,13307,13327,13337,13352,13362],{"__ignoreMap":1247},[1115,13227,13228,13231,13233,13235,13237,13239,13241,13243,13245,13247,13249,13251,13253,13255,13257,13259,13261,13263,13265,13267,13269,13271,13273,13275],{"class":3476,"line":10},[1115,13229,13230],{"class":3479},"x4",[1115,13232,3484],{"class":3483},[1115,13234,3610],{"class":3487},[1115,13236,1647],{"class":3491},[1115,13238,11762],{"class":3499},[1115,13240,1568],{"class":3483},[1115,13242,11767],{"class":3499},[1115,13244,1568],{"class":3483},[1115,13246,11772],{"class":3499},[1115,13248,1568],{"class":3483},[1115,13250,11777],{"class":3499},[1115,13252,1568],{"class":3483},[1115,13254,11772],{"class":3499},[1115,13256,1568],{"class":3483},[1115,13258,11772],{"class":3499},[1115,13260,1568],{"class":3483},[1115,13262,11790],{"class":3499},[1115,13264,1568],{"class":3483},[1115,13266,11795],{"class":3499},[1115,13268,1568],{"class":3483},[1115,13270,11767],{"class":3499},[1115,13272,1568],{"class":3483},[1115,13274,11767],{"class":3499},[1115,13276,3676],{"class":3491},[1115,13278,13279,13281,13283,13285],{"class":3476,"line":27},[1115,13280,11903],{"class":3487},[1115,13282,1647],{"class":3491},[1115,13284,13230],{"class":3479},[1115,13286,3676],{"class":3491},[1115,13288,13289,13291,13293,13295],{"class":3476,"line":148},[1115,13290,11914],{"class":3487},[1115,13292,1647],{"class":3491},[1115,13294,13230],{"class":3479},[1115,13296,3676],{"class":3491},[1115,13298,13299,13301,13303,13305],{"class":3476,"line":111},[1115,13300,11936],{"class":3487},[1115,13302,1647],{"class":3491},[1115,13304,13230],{"class":3479},[1115,13306,3676],{"class":3491},[1115,13308,13309,13311,13313,13315,13317,13319,13321,13323,13325],{"class":3476,"line":96},[1115,13310,11495],{"class":3487},[1115,13312,1647],{"class":3491},[1115,13314,13230],{"class":3479},[1115,13316,4376],{"class":3491},[1115,13318,4413],{"class":3483},[1115,13320,11974],{"class":3487},[1115,13322,1647],{"class":3491},[1115,13324,13230],{"class":3479},[1115,13326,3676],{"class":3491},[1115,13328,13329,13331,13333,13335],{"class":3476,"line":89},[1115,13330,12636],{"class":3487},[1115,13332,1647],{"class":3491},[1115,13334,13230],{"class":3479},[1115,13336,3676],{"class":3491},[1115,13338,13339,13342,13344,13346,13348,13350],{"class":3476,"line":82},[1115,13340,13341],{"class":3479},"f4",[1115,13343,3484],{"class":3483},[1115,13345,12813],{"class":3487},[1115,13347,1647],{"class":3491},[1115,13349,13230],{"class":3479},[1115,13351,3676],{"class":3491},[1115,13353,13354,13356,13358,13360],{"class":3476,"line":75},[1115,13355,12824],{"class":3487},[1115,13357,1647],{"class":3491},[1115,13359,13341],{"class":3479},[1115,13361,3676],{"class":3491},[1115,13363,13364,13366,13368,13370,13372,13374],{"class":3476,"line":3666},[1115,13365,13341],{"class":3487},[1115,13367,1647],{"class":3491},[1115,13369,12824],{"class":3487},[1115,13371,1647],{"class":3491},[1115,13373,13341],{"class":3479},[1115,13375,9270],{"class":3491},[3468,13377,13380],{"className":13378,"code":13379,"language":3698,"meta":1247},[3696],"[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",[3244,13381,13379],{"__ignoreMap":1247},[1110,13383,13384,13385,13408],{},"Průměrný odpad je 3,86 % se směrodatnou odchylkou 0,18 % a mediánem 3,85 %. Pravý panel obrázku výše ukazuje tvar ",[1115,13386,13388],{"className":13387},[1315],[1317,13389,13390],{"xmlns":1319},[1321,13391,13392,13406],{},[1324,13393,13394,13400,13402,13404],{},[1327,13395,13396,13398],{},[1330,13397,6490],{},[1330,13399,1458],{},[1460,13401,1647],{"stretchy":1646},[1330,13403,6495],{},[1460,13405,1658],{"stretchy":1646},[1338,13407,10959],{"encoding":1340},": hodnota 3,8 se v souboru opakuje třikrát, proto zde funkce skáče o 0,3 najednou, stejně jako hodnota 4,0.",[1136,13410,13412],{"id":13411},"třídění-datového-souboru-do-tříd","Třídění datového souboru do tříd",[1110,13414,13415,13416,13419,13420,13433,13434,13437],{},"Je-li rozsah datového souboru velký (řádově přes 30 až 50 pozorování), hodnoty se před dalším zpracováním ",[1302,13417,13418],{},"roztřídí",": variační rozpětí ",[1115,13421,13423],{"className":13422},[1315],[1317,13424,13425],{"xmlns":1319},[1321,13426,13427,13431],{},[1324,13428,13429],{},[1330,13430,10000],{},[1338,13432,10000],{"encoding":1340}," se rozdělí na určitý počet ",[1302,13435,13436],{},"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.",[1110,13439,13440],{},"Výsledkem je tabulka četností se sloupci:",[1204,13442,13443,13523,13544,13565],{},[1207,13444,13445,13463,13464,13477,13478,13522],{},[1115,13446,13448],{"className":13447},[1315],[1317,13449,13450],{"xmlns":1319},[1321,13451,13452,13460],{},[1324,13453,13454],{},[1327,13455,13456,13458],{},[1330,13457,10976],{},[1330,13459,1655],{},[1338,13461,13462],{"encoding":1340},"I_j"," — ",[1115,13465,13467],{"className":13466},[1315],[1317,13468,13469],{"xmlns":1319},[1321,13470,13471,13475],{},[1324,13472,13473],{},[1330,13474,1655],{},[1338,13476,1655],{"encoding":1340},"-tý interval (v této kapitole vždy zleva uzavřený a zprava otevřený, ",[1115,13479,13481],{"className":13480},[1315],[1317,13482,13483],{"xmlns":1319},[1321,13484,13485,13519],{},[1324,13486,13487,13493,13495,13497,13503,13505,13517],{},[1327,13488,13489,13491],{},[1330,13490,10976],{},[1330,13492,1655],{},[1460,13494,1754],{},[1460,13496,8202],{"stretchy":1646},[1327,13498,13499,13501],{},[1330,13500,3494],{},[1330,13502,1655],{},[1460,13504,6669],{"separator":1121},[1327,13506,13507,13509],{},[1330,13508,3494],{},[1324,13510,13511,13513,13515],{},[1330,13512,1655],{},[1460,13514,5252],{},[1334,13516,1565],{},[1460,13518,1658],{"stretchy":1646},[1338,13520,13521],{"encoding":1340},"I_j = \\langle c_j; c_{j+1})","),",[1207,13524,13525,13543],{},[1115,13526,13528],{"className":13527},[1315],[1317,13529,13530],{"xmlns":1319},[1321,13531,13532,13540],{},[1324,13533,13534],{},[1327,13535,13536,13538],{},[1330,13537,8702],{},[1330,13539,1655],{},[1338,13541,13542],{"encoding":1340},"Z_j"," — střed (reprezentant) intervalu,",[1207,13545,13546,13564],{},[1115,13547,13549],{"className":13548},[1315],[1317,13550,13551],{"xmlns":1319},[1321,13552,13553,13561],{},[1324,13554,13555],{},[1327,13556,13557,13559],{},[1330,13558,6546],{},[1330,13560,1655],{},[1338,13562,13563],{"encoding":1340},"f_j"," — četnost, počet hodnot v intervalu,",[1207,13566,13567,13597,13598,5516,13626,1440],{},[1115,13568,13570],{"className":13569},[1315],[1317,13571,13572],{"xmlns":1319},[1321,13573,13574,13594],{},[1324,13575,13576,13582,13584,13590,13592],{},[1327,13577,13578,13580],{},[1330,13579,1110],{},[1330,13581,1655],{},[1460,13583,1754],{},[1327,13585,13586,13588],{},[1330,13587,6546],{},[1330,13589,1655],{},[1330,13591,4379],{"mathvariant":1893},[1330,13593,1458],{},[1338,13595,13596],{"encoding":1340},"p_j = f_j\u002Fn"," — relativní četnost, přičemž ",[1115,13599,13601],{"className":13600},[1315],[1317,13602,13603],{"xmlns":1319},[1321,13604,13605,13623],{},[1324,13606,13607,13613,13619,13621],{},[1327,13608,13609,13611],{},[1460,13610,1760],{},[1330,13612,1655],{},[1327,13614,13615,13617],{},[1330,13616,6546],{},[1330,13618,1655],{},[1460,13620,1754],{},[1330,13622,1458],{},[1338,13624,13625],{"encoding":1340},"\\sum_j f_j = n",[1115,13627,13629],{"className":13628},[1315],[1317,13630,13631],{"xmlns":1319},[1321,13632,13633,13651],{},[1324,13634,13635,13641,13647,13649],{},[1327,13636,13637,13639],{},[1460,13638,1760],{},[1330,13640,1655],{},[1327,13642,13643,13645],{},[1330,13644,1110],{},[1330,13646,1655],{},[1460,13648,1754],{},[1334,13650,1565],{},[1338,13652,13653],{"encoding":1340},"\\sum_j p_j = 1",[1110,13655,13656,13657,13660,13661,13664,13665,13668,13669,13672,13673,4382,13676,13693,13694,13697,13698,4382,13701,1583,13718,13721],{},"V R se třídění provádí příkazem ",[3244,13658,13659],{},"hist()"," — buď necháme R zvolit třídy samo (",[3244,13662,13663],{},"hist(x)","), nebo zadáme hranice přímo (",[3244,13666,13667],{},"hist(x, br = seq(0, 550, by = 50))","). Uložením výsledku do proměnné (",[3244,13670,13671],{},"y \u003C- hist(...)",") získáme jednotlivé sloupce tabulky: ",[3244,13674,13675],{},"y$counts",[1115,13677,13679],{"className":13678},[1315],[1317,13680,13681],{"xmlns":1319},[1321,13682,13683,13691],{},[1324,13684,13685],{},[1327,13686,13687,13689],{},[1330,13688,6546],{},[1330,13690,1655],{},[1338,13692,13563],{"encoding":1340},"), ",[3244,13695,13696],{},"y$breaks"," (hranice tříd), ",[3244,13699,13700],{},"y$mids",[1115,13702,13704],{"className":13703},[1315],[1317,13705,13706],{"xmlns":1319},[1321,13707,13708,13716],{},[1324,13709,13710],{},[1327,13711,13712,13714],{},[1330,13713,8702],{},[1330,13715,1655],{},[1338,13717,13542],{"encoding":1340},[3244,13719,13720],{},"y$density"," (relativní četnosti na škále hustoty).",[1110,13723,13724,13725,13742,13743,13745,13746,13782,13783,13786,13787,1440],{},"Interval ",[1115,13726,13728],{"className":13727},[1315],[1317,13729,13730],{"xmlns":1319},[1321,13731,13732,13740],{},[1324,13733,13734],{},[1327,13735,13736,13738],{},[1330,13737,10976],{},[1330,13739,1655],{},[1338,13741,13462],{"encoding":1340}," je ve výchozím nastavení ",[3244,13744,13659],{}," zleva otevřený a zprava uzavřený, ",[1115,13747,13749],{"className":13748},[1315],[1317,13750,13751],{"xmlns":1319},[1321,13752,13753,13779],{},[1324,13754,13755,13757,13763,13765,13777],{},[1460,13756,1647],{"stretchy":1646},[1327,13758,13759,13761],{},[1330,13760,3494],{},[1330,13762,1655],{},[1460,13764,6669],{"separator":1121},[1327,13766,13767,13769],{},[1330,13768,3494],{},[1324,13770,13771,13773,13775],{},[1330,13772,1655],{},[1460,13774,5252],{},[1334,13776,1565],{},[1460,13778,7219],{"stretchy":1646},[1338,13780,13781],{"encoding":1340},"(c_j; c_{j+1}\\rangle"," — opačně, než jak třídy zapisujeme v této kapitole. Parametr ",[3244,13784,13785],{},"right = FALSE"," třídy obrátí na ",[1115,13788,13790],{"className":13789},[1315],[1317,13791,13792],{"xmlns":1319},[1321,13793,13794,13820],{},[1324,13795,13796,13798,13804,13806,13818],{},[1460,13797,8202],{"stretchy":1646},[1327,13799,13800,13802],{},[1330,13801,3494],{},[1330,13803,1655],{},[1460,13805,6669],{"separator":1121},[1327,13807,13808,13810],{},[1330,13809,3494],{},[1324,13811,13812,13814,13816],{},[1330,13813,1655],{},[1460,13815,5252],{},[1334,13817,1565],{},[1460,13819,1658],{"stretchy":1646},[1338,13821,13822],{"encoding":1340},"\\langle c_j; c_{j+1})",[1110,13824,13825],{},[4158,13826],{"alt":13827,"className":13828,"src":13829},"mask-ps-histogram-trideni",[1130,4162],"\u002Fwiki-assets\u002Fmask-ps-histogram-trideni.png",[1103,13831,13833,13840],{"className":13832,"dataCallout":3251},[1106,3250],[1110,13834,13836,13839],{"className":13835},[1113],[1115,13837],{"className":13838,"ariaHidden":1121},[1118,3258,1120],"Příklad: Třídění datového souboru",[1110,13841,13842],{},"Byly provedeny zkoušky životnosti nového výrobku. Datový soubor obsahuje 68 hodnot doby do poruchy (v minutách). Určete odhady charakteristik a zákona rozdělení.",[3468,13844,13846],{"className":3470,"code":13845,"language":71,"meta":1247,"style":1247},"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",[3244,13847,13848,13905,13956,14006,14057,14107,14155,14195,14205,14225,14289,14298,14328],{"__ignoreMap":1247},[1115,13849,13850,13853,13855,13857,13859,13862,13864,13867,13869,13872,13874,13877,13879,13881,13883,13885,13887,13889,13891,13894,13896,13898,13900,13903],{"class":3476,"line":10},[1115,13851,13852],{"class":3479},"x9",[1115,13854,3484],{"class":3483},[1115,13856,3610],{"class":3487},[1115,13858,1647],{"class":3491},[1115,13860,13861],{"class":3499},"101",[1115,13863,1568],{"class":3483},[1115,13865,13866],{"class":3499}," 338",[1115,13868,1568],{"class":3483},[1115,13870,13871],{"class":3499}," 150",[1115,13873,1568],{"class":3483},[1115,13875,13876],{"class":3499}," 47",[1115,13878,1568],{"class":3483},[1115,13880,9254],{"class":3499},[1115,13882,1568],{"class":3483},[1115,13884,3955],{"class":3499},[1115,13886,1568],{"class":3483},[1115,13888,3509],{"class":3499},[1115,13890,1568],{"class":3483},[1115,13892,13893],{"class":3499}," 392",[1115,13895,1568],{"class":3483},[1115,13897,9771],{"class":3499},[1115,13899,1568],{"class":3483},[1115,13901,13902],{"class":3499}," 73",[1115,13904,3512],{"class":3483},[1115,13906,13907,13910,13912,13915,13917,13920,13922,13925,13927,13929,13931,13934,13936,13939,13941,13944,13946,13949,13951,13954],{"class":3476,"line":27},[1115,13908,13909],{"class":3499},"        367",[1115,13911,1568],{"class":3483},[1115,13913,13914],{"class":3499}," 54",[1115,13916,1568],{"class":3483},[1115,13918,13919],{"class":3499}," 114",[1115,13921,1568],{"class":3483},[1115,13923,13924],{"class":3499}," 213",[1115,13926,1568],{"class":3483},[1115,13928,3527],{"class":3499},[1115,13930,1568],{"class":3483},[1115,13932,13933],{"class":3499}," 341",[1115,13935,1568],{"class":3483},[1115,13937,13938],{"class":3499}," 313",[1115,13940,1568],{"class":3483},[1115,13942,13943],{"class":3499}," 112",[1115,13945,1568],{"class":3483},[1115,13947,13948],{"class":3499}," 343",[1115,13950,1568],{"class":3483},[1115,13952,13953],{"class":3499}," 151",[1115,13955,3512],{"class":3483},[1115,13957,13958,13961,13963,13966,13968,13971,13973,13976,13978,13981,13983,13985,13987,13990,13992,13994,13996,13999,14001,14004],{"class":3476,"line":148},[1115,13959,13960],{"class":3499},"        9",[1115,13962,1568],{"class":3483},[1115,13964,13965],{"class":3499}," 160",[1115,13967,1568],{"class":3483},[1115,13969,13970],{"class":3499}," 18",[1115,13972,1568],{"class":3483},[1115,13974,13975],{"class":3499}," 113",[1115,13977,1568],{"class":3483},[1115,13979,13980],{"class":3499}," 77",[1115,13982,1568],{"class":3483},[1115,13984,3527],{"class":3499},[1115,13986,1568],{"class":3483},[1115,13988,13989],{"class":3499}," 159",[1115,13991,1568],{"class":3483},[1115,13993,3509],{"class":3499},[1115,13995,1568],{"class":3483},[1115,13997,13998],{"class":3499}," 119",[1115,14000,1568],{"class":3483},[1115,14002,14003],{"class":3499}," 130",[1115,14005,3512],{"class":3483},[1115,14007,14008,14011,14013,14016,14018,14021,14023,14025,14027,14030,14032,14035,14037,14040,14042,14045,14047,14050,14052,14055],{"class":3476,"line":111},[1115,14009,14010],{"class":3499},"        140",[1115,14012,1568],{"class":3483},[1115,14014,14015],{"class":3499}," 161",[1115,14017,1568],{"class":3483},[1115,14019,14020],{"class":3499}," 379",[1115,14022,1568],{"class":3483},[1115,14024,13914],{"class":3499},[1115,14026,1568],{"class":3483},[1115,14028,14029],{"class":3499}," 373",[1115,14031,1568],{"class":3483},[1115,14033,14034],{"class":3499}," 168",[1115,14036,1568],{"class":3483},[1115,14038,14039],{"class":3499}," 365",[1115,14041,1568],{"class":3483},[1115,14043,14044],{"class":3499}," 110",[1115,14046,1568],{"class":3483},[1115,14048,14049],{"class":3499}," 145",[1115,14051,1568],{"class":3483},[1115,14053,14054],{"class":3499}," 88",[1115,14056,3512],{"class":3483},[1115,14058,14059,14062,14064,14067,14069,14072,14074,14077,14079,14082,14084,14086,14088,14091,14093,14095,14097,14100,14102,14105],{"class":3476,"line":96},[1115,14060,14061],{"class":3499},"        74",[1115,14063,1568],{"class":3483},[1115,14065,14066],{"class":3499}," 46",[1115,14068,1568],{"class":3483},[1115,14070,14071],{"class":3499}," 246",[1115,14073,1568],{"class":3483},[1115,14075,14076],{"class":3499}," 259",[1115,14078,1568],{"class":3483},[1115,14080,14081],{"class":3499}," 19",[1115,14083,1568],{"class":3483},[1115,14085,13998],{"class":3499},[1115,14087,1568],{"class":3483},[1115,14089,14090],{"class":3499}," 48",[1115,14092,1568],{"class":3483},[1115,14094,10632],{"class":3499},[1115,14096,1568],{"class":3483},[1115,14098,14099],{"class":3499}," 163",[1115,14101,1568],{"class":3483},[1115,14103,14104],{"class":3499}," 179",[1115,14106,3512],{"class":3483},[1115,14108,14109,14112,14114,14116,14118,14121,14123,14126,14128,14131,14133,14135,14137,14139,14141,14143,14145,14148,14150,14153],{"class":3476,"line":89},[1115,14110,14111],{"class":3499},"        194",[1115,14113,1568],{"class":3483},[1115,14115,3920],{"class":3499},[1115,14117,1568],{"class":3483},[1115,14119,14120],{"class":3499}," 49",[1115,14122,1568],{"class":3483},[1115,14124,14125],{"class":3499}," 501",[1115,14127,1568],{"class":3483},[1115,14129,14130],{"class":3499}," 193",[1115,14132,1568],{"class":3483},[1115,14134,14081],{"class":3499},[1115,14136,1568],{"class":3483},[1115,14138,9771],{"class":3499},[1115,14140,1568],{"class":3483},[1115,14142,3955],{"class":3499},[1115,14144,1568],{"class":3483},[1115,14146,14147],{"class":3499}," 221",[1115,14149,1568],{"class":3483},[1115,14151,14152],{"class":3499}," 300",[1115,14154,3512],{"class":3483},[1115,14156,14157,14160,14162,14164,14166,14169,14171,14174,14176,14179,14181,14184,14186,14188,14190,14193],{"class":3476,"line":82},[1115,14158,14159],{"class":3499},"        88",[1115,14161,1568],{"class":3483},[1115,14163,3504],{"class":3499},[1115,14165,1568],{"class":3483},[1115,14167,14168],{"class":3499}," 428",[1115,14170,1568],{"class":3483},[1115,14172,14173],{"class":3499}," 249",[1115,14175,1568],{"class":3483},[1115,14177,14178],{"class":3499}," 25",[1115,14180,1568],{"class":3483},[1115,14182,14183],{"class":3499}," 209",[1115,14185,1568],{"class":3483},[1115,14187,13914],{"class":3499},[1115,14189,1568],{"class":3483},[1115,14191,14192],{"class":3499}," 91",[1115,14194,3676],{"class":3491},[1115,14196,14197,14199,14201,14203],{"class":3476,"line":75},[1115,14198,11903],{"class":3487},[1115,14200,1647],{"class":3491},[1115,14202,13852],{"class":3479},[1115,14204,3676],{"class":3491},[1115,14206,14207,14209,14211,14213,14215,14217,14219,14221,14223],{"class":3476,"line":3666},[1115,14208,11495],{"class":3487},[1115,14210,1647],{"class":3491},[1115,14212,13852],{"class":3479},[1115,14214,4376],{"class":3491},[1115,14216,4413],{"class":3483},[1115,14218,11974],{"class":3487},[1115,14220,1647],{"class":3491},[1115,14222,13852],{"class":3479},[1115,14224,3676],{"class":3491},[1115,14226,14227,14230,14232,14235,14237,14239,14241,14244,14246,14249,14251,14253,14255,14258,14260,14263,14265,14267,14269,14271,14274,14276,14278,14280,14283,14285,14287],{"class":3476,"line":72},[1115,14228,14229],{"class":3479},"y9",[1115,14231,3484],{"class":3483},[1115,14233,14234],{"class":3487}," hist",[1115,14236,1647],{"class":3491},[1115,14238,13852],{"class":3479},[1115,14240,1568],{"class":3483},[1115,14242,14243],{"class":3479}," br",[1115,14245,3572],{"class":3483},[1115,14247,14248],{"class":3487}," seq",[1115,14250,1647],{"class":3491},[1115,14252,1336],{"class":3499},[1115,14254,1568],{"class":3483},[1115,14256,14257],{"class":3499}," 550",[1115,14259,1568],{"class":3483},[1115,14261,14262],{"class":3479}," by",[1115,14264,3572],{"class":3483},[1115,14266,6020],{"class":3499},[1115,14268,1658],{"class":3491},[1115,14270,1568],{"class":3483},[1115,14272,14273],{"class":3479}," right",[1115,14275,3572],{"class":3483},[1115,14277,6113],{"class":3499},[1115,14279,1568],{"class":3483},[1115,14281,14282],{"class":3479}," plot",[1115,14284,3572],{"class":3483},[1115,14286,6113],{"class":3499},[1115,14288,3676],{"class":3491},[1115,14290,14291,14293,14295],{"class":3476,"line":25},[1115,14292,14229],{"class":3479},[1115,14294,3689],{"class":3483},[1115,14296,14297],{"class":3479},"counts\n",[1115,14299,14300,14302,14304,14306,14308,14311,14313,14316,14318,14320,14322,14324,14326],{"class":3476,"line":65},[1115,14301,9757],{"class":3487},[1115,14303,1647],{"class":3491},[1115,14305,14229],{"class":3479},[1115,14307,3689],{"class":3483},[1115,14309,14310],{"class":3479},"counts",[1115,14312,9852],{"class":3483},[1115,14314,14315],{"class":3487}," length",[1115,14317,1647],{"class":3491},[1115,14319,13852],{"class":3479},[1115,14321,1658],{"class":3491},[1115,14323,1568],{"class":3483},[1115,14325,10632],{"class":3499},[1115,14327,3676],{"class":3491},[1115,14329,14330,14332,14334,14336,14338,14340,14342,14344],{"class":3476,"line":63},[1115,14331,11914],{"class":3487},[1115,14333,1647],{"class":3491},[1115,14335,13852],{"class":3479},[1115,14337,11953],{"class":3491},[1115,14339,11936],{"class":3487},[1115,14341,1647],{"class":3491},[1115,14343,13852],{"class":3479},[1115,14345,3676],{"class":3491},[3468,14347,14350],{"className":14348,"code":14349,"language":3698,"meta":1247},[3696],"[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",[3244,14351,14349],{"__ignoreMap":1247},[1110,14353,14354,14355,14383],{},"Variační rozpětí je ",[1115,14356,14358],{"className":14357},[1315],[1317,14359,14360],{"xmlns":1319},[1321,14361,14362,14380],{},[1324,14363,14364,14366,14368,14371,14373,14375,14377],{},[1330,14365,10000],{},[1460,14367,1754],{},[1334,14369,14370],{},"501",[1460,14372,2838],{},[1334,14374,1360],{},[1460,14376,1754],{},[1334,14378,14379],{},"499",[1338,14381,14382],{"encoding":1340},"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:",[1141,14385,14386,14482],{},[1144,14387,14388],{},[1147,14389,14390,14405,14424,14443,14462],{},[1150,14391,14392],{},[1115,14393,14395],{"className":14394},[1315],[1317,14396,14397],{"xmlns":1319},[1321,14398,14399,14403],{},[1324,14400,14401],{},[1330,14402,1655],{},[1338,14404,1655],{"encoding":1340},[1150,14406,14407],{},[1115,14408,14410],{"className":14409},[1315],[1317,14411,14412],{"xmlns":1319},[1321,14413,14414,14422],{},[1324,14415,14416],{},[1327,14417,14418,14420],{},[1330,14419,10976],{},[1330,14421,1655],{},[1338,14423,13462],{"encoding":1340},[1150,14425,14426],{},[1115,14427,14429],{"className":14428},[1315],[1317,14430,14431],{"xmlns":1319},[1321,14432,14433,14441],{},[1324,14434,14435],{},[1327,14436,14437,14439],{},[1330,14438,8702],{},[1330,14440,1655],{},[1338,14442,13542],{"encoding":1340},[1150,14444,14445],{},[1115,14446,14448],{"className":14447},[1315],[1317,14449,14450],{"xmlns":1319},[1321,14451,14452,14460],{},[1324,14453,14454],{},[1327,14455,14456,14458],{},[1330,14457,6546],{},[1330,14459,1655],{},[1338,14461,13563],{"encoding":1340},[1150,14463,14464],{},[1115,14465,14467],{"className":14466},[1315],[1317,14468,14469],{"xmlns":1319},[1321,14470,14471,14479],{},[1324,14472,14473],{},[1327,14474,14475,14477],{},[1330,14476,1110],{},[1330,14478,1655],{},[1338,14480,14481],{"encoding":1340},"p_j",[1157,14483,14484,14499,14514,14529,14542,14557,14572,14586,14601,14615,14630],{},[1147,14485,14486,14488,14491,14493,14496],{},[1162,14487,1565],{},[1162,14489,14490],{},"⟨0; 50)",[1162,14492,3833],{},[1162,14494,14495],{},"19",[1162,14497,14498],{},"0,279",[1147,14500,14501,14503,14506,14509,14511],{},[1162,14502,1360],{},[1162,14504,14505],{},"⟨50; 100)",[1162,14507,14508],{},"75",[1162,14510,2027],{},[1162,14512,14513],{},"0,162",[1147,14515,14516,14518,14521,14524,14526],{},[1162,14517,3366],{},[1162,14519,14520],{},"⟨100; 150)",[1162,14522,14523],{},"125",[1162,14525,8810],{},[1162,14527,14528],{},"0,147",[1147,14530,14531,14533,14536,14538,14540],{},[1162,14532,3316],{},[1162,14534,14535],{},"⟨150; 200)",[1162,14537,7255],{},[1162,14539,8810],{},[1162,14541,14528],{},[1147,14543,14544,14546,14549,14552,14554],{},[1162,14545,9703],{},[1162,14547,14548],{},"⟨200; 250)",[1162,14550,14551],{},"225",[1162,14553,9703],{},[1162,14555,14556],{},"0,074",[1147,14558,14559,14561,14564,14567,14569],{},[1162,14560,3739],{},[1162,14562,14563],{},"⟨250; 300)",[1162,14565,14566],{},"275",[1162,14568,1565],{},[1162,14570,14571],{},"0,015",[1147,14573,14574,14576,14579,14582,14584],{},[1162,14575,13106],{},[1162,14577,14578],{},"⟨300; 350)",[1162,14580,14581],{},"325",[1162,14583,9703],{},[1162,14585,14556],{},[1147,14587,14588,14591,14594,14597,14599],{},[1162,14589,14590],{},"8",[1162,14592,14593],{},"⟨350; 400)",[1162,14595,14596],{},"375",[1162,14598,9703],{},[1162,14600,14556],{},[1147,14602,14603,14605,14608,14611,14613],{},[1162,14604,3369],{},[1162,14606,14607],{},"⟨400; 450)",[1162,14609,14610],{},"425",[1162,14612,1565],{},[1162,14614,14571],{},[1147,14616,14617,14619,14622,14625,14627],{},[1162,14618,8810],{},[1162,14620,14621],{},"⟨450; 500)",[1162,14623,14624],{},"475",[1162,14626,1336],{},[1162,14628,14629],{},"0,000",[1147,14631,14632,14634,14637,14640,14642],{},[1162,14633,2027],{},[1162,14635,14636],{},"⟨500; ∞)",[1162,14638,14639],{},"525",[1162,14641,1565],{},[1162,14643,14571],{},[1110,14645,14646,14647,14664,14665,14682,14683,2725,14706,2725,14734,14753,14754,2725,14777,14796],{},"Asi 27,9 % výrobků vydrželo méně než 50 minut, jen asi 1,5 % mezi 250 a 300 minutami. Charakteristiky spočtené ze středů tříd ",[1115,14648,14650],{"className":14649},[1315],[1317,14651,14652],{"xmlns":1319},[1321,14653,14654,14662],{},[1324,14655,14656],{},[1327,14657,14658,14660],{},[1330,14659,8702],{},[1330,14661,1655],{},[1338,14663,13542],{"encoding":1340}," (vážený průměr a rozptyl se střední hodnotou nahrazenou ",[1115,14666,14668],{"className":14667},[1315],[1317,14669,14670],{"xmlns":1319},[1321,14671,14672,14680],{},[1324,14673,14674],{},[1327,14675,14676,14678],{},[1330,14677,8702],{},[1330,14679,1655],{},[1338,14681,13542],{"encoding":1340},") vycházejí ",[1115,14684,14686],{"className":14685},[1315],[1317,14687,14688],{"xmlns":1319},[1321,14689,14690,14703],{},[1324,14691,14692,14698,14700],{},[2496,14693,14694,14696],{"accent":1121},[1330,14695,6495],{},[1460,14697,11235],{},[1460,14699,9217],{},[1334,14701,14702],{},"149,26",[1338,14704,14705],{"encoding":1340},"\\bar{x} \\approx 149{,}26",[1115,14707,14709],{"className":14708},[1315],[1317,14710,14711],{"xmlns":1319},[1321,14712,14713,14731],{},[1324,14714,14715,14721,14723,14726,14728],{},[1353,14716,14717,14719],{},[1330,14718,1626],{},[1334,14720,1360],{},[1460,14722,9217],{},[1334,14724,14725],{},"15",[2682,14727,2684],{},[1334,14729,14730],{},"484,5",[1338,14732,14733],{"encoding":1340},"s^2 \\approx 15\\,484{,}5",[1115,14735,14737],{"className":14736},[1315],[1317,14738,14739],{"xmlns":1319},[1321,14740,14741,14750],{},[1324,14742,14743,14745,14747],{},[1330,14744,1626],{},[1460,14746,9217],{},[1334,14748,14749],{},"124,44",[1338,14751,14752],{"encoding":1340},"s \\approx 124{,}44"," — blízko hodnotám ",[1115,14755,14757],{"className":14756},[1315],[1317,14758,14759],{"xmlns":1319},[1321,14760,14761,14774],{},[1324,14762,14763,14769,14771],{},[2496,14764,14765,14767],{"accent":1121},[1330,14766,6495],{},[1460,14768,11235],{},[1460,14770,1754],{},[1334,14772,14773],{},"145,44",[1338,14775,14776],{"encoding":1340},"\\bar{x}=145{,}44",[1115,14778,14780],{"className":14779},[1315],[1317,14781,14782],{"xmlns":1319},[1321,14783,14784,14793],{},[1324,14785,14786,14788,14790],{},[1330,14787,1626],{},[1460,14789,1754],{},[1334,14791,14792],{},"126,13",[1338,14794,14795],{"encoding":1340},"s=126{,}13"," spočteným přímo z nerozdělených dat; malý rozdíl vzniká tím, že třídění nahrazuje skutečné hodnoty středy tříd.",[1110,14798,14799,14800,14803,14804,14840,14841,14859,14860,14874,14875,14901,14902,14904,14905,4641],{},"Tvar histogramu — vysoká četnost u krátkých dob, rychlý pokles — odpovídá ",[1302,14801,14802],{},"exponenciálnímu rozdělení",", které se pro dobu do poruchy používá nejčastěji. Jeho hustota je ",[1115,14805,14807],{"className":14806},[1315],[1317,14808,14809],{"xmlns":1319},[1321,14810,14811,14837],{},[1324,14812,14813,14815,14817,14819,14821,14823,14825],{},[1330,14814,6546],{},[1460,14816,1647],{"stretchy":1646},[1330,14818,6495],{},[1460,14820,1658],{"stretchy":1646},[1460,14822,1754],{},[1330,14824,9489],{},[1353,14826,14827,14829],{},[1330,14828,8369],{},[1324,14830,14831,14833,14835],{},[1460,14832,2838],{},[1330,14834,9489],{},[1330,14836,6495],{},[1338,14838,14839],{"encoding":1340},"f(x) = \\lambda e^{-\\lambda x}"," pro ",[1115,14842,14844],{"className":14843},[1315],[1317,14845,14846],{"xmlns":1319},[1321,14847,14848,14856],{},[1324,14849,14850,14852,14854],{},[1330,14851,6495],{},[1460,14853,3125],{},[1334,14855,1336],{},[1338,14857,14858],{"encoding":1340},"x \\ge 0",", s parametrem ",[1115,14861,14863],{"className":14862},[1315],[1317,14864,14865],{"xmlns":1319},[1321,14866,14867,14871],{},[1324,14868,14869],{},[1330,14870,9489],{},[1338,14872,14873],{"encoding":1340},"\\lambda"," odhadnutým jako ",[1115,14876,14878],{"className":14877},[1315],[1317,14879,14880],{"xmlns":1319},[1321,14881,14882,14898],{},[1324,14883,14884,14886,14888,14890,14892],{},[1330,14885,9489],{},[1460,14887,1754],{},[1334,14889,1565],{},[1330,14891,4379],{"mathvariant":1893},[2496,14893,14894,14896],{"accent":1121},[1330,14895,6495],{},[1460,14897,11235],{},[1338,14899,14900],{"encoding":1340},"\\lambda = 1\u002F\\bar{x}"," (v R je ",[3244,14903,9656],{}," parametrem ",[3244,14906,14907],{},"dexp()",[3468,14909,14911],{"className":3470,"code":14910,"language":71,"meta":1247,"style":1247},"rate9 \u003C- 1 \u002F mean(x9)\nrate9\n",[3244,14912,14913,14932],{"__ignoreMap":1247},[1115,14914,14915,14918,14920,14922,14924,14926,14928,14930],{"class":3476,"line":10},[1115,14916,14917],{"class":3479},"rate9",[1115,14919,3484],{"class":3483},[1115,14921,4416],{"class":3499},[1115,14923,9852],{"class":3483},[1115,14925,9008],{"class":3487},[1115,14927,1647],{"class":3491},[1115,14929,13852],{"class":3479},[1115,14931,3676],{"class":3491},[1115,14933,14934],{"class":3476,"line":27},[1115,14935,14936],{"class":3479},"rate9\n",[3468,14938,14941],{"className":14939,"code":14940,"language":3698,"meta":1247},[3696],"[1] 0.006875632\n",[3244,14942,14940],{"__ignoreMap":1247},[1110,14944,14945],{},[4158,14946],{"alt":14947,"className":14948,"src":14949},"mask-ps-hustota-fit",[1130,4162],"\u002Fwiki-assets\u002Fmask-ps-hustota-fit.png",[1110,14951,14952,14953,1440],{},"Proložená křivka dobře sleduje tvar sloupců. Zda data odpovídají exponenciálnímu rozdělení formálně, posuzuje test dobré shody popsaný v ",[1127,14954,1195],{"className":14955,"dataFsResolvedFilePath":1193,"href":1194},[1130],[1103,14957,14959,14966],{"className":14958,"dataCallout":3251},[1106,3250],[1110,14960,14962,14965],{"className":14961},[1113],[1115,14963],{"className":14964,"ariaHidden":1121},[1118,3258,1120],"Příklad: Doba života výrobku",[1110,14967,14968],{},"Sledováním doby života výrobku bylo naměřeno 50 hodnot (v minutách). Určete empirické charakteristiky, roztřiďte datový soubor a nakreslete histogram četností.",[3468,14970,14972],{"className":3470,"code":14971,"language":71,"meta":1247,"style":1247},"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",[3244,14973,14974,15035,15086,15137,15188,15240,15250,15276,15296,15354,15363,15371],{"__ignoreMap":1247},[1115,14975,14976,14979,14981,14983,14985,14988,14990,14993,14995,14998,15000,15003,15005,15008,15010,15013,15015,15018,15020,15023,15025,15028,15030,15033],{"class":3476,"line":10},[1115,14977,14978],{"class":3479},"x5",[1115,14980,3484],{"class":3483},[1115,14982,3610],{"class":3487},[1115,14984,1647],{"class":3491},[1115,14986,14987],{"class":3499},"63",[1115,14989,1568],{"class":3483},[1115,14991,14992],{"class":3499}," 156",[1115,14994,1568],{"class":3483},[1115,14996,14997],{"class":3499}," 184",[1115,14999,1568],{"class":3483},[1115,15001,15002],{"class":3499}," 786",[1115,15004,1568],{"class":3483},[1115,15006,15007],{"class":3499}," 822",[1115,15009,1568],{"class":3483},[1115,15011,15012],{"class":3499}," 278",[1115,15014,1568],{"class":3483},[1115,15016,15017],{"class":3499}," 15",[1115,15019,1568],{"class":3483},[1115,15021,15022],{"class":3499}," 561",[1115,15024,1568],{"class":3483},[1115,15026,15027],{"class":3499}," 229",[1115,15029,1568],{"class":3483},[1115,15031,15032],{"class":3499}," 8",[1115,15034,3512],{"class":3483},[1115,15036,15037,15040,15042,15045,15047,15049,15051,15054,15056,15059,15061,15064,15066,15069,15071,15074,15076,15079,15081,15084],{"class":3476,"line":27},[1115,15038,15039],{"class":3499},"        4",[1115,15041,1568],{"class":3483},[1115,15043,15044],{"class":3499}," 35",[1115,15046,1568],{"class":3483},[1115,15048,13902],{"class":3499},[1115,15050,1568],{"class":3483},[1115,15052,15053],{"class":3499}," 203",[1115,15055,1568],{"class":3483},[1115,15057,15058],{"class":3499}," 178",[1115,15060,1568],{"class":3483},[1115,15062,15063],{"class":3499}," 323",[1115,15065,1568],{"class":3483},[1115,15067,15068],{"class":3499}," 275",[1115,15070,1568],{"class":3483},[1115,15072,15073],{"class":3499}," 176",[1115,15075,1568],{"class":3483},[1115,15077,15078],{"class":3499}," 427",[1115,15080,1568],{"class":3483},[1115,15082,15083],{"class":3499}," 196",[1115,15085,3512],{"class":3483},[1115,15087,15088,15091,15093,15096,15098,15101,15103,15106,15108,15111,15113,15116,15118,15121,15123,15125,15127,15130,15132,15135],{"class":3476,"line":148},[1115,15089,15090],{"class":3499},"        415",[1115,15092,1568],{"class":3483},[1115,15094,15095],{"class":3499}," 140",[1115,15097,1568],{"class":3483},[1115,15099,15100],{"class":3499}," 17",[1115,15102,1568],{"class":3483},[1115,15104,15105],{"class":3499}," 293",[1115,15107,1568],{"class":3483},[1115,15109,15110],{"class":3499}," 991",[1115,15112,1568],{"class":3483},[1115,15114,15115],{"class":3499}," 100",[1115,15117,1568],{"class":3483},[1115,15119,15120],{"class":3499}," 189",[1115,15122,1568],{"class":3483},[1115,15124,15073],{"class":3499},[1115,15126,1568],{"class":3483},[1115,15128,15129],{"class":3499}," 672",[1115,15131,1568],{"class":3483},[1115,15133,15134],{"class":3499}," 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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",[3244,15404,15402],{"__ignoreMap":1247},[1110,15406,15407],{},"Variační rozpětí 987 minut rozdělené do 7 tříd po 150 minutách dává podobný tvar jako u předchozího příkladu: 74 % výrobků vydrželo méně než 300 minut, ojedinělé hodnoty sahají až k 991 minutám. Průměr 246,4 minuty leží výrazně nad mediánem 181 minut — rozdělení je zešikmené k vyšším hodnotám stejně jako u doby do poruchy výše.",[1136,15409,6183],{"id":6182},[1204,15411,15412,15430,15531,15599],{},[1207,15413,15414,1425,15417,15420,15421,15424,15425,15427,15428,1440],{},[1302,15415,15416],{},"Výchozí typ kvantilu v R.",[3244,15418,15419],{},"quantile()"," bez argumentu ",[3244,15422,15423],{},"type"," používá jiný výpočetní vzorec (",[3244,15426,12067],{},") než ruční postup v této kapitole — u některých souborů se hodnoty liší. Pro shodu s ručním výpočtem zadávejte ",[3244,15429,12063],{},[1207,15431,15432,15437,15438,15440,15441,15476,15477,15512,15513,15530],{},[1302,15433,15434,15435,1440],{},"Výchozí ohraničení tříd v ",[3244,15436,13659],{}," Bez ",[3244,15439,13785],{}," jsou třídy zprava uzavřené, ",[1115,15442,15444],{"className":15443},[1315],[1317,15445,15446],{"xmlns":1319},[1321,15447,15448,15474],{},[1324,15449,15450,15452,15458,15460,15472],{},[1460,15451,1647],{"stretchy":1646},[1327,15453,15454,15456],{},[1330,15455,3494],{},[1330,15457,1655],{},[1460,15459,6669],{"separator":1121},[1327,15461,15462,15464],{},[1330,15463,3494],{},[1324,15465,15466,15468,15470],{},[1330,15467,1655],{},[1460,15469,5252],{},[1334,15471,1565],{},[1460,15473,7219],{"stretchy":1646},[1338,15475,13781],{"encoding":1340}," — opačně než konvence ",[1115,15478,15480],{"className":15479},[1315],[1317,15481,15482],{"xmlns":1319},[1321,15483,15484,15510],{},[1324,15485,15486,15488,15494,15496,15508],{},[1460,15487,8202],{"stretchy":1646},[1327,15489,15490,15492],{},[1330,15491,3494],{},[1330,15493,1655],{},[1460,15495,6669],{"separator":1121},[1327,15497,15498,15500],{},[1330,15499,3494],{},[1324,15501,15502,15504,15506],{},[1330,15503,1655],{},[1460,15505,5252],{},[1334,15507,1565],{},[1460,15509,1658],{"stretchy":1646},[1338,15511,13822],{"encoding":1340}," použitá v tabulkách výše. Hodnota ležící přesně na hranici pak spadne do jiné třídy a četnosti ",[1115,15514,15516],{"className":15515},[1315],[1317,15517,15518],{"xmlns":1319},[1321,15519,15520,15528],{},[1324,15521,15522],{},[1327,15523,15524,15526],{},[1330,15525,6546],{},[1330,15527,1655],{},[1338,15529,13563],{"encoding":1340}," vyjdou jinak.",[1207,15532,15533,1425,15536,15554,15555,15568,15569,8825,15582,1440],{},[1302,15534,15535],{},"Rozptyl vs. směrodatná odchylka.",[1115,15537,15539],{"className":15538},[1315],[1317,15540,15541],{"xmlns":1319},[1321,15542,15543,15551],{},[1324,15544,15545],{},[1353,15546,15547,15549],{},[1330,15548,1626],{},[1334,15550,1360],{},[1338,15552,15553],{"encoding":1340},"s^2"," se udává v jednotkách znaku na druhou, ",[1115,15556,15558],{"className":15557},[1315],[1317,15559,15560],{"xmlns":1319},[1321,15561,15562,15566],{},[1324,15563,15564],{},[1330,15565,1626],{},[1338,15567,1626],{"encoding":1340}," ve stejných jednotkách jako data — pro interpretaci (např. „kolísání kolem průměru\") patří vždy ",[1115,15570,15572],{"className":15571},[1315],[1317,15573,15574],{"xmlns":1319},[1321,15575,15576,15580],{},[1324,15577,15578],{},[1330,15579,1626],{},[1338,15581,1626],{"encoding":1340},[1115,15583,15585],{"className":15584},[1315],[1317,15586,15587],{"xmlns":1319},[1321,15588,15589,15597],{},[1324,15590,15591],{},[1353,15592,15593,15595],{},[1330,15594,1626],{},[1334,15596,1360],{},[1338,15598,15553],{"encoding":1340},[1207,15600,15601,15604],{},[1302,15602,15603],{},"Příliš mnoho nebo příliš málo tříd."," Málo tříd skryje tvar rozdělení, moc tříd rozmělní četnosti na jednotky a histogram je nečitelný; volí se kompromis, ne pevné pravidlo.",[1136,15606,1202],{"id":1201},[1204,15608,15609,15614,15619,15624,15629,15634,15639],{},[1207,15610,15611],{},[1127,15612,1133],{"className":15613,"dataFsResolvedFilePath":1131,"href":1132},[1130],[1207,15615,15616],{},[1127,15617,1169],{"className":15618,"dataFsResolvedFilePath":1167,"href":1168},[1130],[1207,15620,15621],{},[1127,15622,1195],{"className":15623,"dataFsResolvedFilePath":1193,"href":1194},[1130],[1207,15625,15626],{},[1127,15627,6399],{"className":15628,"dataFsResolvedFilePath":6397,"href":6398},[1130],[1207,15630,15631],{},[1127,15632,1277],{"className":15633,"dataFsResolvedFilePath":10868,"href":10869},[1130],[1207,15635,15636],{},[1127,15637,6407],{"className":15638,"dataFsResolvedFilePath":6405,"href":6406},[1130],[1207,15640,15641],{},[1127,15642,6413],{"className":15643,"dataFsResolvedFilePath":1232,"href":1233},[1130],[1136,15645,1237],{"id":934},[1110,15647,1240,15648,1245],{},[1242,15649,1244],{},[6421,15651,15652],{},"html pre.shiki code .sP4rz, 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příkladům\u002F9.txt","topics\u002Fpopisna-statistika",[23,67,886,624,732,71],"S7Mr0W_asypsa_HGrO-Qlzv4HzQm_pC2nyjSomTKbnk",{"id":15674,"title":6399,"body":15675,"course":23,"courses":1252,"created":1253,"description":1247,"extension":1254,"meta":20366,"navigation":1256,"path":20367,"seo":20368,"sources":20369,"stem":20372,"tags":20373,"type":6442,"updated":1253,"__hash__":20374},"topics\u002Ftopics\u002Fregresni-a-korelacni-analyza.md",{"type":1096,"value":15676,"toc":20339},[15677,15680,15908,15910,15978,15984,15987,16065,16076,16080,16299,16306,16366,16369,16376,16398,16402,16408,16470,16520,16525,16536,16648,16654,16784,16787,16825,16831,16950,16967,17094,17100,17144,17148,17161,17189,17195,17252,17279,17285,17341,17361,17367,17388,17395,17398,17637,17641,17753,18073,18130,18172,18179,18183,18189,18313,18319,18368,18372,18378,18439,18445,18484,18528,18534,18627,18631,18637,18679,18685,18745,18856,18962,18966,18971,19049,19084,19115,19175,19212,19219,19282,19285,19306,19312,19342,19385,19389,19406,19526,19530,19552,19556,19567,19668,19672,19744,19751,19754,19757,19768,19835,19838,19842,19866,19869,19872,20076,20085,20115,20117,20252,20265,20278,20291,20293,20330,20332,20336],[1099,15678,6399],{"id":15679},"regresní-a-korelační-analýza",[1103,15681,15683,15689],{"className":15682,"dataCallout":1287},[1106,1286],[1110,15684,15686,1295],{"className":15685},[1113],[1115,15687],{"className":15688,"ariaHidden":1121},[1118,1294,1120],[1204,15690,15691,15729,15776,15854,15869,15875],{},[1207,15692,15693,15696,15697,15710,15711,15724,15725,15728],{},[1302,15694,15695],{},"Regresní analýza"," zkoumá jednostrannou závislost vysvětlované proměnné ",[1115,15698,15700],{"className":15699},[1315],[1317,15701,15702],{"xmlns":1319},[1321,15703,15704,15708],{},[1324,15705,15706],{},[1330,15707,6905],{},[1338,15709,6905],{"encoding":1340}," na vysvětlujících proměnných ",[1115,15712,15714],{"className":15713},[1315],[1317,15715,15716],{"xmlns":1319},[1321,15717,15718,15722],{},[1324,15719,15720],{},[1330,15721,6495],{},[1338,15723,6495],{"encoding":1340}," (příčina → následek); ",[1302,15726,15727],{},"korelační analýza"," měří intenzitu (těsnost) vzájemné závislosti.",[1207,15730,15731,15732,15735,15736,1440],{},"Parametry regresní funkce se odhadují ",[1302,15733,15734],{},"metodou nejmenších čtverců"," — minimalizací součtu čtverců reziduí ",[1115,15737,15739],{"className":15738},[1315],[1317,15740,15741],{"xmlns":1319},[1321,15742,15743,15773],{},[1324,15744,15745,15747,15749,15755,15757,15767],{},[1460,15746,1760],{},[1460,15748,1647],{"stretchy":1646},[1327,15750,15751,15753],{},[1330,15752,6905],{},[1330,15754,1650],{},[1460,15756,2838],{},[1327,15758,15759,15765],{},[2496,15760,15761,15763],{"accent":1121},[1330,15762,6905],{},[1460,15764,2502],{},[1330,15766,1650],{},[1353,15768,15769,15771],{},[1460,15770,1658],{"stretchy":1646},[1334,15772,1360],{},[1338,15774,15775],{"encoding":1340},"\\sum(y_i-\\hat y_i)^2",[1207,15777,15778,15779,1425,15782,15800,15801,1425,15804,15828,15829,1425,15832,1440],{},"Kvalitu fitu měří ",[1302,15780,15781],{},"index determinace",[1115,15783,15785],{"className":15784},[1315],[1317,15786,15787],{"xmlns":1319},[1321,15788,15789,15797],{},[1324,15790,15791],{},[1353,15792,15793,15795],{},[1330,15794,10000],{},[1334,15796,1360],{},[1338,15798,15799],{"encoding":1340},"R^2","; obecnou těsnost závislosti ",[1302,15802,15803],{},"index korelace",[1115,15805,15807],{"className":15806},[1315],[1317,15808,15809],{"xmlns":1319},[1321,15810,15811,15825],{},[1324,15812,15813,15815,15817],{},[1330,15814,10976],{},[1460,15816,1754],{},[4228,15818,15819],{},[1353,15820,15821,15823],{},[1330,15822,10000],{},[1334,15824,1360],{},[1338,15826,15827],{"encoding":1340},"I=\\sqrt{R^2}",", který je pro regresní přímku roven ",[1302,15830,15831],{},"koeficientu korelace",[1115,15833,15835],{"className":15834},[1315],[1317,15836,15837],{"xmlns":1319},[1321,15838,15839,15851],{},[1324,15840,15841],{},[1327,15842,15843,15845],{},[1330,15844,71],{},[1324,15846,15847,15849],{},[1330,15848,6495],{},[1330,15850,6905],{},[1338,15852,15853],{"encoding":1340},"r_{xy}",[1207,15855,15856,15857,15860,15861,15864,15865,15868],{},"Když přímka nestačí, volí se ",[1302,15858,15859],{},"parabolická, polynomická, hyperbolická nebo logaritmická"," regrese (stále lineární v parametrech, odhad metodou nejmenších čtverců) nebo ",[1302,15862,15863],{},"exponenciální"," regrese (nelineární v parametrech, odhad přes ",[3244,15866,15867],{},"nls2",").",[1207,15870,15871,15874],{},[1302,15872,15873],{},"Vícenásobná regrese"," rozšiřuje model o více regresorů; vyžaduje výběr proměnných (ENTER\u002Fstepwise), ověření šesti předpokladů modelu a kontrolu multikolinearity přes VIF.",[1207,15876,15877,15878,2725,15881,2725,15884,2725,15887,2725,15890,2725,15893,2725,15896,2725,15899,2725,15902,2725,15905,1440],{},"V R: ",[3244,15879,15880],{},"lm()",[3244,15882,15883],{},"nls2()",[3244,15885,15886],{},"summary()",[3244,15888,15889],{},"confint()",[3244,15891,15892],{},"predict()",[3244,15894,15895],{},"step()",[3244,15897,15898],{},"car::vif()",[3244,15900,15901],{},"lmtest::dwtest()",[3244,15903,15904],{},"whitestrap::white_test()",[3244,15906,15907],{},"shapiro.test()",[1136,15909,11013],{"id":11012},[1110,15911,15912,15915,15916,5516,15929,15942,15943,15945,15946,15959,15960,15973,15974,15977],{},[1127,15913,1133],{"className":15914,"dataFsResolvedFilePath":1131,"href":1132},[1130]," pracuje se dvěma znaky ",[1115,15917,15919],{"className":15918},[1315],[1317,15920,15921],{"xmlns":1319},[1321,15922,15923,15927],{},[1324,15924,15925],{},[1330,15926,6495],{},[1338,15928,6495],{"encoding":1340},[1115,15930,15932],{"className":15931},[1315],[1317,15933,15934],{"xmlns":1319},[1321,15935,15936,15940],{},[1324,15937,15938],{},[1330,15939,6905],{},[1338,15941,6905],{"encoding":1340}," zjištěnými na stejných jednotkách. ",[1302,15944,15695],{}," se zabývá jednostrannými závislostmi, kdy proti sobě stojí vysvětlující (nezávisle) proměnná ",[1115,15947,15949],{"className":15948},[1315],[1317,15950,15951],{"xmlns":1319},[1321,15952,15953,15957],{},[1324,15954,15955],{},[1330,15956,6495],{},[1338,15958,6495],{"encoding":1340}," v úloze příčiny a vysvětlovaná (závisle) proměnná ",[1115,15961,15963],{"className":15962},[1315],[1317,15964,15965],{"xmlns":1319},[1321,15966,15967,15971],{},[1324,15968,15969],{},[1330,15970,6905],{},[1338,15972,6905],{"encoding":1340}," v úloze následku. ",[1302,15975,15976],{},"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.",[1110,15979,15980,15981,15868],{},"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 (",[1302,15982,15983],{},"regresní funkce",[1110,15985,15986],{},"Druh regresní analýzy určuje struktura datového souboru:",[1204,15988,15989,16026],{},[1207,15990,15991,15994,15995,16008,16009,16022,16023,1568],{},[1302,15992,15993],{},"dvourozměrný datový soubor"," (jedna ",[1115,15996,15998],{"className":15997},[1315],[1317,15999,16000],{"xmlns":1319},[1321,16001,16002,16006],{},[1324,16003,16004],{},[1330,16005,6495],{},[1338,16007,6495],{"encoding":1340},", jedna ",[1115,16010,16012],{"className":16011},[1315],[1317,16013,16014],{"xmlns":1319},[1321,16015,16016,16020],{},[1324,16017,16018],{},[1330,16019,6905],{},[1338,16021,6905],{"encoding":1340},") → ",[1302,16024,16025],{},"regresní analýza dvou proměnných",[1207,16027,16028,16031,16032,16022,16062,1440],{},[1302,16029,16030],{},"vícerozměrný datový soubor"," (více ",[1115,16033,16035],{"className":16034},[1315],[1317,16036,16037],{"xmlns":1319},[1321,16038,16039,16059],{},[1324,16040,16041,16047,16049,16051,16053],{},[1327,16042,16043,16045],{},[1330,16044,6495],{},[1334,16046,1565],{},[1460,16048,1568],{"separator":1121},[1460,16050,1571],{},[1460,16052,1568],{"separator":1121},[1327,16054,16055,16057],{},[1330,16056,6495],{},[1330,16058,1110],{},[1338,16060,16061],{"encoding":1340},"x_1,\\dots,x_p",[1302,16063,16064],{},"vícenásobná regresní analýza",[1110,16066,16067,16068,16071,16072,16075],{},"Volba konkrétní regresní funkce by měla vycházet jak z ",[1302,16069,16070],{},"ekonomické teorie"," (ta napovídá, zda závislost roste, nebo klesá, zda je přímková, nebo zakřivená), tak z ",[1302,16073,16074],{},"grafické a matematicko-statistické analýzy"," dat — oba přístupy je vhodné kombinovat.",[1136,16077,16079],{"id":16078},"metoda-nejmenších-čtverců","Metoda nejmenších čtverců",[1110,16081,16082,16083,1425,16086,16140,16141,16159,16160,1425,16163,16219,16220,16238,16239,16256,16257,16295,16296,1440],{},"Rozlišují se ",[1302,16084,16085],{},"teoretická regresní funkce",[1115,16087,16089],{"className":16088},[1315],[1317,16090,16091],{"xmlns":1319},[1321,16092,16093,16137],{},[1324,16094,16095,16098,16100,16102,16104,16106,16108,16115,16117,16123,16125,16127,16129,16135],{},[1330,16096,16097],{},"η",[1460,16099,1754],{},[1330,16101,6546],{},[1460,16103,1647],{"stretchy":1646},[1330,16105,6495],{},[1460,16107,6669],{"separator":1121},[1327,16109,16110,16113],{},[1330,16111,16112],{},"β",[1334,16114,1336],{},[1460,16116,1568],{"separator":1121},[1327,16118,16119,16121],{},[1330,16120,16112],{},[1334,16122,1565],{},[1460,16124,1568],{"separator":1121},[1460,16126,1571],{},[1460,16128,1568],{"separator":1121},[1327,16130,16131,16133],{},[1330,16132,16112],{},[1330,16134,1110],{},[1460,16136,1658],{"stretchy":1646},[1338,16138,16139],{"encoding":1340},"\\eta = f(x;\\beta_0,\\beta_1,\\dots,\\beta_p)"," — neznámá, populační, daná neznámými parametry ",[1115,16142,16144],{"className":16143},[1315],[1317,16145,16146],{"xmlns":1319},[1321,16147,16148,16156],{},[1324,16149,16150],{},[1327,16151,16152,16154],{},[1330,16153,16112],{},[1330,16155,1650],{},[1338,16157,16158],{"encoding":1340},"\\beta_i"," — a ",[1302,16161,16162],{},"empirická regresní funkce",[1115,16164,16166],{"className":16165},[1315],[1317,16167,16168],{"xmlns":1319},[1321,16169,16170,16216],{},[1324,16171,16172,16178,16180,16182,16184,16186,16188,16194,16196,16202,16204,16206,16208,16214],{},[2496,16173,16174,16176],{"accent":1121},[1330,16175,6905],{},[1460,16177,2502],{},[1460,16179,1754],{},[1330,16181,6546],{},[1460,16183,1647],{"stretchy":1646},[1330,16185,6495],{},[1460,16187,6669],{"separator":1121},[1327,16189,16190,16192],{},[1330,16191,11280],{},[1334,16193,1336],{},[1460,16195,1568],{"separator":1121},[1327,16197,16198,16200],{},[1330,16199,11280],{},[1334,16201,1565],{},[1460,16203,1568],{"separator":1121},[1460,16205,1571],{},[1460,16207,1568],{"separator":1121},[1327,16209,16210,16212],{},[1330,16211,11280],{},[1330,16213,1110],{},[1460,16215,1658],{"stretchy":1646},[1338,16217,16218],{"encoding":1340},"\\hat y = f(x; b_0,b_1,\\dots,b_p)",", jejíž odhadnuté parametry ",[1115,16221,16223],{"className":16222},[1315],[1317,16224,16225],{"xmlns":1319},[1321,16226,16227,16235],{},[1324,16228,16229],{},[1327,16230,16231,16233],{},[1330,16232,11280],{},[1330,16234,1650],{},[1338,16236,16237],{"encoding":1340},"b_i"," jsou odhadem ",[1115,16240,16242],{"className":16241},[1315],[1317,16243,16244],{"xmlns":1319},[1321,16245,16246,16254],{},[1324,16247,16248],{},[1327,16249,16250,16252],{},[1330,16251,16112],{},[1330,16253,1650],{},[1338,16255,16158],{"encoding":1340}," vypočteným z konkrétních dat. Odchylky skutečných hodnot od empirické funkce, ",[1115,16258,16260],{"className":16259},[1315],[1317,16261,16262],{"xmlns":1319},[1321,16263,16264,16292],{},[1324,16265,16266,16272,16274,16280,16282],{},[1327,16267,16268,16270],{},[1330,16269,8369],{},[1330,16271,1650],{},[1460,16273,1754],{},[1327,16275,16276,16278],{},[1330,16277,6905],{},[1330,16279,1650],{},[1460,16281,2838],{},[1327,16283,16284,16290],{},[2496,16285,16286,16288],{"accent":1121},[1330,16287,6905],{},[1460,16289,2502],{},[1330,16291,1650],{},[1338,16293,16294],{"encoding":1340},"e_i=y_i-\\hat y_i",", se nazývají ",[1302,16297,16298],{},"rezidua",[1110,16300,16301,16302,16305],{},"Nejpoužívanější metodou odhadu parametrů je ",[1302,16303,16304],{},"metoda nejmenších čtverců (OLS)",": hledají se takové parametry, pro které je součet čtverců reziduí minimální,",[1115,16307,16309],{"className":16308},[1315],[1317,16310,16311],{"xmlns":1319,"display":1736},[1321,16312,16313,16363],{},[1324,16314,16315,16329,16331,16337,16339,16349,16355,16357,16359,16361],{},[1756,16316,16317,16319,16327],{},[1460,16318,1760],{},[1324,16320,16321,16323,16325],{},[1330,16322,1650],{},[1460,16324,1754],{},[1334,16326,1565],{},[1330,16328,1458],{},[1460,16330,1647],{"stretchy":1646},[1327,16332,16333,16335],{},[1330,16334,6905],{},[1330,16336,1650],{},[1460,16338,2838],{},[1327,16340,16341,16347],{},[2496,16342,16343,16345],{"accent":1121},[1330,16344,6905],{},[1460,16346,2502],{},[1330,16348,1650],{},[1353,16350,16351,16353],{},[1460,16352,1658],{"stretchy":1646},[1334,16354,1360],{},[1460,16356,7383],{},[1330,16358,4263],{},[1460,16360,4266],{},[1330,16362,1440],{"mathvariant":1893},[1338,16364,16365],{"encoding":1340},"\\sum_{i=1}^n (y_i - \\hat y_i)^2 \\to \\min.",[1110,16367,16368],{},"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.",[1110,16370,16371],{},[4158,16372],{"alt":16373,"className":16374,"src":16375},"mask-ra-primka-rezidua",[1130,4162],"\u002Fwiki-assets\u002Fmask-ra-primka-rezidua.png",[1110,16377,16378,16379,16397],{},"Obrázek ukazuje přesně to, co metoda minimalizuje: délky červených úseček jsou rezidua ",[1115,16380,16382],{"className":16381},[1315],[1317,16383,16384],{"xmlns":1319},[1321,16385,16386,16394],{},[1324,16387,16388],{},[1327,16389,16390,16392],{},[1330,16391,8369],{},[1330,16393,1650],{},[1338,16395,16396],{"encoding":1340},"e_i",", metoda nejmenších čtverců volí přímku tak, aby součet jejich čtverců byl nejmenší možný.",[1136,16399,16401],{"id":16400},"regresní-přímka","Regresní přímka",[1110,16403,16404,16405,1730],{},"Nejjednodušší regresní funkcí je ",[1302,16406,16407],{},"regresní přímka",[1115,16409,16411],{"className":16410},[1315],[1317,16412,16413],{"xmlns":1319,"display":1736},[1321,16414,16415,16467],{},[1324,16416,16417,16419,16421,16427,16429,16435,16437,16439,16441,16447,16449,16455,16457,16463,16465],{},[1330,16418,16097],{},[1460,16420,1754],{},[1327,16422,16423,16425],{},[1330,16424,16112],{},[1334,16426,1336],{},[1460,16428,5252],{},[1327,16430,16431,16433],{},[1330,16432,16112],{},[1334,16434,1565],{},[1330,16436,6495],{},[1460,16438,1568],{"separator":1121},[1784,16440],{"width":1786},[2496,16442,16443,16445],{"accent":1121},[1330,16444,6905],{},[1460,16446,2502],{},[1460,16448,1754],{},[1327,16450,16451,16453],{},[1330,16452,11280],{},[1334,16454,1336],{},[1460,16456,5252],{},[1327,16458,16459,16461],{},[1330,16460,11280],{},[1334,16462,1565],{},[1330,16464,6495],{},[1330,16466,1440],{"mathvariant":1893},[1338,16468,16469],{"encoding":1340},"\\eta = \\beta_0 + \\beta_1 x, \\qquad \\hat y = b_0 + b_1 x.",[1110,16471,16472,16473,16491,16492,16505,16506,16519],{},"Koeficient ",[1115,16474,16476],{"className":16475},[1315],[1317,16477,16478],{"xmlns":1319},[1321,16479,16480,16488],{},[1324,16481,16482],{},[1327,16483,16484,16486],{},[1330,16485,11280],{},[1334,16487,1565],{},[1338,16489,16490],{"encoding":1340},"b_1"," udává změnu průměru ",[1115,16493,16495],{"className":16494},[1315],[1317,16496,16497],{"xmlns":1319},[1321,16498,16499,16503],{},[1324,16500,16501],{},[1330,16502,6905],{},[1338,16504,6905],{"encoding":1340}," při jednotkové změně ",[1115,16507,16509],{"className":16508},[1315],[1317,16510,16511],{"xmlns":1319},[1321,16512,16513,16517],{},[1324,16514,16515],{},[1330,16516,6495],{},[1338,16518,6495],{"encoding":1340},"; jeho znaménko určuje, zda je závislost přímá, nebo nepřímá.",[16521,16522,16524],"h3",{"id":16523},"v-r","V R",[1110,16526,16527,16528,16531,16532,16535],{},"Vstupní data se nahrají buď ze souboru (",[3244,16529,16530],{},"d \u003C- read.table(\"data.txt\")",", případně ",[3244,16533,16534],{},"d \u003C- read.table(file.choose())","), nebo zapíší přímo jako vektory. Na šesti domácnostech sledujeme počet členů domácnosti a jejich týdenní výdaje:",[3468,16537,16539],{"className":3470,"code":16538,"language":71,"meta":1247,"style":1247},"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",[3244,16540,16541,16576,16617,16638],{"__ignoreMap":1247},[1115,16542,16543,16546,16548,16550,16552,16554,16556,16558,16560,16562,16564,16566,16568,16570,16572,16574],{"class":3476,"line":10},[1115,16544,16545],{"class":3479},"pocet_clenu",[1115,16547,3484],{"class":3483},[1115,16549,3610],{"class":3487},[1115,16551,1647],{"class":3491},[1115,16553,1565],{"class":3499},[1115,16555,1568],{"class":3483},[1115,16557,3955],{"class":3499},[1115,16559,1568],{"class":3483},[1115,16561,10632],{"class":3499},[1115,16563,1568],{"class":3483},[1115,16565,3575],{"class":3499},[1115,16567,1568],{"class":3483},[1115,16569,9771],{"class":3499},[1115,16571,1568],{"class":3483},[1115,16573,12004],{"class":3499},[1115,16575,3676],{"class":3491},[1115,16577,16578,16581,16583,16585,16587,16590,16592,16595,16597,16600,16602,16605,16607,16610,16612,16615],{"class":3476,"line":27},[1115,16579,16580],{"class":3479},"tydenni_vydaje",[1115,16582,3484],{"class":3483},[1115,16584,3610],{"class":3487},[1115,16586,1647],{"class":3491},[1115,16588,16589],{"class":3499},"490",[1115,16591,1568],{"class":3483},[1115,16593,16594],{"class":3499}," 820",[1115,16596,1568],{"class":3483},[1115,16598,16599],{"class":3499}," 1230",[1115,16601,1568],{"class":3483},[1115,16603,16604],{"class":3499}," 1570",[1115,16606,1568],{"class":3483},[1115,16608,16609],{"class":3499}," 1950",[1115,16611,1568],{"class":3483},[1115,16613,16614],{"class":3499}," 2320",[1115,16616,3676],{"class":3491},[1115,16618,16619,16621,16623,16626,16628,16630,16633,16636],{"class":3476,"line":148},[1115,16620,786],{"class":3479},[1115,16622,3484],{"class":3483},[1115,16624,16625],{"class":3487}," lm",[1115,16627,1647],{"class":3491},[1115,16629,16580],{"class":3479},[1115,16631,16632],{"class":3483}," ~",[1115,16634,16635],{"class":3479}," pocet_clenu",[1115,16637,3676],{"class":3491},[1115,16639,16640,16642,16644,16646],{"class":3476,"line":111},[1115,16641,1271],{"class":3487},[1115,16643,1647],{"class":3491},[1115,16645,786],{"class":3479},[1115,16647,3676],{"class":3491},[3468,16649,16652],{"className":16650,"code":16651,"language":3698,"meta":1247},[3696],"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",[3244,16653,16651],{"__ignoreMap":1247},[1110,16655,16656,16657,16689,16690,16693,16694,16724,16725,16755,16756,16759,16760,16783],{},"Odhadnutý model je ",[1115,16658,16660],{"className":16659},[1315],[1317,16661,16662],{"xmlns":1319},[1321,16663,16664,16686],{},[1324,16665,16666,16672,16674,16677,16679,16682,16684],{},[2496,16667,16668,16670],{"accent":1121},[1330,16669,6905],{},[1460,16671,2502],{},[1460,16673,1754],{},[1334,16675,16676],{},"108,7",[1460,16678,5252],{},[1334,16680,16681],{},"368,0",[2682,16683,2684],{},[1330,16685,6495],{},[1338,16687,16688],{"encoding":1340},"\\hat y = 108{,}7 + 368{,}0\\,x",". Sloupec ",[3244,16691,16692],{},"Pr(>|t|)"," je p-hodnota t-testu ",[1115,16695,16697],{"className":16696},[1315],[1317,16698,16699],{"xmlns":1319},[1321,16700,16701,16721],{},[1324,16702,16703,16709,16711,16717,16719],{},[1327,16704,16705,16707],{},[1330,16706,1332],{},[1334,16708,1336],{},[1460,16710,1730],{},[1327,16712,16713,16715],{},[1330,16714,16112],{},[1330,16716,1650],{},[1460,16718,1754],{},[1334,16720,1336],{},[1338,16722,16723],{"encoding":1340},"H_0:\\beta_i=0"," proti ",[1115,16726,16728],{"className":16727},[1315],[1317,16729,16730],{"xmlns":1319},[1321,16731,16732,16752],{},[1324,16733,16734,16740,16742,16748,16750],{},[1327,16735,16736,16738],{},[1330,16737,1332],{},[1334,16739,1565],{},[1460,16741,1730],{},[1327,16743,16744,16746],{},[1330,16745,16112],{},[1330,16747,1650],{},[1460,16749,10733],{"mathvariant":1893},[1334,16751,1336],{},[1338,16753,16754],{"encoding":1340},"H_1:\\beta_i\\neq0"," pro každý parametr — obě p-hodnoty jsou hluboko pod 0,05, oba parametry jsou tedy statisticky významné. ",[3244,16757,16758],{},"Multiple R-squared"," je index determinace ",[1115,16761,16763],{"className":16762},[1315],[1317,16764,16765],{"xmlns":1319},[1321,16766,16767,16780],{},[1324,16768,16769,16775,16777],{},[1353,16770,16771,16773],{},[1330,16772,10000],{},[1334,16774,1360],{},[1460,16776,1754],{},[1334,16778,16779],{},"0,9995",[1338,16781,16782],{"encoding":1340},"R^2=0{,}9995",": model vysvětluje 99,95 % rozptylu výdajů.",[1110,16785,16786],{},"Pro doplňkový přehled slouží přímé přístupové funkce:",[3468,16788,16790],{"className":3470,"code":16789,"language":71,"meta":1247,"style":1247},"coef(model)\nfitted(model)\nresiduals(model)\n",[3244,16791,16792,16803,16814],{"__ignoreMap":1247},[1115,16793,16794,16797,16799,16801],{"class":3476,"line":10},[1115,16795,16796],{"class":3487},"coef",[1115,16798,1647],{"class":3491},[1115,16800,786],{"class":3479},[1115,16802,3676],{"class":3491},[1115,16804,16805,16808,16810,16812],{"class":3476,"line":27},[1115,16806,16807],{"class":3487},"fitted",[1115,16809,1647],{"class":3491},[1115,16811,786],{"class":3479},[1115,16813,3676],{"class":3491},[1115,16815,16816,16819,16821,16823],{"class":3476,"line":148},[1115,16817,16818],{"class":3487},"residuals",[1115,16820,1647],{"class":3491},[1115,16822,786],{"class":3479},[1115,16824,3676],{"class":3491},[3468,16826,16829],{"className":16827,"code":16828,"language":3698,"meta":1247},[3696],"(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",[3244,16830,16828],{"__ignoreMap":1247},[1110,16832,16833,16836,16837,2725,16863,16866,16867,16889,16890,2725,16908,16911,16912,16949],{},[3244,16834,16835],{},"coef()"," vrací odhadnuté parametry ",[1115,16838,16840],{"className":16839},[1315],[1317,16841,16842],{"xmlns":1319},[1321,16843,16844,16860],{},[1324,16845,16846,16852,16854],{},[1327,16847,16848,16850],{},[1330,16849,11280],{},[1334,16851,1336],{},[1460,16853,1568],{"separator":1121},[1327,16855,16856,16858],{},[1330,16857,11280],{},[1334,16859,1565],{},[1338,16861,16862],{"encoding":1340},"b_0,b_1",[3244,16864,16865],{},"fitted()"," predikce ",[1115,16868,16870],{"className":16869},[1315],[1317,16871,16872],{"xmlns":1319},[1321,16873,16874,16886],{},[1324,16875,16876],{},[1327,16877,16878,16884],{},[2496,16879,16880,16882],{"accent":1121},[1330,16881,6905],{},[1460,16883,2502],{},[1330,16885,1650],{},[1338,16887,16888],{"encoding":1340},"\\hat y_i"," pro pozorované ",[1115,16891,16893],{"className":16892},[1315],[1317,16894,16895],{"xmlns":1319},[1321,16896,16897,16905],{},[1324,16898,16899],{},[1327,16900,16901,16903],{},[1330,16902,6495],{},[1330,16904,1650],{},[1338,16906,16907],{"encoding":1340},"x_i",[3244,16909,16910],{},"residuals()"," rezidua ",[1115,16913,16915],{"className":16914},[1315],[1317,16916,16917],{"xmlns":1319},[1321,16918,16919,16947],{},[1324,16920,16921,16927,16929,16935,16937],{},[1327,16922,16923,16925],{},[1330,16924,8369],{},[1330,16926,1650],{},[1460,16928,1754],{},[1327,16930,16931,16933],{},[1330,16932,6905],{},[1330,16934,1650],{},[1460,16936,2838],{},[1327,16938,16939,16945],{},[2496,16940,16941,16943],{"accent":1121},[1330,16942,6905],{},[1460,16944,2502],{},[1330,16946,1650],{},[1338,16948,16294],{"encoding":1340}," — stejná čísla, která na obrázku výše tvoří délky červených úseček.",[1110,16951,16952,16953,16966],{},"Intervaly spolehlivosti pro parametry a pro predikci v nových bodech ",[1115,16954,16956],{"className":16955},[1315],[1317,16957,16958],{"xmlns":1319},[1321,16959,16960,16964],{},[1324,16961,16962],{},[1330,16963,6495],{},[1338,16965,6495],{"encoding":1340}," (zde 7 a 8 členů domácnosti):",[3468,16968,16970],{"className":3470,"code":16969,"language":71,"meta":1247,"style":1247},"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",[3244,16971,16972,16992,17020,17059],{"__ignoreMap":1247},[1115,16973,16974,16977,16979,16981,16983,16986,16988,16990],{"class":3476,"line":10},[1115,16975,16976],{"class":3487},"confint",[1115,16978,1647],{"class":3491},[1115,16980,786],{"class":3479},[1115,16982,1568],{"class":3483},[1115,16984,16985],{"class":3479}," level",[1115,16987,3572],{"class":3483},[1115,16989,9776],{"class":3499},[1115,16991,3676],{"class":3491},[1115,16993,16994,16997,16999,17002,17004,17006,17008,17010,17012,17014,17016,17018],{"class":3476,"line":27},[1115,16995,16996],{"class":3479},"nove",[1115,16998,3484],{"class":3483},[1115,17000,17001],{"class":3487}," data.frame",[1115,17003,1647],{"class":3491},[1115,17005,16545],{"class":3479},[1115,17007,3572],{"class":3483},[1115,17009,3610],{"class":3487},[1115,17011,1647],{"class":3491},[1115,17013,13106],{"class":3499},[1115,17015,1568],{"class":3483},[1115,17017,15032],{"class":3499},[1115,17019,9270],{"class":3491},[1115,17021,17022,17025,17027,17029,17031,17034,17036,17039,17041,17044,17046,17049,17051,17053,17055,17057],{"class":3476,"line":148},[1115,17023,17024],{"class":3487},"predict",[1115,17026,1647],{"class":3491},[1115,17028,786],{"class":3479},[1115,17030,1568],{"class":3483},[1115,17032,17033],{"class":3479}," newdata",[1115,17035,3572],{"class":3483},[1115,17037,17038],{"class":3479}," nove",[1115,17040,1568],{"class":3483},[1115,17042,17043],{"class":3479}," interval",[1115,17045,3572],{"class":3483},[1115,17047,17048],{"class":3615}," \"confidence\"",[1115,17050,1568],{"class":3483},[1115,17052,16985],{"class":3479},[1115,17054,3572],{"class":3483},[1115,17056,9776],{"class":3499},[1115,17058,3676],{"class":3491},[1115,17060,17061,17063,17065,17067,17069,17071,17073,17075,17077,17079,17081,17084,17086,17088,17090,17092],{"class":3476,"line":111},[1115,17062,17024],{"class":3487},[1115,17064,1647],{"class":3491},[1115,17066,786],{"class":3479},[1115,17068,1568],{"class":3483},[1115,17070,17033],{"class":3479},[1115,17072,3572],{"class":3483},[1115,17074,17038],{"class":3479},[1115,17076,1568],{"class":3483},[1115,17078,17043],{"class":3479},[1115,17080,3572],{"class":3483},[1115,17082,17083],{"class":3615}," \"prediction\"",[1115,17085,1568],{"class":3483},[1115,17087,16985],{"class":3479},[1115,17089,3572],{"class":3483},[1115,17091,9776],{"class":3499},[1115,17093,3676],{"class":3491},[3468,17095,17098],{"className":17096,"code":17097,"language":3698,"meta":1247},[3696],"                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",[3244,17099,17097],{"__ignoreMap":1247},[1110,17101,17102,17105,17106,1425,17109,17122,17123,2725,17136,17139,17140,17143],{},[3244,17103,17104],{},"interval = \"confidence\""," dává interval spolehlivosti pro ",[1302,17107,17108],{},"střední hodnotu",[1115,17110,17112],{"className":17111},[1315],[1317,17113,17114],{"xmlns":1319},[1321,17115,17116,17120],{},[1324,17117,17118],{},[1330,17119,6905],{},[1338,17121,6905],{"encoding":1340}," při daném ",[1115,17124,17126],{"className":17125},[1315],[1317,17127,17128],{"xmlns":1319},[1321,17129,17130,17134],{},[1324,17131,17132],{},[1330,17133,6495],{},[1338,17135,6495],{"encoding":1340},[3244,17137,17138],{},"interval = \"prediction\""," širší interval pro ",[1302,17141,17142],{},"jednotlivé budoucí pozorování"," — ten musí zahrnout i rozptyl kolem regresní přímky, proto je vždy širší.",[16521,17145,17147],{"id":17146},"diagnostika-modelu","Diagnostika modelu",[1110,17149,17150,17151,2725,17154,5516,17157,17160],{},"Platnost závěrů z regresní přímky stojí na předpokladech o reziduích: ",[1302,17152,17153],{},"absenci autokorelace",[1302,17155,17156],{},"stálosti rozptylu (homoskedasticitě)",[1302,17158,17159],{},"normalitě",". V R se ověřují takto:",[3468,17162,17164],{"className":3470,"code":17163,"language":71,"meta":1247,"style":1247},"library(lmtest)\ndwtest(model)\n",[3244,17165,17166,17178],{"__ignoreMap":1247},[1115,17167,17168,17171,17173,17176],{"class":3476,"line":10},[1115,17169,17170],{"class":3483},"library",[1115,17172,1647],{"class":3491},[1115,17174,17175],{"class":3479},"lmtest",[1115,17177,3676],{"class":3491},[1115,17179,17180,17183,17185,17187],{"class":3476,"line":27},[1115,17181,17182],{"class":3487},"dwtest",[1115,17184,1647],{"class":3491},[1115,17186,786],{"class":3479},[1115,17188,3676],{"class":3491},[3468,17190,17193],{"className":17191,"code":17192,"language":3698,"meta":1247},[3696],"    Durbin-Watson test\n\ndata:  model\nDW = 3.4121, p-value = 0.9555\nalternative hypothesis: true autocorrelation is greater than 0\n",[3244,17194,17192],{"__ignoreMap":1247},[1110,17196,17197,17198,17215,17216,17233,17234,17251],{},"Durbinův–Watsonův test má ",[1115,17199,17201],{"className":17200},[1315],[1317,17202,17203],{"xmlns":1319},[1321,17204,17205,17213],{},[1324,17206,17207],{},[1327,17208,17209,17211],{},[1330,17210,1332],{},[1334,17212,1336],{},[1338,17214,1341],{"encoding":1340},": v modelu není problém s autokorelací, proti ",[1115,17217,17219],{"className":17218},[1315],[1317,17220,17221],{"xmlns":1319},[1321,17222,17223,17231],{},[1324,17224,17225],{},[1327,17226,17227,17229],{},[1330,17228,1332],{},[1334,17230,1565],{},[1338,17232,2770],{"encoding":1340},": 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, ",[1115,17235,17237],{"className":17236},[1315],[1317,17238,17239],{"xmlns":1319},[1321,17240,17241,17249],{},[1324,17242,17243],{},[1327,17244,17245,17247],{},[1330,17246,1332],{},[1334,17248,1336],{},[1338,17250,1341],{"encoding":1340}," se nezamítá.",[3468,17253,17255],{"className":3470,"code":17254,"language":71,"meta":1247,"style":1247},"library(whitestrap)\nwhite_test(model)\n",[3244,17256,17257,17268],{"__ignoreMap":1247},[1115,17258,17259,17261,17263,17266],{"class":3476,"line":10},[1115,17260,17170],{"class":3483},[1115,17262,1647],{"class":3491},[1115,17264,17265],{"class":3479},"whitestrap",[1115,17267,3676],{"class":3491},[1115,17269,17270,17273,17275,17277],{"class":3476,"line":27},[1115,17271,17272],{"class":3487},"white_test",[1115,17274,1647],{"class":3491},[1115,17276,786],{"class":3479},[1115,17278,3676],{"class":3491},[3468,17280,17283],{"className":17281,"code":17282,"language":3698,"meta":1247},[3696],"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",[3244,17284,17282],{"__ignoreMap":1247},[1110,17286,17287,17288,17305,17306,17323,17324,17251],{},"Whiteův test má ",[1115,17289,17291],{"className":17290},[1315],[1317,17292,17293],{"xmlns":1319},[1321,17294,17295,17303],{},[1324,17296,17297],{},[1327,17298,17299,17301],{},[1330,17300,1332],{},[1334,17302,1336],{},[1338,17304,1341],{"encoding":1340},": rozptyl reziduí je stálý (homoskedasticita), proti ",[1115,17307,17309],{"className":17308},[1315],[1317,17310,17311],{"xmlns":1319},[1321,17312,17313,17321],{},[1324,17314,17315],{},[1327,17316,17317,17319],{},[1330,17318,1332],{},[1334,17320,1565],{},[1338,17322,2770],{"encoding":1340},": rozptyl není stálý (heteroskedasticita). P-hodnota 0,21 je nad 0,05, ",[1115,17325,17327],{"className":17326},[1315],[1317,17328,17329],{"xmlns":1319},[1321,17330,17331,17339],{},[1324,17332,17333],{},[1327,17334,17335,17337],{},[1330,17336,1332],{},[1334,17338,1336],{},[1338,17340,1341],{"encoding":1340},[3468,17342,17344],{"className":3470,"code":17343,"language":71,"meta":1247,"style":1247},"shapiro.test(residuals(model))\n",[3244,17345,17346],{"__ignoreMap":1247},[1115,17347,17348,17351,17353,17355,17357,17359],{"class":3476,"line":10},[1115,17349,17350],{"class":3487},"shapiro.test",[1115,17352,1647],{"class":3491},[1115,17354,16818],{"class":3487},[1115,17356,1647],{"class":3491},[1115,17358,786],{"class":3479},[1115,17360,9270],{"class":3491},[3468,17362,17365],{"className":17363,"code":17364,"language":3698,"meta":1247},[3696],"    Shapiro-Wilk normality test\n\ndata:  residuals(model)\nW = 0.94818, p-value = 0.7255\n",[3244,17366,17364],{"__ignoreMap":1247},[1110,17368,17369,17370,17387],{},"Shapiro–Wilkův test má ",[1115,17371,17373],{"className":17372},[1315],[1317,17374,17375],{"xmlns":1319},[1321,17376,17377,17385],{},[1324,17378,17379],{},[1327,17380,17381,17383],{},[1330,17382,1332],{},[1334,17384,1336],{},[1338,17386,1341],{"encoding":1340},": rezidua pocházejí z normálního rozdělení. P-hodnota 0,73 opět nevede k zamítnutí — všechny tři předpoklady model splňuje.",[1110,17389,17390],{},[4158,17391],{"alt":17392,"className":17393,"src":17394},"mask-ra-diagnostika-rezidui",[1130,4162],"\u002Fwiki-assets\u002Fmask-ra-diagnostika-rezidui.png",[1110,17396,17397],{},"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.",[1103,17399,17401,17408,17439,17474,17539],{"className":17400,"dataCallout":3251},[1106,3250],[1110,17402,17404,17407],{"className":17403},[1113],[1115,17405],{"className":17406,"ariaHidden":1121},[1118,3258,1120],"Příklad: Regresní přímka",[1110,17409,17410,17411,17424,17425,17438],{},"V souboru s údaji o hodnotě produkce (v milionech Kč, proměnná ",[1115,17412,17414],{"className":17413},[1315],[1317,17415,17416],{"xmlns":1319},[1321,17417,17418,17422],{},[1324,17419,17420],{},[1330,17421,6905],{},[1338,17423,6905],{"encoding":1340},") a výši investic (ve stovkách tisíc Kč, proměnná ",[1115,17426,17428],{"className":17427},[1315],[1317,17429,17430],{"xmlns":1319},[1321,17431,17432,17436],{},[1324,17433,17434],{},[1330,17435,6495],{},[1338,17437,6495],{"encoding":1340},") 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.",[1110,17440,17441,17442,1440],{},"Výsledek: ",[1115,17443,17445],{"className":17444},[1315],[1317,17446,17447],{"xmlns":1319},[1321,17448,17449,17471],{},[1324,17450,17451,17457,17459,17462,17464,17467,17469],{},[2496,17452,17453,17455],{"accent":1121},[1330,17454,6905],{},[1460,17456,2502],{},[1460,17458,1754],{},[1334,17460,17461],{},"32,74",[1460,17463,5252],{},[1334,17465,17466],{},"2,15",[2682,17468,2684],{},[1330,17470,6495],{},[1338,17472,17473],{"encoding":1340},"\\hat y = 32{,}74 + 2{,}15\\,x",[1110,17475,16472,17476,17498,17499,17538],{},[1115,17477,17479],{"className":17478},[1315],[1317,17480,17481],{"xmlns":1319},[1321,17482,17483,17495],{},[1324,17484,17485,17491,17493],{},[1327,17486,17487,17489],{},[1330,17488,11280],{},[1334,17490,1565],{},[1460,17492,1754],{},[1334,17494,17466],{},[1338,17496,17497],{"encoding":1340},"b_1=2{,}15"," říká, že se zvýšením investic o 100 000 Kč vzroste produkce v průměru o ",[1115,17500,17502],{"className":17501},[1315],[1317,17503,17504],{"xmlns":1319},[1321,17505,17506,17535],{},[1324,17507,17508,17510,17512,17514,17516,17518,17520,17522,17524,17526,17528,17531,17533],{},[1334,17509,17466],{},[1460,17511,7887],{},[1334,17513,1565],{},[2682,17515,2684],{},[1334,17517,11098],{},[2682,17519,2684],{},[1334,17521,11098],{},[1460,17523,1754],{},[1334,17525,1360],{},[2682,17527,2684],{},[1334,17529,17530],{},"150",[2682,17532,2684],{},[1334,17534,11098],{},[1338,17536,17537],{"encoding":1340},"2{,}15\\cdot 1\\,000\\,000=2\\,150\\,000"," Kč.",[1110,17540,17541,17542,3763,17561,17609,17610,15868],{},"Dosazením libovolné hodnoty investic do empirické regresní funkce dostaneme predikci produkce, například pro třináctou firmu s investicemi ",[1115,17543,17545],{"className":17544},[1315],[1317,17546,17547],{"xmlns":1319},[1321,17548,17549,17558],{},[1324,17550,17551,17553,17555],{},[1330,17552,6495],{},[1460,17554,1754],{},[1334,17556,17557],{},"34",[1338,17559,17560],{"encoding":1340},"x=34",[1115,17562,17564],{"className":17563},[1315],[1317,17565,17566],{"xmlns":1319},[1321,17567,17568,17606],{},[1324,17569,17570,17580,17582,17588,17590,17596,17598,17600,17603],{},[1327,17571,17572,17578],{},[2496,17573,17574,17576],{"accent":1121},[1330,17575,6905],{},[1460,17577,2502],{},[1334,17579,3319],{},[1460,17581,1754],{},[1327,17583,17584,17586],{},[1330,17585,11280],{},[1334,17587,1336],{},[1460,17589,5252],{},[1327,17591,17592,17594],{},[1330,17593,11280],{},[1334,17595,1565],{},[1460,17597,7887],{},[1334,17599,17557],{},[1460,17601,17602],{},"≐",[1334,17604,17605],{},"105,81",[1338,17607,17608],{"encoding":1340},"\\hat y_{13} = b_0 + b_1\\cdot 34 \\doteq 105{,}81"," milionu Kč (se zaokrouhlenými koeficienty ",[1115,17611,17613],{"className":17612},[1315],[1317,17614,17615],{"xmlns":1319},[1321,17616,17617,17634],{},[1324,17618,17619,17621,17623,17625,17627,17629,17631],{},[1334,17620,17461],{},[1460,17622,5252],{},[1334,17624,17466],{},[1460,17626,7887],{},[1334,17628,17557],{},[1460,17630,17602],{},[1334,17632,17633],{},"105,8",[1338,17635,17636],{"encoding":1340},"32{,}74 + 2{,}15\\cdot 34 \\doteq 105{,}8",[1136,17638,17640],{"id":17639},"nelineární-a-vyšší-řády-regresních-funkcí","Nelineární a vyšší řády regresních funkcí",[1110,17642,17643,17644,17647,17648,17715,17716,17734,17735,17752],{},"Když přímka závislost nevystihuje, nabízí se další ",[1302,17645,17646],{},"lineární funkce"," — tedy funkce lineární ve svých parametrech, zapsatelné ve tvaru ",[1115,17649,17651],{"className":17650},[1315],[1317,17652,17653],{"xmlns":1319},[1321,17654,17655,17712],{},[1324,17656,17657,17659,17661,17667,17669,17675,17681,17683,17685,17687,17689,17692,17694,17700,17706,17708,17710],{},[1330,17658,16097],{},[1460,17660,1754],{},[1327,17662,17663,17665],{},[1330,17664,16112],{},[1334,17666,1336],{},[1460,17668,5252],{},[1327,17670,17671,17673],{},[1330,17672,16112],{},[1334,17674,1565],{},[1327,17676,17677,17679],{},[1330,17678,6546],{},[1334,17680,1565],{},[1460,17682,1647],{"stretchy":1646},[1330,17684,6495],{},[1460,17686,1658],{"stretchy":1646},[1460,17688,5252],{},[1460,17690,17691],{},"⋯",[1460,17693,5252],{},[1327,17695,17696,17698],{},[1330,17697,16112],{},[1330,17699,1110],{},[1327,17701,17702,17704],{},[1330,17703,6546],{},[1330,17705,1110],{},[1460,17707,1647],{"stretchy":1646},[1330,17709,6495],{},[1460,17711,1658],{"stretchy":1646},[1338,17713,17714],{"encoding":1340},"\\eta=\\beta_0+\\beta_1 f_1(x)+\\dots+\\beta_p f_p(x)"," se známými funkcemi ",[1115,17717,17719],{"className":17718},[1315],[1317,17720,17721],{"xmlns":1319},[1321,17722,17723,17731],{},[1324,17724,17725],{},[1327,17726,17727,17729],{},[1330,17728,6546],{},[1330,17730,1650],{},[1338,17732,17733],{"encoding":1340},"f_i"," a neznámými parametry ",[1115,17736,17738],{"className":17737},[1315],[1317,17739,17740],{"xmlns":1319},[1321,17741,17742,17750],{},[1324,17743,17744],{},[1327,17745,17746,17748],{},[1330,17747,16112],{},[1330,17749,1650],{},[1338,17751,16158],{"encoding":1340},". I tyto parametry se odhadují metodou nejmenších čtverců, stejně jako u přímky:",[1115,17754,17756],{"className":17755},[1315],[1317,17757,17758],{"xmlns":1319,"display":1736},[1321,17759,17760,18070],{},[17761,17762,17765,17838,17951,18010],"mtable",{"rowspacing":17763,"columnalign":17764,"columnspacing":6534},"0.25em","right left",[17766,17767,17768,17792],"mtr",{},[17769,17770,17771],"mtd",{},[3015,17772,17773],{"scriptlevel":1336,"displaystyle":1121},[1324,17774,17775,17789],{},[1324,17776,17777,17780,17786],{},[2682,17778,17779],{},"parabolick",[2496,17781,17782,17784],{"accent":1121},[2682,17783,1127],{},[1460,17785,11277],{},[2682,17787,17788],{}," regrese: ",[1784,17790],{"width":17791},"1em",[17769,17793,17794],{},[3015,17795,17796],{"scriptlevel":1336,"displaystyle":1121},[1324,17797,17798,17800,17806,17808,17814,17816,17822,17824,17826,17832],{},[1324,17799],{},[2496,17801,17802,17804],{"accent":1121},[1330,17803,6905],{},[1460,17805,2502],{},[1460,17807,1754],{},[1327,17809,17810,17812],{},[1330,17811,11280],{},[1334,17813,1336],{},[1460,17815,5252],{},[1327,17817,17818,17820],{},[1330,17819,11280],{},[1334,17821,1565],{},[1330,17823,6495],{},[1460,17825,5252],{},[1327,17827,17828,17830],{},[1330,17829,11280],{},[1334,17831,1360],{},[1353,17833,17834,17836],{},[1330,17835,6495],{},[1334,17837,1360],{},[17766,17839,17840,17887],{},[17769,17841,17842],{},[3015,17843,17844],{"scriptlevel":1336,"displaystyle":1121},[1324,17845,17846,17885],{},[1324,17847,17848,17851,17857,17860,17864,17867,17873,17876,17882],{},[2682,17849,17850],{},"polynomick",[2496,17852,17853,17855],{"accent":1121},[2682,17854,1127],{},[1460,17856,11277],{},[2682,17858,17859],{}," regrese ",[3015,17861,17862],{"scriptlevel":1336,"displaystyle":1646},[1330,17863,1110],{},[2682,17865,17866],{},"-t",[2496,17868,17869,17871],{"accent":1121},[2682,17870,8369],{},[1460,17872,11277],{},[2682,17874,17875],{},"ho stupn",[2496,17877,17878,17880],{"accent":1121},[2682,17879,8369],{},[1460,17881,11287],{},[2682,17883,17884],{},": ",[1784,17886],{"width":17791},[17769,17888,17889],{},[3015,17890,17891],{"scriptlevel":1336,"displaystyle":1121},[1324,17892,17893,17895,17901,17903,17909,17911,17917,17919,17921,17927,17933,17935,17937,17939,17945],{},[1324,17894],{},[2496,17896,17897,17899],{"accent":1121},[1330,17898,6905],{},[1460,17900,2502],{},[1460,17902,1754],{},[1327,17904,17905,17907],{},[1330,17906,11280],{},[1334,17908,1336],{},[1460,17910,5252],{},[1327,17912,17913,17915],{},[1330,17914,11280],{},[1334,17916,1565],{},[1330,17918,6495],{},[1460,17920,5252],{},[1327,17922,17923,17925],{},[1330,17924,11280],{},[1334,17926,1360],{},[1353,17928,17929,17931],{},[1330,17930,6495],{},[1334,17932,1360],{},[1460,17934,5252],{},[1460,17936,17691],{},[1460,17938,5252],{},[1327,17940,17941,17943],{},[1330,17942,11280],{},[1330,17944,1110],{},[1353,17946,17947,17949],{},[1330,17948,6495],{},[1330,17950,1110],{},[17766,17952,17953,17974],{},[17769,17954,17955],{},[3015,17956,17957],{"scriptlevel":1336,"displaystyle":1121},[1324,17958,17959,17972],{},[1324,17960,17961,17964,17970],{},[2682,17962,17963],{},"hyperbolick",[2496,17965,17966,17968],{"accent":1121},[2682,17967,1127],{},[1460,17969,11277],{},[2682,17971,17788],{},[1784,17973],{"width":17791},[17769,17975,17976],{},[3015,17977,17978],{"scriptlevel":1336,"displaystyle":1121},[1324,17979,17980,17982,17988,17990,17996,17998,18004],{},[1324,17981],{},[2496,17983,17984,17986],{"accent":1121},[1330,17985,6905],{},[1460,17987,2502],{},[1460,17989,1754],{},[1327,17991,17992,17994],{},[1330,17993,11280],{},[1334,17995,1336],{},[1460,17997,5252],{},[1327,17999,18000,18002],{},[1330,18001,11280],{},[1334,18003,1565],{},[2512,18005,18006,18008],{},[1334,18007,1565],{},[1330,18009,6495],{},[17766,18011,18012,18033],{},[17769,18013,18014],{},[3015,18015,18016],{"scriptlevel":1336,"displaystyle":1121},[1324,18017,18018,18031],{},[1324,18019,18020,18023,18029],{},[2682,18021,18022],{},"logaritmick",[2496,18024,18025,18027],{"accent":1121},[2682,18026,1127],{},[1460,18028,11277],{},[2682,18030,17788],{},[1784,18032],{"width":17791},[17769,18034,18035],{},[3015,18036,18037],{"scriptlevel":1336,"displaystyle":1121},[1324,18038,18039,18041,18047,18049,18055,18057,18063,18066,18068],{},[1324,18040],{},[2496,18042,18043,18045],{"accent":1121},[1330,18044,6905],{},[1460,18046,2502],{},[1460,18048,1754],{},[1327,18050,18051,18053],{},[1330,18052,11280],{},[1334,18054,1336],{},[1460,18056,5252],{},[1327,18058,18059,18061],{},[1330,18060,11280],{},[1334,18062,1565],{},[1330,18064,18065],{},"ln",[1460,18067,4266],{},[1330,18069,6495],{},[1338,18071,18072],{"encoding":1340},"\\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}",[1110,18074,18075,18076,18079,18080,18126,18127,1730],{},"Naproti tomu ",[1302,18077,18078],{},"nelineární funkce"," nelze do tvaru ",[1115,18081,18083],{"className":18082},[1315],[1317,18084,18085],{"xmlns":1319},[1321,18086,18087,18123],{},[1324,18088,18089,18091,18093,18099,18101,18107,18113,18115,18117,18119,18121],{},[1330,18090,16097],{},[1460,18092,1754],{},[1327,18094,18095,18097],{},[1330,18096,16112],{},[1334,18098,1336],{},[1460,18100,5252],{},[1327,18102,18103,18105],{},[1330,18104,16112],{},[1334,18106,1565],{},[1327,18108,18109,18111],{},[1330,18110,6546],{},[1334,18112,1565],{},[1460,18114,1647],{"stretchy":1646},[1330,18116,6495],{},[1460,18118,1658],{"stretchy":1646},[1460,18120,5252],{},[1460,18122,1571],{},[1338,18124,18125],{"encoding":1340},"\\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 ",[1302,18128,18129],{},"exponenciální regrese",[1115,18131,18133],{"className":18132},[1315],[1317,18134,18135],{"xmlns":1319,"display":1736},[1321,18136,18137,18169],{},[1324,18138,18139,18145,18147,18153,18155,18167],{},[2496,18140,18141,18143],{"accent":1121},[1330,18142,6905],{},[1460,18144,2502],{},[1460,18146,1754],{},[1327,18148,18149,18151],{},[1330,18150,11280],{},[1334,18152,1336],{},[1460,18154,7887],{},[3127,18156,18157,18159,18161],{},[1330,18158,11280],{},[1334,18160,1565],{},[1324,18162,18163,18165],{},[2682,18164,2684],{},[1330,18166,6495],{},[1330,18168,1440],{"mathvariant":1893},[1338,18170,18171],{"encoding":1340},"\\hat y = b_0 \\cdot b_1^{\\,x}.",[1110,18173,18174],{},[4158,18175],{"alt":18176,"className":18177,"src":18178},"mask-ra-nelinearni-krivky",[1130,4162],"\u002Fwiki-assets\u002Fmask-ra-nelinearni-krivky.png",[16521,18180,18182],{"id":18181},"v-r-parabolická-regrese","V R — parabolická regrese",[1110,18184,18185,18186,1730],{},"Na ročních ziscích firmy (šest let) se parabolická regrese odhadne přidáním kvadratického členu ",[3244,18187,18188],{},"I(x^2)",[3468,18190,18192],{"className":3470,"code":18191,"language":71,"meta":1247,"style":1247},"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",[3244,18193,18194,18229,18269,18303],{"__ignoreMap":1247},[1115,18195,18196,18199,18201,18203,18205,18207,18209,18211,18213,18215,18217,18219,18221,18223,18225,18227],{"class":3476,"line":10},[1115,18197,18198],{"class":3479},"rok",[1115,18200,3484],{"class":3483},[1115,18202,3610],{"class":3487},[1115,18204,1647],{"class":3491},[1115,18206,1565],{"class":3499},[1115,18208,1568],{"class":3483},[1115,18210,3955],{"class":3499},[1115,18212,1568],{"class":3483},[1115,18214,10632],{"class":3499},[1115,18216,1568],{"class":3483},[1115,18218,3575],{"class":3499},[1115,18220,1568],{"class":3483},[1115,18222,9771],{"class":3499},[1115,18224,1568],{"class":3483},[1115,18226,12004],{"class":3499},[1115,18228,3676],{"class":3491},[1115,18230,18231,18233,18235,18237,18239,18242,18244,18247,18249,18252,18254,18257,18259,18262,18264,18267],{"class":3476,"line":27},[1115,18232,1088],{"class":3479},[1115,18234,3484],{"class":3483},[1115,18236,3610],{"class":3487},[1115,18238,1647],{"class":3491},[1115,18240,18241],{"class":3499},"112",[1115,18243,1568],{"class":3483},[1115,18245,18246],{"class":3499}," 149",[1115,18248,1568],{"class":3483},[1115,18250,18251],{"class":3499}," 238",[1115,18253,1568],{"class":3483},[1115,18255,18256],{"class":3499}," 354",[1115,18258,1568],{"class":3483},[1115,18260,18261],{"class":3499}," 580",[1115,18263,1568],{"class":3483},[1115,18265,18266],{"class":3499}," 867",[1115,18268,3676],{"class":3491},[1115,18270,18271,18274,18276,18278,18280,18282,18284,18287,18290,18293,18295,18297,18299,18301],{"class":3476,"line":148},[1115,18272,18273],{"class":3479},"model_parabola",[1115,18275,3484],{"class":3483},[1115,18277,16625],{"class":3487},[1115,18279,1647],{"class":3491},[1115,18281,1088],{"class":3479},[1115,18283,16632],{"class":3483},[1115,18285,18286],{"class":3479}," rok",[1115,18288,18289],{"class":3483}," +",[1115,18291,18292],{"class":3487}," I",[1115,18294,1647],{"class":3491},[1115,18296,18198],{"class":3479},[1115,18298,2502],{"class":3483},[1115,18300,1360],{"class":3499},[1115,18302,9270],{"class":3491},[1115,18304,18305,18307,18309,18311],{"class":3476,"line":111},[1115,18306,1271],{"class":3487},[1115,18308,1647],{"class":3491},[1115,18310,18273],{"class":3479},[1115,18312,3676],{"class":3491},[3468,18314,18317],{"className":18315,"code":18316,"language":3698,"meta":1247},[3696],"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",[3244,18318,18316],{"__ignoreMap":1247},[1110,18320,18321,18322,18367],{},"Odhadnutá parabola ",[1115,18323,18325],{"className":18324},[1315],[1317,18326,18327],{"xmlns":1319},[1321,18328,18329,18364],{},[1324,18330,18331,18337,18339,18342,18344,18347,18349,18351,18353,18356,18358],{},[2496,18332,18333,18335],{"accent":1121},[1330,18334,6905],{},[1460,18336,2502],{},[1460,18338,1754],{},[1334,18340,18341],{},"164,6",[1460,18343,2838],{},[1334,18345,18346],{},"76,6",[2682,18348,2684],{},[1330,18350,6495],{},[1460,18352,5252],{},[1334,18354,18355],{},"32,1",[2682,18357,2684],{},[1353,18359,18360,18362],{},[1330,18361,6495],{},[1334,18363,1360],{},[1338,18365,18366],{"encoding":1340},"\\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.",[16521,18369,18371],{"id":18370},"v-r-exponenciální-regrese","V R — exponenciální regrese",[1110,18373,18374,18375,18377],{},"Nelineární funkce se v R odhadují funkcí ",[3244,18376,15883],{}," ze stejnojmenného balíčku. Bez zadaných počátečních hodnot R upozorní, že parametry nastavil na 1, a odhad dopočítá iteračně:",[3468,18379,18381],{"className":3470,"code":18380,"language":71,"meta":1247,"style":1247},"library(nls2)\nmodel_exp \u003C- nls2(zisk ~ b1 * exp(b2 * rok))\nsummary(model_exp)\n",[3244,18382,18383,18393,18429],{"__ignoreMap":1247},[1115,18384,18385,18387,18389,18391],{"class":3476,"line":10},[1115,18386,17170],{"class":3483},[1115,18388,1647],{"class":3491},[1115,18390,15867],{"class":3479},[1115,18392,3676],{"class":3491},[1115,18394,18395,18398,18400,18403,18405,18407,18409,18412,18415,18418,18420,18423,18425,18427],{"class":3476,"line":27},[1115,18396,18397],{"class":3479},"model_exp",[1115,18399,3484],{"class":3483},[1115,18401,18402],{"class":3487}," nls2",[1115,18404,1647],{"class":3491},[1115,18406,1088],{"class":3479},[1115,18408,16632],{"class":3483},[1115,18410,18411],{"class":3479}," b1",[1115,18413,18414],{"class":3483}," *",[1115,18416,18417],{"class":3487}," exp",[1115,18419,1647],{"class":3491},[1115,18421,18422],{"class":3479},"b2",[1115,18424,18414],{"class":3483},[1115,18426,18286],{"class":3479},[1115,18428,9270],{"class":3491},[1115,18430,18431,18433,18435,18437],{"class":3476,"line":148},[1115,18432,1271],{"class":3487},[1115,18434,1647],{"class":3491},[1115,18436,18397],{"class":3479},[1115,18438,3676],{"class":3491},[3468,18440,18443],{"className":18441,"code":18442,"language":3698,"meta":1247},[3696],"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",[3244,18444,18442],{"__ignoreMap":1247},[1110,18446,18447,18448,1730],{},"Stejnou křivku lze zapsat i v mocninném tvaru ",[1115,18449,18451],{"className":18450},[1315],[1317,18452,18453],{"xmlns":1319},[1321,18454,18455,18481],{},[1324,18456,18457,18463,18465,18471,18473],{},[2496,18458,18459,18461],{"accent":1121},[1330,18460,6905],{},[1460,18462,2502],{},[1460,18464,1754],{},[1327,18466,18467,18469],{},[1330,18468,11280],{},[1334,18470,1565],{},[1460,18472,7887],{},[3127,18474,18475,18477,18479],{},[1330,18476,11280],{},[1334,18478,1360],{},[1330,18480,6495],{},[1338,18482,18483],{"encoding":1340},"\\hat y=b_1\\cdot b_2^{x}",[3468,18485,18487],{"className":3470,"code":18486,"language":71,"meta":1247,"style":1247},"model_pow \u003C- nls2(zisk ~ b1 * (b2^rok))\nsummary(model_pow)\n",[3244,18488,18489,18518],{"__ignoreMap":1247},[1115,18490,18491,18494,18496,18498,18500,18502,18504,18506,18508,18510,18512,18514,18516],{"class":3476,"line":10},[1115,18492,18493],{"class":3479},"model_pow",[1115,18495,3484],{"class":3483},[1115,18497,18402],{"class":3487},[1115,18499,1647],{"class":3491},[1115,18501,1088],{"class":3479},[1115,18503,16632],{"class":3483},[1115,18505,18411],{"class":3479},[1115,18507,18414],{"class":3483},[1115,18509,4382],{"class":3491},[1115,18511,18422],{"class":3479},[1115,18513,2502],{"class":3483},[1115,18515,18198],{"class":3479},[1115,18517,9270],{"class":3491},[1115,18519,18520,18522,18524,18526],{"class":3476,"line":27},[1115,18521,1271],{"class":3487},[1115,18523,1647],{"class":3491},[1115,18525,18493],{"class":3479},[1115,18527,3676],{"class":3491},[3468,18529,18532],{"className":18530,"code":18531,"language":3698,"meta":1247},[3696],"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",[3244,18533,18531],{"__ignoreMap":1247},[1110,18535,18536,18537,18601,18602,18626],{},"Obě varianty popisují stejnou křivku (",[1115,18538,18540],{"className":18539},[1315],[1317,18541,18542],{"xmlns":1319},[1321,18543,18544,18598],{},[1324,18545,18546,18563,18565],{},[3127,18547,18548,18550,18552],{},[1330,18549,11280],{},[1334,18551,1360],{},[1324,18553,18554,18557],{},[2682,18555,18556],{},"mocninn",[2496,18558,18559,18561],{"accent":1121},[2682,18560,6905],{},[1460,18562,11277],{},[1460,18564,1754],{},[1353,18566,18567,18569],{},[1330,18568,8369],{},[1324,18570,18571,18573],{},[2682,18572,2684],{},[3127,18574,18575,18577,18579],{},[1330,18576,11280],{},[1334,18578,1360],{},[1324,18580,18581,18584,18590,18592],{},[2682,18582,18583],{},"exponenci",[2496,18585,18586,18588],{"accent":1121},[2682,18587,1127],{},[1460,18589,11277],{},[2682,18591,18065],{},[2496,18593,18594,18596],{"accent":1121},[2682,18595,11527],{},[1460,18597,11277],{},[1338,18599,18600],{"encoding":1340},"b_2^{\\text{mocninný}} = e^{\\,b_2^{\\text{exponenciální}}}",", zde ",[1115,18603,18605],{"className":18604},[1315],[1317,18606,18607],{"xmlns":1319},[1321,18608,18609,18623],{},[1324,18610,18611,18618,18620],{},[1353,18612,18613,18615],{},[1330,18614,8369],{},[1334,18616,18617],{},"0,4316",[1460,18619,9217],{},[1334,18621,18622],{},"1,540",[1338,18624,18625],{"encoding":1340},"e^{0{,}4316}\\approx 1{,}540",") a mají totožnou reziduální chybu — je to jen otázka parametrizace.",[16521,18628,18630],{"id":18629},"v-r-hyperbolická-regrese","V R — hyperbolická regrese",[1110,18632,18633,18634,1730],{},"Hyperbolická regrese se odhadne jako obyčejná lineární regrese na transformované proměnné ",[3244,18635,18636],{},"I(1\u002Fx)",[3468,18638,18640],{"className":3470,"code":18639,"language":71,"meta":1247,"style":1247},"model_hyperbola \u003C- lm(tydenni_vydaje ~ I(1 \u002F pocet_clenu))\nsummary(model_hyperbola)\n",[3244,18641,18642,18669],{"__ignoreMap":1247},[1115,18643,18644,18647,18649,18651,18653,18655,18657,18659,18661,18663,18665,18667],{"class":3476,"line":10},[1115,18645,18646],{"class":3479},"model_hyperbola",[1115,18648,3484],{"class":3483},[1115,18650,16625],{"class":3487},[1115,18652,1647],{"class":3491},[1115,18654,16580],{"class":3479},[1115,18656,16632],{"class":3483},[1115,18658,18292],{"class":3487},[1115,18660,1647],{"class":3491},[1115,18662,1565],{"class":3499},[1115,18664,9852],{"class":3483},[1115,18666,16635],{"class":3479},[1115,18668,9270],{"class":3491},[1115,18670,18671,18673,18675,18677],{"class":3476,"line":27},[1115,18672,1271],{"class":3487},[1115,18674,1647],{"class":3491},[1115,18676,18646],{"class":3479},[1115,18678,3676],{"class":3491},[3468,18680,18683],{"className":18681,"code":18682,"language":3698,"meta":1247},[3696],"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",[3244,18684,18682],{"__ignoreMap":1247},[1110,18686,18687,18688,18722,18723,18744],{},"Model ",[1115,18689,18691],{"className":18690},[1315],[1317,18692,18693],{"xmlns":1319},[1321,18694,18695,18719],{},[1324,18696,18697,18703,18705,18708,18710],{},[2496,18698,18699,18701],{"accent":1121},[1330,18700,6905],{},[1460,18702,2502],{},[1460,18704,1754],{},[1334,18706,18707],{},"2180,7",[1460,18709,2838],{},[3015,18711,18712],{"scriptlevel":1336,"displaystyle":1121},[2512,18713,18714,18717],{},[1334,18715,18716],{},"1920,0",[1330,18718,6495],{},[1338,18720,18721],{"encoding":1340},"\\hat y = 2180{,}7 - \\dfrac{1920{,}0}{x}"," vysvětluje jen 76,3 % rozptylu — u těchto dat je hyperbola podstatně horší volbou než přímka (",[1115,18724,18726],{"className":18725},[1315],[1317,18727,18728],{"xmlns":1319},[1321,18729,18730,18742],{},[1324,18731,18732,18738,18740],{},[1353,18733,18734,18736],{},[1330,18735,10000],{},[1334,18737,1360],{},[1460,18739,1754],{},[1334,18741,16779],{},[1338,18743,16782],{"encoding":1340},"). Právě k takovému porovnání slouží index determinace: nízká hodnota signalizuje, že zvolený typ funkce k datům nesedí.",[1103,18746,18748,18755,18786,18834],{"className":18747,"dataCallout":3251},[1106,3250],[1110,18749,18751,18754],{"className":18750},[1113],[1115,18752],{"className":18753,"ariaHidden":1121},[1118,3258,1120],"Příklad: Parabolická regrese",[1110,18756,18757,18758,18771,18772,18785],{},"Prodejna počítačových her nechala prodavače absolvovat kurz prodejních dovedností. Při dvaceti měřeních sledovala, kolik zákazníků navštíví prodejnu během prodejní doby (proměnná ",[1115,18759,18761],{"className":18760},[1315],[1317,18762,18763],{"xmlns":1319},[1321,18764,18765,18769],{},[1324,18766,18767],{},[1330,18768,6495],{},[1338,18770,6495],{"encoding":1340},") a jaká je toho dne tržba v tisících Kč (proměnná ",[1115,18773,18775],{"className":18774},[1315],[1317,18776,18777],{"xmlns":1319},[1321,18778,18779,18783],{},[1324,18780,18781],{},[1330,18782,6905],{},[1338,18784,6905],{"encoding":1340},"). Zároveň chtěla zjistit, zda při rostoucím počtu zákazníků stačí stávající počet prodavačů.",[1110,18787,17441,18788,1440],{},[1115,18789,18791],{"className":18790},[1315],[1317,18792,18793],{"xmlns":1319},[1321,18794,18795,18831],{},[1324,18796,18797,18803,18805,18807,18810,18812,18815,18817,18819,18821,18823,18825],{},[2496,18798,18799,18801],{"accent":1121},[1330,18800,6905],{},[1460,18802,2502],{},[1460,18804,1754],{},[1460,18806,2838],{},[1334,18808,18809],{},"60,3",[1460,18811,5252],{},[1334,18813,18814],{},"4,55",[2682,18816,2684],{},[1330,18818,6495],{},[1460,18820,2838],{},[1334,18822,3759],{},[2682,18824,2684],{},[1353,18826,18827,18829],{},[1330,18828,6495],{},[1334,18830,1360],{},[1338,18832,18833],{"encoding":1340},"\\hat y = -60{,}3 + 4{,}55\\,x - 0{,}05\\,x^2",[1110,18835,18836,18837,18855],{},"Záporný koeficient ",[1115,18838,18840],{"className":18839},[1315],[1317,18841,18842],{"xmlns":1319},[1321,18843,18844,18852],{},[1324,18845,18846],{},[1327,18847,18848,18850],{},[1330,18849,11280],{},[1334,18851,1360],{},[1338,18853,18854],{"encoding":1340},"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.",[1103,18857,18859,18866,18896,18941],{"className":18858,"dataCallout":3251},[1106,3250],[1110,18860,18862,18865],{"className":18861},[1113],[1115,18863],{"className":18864,"ariaHidden":1121},[1118,3258,1120],"Příklad: Hyperbolická regrese",[1110,18867,18868,18869,18882,18883,15868],{},"V podniku se podle interního účetnictví sledovala závislost vlastních nákladů na jednotku produkce v Kč (proměnná ",[1115,18870,18872],{"className":18871},[1315],[1317,18873,18874],{"xmlns":1319},[1321,18875,18876,18880],{},[1324,18877,18878],{},[1330,18879,6905],{},[1338,18881,6905],{"encoding":1340},") na objemu produkce v tisících kusů (proměnná ",[1115,18884,18886],{"className":18885},[1315],[1317,18887,18888],{"xmlns":1319},[1321,18889,18890,18894],{},[1324,18891,18892],{},[1330,18893,6495],{},[1338,18895,6495],{"encoding":1340},[1110,18897,17441,18898,1440],{},[1115,18899,18901],{"className":18900},[1315],[1317,18902,18903],{"xmlns":1319},[1321,18904,18905,18938],{},[1324,18906,18907,18913,18915,18917,18920,18922],{},[2496,18908,18909,18911],{"accent":1121},[1330,18910,6905],{},[1460,18912,2502],{},[1460,18914,1754],{},[1460,18916,2838],{},[1334,18918,18919],{},"96,78",[1460,18921,5252],{},[3015,18923,18924],{"scriptlevel":1336,"displaystyle":1121},[2512,18925,18926,18936],{},[1324,18927,18928,18931,18933],{},[1334,18929,18930],{},"250",[2682,18932,2684],{},[1334,18934,18935],{},"528,88",[1330,18937,6495],{},[1338,18939,18940],{"encoding":1340},"\\hat y = -96{,}78 + \\dfrac{250\\,528{,}88}{x}",[1110,18942,18943,18944,18961],{},"Záporná hodnota ",[1115,18945,18947],{"className":18946},[1315],[1317,18948,18949],{"xmlns":1319},[1321,18950,18951,18959],{},[1324,18952,18953],{},[1327,18954,18955,18957],{},[1330,18956,11280],{},[1334,18958,1565],{},[1338,18960,16490],{"encoding":1340}," v čitateli ukazuje klesající náklady na jednotku s rostoucím objemem produkce — typický projev úspor z rozsahu, který hyperbola dobře zachycuje.",[1136,18963,18965],{"id":18964},"kvalita-regresní-funkce-a-korelační-analýza","Kvalita regresní funkce a korelační analýza",[1110,18967,18968,18969,1730],{},"Kvalitu odhadnuté regresní funkce vyjadřuje ",[1302,18970,15781],{},[1115,18972,18974],{"className":18973},[1315],[1317,18975,18976],{"xmlns":1319,"display":1736},[1321,18977,18978,19046],{},[1324,18979,18980,18986,18988,19010,19012,19014,19016,19044],{},[1353,18981,18982,18984],{},[1330,18983,10000],{},[1334,18985,1360],{},[1460,18987,1754],{},[2512,18989,18990,19002],{},[3127,18991,18992,18994,19000],{},[1330,18993,1626],{},[2496,18995,18996,18998],{"accent":1121},[1330,18997,6905],{},[1460,18999,2502],{},[1334,19001,1360],{},[3127,19003,19004,19006,19008],{},[1330,19005,1626],{},[1330,19007,6905],{},[1334,19009,1360],{},[1460,19011,1754],{},[1334,19013,1565],{},[1460,19015,2838],{},[2512,19017,19018,19036],{},[3127,19019,19020,19022,19034],{},[1330,19021,1626],{},[1324,19023,19024,19026,19028],{},[1330,19025,6905],{},[1460,19027,2838],{},[2496,19029,19030,19032],{"accent":1121},[1330,19031,6905],{},[1460,19033,2502],{},[1334,19035,1360],{},[3127,19037,19038,19040,19042],{},[1330,19039,1626],{},[1330,19041,6905],{},[1334,19043,1360],{},[1330,19045,1440],{"mathvariant":1893},[1338,19047,19048],{"encoding":1340},"R^2 = \\frac{s^2_{\\hat y}}{s^2_y} = 1 - \\frac{s^2_{y-\\hat y}}{s^2_y}.",[1110,19050,19051,19052,19069,19070,19083],{},"Čím blíž je ",[1115,19053,19055],{"className":19054},[1315],[1317,19056,19057],{"xmlns":1319},[1321,19058,19059,19067],{},[1324,19060,19061],{},[1353,19062,19063,19065],{},[1330,19064,10000],{},[1334,19066,1360],{},[1338,19068,15799],{"encoding":1340}," k 1, tím silnější je závislost; v procentech udává, jakou část rozptylu závisle proměnné ",[1115,19071,19073],{"className":19072},[1315],[1317,19074,19075],{"xmlns":1319},[1321,19076,19077,19081],{},[1324,19078,19079],{},[1330,19080,6905],{},[1338,19082,6905],{"encoding":1340}," se podařilo vysvětlit zvolenou regresní funkcí. Nízký index determinace může signalizovat špatně zvolený typ regresní funkce, ne nutně absenci závislosti.",[1110,19085,19086,19087,1425,19089,19112,19113,1730],{},"Obecnou mírou těsnosti závislosti — platnou pro libovolný typ regresní funkce — je ",[1302,19088,15803],{},[1115,19090,19092],{"className":19091},[1315],[1317,19093,19094],{"xmlns":1319},[1321,19095,19096,19110],{},[1324,19097,19098,19100,19102],{},[1330,19099,10976],{},[1460,19101,1754],{},[4228,19103,19104],{},[1353,19105,19106,19108],{},[1330,19107,10000],{},[1334,19109,1360],{},[1338,19111,15827],{"encoding":1340},". Je-li zvolenou funkcí regresní přímka, index korelace je roven (až na znaménko) ",[1302,19114,15831],{},[1115,19116,19118],{"className":19117},[1315],[1317,19119,19120],{"xmlns":1319,"display":1736},[1321,19121,19122,19172],{},[1324,19123,19124,19134,19136,19170],{},[1327,19125,19126,19128],{},[1330,19127,71],{},[1324,19129,19130,19132],{},[1330,19131,6495],{},[1330,19133,6905],{},[1460,19135,1754],{},[2512,19137,19138,19148],{},[1327,19139,19140,19142],{},[1330,19141,1626],{},[1324,19143,19144,19146],{},[1330,19145,6495],{},[1330,19147,6905],{},[4228,19149,19150],{},[1324,19151,19152,19160,19162],{},[3127,19153,19154,19156,19158],{},[1330,19155,1626],{},[1330,19157,6495],{},[1334,19159,1360],{},[1460,19161,7887],{},[3127,19163,19164,19166,19168],{},[1330,19165,1626],{},[1330,19167,6905],{},[1334,19169,1360],{},[1330,19171,1440],{"mathvariant":1893},[1338,19173,19174],{"encoding":1340},"r_{xy} = \\frac{s_{xy}}{\\sqrt{s^2_x\\cdot s^2_y}}.",[1110,19176,19177,19178,19194,19195,19211],{},"Koeficient korelace nabývá hodnot od ",[1115,19179,19181],{"className":19180},[1315],[1317,19182,19183],{"xmlns":1319},[1321,19184,19185,19191],{},[1324,19186,19187,19189],{},[1460,19188,2838],{},[1334,19190,1565],{},[1338,19192,19193],{"encoding":1340},"-1"," do ",[1115,19196,19198],{"className":19197},[1315],[1317,19199,19200],{"xmlns":1319},[1321,19201,19202,19208],{},[1324,19203,19204,19206],{},[1460,19205,5252],{},[1334,19207,1565],{},[1338,19209,19210],{"encoding":1340},"+1",": znaménko určuje typ závislosti (pozitivní, nebo negativní), absolutní hodnota její sílu — čím blíž k 0, tím je závislost slabší.",[1110,19213,19214],{},[4158,19215],{"alt":19216,"className":19217,"src":19218},"mask-ra-korelace-sila",[1130,4162],"\u002Fwiki-assets\u002Fmask-ra-korelace-sila.png",[1110,19220,19221,19222,19235,19236,19254,19255,5516,19268,19281],{},"S rostoucí absolutní hodnotou ",[1115,19223,19225],{"className":19224},[1315],[1317,19226,19227],{"xmlns":1319},[1321,19228,19229,19233],{},[1324,19230,19231],{},[1330,19232,71],{},[1338,19234,71],{"encoding":1340}," se body v rozptylovém grafu víc blíží přímce; kolem ",[1115,19237,19239],{"className":19238},[1315],[1317,19240,19241],{"xmlns":1319},[1321,19242,19243,19251],{},[1324,19244,19245,19247,19249],{},[1330,19246,71],{},[1460,19248,9217],{},[1334,19250,1336],{},[1338,19252,19253],{"encoding":1340},"r\\approx 0"," je mezi ",[1115,19256,19258],{"className":19257},[1315],[1317,19259,19260],{"xmlns":1319},[1321,19261,19262,19266],{},[1324,19263,19264],{},[1330,19265,6495],{},[1338,19267,6495],{"encoding":1340},[1115,19269,19271],{"className":19270},[1315],[1317,19272,19273],{"xmlns":1319},[1321,19274,19275,19279],{},[1324,19276,19277],{},[1330,19278,6905],{},[1338,19280,6905],{"encoding":1340}," patrná jen náhodná rozptýlenost bez lineárního trendu.",[16521,19283,16524],{"id":19284},"v-r-1",[3468,19286,19288],{"className":3470,"code":19287,"language":71,"meta":1247,"style":1247},"cor(pocet_clenu, tydenni_vydaje)\n",[3244,19289,19290],{"__ignoreMap":1247},[1115,19291,19292,19295,19297,19299,19301,19304],{"class":3476,"line":10},[1115,19293,19294],{"class":3487},"cor",[1115,19296,1647],{"class":3491},[1115,19298,16545],{"class":3479},[1115,19300,1568],{"class":3483},[1115,19302,19303],{"class":3479}," tydenni_vydaje",[1115,19305,3676],{"class":3491},[3468,19307,19310],{"className":19308,"code":19309,"language":3698,"meta":1247},[3696],"[1] 0.9997441\n",[3244,19311,19309],{"__ignoreMap":1247},[1110,19313,19314,19315,19341],{},"Hodnota 0,9997 odpovídá ",[1115,19316,19318],{"className":19317},[1315],[1317,19319,19320],{"xmlns":1319},[1321,19321,19322,19338],{},[1324,19323,19324,19332,19334],{},[4228,19325,19326],{},[1353,19327,19328,19330],{},[1330,19329,10000],{},[1334,19331,1360],{},[1460,19333,1754],{},[4228,19335,19336],{},[1334,19337,16779],{},[1338,19339,19340],{"encoding":1340},"\\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.",[1103,19343,19345,19352,19355],{"className":19344,"dataCallout":3251},[1106,3250],[1110,19346,19348,19351],{"className":19347},[1113],[1115,19349],{"className":19350,"ariaHidden":1121},[1118,3258,1120],"Příklad: Koeficient korelace",[1110,19353,19354],{},"Pro stejná data o hodnotě produkce a výši investic dvanácti firem jako u regresní přímky byl spočten koeficient korelace mezi oběma proměnnými.",[1110,19356,17441,19357,19384],{},[1115,19358,19360],{"className":19359},[1315],[1317,19361,19362],{"xmlns":1319},[1321,19363,19364,19381],{},[1324,19365,19366,19376,19378],{},[1327,19367,19368,19370],{},[1330,19369,71],{},[1324,19371,19372,19374],{},[1330,19373,6495],{},[1330,19375,6905],{},[1460,19377,1754],{},[1334,19379,19380],{},"0,739",[1338,19382,19383],{"encoding":1340},"r_{xy} = 0{,}739"," — silná kladná závislost hodnoty produkce na výši investic.",[1136,19386,19388],{"id":19387},"vícenásobná-regrese-a-korelace","Vícenásobná regrese a korelace",[1110,19390,19391,19392,19405],{},"Pokud na závisle proměnnou ",[1115,19393,19395],{"className":19394},[1315],[1317,19396,19397],{"xmlns":1319},[1321,19398,19399,19403],{},[1324,19400,19401],{},[1330,19402,6905],{},[1338,19404,6905],{"encoding":1340}," působí víc vysvětlujících proměnných současně, analyzuje se zvlášť vliv každé z nich a výsledná regresní funkce se konstruuje jako součet jednoduchých regresních funkcí:",[1115,19407,19409],{"className":19408},[1315],[1317,19410,19411],{"xmlns":1319,"display":1736},[1321,19412,19413,19523],{},[1324,19414,19415,19417,19419,19425,19427,19433,19439,19441,19447,19453,19455,19457,19459,19465,19471,19473,19475,19481,19483,19489,19491,19497,19503,19505,19507,19509,19515,19521],{},[1330,19416,16097],{},[1460,19418,1754],{},[1327,19420,19421,19423],{},[1330,19422,16112],{},[1334,19424,1336],{},[1460,19426,5252],{},[1327,19428,19429,19431],{},[1330,19430,16112],{},[1334,19432,1565],{},[1327,19434,19435,19437],{},[1330,19436,6495],{},[1334,19438,1565],{},[1460,19440,5252],{},[1327,19442,19443,19445],{},[1330,19444,16112],{},[1334,19446,1360],{},[1327,19448,19449,19451],{},[1330,19450,6495],{},[1334,19452,1360],{},[1460,19454,5252],{},[1460,19456,17691],{},[1460,19458,5252],{},[1327,19460,19461,19463],{},[1330,19462,16112],{},[1330,19464,1110],{},[1327,19466,19467,19469],{},[1330,19468,6495],{},[1330,19470,1110],{},[1460,19472,1568],{"separator":1121},[1784,19474],{"width":1786},[2496,19476,19477,19479],{"accent":1121},[1330,19478,6905],{},[1460,19480,2502],{},[1460,19482,1754],{},[1327,19484,19485,19487],{},[1330,19486,11280],{},[1334,19488,1336],{},[1460,19490,5252],{},[1327,19492,19493,19495],{},[1330,19494,11280],{},[1334,19496,1565],{},[1327,19498,19499,19501],{},[1330,19500,6495],{},[1334,19502,1565],{},[1460,19504,5252],{},[1460,19506,17691],{},[1460,19508,5252],{},[1327,19510,19511,19513],{},[1330,19512,11280],{},[1330,19514,1110],{},[1327,19516,19517,19519],{},[1330,19518,6495],{},[1330,19520,1110],{},[1330,19522,1440],{"mathvariant":1893},[1338,19524,19525],{"encoding":1340},"\\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.",[16521,19527,19529],{"id":19528},"výběr-proměnných","Výběr proměnných",[1204,19531,19532,19538],{},[1207,19533,19534,19537],{},[1302,19535,19536],{},"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.",[1207,19539,19540,19543,19544,19547,19548,19551],{},[1302,19541,19542],{},"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 ",[1302,19545,19546],{},"forward"," proměnné postupně přidává, varianta ",[1302,19549,19550],{},"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.",[16521,19553,19555],{"id":19554},"postup-odhadu","Postup odhadu",[2638,19557,19558,19561,19564],{},[1207,19559,19560],{},"ověření předpokladů regresního modelu,",[1207,19562,19563],{},"samotný odhad parametrů,",[1207,19565,19566],{},"reziduální analýza výsledného modelu.",[1110,19568,19569,19570,19587,19588,3763,19590,19619,19620,19649,19650,19667],{},"Důležitost každého parametru ",[1115,19571,19573],{"className":19572},[1315],[1317,19574,19575],{"xmlns":1319},[1321,19576,19577,19585],{},[1324,19578,19579],{},[1327,19580,19581,19583],{},[1330,19582,11280],{},[1330,19584,1650],{},[1338,19586,16237],{"encoding":1340}," v modelu ověřuje ",[1302,19589,992],{},[1115,19591,19593],{"className":19592},[1315],[1317,19594,19595],{"xmlns":1319},[1321,19596,19597,19617],{},[1324,19598,19599,19605,19607,19613,19615],{},[1327,19600,19601,19603],{},[1330,19602,1332],{},[1334,19604,1336],{},[1460,19606,1730],{},[1327,19608,19609,19611],{},[1330,19610,16112],{},[1330,19612,1650],{},[1460,19614,1754],{},[1334,19616,1336],{},[1338,19618,16723],{"encoding":1340}," (proměnná je v modelu nevýznamná) proti ",[1115,19621,19623],{"className":19622},[1315],[1317,19624,19625],{"xmlns":1319},[1321,19626,19627,19647],{},[1324,19628,19629,19635,19637,19643,19645],{},[1327,19630,19631,19633],{},[1330,19632,1332],{},[1334,19634,1565],{},[1460,19636,1730],{},[1327,19638,19639,19641],{},[1330,19640,16112],{},[1330,19642,1650],{},[1460,19644,10733],{"mathvariant":1893},[1334,19646,1336],{},[1338,19648,16754],{"encoding":1340}," (proměnná je významná). Při nezamítnutí ",[1115,19651,19653],{"className":19652},[1315],[1317,19654,19655],{"xmlns":1319},[1321,19656,19657,19665],{},[1324,19658,19659],{},[1327,19660,19661,19663],{},[1330,19662,1332],{},[1334,19664,1336],{},[1338,19666,1341],{"encoding":1340}," by proměnná — a s ní spojený regresor — v modelu neměla zůstat.",[16521,19669,19671],{"id":19670},"předpoklady-modelu","Předpoklady modelu",[2638,19673,19674,19691,19724,19730,19733,19736],{},[1207,19675,19676,19677,19690],{},"Závisle proměnná ",[1115,19678,19680],{"className":19679},[1315],[1317,19681,19682],{"xmlns":1319},[1321,19683,19684,19688],{},[1324,19685,19686],{},[1330,19687,6905],{},[1338,19689,6905],{"encoding":1340}," musí být aspoň intervalového typu (ne binární, diskrétní s málo hodnotami apod.) — jinak je na místě logistická regrese.",[1207,19692,19693,19694,19723],{},"Nezávislé proměnné ",[1115,19695,19697],{"className":19696},[1315],[1317,19698,19699],{"xmlns":1319},[1321,19700,19701,19721],{},[1324,19702,19703,19709,19711,19713,19715],{},[1327,19704,19705,19707],{},[1330,19706,6495],{},[1334,19708,1565],{},[1460,19710,1568],{"separator":1121},[1460,19712,1571],{},[1460,19714,1568],{"separator":1121},[1327,19716,19717,19719],{},[1330,19718,6495],{},[1330,19720,1110],{},[1338,19722,16061],{"encoding":1340}," jsou rovněž aspoň intervalového typu, mohou být i alternativní.",[1207,19725,19726,19727,1440],{},"Nezávislé proměnné by mezi sebou neměly být příliš vysoce korelované — ",[1302,19728,19729],{},"multikolinearita",[1207,19731,19732],{},"V datech nesmí být odlehlé či extrémní hodnoty; regresní analýza je na ně citlivá a mohou vážně narušit kvalitu odhadů.",[1207,19734,19735],{},"Proměnné musí být ve vzájemně lineárním vztahu — vícenásobná lineární regrese je založená na Pearsonově koeficientu korelace, takže nelineární vztahy mezi proměnnými zůstanou neodhalené.",[1207,19737,19738,19739,19743],{},"Proměnné mají mít ",[1127,19740,19742],{"className":19741,"dataFsResolvedFilePath":1167,"href":1168},[1130],"normální rozložení","; význam tohoto předpokladu ustupuje do pozadí u dostatečně velkého datového souboru díky centrální limitní větě.",[1110,19745,19746,19747,19750],{},"Normalita se u menšího počtu pozorování ověřuje stejnými testy jako u jiných znaků (viz ",[1127,19748,1494],{"className":19749,"dataFsResolvedFilePath":1193,"href":1194},[1130],") — Shapiro–Wilkovým nebo Kolmogorovovým–Smirnovovým testem — nebo graficky grafem reziduí proti predikovaným hodnotám, kde by body měly být rovnoměrně rozptýlené po obou stranách vodorovné osy.",[16521,19752,19753],{"id":19729},"Multikolinearita",[1110,19755,19756],{},"Multikolinearita vzniká, když vysvětlující proměnné silně závisejí jedna na druhé. Je nežádoucí, protože:",[1204,19758,19759,19762,19765],{},[1207,19760,19761],{},"výsledky regrese jsou pak nespolehlivé,",[1207,19763,19764],{},"zvyšuje pravděpodobnost, že se důležitá proměnná jeví jako statisticky nevýznamná a bude z modelu vyřazena,",[1207,19766,19767],{},"směrodatné odchylky odhadnutých parametrů jsou vysoké, testová kritéria t-testů nízká, p-hodnoty vysoké.",[1110,19769,19770,19771,19774,19775,19798,19799,19817,19818,19834],{},"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 ",[1302,19772,19773],{},"VIF (Variance Inflation Factor)",": hodnoty ",[1115,19776,19778],{"className":19777},[1315],[1317,19779,19780],{"xmlns":1319},[1321,19781,19782,19795],{},[1324,19783,19784,19786,19788,19791,19793],{},[1334,19785,1565],{},[1460,19787,4107],{},[2682,19789,19790],{},"VIF",[1460,19792,4107],{},[1334,19794,9703],{},[1338,19796,19797],{"encoding":1340},"1\u003C\\text{VIF}\u003C5"," jsou varující, ",[1115,19800,19802],{"className":19801},[1315],[1317,19803,19804],{"xmlns":1319},[1321,19805,19806,19814],{},[1324,19807,19808,19810,19812],{},[2682,19809,19790],{},[1460,19811,1462],{},[1334,19813,9703],{},[1338,19815,19816],{"encoding":1340},"\\text{VIF}>5"," (přísněji ",[1115,19819,19821],{"className":19820},[1315],[1317,19822,19823],{"xmlns":1319},[1321,19824,19825,19831],{},[1324,19826,19827,19829],{},[1460,19828,1462],{},[1334,19830,8810],{},[1338,19832,19833],{"encoding":1340},">10",") značí vysokou multikolinearitu.",[1110,19836,19837],{},"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.",[16521,19839,19841],{"id":19840},"další-ukazatele-kvality-modelu","Další ukazatele kvality modelu",[1204,19843,19844,19850,19856],{},[1207,19845,19846,19849],{},[1302,19847,19848],{},"F-test"," — testuje hypotézu, že všechny regresní koeficienty jsou rovny nule, proti alternativě, že aspoň jeden v modelu být má (celková významnost modelu).",[1207,19851,19852,19855],{},[1302,19853,19854],{},"RMSE"," (odmocnina z reziduálního rozptylu) — absolutní měřítko vhodnosti funkce (na rozdíl od indexu determinace, který je relativní); nižší hodnota znamená lepší fit.",[1207,19857,19858,19861,19862,19865],{},[1302,19859,19860],{},"AIC"," (Akaikeho informační kritérium) a ",[1302,19863,19864],{},"BIC"," (Bayesovo informační kritérium) — čím nižší hodnoty obou kritérií, tím lepší model; používají se hlavně při stepwise výběru proměnných.",[16521,19867,16524],{"id":19868},"v-r-2",[1110,19870,19871],{},"Pro vícenásobnou regresi je postup v R rozšířením postupu pro regresní přímku — přibývá výběr proměnných a kontrola multikolinearity:",[3468,19873,19875],{"className":3470,"code":19874,"language":71,"meta":1247,"style":1247},"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",[3244,19876,19877,19903,19947,19973,19983,19987,19998,20009,20013,20023,20033,20037,20047,20057,20062],{"__ignoreMap":1247},[1115,19878,19879,19882,19884,19887,19889,19892,19894,19897,19899,19901],{"class":3476,"line":10},[1115,19880,19881],{"class":3479},"data",[1115,19883,3484],{"class":3483},[1115,19885,19886],{"class":3487}," read.table",[1115,19888,1647],{"class":3491},[1115,19890,19891],{"class":3615},"\"4_4.txt\"",[1115,19893,1568],{"class":3483},[1115,19895,19896],{"class":3479}," header",[1115,19898,3572],{"class":3483},[1115,19900,3585],{"class":3499},[1115,19902,3676],{"class":3491},[1115,19904,19905,19908,19910,19912,19914,19916,19918,19921,19923,19926,19928,19931,19933,19936,19938,19941,19943,19945],{"class":3476,"line":27},[1115,19906,19907],{"class":3479},"model_plny",[1115,19909,3484],{"class":3483},[1115,19911,16625],{"class":3487},[1115,19913,1647],{"class":3491},[1115,19915,6905],{"class":3479},[1115,19917,16632],{"class":3483},[1115,19919,19920],{"class":3479}," x1",[1115,19922,18289],{"class":3483},[1115,19924,19925],{"class":3479}," x2",[1115,19927,18289],{"class":3483},[1115,19929,19930],{"class":3479}," x3",[1115,19932,18289],{"class":3483},[1115,19934,19935],{"class":3479}," x4",[1115,19937,1568],{"class":3483},[1115,19939,19940],{"class":3479}," data",[1115,19942,3572],{"class":3483},[1115,19944,19940],{"class":3479},[1115,19946,3676],{"class":3491},[1115,19948,19949,19952,19954,19957,19959,19961,19963,19966,19968,19971],{"class":3476,"line":148},[1115,19950,19951],{"class":3479},"model_krok",[1115,19953,3484],{"class":3483},[1115,19955,19956],{"class":3487}," step",[1115,19958,1647],{"class":3491},[1115,19960,19907],{"class":3479},[1115,19962,1568],{"class":3483},[1115,19964,19965],{"class":3479}," direction",[1115,19967,3572],{"class":3483},[1115,19969,19970],{"class":3615}," \"both\"",[1115,19972,3676],{"class":3491},[1115,19974,19975,19977,19979,19981],{"class":3476,"line":111},[1115,19976,1271],{"class":3487},[1115,19978,1647],{"class":3491},[1115,19980,19951],{"class":3479},[1115,19982,3676],{"class":3491},[1115,19984,19985],{"class":3476,"line":96},[1115,19986,9818],{"emptyLinePlaceholder":1256},[1115,19988,19989,19991,19993,19996],{"class":3476,"line":89},[1115,19990,17170],{"class":3483},[1115,19992,1647],{"class":3491},[1115,19994,19995],{"class":3479},"car",[1115,19997,3676],{"class":3491},[1115,19999,20000,20003,20005,20007],{"class":3476,"line":82},[1115,20001,20002],{"class":3487},"vif",[1115,20004,1647],{"class":3491},[1115,20006,19951],{"class":3479},[1115,20008,3676],{"class":3491},[1115,20010,20011],{"class":3476,"line":75},[1115,20012,9818],{"emptyLinePlaceholder":1256},[1115,20014,20015,20017,20019,20021],{"class":3476,"line":3666},[1115,20016,17170],{"class":3483},[1115,20018,1647],{"class":3491},[1115,20020,17175],{"class":3479},[1115,20022,3676],{"class":3491},[1115,20024,20025,20027,20029,20031],{"class":3476,"line":72},[1115,20026,17182],{"class":3487},[1115,20028,1647],{"class":3491},[1115,20030,19951],{"class":3479},[1115,20032,3676],{"class":3491},[1115,20034,20035],{"class":3476,"line":25},[1115,20036,9818],{"emptyLinePlaceholder":1256},[1115,20038,20039,20041,20043,20045],{"class":3476,"line":65},[1115,20040,17170],{"class":3483},[1115,20042,1647],{"class":3491},[1115,20044,17265],{"class":3479},[1115,20046,3676],{"class":3491},[1115,20048,20049,20051,20053,20055],{"class":3476,"line":63},[1115,20050,17272],{"class":3487},[1115,20052,1647],{"class":3491},[1115,20054,19951],{"class":3479},[1115,20056,3676],{"class":3491},[1115,20058,20060],{"class":3476,"line":20059},14,[1115,20061,9818],{"emptyLinePlaceholder":1256},[1115,20063,20064,20066,20068,20070,20072,20074],{"class":3476,"line":60},[1115,20065,17350],{"class":3487},[1115,20067,1647],{"class":3491},[1115,20069,16818],{"class":3487},[1115,20071,1647],{"class":3491},[1115,20073,19951],{"class":3479},[1115,20075,9270],{"class":3491},[1110,20077,20078,20080,20081,20084],{},[3244,20079,15895],{}," provádí stepwise výběr podle AIC, ",[3244,20082,20083],{},"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.",[1103,20086,20088,20095,20098,20101],{"className":20087,"dataCallout":3251},[1106,3250],[1110,20089,20091,20094],{"className":20090},[1113],[1115,20092],{"className":20093,"ariaHidden":1121},[1118,3258,1120],"Příklad: Vícenásobná regrese",[1110,20096,20097],{},"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.",[1110,20099,20100],{},"Postup: odhad plného modelu → stepwise analýza podle AIC → ověření předpokladů.",[1110,20102,20103,20104,20107,20108,20110,20111,20114],{},"Diagnostika odhaleného modelu ukázala tři problémy: (1) ",[1302,20105,20106],{},"nelinearita"," — mezi některými vysvětlujícími proměnnými a cenou je zjevně jiný než lineární vztah, řešením je zkusit u nich druhou mocninu; (2) ",[1302,20109,19729],{}," mezi dvojicí proměnných popisujících vzdálenost (k silnici a ke spalovně) — doporučeno jednu z nich vynechat; (3) ",[1302,20112,20113],{},"odlehlá pozorování"," — vhodné je provést ještě test a případně je vyřadit. Výsledný model obsahoval i nevýznamné proměnné, jako celek však byl statisticky významný s přibližně průměrným indexem determinace; dalšího zlepšení šlo dosáhnout snížením AIC pomocí stepwise regrese.",[1136,20116,6183],{"id":6182},[1103,20118,20120,20127],{"className":20119,"dataCallout":6188},[1106,6187],[1110,20121,20123,20126],{"className":20122},[1113],[1115,20124],{"className":20125,"ariaHidden":1121},[1118,6195,1120],"Koeficient korelace jen pro přímku",[1110,20128,20129,20130,20186,20187,20204,20205,20225,20226,5516,20239,1440],{},"Vzorec ",[1115,20131,20133],{"className":20132},[1315],[1317,20134,20135],{"xmlns":1319},[1321,20136,20137,20183],{},[1324,20138,20139,20149,20151,20161,20163],{},[1327,20140,20141,20143],{},[1330,20142,71],{},[1324,20144,20145,20147],{},[1330,20146,6495],{},[1330,20148,6905],{},[1460,20150,1754],{},[1327,20152,20153,20155],{},[1330,20154,1626],{},[1324,20156,20157,20159],{},[1330,20158,6495],{},[1330,20160,6905],{},[1330,20162,4379],{"mathvariant":1893},[4228,20164,20165],{},[1324,20166,20167,20175],{},[3127,20168,20169,20171,20173],{},[1330,20170,1626],{},[1330,20172,6495],{},[1334,20174,1360],{},[3127,20176,20177,20179,20181],{},[1330,20178,1626],{},[1330,20180,6905],{},[1334,20182,1360],{},[1338,20184,20185],{"encoding":1340},"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 ",[1115,20188,20190],{"className":20189},[1315],[1317,20191,20192],{"xmlns":1319},[1321,20193,20194,20202],{},[1324,20195,20196],{},[1353,20197,20198,20200],{},[1330,20199,10000],{},[1334,20201,1360],{},[1338,20203,15799],{"encoding":1340},", případně obecným indexem korelace ",[1115,20206,20208],{"className":20207},[1315],[1317,20209,20210],{"xmlns":1319},[1321,20211,20212,20222],{},[1324,20213,20214],{},[4228,20215,20216],{},[1353,20217,20218,20220],{},[1330,20219,10000],{},[1334,20221,1360],{},[1338,20223,20224],{"encoding":1340},"\\sqrt{R^2}"," — ne koeficientem korelace mezi ",[1115,20227,20229],{"className":20228},[1315],[1317,20230,20231],{"xmlns":1319},[1321,20232,20233,20237],{},[1324,20234,20235],{},[1330,20236,6495],{},[1338,20238,6495],{"encoding":1340},[1115,20240,20242],{"className":20241},[1315],[1317,20243,20244],{"xmlns":1319},[1321,20245,20246,20250],{},[1324,20247,20248],{},[1330,20249,6905],{},[1338,20251,6905],{"encoding":1340},[1103,20253,20255,20262],{"className":20254,"dataCallout":6188},[1106,6187],[1110,20256,20258,20261],{"className":20257},[1113],[1115,20259],{"className":20260,"ariaHidden":1121},[1118,6195,1120],"Významný F-test, nevýznamné t-testy",[1110,20263,20264],{},"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.",[1103,20266,20268,20275],{"className":20267,"dataCallout":6188},[1106,6187],[1110,20269,20271,20274],{"className":20270},[1113],[1115,20272],{"className":20273,"ariaHidden":1121},[1118,6195,1120],"Durbin-Watsonova statistika mimo okolí 2",[1110,20276,20277],{},"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.",[1103,20279,20281,20288],{"className":20280,"dataCallout":6188},[1106,6187],[1110,20282,20284,20287],{"className":20283},[1113],[1115,20285],{"className":20286,"ariaHidden":1121},[1118,6195,1120],"Nízký počet pozorování při stepwise výběru",[1110,20289,20290],{},"Metoda ENTER potřebuje aspoň 20 pozorování na proměnnou, stepwise regrese aspoň 40. Při menším vzorku jsou výsledky výběru proměnných nespolehlivé bez ohledu na to, jak hezky vychází AIC.",[1136,20292,1202],{"id":1201},[1204,20294,20295,20300,20305,20310,20315,20320,20325],{},[1207,20296,20297],{},[1127,20298,1133],{"className":20299,"dataFsResolvedFilePath":1131,"href":1132},[1130],[1207,20301,20302],{},[1127,20303,1169],{"className":20304,"dataFsResolvedFilePath":1167,"href":1168},[1130],[1207,20306,20307],{},[1127,20308,1182],{"className":20309,"dataFsResolvedFilePath":1180,"href":1181},[1130],[1207,20311,20312],{},[1127,20313,1195],{"className":20314,"dataFsResolvedFilePath":1193,"href":1194},[1130],[1207,20316,20317],{},[1127,20318,1277],{"className":20319,"dataFsResolvedFilePath":10868,"href":10869},[1130],[1207,20321,20322],{},[1127,20323,6407],{"className":20324,"dataFsResolvedFilePath":6405,"href":6406},[1130],[1207,20326,20327],{},[1127,20328,6413],{"className":20329,"dataFsResolvedFilePath":1232,"href":1233},[1130],[1136,20331,1237],{"id":934},[1110,20333,1240,20334,1245],{},[1242,20335,1244],{},[6421,20337,20338],{},"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.",[1207,20397,20398,20399,2725,20425,5516,20451,1440],{},"Regulace měřením (spojitá veličina s normálním rozdělením): diagramy ",[1115,20400,20402],{"className":20401},[1315],[1317,20403,20404],{"xmlns":1319},[1321,20405,20406,20422],{},[1324,20407,20408,20410,20416,20418,20420],{},[1460,20409,1647],{"stretchy":1646},[2496,20411,20412,20414],{"accent":1121},[1330,20413,6495],{},[1460,20415,11235],{},[1460,20417,1568],{"separator":1121},[1330,20419,10000],{},[1460,20421,1658],{"stretchy":1646},[1338,20423,20424],{"encoding":1340},"(\\bar{x}, R)",[1115,20426,20428],{"className":20427},[1315],[1317,20429,20430],{"xmlns":1319},[1321,20431,20432,20448],{},[1324,20433,20434,20436,20442,20444,20446],{},[1460,20435,1647],{"stretchy":1646},[2496,20437,20438,20440],{"accent":1121},[1330,20439,6495],{},[1460,20441,11235],{},[1460,20443,1568],{"separator":1121},[1330,20445,1626],{},[1460,20447,1658],{"stretchy":1646},[1338,20449,20450],{"encoding":1340},"(\\bar{x}, s)",[1115,20452,20454],{"className":20453},[1315],[1317,20455,20456],{"xmlns":1319},[1321,20457,20458,20487],{},[1324,20459,20460,20462,20468,20470,20485],{},[1460,20461,1647],{"stretchy":1646},[1327,20463,20464,20466],{},[1330,20465,6495],{},[1330,20467,1650],{},[1460,20469,1568],{"separator":1121},[1327,20471,20472,20474],{},[1330,20473,10000],{},[1324,20475,20476,20478,20481,20483],{},[1330,20477,7035],{},[1330,20479,20480],{},"l",[1460,20482,1568],{"separator":1121},[1330,20484,1650],{},[1460,20486,1658],{"stretchy":1646},[1338,20488,20489],{"encoding":1340},"(x_i, R_{kl,i})",[1207,20491,20492,20493,20506,20507,20520,20521,20537,20538,20551],{},"Regulace srovnáváním (diskrétní veličina): počet neshod ",[1115,20494,20496],{"className":20495},[1315],[1317,20497,20498],{"xmlns":1319},[1321,20499,20500,20504],{},[1324,20501,20502],{},[1330,20503,3494],{},[1338,20505,3494],{"encoding":1340}," (konstantní rozsah) a ",[1115,20508,20510],{"className":20509},[1315],[1317,20511,20512],{"xmlns":1319},[1321,20513,20514,20518],{},[1324,20515,20516],{},[1330,20517,11304],{},[1338,20519,11304],{"encoding":1340}," (nekonstantní rozsah), počet neshodných produktů ",[1115,20522,20524],{"className":20523},[1315],[1317,20525,20526],{"xmlns":1319},[1321,20527,20528,20534],{},[1324,20529,20530,20532],{},[1330,20531,1458],{},[1330,20533,1110],{},[1338,20535,20536],{"encoding":1340},"np"," (konstantní rozsah) a jejich podíl ",[1115,20539,20541],{"className":20540},[1315],[1317,20542,20543],{"xmlns":1319},[1321,20544,20545,20549],{},[1324,20546,20547],{},[1330,20548,1110],{},[1338,20550,1110],{"encoding":1340}," (nekonstantní rozsah).",[1207,20553,20554],{},"Podskupiny s vymezitelnou příčinou se po jejím odstranění z výpočtu vyřadí a meze se přepočítají, dokud jsou všechny body uvnitř mezí.",[1207,20556,20557,20558,2725,20577,2725,20599,2725,20621,20645,20646,20667],{},"Indexy způsobilosti ",[1115,20559,20561],{"className":20560},[1315],[1317,20562,20563],{"xmlns":1319},[1321,20564,20565,20574],{},[1324,20566,20567],{},[1327,20568,20569,20572],{},[1330,20570,20571],{},"C",[1330,20573,1110],{},[1338,20575,20576],{"encoding":1340},"C_p",[1115,20578,20580],{"className":20579},[1315],[1317,20581,20582],{"xmlns":1319},[1321,20583,20584,20596],{},[1324,20585,20586],{},[1327,20587,20588,20590],{},[1330,20589,20571],{},[1324,20591,20592,20594],{},[1330,20593,1110],{},[1330,20595,7035],{},[1338,20597,20598],{"encoding":1340},"C_{pk}",[1115,20600,20602],{"className":20601},[1315],[1317,20603,20604],{"xmlns":1319},[1321,20605,20606,20618],{},[1324,20607,20608],{},[1327,20609,20610,20612],{},[1330,20611,20571],{},[1324,20613,20614,20616],{},[1330,20615,1110],{},[1330,20617,4246],{},[1338,20619,20620],{"encoding":1340},"C_{pm}",[1115,20622,20624],{"className":20623},[1315],[1317,20625,20626],{"xmlns":1319},[1321,20627,20628,20642],{},[1324,20629,20630],{},[1327,20631,20632,20634],{},[1330,20633,20571],{},[1324,20635,20636,20638,20640],{},[1330,20637,1110],{},[1330,20639,4246],{},[1330,20641,7035],{},[1338,20643,20644],{"encoding":1340},"C_{pmk}"," posuzují, zda statisticky zvládnutý proces vyhovuje tolerančním mezím; ",[1115,20647,20649],{"className":20648},[1315],[1317,20650,20651],{"xmlns":1319},[1321,20652,20653,20665],{},[1324,20654,20655],{},[1327,20656,20657,20659],{},[1330,20658,20571],{},[1324,20660,20661,20663],{},[1330,20662,1110],{},[1330,20664,7035],{},[1338,20666,20598],{"encoding":1340}," navíc zohledňuje vychýlení střední hodnoty.",[1207,20669,20670,20671,1440],{},"V R diagramy i indexy počítá balíček ",[3244,20672,360],{},[1136,20674,20676],{"id":20675},"statistická-regulace-procesu","Statistická regulace procesu",[1110,20678,20679,20680,20682,20683,1440],{},"Tradiční zabezpečování jakosti kontroluje výrobky až po jejich vyrobení, což je neekonomické. ",[1302,20681,20676],{}," 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 ",[1302,20684,20685],{},"statisticky zvládnutém stavu",[1110,20687,20688,20689,20692],{},"Teorie regulace vychází z ",[1302,20690,20691],{},"variability"," procesu, kterou způsobují dva druhy příčin:",[1141,20694,20695,20707],{},[1144,20696,20697],{},[1147,20698,20699,20701,20704],{},[1150,20700],{},[1150,20702,20703],{},"Náhodné příčiny",[1150,20705,20706],{},"Vymezitelné příčiny",[1157,20708,20709,20720,20731],{},[1147,20710,20711,20714,20717],{},[1162,20712,20713],{},"Povaha",[1162,20715,20716],{},"široká skupina neidentifikovatelných vlivů, každý přispívá k variabilitě malou měrou",[1162,20718,20719],{},"vlivy, které za běžných podmínek na proces nepůsobí; vyvolají nepřirozené kolísání údajů",[1147,20721,20722,20725,20728],{},[1162,20723,20724],{},"Stav procesu",[1162,20726,20727],{},"ustálený, jakost výstupů je předvídatelná, není nutné zasahovat — statisticky zvládnutý",[1162,20729,20730],{},"jakost výstupů není předvídatelná, je nutné zasáhnout — proces není statisticky zvládnutý",[1147,20732,20733,20736,20739],{},[1162,20734,20735],{},"Příklady",[1162,20737,20738],{},"psychický stav pracovníka, chvění stroje, teplota ovzduší",[1162,20740,20741],{},"změna materiálu, nezaškolená obsluha",[1110,20743,20744,20745,20748,20749,20752],{},"Vymezitelné příčiny jsou ",[1302,20746,20747],{},"sporadické"," (vznikají náhle, změny trvají krátce) nebo ",[1302,20750,20751],{},"přetrvávající"," (trvají stále nebo se mění).",[1110,20754,20755],{},[4158,20756],{"alt":20757,"className":20758,"src":20759},"mask-ilu-pricin-variability",[1130,4162],"\u002Fwiki-assets\u002Fmask-ilu-pricin-variability.png",[1110,20761,20762],{},"Regulace probíhá ve třech fázích:",[2638,20764,20765,20775,20781],{},[1207,20766,20767,20770,20771,20774],{},[1302,20768,20769],{},"Fáze přípravná"," — stanoví se sledované znaky jakosti (rozměr, hmotnost, počet vad…), délka časového intervalu mezi měřeními, ",[1302,20772,20773],{},"logická podskupina"," (skupina měření, v níž se předpokládá působení pouze náhodných příčin), typ regulačního diagramu a místa kontroly v procesu.",[1207,20776,20777,20780],{},[1302,20778,20779],{},"Fáze zabezpečování statistické zvládnutosti"," — pomocí regulačních diagramů se identifikují vymezitelné příčiny a odstraní se jejich působení.",[1207,20782,20783,20786],{},[1302,20784,20785],{},"Fáze analýzy a zabezpečení způsobilosti"," — zkoumá se, zda statisticky zvládnutý proces vyhovuje požadavkům zákazníka; k tomu slouží indexy způsobilosti (níže).",[1136,20788,20790],{"id":20789},"princip-regulačního-diagramu","Princip regulačního diagramu",[1110,20792,20793,20796],{},[1302,20794,20795],{},"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.",[1204,20798,20799,20805,20811],{},[1207,20800,20801,20804],{},[1302,20802,20803],{},"CL"," — střední přímka, odpovídá požadované (referenční) hodnotě použité charakteristiky,",[1207,20806,20807,20810],{},[1302,20808,20809],{},"UCL"," — horní akční regulační mez,",[1207,20812,20813,20816],{},[1302,20814,20815],{},"LCL"," — dolní akční regulační mez.",[1110,20818,20819],{},"Akční meze vymezují pásmo působení pouze náhodných příčin variability.",[1110,20821,20822],{},[4158,20823],{"alt":20824,"className":20825,"src":20826},"mask-rd-schema",[1130,4162],"\u002Fwiki-assets\u002Fmask-rd-schema.png",[1110,20828,20829,20832],{},[1302,20830,20831],{},"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.",[1110,20834,20835,20836,20839,20840,20843],{},"Podle charakteru regulované veličiny se diagramy dělí na diagramy pro ",[1302,20837,20838],{},"regulaci měřením"," (regulovaná veličina je spojitá náhodná veličina) a pro ",[1302,20841,20842],{},"regulaci srovnáváním"," (diskrétní náhodná veličina).",[1110,20845,20846],{},"Postup při konstrukci regulačního diagramu:",[2638,20848,20849,20852,20855,20858,20861,20864,20867,20870,20873],{},[1207,20850,20851],{},"volba regulované veličiny,",[1207,20853,20854],{},"sběr a záznam dat,",[1207,20856,20857],{},"ověření požadovaných předpokladů o datech,",[1207,20859,20860],{},"volba rozsahu logických podskupin,",[1207,20862,20863],{},"volba vhodného regulačního diagramu,",[1207,20865,20866],{},"výpočet hodnot zvoleného testového kritéria pro jednotlivé výběry,",[1207,20868,20869],{},"ověření a zajištění statistické zvládnutosti procesu,",[1207,20871,20872],{},"ověření způsobilosti procesu,",[1207,20874,20875],{},"vlastní regulace procesu.",[1136,20877,20879],{"id":20878},"regulace-měřením","Regulace měřením",[1110,20881,20882],{},"Diagramy pro regulaci měřením se používají, když je regulovaná veličina měřitelná. Požaduje se, aby:",[1204,20884,20885,20888],{},[1207,20886,20887],{},"jednotlivá měření byla vzájemně nezávislá,",[1207,20889,20890,20891,20904,20905,20918,20919,20932,20933,20946],{},"regulovaná veličina byla spojitá náhodná veličina s normálním rozdělením se střední hodnotou ",[1115,20892,20894],{"className":20893},[1315],[1317,20895,20896],{"xmlns":1319},[1321,20897,20898,20902],{},[1324,20899,20900],{},[1330,20901,6666],{},[1338,20903,8573],{"encoding":1340}," a směrodatnou odchylkou ",[1115,20906,20908],{"className":20907},[1315],[1317,20909,20910],{"xmlns":1319},[1321,20911,20912,20916],{},[1324,20913,20914],{},[1330,20915,6674],{},[1338,20917,6706],{"encoding":1340}," — tyto dva parametry charakterizují statistickou stabilitu procesu; ",[1115,20920,20922],{"className":20921},[1315],[1317,20923,20924],{"xmlns":1319},[1321,20925,20926,20930],{},[1324,20927,20928],{},[1330,20929,6666],{},[1338,20931,8573],{"encoding":1340}," je hodnota, na niž je proces nastaven, ",[1115,20934,20936],{"className":20935},[1315],[1317,20937,20938],{"xmlns":1319},[1321,20939,20940,20944],{},[1324,20941,20942],{},[1330,20943,6674],{},[1338,20945,6706],{"encoding":1340}," charakterizuje jeho přesnost.",[1110,20948,20949,20950,2725,20975,5516,21000,21037],{},"Jsou-li předpoklady splněny, volí se diagramy, které současně sledují stabilitu polohy i stabilitu rozptylu: ",[1115,20951,20953],{"className":20952},[1315],[1317,20954,20955],{"xmlns":1319},[1321,20956,20957,20973],{},[1324,20958,20959,20961,20967,20969,20971],{},[1460,20960,1647],{"stretchy":1646},[2496,20962,20963,20965],{"accent":1121},[1330,20964,6495],{},[1460,20966,11235],{},[1460,20968,1568],{"separator":1121},[1330,20970,10000],{},[1460,20972,1658],{"stretchy":1646},[1338,20974,20424],{"encoding":1340},[1115,20976,20978],{"className":20977},[1315],[1317,20979,20980],{"xmlns":1319},[1321,20981,20982,20998],{},[1324,20983,20984,20986,20992,20994,20996],{},[1460,20985,1647],{"stretchy":1646},[2496,20987,20988,20990],{"accent":1121},[1330,20989,6495],{},[1460,20991,11235],{},[1460,20993,1568],{"separator":1121},[1330,20995,1626],{},[1460,20997,1658],{"stretchy":1646},[1338,20999,20450],{"encoding":1340},[1115,21001,21003],{"className":21002},[1315],[1317,21004,21005],{"xmlns":1319},[1321,21006,21007,21035],{},[1324,21008,21009,21011,21017,21019,21033],{},[1460,21010,1647],{"stretchy":1646},[1327,21012,21013,21015],{},[1330,21014,6495],{},[1330,21016,1650],{},[1460,21018,1568],{"separator":1121},[1327,21020,21021,21023],{},[1330,21022,10000],{},[1324,21024,21025,21027,21029,21031],{},[1330,21026,7035],{},[1330,21028,20480],{},[1460,21030,1568],{"separator":1121},[1330,21032,1650],{},[1460,21034,1658],{"stretchy":1646},[1338,21036,20489],{"encoding":1340},". Výsledkem jsou vždy dva diagramy.",[16521,21039,21041,21042],{"id":21040},"diagram-xˉrbarx-r","Diagram ",[1115,21043,21045],{"className":21044},[1315],[1317,21046,21047],{"xmlns":1319},[1321,21048,21049,21065],{},[1324,21050,21051,21053,21059,21061,21063],{},[1460,21052,1647],{"stretchy":1646},[2496,21054,21055,21057],{"accent":1121},[1330,21056,6495],{},[1460,21058,11235],{},[1460,21060,1568],{"separator":1121},[1330,21062,10000],{},[1460,21064,1658],{"stretchy":1646},[1338,21066,20424],{"encoding":1340},[1110,21068,21069,21070,21092,21093,21111],{},"Regulované veličiny jsou výběrové průměry ",[1115,21071,21073],{"className":21072},[1315],[1317,21074,21075],{"xmlns":1319},[1321,21076,21077,21089],{},[1324,21078,21079],{},[1327,21080,21081,21087],{},[2496,21082,21083,21085],{"accent":1121},[1330,21084,6495],{},[1460,21086,11235],{},[1330,21088,1650],{},[1338,21090,21091],{"encoding":1340},"\\bar{x}_i"," a výběrová rozpětí ",[1115,21094,21096],{"className":21095},[1315],[1317,21097,21098],{"xmlns":1319},[1321,21099,21100,21108],{},[1324,21101,21102],{},[1327,21103,21104,21106],{},[1330,21105,10000],{},[1330,21107,1650],{},[1338,21109,21110],{"encoding":1340},"R_i"," v logických podskupinách:",[1115,21113,21115],{"className":21114},[1315],[1317,21116,21117],{"xmlns":1319,"display":1736},[1321,21118,21119,21220],{},[1324,21120,21121,21131,21133,21139,21153,21163,21165,21167,21173,21175,21186,21196,21198,21208,21218],{},[1327,21122,21123,21129],{},[2496,21124,21125,21127],{"accent":1121},[1330,21126,6495],{},[1460,21128,11235],{},[1330,21130,1650],{},[1460,21132,1754],{},[2512,21134,21135,21137],{},[1334,21136,1565],{},[1330,21138,1458],{},[1756,21140,21141,21143,21151],{},[1460,21142,1760],{},[1324,21144,21145,21147,21149],{},[1330,21146,1655],{},[1460,21148,1754],{},[1334,21150,1565],{},[1330,21152,1458],{},[1327,21154,21155,21157],{},[1330,21156,6495],{},[1324,21158,21159,21161],{},[1330,21160,1650],{},[1330,21162,1655],{},[1460,21164,1568],{"separator":1121},[1784,21166],{"width":1786},[1327,21168,21169,21171],{},[1330,21170,10000],{},[1330,21172,1650],{},[1460,21174,1754],{},[21176,21177,21178,21184],"munder",{},[1324,21179,21180,21182],{},[1330,21181,11495],{},[1460,21183,4266],{},[1330,21185,1655],{},[1327,21187,21188,21190],{},[1330,21189,6495],{},[1324,21191,21192,21194],{},[1330,21193,1650],{},[1330,21195,1655],{},[1460,21197,2838],{},[21176,21199,21200,21206],{},[1324,21201,21202,21204],{},[1330,21203,4263],{},[1460,21205,4266],{},[1330,21207,1655],{},[1327,21209,21210,21212],{},[1330,21211,6495],{},[1324,21213,21214,21216],{},[1330,21215,1650],{},[1330,21217,1655],{},[1330,21219,1440],{"mathvariant":1893},[1338,21221,21222],{"encoding":1340},"\\bar{x}_i = \\frac{1}{n}\\sum_{j=1}^n x_{ij}, \\qquad R_i = \\max_j x_{ij} - \\min_j x_{ij}.",[1110,21224,21225],{},"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.",[1110,21227,21228,21229,21255,21256,21269,21270,5516,21291,21308,21309,21322,21323,21341,21342,1440],{},"Data se zapisují do tabulky: řádek ",[1115,21230,21232],{"className":21231},[1315],[1317,21233,21234],{"xmlns":1319},[1321,21235,21236,21252],{},[1324,21237,21238,21240,21242,21244,21246,21248,21250],{},[1330,21239,1650],{},[1460,21241,1754],{},[1334,21243,1565],{},[1460,21245,1568],{"separator":1121},[1460,21247,1571],{},[1460,21249,1568],{"separator":1121},[1330,21251,7035],{},[1338,21253,21254],{"encoding":1340},"i = 1, \\dots, k"," je logická podskupina v pořadí, v jakém byla získána, sloupce obsahují ",[1115,21257,21259],{"className":21258},[1315],[1317,21260,21261],{"xmlns":1319},[1321,21262,21263,21267],{},[1324,21264,21265],{},[1330,21266,1458],{},[1338,21268,1458],{"encoding":1340}," naměřených hodnot a poslední dva sloupce ",[1115,21271,21273],{"className":21272},[1315],[1317,21274,21275],{"xmlns":1319},[1321,21276,21277,21289],{},[1324,21278,21279],{},[1327,21280,21281,21287],{},[2496,21282,21283,21285],{"accent":1121},[1330,21284,6495],{},[1460,21286,11235],{},[1330,21288,1650],{},[1338,21290,21091],{"encoding":1340},[1115,21292,21294],{"className":21293},[1315],[1317,21295,21296],{"xmlns":1319},[1321,21297,21298,21306],{},[1324,21299,21300],{},[1327,21301,21302,21304],{},[1330,21303,10000],{},[1330,21305,1650],{},[1338,21307,21110],{"encoding":1340},". Pro sestrojení diagramu je potřeba aspoň 20 podskupin. Nejprve se určí diagram ",[1115,21310,21312],{"className":21311},[1315],[1317,21313,21314],{"xmlns":1319},[1321,21315,21316,21320],{},[1324,21317,21318],{},[1330,21319,10000],{},[1338,21321,10000],{"encoding":1340},", potom diagram ",[1115,21324,21326],{"className":21325},[1315],[1317,21327,21328],{"xmlns":1319},[1321,21329,21330,21338],{},[1324,21331,21332],{},[2496,21333,21334,21336],{"accent":1121},[1330,21335,6495],{},[1460,21337,11235],{},[1338,21339,21340],{"encoding":1340},"\\bar{x}"," — u obou střední přímka a akční meze. V R se diagramy konstruují funkcí ",[3244,21343,21344],{},"qcc()",[1103,21346,21348,21355],{"className":21347,"dataCallout":3251},[1106,3250],[1110,21349,21351,21354],{"className":21350},[1113],[1115,21352],{"className":21353,"ariaHidden":1121},[1118,3258,1120],"Příklad: kontrola rozměru dílu ve 20 logických podskupinách",[1110,21356,21357,21358,21371,21372,2725,21390,21408,21409,1440],{},"Naměřená data znaku jakosti ",[1115,21359,21361],{"className":21360},[1315],[1317,21362,21363],{"xmlns":1319},[1321,21364,21365,21369],{},[1324,21366,21367],{},[1330,21368,6507],{},[1338,21370,6507],{"encoding":1340}," byla získána ve 20 logických podskupinách po 4 měřeních (",[1115,21373,21375],{"className":21374},[1315],[1317,21376,21377],{"xmlns":1319},[1321,21378,21379,21387],{},[1324,21380,21381,21383,21385],{},[1330,21382,7035],{},[1460,21384,1754],{},[1334,21386,3820],{},[1338,21388,21389],{"encoding":1340},"k=20",[1115,21391,21393],{"className":21392},[1315],[1317,21394,21395],{"xmlns":1319},[1321,21396,21397,21405],{},[1324,21398,21399,21401,21403],{},[1330,21400,1458],{},[1460,21402,1754],{},[1334,21404,3316],{},[1338,21406,21407],{"encoding":1340},"n=4","); znak je měřitelný a má normální rozdělení. Sestrojte regulační diagram ",[1115,21410,21412],{"className":21411},[1315],[1317,21413,21414],{"xmlns":1319},[1321,21415,21416,21432],{},[1324,21417,21418,21420,21426,21428,21430],{},[1460,21419,1647],{"stretchy":1646},[2496,21421,21422,21424],{"accent":1121},[1330,21423,6495],{},[1460,21425,11235],{},[1460,21427,1568],{"separator":1121},[1330,21429,10000],{},[1460,21431,1658],{"stretchy":1646},[1338,21433,20424],{"encoding":1340},[1141,21435,21436,21551],{},[1144,21437,21438],{},[1147,21439,21440,21455,21479,21503,21527],{},[1150,21441,21442],{},[1115,21443,21445],{"className":21444},[1315],[1317,21446,21447],{"xmlns":1319},[1321,21448,21449,21453],{},[1324,21450,21451],{},[1330,21452,1650],{},[1338,21454,1650],{"encoding":1340},[1150,21456,21457],{},[1115,21458,21460],{"className":21459},[1315],[1317,21461,21462],{"xmlns":1319},[1321,21463,21464,21476],{},[1324,21465,21466],{},[1327,21467,21468,21470],{},[1330,21469,6495],{},[1324,21471,21472,21474],{},[1330,21473,1650],{},[1334,21475,1565],{},[1338,21477,21478],{"encoding":1340},"x_{i1}",[1150,21480,21481],{},[1115,21482,21484],{"className":21483},[1315],[1317,21485,21486],{"xmlns":1319},[1321,21487,21488,21500],{},[1324,21489,21490],{},[1327,21491,21492,21494],{},[1330,21493,6495],{},[1324,21495,21496,21498],{},[1330,21497,1650],{},[1334,21499,1360],{},[1338,21501,21502],{"encoding":1340},"x_{i2}",[1150,21504,21505],{},[1115,21506,21508],{"className":21507},[1315],[1317,21509,21510],{"xmlns":1319},[1321,21511,21512,21524],{},[1324,21513,21514],{},[1327,21515,21516,21518],{},[1330,21517,6495],{},[1324,21519,21520,21522],{},[1330,21521,1650],{},[1334,21523,3366],{},[1338,21525,21526],{"encoding":1340},"x_{i3}",[1150,21528,21529],{},[1115,21530,21532],{"className":21531},[1315],[1317,21533,21534],{"xmlns":1319},[1321,21535,21536,21548],{},[1324,21537,21538],{},[1327,21539,21540,21542],{},[1330,21541,6495],{},[1324,21543,21544,21546],{},[1330,21545,1650],{},[1334,21547,3316],{},[1338,21549,21550],{"encoding":1340},"x_{i4}",[1157,21552,21553,21567,21582,21598,21613,21625,21639,21651,21664],{},[1147,21554,21555,21557,21560,21563,21565],{},[1162,21556,1565],{},[1162,21558,21559],{},"106",[1162,21561,21562],{},"98",[1162,21564,13861],{},[1162,21566,13861],{},[1147,21568,21569,21571,21574,21577,21580],{},[1162,21570,1360],{},[1162,21572,21573],{},"95",[1162,21575,21576],{},"94",[1162,21578,21579],{},"108",[1162,21581,5899],{},[1147,21583,21584,21586,21589,21592,21595],{},[1162,21585,3366],{},[1162,21587,21588],{},"122",[1162,21590,21591],{},"105",[1162,21593,21594],{},"103",[1162,21596,21597],{},"133",[1147,21599,21600,21602,21605,21607,21610],{},[1162,21601,3316],{},[1162,21603,21604],{},"113",[1162,21606,3338],{},[1162,21608,21609],{},"128",[1162,21611,21612],{},"135",[1147,21614,21615,21617,21619,21621,21623],{},[1162,21616,9703],{},[1162,21618,13861],{},[1162,21620,5899],{},[1162,21622,21594],{},[1162,21624,5899],{},[1147,21626,21627,21629,21631,21633,21636],{},[1162,21628,3739],{},[1162,21630,21562],{},[1162,21632,21594],{},[1162,21634,21635],{},"97",[1162,21637,21638],{},"99",[1147,21640,21641,21643,21645,21647,21649],{},[1162,21642,1571],{},[1162,21644,1571],{},[1162,21646,1571],{},[1162,21648,1571],{},[1162,21650,1571],{},[1147,21652,21653,21655,21657,21659,21662],{},[1162,21654,14495],{},[1162,21656,21609],{},[1162,21658,21597],{},[1162,21660,21661],{},"120",[1162,21663,14523],{},[1147,21665,21666,21668,21670,21672,21674],{},[1162,21667,3820],{},[1162,21669,21562],{},[1162,21671,21594],{},[1162,21673,21635],{},[1162,21675,21638],{},[1110,21677,21678,21679,21700,21701,1730],{},"Pro každou podskupinu se dopočítá výběrový průměr ",[1115,21680,21682],{"className":21681},[1315],[1317,21683,21684],{"xmlns":1319},[1321,21685,21686,21698],{},[1324,21687,21688],{},[1327,21689,21690,21696],{},[2496,21691,21692,21694],{"accent":1121},[1330,21693,6495],{},[1460,21695,11235],{},[1330,21697,1650],{},[1338,21699,21091],{"encoding":1340}," a rozpětí ",[1115,21702,21704],{"className":21703},[1315],[1317,21705,21706],{"xmlns":1319},[1321,21707,21708,21716],{},[1324,21709,21710],{},[1327,21711,21712,21714],{},[1330,21713,10000],{},[1330,21715,1650],{},[1338,21717,21110],{"encoding":1340},[1141,21719,21720,21781],{},[1144,21721,21722],{},[1147,21723,21724,21739,21762],{},[1150,21725,21726],{},[1115,21727,21729],{"className":21728},[1315],[1317,21730,21731],{"xmlns":1319},[1321,21732,21733,21737],{},[1324,21734,21735],{},[1330,21736,1650],{},[1338,21738,1650],{"encoding":1340},[1150,21740,21741],{},[1115,21742,21744],{"className":21743},[1315],[1317,21745,21746],{"xmlns":1319},[1321,21747,21748,21760],{},[1324,21749,21750],{},[1327,21751,21752,21758],{},[2496,21753,21754,21756],{"accent":1121},[1330,21755,6495],{},[1460,21757,11235],{},[1330,21759,1650],{},[1338,21761,21091],{"encoding":1340},[1150,21763,21764],{},[1115,21765,21767],{"className":21766},[1315],[1317,21768,21769],{"xmlns":1319},[1321,21770,21771,21779],{},[1324,21772,21773],{},[1327,21774,21775,21777],{},[1330,21776,10000],{},[1330,21778,1650],{},[1338,21780,21110],{"encoding":1340},[1157,21782,21783,21792,21802,21812,21822,21831,21840,21848,21857],{},[1147,21784,21785,21787,21790],{},[1162,21786,1565],{},[1162,21788,21789],{},"101,50",[1162,21791,14590],{},[1147,21793,21794,21796,21799],{},[1162,21795,1360],{},[1162,21797,21798],{},"97,25",[1162,21800,21801],{},"16",[1147,21803,21804,21806,21809],{},[1162,21805,3366],{},[1162,21807,21808],{},"115,75",[1162,21810,21811],{},"30",[1147,21813,21814,21816,21819],{},[1162,21815,3316],{},[1162,21817,21818],{},"111,75",[1162,21820,21821],{},"64",[1147,21823,21824,21826,21829],{},[1162,21825,9703],{},[1162,21827,21828],{},"97,00",[1162,21830,2027],{},[1147,21832,21833,21835,21838],{},[1162,21834,3739],{},[1162,21836,21837],{},"99,25",[1162,21839,3739],{},[1147,21841,21842,21844,21846],{},[1162,21843,1571],{},[1162,21845,1571],{},[1162,21847,1571],{},[1147,21849,21850,21852,21855],{},[1162,21851,14495],{},[1162,21853,21854],{},"126,50",[1162,21856,3319],{},[1147,21858,21859,21861,21863],{},[1162,21860,3820],{},[1162,21862,21837],{},[1162,21864,3739],{},[1110,21866,21867,21868,21881,21882,2725,21910,2725,21940,21968,21969,21991,21992,2725,22019,2725,22048,22075,22076,1440],{},"Nejprve se posoudí diagram ",[1115,21869,21871],{"className":21870},[1315],[1317,21872,21873],{"xmlns":1319},[1321,21874,21875,21879],{},[1324,21876,21877],{},[1330,21878,10000],{},[1338,21880,10000],{"encoding":1340}," na všech 20 podskupinách: ",[1115,21883,21885],{"className":21884},[1315],[1317,21886,21887],{"xmlns":1319},[1321,21888,21889,21907],{},[1324,21890,21891,21893,21896,21898,21900,21902,21904],{},[1330,21892,20571],{},[1330,21894,21895],{},"L",[1460,21897,1647],{"stretchy":1646},[1330,21899,10000],{},[1460,21901,1658],{"stretchy":1646},[1460,21903,1754],{},[1334,21905,21906],{},"15,8",[1338,21908,21909],{"encoding":1340},"CL(R)=15{,}8",[1115,21911,21913],{"className":21912},[1315],[1317,21914,21915],{"xmlns":1319},[1321,21916,21917,21937],{},[1324,21918,21919,21922,21924,21926,21928,21930,21932,21934],{},[1330,21920,21921],{},"U",[1330,21923,20571],{},[1330,21925,21895],{},[1460,21927,1647],{"stretchy":1646},[1330,21929,10000],{},[1460,21931,1658],{"stretchy":1646},[1460,21933,1754],{},[1334,21935,21936],{},"36,06",[1338,21938,21939],{"encoding":1340},"UCL(R)=36{,}06",[1115,21941,21943],{"className":21942},[1315],[1317,21944,21945],{"xmlns":1319},[1321,21946,21947,21965],{},[1324,21948,21949,21951,21953,21955,21957,21959,21961,21963],{},[1330,21950,21895],{},[1330,21952,20571],{},[1330,21954,21895],{},[1460,21956,1647],{"stretchy":1646},[1330,21958,10000],{},[1460,21960,1658],{"stretchy":1646},[1460,21962,1754],{},[1334,21964,1336],{},[1338,21966,21967],{"encoding":1340},"LCL(R)=0",". Rozpětí čtvrté podskupiny (",[1115,21970,21972],{"className":21971},[1315],[1317,21973,21974],{"xmlns":1319},[1321,21975,21976,21988],{},[1324,21977,21978,21984,21986],{},[1327,21979,21980,21982],{},[1330,21981,10000],{},[1334,21983,3316],{},[1460,21985,1754],{},[1334,21987,21821],{},[1338,21989,21990],{"encoding":1340},"R_4=64",") mez překračuje; po potvrzení vymezitelné příčiny se podskupina 4 z výpočtu vyřadí a meze se přepočítají — ",[1115,21993,21995],{"className":21994},[1315],[1317,21996,21997],{"xmlns":1319},[1321,21998,21999,22016],{},[1324,22000,22001,22003,22005,22007,22009,22011,22013],{},[1330,22002,20571],{},[1330,22004,21895],{},[1460,22006,1647],{"stretchy":1646},[1330,22008,10000],{},[1460,22010,1658],{"stretchy":1646},[1460,22012,1754],{},[1334,22014,22015],{},"13,26",[1338,22017,22018],{"encoding":1340},"CL(R)=13{,}26",[1115,22020,22022],{"className":22021},[1315],[1317,22023,22024],{"xmlns":1319},[1321,22025,22026,22045],{},[1324,22027,22028,22030,22032,22034,22036,22038,22040,22042],{},[1330,22029,21921],{},[1330,22031,20571],{},[1330,22033,21895],{},[1460,22035,1647],{"stretchy":1646},[1330,22037,10000],{},[1460,22039,1658],{"stretchy":1646},[1460,22041,1754],{},[1334,22043,22044],{},"30,27",[1338,22046,22047],{"encoding":1340},"UCL(R)=30{,}27",[1115,22049,22051],{"className":22050},[1315],[1317,22052,22053],{"xmlns":1319},[1321,22054,22055,22073],{},[1324,22056,22057,22059,22061,22063,22065,22067,22069,22071],{},[1330,22058,21895],{},[1330,22060,20571],{},[1330,22062,21895],{},[1460,22064,1647],{"stretchy":1646},[1330,22066,10000],{},[1460,22068,1658],{"stretchy":1646},[1460,22070,1754],{},[1334,22072,1336],{},[1338,22074,21967],{"encoding":1340},". Diagram rozpětí je teď zvládnutý, lze tedy posoudit diagram ",[1115,22077,22079],{"className":22078},[1315],[1317,22080,22081],{"xmlns":1319},[1321,22082,22083,22091],{},[1324,22084,22085],{},[2496,22086,22087,22089],{"accent":1121},[1330,22088,6495],{},[1460,22090,11235],{},[1338,22092,21340],{"encoding":1340},[1110,22094,21041,22095,22112,22113,2725,22144,2725,22177,22210,22211,22224,22225,2725,22252,2725,22281,22308],{},[1115,22096,22098],{"className":22097},[1315],[1317,22099,22100],{"xmlns":1319},[1321,22101,22102,22110],{},[1324,22103,22104],{},[2496,22105,22106,22108],{"accent":1121},[1330,22107,6495],{},[1460,22109,11235],{},[1338,22111,21340],{"encoding":1340}," bez čtvrté podskupiny dává ",[1115,22114,22116],{"className":22115},[1315],[1317,22117,22118],{"xmlns":1319},[1321,22119,22120,22141],{},[1324,22121,22122,22124,22126,22128,22134,22136,22138],{},[1330,22123,20571],{},[1330,22125,21895],{},[1460,22127,1647],{"stretchy":1646},[2496,22129,22130,22132],{"accent":1121},[1330,22131,6495],{},[1460,22133,11235],{},[1460,22135,1658],{"stretchy":1646},[1460,22137,1754],{},[1334,22139,22140],{},"102,01",[1338,22142,22143],{"encoding":1340},"CL(\\bar{x})=102{,}01",[1115,22145,22147],{"className":22146},[1315],[1317,22148,22149],{"xmlns":1319},[1321,22150,22151,22174],{},[1324,22152,22153,22155,22157,22159,22161,22167,22169,22171],{},[1330,22154,21921],{},[1330,22156,20571],{},[1330,22158,21895],{},[1460,22160,1647],{"stretchy":1646},[2496,22162,22163,22165],{"accent":1121},[1330,22164,6495],{},[1460,22166,11235],{},[1460,22168,1658],{"stretchy":1646},[1460,22170,1754],{},[1334,22172,22173],{},"111,68",[1338,22175,22176],{"encoding":1340},"UCL(\\bar{x})=111{,}68",[1115,22178,22180],{"className":22179},[1315],[1317,22181,22182],{"xmlns":1319},[1321,22183,22184,22207],{},[1324,22185,22186,22188,22190,22192,22194,22200,22202,22204],{},[1330,22187,21895],{},[1330,22189,20571],{},[1330,22191,21895],{},[1460,22193,1647],{"stretchy":1646},[2496,22195,22196,22198],{"accent":1121},[1330,22197,6495],{},[1460,22199,11235],{},[1460,22201,1658],{"stretchy":1646},[1460,22203,1754],{},[1334,22205,22206],{},"92,34",[1338,22208,22209],{"encoding":1340},"LCL(\\bar{x})=92{,}34",". Mez teď překračují průměry podskupin 3 a 19. Po potvrzení vymezitelné příčiny se vyřadí obě najednou a meze diagramu ",[1115,22212,22214],{"className":22213},[1315],[1317,22215,22216],{"xmlns":1319},[1321,22217,22218,22222],{},[1324,22219,22220],{},[1330,22221,10000],{},[1338,22223,10000],{"encoding":1340}," se přepočítají bez podskupin 3, 4 a 19: ",[1115,22226,22228],{"className":22227},[1315],[1317,22229,22230],{"xmlns":1319},[1321,22231,22232,22249],{},[1324,22233,22234,22236,22238,22240,22242,22244,22246],{},[1330,22235,20571],{},[1330,22237,21895],{},[1460,22239,1647],{"stretchy":1646},[1330,22241,10000],{},[1460,22243,1658],{"stretchy":1646},[1460,22245,1754],{},[1334,22247,22248],{},"12,29",[1338,22250,22251],{"encoding":1340},"CL(R)=12{,}29",[1115,22253,22255],{"className":22254},[1315],[1317,22256,22257],{"xmlns":1319},[1321,22258,22259,22278],{},[1324,22260,22261,22263,22265,22267,22269,22271,22273,22275],{},[1330,22262,21921],{},[1330,22264,20571],{},[1330,22266,21895],{},[1460,22268,1647],{"stretchy":1646},[1330,22270,10000],{},[1460,22272,1658],{"stretchy":1646},[1460,22274,1754],{},[1334,22276,22277],{},"28,06",[1338,22279,22280],{"encoding":1340},"UCL(R)=28{,}06",[1115,22282,22284],{"className":22283},[1315],[1317,22285,22286],{"xmlns":1319},[1321,22287,22288,22306],{},[1324,22289,22290,22292,22294,22296,22298,22300,22302,22304],{},[1330,22291,21895],{},[1330,22293,20571],{},[1330,22295,21895],{},[1460,22297,1647],{"stretchy":1646},[1330,22299,10000],{},[1460,22301,1658],{"stretchy":1646},[1460,22303,1754],{},[1334,22305,1336],{},[1338,22307,21967],{"encoding":1340}," — žádná z 17 zbývajících podskupin mez nepřekračuje.",[1110,22310,22311,22312,22329,22330,2725,22361,2725,22394,22427],{},"Konečný diagram ",[1115,22313,22315],{"className":22314},[1315],[1317,22316,22317],{"xmlns":1319},[1321,22318,22319,22327],{},[1324,22320,22321],{},[2496,22322,22323,22325],{"accent":1121},[1330,22324,6495],{},[1460,22326,11235],{},[1338,22328,21340],{"encoding":1340}," na stejných 17 podskupinách má ",[1115,22331,22333],{"className":22332},[1315],[1317,22334,22335],{"xmlns":1319},[1321,22336,22337,22358],{},[1324,22338,22339,22341,22343,22345,22351,22353,22355],{},[1330,22340,20571],{},[1330,22342,21895],{},[1460,22344,1647],{"stretchy":1646},[2496,22346,22347,22349],{"accent":1121},[1330,22348,6495],{},[1460,22350,11235],{},[1460,22352,1658],{"stretchy":1646},[1460,22354,1754],{},[1334,22356,22357],{},"99,76",[1338,22359,22360],{"encoding":1340},"CL(\\bar{x})=99{,}76",[1115,22362,22364],{"className":22363},[1315],[1317,22365,22366],{"xmlns":1319},[1321,22367,22368,22391],{},[1324,22369,22370,22372,22374,22376,22378,22384,22386,22388],{},[1330,22371,21921],{},[1330,22373,20571],{},[1330,22375,21895],{},[1460,22377,1647],{"stretchy":1646},[2496,22379,22380,22382],{"accent":1121},[1330,22381,6495],{},[1460,22383,11235],{},[1460,22385,1658],{"stretchy":1646},[1460,22387,1754],{},[1334,22389,22390],{},"108,73",[1338,22392,22393],{"encoding":1340},"UCL(\\bar{x})=108{,}73",[1115,22395,22397],{"className":22396},[1315],[1317,22398,22399],{"xmlns":1319},[1321,22400,22401,22424],{},[1324,22402,22403,22405,22407,22409,22411,22417,22419,22421],{},[1330,22404,21895],{},[1330,22406,20571],{},[1330,22408,21895],{},[1460,22410,1647],{"stretchy":1646},[2496,22412,22413,22415],{"accent":1121},[1330,22414,6495],{},[1460,22416,11235],{},[1460,22418,1658],{"stretchy":1646},[1460,22420,1754],{},[1334,22422,22423],{},"90,80",[1338,22425,22426],{"encoding":1340},"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.",[1110,22429,22430],{},[4158,22431],{"alt":22432,"className":22433,"src":22434},"mask-rd-priklad1-meze",[1130,4162],"\u002Fwiki-assets\u002Fmask-rd-priklad1-meze.png",[1110,22436,22437,22438,22440,22441,22443],{},"V R se diagramy sestrojí funkcí ",[3244,22439,21344],{}," z balíčku ",[3244,22442,360],{},". Data jsou tabulka, v níž řádek odpovídá logické podskupině a sloupce jednotlivým měřením:",[3468,22445,22447],{"className":3470,"code":22446,"language":71,"meta":1247,"style":1247},"library(qcc)\ndata \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"R\")      # diagram R\nqcc(data, type = \"xbar\")   # diagram x̄\n",[3244,22448,22449,22459,22482,22505],{"__ignoreMap":1247},[1115,22450,22451,22453,22455,22457],{"class":3476,"line":10},[1115,22452,17170],{"class":3483},[1115,22454,1647],{"class":3491},[1115,22456,360],{"class":3479},[1115,22458,3676],{"class":3491},[1115,22460,22461,22463,22465,22467,22469,22472,22474,22476,22478,22480],{"class":3476,"line":27},[1115,22462,19881],{"class":3479},[1115,22464,3484],{"class":3483},[1115,22466,19886],{"class":3487},[1115,22468,1647],{"class":3491},[1115,22470,22471],{"class":3615},"\"3_2.txt\"",[1115,22473,1568],{"class":3483},[1115,22475,19896],{"class":3479},[1115,22477,3572],{"class":3483},[1115,22479,3585],{"class":3499},[1115,22481,3676],{"class":3491},[1115,22483,22484,22486,22488,22490,22492,22494,22496,22499,22502],{"class":3476,"line":148},[1115,22485,360],{"class":3487},[1115,22487,1647],{"class":3491},[1115,22489,19881],{"class":3479},[1115,22491,1568],{"class":3483},[1115,22493,11999],{"class":3479},[1115,22495,3572],{"class":3483},[1115,22497,22498],{"class":3615}," \"R\"",[1115,22500,22501],{"class":3491},")      ",[1115,22503,22504],{"class":11809},"# diagram R\n",[1115,22506,22507,22509,22511,22513,22515,22517,22519,22522,22524],{"class":3476,"line":111},[1115,22508,360],{"class":3487},[1115,22510,1647],{"class":3491},[1115,22512,19881],{"class":3479},[1115,22514,1568],{"class":3483},[1115,22516,11999],{"class":3479},[1115,22518,3572],{"class":3483},[1115,22520,22521],{"class":3615}," \"xbar\"",[1115,22523,11806],{"class":3491},[1115,22525,22526],{"class":11809},"# diagram x̄\n",[1110,22528,22529,22530,22533],{},"Funkce vykreslí diagram se střední přímkou a akčními mezemi a body mimo meze zvýrazní. Podskupina s potvrzenou vymezitelnou příčinou se vyřadí z dat (například ",[3244,22531,22532],{},"data[-4, ]",") a diagram se sestrojí znovu.",[16521,22535,21041,22537],{"id":22536},"diagram-xˉsbarx-s",[1115,22538,22540],{"className":22539},[1315],[1317,22541,22542],{"xmlns":1319},[1321,22543,22544,22560],{},[1324,22545,22546,22548,22554,22556,22558],{},[1460,22547,1647],{"stretchy":1646},[2496,22549,22550,22552],{"accent":1121},[1330,22551,6495],{},[1460,22553,11235],{},[1460,22555,1568],{"separator":1121},[1330,22557,1626],{},[1460,22559,1658],{"stretchy":1646},[1338,22561,20450],{"encoding":1340},[1110,22563,21069,22564,22585,22586,22604,22605,22630],{},[1115,22565,22567],{"className":22566},[1315],[1317,22568,22569],{"xmlns":1319},[1321,22570,22571,22583],{},[1324,22572,22573],{},[1327,22574,22575,22581],{},[2496,22576,22577,22579],{"accent":1121},[1330,22578,6495],{},[1460,22580,11235],{},[1330,22582,1650],{},[1338,22584,21091],{"encoding":1340}," a výběrové směrodatné odchylky ",[1115,22587,22589],{"className":22588},[1315],[1317,22590,22591],{"xmlns":1319},[1321,22592,22593,22601],{},[1324,22594,22595],{},[1327,22596,22597,22599],{},[1330,22598,1626],{},[1330,22600,1650],{},[1338,22602,22603],{"encoding":1340},"s_i"," v logických podskupinách. Podmínky použití jsou stejné jako u ",[1115,22606,22608],{"className":22607},[1315],[1317,22609,22610],{"xmlns":1319},[1321,22611,22612,22628],{},[1324,22613,22614,22616,22622,22624,22626],{},[1460,22615,1647],{"stretchy":1646},[2496,22617,22618,22620],{"accent":1121},[1330,22619,6495],{},[1460,22621,11235],{},[1460,22623,1568],{"separator":1121},[1330,22625,10000],{},[1460,22627,1658],{"stretchy":1646},[1338,22629,20424],{"encoding":1340},", logické podskupiny ale sestávají z většího počtu měření. Data se zapisují do obdobné tabulky.",[3468,22632,22634],{"className":3470,"code":22633,"language":71,"meta":1247,"style":1247},"data \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"S\")      # diagram s\nqcc(data, type = \"xbar\")   # diagram x̄\n",[3244,22635,22636,22658,22680],{"__ignoreMap":1247},[1115,22637,22638,22640,22642,22644,22646,22648,22650,22652,22654,22656],{"class":3476,"line":10},[1115,22639,19881],{"class":3479},[1115,22641,3484],{"class":3483},[1115,22643,19886],{"class":3487},[1115,22645,1647],{"class":3491},[1115,22647,22471],{"class":3615},[1115,22649,1568],{"class":3483},[1115,22651,19896],{"class":3479},[1115,22653,3572],{"class":3483},[1115,22655,3585],{"class":3499},[1115,22657,3676],{"class":3491},[1115,22659,22660,22662,22664,22666,22668,22670,22672,22675,22677],{"class":3476,"line":27},[1115,22661,360],{"class":3487},[1115,22663,1647],{"class":3491},[1115,22665,19881],{"class":3479},[1115,22667,1568],{"class":3483},[1115,22669,11999],{"class":3479},[1115,22671,3572],{"class":3483},[1115,22673,22674],{"class":3615}," \"S\"",[1115,22676,22501],{"class":3491},[1115,22678,22679],{"class":11809},"# diagram s\n",[1115,22681,22682,22684,22686,22688,22690,22692,22694,22696,22698],{"class":3476,"line":148},[1115,22683,360],{"class":3487},[1115,22685,1647],{"class":3491},[1115,22687,19881],{"class":3479},[1115,22689,1568],{"class":3483},[1115,22691,11999],{"class":3479},[1115,22693,3572],{"class":3483},[1115,22695,22521],{"class":3615},[1115,22697,11806],{"class":3491},[1115,22699,22526],{"class":11809},[16521,22701,21041,22703],{"id":22702},"diagram-xirklix_i-r_kli",[1115,22704,22706],{"className":22705},[1315],[1317,22707,22708],{"xmlns":1319},[1321,22709,22710,22738],{},[1324,22711,22712,22714,22720,22722,22736],{},[1460,22713,1647],{"stretchy":1646},[1327,22715,22716,22718],{},[1330,22717,6495],{},[1330,22719,1650],{},[1460,22721,1568],{"separator":1121},[1327,22723,22724,22726],{},[1330,22725,10000],{},[1324,22727,22728,22730,22732,22734],{},[1330,22729,7035],{},[1330,22731,20480],{},[1460,22733,1568],{"separator":1121},[1330,22735,1650],{},[1460,22737,1658],{"stretchy":1646},[1338,22739,20489],{"encoding":1340},[1110,22741,22742,22743,22768,22769,1730],{},"Používá se za stejných podmínek jako ",[1115,22744,22746],{"className":22745},[1315],[1317,22747,22748],{"xmlns":1319},[1321,22749,22750,22766],{},[1324,22751,22752,22754,22760,22762,22764],{},[1460,22753,1647],{"stretchy":1646},[2496,22755,22756,22758],{"accent":1121},[1330,22757,6495],{},[1460,22759,11235],{},[1460,22761,1568],{"separator":1121},[1330,22763,10000],{},[1460,22765,1658],{"stretchy":1646},[1338,22767,20424],{"encoding":1340},", 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 ",[1302,22770,22771],{},"klouzavé rozpětí",[1115,22773,22775],{"className":22774},[1315],[1317,22776,22777],{"xmlns":1319,"display":1736},[1321,22778,22779,22906],{},[1324,22780,22781,22795,22797,22800,22806,22808,22820,22822,22824,22826,22828,22830,22832,22834,22836,22838,22840,22842,22844,22846,22848,22862,22864,22876,22890,22904],{},[1327,22782,22783,22785],{},[1330,22784,10000],{},[1324,22786,22787,22789,22791,22793],{},[1330,22788,7035],{},[1330,22790,20480],{},[1460,22792,1568],{"separator":1121},[1330,22794,1650],{},[1460,22796,1754],{},[1330,22798,22799],{"mathvariant":1893},"∣",[1327,22801,22802,22804],{},[1330,22803,6495],{},[1330,22805,1650],{},[1460,22807,2838],{},[1327,22809,22810,22812],{},[1330,22811,6495],{},[1324,22813,22814,22816,22818],{},[1330,22815,1650],{},[1460,22817,2838],{},[1334,22819,1565],{},[1330,22821,22799],{"mathvariant":1893},[1460,22823,1568],{"separator":1121},[1784,22825],{"width":17791},[1330,22827,1650],{},[1460,22829,1754],{},[1334,22831,1360],{},[1460,22833,1568],{"separator":1121},[1334,22835,3366],{},[1460,22837,1568],{"separator":1121},[1460,22839,1571],{},[1460,22841,1568],{"separator":1121},[1330,22843,7035],{},[1460,22845,1568],{"separator":1121},[1784,22847],{"width":1786},[1327,22849,22850,22856],{},[2496,22851,22852,22854],{"accent":1121},[1330,22853,10000],{},[1460,22855,11235],{},[1324,22857,22858,22860],{},[1330,22859,7035],{},[1330,22861,20480],{},[1460,22863,1754],{},[2512,22865,22866,22868],{},[1334,22867,1565],{},[1324,22869,22870,22872,22874],{},[1330,22871,7035],{},[1460,22873,2838],{},[1334,22875,1565],{},[1756,22877,22878,22880,22888],{},[1460,22879,1760],{},[1324,22881,22882,22884,22886],{},[1330,22883,1650],{},[1460,22885,1754],{},[1334,22887,1360],{},[1330,22889,7035],{},[1327,22891,22892,22894],{},[1330,22893,10000],{},[1324,22895,22896,22898,22900,22902],{},[1330,22897,7035],{},[1330,22899,20480],{},[1460,22901,1568],{"separator":1121},[1330,22903,1650],{},[1330,22905,1440],{"mathvariant":1893},[1338,22907,22908],{"encoding":1340},"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}.",[1110,22910,22911,22912,5516,22929,22955,22956,22981,22982,22999],{},"Regulované veličiny jsou hodnoty ",[1115,22913,22915],{"className":22914},[1315],[1317,22916,22917],{"xmlns":1319},[1321,22918,22919,22927],{},[1324,22920,22921],{},[1327,22922,22923,22925],{},[1330,22924,6495],{},[1330,22926,1650],{},[1338,22928,16907],{"encoding":1340},[1115,22930,22932],{"className":22931},[1315],[1317,22933,22934],{"xmlns":1319},[1321,22935,22936,22952],{},[1324,22937,22938],{},[1327,22939,22940,22942],{},[1330,22941,10000],{},[1324,22943,22944,22946,22948,22950],{},[1330,22945,7035],{},[1330,22947,20480],{},[1460,22949,1568],{"separator":1121},[1330,22951,1650],{},[1338,22953,22954],{"encoding":1340},"R_{kl,i}","; nejdříve se určí střední přímka a meze diagramu ",[1115,22957,22959],{"className":22958},[1315],[1317,22960,22961],{"xmlns":1319},[1321,22962,22963,22979],{},[1324,22964,22965],{},[1327,22966,22967,22969],{},[1330,22968,10000],{},[1324,22970,22971,22973,22975,22977],{},[1330,22972,7035],{},[1330,22974,20480],{},[1460,22976,1568],{"separator":1121},[1330,22978,1650],{},[1338,22980,22954],{"encoding":1340},", potom diagramu ",[1115,22983,22985],{"className":22984},[1315],[1317,22986,22987],{"xmlns":1319},[1321,22988,22989,22997],{},[1324,22990,22991],{},[1327,22992,22993,22995],{},[1330,22994,6495],{},[1330,22996,1650],{},[1338,22998,16907],{"encoding":1340},". Data jsou jeden vektor naměřených hodnot:",[3468,23001,23003],{"className":3470,"code":23002,"language":71,"meta":1247,"style":1247},"data \u003C- read.table(\"3_3.txt\", header = TRUE)\nqcc(data[, 1], type = \"xbar.one\")\n",[3244,23004,23005,23028],{"__ignoreMap":1247},[1115,23006,23007,23009,23011,23013,23015,23018,23020,23022,23024,23026],{"class":3476,"line":10},[1115,23008,19881],{"class":3479},[1115,23010,3484],{"class":3483},[1115,23012,19886],{"class":3487},[1115,23014,1647],{"class":3491},[1115,23016,23017],{"class":3615},"\"3_3.txt\"",[1115,23019,1568],{"class":3483},[1115,23021,19896],{"class":3479},[1115,23023,3572],{"class":3483},[1115,23025,3585],{"class":3499},[1115,23027,3676],{"class":3491},[1115,23029,23030,23032,23034,23036,23038,23040,23042,23044,23046,23048,23050,23053],{"class":3476,"line":27},[1115,23031,360],{"class":3487},[1115,23033,1647],{"class":3491},[1115,23035,19881],{"class":3479},[1115,23037,7952],{"class":3491},[1115,23039,1568],{"class":3483},[1115,23041,4416],{"class":3499},[1115,23043,7969],{"class":3491},[1115,23045,1568],{"class":3483},[1115,23047,11999],{"class":3479},[1115,23049,3572],{"class":3483},[1115,23051,23052],{"class":3615}," \"xbar.one\"",[1115,23054,3676],{"class":3491},[1136,23056,23058],{"id":23057},"regulace-srovnáváním","Regulace srovnáváním",[1110,23060,23061],{},"Diagramy pro regulaci srovnáváním se používají, sledují-li se počty neshodných produktů nebo počty neshod na produktech — regulovaná veličina je diskrétní náhodná veličina.",[1141,23063,23064,23077],{},[1144,23065,23066],{},[1147,23067,23068,23071,23074],{},[1150,23069,23070],{},"Sleduje se",[1150,23072,23073],{},"Konstantní rozsah podskupin",[1150,23075,23076],{},"Nekonstantní rozsah podskupin",[1157,23078,23079,23114],{},[1147,23080,23081,23084,23099],{},[1162,23082,23083],{},"počet neshod na produktech (např. vady na stejných tabulích skla)",[1162,23085,23086],{},[1115,23087,23089],{"className":23088},[1315],[1317,23090,23091],{"xmlns":1319},[1321,23092,23093,23097],{},[1324,23094,23095],{},[1330,23096,3494],{},[1338,23098,3494],{"encoding":1340},[1162,23100,23101],{},[1115,23102,23104],{"className":23103},[1315],[1317,23105,23106],{"xmlns":1319},[1321,23107,23108,23112],{},[1324,23109,23110],{},[1330,23111,11304],{},[1338,23113,11304],{"encoding":1340},[1147,23115,23116,23119,23136],{},[1162,23117,23118],{},"počet neshodných produktů ve výběru (např. neshodné kusy ze série na výrobní lince)",[1162,23120,23121],{},[1115,23122,23124],{"className":23123},[1315],[1317,23125,23126],{"xmlns":1319},[1321,23127,23128,23134],{},[1324,23129,23130,23132],{},[1330,23131,1458],{},[1330,23133,1110],{},[1338,23135,20536],{"encoding":1340},[1162,23137,23138],{},[1115,23139,23141],{"className":23140},[1315],[1317,23142,23143],{"xmlns":1319},[1321,23144,23145,23149],{},[1324,23146,23147],{},[1330,23148,1110],{},[1338,23150,1110],{"encoding":1340},[16521,23152,21041,23154],{"id":23153},"diagram-cc",[1115,23155,23157],{"className":23156},[1315],[1317,23158,23159],{"xmlns":1319},[1321,23160,23161,23165],{},[1324,23162,23163],{},[1330,23164,3494],{},[1338,23166,3494],{"encoding":1340},[1110,23168,23169,23170,23188,23189,23202,23203,23228,23229,23242],{},"Regulovanou veličinou ",[1115,23171,23173],{"className":23172},[1315],[1317,23174,23175],{"xmlns":1319},[1321,23176,23177,23185],{},[1324,23178,23179],{},[1327,23180,23181,23183],{},[1330,23182,3494],{},[1330,23184,1650],{},[1338,23186,23187],{"encoding":1340},"c_i"," je počet neshod na produktech v ",[1115,23190,23192],{"className":23191},[1315],[1317,23193,23194],{"xmlns":1319},[1321,23195,23196,23200],{},[1324,23197,23198],{},[1330,23199,1650],{},[1338,23201,1650],{"encoding":1340},"-té logické podskupině, ",[1115,23204,23206],{"className":23205},[1315],[1317,23207,23208],{"xmlns":1319},[1321,23209,23210,23226],{},[1324,23211,23212,23214,23216,23218,23220,23222,23224],{},[1330,23213,1650],{},[1460,23215,1754],{},[1334,23217,1565],{},[1460,23219,1568],{"separator":1121},[1460,23221,1571],{},[1460,23223,1568],{"separator":1121},[1330,23225,7035],{},[1338,23227,21254],{"encoding":1340},"; v každé podskupině je stejný počet ",[1115,23230,23232],{"className":23231},[1315],[1317,23233,23234],{"xmlns":1319},[1321,23235,23236,23240],{},[1324,23237,23238],{},[1330,23239,1458],{},[1338,23241,1458],{"encoding":1340}," 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.",[1103,23244,23246,23253],{"className":23245,"dataCallout":3251},[1106,3250],[1110,23247,23249,23252],{"className":23248},[1113],[1115,23250],{"className":23251,"ariaHidden":1121},[1118,3258,1120],"Příklad: bodové vady na pásech látky",[1110,23254,23255,23256,23273,23274,1440],{},"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 ",[1115,23257,23259],{"className":23258},[1315],[1317,23260,23261],{"xmlns":1319},[1321,23262,23263,23271],{},[1324,23264,23265],{},[1327,23266,23267,23269],{},[1330,23268,3494],{},[1330,23270,1650],{},[1338,23272,23187],{"encoding":1340},". Sestrojte regulační diagram ",[1115,23275,23277],{"className":23276},[1315],[1317,23278,23279],{"xmlns":1319},[1321,23280,23281,23285],{},[1324,23282,23283],{},[1330,23284,3494],{},[1338,23286,3494],{"encoding":1340},[3468,23288,23290],{"className":3470,"code":23289,"language":71,"meta":1247,"style":1247},"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",[3244,23291,23292,23382,23386,23411],{"__ignoreMap":1247},[1115,23293,23294,23296,23298,23300,23302,23304,23306,23308,23310,23312,23314,23316,23318,23320,23322,23324,23326,23328,23330,23332,23334,23336,23338,23340,23342,23344,23346,23348,23350,23352,23354,23356,23358,23360,23362,23364,23366,23368,23370,23372,23374,23376,23378,23380],{"class":3476,"line":10},[1115,23295,23187],{"class":3479},[1115,23297,3484],{"class":3483},[1115,23299,3610],{"class":3487},[1115,23301,1647],{"class":3491},[1115,23303,13106],{"class":3499},[1115,23305,1568],{"class":3483},[1115,23307,4416],{"class":3499},[1115,23309,1568],{"class":3483},[1115,23311,3955],{"class":3499},[1115,23313,1568],{"class":3483},[1115,23315,9771],{"class":3499},[1115,23317,1568],{"class":3483},[1115,23319,9747],{"class":3499},[1115,23321,1568],{"class":3483},[1115,23323,12004],{"class":3499},[1115,23325,1568],{"class":3483},[1115,23327,3955],{"class":3499},[1115,23329,1568],{"class":3483},[1115,23331,9747],{"class":3499},[1115,23333,1568],{"class":3483},[1115,23335,3575],{"class":3499},[1115,23337,1568],{"class":3483},[1115,23339,3575],{"class":3499},[1115,23341,1568],{"class":3483},[1115,23343,12004],{"class":3499},[1115,23345,1568],{"class":3483},[1115,23347,10632],{"class":3499},[1115,23349,1568],{"class":3483},[1115,23351,10632],{"class":3499},[1115,23353,1568],{"class":3483},[1115,23355,10632],{"class":3499},[1115,23357,1568],{"class":3483},[1115,23359,4416],{"class":3499},[1115,23361,1568],{"class":3483},[1115,23363,12004],{"class":3499},[1115,23365,1568],{"class":3483},[1115,23367,10632],{"class":3499},[1115,23369,1568],{"class":3483},[1115,23371,4416],{"class":3499},[1115,23373,1568],{"class":3483},[1115,23375,9771],{"class":3499},[1115,23377,1568],{"class":3483},[1115,23379,12004],{"class":3499},[1115,23381,3676],{"class":3491},[1115,23383,23384],{"class":3476,"line":27},[1115,23385,9818],{"emptyLinePlaceholder":1256},[1115,23387,23388,23391,23393,23396,23398,23400,23402,23404,23406,23409],{"class":3476,"line":148},[1115,23389,23390],{"class":3479},"q_c",[1115,23392,3484],{"class":3483},[1115,23394,23395],{"class":3487}," qcc",[1115,23397,1647],{"class":3491},[1115,23399,23187],{"class":3479},[1115,23401,1568],{"class":3483},[1115,23403,11999],{"class":3479},[1115,23405,3572],{"class":3483},[1115,23407,23408],{"class":3615}," \"c\"",[1115,23410,3676],{"class":3491},[1115,23412,23413,23415,23417,23419],{"class":3476,"line":111},[1115,23414,1271],{"class":3487},[1115,23416,1647],{"class":3491},[1115,23418,23390],{"class":3479},[1115,23420,3676],{"class":3491},[3468,23422,23425],{"className":23423,"code":23424,"language":3698,"meta":1247},[3696],"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",[3244,23426,23424],{"__ignoreMap":1247},[1110,23428,23429,23430,23459,23460,23483,23484,23506],{},"Průměrný počet vad na pás je ",[1115,23431,23433],{"className":23432},[1315],[1317,23434,23435],{"xmlns":1319},[1321,23436,23437,23456],{},[1324,23438,23439,23441,23443,23445,23451,23453],{},[1330,23440,20571],{},[1330,23442,21895],{},[1460,23444,1754],{},[2496,23446,23447,23449],{"accent":1121},[1330,23448,3494],{},[1460,23450,11235],{},[1460,23452,1754],{},[1334,23454,23455],{},"3,4",[1338,23457,23458],{"encoding":1340},"CL = \\bar{c} = 3{,}4",", horní mez ",[1115,23461,23463],{"className":23462},[1315],[1317,23464,23465],{"xmlns":1319},[1321,23466,23467,23480],{},[1324,23468,23469,23471,23473,23475,23477],{},[1330,23470,21921],{},[1330,23472,20571],{},[1330,23474,21895],{},[1460,23476,1754],{},[1334,23478,23479],{},"8,93",[1338,23481,23482],{"encoding":1340},"UCL = 8{,}93"," a dolní mez ",[1115,23485,23487],{"className":23486},[1315],[1317,23488,23489],{"xmlns":1319},[1321,23490,23491,23503],{},[1324,23492,23493,23495,23497,23499,23501],{},[1330,23494,21895],{},[1330,23496,20571],{},[1330,23498,21895],{},[1460,23500,1754],{},[1334,23502,1336],{},[1338,23504,23505],{"encoding":1340},"LCL = 0",". Žádný pás meze nepřekračuje — proces je zvládnutý.",[1110,23508,23509],{},[4158,23510],{"alt":23511,"className":23512,"src":23513},"mask-rd-priklad2-c",[1130,4162],"\u002Fwiki-assets\u002Fmask-rd-priklad2-c.png",[16521,23515,21041,23517],{"id":23516},"diagram-uu",[1115,23518,23520],{"className":23519},[1315],[1317,23521,23522],{"xmlns":1319},[1321,23523,23524,23528],{},[1324,23525,23526],{},[1330,23527,11304],{},[1338,23529,11304],{"encoding":1340},[1110,23531,23169,23532,23566,23567,23585],{},[1115,23533,23535],{"className":23534},[1315],[1317,23536,23537],{"xmlns":1319},[1321,23538,23539,23563],{},[1324,23540,23541,23547,23549,23555,23557],{},[1327,23542,23543,23545],{},[1330,23544,11304],{},[1330,23546,1650],{},[1460,23548,1754],{},[1327,23550,23551,23553],{},[1330,23552,3494],{},[1330,23554,1650],{},[1330,23556,4379],{"mathvariant":1893},[1327,23558,23559,23561],{},[1330,23560,1458],{},[1330,23562,1650],{},[1338,23564,23565],{"encoding":1340},"u_i = c_i\u002Fn_i"," je průměrný počet neshod přepočítaný na jeden produkt z logické podskupiny; rozsah podskupin ",[1115,23568,23570],{"className":23569},[1315],[1317,23571,23572],{"xmlns":1319},[1321,23573,23574,23582],{},[1324,23575,23576],{},[1327,23577,23578,23580],{},[1330,23579,1458],{},[1330,23581,1650],{},[1338,23583,23584],{"encoding":1340},"n_i"," není konstantní, a proto se bod od bodu mění i meze.",[1110,23587,23588,23589,23592],{},"Za ",[3244,23590,23591],{},"sizes"," se dosadí vektor rozsahů jednotlivých logických podskupin, resp. rozměr jejich jednotek:",[3468,23594,23596],{"className":3470,"code":23595,"language":71,"meta":1247,"style":1247},"data \u003C- read.table(\"3_4.txt\", header = TRUE)   # počty suků a rozměry prken\nqcc(data[, 1], type = \"u\", sizes = data[, 2])\n",[3244,23597,23598,23624],{"__ignoreMap":1247},[1115,23599,23600,23602,23604,23606,23608,23611,23613,23615,23617,23619,23621],{"class":3476,"line":10},[1115,23601,19881],{"class":3479},[1115,23603,3484],{"class":3483},[1115,23605,19886],{"class":3487},[1115,23607,1647],{"class":3491},[1115,23609,23610],{"class":3615},"\"3_4.txt\"",[1115,23612,1568],{"class":3483},[1115,23614,19896],{"class":3479},[1115,23616,3572],{"class":3483},[1115,23618,3585],{"class":3499},[1115,23620,11806],{"class":3491},[1115,23622,23623],{"class":11809},"# počty suků a rozměry prken\n",[1115,23625,23626,23628,23630,23632,23634,23636,23638,23640,23642,23644,23646,23649,23651,23654,23656,23658,23660,23662,23664],{"class":3476,"line":27},[1115,23627,360],{"class":3487},[1115,23629,1647],{"class":3491},[1115,23631,19881],{"class":3479},[1115,23633,7952],{"class":3491},[1115,23635,1568],{"class":3483},[1115,23637,4416],{"class":3499},[1115,23639,7969],{"class":3491},[1115,23641,1568],{"class":3483},[1115,23643,11999],{"class":3479},[1115,23645,3572],{"class":3483},[1115,23647,23648],{"class":3615}," \"u\"",[1115,23650,1568],{"class":3483},[1115,23652,23653],{"class":3479}," sizes",[1115,23655,3572],{"class":3483},[1115,23657,19940],{"class":3479},[1115,23659,7952],{"class":3491},[1115,23661,1568],{"class":3483},[1115,23663,3955],{"class":3499},[1115,23665,23666],{"class":3491},"])\n",[16521,23668,21041,23670],{"id":23669},"diagram-npnp",[1115,23671,23673],{"className":23672},[1315],[1317,23674,23675],{"xmlns":1319},[1321,23676,23677,23683],{},[1324,23678,23679,23681],{},[1330,23680,1458],{},[1330,23682,1110],{},[1338,23684,20536],{"encoding":1340},[1110,23686,23687,23688,6556,23703,23716],{},"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 ",[1115,23689,23691],{"className":23690},[1315],[1317,23692,23693],{"xmlns":1319},[1321,23694,23695,23701],{},[1324,23696,23697,23699],{},[1330,23698,1458],{},[1330,23700,1110],{},[1338,23702,20536],{"encoding":1340},[1115,23704,23706],{"className":23705},[1315],[1317,23707,23708],{"xmlns":1319},[1321,23709,23710,23714],{},[1324,23711,23712],{},[1330,23713,1110],{},[1338,23715,1110],{"encoding":1340}," je pravděpodobnost, že vyrobený produkt je neshodný.",[1110,23718,23719,23720,1730],{},"Pro konstantní rozsah ",[1115,23721,23723],{"className":23722},[1315],[1317,23724,23725],{"xmlns":1319},[1321,23726,23727,23731],{},[1324,23728,23729],{},[1330,23730,1458],{},[1338,23732,1458],{"encoding":1340},[3468,23734,23736],{"className":3470,"code":23735,"language":71,"meta":1247,"style":1247},"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",[3244,23737,23738,23764],{"__ignoreMap":1247},[1115,23739,23740,23742,23744,23746,23748,23751,23753,23755,23757,23759,23761],{"class":3476,"line":10},[1115,23741,19881],{"class":3479},[1115,23743,3484],{"class":3483},[1115,23745,19886],{"class":3487},[1115,23747,1647],{"class":3491},[1115,23749,23750],{"class":3615},"\"3_7.txt\"",[1115,23752,1568],{"class":3483},[1115,23754,19896],{"class":3479},[1115,23756,3572],{"class":3483},[1115,23758,3585],{"class":3499},[1115,23760,11806],{"class":3491},[1115,23762,23763],{"class":11809},"# počty vadných tabletů v sériích po 100 kusech\n",[1115,23765,23766,23768,23770,23772,23774,23776,23778,23780,23782,23784,23786,23789,23791,23793,23795,23797],{"class":3476,"line":27},[1115,23767,360],{"class":3487},[1115,23769,1647],{"class":3491},[1115,23771,19881],{"class":3479},[1115,23773,7952],{"class":3491},[1115,23775,1568],{"class":3483},[1115,23777,4416],{"class":3499},[1115,23779,7969],{"class":3491},[1115,23781,1568],{"class":3483},[1115,23783,11999],{"class":3479},[1115,23785,3572],{"class":3483},[1115,23787,23788],{"class":3615}," \"np\"",[1115,23790,1568],{"class":3483},[1115,23792,23653],{"class":3479},[1115,23794,3572],{"class":3483},[1115,23796,15115],{"class":3499},[1115,23798,3676],{"class":3491},[16521,23800,21041,23802],{"id":23801},"diagram-pp",[1115,23803,23805],{"className":23804},[1315],[1317,23806,23807],{"xmlns":1319},[1321,23808,23809,23813],{},[1324,23810,23811],{},[1330,23812,1110],{},[1338,23814,1110],{"encoding":1340},[1110,23816,23817,23818,23854],{},"Regulovanou veličinou je počet neshodných produktů v logické podskupině přepočtený na jednotku, ",[1115,23819,23821],{"className":23820},[1315],[1317,23822,23823],{"xmlns":1319},[1321,23824,23825,23851],{},[1324,23826,23827,23833,23835,23837,23843,23845],{},[1327,23828,23829,23831],{},[1330,23830,1110],{},[1330,23832,1650],{},[1460,23834,1754],{},[1330,23836,1458],{},[1327,23838,23839,23841],{},[1330,23840,1110],{},[1330,23842,1650],{},[1330,23844,4379],{"mathvariant":1893},[1327,23846,23847,23849],{},[1330,23848,1458],{},[1330,23850,1650],{},[1338,23852,23853],{"encoding":1340},"p_i = np_i\u002Fn_i","; rozsahy podskupin nemusí být konstantní.",[1110,23856,23588,23857,23859],{},[3244,23858,23591],{}," se dosadí vektor rozsahů logických podskupin:",[3468,23861,23863],{"className":3470,"code":23862,"language":71,"meta":1247,"style":1247},"data \u003C- read.table(\"3_6.txt\", header = TRUE)   # počty vadných tabletů a rozsahy sérií\nqcc(data[, 1], type = \"p\", sizes = data[, 2])\n",[3244,23864,23865,23891],{"__ignoreMap":1247},[1115,23866,23867,23869,23871,23873,23875,23878,23880,23882,23884,23886,23888],{"class":3476,"line":10},[1115,23868,19881],{"class":3479},[1115,23870,3484],{"class":3483},[1115,23872,19886],{"class":3487},[1115,23874,1647],{"class":3491},[1115,23876,23877],{"class":3615},"\"3_6.txt\"",[1115,23879,1568],{"class":3483},[1115,23881,19896],{"class":3479},[1115,23883,3572],{"class":3483},[1115,23885,3585],{"class":3499},[1115,23887,11806],{"class":3491},[1115,23889,23890],{"class":11809},"# počty vadných tabletů a rozsahy sérií\n",[1115,23892,23893,23895,23897,23899,23901,23903,23905,23907,23909,23911,23913,23916,23918,23920,23922,23924,23926,23928,23930],{"class":3476,"line":27},[1115,23894,360],{"class":3487},[1115,23896,1647],{"class":3491},[1115,23898,19881],{"class":3479},[1115,23900,7952],{"class":3491},[1115,23902,1568],{"class":3483},[1115,23904,4416],{"class":3499},[1115,23906,7969],{"class":3491},[1115,23908,1568],{"class":3483},[1115,23910,11999],{"class":3479},[1115,23912,3572],{"class":3483},[1115,23914,23915],{"class":3615}," \"p\"",[1115,23917,1568],{"class":3483},[1115,23919,23653],{"class":3479},[1115,23921,3572],{"class":3483},[1115,23923,19940],{"class":3479},[1115,23925,7952],{"class":3491},[1115,23927,1568],{"class":3483},[1115,23929,3955],{"class":3499},[1115,23931,23666],{"class":3491},[1136,23933,23935],{"id":23934},"indexy-způsobilosti","Indexy způsobilosti",[1110,23937,23938,23939,23958,23959,23977],{},"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 ",[1115,23940,23942],{"className":23941},[1315],[1317,23943,23944],{"xmlns":1319},[1321,23945,23946,23955],{},[1324,23947,23948,23950,23953],{},[1330,23949,21895],{},[1330,23951,23952],{},"S",[1330,23954,21895],{},[1338,23956,23957],{"encoding":1340},"LSL"," a horní meze ",[1115,23960,23962],{"className":23961},[1315],[1317,23963,23964],{"xmlns":1319},[1321,23965,23966,23974],{},[1324,23967,23968,23970,23972],{},[1330,23969,21921],{},[1330,23971,23952],{},[1330,23973,21895],{},[1338,23975,23976],{"encoding":1340},"USL",". Způsobilost se zkoumá až pro proces, který je podle regulačních diagramů statisticky zvládnutý (třetí fáze regulace).",[16521,23979,23981,23998],{"id":23980},"cpc_p-index-způsobilosti",[1115,23982,23984],{"className":23983},[1315],[1317,23985,23986],{"xmlns":1319},[1321,23987,23988,23996],{},[1324,23989,23990],{},[1327,23991,23992,23994],{},[1330,23993,20571],{},[1330,23995,1110],{},[1338,23997,20576],{"encoding":1340}," — index způsobilosti",[1110,24000,24001,24002,1730],{},"Podíl mezi délkou tolerančního intervalu a délkou intervalu, ve kterém by za normálního rozdělení mělo ležet skoro všech 99,73 % hodnot znaku, tedy ",[1115,24003,24005],{"className":24004},[1315],[1317,24006,24007],{"xmlns":1319},[1321,24008,24009,24015],{},[1324,24010,24011,24013],{},[1334,24012,3739],{},[1330,24014,6674],{},[1338,24016,24017],{"encoding":1340},"6\\sigma",[1115,24019,24021],{"className":24020},[1315],[1317,24022,24023],{"xmlns":1319,"display":1736},[1321,24024,24025,24061],{},[1324,24026,24027,24033,24035,24059],{},[1327,24028,24029,24031],{},[1330,24030,20571],{},[1330,24032,1110],{},[1460,24034,1754],{},[2512,24036,24037,24053],{},[1324,24038,24039,24041,24043,24045,24047,24049,24051],{},[1330,24040,21921],{},[1330,24042,23952],{},[1330,24044,21895],{},[1460,24046,2838],{},[1330,24048,21895],{},[1330,24050,23952],{},[1330,24052,21895],{},[1324,24054,24055,24057],{},[1334,24056,3739],{},[1330,24058,6674],{},[1330,24060,1440],{"mathvariant":1893},[1338,24062,24063],{"encoding":1340},"C_p = \\frac{USL - LSL}{6\\sigma}.",[1110,24065,24066,24083,24084,24097,24098,1440],{},[1115,24067,24069],{"className":24068},[1315],[1317,24070,24071],{"xmlns":1319},[1321,24072,24073,24081],{},[1324,24074,24075],{},[1327,24076,24077,24079],{},[1330,24078,20571],{},[1330,24080,1110],{},[1338,24082,20576],{"encoding":1340}," srovnává jen délky, nevšímá si, kde uprostřed tolerance proces leží — centrovaný i silně vychýlený proces se stejným ",[1115,24085,24087],{"className":24086},[1315],[1317,24088,24089],{"xmlns":1319},[1321,24090,24091,24095],{},[1324,24092,24093],{},[1330,24094,6674],{},[1338,24096,6706],{"encoding":1340}," mají stejné ",[1115,24099,24101],{"className":24100},[1315],[1317,24102,24103],{"xmlns":1319},[1321,24104,24105,24113],{},[1324,24106,24107],{},[1327,24108,24109,24111],{},[1330,24110,20571],{},[1330,24112,1110],{},[1338,24114,20576],{"encoding":1340},[1110,24116,24117],{},"Doplňkové charakteristiky využití tolerančního intervalu:",[1204,24119,24120,24154,24242],{},[1207,24121,24122,3763,24125,24153],{},[1302,24123,24124],{},"míra využití tolerančního intervalu",[1115,24126,24128],{"className":24127},[1315],[1317,24129,24130],{"xmlns":1319},[1321,24131,24132,24150],{},[1324,24133,24134,24146,24148],{},[3015,24135,24136],{"scriptlevel":1336,"displaystyle":1121},[2512,24137,24138,24140],{},[1334,24139,11594],{},[1327,24141,24142,24144],{},[1330,24143,20571],{},[1330,24145,1110],{},[2682,24147,2684],{},[1330,24149,11601],{"mathvariant":1893},[1338,24151,24152],{"encoding":1340},"\\dfrac{100}{C_p}\\,\\%"," — na kolik procent je toleranční interval využíván sledovaným znakem,",[1207,24155,24156,24159,24160,24177,24178,5516,24210,1568],{},[1302,24157,24158],{},"robustnost procesu",": rezerva, kterou máme v tolerančních mezích, než index ",[1115,24161,24163],{"className":24162},[1315],[1317,24164,24165],{"xmlns":1319},[1321,24166,24167,24175],{},[1324,24168,24169],{},[1327,24170,24171,24173],{},[1330,24172,20571],{},[1330,24174,1110],{},[1338,24176,20576],{"encoding":1340}," nabyde hodnotu 1 — rovná se menší hodnotě z výrazů ",[1115,24179,24181],{"className":24180},[1315],[1317,24182,24183],{"xmlns":1319},[1321,24184,24185,24207],{},[1324,24186,24187,24189,24191,24193,24195,24197,24199,24201,24203,24205],{},[1330,24188,21921],{},[1330,24190,23952],{},[1330,24192,21895],{},[1460,24194,2838],{},[1460,24196,1647],{"stretchy":1646},[1330,24198,6666],{},[1460,24200,5252],{},[1334,24202,3366],{},[1330,24204,6674],{},[1460,24206,1658],{"stretchy":1646},[1338,24208,24209],{"encoding":1340},"USL-(\\mu+3\\sigma)",[1115,24211,24213],{"className":24212},[1315],[1317,24214,24215],{"xmlns":1319},[1321,24216,24217,24239],{},[1324,24218,24219,24221,24223,24225,24227,24229,24231,24233,24235,24237],{},[1460,24220,1647],{"stretchy":1646},[1330,24222,6666],{},[1460,24224,2838],{},[1334,24226,3366],{},[1330,24228,6674],{},[1460,24230,1658],{"stretchy":1646},[1460,24232,2838],{},[1330,24234,21895],{},[1330,24236,23952],{},[1330,24238,21895],{},[1338,24240,24241],{"encoding":1340},"(\\mu-3\\sigma)-LSL",[1207,24243,24244,3763,24247,6556,24287,24301],{},[1302,24245,24246],{},"podíl zmetků",[1115,24248,24250],{"className":24249},[1315],[1317,24251,24252],{"xmlns":1319},[1321,24253,24254,24284],{},[1324,24255,24256,24263,24265,24267,24270,24272,24274,24276,24282],{},[1327,24257,24258,24260],{},[1330,24259,6502],{},[1330,24261,24262],{},"z",[1460,24264,1754],{},[1334,24266,1360],{},[1330,24268,24269],{"mathvariant":1893},"Φ",[1460,24271,1647],{"stretchy":1646},[1460,24273,2838],{},[1334,24275,3366],{},[1327,24277,24278,24280],{},[1330,24279,20571],{},[1330,24281,1110],{},[1460,24283,1658],{"stretchy":1646},[1338,24285,24286],{"encoding":1340},"P_z = 2\\Phi(-3C_p)",[1115,24288,24290],{"className":24289},[1315],[1317,24291,24292],{"xmlns":1319},[1321,24293,24294,24298],{},[1324,24295,24296],{},[1330,24297,24269],{"mathvariant":1893},[1338,24299,24300],{"encoding":1340},"\\Phi"," je distribuční funkce normovaného normálního rozdělení.",[16521,24303,24305,24326],{"id":24304},"cpkc_pk-index-způsobilosti-s-ohledem-na-vychýlení",[1115,24306,24308],{"className":24307},[1315],[1317,24309,24310],{"xmlns":1319},[1321,24311,24312,24324],{},[1324,24313,24314],{},[1327,24315,24316,24318],{},[1330,24317,20571],{},[1324,24319,24320,24322],{},[1330,24321,1110],{},[1330,24323,7035],{},[1338,24325,20598],{"encoding":1340}," — index způsobilosti s ohledem na vychýlení",[1110,24328,24329],{},"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:",[1115,24331,24333],{"className":24332},[1315],[1317,24334,24335],{"xmlns":1319,"display":1736},[1321,24336,24337,24407],{},[1324,24338,24339,24349,24351,24353,24355,24405],{},[1327,24340,24341,24343],{},[1330,24342,20571],{},[1324,24344,24345,24347],{},[1330,24346,1110],{},[1330,24348,7035],{},[1460,24350,1754],{},[1330,24352,4263],{},[1460,24354,4266],{},[1324,24356,24357,24359,24379,24381,24383,24403],{},[1460,24358,1647],{"fence":1121},[2512,24360,24361,24373],{},[1324,24362,24363,24365,24367,24369,24371],{},[1330,24364,21921],{},[1330,24366,23952],{},[1330,24368,21895],{},[1460,24370,2838],{},[1330,24372,6666],{},[1324,24374,24375,24377],{},[1334,24376,3366],{},[1330,24378,6674],{},[1460,24380,1568],{"separator":1121},[2682,24382,11090],{},[2512,24384,24385,24397],{},[1324,24386,24387,24389,24391,24393,24395],{},[1330,24388,6666],{},[1460,24390,2838],{},[1330,24392,21895],{},[1330,24394,23952],{},[1330,24396,21895],{},[1324,24398,24399,24401],{},[1334,24400,3366],{},[1330,24402,6674],{},[1460,24404,1658],{"fence":1121},[1330,24406,1440],{"mathvariant":1893},[1338,24408,24409],{"encoding":1340},"C_{pk} = \\min\\left(\\frac{USL-\\mu}{3\\sigma},\\ \\frac{\\mu-LSL}{3\\sigma}\\right).",[1110,24411,24412,24413,24426,24427,24457,24458,24479,24480,1440],{},"Vyjde-li některý z obou podílů záporný, položí se roven nule; to nastane, když střední hodnota ",[1115,24414,24416],{"className":24415},[1315],[1317,24417,24418],{"xmlns":1319},[1321,24419,24420,24424],{},[1324,24421,24422],{},[1330,24423,6666],{},[1338,24425,8573],{"encoding":1340}," leží mimo toleranční interval, a proces pak není pod statistickou kontrolou. U centrovaného procesu jsou oba podíly stejné a ",[1115,24428,24430],{"className":24429},[1315],[1317,24431,24432],{"xmlns":1319},[1321,24433,24434,24454],{},[1324,24435,24436,24446,24448],{},[1327,24437,24438,24440],{},[1330,24439,20571],{},[1324,24441,24442,24444],{},[1330,24443,1110],{},[1330,24445,7035],{},[1460,24447,1754],{},[1327,24449,24450,24452],{},[1330,24451,20571],{},[1330,24453,1110],{},[1338,24455,24456],{"encoding":1340},"C_{pk} = C_p","; čím víc je proces vychýlený, tím víc je ",[1115,24459,24461],{"className":24460},[1315],[1317,24462,24463],{"xmlns":1319},[1321,24464,24465,24477],{},[1324,24466,24467],{},[1327,24468,24469,24471],{},[1330,24470,20571],{},[1324,24472,24473,24475],{},[1330,24474,1110],{},[1330,24476,7035],{},[1338,24478,20598],{"encoding":1340}," menší než ",[1115,24481,24483],{"className":24482},[1315],[1317,24484,24485],{"xmlns":1319},[1321,24486,24487,24495],{},[1324,24488,24489],{},[1327,24490,24491,24493],{},[1330,24492,20571],{},[1330,24494,1110],{},[1338,24496,20576],{"encoding":1340},[16521,24498,24500,5516,24521,24544],{"id":24499},"cpmc_pm-a-cpmkc_pmk-indexy-vztažené-k-cíli",[1115,24501,24503],{"className":24502},[1315],[1317,24504,24505],{"xmlns":1319},[1321,24506,24507,24519],{},[1324,24508,24509],{},[1327,24510,24511,24513],{},[1330,24512,20571],{},[1324,24514,24515,24517],{},[1330,24516,1110],{},[1330,24518,4246],{},[1338,24520,20620],{"encoding":1340},[1115,24522,24524],{"className":24523},[1315],[1317,24525,24526],{"xmlns":1319},[1321,24527,24528,24542],{},[1324,24529,24530],{},[1327,24531,24532,24534],{},[1330,24533,20571],{},[1324,24535,24536,24538,24540],{},[1330,24537,1110],{},[1330,24539,4246],{},[1330,24541,7035],{},[1338,24543,20644],{"encoding":1340}," — indexy vztažené k cíli",[1110,24546,24547,24548,24561,24562,24575,24576,24619,24620,1730],{},"Pokud má proces zadaný cílový střed ",[1115,24549,24551],{"className":24550},[1315],[1317,24552,24553],{"xmlns":1319},[1321,24554,24555,24559],{},[1324,24556,24557],{},[1330,24558,6877],{},[1338,24560,6877],{"encoding":1340}," (ne nutně střed tolerance), nahradí se ",[1115,24563,24565],{"className":24564},[1315],[1317,24566,24567],{"xmlns":1319},[1321,24568,24569,24573],{},[1324,24570,24571],{},[1330,24572,6674],{},[1338,24574,6706],{"encoding":1340}," odmocninou ze střední čtvercové odchylky od cíle ",[1115,24577,24579],{"className":24578},[1315],[1317,24580,24581],{"xmlns":1319},[1321,24582,24583,24616],{},[1324,24584,24585,24588,24590],{},[1330,24586,24587],{},"τ",[1460,24589,1754],{},[4228,24591,24592],{},[1324,24593,24594,24600,24602,24604,24606,24608,24610],{},[1353,24595,24596,24598],{},[1330,24597,6674],{},[1334,24599,1360],{},[1460,24601,5252],{},[1460,24603,1647],{"stretchy":1646},[1330,24605,6666],{},[1460,24607,2838],{},[1330,24609,6877],{},[1353,24611,24612,24614],{},[1460,24613,1658],{"stretchy":1646},[1334,24615,1360],{},[1338,24617,24618],{"encoding":1340},"\\tau = \\sqrt{\\sigma^2+(\\mu-T)^2}",", která trestá i vychýlení od ",[1115,24621,24623],{"className":24622},[1315],[1317,24624,24625],{"xmlns":1319},[1321,24626,24627,24631],{},[1324,24628,24629],{},[1330,24630,6877],{},[1338,24632,6877],{"encoding":1340},[1115,24634,24636],{"className":24635},[1315],[1317,24637,24638],{"xmlns":1319,"display":1736},[1321,24639,24640,24752],{},[1324,24641,24642,24652,24654,24678,24680,24682,24694,24696,24698,24700,24750],{},[1327,24643,24644,24646],{},[1330,24645,20571],{},[1324,24647,24648,24650],{},[1330,24649,1110],{},[1330,24651,4246],{},[1460,24653,1754],{},[2512,24655,24656,24672],{},[1324,24657,24658,24660,24662,24664,24666,24668,24670],{},[1330,24659,21921],{},[1330,24661,23952],{},[1330,24663,21895],{},[1460,24665,2838],{},[1330,24667,21895],{},[1330,24669,23952],{},[1330,24671,21895],{},[1324,24673,24674,24676],{},[1334,24675,3739],{},[1330,24677,24587],{},[1460,24679,1568],{"separator":1121},[1784,24681],{"width":1786},[1327,24683,24684,24686],{},[1330,24685,20571],{},[1324,24687,24688,24690,24692],{},[1330,24689,1110],{},[1330,24691,4246],{},[1330,24693,7035],{},[1460,24695,1754],{},[1330,24697,4263],{},[1460,24699,4266],{},[1324,24701,24702,24704,24724,24726,24728,24748],{},[1460,24703,1647],{"fence":1121},[2512,24705,24706,24718],{},[1324,24707,24708,24710,24712,24714,24716],{},[1330,24709,21921],{},[1330,24711,23952],{},[1330,24713,21895],{},[1460,24715,2838],{},[1330,24717,6666],{},[1324,24719,24720,24722],{},[1334,24721,3366],{},[1330,24723,24587],{},[1460,24725,1568],{"separator":1121},[2682,24727,11090],{},[2512,24729,24730,24742],{},[1324,24731,24732,24734,24736,24738,24740],{},[1330,24733,6666],{},[1460,24735,2838],{},[1330,24737,21895],{},[1330,24739,23952],{},[1330,24741,21895],{},[1324,24743,24744,24746],{},[1334,24745,3366],{},[1330,24747,24587],{},[1460,24749,1658],{"fence":1121},[1330,24751,1440],{"mathvariant":1893},[1338,24753,24754],{"encoding":1340},"C_{pm} = \\frac{USL-LSL}{6\\tau}, \\qquad C_{pmk} = \\min\\left(\\frac{USL-\\mu}{3\\tau},\\ \\frac{\\mu-LSL}{3\\tau}\\right).",[16521,24756,24758],{"id":24757},"interpretace","Interpretace",[1141,24760,24761,24788],{},[1144,24762,24763],{},[1147,24764,24765,24785],{},[1150,24766,24767,24768],{},"Hodnota ",[1115,24769,24771],{"className":24770},[1315],[1317,24772,24773],{"xmlns":1319},[1321,24774,24775,24783],{},[1324,24776,24777],{},[1327,24778,24779,24781],{},[1330,24780,20571],{},[1330,24782,1110],{},[1338,24784,20576],{"encoding":1340},[1150,24786,24787],{},"Způsobilost procesu",[1157,24789,24790,24819,24862],{},[1147,24791,24792,24816],{},[1162,24793,24794],{},[1115,24795,24797],{"className":24796},[1315],[1317,24798,24799],{"xmlns":1319},[1321,24800,24801,24813],{},[1324,24802,24803,24809,24811],{},[1327,24804,24805,24807],{},[1330,24806,20571],{},[1330,24808,1110],{},[1460,24810,4107],{},[1334,24812,1565],{},[1338,24814,24815],{"encoding":1340},"C_p \u003C 1",[1162,24817,24818],{},"dosahovaná přesnost je menší než předepsaná — proces je nezpůsobilý",[1147,24820,24821,24845],{},[1162,24822,24823],{},[1115,24824,24826],{"className":24825},[1315],[1317,24827,24828],{"xmlns":1319},[1321,24829,24830,24842],{},[1324,24831,24832,24838,24840],{},[1327,24833,24834,24836],{},[1330,24835,20571],{},[1330,24837,1110],{},[1460,24839,1754],{},[1334,24841,1565],{},[1338,24843,24844],{"encoding":1340},"C_p = 1",[1162,24846,24847,24848,24861],{},"dosahovaná přesnost je rovna předepsané — proces je způsobilý, ale sebemenší zvětšení ",[1115,24849,24851],{"className":24850},[1315],[1317,24852,24853],{"xmlns":1319},[1321,24854,24855,24859],{},[1324,24856,24857],{},[1330,24858,6674],{},[1338,24860,6706],{"encoding":1340}," jej posune na nezpůsobilý",[1147,24863,24864,24888],{},[1162,24865,24866],{},[1115,24867,24869],{"className":24868},[1315],[1317,24870,24871],{"xmlns":1319},[1321,24872,24873,24885],{},[1324,24874,24875,24881,24883],{},[1327,24876,24877,24879],{},[1330,24878,20571],{},[1330,24880,1110],{},[1460,24882,1462],{},[1334,24884,1565],{},[1338,24886,24887],{"encoding":1340},"C_p > 1",[1162,24889,24890],{},"dosahovaná přesnost je větší než předepsaná — proces je způsobilý",[1110,24892,24893,24894,24915,24916,1440],{},"U indexu ",[1115,24895,24897],{"className":24896},[1315],[1317,24898,24899],{"xmlns":1319},[1321,24900,24901,24913],{},[1324,24902,24903],{},[1327,24904,24905,24907],{},[1330,24906,20571],{},[1324,24908,24909,24911],{},[1330,24910,1110],{},[1330,24912,7035],{},[1338,24914,20598],{"encoding":1340}," se v praxi požaduje víc než jen hodnota nad 1: s rozvojem technologií roste nárok na rezervu, a běžně se dnes vyžaduje hodnota alespoň ",[1115,24917,24919],{"className":24918},[1315],[1317,24920,24921],{"xmlns":1319},[1321,24922,24923,24928],{},[1324,24924,24925],{},[1334,24926,24927],{},"1,5",[1338,24929,24930],{"encoding":1340},"1{,}5",[1110,24932,24933],{},[4158,24934],{"alt":24935,"className":24936,"src":24937},"mask-rd-cp-panely",[1130,4162],"\u002Fwiki-assets\u002Fmask-rd-cp-panely.png",[1110,24939,24940],{},[4158,24941],{"alt":24942,"className":24943,"src":24944},"mask-rd-cpk-off-centre",[1130,4162],"\u002Fwiki-assets\u002Fmask-rd-cpk-off-centre.png",[16521,24946,24948],{"id":24947},"výpočet-v-r","Výpočet v R",[1110,24950,24951,24952,24955,24956,24959,24960,24963,24964,5516,24981,2725,24998,25001,25002,25015],{},"Indexy způsobilosti počítá ",[3244,24953,24954],{},"process.capability()"," z výstupu regulačního diagramu ",[3244,24957,24958],{},"q","; ",[3244,24961,24962],{},"spec.limits"," jsou toleranční meze ",[1115,24965,24967],{"className":24966},[1315],[1317,24968,24969],{"xmlns":1319},[1321,24970,24971,24979],{},[1324,24972,24973,24975,24977],{},[1330,24974,21895],{},[1330,24976,23952],{},[1330,24978,21895],{},[1338,24980,23957],{"encoding":1340},[1115,24982,24984],{"className":24983},[1315],[1317,24985,24986],{"xmlns":1319},[1321,24987,24988,24996],{},[1324,24989,24990,24992,24994],{},[1330,24991,21921],{},[1330,24993,23952],{},[1330,24995,21895],{},[1338,24997,23976],{"encoding":1340},[3244,24999,25000],{},"target"," cílová hodnota ",[1115,25003,25005],{"className":25004},[1315],[1317,25006,25007],{"xmlns":1319},[1321,25008,25009,25013],{},[1324,25010,25011],{},[1330,25012,6877],{},[1338,25014,6877],{"encoding":1340},". Pro velikost výrobku v mm s tolerančními mezemi 100 a 110 mm a cílovou hodnotou 105 mm:",[3468,25017,25019],{"className":3470,"code":25018,"language":71,"meta":1247,"style":1247},"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",[3244,25020,25021,25031,25054,25069,25091],{"__ignoreMap":1247},[1115,25022,25023,25025,25027,25029],{"class":3476,"line":10},[1115,25024,17170],{"class":3483},[1115,25026,1647],{"class":3491},[1115,25028,360],{"class":3479},[1115,25030,3676],{"class":3491},[1115,25032,25033,25035,25037,25039,25041,25044,25046,25048,25050,25052],{"class":3476,"line":27},[1115,25034,19881],{"class":3479},[1115,25036,3484],{"class":3483},[1115,25038,19886],{"class":3487},[1115,25040,1647],{"class":3491},[1115,25042,25043],{"class":3615},"\"3_8.txt\"",[1115,25045,1568],{"class":3483},[1115,25047,19896],{"class":3479},[1115,25049,3572],{"class":3483},[1115,25051,3585],{"class":3499},[1115,25053,3676],{"class":3491},[1115,25055,25056,25058,25060,25063,25065,25067],{"class":3476,"line":148},[1115,25057,6495],{"class":3479},[1115,25059,3484],{"class":3483},[1115,25061,25062],{"class":3487}," as.matrix",[1115,25064,1647],{"class":3491},[1115,25066,19881],{"class":3479},[1115,25068,3676],{"class":3491},[1115,25070,25071,25073,25075,25077,25079,25081,25083,25085,25087,25089],{"class":3476,"line":111},[1115,25072,24958],{"class":3479},[1115,25074,3484],{"class":3483},[1115,25076,23395],{"class":3487},[1115,25078,1647],{"class":3491},[1115,25080,6495],{"class":3479},[1115,25082,1568],{"class":3483},[1115,25084,11999],{"class":3479},[1115,25086,3572],{"class":3483},[1115,25088,22521],{"class":3615},[1115,25090,3676],{"class":3491},[1115,25092,25093,25096,25098,25100,25102,25105,25107,25109,25111,25113,25115,25117,25119,25121,25124,25126,25129,25131,25134,25136,25138,25140,25142],{"class":3476,"line":96},[1115,25094,25095],{"class":3487},"process.capability",[1115,25097,1647],{"class":3491},[1115,25099,24958],{"class":3479},[1115,25101,1568],{"class":3483},[1115,25103,25104],{"class":3479}," spec.limits",[1115,25106,3572],{"class":3483},[1115,25108,3610],{"class":3487},[1115,25110,1647],{"class":3491},[1115,25112,11594],{"class":3499},[1115,25114,1568],{"class":3483},[1115,25116,14044],{"class":3499},[1115,25118,1658],{"class":3491},[1115,25120,1568],{"class":3483},[1115,25122,25123],{"class":3479}," target",[1115,25125,3572],{"class":3483},[1115,25127,25128],{"class":3499}," 105",[1115,25130,1568],{"class":3483},[1115,25132,25133],{"class":3479}," std.dev",[1115,25135,3572],{"class":3483},[1115,25137,9018],{"class":3487},[1115,25139,1647],{"class":3491},[1115,25141,6495],{"class":3479},[1115,25143,9270],{"class":3491},[1110,25145,25146,25147,2725,25150,2725,25153,2725,25156,5516,25159,25162,25163,5516,25165,25167,25168,25189,25190,25213],{},"Výpis obsahuje řádky ",[3244,25148,25149],{},"Cp",[3244,25151,25152],{},"Cp_l",[3244,25154,25155],{},"Cp_u",[3244,25157,25158],{},"Cp_k",[3244,25160,25161],{},"Cpm"," s hodnotou indexu a 95% intervalem spolehlivosti. ",[3244,25164,25152],{},[3244,25166,25155],{}," jsou dílčí poměry k dolní a horní mezi, jejich minimum je ",[1115,25169,25171],{"className":25170},[1315],[1317,25172,25173],{"xmlns":1319},[1321,25174,25175,25187],{},[1324,25176,25177],{},[1327,25178,25179,25181],{},[1330,25180,20571],{},[1324,25182,25183,25185],{},[1330,25184,1110],{},[1330,25186,7035],{},[1338,25188,20598],{"encoding":1340},". Index ",[1115,25191,25193],{"className":25192},[1315],[1317,25194,25195],{"xmlns":1319},[1321,25196,25197,25211],{},[1324,25198,25199],{},[1327,25200,25201,25203],{},[1330,25202,20571],{},[1324,25204,25205,25207,25209],{},[1330,25206,1110],{},[1330,25208,4246],{},[1330,25210,7035],{},[1338,25212,20644],{"encoding":1340}," a doplňkové charakteristiky se dopočítají ze vzorců výše:",[3468,25215,25217],{"className":3470,"code":25216,"language":71,"meta":1247,"style":1247},"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",[3244,25218,25219,25246,25271,25308,25338,25396,25410,25461],{"__ignoreMap":1247},[1115,25220,25221,25224,25226,25228,25230,25232,25234,25236,25238,25240,25242,25244],{"class":3476,"line":10},[1115,25222,25223],{"class":3479},"mu",[1115,25225,3484],{"class":3483},[1115,25227,9008],{"class":3487},[1115,25229,1647],{"class":3491},[1115,25231,6495],{"class":3479},[1115,25233,11953],{"class":3491},[1115,25235,380],{"class":3479},[1115,25237,3484],{"class":3483},[1115,25239,9018],{"class":3487},[1115,25241,1647],{"class":3491},[1115,25243,6495],{"class":3479},[1115,25245,3676],{"class":3491},[1115,25247,25248,25250,25252,25254,25256,25258,25260,25262,25264,25266,25268],{"class":3476,"line":27},[1115,25249,23957],{"class":3479},[1115,25251,3484],{"class":3483},[1115,25253,15115],{"class":3499},[1115,25255,24959],{"class":3491},[1115,25257,23976],{"class":3479},[1115,25259,3484],{"class":3483},[1115,25261,14044],{"class":3499},[1115,25263,24959],{"class":3491},[1115,25265,6877],{"class":3479},[1115,25267,3484],{"class":3483},[1115,25269,25270],{"class":3499}," 105\n",[1115,25272,25273,25276,25278,25280,25282,25284,25286,25288,25290,25292,25294,25297,25300,25302,25304,25306],{"class":3476,"line":148},[1115,25274,25275],{"class":3479},"tau",[1115,25277,3484],{"class":3483},[1115,25279,4353],{"class":3487},[1115,25281,1647],{"class":3491},[1115,25283,380],{"class":3479},[1115,25285,2502],{"class":3483},[1115,25287,1360],{"class":3499},[1115,25289,18289],{"class":3483},[1115,25291,4382],{"class":3491},[1115,25293,25223],{"class":3479},[1115,25295,25296],{"class":3483}," -",[1115,25298,25299],{"class":3479}," T",[1115,25301,1658],{"class":3491},[1115,25303,2502],{"class":3483},[1115,25305,1360],{"class":3499},[1115,25307,3676],{"class":3491},[1115,25309,25310,25312,25314,25316,25318,25320,25323,25325,25327,25329,25331,25333,25336],{"class":3476,"line":111},[1115,25311,25149],{"class":3479},[1115,25313,3484],{"class":3483},[1115,25315,4382],{"class":3491},[1115,25317,23976],{"class":3479},[1115,25319,25296],{"class":3483},[1115,25321,25322],{"class":3479}," LSL",[1115,25324,4376],{"class":3491},[1115,25326,4379],{"class":3483},[1115,25328,4382],{"class":3491},[1115,25330,3739],{"class":3499},[1115,25332,18414],{"class":3483},[1115,25334,25335],{"class":3479}," sigma",[1115,25337,3676],{"class":3491},[1115,25339,25340,25343,25345,25347,25350,25352,25354,25357,25359,25361,25363,25365,25367,25370,25372,25374,25376,25378,25380,25382,25384,25386,25388,25390,25392,25394],{"class":3476,"line":96},[1115,25341,25342],{"class":3479},"Cpmk",[1115,25344,3484],{"class":3483},[1115,25346,11974],{"class":3487},[1115,25348,25349],{"class":3491},"((",[1115,25351,23976],{"class":3479},[1115,25353,25296],{"class":3483},[1115,25355,25356],{"class":3479}," mu",[1115,25358,4376],{"class":3491},[1115,25360,4379],{"class":3483},[1115,25362,4382],{"class":3491},[1115,25364,3366],{"class":3499},[1115,25366,18414],{"class":3483},[1115,25368,25369],{"class":3479}," tau",[1115,25371,1658],{"class":3491},[1115,25373,1568],{"class":3483},[1115,25375,4382],{"class":3491},[1115,25377,25223],{"class":3479},[1115,25379,25296],{"class":3483},[1115,25381,25322],{"class":3479},[1115,25383,4376],{"class":3491},[1115,25385,4379],{"class":3483},[1115,25387,4382],{"class":3491},[1115,25389,3366],{"class":3499},[1115,25391,18414],{"class":3483},[1115,25393,25369],{"class":3479},[1115,25395,9270],{"class":3491},[1115,25397,25398,25401,25403,25405,25407],{"class":3476,"line":89},[1115,25399,25400],{"class":3479},"miravyuziti",[1115,25402,3484],{"class":3483},[1115,25404,15115],{"class":3499},[1115,25406,9852],{"class":3483},[1115,25408,25409],{"class":3479}," Cp\n",[1115,25411,25412,25415,25417,25419,25421,25423,25425,25427,25429,25431,25433,25435,25437,25439,25441,25443,25445,25447,25449,25451,25453,25455,25457,25459],{"class":3476,"line":82},[1115,25413,25414],{"class":3479},"robustnost",[1115,25416,3484],{"class":3483},[1115,25418,11974],{"class":3487},[1115,25420,1647],{"class":3491},[1115,25422,23976],{"class":3479},[1115,25424,25296],{"class":3483},[1115,25426,4382],{"class":3491},[1115,25428,25223],{"class":3479},[1115,25430,18289],{"class":3483},[1115,25432,10632],{"class":3499},[1115,25434,18414],{"class":3483},[1115,25436,25335],{"class":3479},[1115,25438,1658],{"class":3491},[1115,25440,1568],{"class":3483},[1115,25442,4382],{"class":3491},[1115,25444,25223],{"class":3479},[1115,25446,25296],{"class":3483},[1115,25448,10632],{"class":3499},[1115,25450,18414],{"class":3483},[1115,25452,25335],{"class":3479},[1115,25454,4376],{"class":3491},[1115,25456,4413],{"class":3483},[1115,25458,25322],{"class":3479},[1115,25460,3676],{"class":3491},[1115,25462,25463,25466,25468,25470,25472,25474,25476,25478,25480,25482,25485],{"class":3476,"line":75},[1115,25464,25465],{"class":3479},"Pz",[1115,25467,3484],{"class":3483},[1115,25469,3955],{"class":3499},[1115,25471,18414],{"class":3483},[1115,25473,9128],{"class":3487},[1115,25475,1647],{"class":3491},[1115,25477,4413],{"class":3483},[1115,25479,3366],{"class":3499},[1115,25481,18414],{"class":3483},[1115,25483,25484],{"class":3479}," Cp",[1115,25486,3676],{"class":3491},[1136,25488,6183],{"id":6182},[1204,25490,25491,25494,25554,25645,25711],{},[1207,25492,25493],{},"Počítat indexy způsobilosti pro proces, který není statisticky zvládnutý — způsobilost se zkoumá až ve třetí fázi regulace.",[1207,25495,25496,25497,25514,25515,25532,25533,1440],{},"Posuzovat jen ",[1115,25498,25500],{"className":25499},[1315],[1317,25501,25502],{"xmlns":1319},[1321,25503,25504,25512],{},[1324,25505,25506],{},[1327,25507,25508,25510],{},[1330,25509,20571],{},[1330,25511,1110],{},[1338,25513,20576],{"encoding":1340}," u vychýleného procesu — ",[1115,25516,25518],{"className":25517},[1315],[1317,25519,25520],{"xmlns":1319},[1321,25521,25522,25530],{},[1324,25523,25524],{},[1327,25525,25526,25528],{},[1330,25527,20571],{},[1330,25529,1110],{},[1338,25531,20576],{"encoding":1340}," polohu střední hodnoty nezohledňuje, vychýlení zachytí až ",[1115,25534,25536],{"className":25535},[1315],[1317,25537,25538],{"xmlns":1319},[1321,25539,25540,25552],{},[1324,25541,25542],{},[1327,25543,25544,25546],{},[1330,25545,20571],{},[1324,25547,25548,25550],{},[1330,25549,1110],{},[1330,25551,7035],{},[1338,25553,20598],{"encoding":1340},[1207,25555,25556,25557,25570,25571,25584,25585,25570,25600,25613,25614,25627,25628,25641,25642,25644],{},"Zaměnit diagram ",[1115,25558,25560],{"className":25559},[1315],[1317,25561,25562],{"xmlns":1319},[1321,25563,25564,25568],{},[1324,25565,25566],{},[1330,25567,3494],{},[1338,25569,3494],{"encoding":1340}," s diagramem ",[1115,25572,25574],{"className":25573},[1315],[1317,25575,25576],{"xmlns":1319},[1321,25577,25578,25582],{},[1324,25579,25580],{},[1330,25581,11304],{},[1338,25583,11304],{"encoding":1340}," nebo diagram ",[1115,25586,25588],{"className":25587},[1315],[1317,25589,25590],{"xmlns":1319},[1321,25591,25592,25598],{},[1324,25593,25594,25596],{},[1330,25595,1458],{},[1330,25597,1110],{},[1338,25599,20536],{"encoding":1340},[1115,25601,25603],{"className":25602},[1315],[1317,25604,25605],{"xmlns":1319},[1321,25606,25607,25611],{},[1324,25608,25609],{},[1330,25610,1110],{},[1338,25612,1110],{"encoding":1340}," — při nekonstantním rozsahu podskupin se volí ",[1115,25615,25617],{"className":25616},[1315],[1317,25618,25619],{"xmlns":1319},[1321,25620,25621,25625],{},[1324,25622,25623],{},[1330,25624,11304],{},[1338,25626,11304],{"encoding":1340},", resp. ",[1115,25629,25631],{"className":25630},[1315],[1317,25632,25633],{"xmlns":1319},[1321,25634,25635,25639],{},[1324,25636,25637],{},[1330,25638,1110],{},[1338,25640,1110],{"encoding":1340},", a do ",[3244,25643,23591],{}," se zadává vektor rozsahů.",[1207,25646,25647,25648,25665,25666,25679,25680,25693,25694,1440],{},"Posuzovat diagram ",[1115,25649,25651],{"className":25650},[1315],[1317,25652,25653],{"xmlns":1319},[1321,25654,25655,25663],{},[1324,25656,25657],{},[2496,25658,25659,25661],{"accent":1121},[1330,25660,6495],{},[1460,25662,11235],{},[1338,25664,21340],{"encoding":1340}," dřív než diagram rozpětí — nejprve se určí a stabilizuje diagram ",[1115,25667,25669],{"className":25668},[1315],[1317,25670,25671],{"xmlns":1319},[1321,25672,25673,25677],{},[1324,25674,25675],{},[1330,25676,10000],{},[1338,25678,10000],{"encoding":1340}," (resp. ",[1115,25681,25683],{"className":25682},[1315],[1317,25684,25685],{"xmlns":1319},[1321,25686,25687,25691],{},[1324,25688,25689],{},[1330,25690,1626],{},[1338,25692,1626],{"encoding":1340},"), potom diagram ",[1115,25695,25697],{"className":25696},[1315],[1317,25698,25699],{"xmlns":1319},[1321,25700,25701,25709],{},[1324,25702,25703],{},[2496,25704,25705,25707],{"accent":1121},[1330,25706,6495],{},[1460,25708,11235],{},[1338,25710,21340],{"encoding":1340},[1207,25712,25713],{},"Vyřadit podskupinu jen podle polohy bodu — vyřazuje se až po zjištění a odstranění vymezitelné příčiny.",[1136,25715,1202],{"id":1201},[1204,25717,25718,25723,25728,25734,25739,25744,25749],{},[1207,25719,25720],{},[1127,25721,1133],{"className":25722,"dataFsResolvedFilePath":1131,"href":1132},[1130],[1207,25724,25725],{},[1127,25726,886],{"className":25727,"dataFsResolvedFilePath":1180,"href":1181},[1130],[1207,25729,25730],{},[1127,25731,25733],{"className":25732,"dataFsResolvedFilePath":1167,"href":1168},[1130],"nahodne-veliciny-a-rozdeleni",[1207,25735,25736],{},[1127,25737,141],{"className":25738,"dataFsResolvedFilePath":1193,"href":1194},[1130],[1207,25740,25741],{},[1127,25742,10862],{"className":25743,"dataFsResolvedFilePath":6397,"href":6398},[1130],[1207,25745,25746],{},[1127,25747,716],{"className":25748,"dataFsResolvedFilePath":10868,"href":10869},[1130],[1207,25750,25751],{},[1127,25752,6413],{"className":25753,"dataFsResolvedFilePath":1232,"href":1233},[1130],[1136,25755,1237],{"id":934},[1110,25757,1240,25758,1245],{},[1242,25759,1244],{},[1110,25761,25762,25763,25766],{},"MONTGOMERY, D. C. ",[1242,25764,25765],{},"Introduction to Statistical Quality Control",". 6. vyd. John Wiley & Sons, 2005.",[1110,25768,25769,25770,25773],{},"ČSN ISO 8258. ",[1242,25771,25772],{},"Shewhartovy regulační diagramy",". Praha: Český normalizační institut, 1994.",[1110,25775,25776,25777,25780],{},"KUPKA, K. ",[1242,25778,25779],{},"Statistické řízení jakosti",". Pardubice: TriloByte, 1997.",[6421,25782,25783],{},"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":23934,"depth":27,"text":23935,"children":25807},[25808,25810,25812,25814,25815],{"id":23980,"depth":148,"text":25809},"CpC_p — index způsobilosti",{"id":24304,"depth":148,"text":25811},"CpkC_{pk} — index způsobilosti s ohledem na vychýlení",{"id":24499,"depth":148,"text":25813},"CpmC_{pm} a CpmkC_{pmk} — indexy vztažené k cíli",{"id":24757,"depth":148,"text":24758},{"id":24947,"depth":148,"text":24948},{"id":6182,"depth":27,"text":6183},{"id":1201,"depth":27,"text":1202},{"id":934,"depth":27,"text":1237},{},"\u002Ftopics\u002Fregulacni-diagramy-a-indexy-zpusobilosti",{"title":6407,"description":1247},[25823,25824,25825,25826],"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":25831,"title":1195,"body":25832,"course":23,"courses":1252,"created":1253,"description":1247,"extension":1254,"meta":35643,"navigation":1256,"path":35644,"seo":35645,"sources":35646,"stem":35648,"tags":35649,"type":6442,"updated":1253,"__hash__":35650},"topics\u002Ftopics\u002Ftestovani-hypotez.md",{"type":1096,"value":25833,"toc":35616},[25834,25837,26036,26080,26084,26094,26097,26163,26213,26366,26370,26373,26467,26617,26636,26643,26732,26736,26771,26808,26846,26881,26885,26892,27110,27229,27233,27365,27419,27441,27783,27790,27878,27884,27925,28210,28219,28334,28340,28347,28352,28358,28452,28458,28484,28490,28582,28588,28638,28642,28838,28898,29260,29599,29698,29704,29932,29936,30202,30206,30209,30275,30322,30778,30782,30785,30972,31005,31227,31546,31585,31592,32249,32388,32394,32550,32556,32563,32616,32622,32795,32801,32865,32870,33055,33061,33106,33110,33113,33117,33164,33392,33408,33497,33503,33529,33533,33536,33608,33701,33770,33776,33799,34246,34253,34257,34287,34291,34541,34560,34621,34630,34786,34792,34818,34993,34997,35018,35049,35053,35077,35107,35111,35171,35229,35233,35240,35413,35415,35568,35570,35607,35609,35613],[1099,25835,1195],{"id":25836},"testování-statistických-hypotéz",[1103,25838,25840,25846],{"className":25839,"dataCallout":1287},[1106,1286],[1110,25841,25843,1295],{"className":25842},[1113],[1115,25844],{"className":25845,"ariaHidden":1121},[1118,1294,1120],[1204,25847,25848,25918,26000,26003,26006],{},[1207,25849,25850,25851,25868,25869,25886,25887,2725,25900,25917],{},"Test porovnává tvrzení ",[1115,25852,25854],{"className":25853},[1315],[1317,25855,25856],{"xmlns":1319},[1321,25857,25858,25866],{},[1324,25859,25860],{},[1327,25861,25862,25864],{},[1330,25863,1332],{},[1334,25865,1336],{},[1338,25867,1341],{"encoding":1340}," s alternativou ",[1115,25870,25872],{"className":25871},[1315],[1317,25873,25874],{"xmlns":1319},[1321,25875,25876,25884],{},[1324,25877,25878],{},[1327,25879,25880,25882],{},[1330,25881,1332],{},[1334,25883,1565],{},[1338,25885,2770],{"encoding":1340}," pomocí testového kritéria spočteného z výběru; padne-li kritérium do kritického oboru ",[1115,25888,25890],{"className":25889},[1315],[1317,25891,25892],{"xmlns":1319},[1321,25893,25894,25898],{},[1324,25895,25896],{},[1330,25897,1376],{},[1338,25899,1376],{"encoding":1340},[1115,25901,25903],{"className":25902},[1315],[1317,25904,25905],{"xmlns":1319},[1321,25906,25907,25915],{},[1324,25908,25909],{},[1327,25910,25911,25913],{},[1330,25912,1332],{},[1334,25914,1336],{},[1338,25916,1341],{"encoding":1340}," zamítáme.",[1207,25919,25920,25921,25934,25935,25952,25953,25967,25968,25985,25986,25999],{},"Rozhodnutí nese dva typy chyb: chybu I. druhu (",[1115,25922,25924],{"className":25923},[1315],[1317,25925,25926],{"xmlns":1319},[1321,25927,25928,25932],{},[1324,25929,25930],{},[1330,25931,3139],{},[1338,25933,3202],{"encoding":1340},", zamítnutí platné ",[1115,25936,25938],{"className":25937},[1315],[1317,25939,25940],{"xmlns":1319},[1321,25941,25942,25950],{},[1324,25943,25944],{},[1327,25945,25946,25948],{},[1330,25947,1332],{},[1334,25949,1336],{},[1338,25951,1341],{"encoding":1340},") a chybu II. druhu (",[1115,25954,25956],{"className":25955},[1315],[1317,25957,25958],{"xmlns":1319},[1321,25959,25960,25964],{},[1324,25961,25962],{},[1330,25963,16112],{},[1338,25965,25966],{"encoding":1340},"\\beta",", přijetí neplatné ",[1115,25969,25971],{"className":25970},[1315],[1317,25972,25973],{"xmlns":1319},[1321,25974,25975,25983],{},[1324,25976,25977],{},[1327,25978,25979,25981],{},[1330,25980,1332],{},[1334,25982,1336],{},[1338,25984,1341],{"encoding":1340},"). Hladina významnosti ",[1115,25987,25989],{"className":25988},[1315],[1317,25990,25991],{"xmlns":1319},[1321,25992,25993,25997],{},[1324,25994,25995],{},[1330,25996,3139],{},[1338,25998,3202],{"encoding":1340}," se volí předem, obvykle 0,05.",[1207,26001,26002],{},"Pro střední hodnotu normálního rozdělení slouží jednovýběrový a párový t-test; pro srovnání dvou souborů F-test (rozptyly) a dvouvýběrový t-test (střední hodnoty).",[1207,26004,26005],{},"Normalitu ověřuje Shapiro-Wilkův test, shodu s libovolným rozdělením Kolmogorov-Smirnovův test; při porušené normalitě nastupují neparametrické testy (Wilcoxonovy, Kruskalův-Wallisův, mediánový, Friedmanův).",[1207,26007,26008,26009,26022,26023,1440],{},"Rozhodnutí lze číst dvěma rovnocennými způsoby — podle polohy kritéria vůči ",[1115,26010,26012],{"className":26011},[1315],[1317,26013,26014],{"xmlns":1319},[1321,26015,26016,26020],{},[1324,26017,26018],{},[1330,26019,1376],{},[1338,26021,1376],{"encoding":1340},", nebo podle p-hodnoty vůči ",[1115,26024,26026],{"className":26025},[1315],[1317,26027,26028],{"xmlns":1319},[1321,26029,26030,26034],{},[1324,26031,26032],{},[1330,26033,3139],{},[1338,26035,3202],{"encoding":1340},[1110,26037,26038,26039,26043,26044,26048,26049,26053,26054,2725,26067,15868],{},"Testy statistických hypotéz jsou nástroj ",[1127,26040,26042],{"className":26041,"dataFsResolvedFilePath":1131,"href":1132},[1130],"Metod aplikované statistiky"," pro rozhodování o parametrech nebo tvaru rozdělení na základě náhodného výběru, nikoli vyčerpávajícího šetření celého základního souboru. Vycházejí z charakteristik, které lze předem spočítat jako ",[1127,26045,26047],{"className":26046,"dataFsResolvedFilePath":1180,"href":1181},[1130],"popisnou statistiku"," výběru, a z rozdělení uvedených u ",[1127,26050,26052],{"className":26051,"dataFsResolvedFilePath":1167,"href":1168},[1130],"náhodných veličin"," (normální, ",[1115,26055,26057],{"className":26056},[1315],[1317,26058,26059],{"xmlns":1319},[1321,26060,26061,26065],{},[1324,26062,26063],{},[1330,26064,6919],{},[1338,26066,6919],{"encoding":1340},[1115,26068,26070],{"className":26069},[1315],[1317,26071,26072],{"xmlns":1319},[1321,26073,26074,26078],{},[1324,26075,26076],{},[1330,26077,6490],{},[1338,26079,6490],{"encoding":1340},[1136,26081,26083],{"id":26082},"statistická-hypotéza-a-její-test","Statistická hypotéza a její test",[1110,26085,26086,26089,26090,26093],{},[1302,26087,26088],{},"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. ",[1302,26091,26092],{},"Testování hypotéz"," je proces ověření správnosti nebo nesprávnosti hypotézy pomocí výsledků získaných náhodným výběrem.",[1110,26095,26096],{},"Proti sobě stojí dvě hypotézy:",[1204,26098,26099,26122],{},[1207,26100,26101,26121],{},[1302,26102,26103,26104],{},"Nulová hypotéza ",[1115,26105,26107],{"className":26106},[1315],[1317,26108,26109],{"xmlns":1319},[1321,26110,26111,26119],{},[1324,26112,26113],{},[1327,26114,26115,26117],{},[1330,26116,1332],{},[1334,26118,1336],{},[1338,26120,1341],{"encoding":1340}," — tvrzení o parametru nebo rozdělení, které chceme ověřit.",[1207,26123,26124,26144,26145,26162],{},[1302,26125,26126,26127],{},"Alternativní hypotéza ",[1115,26128,26130],{"className":26129},[1315],[1317,26131,26132],{"xmlns":1319},[1321,26133,26134,26142],{},[1324,26135,26136],{},[1327,26137,26138,26140],{},[1330,26139,1332],{},[1334,26141,1565],{},[1338,26143,2770],{"encoding":1340}," — staví se proti ",[1115,26146,26148],{"className":26147},[1315],[1317,26149,26150],{"xmlns":1319},[1321,26151,26152,26160],{},[1324,26153,26154],{},[1327,26155,26156,26158],{},[1330,26157,1332],{},[1334,26159,1336],{},[1338,26161,1341],{"encoding":1340}," a určitým způsobem popírá její tvrzení.",[1110,26164,1471,26165,26195,26196,1730],{},[1115,26166,26168],{"className":26167},[1315],[1317,26169,26170],{"xmlns":1319},[1321,26171,26172,26192],{},[1324,26173,26174,26180,26182,26184,26186],{},[1327,26175,26176,26178],{},[1330,26177,1332],{},[1334,26179,1336],{},[1460,26181,1730],{},[1330,26183,6666],{},[1460,26185,1754],{},[1327,26187,26188,26190],{},[1330,26189,6666],{},[1334,26191,1336],{},[1338,26193,26194],{"encoding":1340},"H_0: \\mu = \\mu_0"," existují tři varianty ",[1115,26197,26199],{"className":26198},[1315],[1317,26200,26201],{"xmlns":1319},[1321,26202,26203,26211],{},[1324,26204,26205],{},[1327,26206,26207,26209],{},[1330,26208,1332],{},[1334,26210,1565],{},[1338,26212,2770],{"encoding":1340},[1141,26214,26215,26245],{},[1144,26216,26217],{},[1147,26218,26219,26239,26242],{},[1150,26220,26221,26222],{},"Tvar ",[1115,26223,26225],{"className":26224},[1315],[1317,26226,26227],{"xmlns":1319},[1321,26228,26229,26237],{},[1324,26230,26231],{},[1327,26232,26233,26235],{},[1330,26234,1332],{},[1334,26236,1565],{},[1338,26238,2770],{"encoding":1340},[1150,26240,26241],{},"Zápis",[1150,26243,26244],{},"Typ",[1157,26246,26247,26287,26327],{},[1147,26248,26249,26252,26284],{},[1162,26250,26251],{},"nerovnost",[1162,26253,26254],{},[1115,26255,26257],{"className":26256},[1315],[1317,26258,26259],{"xmlns":1319},[1321,26260,26261,26281],{},[1324,26262,26263,26269,26271,26273,26275],{},[1327,26264,26265,26267],{},[1330,26266,1332],{},[1334,26268,1565],{},[1460,26270,1730],{},[1330,26272,6666],{},[1460,26274,10733],{"mathvariant":1893},[1327,26276,26277,26279],{},[1330,26278,6666],{},[1334,26280,1336],{},[1338,26282,26283],{"encoding":1340},"H_1: \\mu \\neq \\mu_0",[1162,26285,26286],{},"dvoustranná",[1147,26288,26289,26292,26324],{},[1162,26290,26291],{},"větší",[1162,26293,26294],{},[1115,26295,26297],{"className":26296},[1315],[1317,26298,26299],{"xmlns":1319},[1321,26300,26301,26321],{},[1324,26302,26303,26309,26311,26313,26315],{},[1327,26304,26305,26307],{},[1330,26306,1332],{},[1334,26308,1565],{},[1460,26310,1730],{},[1330,26312,6666],{},[1460,26314,1462],{},[1327,26316,26317,26319],{},[1330,26318,6666],{},[1334,26320,1336],{},[1338,26322,26323],{"encoding":1340},"H_1: \\mu > \\mu_0",[1162,26325,26326],{},"jednostranná",[1147,26328,26329,26332,26364],{},[1162,26330,26331],{},"menší",[1162,26333,26334],{},[1115,26335,26337],{"className":26336},[1315],[1317,26338,26339],{"xmlns":1319},[1321,26340,26341,26361],{},[1324,26342,26343,26349,26351,26353,26355],{},[1327,26344,26345,26347],{},[1330,26346,1332],{},[1334,26348,1565],{},[1460,26350,1730],{},[1330,26352,6666],{},[1460,26354,4107],{},[1327,26356,26357,26359],{},[1330,26358,6666],{},[1334,26360,1336],{},[1338,26362,26363],{"encoding":1340},"H_1: \\mu \u003C \\mu_0",[1162,26365,26326],{},[16521,26367,26369],{"id":26368},"chyba-i-a-ii-druhu","Chyba I. a II. druhu",[1110,26371,26372],{},"Protože je úsudek odvozen z náhodného výběru, může vést ke dvěma typům chybného rozhodnutí:",[1204,26374,26375,26412],{},[1207,26376,26377,26380,26381,26398,26399,1440],{},[1302,26378,26379],{},"Chyba I. druhu"," — zamítnutí ",[1115,26382,26384],{"className":26383},[1315],[1317,26385,26386],{"xmlns":1319},[1321,26387,26388,26396],{},[1324,26389,26390],{},[1327,26391,26392,26394],{},[1330,26393,1332],{},[1334,26395,1336],{},[1338,26397,1341],{"encoding":1340},", ačkoliv ve skutečnosti platí. Pravděpodobnost ",[1115,26400,26402],{"className":26401},[1315],[1317,26403,26404],{"xmlns":1319},[1321,26405,26406,26410],{},[1324,26407,26408],{},[1330,26409,3139],{},[1338,26411,3202],{"encoding":1340},[1207,26413,26414,26417,26418,26435,26436,26453,26454,1440],{},[1302,26415,26416],{},"Chyba II. druhu"," — přijetí ",[1115,26419,26421],{"className":26420},[1315],[1317,26422,26423],{"xmlns":1319},[1321,26424,26425,26433],{},[1324,26426,26427],{},[1327,26428,26429,26431],{},[1330,26430,1332],{},[1334,26432,1336],{},[1338,26434,1341],{"encoding":1340},", ačkoliv platí ",[1115,26437,26439],{"className":26438},[1315],[1317,26440,26441],{"xmlns":1319},[1321,26442,26443,26451],{},[1324,26444,26445],{},[1327,26446,26447,26449],{},[1330,26448,1332],{},[1334,26450,1565],{},[1338,26452,2770],{"encoding":1340},". Pravděpodobnost ",[1115,26455,26457],{"className":26456},[1315],[1317,26458,26459],{"xmlns":1319},[1321,26460,26461,26465],{},[1324,26462,26463],{},[1330,26464,16112],{},[1338,26466,25966],{"encoding":1340},[1141,26468,26469,26532],{},[1144,26470,26471],{},[1147,26472,26473,26493,26512],{},[1150,26474,26475,26476],{},"Úsudek o ",[1115,26477,26479],{"className":26478},[1315],[1317,26480,26481],{"xmlns":1319},[1321,26482,26483,26491],{},[1324,26484,26485],{},[1327,26486,26487,26489],{},[1330,26488,1332],{},[1334,26490,1336],{},[1338,26492,1341],{"encoding":1340},[1150,26494,26495,8128],{},[1115,26496,26498],{"className":26497},[1315],[1317,26499,26500],{"xmlns":1319},[1321,26501,26502,26510],{},[1324,26503,26504],{},[1327,26505,26506,26508],{},[1330,26507,1332],{},[1334,26509,1336],{},[1338,26511,1341],{"encoding":1340},[1150,26513,26514,26531],{},[1115,26515,26517],{"className":26516},[1315],[1317,26518,26519],{"xmlns":1319},[1321,26520,26521,26529],{},[1324,26522,26523],{},[1327,26524,26525,26527],{},[1330,26526,1332],{},[1334,26528,1336],{},[1338,26530,1341],{"encoding":1340}," neplatí",[1157,26533,26534,26576],{},[1147,26535,26536,26539,26560],{},[1162,26537,26538],{},"Nezamítá se",[1162,26540,26541,26542],{},"správné rozhodnutí, ",[1115,26543,26545],{"className":26544},[1315],[1317,26546,26547],{"xmlns":1319},[1321,26548,26549,26557],{},[1324,26550,26551,26553,26555],{},[1334,26552,1565],{},[1460,26554,2838],{},[1330,26556,3139],{},[1338,26558,26559],{"encoding":1340},"1-\\alpha",[1162,26561,26562,26563],{},"chyba II. druhu, ",[1115,26564,26566],{"className":26565},[1315],[1317,26567,26568],{"xmlns":1319},[1321,26569,26570,26574],{},[1324,26571,26572],{},[1330,26573,16112],{},[1338,26575,25966],{"encoding":1340},[1147,26577,26578,26581,26597],{},[1162,26579,26580],{},"Zamítá se",[1162,26582,26583,26584],{},"chyba I. druhu, ",[1115,26585,26587],{"className":26586},[1315],[1317,26588,26589],{"xmlns":1319},[1321,26590,26591,26595],{},[1324,26592,26593],{},[1330,26594,3139],{},[1338,26596,3202],{"encoding":1340},[1162,26598,26541,26599],{},[1115,26600,26602],{"className":26601},[1315],[1317,26603,26604],{"xmlns":1319},[1321,26605,26606,26614],{},[1324,26607,26608,26610,26612],{},[1334,26609,1565],{},[1460,26611,2838],{},[1330,26613,16112],{},[1338,26615,26616],{"encoding":1340},"1-\\beta",[1110,26618,26619,1425,26622,26635],{},[1302,26620,26621],{},"Hladina významnosti",[1115,26623,26625],{"className":26624},[1315],[1317,26626,26627],{"xmlns":1319},[1321,26628,26629,26633],{},[1324,26630,26631],{},[1330,26632,3139],{},[1338,26634,3202],{"encoding":1340}," 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.",[1110,26637,26638],{},[4158,26639],{"alt":26640,"className":26641,"src":26642},"mask-th-chyba-i-ii",[1130,4162],"\u002Fwiki-assets\u002Fmask-th-chyba-i-ii.png",[1110,26644,26645,26646,26659,26660,26673,26674,26687,26688,1662,26701,26714,26715,1440],{},"Obrázek ukazuje, proč jde o kompromis: posunutí kritické hodnoty ",[1115,26647,26649],{"className":26648},[1315],[1317,26650,26651],{"xmlns":1319},[1321,26652,26653,26657],{},[1324,26654,26655],{},[1330,26656,3494],{},[1338,26658,3494],{"encoding":1340}," doleva zmenší ",[1115,26661,26663],{"className":26662},[1315],[1317,26664,26665],{"xmlns":1319},[1321,26666,26667,26671],{},[1324,26668,26669],{},[1330,26670,16112],{},[1338,26672,25966],{"encoding":1340},", ale zvětší ",[1115,26675,26677],{"className":26676},[1315],[1317,26678,26679],{"xmlns":1319},[1321,26680,26681,26685],{},[1324,26682,26683],{},[1330,26684,3139],{},[1338,26686,3202],{"encoding":1340},", a naopak. Pro danou hladinu ",[1115,26689,26691],{"className":26690},[1315],[1317,26692,26693],{"xmlns":1319},[1321,26694,26695,26699],{},[1324,26696,26697],{},[1330,26698,3139],{},[1338,26700,3202],{"encoding":1340},[1115,26702,26704],{"className":26703},[1315],[1317,26705,26706],{"xmlns":1319},[1321,26707,26708,26712],{},[1324,26709,26710],{},[1330,26711,3494],{},[1338,26713,3494],{"encoding":1340}," jednoznačně určena rozdělením kritéria za platnosti ",[1115,26716,26718],{"className":26717},[1315],[1317,26719,26720],{"xmlns":1319},[1321,26721,26722,26730],{},[1324,26723,26724],{},[1327,26725,26726,26728],{},[1330,26727,1332],{},[1334,26729,1336],{},[1338,26731,1341],{"encoding":1340},[16521,26733,26735],{"id":26734},"testové-kritérium-a-kritický-obor","Testové kritérium a kritický obor",[1110,26737,26738,1425,26740,26753,26754,1440],{},[1302,26739,2774],{},[1115,26741,26743],{"className":26742},[1315],[1317,26744,26745],{"xmlns":1319},[1321,26746,26747,26751],{},[1324,26748,26749],{},[1330,26750,6877],{},[1338,26752,6877],{"encoding":1340}," je statistika spočtená z výběru; aby bylo možné test provést, musí být známo jeho rozdělení za platnosti ",[1115,26755,26757],{"className":26756},[1315],[1317,26758,26759],{"xmlns":1319},[1321,26760,26761,26769],{},[1324,26762,26763],{},[1327,26764,26765,26767],{},[1330,26766,1332],{},[1334,26768,1336],{},[1338,26770,1341],{"encoding":1340},[1110,26772,26773,1425,26776,26789,26790,26807],{},[1302,26774,26775],{},"Kritický obor",[1115,26777,26779],{"className":26778},[1315],[1317,26780,26781],{"xmlns":1319},[1321,26782,26783,26787],{},[1324,26784,26785],{},[1330,26786,1376],{},[1338,26788,1376],{"encoding":1340}," je množina hodnot svědčících pro ",[1115,26791,26793],{"className":26792},[1315],[1317,26794,26795],{"xmlns":1319},[1321,26796,26797,26805],{},[1324,26798,26799],{},[1327,26800,26801,26803],{},[1330,26802,1332],{},[1334,26804,1565],{},[1338,26806,2770],{"encoding":1340},". Je zkonstruován tak, aby",[1115,26809,26811],{"className":26810},[1315],[1317,26812,26813],{"xmlns":1319,"display":1736},[1321,26814,26815,26843],{},[1324,26816,26817,26819,26821,26823,26825,26827,26829,26835,26837,26839,26841],{},[1330,26818,6502],{},[1460,26820,1647],{"stretchy":1646},[1330,26822,6877],{},[1460,26824,6794],{},[1330,26826,1376],{},[1460,26828,22799],{},[1327,26830,26831,26833],{},[1330,26832,1332],{},[1334,26834,1336],{},[1460,26836,1658],{"stretchy":1646},[1460,26838,1754],{},[1330,26840,3139],{},[1460,26842,1568],{"separator":1121},[1338,26844,26845],{"encoding":1340},"P(T \\in W \\mid H_0) = \\alpha,",[1110,26847,26848,26849,26862,26863,26880],{},"tedy aby pravděpodobnost, že výběr dá hodnotu kritéria v ",[1115,26850,26852],{"className":26851},[1315],[1317,26853,26854],{"xmlns":1319},[1321,26855,26856,26860],{},[1324,26857,26858],{},[1330,26859,1376],{},[1338,26861,1376],{"encoding":1340}," i při platné ",[1115,26864,26866],{"className":26865},[1315],[1317,26867,26868],{"xmlns":1319},[1321,26869,26870,26878],{},[1324,26871,26872],{},[1327,26873,26874,26876],{},[1330,26875,1332],{},[1334,26877,1336],{},[1338,26879,1341],{"encoding":1340},", byla rovna zvolené hladině významnosti.",[16521,26882,26884],{"id":26883},"postup-testování-hypotézy","Postup testování hypotézy",[1110,26886,26887],{},[4158,26888],{"alt":26889,"className":26890,"src":26891},"mask-ilu-postup-testovani",[1130,4162],"\u002Fwiki-assets\u002Fmask-ilu-postup-testovani.png",[2638,26893,26894,26931,26934,26950],{},[1207,26895,26896,26897,5516,26914,1440],{},"Formulace hypotéz ",[1115,26898,26900],{"className":26899},[1315],[1317,26901,26902],{"xmlns":1319},[1321,26903,26904,26912],{},[1324,26905,26906],{},[1327,26907,26908,26910],{},[1330,26909,1332],{},[1334,26911,1336],{},[1338,26913,1341],{"encoding":1340},[1115,26915,26917],{"className":26916},[1315],[1317,26918,26919],{"xmlns":1319},[1321,26920,26921,26929],{},[1324,26922,26923],{},[1327,26924,26925,26927],{},[1330,26926,1332],{},[1334,26928,1565],{},[1338,26930,2770],{"encoding":1340},[1207,26932,26933],{},"Volba testového kritéria a výpočet jeho hodnoty.",[1207,26935,26936,26937,1440],{},"Volba hladiny významnosti a sestrojení příslušného kritického oboru ",[1115,26938,26940],{"className":26939},[1315],[1317,26941,26942],{"xmlns":1319},[1321,26943,26944,26948],{},[1324,26945,26946],{},[1330,26947,1376],{},[1338,26949,1376],{"encoding":1340},[1207,26951,26952,26953],{},"Formulace závěru:\n",[1204,26954,26955,27033],{},[1207,26956,26957,26958,3763,26976,26993,26994,27014,27015,27032],{},"pokud ",[1115,26959,26961],{"className":26960},[1315],[1317,26962,26963],{"xmlns":1319},[1321,26964,26965,26973],{},[1324,26966,26967,26969,26971],{},[1330,26968,6877],{},[1460,26970,6794],{},[1330,26972,1376],{},[1338,26974,26975],{"encoding":1340},"T \\in W",[1115,26977,26979],{"className":26978},[1315],[1317,26980,26981],{"xmlns":1319},[1321,26982,26983,26991],{},[1324,26984,26985],{},[1327,26986,26987,26989],{},[1330,26988,1332],{},[1334,26990,1565],{},[1338,26992,2770],{"encoding":1340}," je testem prokázána na hladině významnosti ",[1115,26995,26997],{"className":26996},[1315],[1317,26998,26999],{"xmlns":1319},[1321,27000,27001,27011],{},[1324,27002,27003,27005,27007,27009],{},[1334,27004,11594],{},[1330,27006,3139],{},[2682,27008,2684],{},[1330,27010,11601],{"mathvariant":1893},[1338,27012,27013],{"encoding":1340},"100\\alpha\\,\\%"," (zamítáme ",[1115,27016,27018],{"className":27017},[1315],[1317,27019,27020],{"xmlns":1319},[1321,27021,27022,27030],{},[1324,27023,27024],{},[1327,27025,27026,27028],{},[1330,27027,1332],{},[1334,27029,1336],{},[1338,27031,1341],{"encoding":1340},");",[1207,27034,26957,27035,3763,27054,27071,27072,27091,27092,27109],{},[1115,27036,27038],{"className":27037},[1315],[1317,27039,27040],{"xmlns":1319},[1321,27041,27042,27051],{},[1324,27043,27044,27046,27049],{},[1330,27045,6877],{},[1460,27047,27048],{"mathvariant":1893},"∉",[1330,27050,1376],{},[1338,27052,27053],{"encoding":1340},"T \\notin W",[1115,27055,27057],{"className":27056},[1315],[1317,27058,27059],{"xmlns":1319},[1321,27060,27061,27069],{},[1324,27062,27063],{},[1327,27064,27065,27067],{},[1330,27066,1332],{},[1334,27068,1565],{},[1338,27070,2770],{"encoding":1340}," není testem prokázána na hladině významnosti ",[1115,27073,27075],{"className":27074},[1315],[1317,27076,27077],{"xmlns":1319},[1321,27078,27079,27089],{},[1324,27080,27081,27083,27085,27087],{},[1334,27082,11594],{},[1330,27084,3139],{},[2682,27086,2684],{},[1330,27088,11601],{"mathvariant":1893},[1338,27090,27013],{"encoding":1340}," ; ",[1115,27093,27095],{"className":27094},[1315],[1317,27096,27097],{"xmlns":1319},[1321,27098,27099,27107],{},[1324,27100,27101],{},[1327,27102,27103,27105],{},[1330,27104,1332],{},[1334,27106,1336],{},[1338,27108,1341],{"encoding":1340}," nezamítáme.",[1110,27111,27112,27113,27116,27117,27134,27135,27152,27153,27173,27174,24959,27191,1425,27211,27228],{},"Rovnocennou alternativou je ",[1302,27114,27115],{},"p-hodnota",": udává, nakolik jsou data slučitelná s ",[1115,27118,27120],{"className":27119},[1315],[1317,27121,27122],{"xmlns":1319},[1321,27123,27124,27132],{},[1324,27125,27126],{},[1327,27127,27128,27130],{},[1330,27129,1332],{},[1334,27131,1336],{},[1338,27133,1341],{"encoding":1340},". Čím menší p-hodnota, tím více data svědčí proti ",[1115,27136,27138],{"className":27137},[1315],[1317,27139,27140],{"xmlns":1319},[1321,27141,27142,27150],{},[1324,27143,27144],{},[1327,27145,27146,27148],{},[1330,27147,1332],{},[1334,27149,1336],{},[1338,27151,1341],{"encoding":1340},". Rozhodovací pravidlo: ",[1115,27154,27156],{"className":27155},[1315],[1317,27157,27158],{"xmlns":1319},[1321,27159,27160,27170],{},[1324,27161,27162,27164,27166,27168],{},[1330,27163,1110],{},[1460,27165,6510],{},[1330,27167,3139],{},[1460,27169,7325],{},[1338,27171,27172],{"encoding":1340},"p \\le \\alpha \\Rightarrow"," zamítáme ",[1115,27175,27177],{"className":27176},[1315],[1317,27178,27179],{"xmlns":1319},[1321,27180,27181,27189],{},[1324,27182,27183],{},[1327,27184,27185,27187],{},[1330,27186,1332],{},[1334,27188,1336],{},[1338,27190,1341],{"encoding":1340},[1115,27192,27194],{"className":27193},[1315],[1317,27195,27196],{"xmlns":1319},[1321,27197,27198,27208],{},[1324,27199,27200,27202,27204,27206],{},[1330,27201,1110],{},[1460,27203,1462],{},[1330,27205,3139],{},[1460,27207,7325],{},[1338,27209,27210],{"encoding":1340},"p > \\alpha \\Rightarrow",[1115,27212,27214],{"className":27213},[1315],[1317,27215,27216],{"xmlns":1319},[1321,27217,27218,27226],{},[1324,27219,27220],{},[1327,27221,27222,27224],{},[1330,27223,1332],{},[1334,27225,1336],{},[1338,27227,1341],{"encoding":1340}," nezamítáme. Obě cesty — kritický obor i p-hodnota — vedou vždy ke stejnému závěru; R u všech testů vrací p-hodnotu přímo.",[1136,27230,27232],{"id":27231},"jednovýběrový-t-test","Jednovýběrový t-test",[1110,27234,27235,27236,27249,27250,27282,27283,27296,27297,5516,27314,27331,27332,27350,27351,27364],{},"Test o střední hodnotě ",[1115,27237,27239],{"className":27238},[1315],[1317,27240,27241],{"xmlns":1319},[1321,27242,27243,27247],{},[1324,27244,27245],{},[1330,27246,6666],{},[1338,27248,8573],{"encoding":1340}," rozdělení ",[1115,27251,27253],{"className":27252},[1315],[1317,27254,27255],{"xmlns":1319},[1321,27256,27257,27279],{},[1324,27258,27259,27261,27263,27265,27267,27269,27271,27277],{},[1330,27260,6507],{},[1460,27262,8960],{},[1330,27264,6661],{},[1460,27266,1647],{"stretchy":1646},[1330,27268,6666],{},[1460,27270,1568],{"separator":1121},[1353,27272,27273,27275],{},[1330,27274,6674],{},[1334,27276,1360],{},[1460,27278,1658],{"stretchy":1646},[1338,27280,27281],{"encoding":1340},"X \\sim N(\\mu, \\sigma^2)",". Z výběru o rozsahu ",[1115,27284,27286],{"className":27285},[1315],[1317,27287,27288],{"xmlns":1319},[1321,27289,27290,27294],{},[1324,27291,27292],{},[1330,27293,1458],{},[1338,27295,1458],{"encoding":1340}," se určí charakteristiky ",[1115,27298,27300],{"className":27299},[1315],[1317,27301,27302],{"xmlns":1319},[1321,27303,27304,27312],{},[1324,27305,27306],{},[2496,27307,27308,27310],{"accent":1121},[1330,27309,6495],{},[1460,27311,11235],{},[1338,27313,21340],{"encoding":1340},[1115,27315,27317],{"className":27316},[1315],[1317,27318,27319],{"xmlns":1319},[1321,27320,27321,27329],{},[1324,27322,27323],{},[1353,27324,27325,27327],{},[1330,27326,1626],{},[1334,27328,1360],{},[1338,27330,15553],{"encoding":1340},"; testem se posuzuje vztah mezi zvoleným číslem ",[1115,27333,27335],{"className":27334},[1315],[1317,27336,27337],{"xmlns":1319},[1321,27338,27339,27347],{},[1324,27340,27341],{},[1327,27342,27343,27345],{},[1330,27344,6666],{},[1334,27346,1336],{},[1338,27348,27349],{"encoding":1340},"\\mu_0"," a neznámou hodnotou ",[1115,27352,27354],{"className":27353},[1315],[1317,27355,27356],{"xmlns":1319},[1321,27357,27358,27362],{},[1324,27359,27360],{},[1330,27361,6666],{},[1338,27363,8573],{"encoding":1340},". Testové kritérium",[1115,27366,27368],{"className":27367},[1315],[1317,27369,27370],{"xmlns":1319,"display":1736},[1321,27371,27372,27416],{},[1324,27373,27374,27376,27378,27398,27402,27404],{},[1330,27375,6877],{},[1460,27377,1754],{},[2512,27379,27380,27396],{},[1324,27381,27382,27388,27390],{},[2496,27383,27384,27386],{"accent":1121},[1330,27385,6495],{},[1460,27387,11235],{},[1460,27389,2838],{},[1327,27391,27392,27394],{},[1330,27393,6666],{},[1334,27395,1336],{},[1330,27397,1626],{},[4228,27399,27400],{},[1330,27401,1458],{},[1460,27403,8960],{},[1327,27405,27406,27408],{},[1330,27407,6919],{},[1324,27409,27410,27412,27414],{},[1330,27411,1458],{},[1460,27413,2838],{},[1334,27415,1565],{},[1338,27417,27418],{"encoding":1340},"T = \\frac{\\bar{x} - \\mu_0}{s}\\sqrt{n} \\sim t_{n-1}",[1110,27420,27421,27422,27440],{},"má Studentovo rozdělení o ",[1115,27423,27425],{"className":27424},[1315],[1317,27426,27427],{"xmlns":1319},[1321,27428,27429,27437],{},[1324,27430,27431,27433,27435],{},[1330,27432,1458],{},[1460,27434,2838],{},[1334,27436,1565],{},[1338,27438,27439],{"encoding":1340},"n-1"," stupních volnosti.",[1141,27442,27443,27501],{},[1144,27444,27445],{},[1147,27446,27447,27466,27485],{},[1150,27448,27449],{},[1115,27450,27452],{"className":27451},[1315],[1317,27453,27454],{"xmlns":1319},[1321,27455,27456,27464],{},[1324,27457,27458],{},[1327,27459,27460,27462],{},[1330,27461,1332],{},[1334,27463,1336],{},[1338,27465,1341],{"encoding":1340},[1150,27467,27468],{},[1115,27469,27471],{"className":27470},[1315],[1317,27472,27473],{"xmlns":1319},[1321,27474,27475,27483],{},[1324,27476,27477],{},[1327,27478,27479,27481],{},[1330,27480,1332],{},[1334,27482,1565],{},[1338,27484,2770],{"encoding":1340},[1150,27486,27487,27488],{},"Kritický obor ",[1115,27489,27491],{"className":27490},[1315],[1317,27492,27493],{"xmlns":1319},[1321,27494,27495,27499],{},[1324,27496,27497],{},[1330,27498,1376],{},[1338,27500,1376],{"encoding":1340},[1157,27502,27503,27593,27691],{},[1147,27504,27505,27529,27553],{},[1162,27506,27507],{},[1115,27508,27510],{"className":27509},[1315],[1317,27511,27512],{"xmlns":1319},[1321,27513,27514,27526],{},[1324,27515,27516,27518,27520],{},[1330,27517,6666],{},[1460,27519,6510],{},[1327,27521,27522,27524],{},[1330,27523,6666],{},[1334,27525,1336],{},[1338,27527,27528],{"encoding":1340},"\\mu \\le \\mu_0",[1162,27530,27531],{},[1115,27532,27534],{"className":27533},[1315],[1317,27535,27536],{"xmlns":1319},[1321,27537,27538,27550],{},[1324,27539,27540,27542,27544],{},[1330,27541,6666],{},[1460,27543,1462],{},[1327,27545,27546,27548],{},[1330,27547,6666],{},[1334,27549,1336],{},[1338,27551,27552],{"encoding":1340},"\\mu > \\mu_0",[1162,27554,27555],{},[1115,27556,27558],{"className":27557},[1315],[1317,27559,27560],{"xmlns":1319},[1321,27561,27562,27590],{},[1324,27563,27564,27566,27568,27580,27582,27584,27586,27588],{},[1330,27565,6919],{},[1460,27567,3125],{},[1327,27569,27570,27572],{},[1330,27571,6919],{},[1324,27573,27574,27576,27578],{},[1334,27575,1565],{},[1460,27577,2838],{},[1330,27579,3139],{},[1460,27581,1647],{"stretchy":1646},[1330,27583,1458],{},[1460,27585,2838],{},[1334,27587,1565],{},[1460,27589,1658],{"stretchy":1646},[1338,27591,27592],{"encoding":1340},"t \\ge t_{1-\\alpha}(n-1)",[1147,27594,27595,27619,27643],{},[1162,27596,27597],{},[1115,27598,27600],{"className":27599},[1315],[1317,27601,27602],{"xmlns":1319},[1321,27603,27604,27616],{},[1324,27605,27606,27608,27610],{},[1330,27607,6666],{},[1460,27609,1754],{},[1327,27611,27612,27614],{},[1330,27613,6666],{},[1334,27615,1336],{},[1338,27617,27618],{"encoding":1340},"\\mu = \\mu_0",[1162,27620,27621],{},[1115,27622,27624],{"className":27623},[1315],[1317,27625,27626],{"xmlns":1319},[1321,27627,27628,27640],{},[1324,27629,27630,27632,27634],{},[1330,27631,6666],{},[1460,27633,10733],{"mathvariant":1893},[1327,27635,27636,27638],{},[1330,27637,6666],{},[1334,27639,1336],{},[1338,27641,27642],{"encoding":1340},"\\mu \\neq \\mu_0",[1162,27644,27645],{},[1115,27646,27648],{"className":27647},[1315],[1317,27649,27650],{"xmlns":1319},[1321,27651,27652,27688],{},[1324,27653,27654,27656,27658,27660,27662,27678,27680,27682,27684,27686],{},[1460,27655,22799],{"stretchy":1646},[1330,27657,6919],{},[1460,27659,22799],{"stretchy":1646},[1460,27661,3125],{},[1327,27663,27664,27666],{},[1330,27665,6919],{},[1324,27667,27668,27670,27672,27674,27676],{},[1334,27669,1565],{},[1460,27671,2838],{},[1330,27673,3139],{},[1330,27675,4379],{"mathvariant":1893},[1334,27677,1360],{},[1460,27679,1647],{"stretchy":1646},[1330,27681,1458],{},[1460,27683,2838],{},[1334,27685,1565],{},[1460,27687,1658],{"stretchy":1646},[1338,27689,27690],{"encoding":1340},"\\lvert t \\rvert \\ge t_{1-\\alpha\u002F2}(n-1)",[1147,27692,27693,27717,27741],{},[1162,27694,27695],{},[1115,27696,27698],{"className":27697},[1315],[1317,27699,27700],{"xmlns":1319},[1321,27701,27702,27714],{},[1324,27703,27704,27706,27708],{},[1330,27705,6666],{},[1460,27707,3125],{},[1327,27709,27710,27712],{},[1330,27711,6666],{},[1334,27713,1336],{},[1338,27715,27716],{"encoding":1340},"\\mu \\ge \\mu_0",[1162,27718,27719],{},[1115,27720,27722],{"className":27721},[1315],[1317,27723,27724],{"xmlns":1319},[1321,27725,27726,27738],{},[1324,27727,27728,27730,27732],{},[1330,27729,6666],{},[1460,27731,4107],{},[1327,27733,27734,27736],{},[1330,27735,6666],{},[1334,27737,1336],{},[1338,27739,27740],{"encoding":1340},"\\mu \u003C \\mu_0",[1162,27742,27743],{},[1115,27744,27746],{"className":27745},[1315],[1317,27747,27748],{"xmlns":1319},[1321,27749,27750,27780],{},[1324,27751,27752,27754,27756,27758,27770,27772,27774,27776,27778],{},[1330,27753,6919],{},[1460,27755,6510],{},[1460,27757,2838],{},[1327,27759,27760,27762],{},[1330,27761,6919],{},[1324,27763,27764,27766,27768],{},[1334,27765,1565],{},[1460,27767,2838],{},[1330,27769,3139],{},[1460,27771,1647],{"stretchy":1646},[1330,27773,1458],{},[1460,27775,2838],{},[1334,27777,1565],{},[1460,27779,1658],{"stretchy":1646},[1338,27781,27782],{"encoding":1340},"t \\le -t_{1-\\alpha}(n-1)",[1110,27784,27785,27786,27789],{},"V R test provádí ",[3244,27787,27788],{},"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?",[3468,27791,27793],{"className":3470,"code":27792,"language":71,"meta":1247,"style":1247},"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",[3244,27794,27795,27849],{"__ignoreMap":1247},[1115,27796,27797,27799,27801,27803,27805,27808,27810,27813,27815,27818,27820,27823,27825,27828,27830,27833,27835,27837,27839,27842,27844,27847],{"class":3476,"line":10},[1115,27798,6495],{"class":3479},[1115,27800,3484],{"class":3483},[1115,27802,3610],{"class":3487},[1115,27804,1647],{"class":3491},[1115,27806,27807],{"class":3499},"12.5",[1115,27809,1568],{"class":3483},[1115,27811,27812],{"class":3499}," 13.5",[1115,27814,1568],{"class":3483},[1115,27816,27817],{"class":3499}," 11.9",[1115,27819,1568],{"class":3483},[1115,27821,27822],{"class":3499}," 12.2",[1115,27824,1568],{"class":3483},[1115,27826,27827],{"class":3499}," 13.0",[1115,27829,1568],{"class":3483},[1115,27831,27832],{"class":3499}," 14.3",[1115,27834,1568],{"class":3483},[1115,27836,27822],{"class":3499},[1115,27838,1568],{"class":3483},[1115,27840,27841],{"class":3499}," 11.8",[1115,27843,1568],{"class":3483},[1115,27845,27846],{"class":3499}," 14.0",[1115,27848,3676],{"class":3491},[1115,27850,27851,27854,27856,27858,27860,27862,27864,27866,27868,27871,27873,27876],{"class":3476,"line":27},[1115,27852,27853],{"class":3487},"t.test",[1115,27855,1647],{"class":3491},[1115,27857,6495],{"class":3479},[1115,27859,1568],{"class":3483},[1115,27861,25356],{"class":3479},[1115,27863,3572],{"class":3483},[1115,27865,3509],{"class":3499},[1115,27867,1568],{"class":3483},[1115,27869,27870],{"class":3479}," alternative",[1115,27872,3572],{"class":3483},[1115,27874,27875],{"class":3615}," \"two.sided\"",[1115,27877,3676],{"class":3491},[3468,27879,27882],{"className":27880,"code":27881,"language":3698,"meta":1247},[3696],"    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",[3244,27883,27881],{"__ignoreMap":1247},[1110,27885,27886,27888,27889,27892,27893,27896,27897,27900,27901,27924],{},[3244,27887,6919],{}," je testové kritérium, ",[3244,27890,27891],{},"df"," stupně volnosti, ",[3244,27894,27895],{},"p-value"," p-hodnota pro zvolenou alternativu a ",[3244,27898,27899],{},"mean of x"," výběrový průměr. Zde ",[1115,27902,27904],{"className":27903},[1315],[1317,27905,27906],{"xmlns":1319},[1321,27907,27908,27921],{},[1324,27909,27910,27912,27914,27917,27919],{},[1330,27911,1110],{},[1460,27913,1754],{},[1334,27915,27916],{},"0,02843",[1460,27918,4107],{},[1334,27920,3759],{},[1338,27922,27923],{"encoding":1340},"p = 0{,}02843 \u003C 0{,}05",": úprava trasy průměrnou dobu jízdy (původně 12 minut) statisticky významně změnila.",[1103,27926,27928,27935,28023,28079,28171],{"className":27927,"dataCallout":3251},[1106,3250],[1110,27929,27931,27934],{"className":27930},[1113],[1115,27932],{"className":27933,"ariaHidden":1121},[1118,3258,1120],"Příklad: Kontrola objemu lahví",[1110,27936,27937,27938,27960,27961,27979,27980,28003,28004,28022],{},"Pivovar plní lahve, deklarovaný objem je ",[1115,27939,27941],{"className":27940},[1315],[1317,27942,27943],{"xmlns":1319},[1321,27944,27945,27957],{},[1324,27946,27947,27953,27955],{},[1327,27948,27949,27951],{},[1330,27950,6666],{},[1334,27952,1336],{},[1460,27954,1754],{},[1334,27956,8234],{},[1338,27958,27959],{"encoding":1340},"\\mu_0 = 0{,}5"," l. Náhodný výběr ",[1115,27962,27964],{"className":27963},[1315],[1317,27965,27966],{"xmlns":1319},[1321,27967,27968,27976],{},[1324,27969,27970,27972,27974],{},[1330,27971,1458],{},[1460,27973,1754],{},[1334,27975,3820],{},[1338,27977,27978],{"encoding":1340},"n = 20"," lahví dal ",[1115,27981,27983],{"className":27982},[1315],[1317,27984,27985],{"xmlns":1319},[1321,27986,27987,28000],{},[1324,27988,27989,27995,27997],{},[2496,27990,27991,27993],{"accent":1121},[1330,27992,6495],{},[1460,27994,11235],{},[1460,27996,1754],{},[1334,27998,27999],{},"0,492",[1338,28001,28002],{"encoding":1340},"\\bar{x} = 0{,}492"," l, ",[1115,28005,28007],{"className":28006},[1315],[1317,28008,28009],{"xmlns":1319},[1321,28010,28011,28019],{},[1324,28012,28013,28015,28017],{},[1330,28014,1626],{},[1460,28016,1754],{},[1334,28018,14571],{},[1338,28020,28021],{"encoding":1340},"s = 0{,}015"," l. Na hladině významnosti 5 % ověřte podezření, že pivovar lahve nedoplňuje.",[1110,28024,28025,28051,28052,28078],{},[1115,28026,28028],{"className":28027},[1315],[1317,28029,28030],{"xmlns":1319},[1321,28031,28032,28048],{},[1324,28033,28034,28040,28042,28044,28046],{},[1327,28035,28036,28038],{},[1330,28037,1332],{},[1334,28039,1336],{},[1460,28041,1730],{},[1330,28043,6666],{},[1460,28045,3125],{},[1334,28047,8234],{},[1338,28049,28050],{"encoding":1340},"H_0: \\mu \\ge 0{,}5"," l (objem je v pořádku nebo větší), ",[1115,28053,28055],{"className":28054},[1315],[1317,28056,28057],{"xmlns":1319},[1321,28058,28059,28075],{},[1324,28060,28061,28067,28069,28071,28073],{},[1327,28062,28063,28065],{},[1330,28064,1332],{},[1334,28066,1565],{},[1460,28068,1730],{},[1330,28070,6666],{},[1460,28072,4107],{},[1334,28074,8234],{},[1338,28076,28077],{"encoding":1340},"H_1: \\mu \u003C 0{,}5"," l (lahve jsou nedoplněné).",[1110,28080,28081],{},[1115,28082,28084],{"className":28083},[1315],[1317,28085,28086],{"xmlns":1319},[1321,28087,28088,28168],{},[1324,28089,28090,28092,28094,28106,28110,28112,28114,28117,28119,28121,28123,28125,28127,28129,28131,28133,28145,28147,28149,28151,28153,28155,28157,28159,28161,28163,28166],{},[1330,28091,6919],{},[1460,28093,1754],{},[2512,28095,28096,28104],{},[1324,28097,28098,28100,28102],{},[1334,28099,27999],{},[1460,28101,2838],{},[1334,28103,8234],{},[1334,28105,14571],{},[4228,28107,28108],{},[1334,28109,3820],{},[1460,28111,1754],{},[1460,28113,2838],{},[1334,28115,28116],{},"2,385",[1460,28118,1568],{"separator":1121},[1784,28120],{"width":1786},[1330,28122,1376],{},[1460,28124,1754],{},[1460,28126,3108],{"stretchy":1646},[1330,28128,6919],{},[1460,28130,6510],{},[1460,28132,2838],{},[1327,28134,28135,28137],{},[1330,28136,6919],{},[1324,28138,28139,28141,28143],{},[1334,28140,1336],{},[1460,28142,1568],{"separator":1121},[1334,28144,21573],{},[1460,28146,1647],{"stretchy":1646},[1334,28148,14495],{},[1460,28150,1658],{"stretchy":1646},[1460,28152,3168],{"stretchy":1646},[1460,28154,1754],{},[1460,28156,3108],{"stretchy":1646},[1330,28158,6919],{},[1460,28160,6510],{},[1460,28162,2838],{},[1334,28164,28165],{},"1,729",[1460,28167,3168],{"stretchy":1646},[1338,28169,28170],{"encoding":1340},"t = \\frac{0{,}492 - 0{,}5}{0{,}015}\\sqrt{20} = -2{,}385, \\qquad W = \\{t \\le -t_{0,95}(19)\\} = \\{t \\le -1{,}729\\}",[1110,28172,28173,28174,5782,28192,28209],{},"Protože ",[1115,28175,28177],{"className":28176},[1315],[1317,28178,28179],{"xmlns":1319},[1321,28180,28181,28189],{},[1324,28182,28183,28185,28187],{},[1330,28184,6919],{},[1460,28186,6794],{},[1330,28188,1376],{},[1338,28190,28191],{"encoding":1340},"t \\in W",[1115,28193,28195],{"className":28194},[1315],[1317,28196,28197],{"xmlns":1319},[1321,28198,28199,28207],{},[1324,28200,28201],{},[1327,28202,28203,28205],{},[1330,28204,1332],{},[1334,28206,1336],{},[1338,28208,1341],{"encoding":1340},": na hladině významnosti 5 % se potvrdilo, že pivovar plní lahve pod deklarovaný objem.",[1110,28211,28212,28213,28215,28216,1730],{},"Ze souhrnných charakteristik bez surových dat ",[3244,28214,27788],{}," spustit nelze — kritérium a kritická hodnota se dopočítají přímo z definice pomocí ",[3244,28217,28218],{},"qt()",[3468,28220,28222],{"className":3470,"code":28221,"language":71,"meta":1247,"style":1247},"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",[3244,28223,28224,28262,28294,28324,28329],{"__ignoreMap":1247},[1115,28225,28226,28229,28231,28234,28236,28238,28240,28243,28245,28247,28249,28252,28254,28257,28259],{"class":3476,"line":10},[1115,28227,28228],{"class":3479},"xbar",[1115,28230,3484],{"class":3483},[1115,28232,28233],{"class":3499}," 0.492",[1115,28235,24959],{"class":3491},[1115,28237,1626],{"class":3479},[1115,28239,3484],{"class":3483},[1115,28241,28242],{"class":3499}," 0.015",[1115,28244,24959],{"class":3491},[1115,28246,1458],{"class":3479},[1115,28248,3484],{"class":3483},[1115,28250,28251],{"class":3499}," 20",[1115,28253,24959],{"class":3491},[1115,28255,28256],{"class":3479},"mu0",[1115,28258,3484],{"class":3483},[1115,28260,28261],{"class":3499}," 0.5\n",[1115,28263,28264,28266,28268,28270,28272,28274,28277,28279,28281,28284,28286,28288,28290,28292],{"class":3476,"line":27},[1115,28265,6919],{"class":3479},[1115,28267,3484],{"class":3483},[1115,28269,4382],{"class":3491},[1115,28271,28228],{"class":3479},[1115,28273,25296],{"class":3483},[1115,28275,28276],{"class":3479}," mu0",[1115,28278,4376],{"class":3491},[1115,28280,4379],{"class":3483},[1115,28282,28283],{"class":3479}," s",[1115,28285,18414],{"class":3483},[1115,28287,4353],{"class":3487},[1115,28289,1647],{"class":3491},[1115,28291,1458],{"class":3479},[1115,28293,3676],{"class":3491},[1115,28295,28296,28299,28301,28304,28306,28309,28311,28313,28315,28318,28320,28322],{"class":3476,"line":148},[1115,28297,28298],{"class":3479},"t_krit",[1115,28300,3484],{"class":3483},[1115,28302,28303],{"class":3487}," qt",[1115,28305,1647],{"class":3491},[1115,28307,28308],{"class":3499},"0.05",[1115,28310,1568],{"class":3483},[1115,28312,10586],{"class":3479},[1115,28314,3572],{"class":3483},[1115,28316,28317],{"class":3479}," n",[1115,28319,25296],{"class":3483},[1115,28321,4416],{"class":3499},[1115,28323,3676],{"class":3491},[1115,28325,28326],{"class":3476,"line":111},[1115,28327,28328],{"class":3479},"t\n",[1115,28330,28331],{"class":3476,"line":96},[1115,28332,28333],{"class":3479},"t_krit\n",[3468,28335,28338],{"className":28336,"code":28337,"language":3698,"meta":1247},[3696],"[1] -2.385139\n[1] -1.729133\n",[3244,28339,28337],{"__ignoreMap":1247},[1110,28341,28342],{},[4158,28343],{"alt":28344,"className":28345,"src":28346},"mask-th-t-jednostranny",[1130,4162],"\u002Fwiki-assets\u002Fmask-th-t-jednostranny.png",[1110,28348,28349,28350,1730],{},"Další dva příklady mají k dispozici surová data, takže je lze otestovat přímo ",[3244,28351,27788],{},[1110,28353,28354,28357],{},[1302,28355,28356],{},"Životnost baterií."," Výrobce udává průměrnou životnost 10 hodin, na 11 bateriích byly naměřeny hodnoty v hodinách.",[3468,28359,28361],{"className":3470,"code":28360,"language":71,"meta":1247,"style":1247},"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",[3244,28362,28363,28426],{"__ignoreMap":1247},[1115,28364,28365,28368,28370,28372,28374,28377,28379,28382,28384,28387,28389,28392,28394,28397,28399,28402,28404,28406,28408,28411,28413,28415,28417,28420,28422,28424],{"class":3476,"line":10},[1115,28366,28367],{"class":3479},"x2",[1115,28369,3484],{"class":3483},[1115,28371,3610],{"class":3487},[1115,28373,1647],{"class":3491},[1115,28375,28376],{"class":3499},"9.5",[1115,28378,1568],{"class":3483},[1115,28380,28381],{"class":3499}," 10.5",[1115,28383,1568],{"class":3483},[1115,28385,28386],{"class":3499}," 8.9",[1115,28388,1568],{"class":3483},[1115,28390,28391],{"class":3499}," 9.2",[1115,28393,1568],{"class":3483},[1115,28395,28396],{"class":3499}," 10.0",[1115,28398,1568],{"class":3483},[1115,28400,28401],{"class":3499}," 8.5",[1115,28403,1568],{"class":3483},[1115,28405,28391],{"class":3499},[1115,28407,1568],{"class":3483},[1115,28409,28410],{"class":3499}," 8.8",[1115,28412,1568],{"class":3483},[1115,28414,28396],{"class":3499},[1115,28416,1568],{"class":3483},[1115,28418,28419],{"class":3499}," 9.5",[1115,28421,1568],{"class":3483},[1115,28423,28391],{"class":3499},[1115,28425,3676],{"class":3491},[1115,28427,28428,28430,28432,28434,28436,28438,28440,28442,28444,28446,28448,28450],{"class":3476,"line":27},[1115,28429,27853],{"class":3487},[1115,28431,1647],{"class":3491},[1115,28433,28367],{"class":3479},[1115,28435,1568],{"class":3483},[1115,28437,25356],{"class":3479},[1115,28439,3572],{"class":3483},[1115,28441,9254],{"class":3499},[1115,28443,1568],{"class":3483},[1115,28445,27870],{"class":3479},[1115,28447,3572],{"class":3483},[1115,28449,27875],{"class":3615},[1115,28451,3676],{"class":3491},[3468,28453,28456],{"className":28454,"code":28455,"language":3698,"meta":1247},[3696],"    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",[3244,28457,28455],{"__ignoreMap":1247},[1110,28459,28460,28483],{},[1115,28461,28463],{"className":28462},[1315],[1317,28464,28465],{"xmlns":1319},[1321,28466,28467,28480],{},[1324,28468,28469,28471,28473,28476,28478],{},[1330,28470,1110],{},[1460,28472,1754],{},[1334,28474,28475],{},"0,006548",[1460,28477,4107],{},[1334,28479,3759],{},[1338,28481,28482],{"encoding":1340},"p = 0{,}006548 \u003C 0{,}05",": skutečná životnost se od deklarovaných 10 hodin statisticky významně liší (baterie vydrží méně).",[1110,28485,28486,28489],{},[1302,28487,28488],{},"Odpad materiálu."," Na deseti obráběných kusech byl naměřen odpad materiálu v procentech; testuje se rozdíl proti 4 % a zároveň normalita dat.",[3468,28491,28493],{"className":3470,"code":28492,"language":71,"meta":1247,"style":1247},"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",[3244,28494,28495,28546,28572],{"__ignoreMap":1247},[1115,28496,28497,28500,28502,28504,28506,28508,28510,28512,28514,28516,28518,28520,28522,28524,28526,28528,28530,28532,28534,28536,28538,28540,28542,28544],{"class":3476,"line":10},[1115,28498,28499],{"class":3479},"x3",[1115,28501,3484],{"class":3483},[1115,28503,3610],{"class":3487},[1115,28505,1647],{"class":3491},[1115,28507,11762],{"class":3499},[1115,28509,1568],{"class":3483},[1115,28511,11767],{"class":3499},[1115,28513,1568],{"class":3483},[1115,28515,11772],{"class":3499},[1115,28517,1568],{"class":3483},[1115,28519,11777],{"class":3499},[1115,28521,1568],{"class":3483},[1115,28523,11772],{"class":3499},[1115,28525,1568],{"class":3483},[1115,28527,11772],{"class":3499},[1115,28529,1568],{"class":3483},[1115,28531,11790],{"class":3499},[1115,28533,1568],{"class":3483},[1115,28535,11795],{"class":3499},[1115,28537,1568],{"class":3483},[1115,28539,11767],{"class":3499},[1115,28541,1568],{"class":3483},[1115,28543,11767],{"class":3499},[1115,28545,3676],{"class":3491},[1115,28547,28548,28550,28552,28554,28556,28558,28560,28562,28564,28566,28568,28570],{"class":3476,"line":27},[1115,28549,27853],{"class":3487},[1115,28551,1647],{"class":3491},[1115,28553,28499],{"class":3479},[1115,28555,1568],{"class":3483},[1115,28557,25356],{"class":3479},[1115,28559,3572],{"class":3483},[1115,28561,3575],{"class":3499},[1115,28563,1568],{"class":3483},[1115,28565,27870],{"class":3479},[1115,28567,3572],{"class":3483},[1115,28569,27875],{"class":3615},[1115,28571,3676],{"class":3491},[1115,28573,28574,28576,28578,28580],{"class":3476,"line":148},[1115,28575,17350],{"class":3487},[1115,28577,1647],{"class":3491},[1115,28579,28499],{"class":3479},[1115,28581,3676],{"class":3491},[3468,28583,28586],{"className":28584,"code":28585,"language":3698,"meta":1247},[3696],"    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",[3244,28587,28585],{"__ignoreMap":1247},[1110,28589,28590,28613,28614,28637],{},[1115,28591,28593],{"className":28592},[1315],[1317,28594,28595],{"xmlns":1319},[1321,28596,28597,28610],{},[1324,28598,28599,28601,28603,28606,28608],{},[1330,28600,1110],{},[1460,28602,1754],{},[1334,28604,28605],{},"0,0343",[1460,28607,4107],{},[1334,28609,3759],{},[1338,28611,28612],{"encoding":1340},"p = 0{,}0343 \u003C 0{,}05",": průměrný odpad se od 4 % statisticky významně liší (výběrový průměr 3,86 %). Shapiro-Wilkův test dává ",[1115,28615,28617],{"className":28616},[1315],[1317,28618,28619],{"xmlns":1319},[1321,28620,28621,28634],{},[1324,28622,28623,28625,28627,28630,28632],{},[1330,28624,1110],{},[1460,28626,1754],{},[1334,28628,28629],{},"0,4634",[1460,28631,1462],{},[1334,28633,3759],{},[1338,28635,28636],{"encoding":1340},"p = 0{,}4634 > 0{,}05",", předpoklad normality pro t-test je v pořádku.",[1136,28639,28641],{"id":28640},"párový-t-test","Párový t-test",[1110,28643,28644,28645,28675,28676,6556,28710,28748,28749,28762,28763,5516,28781,28801,28802,28819,28820,27364],{},"Používá se, když jsou měření závislá — na stejných objektech se měří dvě hodnoty ",[1115,28646,28648],{"className":28647},[1315],[1317,28649,28650],{"xmlns":1319},[1321,28651,28652,28672],{},[1324,28653,28654,28656,28662,28664,28670],{},[1460,28655,1647],{"stretchy":1646},[1327,28657,28658,28660],{},[1330,28659,6507],{},[1330,28661,1650],{},[1460,28663,1568],{"separator":1121},[1327,28665,28666,28668],{},[1330,28667,6863],{},[1330,28669,1650],{},[1460,28671,1658],{"stretchy":1646},[1338,28673,28674],{"encoding":1340},"(X_i, Y_i)"," a vyhodnocují se jejich diference ",[1115,28677,28679],{"className":28678},[1315],[1317,28680,28681],{"xmlns":1319},[1321,28682,28683,28707],{},[1324,28684,28685,28691,28693,28699,28701],{},[1327,28686,28687,28689],{},[1330,28688,7929],{},[1330,28690,1650],{},[1460,28692,1754],{},[1327,28694,28695,28697],{},[1330,28696,6507],{},[1330,28698,1650],{},[1460,28700,2838],{},[1327,28702,28703,28705],{},[1330,28704,6863],{},[1330,28706,1650],{},[1338,28708,28709],{"encoding":1340},"D_i = X_i - Y_i",[1115,28711,28713],{"className":28712},[1315],[1317,28714,28715],{"xmlns":1319},[1321,28716,28717,28745],{},[1324,28718,28719,28721,28723,28725,28727,28733,28735,28743],{},[1330,28720,7929],{},[1460,28722,8960],{},[1330,28724,6661],{},[1460,28726,1647],{"stretchy":1646},[1327,28728,28729,28731],{},[1330,28730,6666],{},[1330,28732,7929],{},[1460,28734,1568],{"separator":1121},[3127,28736,28737,28739,28741],{},[1330,28738,6674],{},[1330,28740,7929],{},[1334,28742,1360],{},[1460,28744,1658],{"stretchy":1646},[1338,28746,28747],{"encoding":1340},"D \\sim N(\\mu_D, \\sigma_D^2)",". Z ",[1115,28750,28752],{"className":28751},[1315],[1317,28753,28754],{"xmlns":1319},[1321,28755,28756,28760],{},[1324,28757,28758],{},[1330,28759,1458],{},[1338,28761,1458],{"encoding":1340}," dvojic se určí ",[1115,28764,28766],{"className":28765},[1315],[1317,28767,28768],{"xmlns":1319},[1321,28769,28770,28778],{},[1324,28771,28772],{},[2496,28773,28774,28776],{"accent":1121},[1330,28775,7572],{},[1460,28777,11235],{},[1338,28779,28780],{"encoding":1340},"\\bar{d}",[1115,28782,28784],{"className":28783},[1315],[1317,28785,28786],{"xmlns":1319},[1321,28787,28788,28798],{},[1324,28789,28790],{},[3127,28791,28792,28794,28796],{},[1330,28793,1626],{},[1330,28795,7572],{},[1334,28797,1360],{},[1338,28799,28800],{"encoding":1340},"s_d^2","; testuje se vztah mezi zvoleným číslem ",[1115,28803,28805],{"className":28804},[1315],[1317,28806,28807],{"xmlns":1319},[1321,28808,28809,28817],{},[1324,28810,28811],{},[1327,28812,28813,28815],{},[1330,28814,6666],{},[1334,28816,1336],{},[1338,28818,27349],{"encoding":1340}," (obvykle 0) a ",[1115,28821,28823],{"className":28822},[1315],[1317,28824,28825],{"xmlns":1319},[1321,28826,28827,28835],{},[1324,28828,28829],{},[1327,28830,28831,28833],{},[1330,28832,6666],{},[1330,28834,7929],{},[1338,28836,28837],{"encoding":1340},"\\mu_D",[1115,28839,28841],{"className":28840},[1315],[1317,28842,28843],{"xmlns":1319,"display":1736},[1321,28844,28845,28895],{},[1324,28846,28847,28849,28851,28875,28879,28881,28893],{},[1330,28848,6877],{},[1460,28850,1754],{},[2512,28852,28853,28869],{},[1324,28854,28855,28861,28863],{},[2496,28856,28857,28859],{"accent":1121},[1330,28858,7572],{},[1460,28860,11235],{},[1460,28862,2838],{},[1327,28864,28865,28867],{},[1330,28866,6666],{},[1334,28868,1336],{},[1327,28870,28871,28873],{},[1330,28872,1626],{},[1330,28874,7572],{},[4228,28876,28877],{},[1330,28878,1458],{},[1460,28880,8960],{},[1327,28882,28883,28885],{},[1330,28884,6919],{},[1324,28886,28887,28889,28891],{},[1330,28888,1458],{},[1460,28890,2838],{},[1334,28892,1565],{},[1330,28894,1440],{"mathvariant":1893},[1338,28896,28897],{"encoding":1340},"T = \\frac{\\bar{d} - \\mu_0}{s_d}\\sqrt{n} \\sim t_{n-1}.",[1141,28899,28900,28957],{},[1144,28901,28902],{},[1147,28903,28904,28923,28942],{},[1150,28905,28906],{},[1115,28907,28909],{"className":28908},[1315],[1317,28910,28911],{"xmlns":1319},[1321,28912,28913,28921],{},[1324,28914,28915],{},[1327,28916,28917,28919],{},[1330,28918,1332],{},[1334,28920,1336],{},[1338,28922,1341],{"encoding":1340},[1150,28924,28925],{},[1115,28926,28928],{"className":28927},[1315],[1317,28929,28930],{"xmlns":1319},[1321,28931,28932,28940],{},[1324,28933,28934],{},[1327,28935,28936,28938],{},[1330,28937,1332],{},[1334,28939,1565],{},[1338,28941,2770],{"encoding":1340},[1150,28943,27487,28944],{},[1115,28945,28947],{"className":28946},[1315],[1317,28948,28949],{"xmlns":1319},[1321,28950,28951,28955],{},[1324,28952,28953],{},[1330,28954,1376],{},[1338,28956,1376],{"encoding":1340},[1157,28958,28959,29056,29161],{},[1147,28960,28961,28989,29017],{},[1162,28962,28963],{},[1115,28964,28966],{"className":28965},[1315],[1317,28967,28968],{"xmlns":1319},[1321,28969,28970,28986],{},[1324,28971,28972,28978,28980],{},[1327,28973,28974,28976],{},[1330,28975,6666],{},[1330,28977,7929],{},[1460,28979,6510],{},[1327,28981,28982,28984],{},[1330,28983,6666],{},[1334,28985,1336],{},[1338,28987,28988],{"encoding":1340},"\\mu_D \\le \\mu_0",[1162,28990,28991],{},[1115,28992,28994],{"className":28993},[1315],[1317,28995,28996],{"xmlns":1319},[1321,28997,28998,29014],{},[1324,28999,29000,29006,29008],{},[1327,29001,29002,29004],{},[1330,29003,6666],{},[1330,29005,7929],{},[1460,29007,1462],{},[1327,29009,29010,29012],{},[1330,29011,6666],{},[1334,29013,1336],{},[1338,29015,29016],{"encoding":1340},"\\mu_D > \\mu_0",[1162,29018,29019],{},[1115,29020,29022],{"className":29021},[1315],[1317,29023,29024],{"xmlns":1319},[1321,29025,29026,29054],{},[1324,29027,29028,29030,29032,29044,29046,29048,29050,29052],{},[1330,29029,6919],{},[1460,29031,3125],{},[1327,29033,29034,29036],{},[1330,29035,6919],{},[1324,29037,29038,29040,29042],{},[1334,29039,1565],{},[1460,29041,2838],{},[1330,29043,3139],{},[1460,29045,1647],{"stretchy":1646},[1330,29047,1458],{},[1460,29049,2838],{},[1334,29051,1565],{},[1460,29053,1658],{"stretchy":1646},[1338,29055,27592],{"encoding":1340},[1147,29057,29058,29086,29114],{},[1162,29059,29060],{},[1115,29061,29063],{"className":29062},[1315],[1317,29064,29065],{"xmlns":1319},[1321,29066,29067,29083],{},[1324,29068,29069,29075,29077],{},[1327,29070,29071,29073],{},[1330,29072,6666],{},[1330,29074,7929],{},[1460,29076,1754],{},[1327,29078,29079,29081],{},[1330,29080,6666],{},[1334,29082,1336],{},[1338,29084,29085],{"encoding":1340},"\\mu_D = \\mu_0",[1162,29087,29088],{},[1115,29089,29091],{"className":29090},[1315],[1317,29092,29093],{"xmlns":1319},[1321,29094,29095,29111],{},[1324,29096,29097,29103,29105],{},[1327,29098,29099,29101],{},[1330,29100,6666],{},[1330,29102,7929],{},[1460,29104,10733],{"mathvariant":1893},[1327,29106,29107,29109],{},[1330,29108,6666],{},[1334,29110,1336],{},[1338,29112,29113],{"encoding":1340},"\\mu_D \\neq \\mu_0",[1162,29115,29116],{},[1115,29117,29119],{"className":29118},[1315],[1317,29120,29121],{"xmlns":1319},[1321,29122,29123,29159],{},[1324,29124,29125,29127,29129,29131,29133,29149,29151,29153,29155,29157],{},[1460,29126,22799],{"stretchy":1646},[1330,29128,6919],{},[1460,29130,22799],{"stretchy":1646},[1460,29132,3125],{},[1327,29134,29135,29137],{},[1330,29136,6919],{},[1324,29138,29139,29141,29143,29145,29147],{},[1334,29140,1565],{},[1460,29142,2838],{},[1330,29144,3139],{},[1330,29146,4379],{"mathvariant":1893},[1334,29148,1360],{},[1460,29150,1647],{"stretchy":1646},[1330,29152,1458],{},[1460,29154,2838],{},[1334,29156,1565],{},[1460,29158,1658],{"stretchy":1646},[1338,29160,27690],{"encoding":1340},[1147,29162,29163,29191,29219],{},[1162,29164,29165],{},[1115,29166,29168],{"className":29167},[1315],[1317,29169,29170],{"xmlns":1319},[1321,29171,29172,29188],{},[1324,29173,29174,29180,29182],{},[1327,29175,29176,29178],{},[1330,29177,6666],{},[1330,29179,7929],{},[1460,29181,3125],{},[1327,29183,29184,29186],{},[1330,29185,6666],{},[1334,29187,1336],{},[1338,29189,29190],{"encoding":1340},"\\mu_D \\ge \\mu_0",[1162,29192,29193],{},[1115,29194,29196],{"className":29195},[1315],[1317,29197,29198],{"xmlns":1319},[1321,29199,29200,29216],{},[1324,29201,29202,29208,29210],{},[1327,29203,29204,29206],{},[1330,29205,6666],{},[1330,29207,7929],{},[1460,29209,4107],{},[1327,29211,29212,29214],{},[1330,29213,6666],{},[1334,29215,1336],{},[1338,29217,29218],{"encoding":1340},"\\mu_D \u003C \\mu_0",[1162,29220,29221],{},[1115,29222,29224],{"className":29223},[1315],[1317,29225,29226],{"xmlns":1319},[1321,29227,29228,29258],{},[1324,29229,29230,29232,29234,29236,29248,29250,29252,29254,29256],{},[1330,29231,6919],{},[1460,29233,6510],{},[1460,29235,2838],{},[1327,29237,29238,29240],{},[1330,29239,6919],{},[1324,29241,29242,29244,29246],{},[1334,29243,1565],{},[1460,29245,2838],{},[1330,29247,3139],{},[1460,29249,1647],{"stretchy":1646},[1330,29251,1458],{},[1460,29253,2838],{},[1334,29255,1565],{},[1460,29257,1658],{"stretchy":1646},[1338,29259,27782],{"encoding":1340},[1103,29261,29263,29270,29412,29476,29562],{"className":29262,"dataCallout":3251},[1106,3250],[1110,29264,29266,29269],{"className":29265},[1113],[1115,29267],{"className":29268,"ariaHidden":1121},[1118,3258,1120],"Příklad: Snížení spotřeby paliva aditivem",[1110,29271,29272,29273,29291,29292,29310,29311,29329,29330,29363,29364,29387,29388,29411],{},"U ",[1115,29274,29276],{"className":29275},[1315],[1317,29277,29278],{"xmlns":1319},[1321,29279,29280,29288],{},[1324,29281,29282,29284,29286],{},[1330,29283,1458],{},[1460,29285,1754],{},[1334,29287,8810],{},[1338,29289,29290],{"encoding":1340},"n = 10"," vozů se změřila spotřeba před přidáním aditiva (",[1115,29293,29295],{"className":29294},[1315],[1317,29296,29297],{"xmlns":1319},[1321,29298,29299,29307],{},[1324,29300,29301],{},[1327,29302,29303,29305],{},[1330,29304,6507],{},[1330,29306,1650],{},[1338,29308,29309],{"encoding":1340},"X_i",") a po něm (",[1115,29312,29314],{"className":29313},[1315],[1317,29315,29316],{"xmlns":1319},[1321,29317,29318,29326],{},[1324,29319,29320],{},[1327,29321,29322,29324],{},[1330,29323,6863],{},[1330,29325,1650],{},[1338,29327,29328],{"encoding":1340},"Y_i","), diference ",[1115,29331,29333],{"className":29332},[1315],[1317,29334,29335],{"xmlns":1319},[1321,29336,29337,29361],{},[1324,29338,29339,29345,29347,29353,29355],{},[1327,29340,29341,29343],{},[1330,29342,7929],{},[1330,29344,1650],{},[1460,29346,1754],{},[1327,29348,29349,29351],{},[1330,29350,6507],{},[1330,29352,1650],{},[1460,29354,2838],{},[1327,29356,29357,29359],{},[1330,29358,6863],{},[1330,29360,1650],{},[1338,29362,28709],{"encoding":1340}," představují úsporu paliva. Z dat vyšla průměrná úspora ",[1115,29365,29367],{"className":29366},[1315],[1317,29368,29369],{"xmlns":1319},[1321,29370,29371,29384],{},[1324,29372,29373,29379,29381],{},[2496,29374,29375,29377],{"accent":1121},[1330,29376,7572],{},[1460,29378,11235],{},[1460,29380,1754],{},[1334,29382,29383],{},"0,4",[1338,29385,29386],{"encoding":1340},"\\bar{d} = 0{,}4"," l\u002F100 km, ",[1115,29389,29391],{"className":29390},[1315],[1317,29392,29393],{"xmlns":1319},[1321,29394,29395,29408],{},[1324,29396,29397,29403,29405],{},[1327,29398,29399,29401],{},[1330,29400,1626],{},[1330,29402,7572],{},[1460,29404,1754],{},[1334,29406,29407],{},"0,35",[1338,29409,29410],{"encoding":1340},"s_d = 0{,}35"," l\u002F100 km. Ověřte, že aditivum spotřebu statisticky významně snižuje.",[1110,29413,29414,29444,29445,29475],{},[1115,29415,29417],{"className":29416},[1315],[1317,29418,29419],{"xmlns":1319},[1321,29420,29421,29441],{},[1324,29422,29423,29429,29431,29437,29439],{},[1327,29424,29425,29427],{},[1330,29426,1332],{},[1334,29428,1336],{},[1460,29430,1730],{},[1327,29432,29433,29435],{},[1330,29434,6666],{},[1330,29436,7929],{},[1460,29438,6510],{},[1334,29440,1336],{},[1338,29442,29443],{"encoding":1340},"H_0: \\mu_D \\le 0"," (aditivum nemá vliv nebo spotřebu zvyšuje), ",[1115,29446,29448],{"className":29447},[1315],[1317,29449,29450],{"xmlns":1319},[1321,29451,29452,29472],{},[1324,29453,29454,29460,29462,29468,29470],{},[1327,29455,29456,29458],{},[1330,29457,1332],{},[1334,29459,1565],{},[1460,29461,1730],{},[1327,29463,29464,29466],{},[1330,29465,6666],{},[1330,29467,7929],{},[1460,29469,1462],{},[1334,29471,1336],{},[1338,29473,29474],{"encoding":1340},"H_1: \\mu_D > 0"," (aditivum spotřebu snižuje).",[1110,29477,29478],{},[1115,29479,29481],{"className":29480},[1315],[1317,29482,29483],{"xmlns":1319},[1321,29484,29485,29559],{},[1324,29486,29487,29489,29491,29503,29507,29509,29512,29514,29516,29518,29520,29522,29524,29526,29538,29540,29542,29544,29546,29548,29550,29552,29554,29557],{},[1330,29488,6919],{},[1460,29490,1754],{},[2512,29492,29493,29501],{},[1324,29494,29495,29497,29499],{},[1334,29496,29383],{},[1460,29498,2838],{},[1334,29500,1336],{},[1334,29502,29407],{},[4228,29504,29505],{},[1334,29506,8810],{},[1460,29508,1754],{},[1334,29510,29511],{},"3,614",[1460,29513,1568],{"separator":1121},[1784,29515],{"width":1786},[1330,29517,1376],{},[1460,29519,1754],{},[1460,29521,3108],{"stretchy":1646},[1330,29523,6919],{},[1460,29525,3125],{},[1327,29527,29528,29530],{},[1330,29529,6919],{},[1324,29531,29532,29534,29536],{},[1334,29533,1336],{},[1460,29535,1568],{"separator":1121},[1334,29537,21573],{},[1460,29539,1647],{"stretchy":1646},[1334,29541,3369],{},[1460,29543,1658],{"stretchy":1646},[1460,29545,3168],{"stretchy":1646},[1460,29547,1754],{},[1460,29549,3108],{"stretchy":1646},[1330,29551,6919],{},[1460,29553,3125],{},[1334,29555,29556],{},"1,833",[1460,29558,3168],{"stretchy":1646},[1338,29560,29561],{"encoding":1340},"t = \\frac{0{,}4 - 0}{0{,}35}\\sqrt{10} = 3{,}614, \\qquad W = \\{t \\ge t_{0,95}(9)\\} = \\{t \\ge 1{,}833\\}",[1110,29563,28173,29564,5782,29581,29598],{},[1115,29565,29567],{"className":29566},[1315],[1317,29568,29569],{"xmlns":1319},[1321,29570,29571,29579],{},[1324,29572,29573,29575,29577],{},[1330,29574,6919],{},[1460,29576,6794],{},[1330,29578,1376],{},[1338,29580,28191],{"encoding":1340},[1115,29582,29584],{"className":29583},[1315],[1317,29585,29586],{"xmlns":1319},[1321,29587,29588,29596],{},[1324,29589,29590],{},[1327,29591,29592,29594],{},[1330,29593,1332],{},[1334,29595,1336],{},[1338,29597,1341],{"encoding":1340},": aditivum prokazatelně snižuje průměrnou spotřebu paliva.",[3468,29600,29602],{"className":3470,"code":29601,"language":71,"meta":1247,"style":1247},"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",[3244,29603,29604,29633,29664,29690,29694],{"__ignoreMap":1247},[1115,29605,29606,29609,29611,29614,29616,29619,29621,29624,29626,29628,29630],{"class":3476,"line":10},[1115,29607,29608],{"class":3479},"dbar",[1115,29610,3484],{"class":3483},[1115,29612,29613],{"class":3499}," 0.4",[1115,29615,24959],{"class":3491},[1115,29617,29618],{"class":3479},"sd_d",[1115,29620,3484],{"class":3483},[1115,29622,29623],{"class":3499}," 0.35",[1115,29625,24959],{"class":3491},[1115,29627,1458],{"class":3479},[1115,29629,3484],{"class":3483},[1115,29631,29632],{"class":3499}," 10\n",[1115,29634,29635,29637,29639,29641,29643,29645,29647,29649,29651,29654,29656,29658,29660,29662],{"class":3476,"line":27},[1115,29636,6919],{"class":3479},[1115,29638,3484],{"class":3483},[1115,29640,4382],{"class":3491},[1115,29642,29608],{"class":3479},[1115,29644,25296],{"class":3483},[1115,29646,9747],{"class":3499},[1115,29648,4376],{"class":3491},[1115,29650,4379],{"class":3483},[1115,29652,29653],{"class":3479}," sd_d",[1115,29655,18414],{"class":3483},[1115,29657,4353],{"class":3487},[1115,29659,1647],{"class":3491},[1115,29661,1458],{"class":3479},[1115,29663,3676],{"class":3491},[1115,29665,29666,29668,29670,29672,29674,29676,29678,29680,29682,29684,29686,29688],{"class":3476,"line":148},[1115,29667,28298],{"class":3479},[1115,29669,3484],{"class":3483},[1115,29671,28303],{"class":3487},[1115,29673,1647],{"class":3491},[1115,29675,10603],{"class":3499},[1115,29677,1568],{"class":3483},[1115,29679,10586],{"class":3479},[1115,29681,3572],{"class":3483},[1115,29683,28317],{"class":3479},[1115,29685,25296],{"class":3483},[1115,29687,4416],{"class":3499},[1115,29689,3676],{"class":3491},[1115,29691,29692],{"class":3476,"line":111},[1115,29693,28328],{"class":3479},[1115,29695,29696],{"class":3476,"line":96},[1115,29697,28333],{"class":3479},[3468,29699,29702],{"className":29700,"code":29701,"language":3698,"meta":1247},[3696],"[1] 3.614032\n[1] 1.833113\n",[3244,29703,29701],{"__ignoreMap":1247},[1103,29705,29707,29714,29717,29862,29868],{"className":29706,"dataCallout":6188},[1106,6187],[1110,29708,29710,29713],{"className":29709},[1113],[1115,29711],{"className":29712,"ariaHidden":1121},[1118,6195,1120],"Ověřte normalitu diferencí, ne jen výsledek testu",[1110,29715,29716],{},"Realitní kancelář nechala dva odhadce ocenit osm nemovitostí (tisíce Kč):",[3468,29718,29720],{"className":3470,"code":29719,"language":71,"meta":1247,"style":1247},"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",[3244,29721,29722,29773,29824,29848],{"__ignoreMap":1247},[1115,29723,29724,29727,29729,29731,29733,29736,29738,29741,29743,29746,29748,29751,29753,29756,29758,29761,29763,29766,29768,29771],{"class":3476,"line":10},[1115,29725,29726],{"class":3479},"estA",[1115,29728,3484],{"class":3483},[1115,29730,3610],{"class":3487},[1115,29732,1647],{"class":3491},[1115,29734,29735],{"class":3499},"3282",[1115,29737,1568],{"class":3483},[1115,29739,29740],{"class":3499}," 2506",[1115,29742,1568],{"class":3483},[1115,29744,29745],{"class":3499}," 2812",[1115,29747,1568],{"class":3483},[1115,29749,29750],{"class":3499}," 5453",[1115,29752,1568],{"class":3483},[1115,29754,29755],{"class":3499}," 3263",[1115,29757,1568],{"class":3483},[1115,29759,29760],{"class":3499}," 4571",[1115,29762,1568],{"class":3483},[1115,29764,29765],{"class":3499}," 3121",[1115,29767,1568],{"class":3483},[1115,29769,29770],{"class":3499}," 2963",[1115,29772,3676],{"class":3491},[1115,29774,29775,29778,29780,29782,29784,29787,29789,29792,29794,29797,29799,29802,29804,29807,29809,29812,29814,29817,29819,29822],{"class":3476,"line":27},[1115,29776,29777],{"class":3479},"estB",[1115,29779,3484],{"class":3483},[1115,29781,3610],{"class":3487},[1115,29783,1647],{"class":3491},[1115,29785,29786],{"class":3499},"3271",[1115,29788,1568],{"class":3483},[1115,29790,29791],{"class":3499}," 2531",[1115,29793,1568],{"class":3483},[1115,29795,29796],{"class":3499}," 2799",[1115,29798,1568],{"class":3483},[1115,29800,29801],{"class":3499}," 5471",[1115,29803,1568],{"class":3483},[1115,29805,29806],{"class":3499}," 3285",[1115,29808,1568],{"class":3483},[1115,29810,29811],{"class":3499}," 4557",[1115,29813,1568],{"class":3483},[1115,29815,29816],{"class":3499}," 3139",[1115,29818,1568],{"class":3483},[1115,29820,29821],{"class":3499}," 2976",[1115,29823,3676],{"class":3491},[1115,29825,29826,29828,29830,29832,29834,29837,29839,29842,29844,29846],{"class":3476,"line":148},[1115,29827,27853],{"class":3487},[1115,29829,1647],{"class":3491},[1115,29831,29726],{"class":3479},[1115,29833,1568],{"class":3483},[1115,29835,29836],{"class":3479}," estB",[1115,29838,1568],{"class":3483},[1115,29840,29841],{"class":3479}," paired",[1115,29843,3572],{"class":3483},[1115,29845,3585],{"class":3499},[1115,29847,3676],{"class":3491},[1115,29849,29850,29852,29854,29856,29858,29860],{"class":3476,"line":111},[1115,29851,17350],{"class":3487},[1115,29853,1647],{"class":3491},[1115,29855,29726],{"class":3479},[1115,29857,25296],{"class":3483},[1115,29859,29836],{"class":3479},[1115,29861,3676],{"class":3491},[3468,29863,29866],{"className":29864,"code":29865,"language":3698,"meta":1247},[3696],"    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",[3244,29867,29865],{"__ignoreMap":1247},[1110,29869,29870,29871,4382,29888,29907,29908,29931],{},"Párový t-test sám nezamítá ",[1115,29872,29874],{"className":29873},[1315],[1317,29875,29876],{"xmlns":1319},[1321,29877,29878,29886],{},[1324,29879,29880],{},[1327,29881,29882,29884],{},[1330,29883,1332],{},[1334,29885,1336],{},[1338,29887,1341],{"encoding":1340},[1115,29889,29891],{"className":29890},[1315],[1317,29892,29893],{"xmlns":1319},[1321,29894,29895,29904],{},[1324,29896,29897,29899,29901],{},[1330,29898,1110],{},[1460,29900,1754],{},[1334,29902,29903],{},"0,2635",[1338,29905,29906],{"encoding":1340},"p = 0{,}2635","): odhadci se podle něj neliší. Shapiro-Wilkův test na diferencích ale dává ",[1115,29909,29911],{"className":29910},[1315],[1317,29912,29913],{"xmlns":1319},[1321,29914,29915,29928],{},[1324,29916,29917,29919,29921,29924,29926],{},[1330,29918,1110],{},[1460,29920,1754],{},[1334,29922,29923],{},"0,03203",[1460,29925,4107],{},[1334,29927,3759],{},[1338,29929,29930],{"encoding":1340},"p = 0{,}03203 \u003C 0{,}05"," — předpoklad normality diferencí je porušen a výsledek t-testu proto není spolehlivý. Správný postup je ověřit normalitu diferencí dříve, než se párový t-test interpretuje, a při jejím porušení použít párový Wilcoxonův test (viz oddíl Neparametrické testy níže).",[1136,29933,29935],{"id":29934},"testy-o-dvou-základních-souborech","Testy o dvou základních souborech",[1110,29937,29938,29939,29965,29966,30004,30005,5516,30023,30004,30061,30079,30080,5516,30112,30144,30145,30171,30172,1440],{},"Uvažují se dva nezávislé základní soubory ",[1115,29940,29942],{"className":29941},[1315],[1317,29943,29944],{"xmlns":1319},[1321,29945,29946,29962],{},[1324,29947,29948,29954,29956],{},[1327,29949,29950,29952],{},[1330,29951,8702],{},[1334,29953,1565],{},[1460,29955,1568],{"separator":1121},[1327,29957,29958,29960],{},[1330,29959,8702],{},[1334,29961,1360],{},[1338,29963,29964],{"encoding":1340},"Z_1, Z_2"," se znakem ",[1115,29967,29969],{"className":29968},[1315],[1317,29970,29971],{"xmlns":1319},[1321,29972,29973,30001],{},[1324,29974,29975,29977,29979,29981,29983,29989,29991,29999],{},[1330,29976,6507],{},[1460,29978,8960],{},[1330,29980,6661],{},[1460,29982,1647],{"stretchy":1646},[1327,29984,29985,29987],{},[1330,29986,6666],{},[1334,29988,1565],{},[1460,29990,1568],{"separator":1121},[3127,29992,29993,29995,29997],{},[1330,29994,6674],{},[1334,29996,1565],{},[1334,29998,1360],{},[1460,30000,1658],{"stretchy":1646},[1338,30002,30003],{"encoding":1340},"X \\sim N(\\mu_1, \\sigma_1^2)"," v ",[1115,30006,30008],{"className":30007},[1315],[1317,30009,30010],{"xmlns":1319},[1321,30011,30012,30020],{},[1324,30013,30014],{},[1327,30015,30016,30018],{},[1330,30017,8702],{},[1334,30019,1565],{},[1338,30021,30022],{"encoding":1340},"Z_1",[1115,30024,30026],{"className":30025},[1315],[1317,30027,30028],{"xmlns":1319},[1321,30029,30030,30058],{},[1324,30031,30032,30034,30036,30038,30040,30046,30048,30056],{},[1330,30033,6507],{},[1460,30035,8960],{},[1330,30037,6661],{},[1460,30039,1647],{"stretchy":1646},[1327,30041,30042,30044],{},[1330,30043,6666],{},[1334,30045,1360],{},[1460,30047,1568],{"separator":1121},[3127,30049,30050,30052,30054],{},[1330,30051,6674],{},[1334,30053,1360],{},[1334,30055,1360],{},[1460,30057,1658],{"stretchy":1646},[1338,30059,30060],{"encoding":1340},"X \\sim N(\\mu_2, \\sigma_2^2)",[1115,30062,30064],{"className":30063},[1315],[1317,30065,30066],{"xmlns":1319},[1321,30067,30068,30076],{},[1324,30069,30070],{},[1327,30071,30072,30074],{},[1330,30073,8702],{},[1334,30075,1360],{},[1338,30077,30078],{"encoding":1340},"Z_2",". Z výběrů se určí ",[1115,30081,30083],{"className":30082},[1315],[1317,30084,30085],{"xmlns":1319},[1321,30086,30087,30109],{},[1324,30088,30089,30099,30101],{},[1327,30090,30091,30097],{},[2496,30092,30093,30095],{"accent":1121},[1330,30094,6495],{},[1460,30096,11235],{},[1334,30098,1565],{},[1460,30100,1568],{"separator":1121},[3127,30102,30103,30105,30107],{},[1330,30104,1626],{},[1334,30106,1565],{},[1334,30108,1360],{},[1338,30110,30111],{"encoding":1340},"\\bar{x}_1, s_1^2",[1115,30113,30115],{"className":30114},[1315],[1317,30116,30117],{"xmlns":1319},[1321,30118,30119,30141],{},[1324,30120,30121,30131,30133],{},[1327,30122,30123,30129],{},[2496,30124,30125,30127],{"accent":1121},[1330,30126,6495],{},[1460,30128,11235],{},[1334,30130,1360],{},[1460,30132,1568],{"separator":1121},[3127,30134,30135,30137,30139],{},[1330,30136,1626],{},[1334,30138,1360],{},[1334,30140,1360],{},[1338,30142,30143],{"encoding":1340},"\\bar{x}_2, s_2^2",". Testují se varianty vztahů mezi ",[1115,30146,30148],{"className":30147},[1315],[1317,30149,30150],{"xmlns":1319},[1321,30151,30152,30168],{},[1324,30153,30154,30160,30162],{},[1327,30155,30156,30158],{},[1330,30157,6666],{},[1334,30159,1565],{},[1460,30161,1568],{"separator":1121},[1327,30163,30164,30166],{},[1330,30165,6666],{},[1334,30167,1360],{},[1338,30169,30170],{"encoding":1340},"\\mu_1, \\mu_2",", resp. mezi ",[1115,30173,30175],{"className":30174},[1315],[1317,30176,30177],{"xmlns":1319},[1321,30178,30179,30199],{},[1324,30180,30181,30189,30191],{},[3127,30182,30183,30185,30187],{},[1330,30184,6674],{},[1334,30186,1565],{},[1334,30188,1360],{},[1460,30190,1568],{"separator":1121},[3127,30192,30193,30195,30197],{},[1330,30194,6674],{},[1334,30196,1360],{},[1334,30198,1360],{},[1338,30200,30201],{"encoding":1340},"\\sigma_1^2, \\sigma_2^2",[16521,30203,30205],{"id":30204},"f-test-o-rozptylech","F-test o rozptylech",[1110,30207,30208],{},"Statistika",[1115,30210,30212],{"className":30211},[1315],[1317,30213,30214],{"xmlns":1319,"display":1736},[1321,30215,30216,30272],{},[1324,30217,30218,30220,30222,30240,30242],{},[1330,30219,6490],{},[1460,30221,1754],{},[2512,30223,30224,30232],{},[3127,30225,30226,30228,30230],{},[1330,30227,1626],{},[1334,30229,1565],{},[1334,30231,1360],{},[3127,30233,30234,30236,30238],{},[1330,30235,1626],{},[1334,30237,1360],{},[1334,30239,1360],{},[1460,30241,8960],{},[1327,30243,30244,30246],{},[1330,30245,6490],{},[1324,30247,30248,30254,30256,30258,30260,30262,30268,30270],{},[1327,30249,30250,30252],{},[1330,30251,1458],{},[1334,30253,1565],{},[1460,30255,2838],{},[1334,30257,1565],{},[1460,30259,1568],{"separator":1121},[2682,30261,2684],{},[1327,30263,30264,30266],{},[1330,30265,1458],{},[1334,30267,1360],{},[1460,30269,2838],{},[1334,30271,1565],{},[1338,30273,30274],{"encoding":1340},"F = \\frac{s_1^2}{s_2^2} \\sim F_{n_1-1,\\,n_2-1}",[1110,30276,30277,30278,5516,30300,27440],{},"má Fisherovo-Snedecorovo rozdělení o ",[1115,30279,30281],{"className":30280},[1315],[1317,30282,30283],{"xmlns":1319},[1321,30284,30285,30297],{},[1324,30286,30287,30293,30295],{},[1327,30288,30289,30291],{},[1330,30290,1458],{},[1334,30292,1565],{},[1460,30294,2838],{},[1334,30296,1565],{},[1338,30298,30299],{"encoding":1340},"n_1-1",[1115,30301,30303],{"className":30302},[1315],[1317,30304,30305],{"xmlns":1319},[1321,30306,30307,30319],{},[1324,30308,30309,30315,30317],{},[1327,30310,30311,30313],{},[1330,30312,1458],{},[1334,30314,1360],{},[1460,30316,2838],{},[1334,30318,1565],{},[1338,30320,30321],{"encoding":1340},"n_2-1",[1141,30323,30324,30381],{},[1144,30325,30326],{},[1147,30327,30328,30347,30366],{},[1150,30329,30330],{},[1115,30331,30333],{"className":30332},[1315],[1317,30334,30335],{"xmlns":1319},[1321,30336,30337,30345],{},[1324,30338,30339],{},[1327,30340,30341,30343],{},[1330,30342,1332],{},[1334,30344,1336],{},[1338,30346,1341],{"encoding":1340},[1150,30348,30349],{},[1115,30350,30352],{"className":30351},[1315],[1317,30353,30354],{"xmlns":1319},[1321,30355,30356,30364],{},[1324,30357,30358],{},[1327,30359,30360,30362],{},[1330,30361,1332],{},[1334,30363,1565],{},[1338,30365,2770],{"encoding":1340},[1150,30367,27487,30368],{},[1115,30369,30371],{"className":30370},[1315],[1317,30372,30373],{"xmlns":1319},[1321,30374,30375,30379],{},[1324,30376,30377],{},[1330,30378,1376],{},[1338,30380,1376],{"encoding":1340},[1157,30382,30383,30497,30670],{},[1147,30384,30385,30413,30441],{},[1162,30386,30387],{},[1115,30388,30390],{"className":30389},[1315],[1317,30391,30392],{"xmlns":1319},[1321,30393,30394,30410],{},[1324,30395,30396,30402,30404],{},[1327,30397,30398,30400],{},[1330,30399,6674],{},[1334,30401,1565],{},[1460,30403,6510],{},[1327,30405,30406,30408],{},[1330,30407,6674],{},[1334,30409,1360],{},[1338,30411,30412],{"encoding":1340},"\\sigma_1 \\le \\sigma_2",[1162,30414,30415],{},[1115,30416,30418],{"className":30417},[1315],[1317,30419,30420],{"xmlns":1319},[1321,30421,30422,30438],{},[1324,30423,30424,30430,30432],{},[1327,30425,30426,30428],{},[1330,30427,6674],{},[1334,30429,1565],{},[1460,30431,1462],{},[1327,30433,30434,30436],{},[1330,30435,6674],{},[1334,30437,1360],{},[1338,30439,30440],{"encoding":1340},"\\sigma_1 > \\sigma_2",[1162,30442,30443],{},[1115,30444,30446],{"className":30445},[1315],[1317,30447,30448],{"xmlns":1319},[1321,30449,30450,30494],{},[1324,30451,30452,30454,30456,30468,30470,30476,30478,30480,30482,30488,30490,30492],{},[1330,30453,6490],{},[1460,30455,3125],{},[1327,30457,30458,30460],{},[1330,30459,6490],{},[1324,30461,30462,30464,30466],{},[1334,30463,1565],{},[1460,30465,2838],{},[1330,30467,3139],{},[1460,30469,1647],{"stretchy":1646},[1327,30471,30472,30474],{},[1330,30473,1458],{},[1334,30475,1565],{},[1460,30477,2838],{},[1334,30479,1565],{},[1460,30481,1568],{"separator":1121},[1327,30483,30484,30486],{},[1330,30485,1458],{},[1334,30487,1360],{},[1460,30489,2838],{},[1334,30491,1565],{},[1460,30493,1658],{"stretchy":1646},[1338,30495,30496],{"encoding":1340},"F \\ge F_{1-\\alpha}(n_1-1, n_2-1)",[1147,30498,30499,30527,30555],{},[1162,30500,30501],{},[1115,30502,30504],{"className":30503},[1315],[1317,30505,30506],{"xmlns":1319},[1321,30507,30508,30524],{},[1324,30509,30510,30516,30518],{},[1327,30511,30512,30514],{},[1330,30513,6674],{},[1334,30515,1565],{},[1460,30517,1754],{},[1327,30519,30520,30522],{},[1330,30521,6674],{},[1334,30523,1360],{},[1338,30525,30526],{"encoding":1340},"\\sigma_1 = \\sigma_2",[1162,30528,30529],{},[1115,30530,30532],{"className":30531},[1315],[1317,30533,30534],{"xmlns":1319},[1321,30535,30536,30552],{},[1324,30537,30538,30544,30546],{},[1327,30539,30540,30542],{},[1330,30541,6674],{},[1334,30543,1565],{},[1460,30545,10733],{"mathvariant":1893},[1327,30547,30548,30550],{},[1330,30549,6674],{},[1334,30551,1360],{},[1338,30553,30554],{"encoding":1340},"\\sigma_1 \\neq \\sigma_2",[1162,30556,30557,30611,30612],{},[1115,30558,30560],{"className":30559},[1315],[1317,30561,30562],{"xmlns":1319},[1321,30563,30564,30608],{},[1324,30565,30566,30568,30570,30582,30584,30590,30592,30594,30596,30602,30604,30606],{},[1330,30567,6490],{},[1460,30569,6510],{},[1327,30571,30572,30574],{},[1330,30573,6490],{},[1324,30575,30576,30578,30580],{},[1330,30577,3139],{},[1330,30579,4379],{"mathvariant":1893},[1334,30581,1360],{},[1460,30583,1647],{"stretchy":1646},[1327,30585,30586,30588],{},[1330,30587,1458],{},[1334,30589,1565],{},[1460,30591,2838],{},[1334,30593,1565],{},[1460,30595,1568],{"separator":1121},[1327,30597,30598,30600],{},[1330,30599,1458],{},[1334,30601,1360],{},[1460,30603,2838],{},[1334,30605,1565],{},[1460,30607,1658],{"stretchy":1646},[1338,30609,30610],{"encoding":1340},"F \\le F_{\\alpha\u002F2}(n_1-1, n_2-1)"," nebo ",[1115,30613,30615],{"className":30614},[1315],[1317,30616,30617],{"xmlns":1319},[1321,30618,30619,30667],{},[1324,30620,30621,30623,30625,30641,30643,30649,30651,30653,30655,30661,30663,30665],{},[1330,30622,6490],{},[1460,30624,3125],{},[1327,30626,30627,30629],{},[1330,30628,6490],{},[1324,30630,30631,30633,30635,30637,30639],{},[1334,30632,1565],{},[1460,30634,2838],{},[1330,30636,3139],{},[1330,30638,4379],{"mathvariant":1893},[1334,30640,1360],{},[1460,30642,1647],{"stretchy":1646},[1327,30644,30645,30647],{},[1330,30646,1458],{},[1334,30648,1565],{},[1460,30650,2838],{},[1334,30652,1565],{},[1460,30654,1568],{"separator":1121},[1327,30656,30657,30659],{},[1330,30658,1458],{},[1334,30660,1360],{},[1460,30662,2838],{},[1334,30664,1565],{},[1460,30666,1658],{"stretchy":1646},[1338,30668,30669],{"encoding":1340},"F \\ge F_{1-\\alpha\u002F2}(n_1-1, n_2-1)",[1147,30671,30672,30700,30728],{},[1162,30673,30674],{},[1115,30675,30677],{"className":30676},[1315],[1317,30678,30679],{"xmlns":1319},[1321,30680,30681,30697],{},[1324,30682,30683,30689,30691],{},[1327,30684,30685,30687],{},[1330,30686,6674],{},[1334,30688,1565],{},[1460,30690,3125],{},[1327,30692,30693,30695],{},[1330,30694,6674],{},[1334,30696,1360],{},[1338,30698,30699],{"encoding":1340},"\\sigma_1 \\ge \\sigma_2",[1162,30701,30702],{},[1115,30703,30705],{"className":30704},[1315],[1317,30706,30707],{"xmlns":1319},[1321,30708,30709,30725],{},[1324,30710,30711,30717,30719],{},[1327,30712,30713,30715],{},[1330,30714,6674],{},[1334,30716,1565],{},[1460,30718,4107],{},[1327,30720,30721,30723],{},[1330,30722,6674],{},[1334,30724,1360],{},[1338,30726,30727],{"encoding":1340},"\\sigma_1 \u003C \\sigma_2",[1162,30729,30730],{},[1115,30731,30733],{"className":30732},[1315],[1317,30734,30735],{"xmlns":1319},[1321,30736,30737,30775],{},[1324,30738,30739,30741,30743,30749,30751,30757,30759,30761,30763,30769,30771,30773],{},[1330,30740,6490],{},[1460,30742,6510],{},[1327,30744,30745,30747],{},[1330,30746,6490],{},[1330,30748,3139],{},[1460,30750,1647],{"stretchy":1646},[1327,30752,30753,30755],{},[1330,30754,1458],{},[1334,30756,1565],{},[1460,30758,2838],{},[1334,30760,1565],{},[1460,30762,1568],{"separator":1121},[1327,30764,30765,30767],{},[1330,30766,1458],{},[1334,30768,1360],{},[1460,30770,2838],{},[1334,30772,1565],{},[1460,30774,1658],{"stretchy":1646},[1338,30776,30777],{"encoding":1340},"F \\le F_{\\alpha}(n_1-1, n_2-1)",[16521,30779,30781],{"id":30780},"dvouvýběrový-t-test-o-středních-hodnotách","Dvouvýběrový t-test o středních hodnotách",[1110,30783,30784],{},"Volba statistiky závisí na tom, zda jsou rozptyly považovány za shodné:",[1115,30786,30788],{"className":30787},[1315],[1317,30789,30790],{"xmlns":1319,"display":1736},[1321,30791,30792,30969],{},[1324,30793,30794,30800,30802,30878,30926,30928,30930,30939,30941,30947,30949,30955,30957,30963,30965,30967],{},[1327,30795,30796,30798],{},[1330,30797,6877],{},[1334,30799,1565],{},[1460,30801,1754],{},[2512,30803,30804,30828],{},[1324,30805,30806,30816,30818],{},[1327,30807,30808,30814],{},[2496,30809,30810,30812],{"accent":1121},[1330,30811,6495],{},[1460,30813,11235],{},[1334,30815,1565],{},[1460,30817,2838],{},[1327,30819,30820,30826],{},[2496,30821,30822,30824],{"accent":1121},[1330,30823,6495],{},[1460,30825,11235],{},[1334,30827,1360],{},[4228,30829,30830],{},[1324,30831,30832,30834,30840,30842,30844,30846,30854,30856,30858,30864,30866,30868,30870],{},[1460,30833,1647],{"stretchy":1646},[1327,30835,30836,30838],{},[1330,30837,1458],{},[1334,30839,1565],{},[1460,30841,2838],{},[1334,30843,1565],{},[1460,30845,1658],{"stretchy":1646},[3127,30847,30848,30850,30852],{},[1330,30849,1626],{},[1334,30851,1565],{},[1334,30853,1360],{},[1460,30855,5252],{},[1460,30857,1647],{"stretchy":1646},[1327,30859,30860,30862],{},[1330,30861,1458],{},[1334,30863,1360],{},[1460,30865,2838],{},[1334,30867,1565],{},[1460,30869,1658],{"stretchy":1646},[3127,30871,30872,30874,30876],{},[1330,30873,1626],{},[1334,30875,1360],{},[1334,30877,1360],{},[4228,30879,30880],{},[2512,30881,30882,30902],{},[1324,30883,30884,30890,30892,30898,30900],{},[1327,30885,30886,30888],{},[1330,30887,1458],{},[1334,30889,1565],{},[1460,30891,5252],{},[1327,30893,30894,30896],{},[1330,30895,1458],{},[1334,30897,1360],{},[1460,30899,2838],{},[1334,30901,1360],{},[1324,30903,30904,30914,30916],{},[2512,30905,30906,30908],{},[1334,30907,1565],{},[1327,30909,30910,30912],{},[1330,30911,1458],{},[1334,30913,1565],{},[1460,30915,5252],{},[2512,30917,30918,30920],{},[1334,30919,1565],{},[1327,30921,30922,30924],{},[1330,30923,1458],{},[1334,30925,1360],{},[1460,30927,1568],{"separator":1121},[1784,30929],{"width":1786},[3127,30931,30932,30934,30936],{},[1330,30933,6919],{},[1330,30935,1110],{},[1460,30937,30938],{},"∗",[1460,30940,1754],{},[1327,30942,30943,30945],{},[1330,30944,6919],{},[1330,30946,1110],{},[1460,30948,1647],{"stretchy":1646},[1327,30950,30951,30953],{},[1330,30952,1458],{},[1334,30954,1565],{},[1460,30956,5252],{},[1327,30958,30959,30961],{},[1330,30960,1458],{},[1334,30962,1360],{},[1460,30964,2838],{},[1334,30966,1360],{},[1460,30968,1658],{"stretchy":1646},[1338,30970,30971],{"encoding":1340},"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)",[1110,30973,30974,30975,31004],{},"se použije, pokud jsou rozptyly ",[1115,30976,30978],{"className":30977},[1315],[1317,30979,30980],{"xmlns":1319},[1321,30981,30982,31002],{},[1324,30983,30984,30992,30994],{},[3127,30985,30986,30988,30990],{},[1330,30987,6674],{},[1334,30989,1565],{},[1334,30991,1360],{},[1460,30993,1568],{"separator":1121},[3127,30995,30996,30998,31000],{},[1330,30997,6674],{},[1334,30999,1360],{},[1334,31001,1360],{},[1338,31003,30201],{"encoding":1340}," alespoň přibližně shodné; při rozdílných rozptylech",[1115,31006,31008],{"className":31007},[1315],[1317,31009,31010],{"xmlns":1319,"display":1736},[1321,31011,31012,31224],{},[1324,31013,31014,31020,31022,31086,31088,31090,31098,31100,31222],{},[1327,31015,31016,31018],{},[1330,31017,6877],{},[1334,31019,1360],{},[1460,31021,1754],{},[2512,31023,31024,31048],{},[1324,31025,31026,31036,31038],{},[1327,31027,31028,31034],{},[2496,31029,31030,31032],{"accent":1121},[1330,31031,6495],{},[1460,31033,11235],{},[1334,31035,1565],{},[1460,31037,2838],{},[1327,31039,31040,31046],{},[2496,31041,31042,31044],{"accent":1121},[1330,31043,6495],{},[1460,31045,11235],{},[1334,31047,1360],{},[4228,31049,31050],{},[1324,31051,31052,31060,31062,31068,31070,31078,31080],{},[3127,31053,31054,31056,31058],{},[1330,31055,1626],{},[1334,31057,1565],{},[1334,31059,1360],{},[1330,31061,4379],{"mathvariant":1893},[1327,31063,31064,31066],{},[1330,31065,1458],{},[1334,31067,1565],{},[1460,31069,5252],{},[3127,31071,31072,31074,31076],{},[1330,31073,1626],{},[1334,31075,1360],{},[1334,31077,1360],{},[1330,31079,4379],{"mathvariant":1893},[1327,31081,31082,31084],{},[1330,31083,1458],{},[1334,31085,1360],{},[1460,31087,1568],{"separator":1121},[1784,31089],{"width":1786},[3127,31091,31092,31094,31096],{},[1330,31093,6919],{},[1330,31095,1110],{},[1460,31097,30938],{},[1460,31099,1754],{},[2512,31101,31102,31182],{},[1324,31103,31104,31122,31128,31130,31136,31138,31140,31142,31144,31162,31168,31170,31176,31178,31180],{},[3015,31105,31106],{"scriptlevel":1336,"displaystyle":1121},[2512,31107,31108,31116],{},[3127,31109,31110,31112,31114],{},[1330,31111,1626],{},[1334,31113,1565],{},[1334,31115,1360],{},[1327,31117,31118,31120],{},[1330,31119,1458],{},[1334,31121,1565],{},[1327,31123,31124,31126],{},[1330,31125,6919],{},[1330,31127,1110],{},[1460,31129,1647],{"stretchy":1646},[1327,31131,31132,31134],{},[1330,31133,1458],{},[1334,31135,1565],{},[1460,31137,2838],{},[1334,31139,1565],{},[1460,31141,1658],{"stretchy":1646},[1460,31143,5252],{},[3015,31145,31146],{"scriptlevel":1336,"displaystyle":1121},[2512,31147,31148,31156],{},[3127,31149,31150,31152,31154],{},[1330,31151,1626],{},[1334,31153,1360],{},[1334,31155,1360],{},[1327,31157,31158,31160],{},[1330,31159,1458],{},[1334,31161,1360],{},[1327,31163,31164,31166],{},[1330,31165,6919],{},[1330,31167,1110],{},[1460,31169,1647],{"stretchy":1646},[1327,31171,31172,31174],{},[1330,31173,1458],{},[1334,31175,1360],{},[1460,31177,2838],{},[1334,31179,1565],{},[1460,31181,1658],{"stretchy":1646},[1324,31183,31184,31202,31204],{},[3015,31185,31186],{"scriptlevel":1336,"displaystyle":1121},[2512,31187,31188,31196],{},[3127,31189,31190,31192,31194],{},[1330,31191,1626],{},[1334,31193,1565],{},[1334,31195,1360],{},[1327,31197,31198,31200],{},[1330,31199,1458],{},[1334,31201,1565],{},[1460,31203,5252],{},[3015,31205,31206],{"scriptlevel":1336,"displaystyle":1121},[2512,31207,31208,31216],{},[3127,31209,31210,31212,31214],{},[1330,31211,1626],{},[1334,31213,1360],{},[1334,31215,1360],{},[1327,31217,31218,31220],{},[1330,31219,1458],{},[1334,31221,1360],{},[1330,31223,1440],{"mathvariant":1893},[1338,31225,31226],{"encoding":1340},"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}}.",[1141,31228,31229,31286],{},[1144,31230,31231],{},[1147,31232,31233,31252,31271],{},[1150,31234,31235],{},[1115,31236,31238],{"className":31237},[1315],[1317,31239,31240],{"xmlns":1319},[1321,31241,31242,31250],{},[1324,31243,31244],{},[1327,31245,31246,31248],{},[1330,31247,1332],{},[1334,31249,1336],{},[1338,31251,1341],{"encoding":1340},[1150,31253,31254],{},[1115,31255,31257],{"className":31256},[1315],[1317,31258,31259],{"xmlns":1319},[1321,31260,31261,31269],{},[1324,31262,31263],{},[1327,31264,31265,31267],{},[1330,31266,1332],{},[1334,31268,1565],{},[1338,31270,2770],{"encoding":1340},[1150,31272,27487,31273],{},[1115,31274,31276],{"className":31275},[1315],[1317,31277,31278],{"xmlns":1319},[1321,31279,31280,31284],{},[1324,31281,31282],{},[1330,31283,1376],{},[1338,31285,1376],{"encoding":1340},[1157,31287,31288,31372,31460],{},[1147,31289,31290,31318,31346],{},[1162,31291,31292],{},[1115,31293,31295],{"className":31294},[1315],[1317,31296,31297],{"xmlns":1319},[1321,31298,31299,31315],{},[1324,31300,31301,31307,31309],{},[1327,31302,31303,31305],{},[1330,31304,6666],{},[1334,31306,1565],{},[1460,31308,6510],{},[1327,31310,31311,31313],{},[1330,31312,6666],{},[1334,31314,1360],{},[1338,31316,31317],{"encoding":1340},"\\mu_1 \\le \\mu_2",[1162,31319,31320],{},[1115,31321,31323],{"className":31322},[1315],[1317,31324,31325],{"xmlns":1319},[1321,31326,31327,31343],{},[1324,31328,31329,31335,31337],{},[1327,31330,31331,31333],{},[1330,31332,6666],{},[1334,31334,1565],{},[1460,31336,1462],{},[1327,31338,31339,31341],{},[1330,31340,6666],{},[1334,31342,1360],{},[1338,31344,31345],{"encoding":1340},"\\mu_1 > \\mu_2",[1162,31347,31348],{},[1115,31349,31351],{"className":31350},[1315],[1317,31352,31353],{"xmlns":1319},[1321,31354,31355,31369],{},[1324,31356,31357,31359,31361],{},[1330,31358,6919],{},[1460,31360,3125],{},[3127,31362,31363,31365,31367],{},[1330,31364,6919],{},[1330,31366,1110],{},[1460,31368,30938],{},[1338,31370,31371],{"encoding":1340},"t \\ge t_p^*",[1147,31373,31374,31402,31430],{},[1162,31375,31376],{},[1115,31377,31379],{"className":31378},[1315],[1317,31380,31381],{"xmlns":1319},[1321,31382,31383,31399],{},[1324,31384,31385,31391,31393],{},[1327,31386,31387,31389],{},[1330,31388,6666],{},[1334,31390,1565],{},[1460,31392,1754],{},[1327,31394,31395,31397],{},[1330,31396,6666],{},[1334,31398,1360],{},[1338,31400,31401],{"encoding":1340},"\\mu_1 = \\mu_2",[1162,31403,31404],{},[1115,31405,31407],{"className":31406},[1315],[1317,31408,31409],{"xmlns":1319},[1321,31410,31411,31427],{},[1324,31412,31413,31419,31421],{},[1327,31414,31415,31417],{},[1330,31416,6666],{},[1334,31418,1565],{},[1460,31420,10733],{"mathvariant":1893},[1327,31422,31423,31425],{},[1330,31424,6666],{},[1334,31426,1360],{},[1338,31428,31429],{"encoding":1340},"\\mu_1 \\neq \\mu_2",[1162,31431,31432],{},[1115,31433,31435],{"className":31434},[1315],[1317,31436,31437],{"xmlns":1319},[1321,31438,31439,31457],{},[1324,31440,31441,31443,31445,31447,31449],{},[1460,31442,22799],{"stretchy":1646},[1330,31444,6919],{},[1460,31446,22799],{"stretchy":1646},[1460,31448,3125],{},[3127,31450,31451,31453,31455],{},[1330,31452,6919],{},[1330,31454,1110],{},[1460,31456,30938],{},[1338,31458,31459],{"encoding":1340},"\\lvert t \\rvert \\ge t_p^*",[1147,31461,31462,31490,31518],{},[1162,31463,31464],{},[1115,31465,31467],{"className":31466},[1315],[1317,31468,31469],{"xmlns":1319},[1321,31470,31471,31487],{},[1324,31472,31473,31479,31481],{},[1327,31474,31475,31477],{},[1330,31476,6666],{},[1334,31478,1565],{},[1460,31480,3125],{},[1327,31482,31483,31485],{},[1330,31484,6666],{},[1334,31486,1360],{},[1338,31488,31489],{"encoding":1340},"\\mu_1 \\ge \\mu_2",[1162,31491,31492],{},[1115,31493,31495],{"className":31494},[1315],[1317,31496,31497],{"xmlns":1319},[1321,31498,31499,31515],{},[1324,31500,31501,31507,31509],{},[1327,31502,31503,31505],{},[1330,31504,6666],{},[1334,31506,1565],{},[1460,31508,4107],{},[1327,31510,31511,31513],{},[1330,31512,6666],{},[1334,31514,1360],{},[1338,31516,31517],{"encoding":1340},"\\mu_1 \u003C \\mu_2",[1162,31519,31520],{},[1115,31521,31523],{"className":31522},[1315],[1317,31524,31525],{"xmlns":1319},[1321,31526,31527,31543],{},[1324,31528,31529,31531,31533,31535],{},[1330,31530,6919],{},[1460,31532,6510],{},[1460,31534,2838],{},[3127,31536,31537,31539,31541],{},[1330,31538,6919],{},[1330,31540,1110],{},[1460,31542,30938],{},[1338,31544,31545],{"encoding":1340},"t \\le -t_p^*",[1110,31547,31548,31549,30611,31567,1440],{},"Postup je dvoukrokový: nejprve F-test rozhodne o shodě rozptylů, pak se podle výsledku zvolí ",[1115,31550,31552],{"className":31551},[1315],[1317,31553,31554],{"xmlns":1319},[1321,31555,31556,31564],{},[1324,31557,31558],{},[1327,31559,31560,31562],{},[1330,31561,6877],{},[1334,31563,1565],{},[1338,31565,31566],{"encoding":1340},"T_1",[1115,31568,31570],{"className":31569},[1315],[1317,31571,31572],{"xmlns":1319},[1321,31573,31574,31582],{},[1324,31575,31576],{},[1327,31577,31578,31580],{},[1330,31579,6877],{},[1334,31581,1360],{},[1338,31583,31584],{"encoding":1340},"T_2",[1110,31586,31587],{},[4158,31588],{"alt":31589,"className":31590,"src":31591},"mask-th-f-kriticky-obor",[1130,4162],"\u002Fwiki-assets\u002Fmask-th-f-kriticky-obor.png",[1103,31593,31595,31602,31752,31833,31962,32000,32073,32212],{"className":31594,"dataCallout":3251},[1106,3250],[1110,31596,31598,31601],{"className":31597},[1113],[1115,31599],{"className":31600,"ariaHidden":1121},[1118,3258,1120],"Příklad: Porovnání dvou dodavatelů součástek",[1110,31603,31604,31605,2725,31627,31653,31654,31678,31679,2725,31701,31653,31727,31751],{},"Pevnost plastových dílů: dodavatel A (",[1115,31606,31608],{"className":31607},[1315],[1317,31609,31610],{"xmlns":1319},[1321,31611,31612,31624],{},[1324,31613,31614,31620,31622],{},[1327,31615,31616,31618],{},[1330,31617,1458],{},[1334,31619,1565],{},[1460,31621,1754],{},[1334,31623,8810],{},[1338,31625,31626],{"encoding":1340},"n_1 = 10",[1115,31628,31630],{"className":31629},[1315],[1317,31631,31632],{"xmlns":1319},[1321,31633,31634,31650],{},[1324,31635,31636,31646,31648],{},[1327,31637,31638,31644],{},[2496,31639,31640,31642],{"accent":1121},[1330,31641,6495],{},[1460,31643,11235],{},[1334,31645,1565],{},[1460,31647,1754],{},[1334,31649,3402],{},[1338,31651,31652],{"encoding":1340},"\\bar{x}_1 = 82"," MPa, ",[1115,31655,31657],{"className":31656},[1315],[1317,31658,31659],{"xmlns":1319},[1321,31660,31661,31675],{},[1324,31662,31663,31671,31673],{},[3127,31664,31665,31667,31669],{},[1330,31666,1626],{},[1334,31668,1565],{},[1334,31670,1360],{},[1460,31672,1754],{},[1334,31674,3833],{},[1338,31676,31677],{"encoding":1340},"s_1^2 = 25","), dodavatel B (",[1115,31680,31682],{"className":31681},[1315],[1317,31683,31684],{"xmlns":1319},[1321,31685,31686,31698],{},[1324,31687,31688,31694,31696],{},[1327,31689,31690,31692],{},[1330,31691,1458],{},[1334,31693,1360],{},[1460,31695,1754],{},[1334,31697,2048],{},[1338,31699,31700],{"encoding":1340},"n_2 = 12",[1115,31702,31704],{"className":31703},[1315],[1317,31705,31706],{"xmlns":1319},[1321,31707,31708,31724],{},[1324,31709,31710,31720,31722],{},[1327,31711,31712,31718],{},[2496,31713,31714,31716],{"accent":1121},[1330,31715,6495],{},[1460,31717,11235],{},[1334,31719,1360],{},[1460,31721,1754],{},[1334,31723,14508],{},[1338,31725,31726],{"encoding":1340},"\\bar{x}_2 = 75",[1115,31728,31730],{"className":31729},[1315],[1317,31731,31732],{"xmlns":1319},[1321,31733,31734,31748],{},[1324,31735,31736,31744,31746],{},[3127,31737,31738,31740,31742],{},[1330,31739,1626],{},[1334,31741,1360],{},[1334,31743,1360],{},[1460,31745,1754],{},[1334,31747,21801],{},[1338,31749,31750],{"encoding":1340},"s_2^2 = 16","). Předpokládá se normalita obou rozdělení.",[1110,31753,31754,1425,31757,2725,31795,1440],{},[1302,31755,31756],{},"Krok 1 — F-test rozptylů.",[1115,31758,31760],{"className":31759},[1315],[1317,31761,31762],{"xmlns":1319},[1321,31763,31764,31792],{},[1324,31765,31766,31772,31774,31782,31784],{},[1327,31767,31768,31770],{},[1330,31769,1332],{},[1334,31771,1336],{},[1460,31773,1730],{},[3127,31775,31776,31778,31780],{},[1330,31777,6674],{},[1334,31779,1565],{},[1334,31781,1360],{},[1460,31783,1754],{},[3127,31785,31786,31788,31790],{},[1330,31787,6674],{},[1334,31789,1360],{},[1334,31791,1360],{},[1338,31793,31794],{"encoding":1340},"H_0: \\sigma_1^2 = \\sigma_2^2",[1115,31796,31798],{"className":31797},[1315],[1317,31799,31800],{"xmlns":1319},[1321,31801,31802,31830],{},[1324,31803,31804,31810,31812,31820,31822],{},[1327,31805,31806,31808],{},[1330,31807,1332],{},[1334,31809,1565],{},[1460,31811,1730],{},[3127,31813,31814,31816,31818],{},[1330,31815,6674],{},[1334,31817,1565],{},[1334,31819,1360],{},[1460,31821,10733],{"mathvariant":1893},[3127,31823,31824,31826,31828],{},[1330,31825,6674],{},[1334,31827,1360],{},[1334,31829,1360],{},[1338,31831,31832],{"encoding":1340},"H_1: \\sigma_1^2 \\neq \\sigma_2^2",[1110,31834,31835],{},[1115,31836,31838],{"className":31837},[1315],[1317,31839,31840],{"xmlns":1319},[1321,31841,31842,31959],{},[1324,31843,31844,31846,31848,31854,31856,31859,31861,31863,31865,31867,31869,31871,31873,31886,31888,31890,31892,31894,31896,31899,31902,31904,31906,31908,31921,31923,31925,31927,31929,31931,31933,31935,31937,31939,31941,31944,31946,31948,31950,31952,31954,31957],{},[1330,31845,6490],{},[1460,31847,1754],{},[2512,31849,31850,31852],{},[1334,31851,3833],{},[1334,31853,21801],{},[1460,31855,1754],{},[1334,31857,31858],{},"1,5625",[1460,31860,1568],{"separator":1121},[1784,31862],{"width":1786},[1330,31864,1376],{},[1460,31866,1754],{},[1460,31868,3108],{"stretchy":1646},[1330,31870,6490],{},[1460,31872,6510],{},[1327,31874,31875,31877],{},[1330,31876,6490],{},[1324,31878,31879,31881,31883],{},[1334,31880,1336],{},[1460,31882,1568],{"separator":1121},[1334,31884,31885],{},"025",[1460,31887,1647],{"stretchy":1646},[1334,31889,3369],{},[1460,31891,1568],{"separator":1121},[1334,31893,2027],{},[1460,31895,1658],{"stretchy":1646},[2682,31897,31898],{},"  ",[2682,31900,31901],{},"nebo",[2682,31903,31898],{},[1330,31905,6490],{},[1460,31907,3125],{},[1327,31909,31910,31912],{},[1330,31911,6490],{},[1324,31913,31914,31916,31918],{},[1334,31915,1336],{},[1460,31917,1568],{"separator":1121},[1334,31919,31920],{},"975",[1460,31922,1647],{"stretchy":1646},[1334,31924,3369],{},[1460,31926,1568],{"separator":1121},[1334,31928,2027],{},[1460,31930,1658],{"stretchy":1646},[1460,31932,3168],{"stretchy":1646},[1460,31934,1754],{},[1460,31936,3108],{"stretchy":1646},[1330,31938,6490],{},[1460,31940,6510],{},[1334,31942,31943],{},"0,256",[2682,31945,31898],{},[2682,31947,31901],{},[2682,31949,31898],{},[1330,31951,6490],{},[1460,31953,3125],{},[1334,31955,31956],{},"3,588",[1460,31958,3168],{"stretchy":1646},[1338,31960,31961],{"encoding":1340},"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\\}",[1110,31963,31964,31982,31983,1440],{},[1115,31965,31967],{"className":31966},[1315],[1317,31968,31969],{"xmlns":1319},[1321,31970,31971,31979],{},[1324,31972,31973,31975,31977],{},[1330,31974,6490],{},[1460,31976,27048],{"mathvariant":1893},[1330,31978,1376],{},[1338,31980,31981],{"encoding":1340},"F \\notin W",", rozptyly nezamítáme jako shodné — pro t-test se použije ",[1115,31984,31986],{"className":31985},[1315],[1317,31987,31988],{"xmlns":1319},[1321,31989,31990,31998],{},[1324,31991,31992],{},[1327,31993,31994,31996],{},[1330,31995,6877],{},[1334,31997,1565],{},[1338,31999,31566],{"encoding":1340},[1110,32001,32002,1425,32005,2725,32039,1440],{},[1302,32003,32004],{},"Krok 2 — dvouvýběrový t-test středních hodnot.",[1115,32006,32008],{"className":32007},[1315],[1317,32009,32010],{"xmlns":1319},[1321,32011,32012,32036],{},[1324,32013,32014,32020,32022,32028,32030],{},[1327,32015,32016,32018],{},[1330,32017,1332],{},[1334,32019,1336],{},[1460,32021,1730],{},[1327,32023,32024,32026],{},[1330,32025,6666],{},[1334,32027,1565],{},[1460,32029,1754],{},[1327,32031,32032,32034],{},[1330,32033,6666],{},[1334,32035,1360],{},[1338,32037,32038],{"encoding":1340},"H_0: \\mu_1 = \\mu_2",[1115,32040,32042],{"className":32041},[1315],[1317,32043,32044],{"xmlns":1319},[1321,32045,32046,32070],{},[1324,32047,32048,32054,32056,32062,32064],{},[1327,32049,32050,32052],{},[1330,32051,1332],{},[1334,32053,1565],{},[1460,32055,1730],{},[1327,32057,32058,32060],{},[1330,32059,6666],{},[1334,32061,1565],{},[1460,32063,10733],{"mathvariant":1893},[1327,32065,32066,32068],{},[1330,32067,6666],{},[1334,32069,1360],{},[1338,32071,32072],{"encoding":1340},"H_1: \\mu_1 \\neq \\mu_2",[1110,32074,32075],{},[1115,32076,32078],{"className":32077},[1315],[1317,32079,32080],{"xmlns":1319},[1321,32081,32082,32209],{},[1324,32083,32084,32092,32094,32114,32116,32119,32121,32123,32125,32127,32141,32149,32151,32154,32156,32158,32160,32162,32164,32166,32168,32170,32172,32184,32186,32188,32190,32192,32194,32196,32198,32200,32202,32204,32207],{},[3127,32085,32086,32088,32090],{},[1330,32087,1626],{},[1330,32089,1110],{},[1334,32091,1360],{},[1460,32093,1754],{},[2512,32095,32096,32112],{},[1324,32097,32098,32100,32102,32104,32106,32108,32110],{},[1334,32099,3369],{},[1460,32101,7887],{},[1334,32103,3833],{},[1460,32105,5252],{},[1334,32107,2027],{},[1460,32109,7887],{},[1334,32111,21801],{},[1334,32113,3820],{},[1460,32115,1754],{},[1334,32117,32118],{},"20,05",[1460,32120,1568],{"separator":1121},[1784,32122],{"width":1786},[1330,32124,6919],{},[1460,32126,1754],{},[2512,32128,32129,32137],{},[1324,32130,32131,32133,32135],{},[1334,32132,3402],{},[1460,32134,2838],{},[1334,32136,14508],{},[4228,32138,32139],{},[1334,32140,32118],{},[4228,32142,32143],{},[2512,32144,32145,32147],{},[1334,32146,21661],{},[1334,32148,2162],{},[1460,32150,9217],{},[1334,32152,32153],{},"3,651",[1460,32155,1568],{"separator":1121},[1784,32157],{"width":1786},[1330,32159,1376],{},[1460,32161,1754],{},[1460,32163,3108],{"stretchy":1646},[1460,32165,22799],{"stretchy":1646},[1330,32167,6919],{},[1460,32169,22799],{"stretchy":1646},[1460,32171,3125],{},[1327,32173,32174,32176],{},[1330,32175,6919],{},[1324,32177,32178,32180,32182],{},[1334,32179,1336],{},[1460,32181,1568],{"separator":1121},[1334,32183,31920],{},[1460,32185,1647],{"stretchy":1646},[1334,32187,3820],{},[1460,32189,1658],{"stretchy":1646},[1460,32191,3168],{"stretchy":1646},[1460,32193,1754],{},[1460,32195,3108],{"stretchy":1646},[1460,32197,22799],{"stretchy":1646},[1330,32199,6919],{},[1460,32201,22799],{"stretchy":1646},[1460,32203,3125],{},[1334,32205,32206],{},"2,086",[1460,32208,3168],{"stretchy":1646},[1338,32210,32211],{"encoding":1340},"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\\}",[1110,32213,32214,5782,32231,32248],{},[1115,32215,32217],{"className":32216},[1315],[1317,32218,32219],{"xmlns":1319},[1321,32220,32221,32229],{},[1324,32222,32223,32225,32227],{},[1330,32224,6919],{},[1460,32226,6794],{},[1330,32228,1376],{},[1338,32230,28191],{"encoding":1340},[1115,32232,32234],{"className":32233},[1315],[1317,32235,32236],{"xmlns":1319},[1321,32237,32238,32246],{},[1324,32239,32240],{},[1327,32241,32242,32244],{},[1330,32243,1332],{},[1334,32245,1336],{},[1338,32247,1341],{"encoding":1340},": pevnost součástek od obou dodavatelů se statisticky významně liší.",[3468,32250,32252],{"className":3470,"code":32251,"language":71,"meta":1247,"style":1247},"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",[3244,32253,32254,32272,32292,32307,32342,32373,32378,32383],{"__ignoreMap":1247},[1115,32255,32256,32259,32261,32263,32265,32268,32270],{"class":3476,"line":10},[1115,32257,32258],{"class":3479},"s1",[1115,32260,3484],{"class":3483},[1115,32262,14178],{"class":3499},[1115,32264,24959],{"class":3491},[1115,32266,32267],{"class":3479},"n1",[1115,32269,3484],{"class":3483},[1115,32271,29632],{"class":3499},[1115,32273,32274,32277,32279,32282,32284,32287,32289],{"class":3476,"line":27},[1115,32275,32276],{"class":3479},"s2",[1115,32278,3484],{"class":3483},[1115,32280,32281],{"class":3499}," 16",[1115,32283,24959],{"class":3491},[1115,32285,32286],{"class":3479},"n2",[1115,32288,3484],{"class":3483},[1115,32290,32291],{"class":3499}," 12\n",[1115,32293,32294,32297,32299,32302,32304],{"class":3476,"line":148},[1115,32295,32296],{"class":3479},"Fstat",[1115,32298,3484],{"class":3483},[1115,32300,32301],{"class":3479}," s1",[1115,32303,9852],{"class":3483},[1115,32305,32306],{"class":3479}," s2\n",[1115,32308,32309,32312,32314,32317,32319,32322,32324,32327,32329,32331,32333,32336,32338,32340],{"class":3476,"line":111},[1115,32310,32311],{"class":3479},"F_dolni",[1115,32313,3484],{"class":3483},[1115,32315,32316],{"class":3487}," qf",[1115,32318,1647],{"class":3491},[1115,32320,32321],{"class":3499},"0.025",[1115,32323,1568],{"class":3483},[1115,32325,32326],{"class":3479}," n1",[1115,32328,25296],{"class":3483},[1115,32330,4416],{"class":3499},[1115,32332,1568],{"class":3483},[1115,32334,32335],{"class":3479}," n2",[1115,32337,25296],{"class":3483},[1115,32339,4416],{"class":3499},[1115,32341,3676],{"class":3491},[1115,32343,32344,32347,32349,32351,32353,32355,32357,32359,32361,32363,32365,32367,32369,32371],{"class":3476,"line":96},[1115,32345,32346],{"class":3479},"F_horni",[1115,32348,3484],{"class":3483},[1115,32350,32316],{"class":3487},[1115,32352,1647],{"class":3491},[1115,32354,8866],{"class":3499},[1115,32356,1568],{"class":3483},[1115,32358,32326],{"class":3479},[1115,32360,25296],{"class":3483},[1115,32362,4416],{"class":3499},[1115,32364,1568],{"class":3483},[1115,32366,32335],{"class":3479},[1115,32368,25296],{"class":3483},[1115,32370,4416],{"class":3499},[1115,32372,3676],{"class":3491},[1115,32374,32375],{"class":3476,"line":89},[1115,32376,32377],{"class":3479},"Fstat\n",[1115,32379,32380],{"class":3476,"line":82},[1115,32381,32382],{"class":3479},"F_dolni\n",[1115,32384,32385],{"class":3476,"line":75},[1115,32386,32387],{"class":3479},"F_horni\n",[3468,32389,32392],{"className":32390,"code":32391,"language":3698,"meta":1247},[3696],"[1] 1.5625\n[1] 0.2556189\n[1] 3.587899\n",[3244,32393,32391],{"__ignoreMap":1247},[3468,32395,32397],{"className":3470,"code":32396,"language":71,"meta":1247,"style":1247},"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",[3244,32398,32399,32456,32507,32537,32542,32546],{"__ignoreMap":1247},[1115,32400,32401,32404,32406,32409,32411,32413,32415,32417,32419,32421,32423,32425,32427,32429,32431,32433,32435,32438,32440,32442,32444,32446,32448,32450,32452,32454],{"class":3476,"line":10},[1115,32402,32403],{"class":3479},"sp2",[1115,32405,3484],{"class":3483},[1115,32407,32408],{"class":3491}," ((",[1115,32410,32267],{"class":3479},[1115,32412,25296],{"class":3483},[1115,32414,4416],{"class":3499},[1115,32416,4376],{"class":3491},[1115,32418,4394],{"class":3483},[1115,32420,32301],{"class":3479},[1115,32422,18289],{"class":3483},[1115,32424,4382],{"class":3491},[1115,32426,32286],{"class":3479},[1115,32428,25296],{"class":3483},[1115,32430,4416],{"class":3499},[1115,32432,4376],{"class":3491},[1115,32434,4394],{"class":3483},[1115,32436,32437],{"class":3479}," s2",[1115,32439,4376],{"class":3491},[1115,32441,4379],{"class":3483},[1115,32443,4382],{"class":3491},[1115,32445,32267],{"class":3479},[1115,32447,18289],{"class":3483},[1115,32449,32335],{"class":3479},[1115,32451,25296],{"class":3483},[1115,32453,3955],{"class":3499},[1115,32455,3676],{"class":3491},[1115,32457,32458,32460,32462,32464,32466,32468,32471,32473,32475,32477,32479,32481,32483,32485,32487,32489,32491,32493,32495,32497,32499,32501,32503,32505],{"class":3476,"line":27},[1115,32459,6919],{"class":3479},[1115,32461,3484],{"class":3483},[1115,32463,4382],{"class":3491},[1115,32465,3402],{"class":3499},[1115,32467,25296],{"class":3483},[1115,32469,32470],{"class":3499}," 75",[1115,32472,4376],{"class":3491},[1115,32474,4379],{"class":3483},[1115,32476,4353],{"class":3487},[1115,32478,1647],{"class":3491},[1115,32480,32403],{"class":3479},[1115,32482,4376],{"class":3491},[1115,32484,4394],{"class":3483},[1115,32486,4353],{"class":3487},[1115,32488,1647],{"class":3491},[1115,32490,32267],{"class":3479},[1115,32492,18414],{"class":3483},[1115,32494,32335],{"class":3479},[1115,32496,9852],{"class":3483},[1115,32498,4382],{"class":3491},[1115,32500,32267],{"class":3479},[1115,32502,18289],{"class":3483},[1115,32504,32335],{"class":3479},[1115,32506,9270],{"class":3491},[1115,32508,32509,32511,32513,32515,32517,32519,32521,32523,32525,32527,32529,32531,32533,32535],{"class":3476,"line":148},[1115,32510,28298],{"class":3479},[1115,32512,3484],{"class":3483},[1115,32514,28303],{"class":3487},[1115,32516,1647],{"class":3491},[1115,32518,8866],{"class":3499},[1115,32520,1568],{"class":3483},[1115,32522,10586],{"class":3479},[1115,32524,3572],{"class":3483},[1115,32526,32326],{"class":3479},[1115,32528,18289],{"class":3483},[1115,32530,32335],{"class":3479},[1115,32532,25296],{"class":3483},[1115,32534,3955],{"class":3499},[1115,32536,3676],{"class":3491},[1115,32538,32539],{"class":3476,"line":111},[1115,32540,32541],{"class":3479},"sp2\n",[1115,32543,32544],{"class":3476,"line":96},[1115,32545,28328],{"class":3479},[1115,32547,32548],{"class":3476,"line":89},[1115,32549,28333],{"class":3479},[3468,32551,32554],{"className":32552,"code":32553,"language":3698,"meta":1247},[3696],"[1] 20.05\n[1] 3.65107\n[1] 2.085963\n",[3244,32555,32553],{"__ignoreMap":1247},[1110,32557,32558],{},[4158,32559],{"alt":32560,"className":32561,"src":32562},"mask-th-t-dvoustranny",[1130,4162],"\u002Fwiki-assets\u002Fmask-th-t-dvoustranny.png",[1110,32564,32565,32566,5516,32569,32571,32572,32575,32576,5516,32593,3763,32610,32612,32613,32615],{},"V R provede obě kroky ",[3244,32567,32568],{},"var.test()",[3244,32570,27788],{},". Parametr ",[3244,32573,32574],{},"var.equal"," nastavuje volbu mezi ",[1115,32577,32579],{"className":32578},[1315],[1317,32580,32581],{"xmlns":1319},[1321,32582,32583,32591],{},[1324,32584,32585],{},[1327,32586,32587,32589],{},[1330,32588,6877],{},[1334,32590,1565],{},[1338,32592,31566],{"encoding":1340},[1115,32594,32596],{"className":32595},[1315],[1317,32597,32598],{"xmlns":1319},[1321,32599,32600,32608],{},[1324,32601,32602],{},[1327,32603,32604,32606],{},[1330,32605,6877],{},[1334,32607,1360],{},[1338,32609,31584],{"encoding":1340},[3244,32611,9301],{}," znamená předpoklad shodných rozptylů (podle výsledku F-testu), ",[3244,32614,9304],{}," předpoklad rozdílných rozptylů.",[1110,32617,32618,32621],{},[1302,32619,32620],{},"Kabely A\u002FB."," Pevnost v tahu dvou výrobců (MPa, 12 kabelů od každého):",[3468,32623,32625],{"className":3470,"code":32624,"language":71,"meta":1247,"style":1247},"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",[3244,32626,32627,32693,32756,32772],{"__ignoreMap":1247},[1115,32628,32629,32631,32633,32635,32637,32640,32642,32645,32647,32650,32652,32655,32657,32659,32661,32664,32666,32669,32671,32673,32675,32678,32680,32682,32684,32687,32689,32691],{"class":3476,"line":10},[1115,32630,1546],{"class":3479},[1115,32632,3484],{"class":3483},[1115,32634,3610],{"class":3487},[1115,32636,1647],{"class":3491},[1115,32638,32639],{"class":3499},"313",[1115,32641,1568],{"class":3483},[1115,32643,32644],{"class":3499}," 299",[1115,32646,1568],{"class":3483},[1115,32648,32649],{"class":3499}," 315",[1115,32651,1568],{"class":3483},[1115,32653,32654],{"class":3499}," 312",[1115,32656,1568],{"class":3483},[1115,32658,15146],{"class":3499},[1115,32660,1568],{"class":3483},[1115,32662,32663],{"class":3499}," 308",[1115,32665,1568],{"class":3483},[1115,32667,32668],{"class":3499}," 314",[1115,32670,1568],{"class":3483},[1115,32672,13938],{"class":3499},[1115,32674,1568],{"class":3483},[1115,32676,32677],{"class":3499}," 305",[1115,32679,1568],{"class":3483},[1115,32681,15146],{"class":3499},[1115,32683,1568],{"class":3483},[1115,32685,32686],{"class":3499}," 309",[1115,32688,1568],{"class":3483},[1115,32690,32668],{"class":3499},[1115,32692,3676],{"class":3491},[1115,32694,32695,32697,32699,32701,32703,32706,32708,32711,32713,32715,32717,32719,32721,32724,32726,32729,32731,32733,32735,32737,32739,32741,32743,32746,32748,32750,32752,32754],{"class":3476,"line":27},[1115,32696,1595],{"class":3479},[1115,32698,3484],{"class":3483},[1115,32700,3610],{"class":3487},[1115,32702,1647],{"class":3491},[1115,32704,32705],{"class":3499},"307",[1115,32707,1568],{"class":3483},[1115,32709,32710],{"class":3499}," 322",[1115,32712,1568],{"class":3483},[1115,32714,13938],{"class":3499},[1115,32716,1568],{"class":3483},[1115,32718,13938],{"class":3499},[1115,32720,1568],{"class":3483},[1115,32722,32723],{"class":3499}," 311",[1115,32725,1568],{"class":3483},[1115,32727,32728],{"class":3499}," 316",[1115,32730,1568],{"class":3483},[1115,32732,32649],{"class":3499},[1115,32734,1568],{"class":3483},[1115,32736,32668],{"class":3499},[1115,32738,1568],{"class":3483},[1115,32740,32663],{"class":3499},[1115,32742,1568],{"class":3483},[1115,32744,32745],{"class":3499}," 319",[1115,32747,1568],{"class":3483},[1115,32749,13938],{"class":3499},[1115,32751,1568],{"class":3483},[1115,32753,32654],{"class":3499},[1115,32755,3676],{"class":3491},[1115,32757,32758,32761,32763,32765,32767,32770],{"class":3476,"line":148},[1115,32759,32760],{"class":3487},"var.test",[1115,32762,1647],{"class":3491},[1115,32764,1546],{"class":3479},[1115,32766,1568],{"class":3483},[1115,32768,32769],{"class":3479}," B",[1115,32771,3676],{"class":3491},[1115,32773,32774,32776,32778,32780,32782,32784,32786,32789,32791,32793],{"class":3476,"line":111},[1115,32775,27853],{"class":3487},[1115,32777,1647],{"class":3491},[1115,32779,1546],{"class":3479},[1115,32781,1568],{"class":3483},[1115,32783,32769],{"class":3479},[1115,32785,1568],{"class":3483},[1115,32787,32788],{"class":3479}," var.equal",[1115,32790,3572],{"class":3483},[1115,32792,3585],{"class":3499},[1115,32794,3676],{"class":3491},[3468,32796,32799],{"className":32797,"code":32798,"language":3698,"meta":1247},[3696],"    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",[3244,32800,32798],{"__ignoreMap":1247},[1110,32802,32803,32804,11830,32823,32826,32827,32846,32847,32864],{},"F-test shodu rozptylů nezamítá (",[1115,32805,32807],{"className":32806},[1315],[1317,32808,32809],{"xmlns":1319},[1321,32810,32811,32820],{},[1324,32812,32813,32815,32817],{},[1330,32814,1110],{},[1460,32816,1754],{},[1334,32818,32819],{},"0,7776",[1338,32821,32822],{"encoding":1340},"p = 0{,}7776",[3244,32824,32825],{},"var.equal = TRUE",". Výsledný t-test dává ",[1115,32828,32830],{"className":32829},[1315],[1317,32831,32832],{"xmlns":1319},[1321,32833,32834,32843],{},[1324,32835,32836,32838,32840],{},[1330,32837,1110],{},[1460,32839,1754],{},[1334,32841,32842],{},"0,06932",[1338,32844,32845],{"encoding":1340},"p = 0{,}06932"," — na hladině 5 % se ",[1115,32848,32850],{"className":32849},[1315],[1317,32851,32852],{"xmlns":1319},[1321,32853,32854,32862],{},[1324,32855,32856],{},[1327,32857,32858,32860],{},[1330,32859,1332],{},[1334,32861,1336],{},[1338,32863,1341],{"encoding":1340}," nezamítá, ale hodnota je těsně nad hranicí.",[1110,32866,32867],{},[1302,32868,32869],{},"Výšky chlapců a dívek v páté třídě:",[3468,32871,32873],{"className":3470,"code":32872,"language":71,"meta":1247,"style":1247},"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",[3244,32874,32875,32955,33018,33033],{"__ignoreMap":1247},[1115,32876,32877,32880,32882,32884,32886,32889,32891,32893,32895,32898,32900,32903,32905,32908,32910,32913,32915,32917,32919,32921,32923,32925,32927,32929,32931,32934,32936,32939,32941,32944,32946,32948,32950,32953],{"class":3476,"line":10},[1115,32878,32879],{"class":3479},"boys",[1115,32881,3484],{"class":3483},[1115,32883,3610],{"class":3487},[1115,32885,1647],{"class":3491},[1115,32887,32888],{"class":3499},"130",[1115,32890,1568],{"class":3483},[1115,32892,15095],{"class":3499},[1115,32894,1568],{"class":3483},[1115,32896,32897],{"class":3499}," 136",[1115,32899,1568],{"class":3483},[1115,32901,32902],{"class":3499}," 141",[1115,32904,1568],{"class":3483},[1115,32906,32907],{"class":3499}," 139",[1115,32909,1568],{"class":3483},[1115,32911,32912],{"class":3499}," 133",[1115,32914,1568],{"class":3483},[1115,32916,18246],{"class":3499},[1115,32918,1568],{"class":3483},[1115,32920,13953],{"class":3499},[1115,32922,1568],{"class":3483},[1115,32924,32907],{"class":3499},[1115,32926,1568],{"class":3483},[1115,32928,32897],{"class":3499},[1115,32930,1568],{"class":3483},[1115,32932,32933],{"class":3499}," 138",[1115,32935,1568],{"class":3483},[1115,32937,32938],{"class":3499}," 142",[1115,32940,1568],{"class":3483},[1115,32942,32943],{"class":3499}," 127",[1115,32945,1568],{"class":3483},[1115,32947,32907],{"class":3499},[1115,32949,1568],{"class":3483},[1115,32951,32952],{"class":3499}," 147",[1115,32954,3676],{"class":3491},[1115,32956,32957,32960,32962,32964,32966,32968,32970,32972,32974,32977,32979,32982,32984,32987,32989,32991,32993,32995,32997,32999,33001,33003,33005,33008,33010,33012,33014,33016],{"class":3476,"line":27},[1115,32958,32959],{"class":3479},"girls",[1115,32961,3484],{"class":3483},[1115,32963,3610],{"class":3487},[1115,32965,1647],{"class":3491},[1115,32967,21612],{"class":3499},[1115,32969,1568],{"class":3483},[1115,32971,32902],{"class":3499},[1115,32973,1568],{"class":3483},[1115,32975,32976],{"class":3499}," 143",[1115,32978,1568],{"class":3483},[1115,32980,32981],{"class":3499}," 132",[1115,32983,1568],{"class":3483},[1115,32985,32986],{"class":3499}," 146",[1115,32988,1568],{"class":3483},[1115,32990,32986],{"class":3499},[1115,32992,1568],{"class":3483},[1115,32994,13953],{"class":3499},[1115,32996,1568],{"class":3483},[1115,32998,32902],{"class":3499},[1115,33000,1568],{"class":3483},[1115,33002,32902],{"class":3499},[1115,33004,1568],{"class":3483},[1115,33006,33007],{"class":3499}," 131",[1115,33009,1568],{"class":3483},[1115,33011,32938],{"class":3499},[1115,33013,1568],{"class":3483},[1115,33015,32902],{"class":3499},[1115,33017,3676],{"class":3491},[1115,33019,33020,33022,33024,33026,33028,33031],{"class":3476,"line":148},[1115,33021,32760],{"class":3487},[1115,33023,1647],{"class":3491},[1115,33025,32879],{"class":3479},[1115,33027,1568],{"class":3483},[1115,33029,33030],{"class":3479}," girls",[1115,33032,3676],{"class":3491},[1115,33034,33035,33037,33039,33041,33043,33045,33047,33049,33051,33053],{"class":3476,"line":111},[1115,33036,27853],{"class":3487},[1115,33038,1647],{"class":3491},[1115,33040,32879],{"class":3479},[1115,33042,1568],{"class":3483},[1115,33044,33030],{"class":3479},[1115,33046,1568],{"class":3483},[1115,33048,32788],{"class":3479},[1115,33050,3572],{"class":3483},[1115,33052,3585],{"class":3499},[1115,33054,3676],{"class":3491},[3468,33056,33059],{"className":33057,"code":33058,"language":3698,"meta":1247},[3696],"    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",[3244,33060,33058],{"__ignoreMap":1247},[1110,33062,32803,33063,33082,33083,33085,33086,33105],{},[1115,33064,33066],{"className":33065},[1315],[1317,33067,33068],{"xmlns":1319},[1321,33069,33070,33079],{},[1324,33071,33072,33074,33076],{},[1330,33073,1110],{},[1460,33075,1754],{},[1334,33077,33078],{},"0,6977",[1338,33080,33081],{"encoding":1340},"p = 0{,}6977","), t-test s ",[3244,33084,32825],{}," dává ",[1115,33087,33089],{"className":33088},[1315],[1317,33090,33091],{"xmlns":1319},[1321,33092,33093,33102],{},[1324,33094,33095,33097,33099],{},[1330,33096,1110],{},[1460,33098,1754],{},[1334,33100,33101],{},"0,4883",[1338,33103,33104],{"encoding":1340},"p = 0{,}4883",": na hladině 5 % se rozdíl průměrných výšek chlapců a dívek neprokázal.",[1136,33107,33109],{"id":33108},"testy-dobré-shody-a-normalita","Testy dobré shody a normalita",[1110,33111,33112],{},"Testy dobré shody ověřují, zda datový soubor pochází ze základního souboru s určitým typem rozdělení (normální, exponenciální apod.).",[16521,33114,33116],{"id":33115},"kolmogorovův-smirnovův-test","Kolmogorovův-Smirnovův test",[1110,33118,33119,33120,33143,33144,33163],{},"Univerzální test pro spojitá rozdělení. Porovnává empirickou distribuční funkci ",[1115,33121,33123],{"className":33122},[1315],[1317,33124,33125],{"xmlns":1319},[1321,33126,33127,33141],{},[1324,33128,33129,33135,33137,33139],{},[1327,33130,33131,33133],{},[1330,33132,6490],{},[1330,33134,1458],{},[1460,33136,1647],{"stretchy":1646},[1330,33138,6495],{},[1460,33140,1658],{"stretchy":1646},[1338,33142,10959],{"encoding":1340}," s teoretickou distribuční funkcí ",[1115,33145,33147],{"className":33146},[1315],[1317,33148,33149],{"xmlns":1319},[1321,33150,33151,33161],{},[1324,33152,33153,33155,33157,33159],{},[1330,33154,6490],{},[1460,33156,1647],{"stretchy":1646},[1330,33158,6495],{},[1460,33160,1658],{"stretchy":1646},[1338,33162,7111],{"encoding":1340}," testovaného rozdělení.",[1204,33165,33166,33229,33249,33305],{},[1207,33167,33168,33185,33186,5516,33209,33228],{},[1115,33169,33171],{"className":33170},[1315],[1317,33172,33173],{"xmlns":1319},[1321,33174,33175,33183],{},[1324,33176,33177],{},[1327,33178,33179,33181],{},[1330,33180,1332],{},[1334,33182,1336],{},[1338,33184,1341],{"encoding":1340},": odchylky mezi ",[1115,33187,33189],{"className":33188},[1315],[1317,33190,33191],{"xmlns":1319},[1321,33192,33193,33207],{},[1324,33194,33195,33201,33203,33205],{},[1327,33196,33197,33199],{},[1330,33198,6490],{},[1330,33200,1458],{},[1460,33202,1647],{"stretchy":1646},[1330,33204,6495],{},[1460,33206,1658],{"stretchy":1646},[1338,33208,10959],{"encoding":1340},[1115,33210,33212],{"className":33211},[1315],[1317,33213,33214],{"xmlns":1319},[1321,33215,33216,33226],{},[1324,33217,33218,33220,33222,33224],{},[1330,33219,6490],{},[1460,33221,1647],{"stretchy":1646},[1330,33223,6495],{},[1460,33225,1658],{"stretchy":1646},[1338,33227,7111],{"encoding":1340}," jsou náhodné (data mají dané rozdělení).",[1207,33230,33231,33248],{},[1115,33232,33234],{"className":33233},[1315],[1317,33235,33236],{"xmlns":1319},[1321,33237,33238,33246],{},[1324,33239,33240],{},[1327,33241,33242,33244],{},[1330,33243,1332],{},[1334,33245,1565],{},[1338,33247,2770],{"encoding":1340},": data nemají dané rozdělení.",[1207,33250,33251,33252,1440],{},"Testové kritérium: ",[1115,33253,33255],{"className":33254},[1315],[1317,33256,33257],{"xmlns":1319},[1321,33258,33259,33302],{},[1324,33260,33261,33263,33265,33276,33278,33284,33286,33288,33290,33292,33294,33296,33298,33300],{},[1330,33262,7929],{},[1460,33264,1754],{},[1327,33266,33267,33274],{},[1324,33268,33269,33272],{},[1330,33270,33271],{},"sup",[1460,33273,4266],{},[1330,33275,6495],{},[1460,33277,22799],{"stretchy":1646},[1327,33279,33280,33282],{},[1330,33281,6490],{},[1330,33283,1458],{},[1460,33285,1647],{"stretchy":1646},[1330,33287,6495],{},[1460,33289,1658],{"stretchy":1646},[1460,33291,2838],{},[1330,33293,6490],{},[1460,33295,1647],{"stretchy":1646},[1330,33297,6495],{},[1460,33299,1658],{"stretchy":1646},[1460,33301,22799],{"stretchy":1646},[1338,33303,33304],{"encoding":1340},"D = \\sup_x \\lvert F_n(x) - F(x) \\rvert",[1207,33306,3092,33307,33351,33352,33370,33371,1440],{},[1115,33308,33310],{"className":33309},[1315],[1317,33311,33312],{"xmlns":1319},[1321,33313,33314,33348],{},[1324,33315,33316,33322,33324,33326,33328,33330,33332,33334,33340,33342,33344,33346],{},[1327,33317,33318,33320],{},[1330,33319,1376],{},[1330,33321,3139],{},[1460,33323,1754],{},[1460,33325,3108],{"stretchy":1646},[1330,33327,7572],{},[1460,33329,1730],{},[1330,33331,7572],{},[1460,33333,1462],{},[1327,33335,33336,33338],{},[1330,33337,7929],{},[1330,33339,3139],{},[1460,33341,1647],{"stretchy":1646},[1330,33343,1458],{},[1460,33345,1658],{"stretchy":1646},[1460,33347,3168],{"stretchy":1646},[1338,33349,33350],{"encoding":1340},"W_\\alpha = \\{d : d > D_\\alpha(n)\\}","; pro ",[1115,33353,33355],{"className":33354},[1315],[1317,33356,33357],{"xmlns":1319},[1321,33358,33359,33367],{},[1324,33360,33361,33363,33365],{},[1330,33362,1458],{},[1460,33364,1462],{},[1334,33366,21811],{},[1338,33368,33369],{"encoding":1340},"n>30"," se kritická hodnota aproximuje zlomkem ",[1115,33372,33374],{"className":33373},[1315],[1317,33375,33376],{"xmlns":1319},[1321,33377,33378,33389],{},[1324,33379,33380,33383,33385],{},[1334,33381,33382],{},"1,36",[1330,33384,4379],{"mathvariant":1893},[4228,33386,33387],{},[1330,33388,1458],{},[1338,33390,33391],{"encoding":1340},"1{,}36\u002F\\sqrt{n}",[1110,33393,27785,33394,33397,33398,33400,33401,2725,33404,33407],{},[3244,33395,33396],{},"ks.test()",", kde se za ",[3244,33399,7111],{}," dosadí příslušná distribuční funkce (",[3244,33402,33403],{},"\"pnorm\"",[3244,33405,33406],{},"\"pexp\"",", …) s jejími parametry:",[3468,33409,33411],{"className":3470,"code":33410,"language":71,"meta":1247,"style":1247},"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",[3244,33412,33413,33463],{"__ignoreMap":1247},[1115,33414,33415,33417,33419,33421,33423,33425,33427,33429,33431,33433,33435,33437,33439,33441,33443,33445,33447,33449,33451,33453,33455,33457,33459,33461],{"class":3476,"line":10},[1115,33416,28499],{"class":3479},[1115,33418,3484],{"class":3483},[1115,33420,3610],{"class":3487},[1115,33422,1647],{"class":3491},[1115,33424,11762],{"class":3499},[1115,33426,1568],{"class":3483},[1115,33428,11767],{"class":3499},[1115,33430,1568],{"class":3483},[1115,33432,11772],{"class":3499},[1115,33434,1568],{"class":3483},[1115,33436,11777],{"class":3499},[1115,33438,1568],{"class":3483},[1115,33440,11772],{"class":3499},[1115,33442,1568],{"class":3483},[1115,33444,11772],{"class":3499},[1115,33446,1568],{"class":3483},[1115,33448,11790],{"class":3499},[1115,33450,1568],{"class":3483},[1115,33452,11795],{"class":3499},[1115,33454,1568],{"class":3483},[1115,33456,11767],{"class":3499},[1115,33458,1568],{"class":3483},[1115,33460,11767],{"class":3499},[1115,33462,3676],{"class":3491},[1115,33464,33465,33468,33470,33472,33474,33477,33479,33481,33483,33485,33487,33489,33491,33493,33495],{"class":3476,"line":27},[1115,33466,33467],{"class":3487},"ks.test",[1115,33469,1647],{"class":3491},[1115,33471,28499],{"class":3479},[1115,33473,1568],{"class":3483},[1115,33475,33476],{"class":3615}," \"pnorm\"",[1115,33478,1568],{"class":3483},[1115,33480,9008],{"class":3487},[1115,33482,1647],{"class":3491},[1115,33484,28499],{"class":3479},[1115,33486,1658],{"class":3491},[1115,33488,1568],{"class":3483},[1115,33490,9018],{"class":3487},[1115,33492,1647],{"class":3491},[1115,33494,28499],{"class":3479},[1115,33496,9270],{"class":3491},[3468,33498,33501],{"className":33499,"code":33500,"language":3698,"meta":1247},[3696],"    Asymptotic one-sample Kolmogorov-Smirnov test\n\ndata:  x3\nD = 0.18469, p-value = 0.8847\nalternative hypothesis: two-sided\n",[3244,33502,33500],{"__ignoreMap":1247},[1110,33504,33505,33528],{},[1115,33506,33508],{"className":33507},[1315],[1317,33509,33510],{"xmlns":1319},[1321,33511,33512,33525],{},[1324,33513,33514,33516,33518,33521,33523],{},[1330,33515,1110],{},[1460,33517,1754],{},[1334,33519,33520],{},"0,8847",[1460,33522,1462],{},[1334,33524,3759],{},[1338,33526,33527],{"encoding":1340},"p = 0{,}8847 > 0{,}05",": odpad materiálu je slučitelný s normálním rozdělením se stejným průměrem a směrodatnou odchylkou.",[16521,33530,33532],{"id":33531},"shapiro-wilkův-test","Shapiro-Wilkův test",[1110,33534,33535],{},"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.",[1204,33537,33538,33558,33578],{},[1207,33539,33540,33557],{},[1115,33541,33543],{"className":33542},[1315],[1317,33544,33545],{"xmlns":1319},[1321,33546,33547,33555],{},[1324,33548,33549],{},[1327,33550,33551,33553],{},[1330,33552,1332],{},[1334,33554,1336],{},[1338,33556,1341],{"encoding":1340},": data mají normální rozdělení.",[1207,33559,33560,33577],{},[1115,33561,33563],{"className":33562},[1315],[1317,33564,33565],{"xmlns":1319},[1321,33566,33567,33575],{},[1324,33568,33569],{},[1327,33570,33571,33573],{},[1330,33572,1332],{},[1334,33574,1565],{},[1338,33576,2770],{"encoding":1340},": data nemají normální rozdělení.",[1207,33579,33580,33581,33607],{},"Testová statistika ",[1115,33582,33584],{"className":33583},[1315],[1317,33585,33586],{"xmlns":1319},[1321,33587,33588,33604],{},[1324,33589,33590,33592,33594,33596,33598,33600,33602],{},[1330,33591,1376],{},[1460,33593,6794],{},[1460,33595,8202],{"stretchy":1646},[1334,33597,1336],{},[1460,33599,1568],{"separator":1121},[1334,33601,1565],{},[1460,33603,7219],{"stretchy":1646},[1338,33605,33606],{"encoding":1340},"W \\in \\langle 0,1 \\rangle","; hodnoty blízké 1 indikují shodu s normalitou.",[1110,33609,33610,33611,33624,33625,1425,33645,33662,33663,1425,33683,33700],{},"Na rozdíl od ostatních testů v této kapitole se Shapiro-Wilkův test v praxi vyhodnocuje pouze přes p-hodnotu (tabulka kritických hodnot pro ",[1115,33612,33614],{"className":33613},[1315],[1317,33615,33616],{"xmlns":1319},[1321,33617,33618,33622],{},[1324,33619,33620],{},[1330,33621,1376],{},[1338,33623,1376],{"encoding":1340}," se běžně neudává): ",[1115,33626,33628],{"className":33627},[1315],[1317,33629,33630],{"xmlns":1319},[1321,33631,33632,33642],{},[1324,33633,33634,33636,33638,33640],{},[1330,33635,1110],{},[1460,33637,3125],{},[1330,33639,3139],{},[1460,33641,7325],{},[1338,33643,33644],{"encoding":1340},"p \\ge \\alpha \\Rightarrow",[1115,33646,33648],{"className":33647},[1315],[1317,33649,33650],{"xmlns":1319},[1321,33651,33652,33660],{},[1324,33653,33654],{},[1327,33655,33656,33658],{},[1330,33657,1332],{},[1334,33659,1336],{},[1338,33661,1341],{"encoding":1340}," nezamítáme (normalitu lze předpokládat); ",[1115,33664,33666],{"className":33665},[1315],[1317,33667,33668],{"xmlns":1319},[1321,33669,33670,33680],{},[1324,33671,33672,33674,33676,33678],{},[1330,33673,1110],{},[1460,33675,4107],{},[1330,33677,3139],{},[1460,33679,7325],{},[1338,33681,33682],{"encoding":1340},"p \u003C \\alpha \\Rightarrow",[1115,33684,33686],{"className":33685},[1315],[1317,33687,33688],{"xmlns":1319},[1321,33689,33690,33698],{},[1324,33691,33692],{},[1327,33693,33694,33696],{},[1330,33695,1332],{},[1334,33697,1336],{},[1338,33699,1341],{"encoding":1340}," zamítáme (předpoklad normality je porušen).",[3468,33702,33704],{"className":3470,"code":33703,"language":71,"meta":1247,"style":1247},"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",[3244,33705,33706,33760],{"__ignoreMap":1247},[1115,33707,33708,33710,33712,33714,33716,33718,33720,33722,33724,33726,33728,33730,33732,33734,33736,33738,33740,33742,33744,33746,33748,33750,33752,33754,33756,33758],{"class":3476,"line":10},[1115,33709,28367],{"class":3479},[1115,33711,3484],{"class":3483},[1115,33713,3610],{"class":3487},[1115,33715,1647],{"class":3491},[1115,33717,28376],{"class":3499},[1115,33719,1568],{"class":3483},[1115,33721,28381],{"class":3499},[1115,33723,1568],{"class":3483},[1115,33725,28386],{"class":3499},[1115,33727,1568],{"class":3483},[1115,33729,28391],{"class":3499},[1115,33731,1568],{"class":3483},[1115,33733,28396],{"class":3499},[1115,33735,1568],{"class":3483},[1115,33737,28401],{"class":3499},[1115,33739,1568],{"class":3483},[1115,33741,28391],{"class":3499},[1115,33743,1568],{"class":3483},[1115,33745,28410],{"class":3499},[1115,33747,1568],{"class":3483},[1115,33749,28396],{"class":3499},[1115,33751,1568],{"class":3483},[1115,33753,28419],{"class":3499},[1115,33755,1568],{"class":3483},[1115,33757,28391],{"class":3499},[1115,33759,3676],{"class":3491},[1115,33761,33762,33764,33766,33768],{"class":3476,"line":27},[1115,33763,17350],{"class":3487},[1115,33765,1647],{"class":3491},[1115,33767,28367],{"class":3479},[1115,33769,3676],{"class":3491},[3468,33771,33774],{"className":33772,"code":33773,"language":3698,"meta":1247},[3696],"    Shapiro-Wilk normality test\n\ndata:  x2\nW = 0.96022, p-value = 0.7744\n",[3244,33775,33773],{"__ignoreMap":1247},[1110,33777,33778,33779,33798],{},"U dat o životnosti baterií se normalita nezamítá (",[1115,33780,33782],{"className":33781},[1315],[1317,33783,33784],{"xmlns":1319},[1321,33785,33786,33795],{},[1324,33787,33788,33790,33792],{},[1330,33789,1110],{},[1460,33791,1754],{},[1334,33793,33794],{},"0,7744",[1338,33796,33797],{"encoding":1340},"p = 0{,}7744","), předpoklad t-testu je tedy splněn.",[1103,33800,33802,33809,33812,34179,34185],{"className":33801,"dataCallout":3251},[1106,3250],[1110,33803,33805,33808],{"className":33804},[1113],[1115,33806],{"className":33807,"ariaHidden":1121},[1118,3258,1120],"Příklad: Doba do poruchy výrobku",[1110,33810,33811],{},"Zkoušky životnosti nového výrobku daly soubor 68 hodnot doby do poruchy (v minutách). Odhadněte charakteristiky a zákon rozdělení.",[3468,33813,33815],{"className":3470,"code":33814,"language":71,"meta":1247,"style":1247},"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",[3244,33816,33817,33908,33986,34074,34108,34118,34128,34138,34148],{"__ignoreMap":1247},[1115,33818,33819,33821,33823,33825,33827,33829,33831,33833,33835,33837,33839,33841,33843,33845,33847,33849,33851,33853,33855,33857,33859,33861,33863,33865,33867,33870,33872,33874,33876,33878,33880,33882,33884,33886,33888,33890,33892,33894,33896,33898,33900,33902,33904,33906],{"class":3476,"line":10},[1115,33820,13852],{"class":3479},[1115,33822,3484],{"class":3483},[1115,33824,3610],{"class":3487},[1115,33826,1647],{"class":3491},[1115,33828,13861],{"class":3499},[1115,33830,1568],{"class":3483},[1115,33832,13866],{"class":3499},[1115,33834,1568],{"class":3483},[1115,33836,13871],{"class":3499},[1115,33838,1568],{"class":3483},[1115,33840,13876],{"class":3499},[1115,33842,1568],{"class":3483},[1115,33844,9254],{"class":3499},[1115,33846,1568],{"class":3483},[1115,33848,3955],{"class":3499},[1115,33850,1568],{"class":3483},[1115,33852,3509],{"class":3499},[1115,33854,1568],{"class":3483},[1115,33856,13893],{"class":3499},[1115,33858,1568],{"class":3483},[1115,33860,9771],{"class":3499},[1115,33862,1568],{"class":3483},[1115,33864,13902],{"class":3499},[1115,33866,1568],{"class":3483},[1115,33868,33869],{"class":3499}," 367",[1115,33871,1568],{"class":3483},[1115,33873,13914],{"class":3499},[1115,33875,1568],{"class":3483},[1115,33877,13919],{"class":3499},[1115,33879,1568],{"class":3483},[1115,33881,13924],{"class":3499},[1115,33883,1568],{"class":3483},[1115,33885,3527],{"class":3499},[1115,33887,1568],{"class":3483},[1115,33889,13933],{"class":3499},[1115,33891,1568],{"class":3483},[1115,33893,13938],{"class":3499},[1115,33895,1568],{"class":3483},[1115,33897,13943],{"class":3499},[1115,33899,1568],{"class":3483},[1115,33901,13948],{"class":3499},[1115,33903,1568],{"class":3483},[1115,33905,13953],{"class":3499},[1115,33907,3512],{"class":3483},[1115,33909,33910,33912,33914,33916,33918,33920,33922,33924,33926,33928,33930,33932,33934,33936,33938,33940,33942,33944,33946,33948,33950,33952,33954,33956,33958,33960,33962,33964,33966,33968,33970,33972,33974,33976,33978,33980,33982,33984],{"class":3476,"line":27},[1115,33911,13960],{"class":3499},[1115,33913,1568],{"class":3483},[1115,33915,13965],{"class":3499},[1115,33917,1568],{"class":3483},[1115,33919,13970],{"class":3499},[1115,33921,1568],{"class":3483},[1115,33923,13975],{"class":3499},[1115,33925,1568],{"class":3483},[1115,33927,13980],{"class":3499},[1115,33929,1568],{"class":3483},[1115,33931,3527],{"class":3499},[1115,33933,1568],{"class":3483},[1115,33935,13989],{"class":3499},[1115,33937,1568],{"class":3483},[1115,33939,3509],{"class":3499},[1115,33941,1568],{"class":3483},[1115,33943,13998],{"class":3499},[1115,33945,1568],{"class":3483},[1115,33947,14003],{"class":3499},[1115,33949,1568],{"class":3483},[1115,33951,15095],{"class":3499},[1115,33953,1568],{"class":3483},[1115,33955,14015],{"class":3499},[1115,33957,1568],{"class":3483},[1115,33959,14020],{"class":3499},[1115,33961,1568],{"class":3483},[1115,33963,13914],{"class":3499},[1115,33965,1568],{"class":3483},[1115,33967,14029],{"class":3499},[1115,33969,1568],{"class":3483},[1115,33971,14034],{"class":3499},[1115,33973,1568],{"class":3483},[1115,33975,14039],{"class":3499},[1115,33977,1568],{"class":3483},[1115,33979,14044],{"class":3499},[1115,33981,1568],{"class":3483},[1115,33983,14049],{"class":3499},[1115,33985,3512],{"class":3483},[1115,33987,33988,33990,33992,33995,33997,33999,34001,34003,34005,34007,34009,34011,34013,34015,34017,34019,34021,34023,34025,34027,34029,34031,34033,34036,34038,34040,34042,34044,34046,34048,34050,34052,34054,34056,34058,34060,34062,34064,34066,34068,34070,34072],{"class":3476,"line":148},[1115,33989,14159],{"class":3499},[1115,33991,1568],{"class":3483},[1115,33993,33994],{"class":3499}," 74",[1115,33996,1568],{"class":3483},[1115,33998,14066],{"class":3499},[1115,34000,1568],{"class":3483},[1115,34002,14071],{"class":3499},[1115,34004,1568],{"class":3483},[1115,34006,14076],{"class":3499},[1115,34008,1568],{"class":3483},[1115,34010,14081],{"class":3499},[1115,34012,1568],{"class":3483},[1115,34014,13998],{"class":3499},[1115,34016,1568],{"class":3483},[1115,34018,14090],{"class":3499},[1115,34020,1568],{"class":3483},[1115,34022,10632],{"class":3499},[1115,34024,1568],{"class":3483},[1115,34026,14099],{"class":3499},[1115,34028,1568],{"class":3483},[1115,34030,14104],{"class":3499},[1115,34032,1568],{"class":3483},[1115,34034,34035],{"class":3499}," 194",[1115,34037,1568],{"class":3483},[1115,34039,3920],{"class":3499},[1115,34041,1568],{"class":3483},[1115,34043,14120],{"class":3499},[1115,34045,1568],{"class":3483},[1115,34047,14125],{"class":3499},[1115,34049,1568],{"class":3483},[1115,34051,14130],{"class":3499},[1115,34053,1568],{"class":3483},[1115,34055,14081],{"class":3499},[1115,34057,1568],{"class":3483},[1115,34059,9771],{"class":3499},[1115,34061,1568],{"class":3483},[1115,34063,3955],{"class":3499},[1115,34065,1568],{"class":3483},[1115,34067,14147],{"class":3499},[1115,34069,1568],{"class":3483},[1115,34071,14152],{"class":3499},[1115,34073,3512],{"class":3483},[1115,34075,34076,34078,34080,34082,34084,34086,34088,34090,34092,34094,34096,34098,34100,34102,34104,34106],{"class":3476,"line":111},[1115,34077,14159],{"class":3499},[1115,34079,1568],{"class":3483},[1115,34081,3504],{"class":3499},[1115,34083,1568],{"class":3483},[1115,34085,14168],{"class":3499},[1115,34087,1568],{"class":3483},[1115,34089,14173],{"class":3499},[1115,34091,1568],{"class":3483},[1115,34093,14178],{"class":3499},[1115,34095,1568],{"class":3483},[1115,34097,14183],{"class":3499},[1115,34099,1568],{"class":3483},[1115,34101,13914],{"class":3499},[1115,34103,1568],{"class":3483},[1115,34105,14192],{"class":3499},[1115,34107,3676],{"class":3491},[1115,34109,34110,34112,34114,34116],{"class":3476,"line":96},[1115,34111,11914],{"class":3487},[1115,34113,1647],{"class":3491},[1115,34115,13852],{"class":3479},[1115,34117,3676],{"class":3491},[1115,34119,34120,34122,34124,34126],{"class":3476,"line":89},[1115,34121,11936],{"class":3487},[1115,34123,1647],{"class":3491},[1115,34125,13852],{"class":3479},[1115,34127,3676],{"class":3491},[1115,34129,34130,34132,34134,34136],{"class":3476,"line":82},[1115,34131,12636],{"class":3487},[1115,34133,1647],{"class":3491},[1115,34135,13852],{"class":3479},[1115,34137,3676],{"class":3491},[1115,34139,34140,34142,34144,34146],{"class":3476,"line":75},[1115,34141,17350],{"class":3487},[1115,34143,1647],{"class":3491},[1115,34145,13852],{"class":3479},[1115,34147,3676],{"class":3491},[1115,34149,34150,34152,34154,34156,34158,34161,34163,34165,34167,34169,34171,34173,34175,34177],{"class":3476,"line":3666},[1115,34151,33467],{"class":3487},[1115,34153,1647],{"class":3491},[1115,34155,13852],{"class":3479},[1115,34157,1568],{"class":3483},[1115,34159,34160],{"class":3615}," \"pexp\"",[1115,34162,1568],{"class":3483},[1115,34164,9845],{"class":3479},[1115,34166,3572],{"class":3483},[1115,34168,4416],{"class":3499},[1115,34170,9852],{"class":3483},[1115,34172,9008],{"class":3487},[1115,34174,1647],{"class":3491},[1115,34176,13852],{"class":3479},[1115,34178,9270],{"class":3491},[3468,34180,34183],{"className":34181,"code":34182,"language":3698,"meta":1247},[3696],"[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",[3244,34184,34182],{"__ignoreMap":1247},[1110,34186,34187,34188,34207,34208,34225,34226,34245],{},"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 (",[1115,34189,34191],{"className":34190},[1315],[1317,34192,34193],{"xmlns":1319},[1321,34194,34195,34204],{},[1324,34196,34197,34199,34201],{},[1330,34198,1110],{},[1460,34200,4107],{},[1334,34202,34203],{},"0,0001",[1338,34205,34206],{"encoding":1340},"p \u003C 0{,}0001","), zatímco Kolmogorov-Smirnovův test proti exponenciálnímu rozdělení se střední hodnotou ",[1115,34209,34211],{"className":34210},[1315],[1317,34212,34213],{"xmlns":1319},[1321,34214,34215,34223],{},[1324,34216,34217],{},[2496,34218,34219,34221],{"accent":1121},[1330,34220,6495],{},[1460,34222,11235],{},[1338,34224,21340],{"encoding":1340}," shodu nezamítá (",[1115,34227,34229],{"className":34228},[1315],[1317,34230,34231],{"xmlns":1319},[1321,34232,34233,34242],{},[1324,34234,34235,34237,34239],{},[1330,34236,1110],{},[1460,34238,1754],{},[1334,34240,34241],{},"0,8421",[1338,34243,34244],{"encoding":1340},"p = 0{,}8421","): data odpovídají spíše exponenciálnímu rozdělení než normálnímu.",[1110,34247,34248],{},[4158,34249],{"alt":34250,"className":34251,"src":34252},"mask-th-exponencialni-shoda",[1130,4162],"\u002Fwiki-assets\u002Fmask-th-exponencialni-shoda.png",[1136,34254,34256],{"id":34255},"neparametrické-testy","Neparametrické testy",[1110,34258,34259,34260,4382,34262,34286],{},"Když předpoklad normality neplatí, nahrazují t-testy jejich neparametrické obdoby — Wilcoxonovy testy posuzují ",[1302,34261,11327],{},[1115,34263,34265],{"className":34264},[1315],[1317,34266,34267],{"xmlns":1319},[1321,34268,34269,34283],{},[1324,34270,34271],{},[1327,34272,34273,34275],{},[1330,34274,6495],{},[1324,34276,34277,34279,34281],{},[1334,34278,1336],{},[1460,34280,1568],{"separator":1121},[1334,34282,9703],{},[1338,34284,34285],{"encoding":1340},"x_{0,5}",") místo střední hodnoty a nevyžadují normalitu dat.",[16521,34288,34290],{"id":34289},"wilcoxonovy-testy","Wilcoxonovy testy",[1141,34292,34293,34338],{},[1144,34294,34295],{},[1147,34296,34297,34316,34335],{},[1150,34298,34299],{},[1115,34300,34302],{"className":34301},[1315],[1317,34303,34304],{"xmlns":1319},[1321,34305,34306,34314],{},[1324,34307,34308],{},[1327,34309,34310,34312],{},[1330,34311,1332],{},[1334,34313,1336],{},[1338,34315,1341],{"encoding":1340},[1150,34317,34318],{},[1115,34319,34321],{"className":34320},[1315],[1317,34322,34323],{"xmlns":1319},[1321,34324,34325,34333],{},[1324,34326,34327],{},[1327,34328,34329,34331],{},[1330,34330,1332],{},[1334,34332,1565],{},[1338,34334,2770],{"encoding":1340},[1150,34336,34337],{},"Příkaz v R",[1157,34339,34340,34407,34474],{},[1147,34341,34342,34372,34402],{},[1162,34343,34344],{},[1115,34345,34347],{"className":34346},[1315],[1317,34348,34349],{"xmlns":1319},[1321,34350,34351,34369],{},[1324,34352,34353,34365,34367],{},[1327,34354,34355,34357],{},[1330,34356,6495],{},[1324,34358,34359,34361,34363],{},[1334,34360,1336],{},[1460,34362,1568],{"separator":1121},[1334,34364,9703],{},[1460,34366,6510],{},[1330,34368,3494],{},[1338,34370,34371],{"encoding":1340},"x_{0,5} \\le c",[1162,34373,34374],{},[1115,34375,34377],{"className":34376},[1315],[1317,34378,34379],{"xmlns":1319},[1321,34380,34381,34399],{},[1324,34382,34383,34395,34397],{},[1327,34384,34385,34387],{},[1330,34386,6495],{},[1324,34388,34389,34391,34393],{},[1334,34390,1336],{},[1460,34392,1568],{"separator":1121},[1334,34394,9703],{},[1460,34396,1462],{},[1330,34398,3494],{},[1338,34400,34401],{"encoding":1340},"x_{0,5} > c",[1162,34403,34404],{},[3244,34405,34406],{},"wilcox.test(x, alternative = \"greater\", mu = c)",[1147,34408,34409,34439,34469],{},[1162,34410,34411],{},[1115,34412,34414],{"className":34413},[1315],[1317,34415,34416],{"xmlns":1319},[1321,34417,34418,34436],{},[1324,34419,34420,34432,34434],{},[1327,34421,34422,34424],{},[1330,34423,6495],{},[1324,34425,34426,34428,34430],{},[1334,34427,1336],{},[1460,34429,1568],{"separator":1121},[1334,34431,9703],{},[1460,34433,1754],{},[1330,34435,3494],{},[1338,34437,34438],{"encoding":1340},"x_{0,5} = c",[1162,34440,34441],{},[1115,34442,34444],{"className":34443},[1315],[1317,34445,34446],{"xmlns":1319},[1321,34447,34448,34466],{},[1324,34449,34450,34462,34464],{},[1327,34451,34452,34454],{},[1330,34453,6495],{},[1324,34455,34456,34458,34460],{},[1334,34457,1336],{},[1460,34459,1568],{"separator":1121},[1334,34461,9703],{},[1460,34463,10733],{"mathvariant":1893},[1330,34465,3494],{},[1338,34467,34468],{"encoding":1340},"x_{0,5} \\neq c",[1162,34470,34471],{},[3244,34472,34473],{},"wilcox.test(x, alternative = \"two.sided\", mu = c)",[1147,34475,34476,34506,34536],{},[1162,34477,34478],{},[1115,34479,34481],{"className":34480},[1315],[1317,34482,34483],{"xmlns":1319},[1321,34484,34485,34503],{},[1324,34486,34487,34499,34501],{},[1327,34488,34489,34491],{},[1330,34490,6495],{},[1324,34492,34493,34495,34497],{},[1334,34494,1336],{},[1460,34496,1568],{"separator":1121},[1334,34498,9703],{},[1460,34500,3125],{},[1330,34502,3494],{},[1338,34504,34505],{"encoding":1340},"x_{0,5} \\ge c",[1162,34507,34508],{},[1115,34509,34511],{"className":34510},[1315],[1317,34512,34513],{"xmlns":1319},[1321,34514,34515,34533],{},[1324,34516,34517,34529,34531],{},[1327,34518,34519,34521],{},[1330,34520,6495],{},[1324,34522,34523,34525,34527],{},[1334,34524,1336],{},[1460,34526,1568],{"separator":1121},[1334,34528,9703],{},[1460,34530,4107],{},[1330,34532,3494],{},[1338,34534,34535],{"encoding":1340},"x_{0,5} \u003C c",[1162,34537,34538],{},[3244,34539,34540],{},"wilcox.test(x, alternative = \"less\", mu = c)",[1110,34542,34543,34546,34547,1440],{},[1242,34544,34545],{},"Jednovýběrový Wilcoxonův test"," (obdoba t-testu) posuzuje odchylku mediánu od konstanty ",[1115,34548,34550],{"className":34549},[1315],[1317,34551,34552],{"xmlns":1319},[1321,34553,34554,34558],{},[1324,34555,34556],{},[1330,34557,3494],{},[1338,34559,3494],{"encoding":1340},[1110,34561,34562,34565,34566,8611,34604,34617,34618,1440],{},[1242,34563,34564],{},"Jednovýběrový Wilcoxonův test na diferencích"," (obdoba párového t-testu) posuzuje odchylku mediánu rozdílu ",[1115,34567,34569],{"className":34568},[1315],[1317,34570,34571],{"xmlns":1319},[1321,34572,34573,34601],{},[1324,34574,34575,34587,34589],{},[1327,34576,34577,34579],{},[1330,34578,6495],{},[1324,34580,34581,34583,34585],{},[1334,34582,1336],{},[1460,34584,1568],{"separator":1121},[1334,34586,9703],{},[1460,34588,2838],{},[1327,34590,34591,34593],{},[1330,34592,6905],{},[1324,34594,34595,34597,34599],{},[1334,34596,1336],{},[1460,34598,1568],{"separator":1121},[1334,34600,9703],{},[1338,34602,34603],{"encoding":1340},"x_{0,5}-y_{0,5}",[1115,34605,34607],{"className":34606},[1315],[1317,34608,34609],{"xmlns":1319},[1321,34610,34611,34615],{},[1324,34612,34613],{},[1330,34614,3494],{},[1338,34616,3494],{"encoding":1340},"; v R se volá se stejnými argumenty jako výše a navíc ",[3244,34619,34620],{},"paired = TRUE",[1110,34622,34623,34626,34627,34629],{},[1242,34624,34625],{},"Dvouvýběrový Wilcoxonův test"," (obdoba dvouvýběrového t-testu) posuzuje odchylku mediánů dvou nezávislých výběrů; argument ",[3244,34628,25223],{}," odpadá. Pro výšky chlapců a dívek z příkladu výše:",[3468,34631,34633],{"className":3470,"code":34632,"language":71,"meta":1247,"style":1247},"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",[3244,34634,34635,34705,34763],{"__ignoreMap":1247},[1115,34636,34637,34639,34641,34643,34645,34647,34649,34651,34653,34655,34657,34659,34661,34663,34665,34667,34669,34671,34673,34675,34677,34679,34681,34683,34685,34687,34689,34691,34693,34695,34697,34699,34701,34703],{"class":3476,"line":10},[1115,34638,32879],{"class":3479},[1115,34640,3484],{"class":3483},[1115,34642,3610],{"class":3487},[1115,34644,1647],{"class":3491},[1115,34646,32888],{"class":3499},[1115,34648,1568],{"class":3483},[1115,34650,15095],{"class":3499},[1115,34652,1568],{"class":3483},[1115,34654,32897],{"class":3499},[1115,34656,1568],{"class":3483},[1115,34658,32902],{"class":3499},[1115,34660,1568],{"class":3483},[1115,34662,32907],{"class":3499},[1115,34664,1568],{"class":3483},[1115,34666,32912],{"class":3499},[1115,34668,1568],{"class":3483},[1115,34670,18246],{"class":3499},[1115,34672,1568],{"class":3483},[1115,34674,13953],{"class":3499},[1115,34676,1568],{"class":3483},[1115,34678,32907],{"class":3499},[1115,34680,1568],{"class":3483},[1115,34682,32897],{"class":3499},[1115,34684,1568],{"class":3483},[1115,34686,32933],{"class":3499},[1115,34688,1568],{"class":3483},[1115,34690,32938],{"class":3499},[1115,34692,1568],{"class":3483},[1115,34694,32943],{"class":3499},[1115,34696,1568],{"class":3483},[1115,34698,32907],{"class":3499},[1115,34700,1568],{"class":3483},[1115,34702,32952],{"class":3499},[1115,34704,3676],{"class":3491},[1115,34706,34707,34709,34711,34713,34715,34717,34719,34721,34723,34725,34727,34729,34731,34733,34735,34737,34739,34741,34743,34745,34747,34749,34751,34753,34755,34757,34759,34761],{"class":3476,"line":27},[1115,34708,32959],{"class":3479},[1115,34710,3484],{"class":3483},[1115,34712,3610],{"class":3487},[1115,34714,1647],{"class":3491},[1115,34716,21612],{"class":3499},[1115,34718,1568],{"class":3483},[1115,34720,32902],{"class":3499},[1115,34722,1568],{"class":3483},[1115,34724,32976],{"class":3499},[1115,34726,1568],{"class":3483},[1115,34728,32981],{"class":3499},[1115,34730,1568],{"class":3483},[1115,34732,32986],{"class":3499},[1115,34734,1568],{"class":3483},[1115,34736,32986],{"class":3499},[1115,34738,1568],{"class":3483},[1115,34740,13953],{"class":3499},[1115,34742,1568],{"class":3483},[1115,34744,32902],{"class":3499},[1115,34746,1568],{"class":3483},[1115,34748,32902],{"class":3499},[1115,34750,1568],{"class":3483},[1115,34752,33007],{"class":3499},[1115,34754,1568],{"class":3483},[1115,34756,32938],{"class":3499},[1115,34758,1568],{"class":3483},[1115,34760,32902],{"class":3499},[1115,34762,3676],{"class":3491},[1115,34764,34765,34768,34770,34772,34774,34776,34778,34780,34782,34784],{"class":3476,"line":148},[1115,34766,34767],{"class":3487},"wilcox.test",[1115,34769,1647],{"class":3491},[1115,34771,32879],{"class":3479},[1115,34773,1568],{"class":3483},[1115,34775,33030],{"class":3479},[1115,34777,1568],{"class":3483},[1115,34779,27870],{"class":3479},[1115,34781,3572],{"class":3483},[1115,34783,27875],{"class":3615},[1115,34785,3676],{"class":3491},[3468,34787,34790],{"className":34788,"code":34789,"language":3698,"meta":1247},[3696],"    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",[3244,34791,34789],{"__ignoreMap":1247},[1110,34793,34794,34817],{},[1115,34795,34797],{"className":34796},[1315],[1317,34798,34799],{"xmlns":1319},[1321,34800,34801,34814],{},[1324,34802,34803,34805,34807,34810,34812],{},[1330,34804,1110],{},[1460,34806,1754],{},[1334,34808,34809],{},"0,315",[1460,34811,1462],{},[1334,34813,3759],{},[1338,34815,34816],{"encoding":1340},"p = 0{,}315 > 0{,}05",": mediány výšek chlapců a dívek se statisticky významně neliší — stejný závěr jako u dvouvýběrového t-testu.",[1103,34819,34821,34828,34850,34961,34967],{"className":34820,"dataCallout":3251},[1106,3250],[1110,34822,34824,34827],{"className":34823},[1113],[1115,34825],{"className":34826,"ariaHidden":1121},[1118,3258,1120],"Příklad: Realitní odhadci — neparametrická alternativa",[1110,34829,34830,34831,34849],{},"U odhadů cen z párového t-testu výše normalita diferencí neplatí (",[1115,34832,34834],{"className":34833},[1315],[1317,34835,34836],{"xmlns":1319},[1321,34837,34838,34846],{},[1324,34839,34840,34842,34844],{},[1330,34841,1110],{},[1460,34843,1754],{},[1334,34845,29923],{},[1338,34847,34848],{"encoding":1340},"p = 0{,}03203","). Správnou volbou je párový Wilcoxonův test:",[3468,34851,34853],{"className":3470,"code":34852,"language":71,"meta":1247,"style":1247},"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",[3244,34854,34855,34897,34939],{"__ignoreMap":1247},[1115,34856,34857,34859,34861,34863,34865,34867,34869,34871,34873,34875,34877,34879,34881,34883,34885,34887,34889,34891,34893,34895],{"class":3476,"line":10},[1115,34858,29726],{"class":3479},[1115,34860,3484],{"class":3483},[1115,34862,3610],{"class":3487},[1115,34864,1647],{"class":3491},[1115,34866,29735],{"class":3499},[1115,34868,1568],{"class":3483},[1115,34870,29740],{"class":3499},[1115,34872,1568],{"class":3483},[1115,34874,29745],{"class":3499},[1115,34876,1568],{"class":3483},[1115,34878,29750],{"class":3499},[1115,34880,1568],{"class":3483},[1115,34882,29755],{"class":3499},[1115,34884,1568],{"class":3483},[1115,34886,29760],{"class":3499},[1115,34888,1568],{"class":3483},[1115,34890,29765],{"class":3499},[1115,34892,1568],{"class":3483},[1115,34894,29770],{"class":3499},[1115,34896,3676],{"class":3491},[1115,34898,34899,34901,34903,34905,34907,34909,34911,34913,34915,34917,34919,34921,34923,34925,34927,34929,34931,34933,34935,34937],{"class":3476,"line":27},[1115,34900,29777],{"class":3479},[1115,34902,3484],{"class":3483},[1115,34904,3610],{"class":3487},[1115,34906,1647],{"class":3491},[1115,34908,29786],{"class":3499},[1115,34910,1568],{"class":3483},[1115,34912,29791],{"class":3499},[1115,34914,1568],{"class":3483},[1115,34916,29796],{"class":3499},[1115,34918,1568],{"class":3483},[1115,34920,29801],{"class":3499},[1115,34922,1568],{"class":3483},[1115,34924,29806],{"class":3499},[1115,34926,1568],{"class":3483},[1115,34928,29811],{"class":3499},[1115,34930,1568],{"class":3483},[1115,34932,29816],{"class":3499},[1115,34934,1568],{"class":3483},[1115,34936,29821],{"class":3499},[1115,34938,3676],{"class":3491},[1115,34940,34941,34943,34945,34947,34949,34951,34953,34955,34957,34959],{"class":3476,"line":148},[1115,34942,34767],{"class":3487},[1115,34944,1647],{"class":3491},[1115,34946,29726],{"class":3479},[1115,34948,1568],{"class":3483},[1115,34950,29836],{"class":3479},[1115,34952,1568],{"class":3483},[1115,34954,29841],{"class":3479},[1115,34956,3572],{"class":3483},[1115,34958,3585],{"class":3499},[1115,34960,3676],{"class":3491},[3468,34962,34965],{"className":34963,"code":34964,"language":3698,"meta":1247},[3696],"    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",[3244,34966,34964],{"__ignoreMap":1247},[1110,34968,34969,34992],{},[1115,34970,34972],{"className":34971},[1315],[1317,34973,34974],{"xmlns":1319},[1321,34975,34976,34989],{},[1324,34977,34978,34980,34982,34985,34987],{},[1330,34979,1110],{},[1460,34981,1754],{},[1334,34983,34984],{},"0,1484",[1460,34986,1462],{},[1334,34988,3759],{},[1338,34990,34991],{"encoding":1340},"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.",[16521,34994,34996],{"id":34995},"kruskalův-wallisův-test","Kruskalův-Wallisův test",[1110,34998,34999,35000,35017],{},"Zobecnění dvouvýběrového Wilcoxonova testu, neparametrická obdoba analýzy rozptylu jednoduchého třídění. ",[1115,35001,35003],{"className":35002},[1315],[1317,35004,35005],{"xmlns":1319},[1321,35006,35007,35015],{},[1324,35008,35009],{},[1327,35010,35011,35013],{},[1330,35012,1332],{},[1334,35014,1336],{},[1338,35016,1341],{"encoding":1340},": všechny výběry pocházejí ze stejného rozdělení.",[3468,35019,35021],{"className":3470,"code":35020,"language":71,"meta":1247,"style":1247},"kruskal.test(kvantitativní_proměnná ~ faktor, data = soubor)\n",[3244,35022,35023],{"__ignoreMap":1247},[1115,35024,35025,35028,35030,35033,35035,35038,35040,35042,35044,35047],{"class":3476,"line":10},[1115,35026,35027],{"class":3487},"kruskal.test",[1115,35029,1647],{"class":3491},[1115,35031,35032],{"class":3479},"kvantitativní_proměnná",[1115,35034,16632],{"class":3483},[1115,35036,35037],{"class":3479}," faktor",[1115,35039,1568],{"class":3483},[1115,35041,19940],{"class":3479},[1115,35043,3572],{"class":3483},[1115,35045,35046],{"class":3479}," soubor",[1115,35048,3676],{"class":3491},[16521,35050,35052],{"id":35051},"mediánový-test","Mediánový test",[1110,35054,35055,35056,35073,35074,1730],{},"Má stejný účel jako Kruskalův-Wallisův test (obdoba analýzy rozptylu jednoduchého třídění, ",[1115,35057,35059],{"className":35058},[1315],[1317,35060,35061],{"xmlns":1319},[1321,35062,35063,35071],{},[1324,35064,35065],{},[1327,35066,35067,35069],{},[1330,35068,1332],{},[1334,35070,1336],{},[1338,35072,1341],{"encoding":1340},": všechny výběry pocházejí ze stejného rozdělení) a je součástí balíčku ",[3244,35075,35076],{},"agricolae",[3468,35078,35080],{"className":3470,"code":35079,"language":71,"meta":1247,"style":1247},"library(agricolae)\nMedian.test(kvantitativní_proměnná, faktor)\n",[3244,35081,35082,35092],{"__ignoreMap":1247},[1115,35083,35084,35086,35088,35090],{"class":3476,"line":10},[1115,35085,17170],{"class":3483},[1115,35087,1647],{"class":3491},[1115,35089,35076],{"class":3479},[1115,35091,3676],{"class":3491},[1115,35093,35094,35097,35099,35101,35103,35105],{"class":3476,"line":27},[1115,35095,35096],{"class":3487},"Median.test",[1115,35098,1647],{"class":3491},[1115,35100,35032],{"class":3479},[1115,35102,1568],{"class":3483},[1115,35104,35037],{"class":3479},[1115,35106,3676],{"class":3491},[16521,35108,35110],{"id":35109},"friedmanův-test","Friedmanův test",[1110,35112,35113,35114,35131,35132,35170],{},"Neparametrická obdoba analýzy rozptylu dvojného třídění s jedním pozorováním v každé podtřídě. ",[1115,35115,35117],{"className":35116},[1315],[1317,35118,35119],{"xmlns":1319},[1321,35120,35121,35129],{},[1324,35122,35123],{},[1327,35124,35125,35127],{},[1330,35126,1332],{},[1334,35128,1336],{},[1338,35130,1341],{"encoding":1340},": distribuční funkce veličin ",[1115,35133,35135],{"className":35134},[1315],[1317,35136,35137],{"xmlns":1319},[1321,35138,35139,35167],{},[1324,35140,35141,35151,35153,35155,35157],{},[1327,35142,35143,35145],{},[1330,35144,6507],{},[1324,35146,35147,35149],{},[1330,35148,1650],{},[1334,35150,1565],{},[1460,35152,1568],{"separator":1121},[1460,35154,1571],{},[1460,35156,1568],{"separator":1121},[1327,35158,35159,35161],{},[1330,35160,6507],{},[1324,35162,35163,35165],{},[1330,35164,1650],{},[1330,35166,7035],{},[1338,35168,35169],{"encoding":1340},"X_{i1}, \\dots, X_{ik}"," jsou totožné.",[3468,35172,35174],{"className":3470,"code":35173,"language":71,"meta":1247,"style":1247},"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",[3244,35175,35176,35206,35211],{"__ignoreMap":1247},[1115,35177,35178,35181,35183,35185,35187,35190,35193,35196,35198,35200,35202,35204],{"class":3476,"line":10},[1115,35179,35180],{"class":3487},"friedman.test",[1115,35182,1647],{"class":3491},[1115,35184,35032],{"class":3479},[1115,35186,16632],{"class":3483},[1115,35188,35189],{"class":3479}," faktor_A",[1115,35191,35192],{"class":3483}," |",[1115,35194,35195],{"class":3479}," faktor_B",[1115,35197,1568],{"class":3483},[1115,35199,19940],{"class":3479},[1115,35201,3572],{"class":3483},[1115,35203,35046],{"class":3479},[1115,35205,3676],{"class":3491},[1115,35207,35208],{"class":3476,"line":27},[1115,35209,35210],{"class":11809},"# jsou-li proměnné samostatné vektory (bez argumentu data):\n",[1115,35212,35213,35215,35217,35219,35221,35223,35225,35227],{"class":3476,"line":148},[1115,35214,35180],{"class":3487},[1115,35216,1647],{"class":3491},[1115,35218,35032],{"class":3479},[1115,35220,1568],{"class":3483},[1115,35222,35189],{"class":3479},[1115,35224,1568],{"class":3483},[1115,35226,35195],{"class":3479},[1115,35228,3676],{"class":3491},[1136,35230,35232],{"id":35231},"přehled-testů","Přehled testů",[1110,35234,35235],{},[4158,35236],{"alt":35237,"className":35238,"src":35239},"mask-ilu-volba-testu",[1130,4162],"\u002Fwiki-assets\u002Fmask-ilu-volba-testu.png",[1141,35241,35242,35255],{},[1144,35243,35244],{},[1147,35245,35246,35249,35252],{},[1150,35247,35248],{},"Situace",[1150,35250,35251],{},"Test",[1150,35253,35254],{},"R funkce",[1157,35256,35257,35270,35283,35295,35308,35323,35335,35348,35361,35374,35386,35401],{},[1147,35258,35259,35262,35265],{},[1162,35260,35261],{},"Jedna střední hodnota vs. zadané číslo, normální data",[1162,35263,35264],{},"jednovýběrový t-test",[1162,35266,35267],{},[3244,35268,35269],{},"t.test(x, mu = ..., alternative = ...)",[1147,35271,35272,35275,35278],{},[1162,35273,35274],{},"Rozdíl dvou závislých měření, diference normální",[1162,35276,35277],{},"párový t-test",[1162,35279,35280],{},[3244,35281,35282],{},"t.test(x, y, paired = TRUE)",[1147,35284,35285,35288,35290],{},[1162,35286,35287],{},"Shoda rozptylů dvou nezávislých normálních výběrů",[1162,35289,19848],{},[1162,35291,35292],{},[3244,35293,35294],{},"var.test(x, y)",[1147,35296,35297,35300,35303],{},[1162,35298,35299],{},"Shoda středních hodnot dvou nezávislých normálních výběrů",[1162,35301,35302],{},"dvouvýběrový t-test",[1162,35304,35305],{},[3244,35306,35307],{},"t.test(x, y, var.equal = TRUE\u002FFALSE)",[1147,35309,35310,35313,35315],{},[1162,35311,35312],{},"Shoda dat se zadaným typem rozdělení (normální, exponenciální, …)",[1162,35314,33116],{},[1162,35316,35317,2725,35320],{},[3244,35318,35319],{},"ks.test(x, \"pnorm\", mu, sigma)",[3244,35321,35322],{},"ks.test(x, \"pexp\", 1\u002Fdelta)",[1147,35324,35325,35328,35330],{},[1162,35326,35327],{},"Normalita dat",[1162,35329,33532],{},[1162,35331,35332],{},[3244,35333,35334],{},"shapiro.test(x)",[1147,35336,35337,35340,35343],{},[1162,35338,35339],{},"Medián jednoho výběru vs. konstanta, data nejsou normální",[1162,35341,35342],{},"jednovýběrový Wilcoxonův test",[1162,35344,35345],{},[3244,35346,35347],{},"wilcox.test(x, mu = c, alternative = ...)",[1147,35349,35350,35353,35356],{},[1162,35351,35352],{},"Medián diferencí dvou závislých měření, data nejsou normální",[1162,35354,35355],{},"párový Wilcoxonův test",[1162,35357,35358],{},[3244,35359,35360],{},"wilcox.test(x, y, paired = TRUE, mu = c)",[1147,35362,35363,35366,35369],{},[1162,35364,35365],{},"Mediány dvou nezávislých výběrů, data nejsou normální",[1162,35367,35368],{},"dvouvýběrový Wilcoxonův test",[1162,35370,35371],{},[3244,35372,35373],{},"wilcox.test(x, y)",[1147,35375,35376,35379,35381],{},[1162,35377,35378],{},"Více než dva nezávislé výběry, data nejsou normální",[1162,35380,34996],{},[1162,35382,35383],{},[3244,35384,35385],{},"kruskal.test(y ~ faktor, data)",[1147,35387,35388,35391,35394],{},[1162,35389,35390],{},"Více než dva nezávislé výběry, data nejsou normální (alternativa)",[1162,35392,35393],{},"mediánový test",[1162,35395,35396,22440,35399],{},[3244,35397,35398],{},"Median.test(y, faktor)",[3244,35400,35076],{},[1147,35402,35403,35406,35408],{},[1162,35404,35405],{},"Více než dva závislé výběry (dvojné třídění, jedno pozorování na podtřídu)",[1162,35407,35110],{},[1162,35409,35410],{},[3244,35411,35412],{},"friedman.test(y ~ A | B, data)",[1136,35414,6183],{"id":6182},[1204,35416,35417,35494,35500,35517,35548],{},[1207,35418,35419,35458,35459,32846,35476,35493],{},[1302,35420,35421,35422,35439,35440,35457],{},"Nezamítnutí ",[1115,35423,35425],{"className":35424},[1315],[1317,35426,35427],{"xmlns":1319},[1321,35428,35429,35437],{},[1324,35430,35431],{},[1327,35432,35433,35435],{},[1330,35434,1332],{},[1334,35436,1336],{},[1338,35438,1341],{"encoding":1340}," není důkaz, že ",[1115,35441,35443],{"className":35442},[1315],[1317,35444,35445],{"xmlns":1319},[1321,35446,35447,35455],{},[1324,35448,35449],{},[1327,35450,35451,35453],{},[1330,35452,1332],{},[1334,35454,1336],{},[1338,35456,1341],{"encoding":1340}," platí."," U kabelů A\u002FB vyšlo ",[1115,35460,35462],{"className":35461},[1315],[1317,35463,35464],{"xmlns":1319},[1321,35465,35466,35474],{},[1324,35467,35468,35470,35472],{},[1330,35469,1110],{},[1460,35471,1754],{},[1334,35473,32842],{},[1338,35475,32845],{"encoding":1340},[1115,35477,35479],{"className":35478},[1315],[1317,35480,35481],{"xmlns":1319},[1321,35482,35483,35491],{},[1324,35484,35485],{},[1327,35486,35487,35489],{},[1330,35488,1332],{},[1334,35490,1336],{},[1338,35492,1341],{"encoding":1340}," nezamítá, ale hodnota je blízko hranice; správná interpretace je „data rovnost průměrů nevyvracejí“, ne „rovnost je prokázána“.",[1207,35495,35496,35499],{},[1302,35497,35498],{},"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.",[1207,35501,35502,35509,35510,35513,35514,35516],{},[1302,35503,35504,30004,35506,35508],{},[3244,35505,32574],{},[3244,35507,27788],{}," se volí podle F-testu, ne podle výchozí hodnoty."," Výchozí nastavení R je ",[3244,35511,35512],{},"var.equal = FALSE"," (Welchova varianta); pokud F-test potvrdí shodné rozptyly, je třeba explicitně napsat ",[3244,35515,32825],{},", jinak se použije jiná statistika a jiné stupně volnosti.",[1207,35518,35519,35522,35523,35526,35527,35544,35545,1440],{},[1302,35520,35521],{},"Jednostranná vs. dvoustranná alternativa mění kritický obor i závěr."," Volba ",[3244,35524,35525],{},"alternative = \"greater\"\u002F\"less\"\u002F\"two.sided\""," musí odpovídat formulaci ",[1115,35528,35530],{"className":35529},[1315],[1317,35531,35532],{"xmlns":1319},[1321,35533,35534,35542],{},[1324,35535,35536],{},[1327,35537,35538,35540],{},[1330,35539,1332],{},[1334,35541,1565],{},[1338,35543,2770],{"encoding":1340}," v zadání, ne být ponechána na výchozí hodnotě ",[3244,35546,35547],{},"\"two.sided\"",[1207,35549,35550,35553,35554,35567],{},[1302,35551,35552],{},"Shapiro-Wilkův test se vyhodnocuje jen přes p-hodnotu",", ne porovnáním ",[1115,35555,35557],{"className":35556},[1315],[1317,35558,35559],{"xmlns":1319},[1321,35560,35561,35565],{},[1324,35562,35563],{},[1330,35564,1376],{},[1338,35566,1376],{"encoding":1340}," s tabulkovou kritickou hodnotou jako u ostatních testů v této kapitole.",[1136,35569,1202],{"id":1201},[1204,35571,35572,35577,35582,35587,35592,35597,35602],{},[1207,35573,35574],{},[1127,35575,1133],{"className":35576,"dataFsResolvedFilePath":1131,"href":1132},[1130],[1207,35578,35579],{},[1127,35580,1169],{"className":35581,"dataFsResolvedFilePath":1167,"href":1168},[1130],[1207,35583,35584],{},[1127,35585,1182],{"className":35586,"dataFsResolvedFilePath":1180,"href":1181},[1130],[1207,35588,35589],{},[1127,35590,6399],{"className":35591,"dataFsResolvedFilePath":6397,"href":6398},[1130],[1207,35593,35594],{},[1127,35595,1277],{"className":35596,"dataFsResolvedFilePath":10868,"href":10869},[1130],[1207,35598,35599],{},[1127,35600,6407],{"className":35601,"dataFsResolvedFilePath":6405,"href":6406},[1130],[1207,35603,35604],{},[1127,35605,6413],{"className":35606,"dataFsResolvedFilePath":1232,"href":1233},[1130],[1136,35608,1237],{"id":934},[1110,35610,1240,35611,1245],{},[1242,35612,1244],{},[6421,35614,35615],{},"html pre.shiki code .sP4rz, 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