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",[1115,1182,1184],{"className":1183},[1133],[1135,1185,1186],{"xmlns":1137},[1139,1187,1188,1193],{},[1142,1189,1190],{},[1148,1191,1192],{},"W",[1156,1194,1192],{"encoding":1158},", ",[1115,1197,1199],{"className":1198},[1133],[1135,1200,1201],{"xmlns":1137},[1139,1202,1203,1211],{},[1142,1204,1205],{},[1145,1206,1207,1209],{},[1148,1208,1150],{},[1152,1210,1154],{},[1156,1212,1159],{"encoding":1158}," zamítáme.",[1127,1215,1216,1217,1232,1233,1250,1251,1266,1267,1284,1285,1298],{},"Rozhodnutí nese dva typy chyb: chybu I. druhu (",[1115,1218,1220],{"className":1219},[1133],[1135,1221,1222],{"xmlns":1137},[1139,1223,1224,1229],{},[1142,1225,1226],{},[1148,1227,1228],{},"α",[1156,1230,1231],{"encoding":1158},"\\alpha",", zamítnutí platné ",[1115,1234,1236],{"className":1235},[1133],[1135,1237,1238],{"xmlns":1137},[1139,1239,1240,1248],{},[1142,1241,1242],{},[1145,1243,1244,1246],{},[1148,1245,1150],{},[1152,1247,1154],{},[1156,1249,1159],{"encoding":1158},") a chybu II. druhu (",[1115,1252,1254],{"className":1253},[1133],[1135,1255,1256],{"xmlns":1137},[1139,1257,1258,1263],{},[1142,1259,1260],{},[1148,1261,1262],{},"β",[1156,1264,1265],{"encoding":1158},"\\beta",", přijetí neplatné ",[1115,1268,1270],{"className":1269},[1133],[1135,1271,1272],{"xmlns":1137},[1139,1273,1274,1282],{},[1142,1275,1276],{},[1145,1277,1278,1280],{},[1148,1279,1150],{},[1152,1281,1154],{},[1156,1283,1159],{"encoding":1158},"). Hladina významnosti ",[1115,1286,1288],{"className":1287},[1133],[1135,1289,1290],{"xmlns":1137},[1139,1291,1292,1296],{},[1142,1293,1294],{},[1148,1295,1228],{},[1156,1297,1231],{"encoding":1158}," se volí předem, obvykle 0,05.",[1127,1300,1301],{},"Pro střední hodnotu normálního rozdělení slouží jednovýběrový a párový t-test; pro srovnání dvou souborů F-test (rozptyly) a dvouvýběrový t-test (střední hodnoty).",[1127,1303,1304],{},"Normalitu ověřuje Shapiro-Wilkův test, shodu s libovolným rozdělením Kolmogorov-Smirnovův test; při porušené normalitě nastupují neparametrické testy (Wilcoxonovy, Kruskalův-Wallisův, mediánový, Friedmanův).",[1127,1306,1307,1308,1321,1322,1335],{},"Rozhodnutí lze číst dvěma rovnocennými způsoby — podle polohy kritéria vůči ",[1115,1309,1311],{"className":1310},[1133],[1135,1312,1313],{"xmlns":1137},[1139,1314,1315,1319],{},[1142,1316,1317],{},[1148,1318,1192],{},[1156,1320,1192],{"encoding":1158},", nebo podle p-hodnoty vůči ",[1115,1323,1325],{"className":1324},[1133],[1135,1326,1327],{"xmlns":1137},[1139,1328,1329,1333],{},[1142,1330,1331],{},[1148,1332,1228],{},[1156,1334,1231],{"encoding":1158},".",[1110,1337,1338,1339,1347,1348,1354,1355,1361,1362,1195,1376,1390],{},"Testy statistických hypotéz jsou nástroj ",[1340,1341,1346],"a",{"className":1342,"dataFsResolvedFilePath":1344,"href":1345},[1343],"wikilink","courses\u002Fmask.md","\u002Fwiki\u002Fmask","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 ",[1340,1349,1353],{"className":1350,"dataFsResolvedFilePath":1351,"href":1352},[1343],"topics\u002Fpopisna-statistika.md","\u002Fwiki\u002Fpopisna-statistika","popisnou statistiku"," výběru, a z rozdělení uvedených u ",[1340,1356,1360],{"className":1357,"dataFsResolvedFilePath":1358,"href":1359},[1343],"topics\u002Fnahodne-veliciny-a-rozdeleni.md","\u002Fwiki\u002Fnahodne-veliciny-a-rozdeleni","náhodných veličin"," (normální, ",[1115,1363,1365],{"className":1364},[1133],[1135,1366,1367],{"xmlns":1137},[1139,1368,1369,1374],{},[1142,1370,1371],{},[1148,1372,1373],{},"t",[1156,1375,1373],{"encoding":1158},[1115,1377,1379],{"className":1378},[1133],[1135,1380,1381],{"xmlns":1137},[1139,1382,1383,1388],{},[1142,1384,1385],{},[1148,1386,1387],{},"F",[1156,1389,1387],{"encoding":1158},").",[1392,1393,1395],"h2",{"id":1394},"statistická-hypotéza-a-její-test","Statistická hypotéza a její test",[1110,1397,1398,1402,1403,1406],{},[1399,1400,1401],"strong",{},"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. ",[1399,1404,1405],{},"Testování hypotéz"," je proces ověření správnosti nebo nesprávnosti hypotézy pomocí výsledků získaných náhodným výběrem.",[1110,1408,1409],{},"Proti sobě stojí dvě hypotézy:",[1124,1411,1412,1435],{},[1127,1413,1414,1434],{},[1399,1415,1416,1417],{},"Nulová hypotéza ",[1115,1418,1420],{"className":1419},[1133],[1135,1421,1422],{"xmlns":1137},[1139,1423,1424,1432],{},[1142,1425,1426],{},[1145,1427,1428,1430],{},[1148,1429,1150],{},[1152,1431,1154],{},[1156,1433,1159],{"encoding":1158}," — tvrzení o parametru nebo rozdělení, které chceme ověřit.",[1127,1436,1437,1457,1458,1475],{},[1399,1438,1439,1440],{},"Alternativní hypotéza ",[1115,1441,1443],{"className":1442},[1133],[1135,1444,1445],{"xmlns":1137},[1139,1446,1447,1455],{},[1142,1448,1449],{},[1145,1450,1451,1453],{},[1148,1452,1150],{},[1152,1454,1176],{},[1156,1456,1179],{"encoding":1158}," — staví se proti ",[1115,1459,1461],{"className":1460},[1133],[1135,1462,1463],{"xmlns":1137},[1139,1464,1465,1473],{},[1142,1466,1467],{},[1145,1468,1469,1471],{},[1148,1470,1150],{},[1152,1472,1154],{},[1156,1474,1159],{"encoding":1158}," a určitým způsobem popírá její tvrzení.",[1110,1477,1478,1479,1513,1514,1497],{},"Pro ",[1115,1480,1482],{"className":1481},[1133],[1135,1483,1484],{"xmlns":1137},[1139,1485,1486,1510],{},[1142,1487,1488,1494,1498,1501,1504],{},[1145,1489,1490,1492],{},[1148,1491,1150],{},[1152,1493,1154],{},[1495,1496,1497],"mo",{},":",[1148,1499,1500],{},"μ",[1495,1502,1503],{},"=",[1145,1505,1506,1508],{},[1148,1507,1500],{},[1152,1509,1154],{},[1156,1511,1512],{"encoding":1158},"H_0: \\mu = \\mu_0"," existují tři varianty ",[1115,1515,1517],{"className":1516},[1133],[1135,1518,1519],{"xmlns":1137},[1139,1520,1521,1529],{},[1142,1522,1523],{},[1145,1524,1525,1527],{},[1148,1526,1150],{},[1152,1528,1176],{},[1156,1530,1179],{"encoding":1158},[1532,1533,1534,1567],"table",{},[1535,1536,1537],"thead",{},[1538,1539,1540,1561,1564],"tr",{},[1541,1542,1543,1544],"th",{},"Tvar ",[1115,1545,1547],{"className":1546},[1133],[1135,1548,1549],{"xmlns":1137},[1139,1550,1551,1559],{},[1142,1552,1553],{},[1145,1554,1555,1557],{},[1148,1556,1150],{},[1152,1558,1176],{},[1156,1560,1179],{"encoding":1158},[1541,1562,1563],{},"Zápis",[1541,1565,1566],{},"Typ",[1568,1569,1570,1613,1654],"tbody",{},[1538,1571,1572,1576,1610],{},[1573,1574,1575],"td",{},"nerovnost",[1573,1577,1578],{},[1115,1579,1581],{"className":1580},[1133],[1135,1582,1583],{"xmlns":1137},[1139,1584,1585,1607],{},[1142,1586,1587,1593,1595,1597,1601],{},[1145,1588,1589,1591],{},[1148,1590,1150],{},[1152,1592,1176],{},[1495,1594,1497],{},[1148,1596,1500],{},[1495,1598,1600],{"mathvariant":1599},"normal","≠",[1145,1602,1603,1605],{},[1148,1604,1500],{},[1152,1606,1154],{},[1156,1608,1609],{"encoding":1158},"H_1: \\mu \\neq \\mu_0",[1573,1611,1612],{},"dvoustranná",[1538,1614,1615,1618,1651],{},[1573,1616,1617],{},"větší",[1573,1619,1620],{},[1115,1621,1623],{"className":1622},[1133],[1135,1624,1625],{"xmlns":1137},[1139,1626,1627,1648],{},[1142,1628,1629,1635,1637,1639,1642],{},[1145,1630,1631,1633],{},[1148,1632,1150],{},[1152,1634,1176],{},[1495,1636,1497],{},[1148,1638,1500],{},[1495,1640,1641],{},">",[1145,1643,1644,1646],{},[1148,1645,1500],{},[1152,1647,1154],{},[1156,1649,1650],{"encoding":1158},"H_1: \\mu > \\mu_0",[1573,1652,1653],{},"jednostranná",[1538,1655,1656,1659,1692],{},[1573,1657,1658],{},"menší",[1573,1660,1661],{},[1115,1662,1664],{"className":1663},[1133],[1135,1665,1666],{"xmlns":1137},[1139,1667,1668,1689],{},[1142,1669,1670,1676,1678,1680,1683],{},[1145,1671,1672,1674],{},[1148,1673,1150],{},[1152,1675,1176],{},[1495,1677,1497],{},[1148,1679,1500],{},[1495,1681,1682],{},"\u003C",[1145,1684,1685,1687],{},[1148,1686,1500],{},[1152,1688,1154],{},[1156,1690,1691],{"encoding":1158},"H_1: \\mu \u003C \\mu_0",[1573,1693,1653],{},[1695,1696,1698],"h3",{"id":1697},"chyba-i-a-ii-druhu","Chyba I. a II. druhu",[1110,1700,1701],{},"Protože je úsudek odvozen z náhodného výběru, může vést ke dvěma typům chybného rozhodnutí:",[1124,1703,1704,1741],{},[1127,1705,1706,1709,1710,1727,1728,1335],{},[1399,1707,1708],{},"Chyba I. druhu"," — zamítnutí ",[1115,1711,1713],{"className":1712},[1133],[1135,1714,1715],{"xmlns":1137},[1139,1716,1717,1725],{},[1142,1718,1719],{},[1145,1720,1721,1723],{},[1148,1722,1150],{},[1152,1724,1154],{},[1156,1726,1159],{"encoding":1158},", ačkoliv ve skutečnosti platí. Pravděpodobnost ",[1115,1729,1731],{"className":1730},[1133],[1135,1732,1733],{"xmlns":1137},[1139,1734,1735,1739],{},[1142,1736,1737],{},[1148,1738,1228],{},[1156,1740,1231],{"encoding":1158},[1127,1742,1743,1746,1747,1764,1765,1782,1783,1335],{},[1399,1744,1745],{},"Chyba II. druhu"," — přijetí ",[1115,1748,1750],{"className":1749},[1133],[1135,1751,1752],{"xmlns":1137},[1139,1753,1754,1762],{},[1142,1755,1756],{},[1145,1757,1758,1760],{},[1148,1759,1150],{},[1152,1761,1154],{},[1156,1763,1159],{"encoding":1158},", ačkoliv platí ",[1115,1766,1768],{"className":1767},[1133],[1135,1769,1770],{"xmlns":1137},[1139,1771,1772,1780],{},[1142,1773,1774],{},[1145,1775,1776,1778],{},[1148,1777,1150],{},[1152,1779,1176],{},[1156,1781,1179],{"encoding":1158},". Pravděpodobnost ",[1115,1784,1786],{"className":1785},[1133],[1135,1787,1788],{"xmlns":1137},[1139,1789,1790,1794],{},[1142,1791,1792],{},[1148,1793,1262],{},[1156,1795,1265],{"encoding":1158},[1532,1797,1798,1862],{},[1535,1799,1800],{},[1538,1801,1802,1822,1842],{},[1541,1803,1804,1805],{},"Úsudek o ",[1115,1806,1808],{"className":1807},[1133],[1135,1809,1810],{"xmlns":1137},[1139,1811,1812,1820],{},[1142,1813,1814],{},[1145,1815,1816,1818],{},[1148,1817,1150],{},[1152,1819,1154],{},[1156,1821,1159],{"encoding":1158},[1541,1823,1824,1841],{},[1115,1825,1827],{"className":1826},[1133],[1135,1828,1829],{"xmlns":1137},[1139,1830,1831,1839],{},[1142,1832,1833],{},[1145,1834,1835,1837],{},[1148,1836,1150],{},[1152,1838,1154],{},[1156,1840,1159],{"encoding":1158}," platí",[1541,1843,1844,1861],{},[1115,1845,1847],{"className":1846},[1133],[1135,1848,1849],{"xmlns":1137},[1139,1850,1851,1859],{},[1142,1852,1853],{},[1145,1854,1855,1857],{},[1148,1856,1150],{},[1152,1858,1154],{},[1156,1860,1159],{"encoding":1158}," neplatí",[1568,1863,1864,1907],{},[1538,1865,1866,1869,1891],{},[1573,1867,1868],{},"Nezamítá se",[1573,1870,1871,1872],{},"správné rozhodnutí, ",[1115,1873,1875],{"className":1874},[1133],[1135,1876,1877],{"xmlns":1137},[1139,1878,1879,1888],{},[1142,1880,1881,1883,1886],{},[1152,1882,1176],{},[1495,1884,1885],{},"−",[1148,1887,1228],{},[1156,1889,1890],{"encoding":1158},"1-\\alpha",[1573,1892,1893,1894],{},"chyba II. druhu, ",[1115,1895,1897],{"className":1896},[1133],[1135,1898,1899],{"xmlns":1137},[1139,1900,1901,1905],{},[1142,1902,1903],{},[1148,1904,1262],{},[1156,1906,1265],{"encoding":1158},[1538,1908,1909,1912,1928],{},[1573,1910,1911],{},"Zamítá se",[1573,1913,1914,1915],{},"chyba I. druhu, ",[1115,1916,1918],{"className":1917},[1133],[1135,1919,1920],{"xmlns":1137},[1139,1921,1922,1926],{},[1142,1923,1924],{},[1148,1925,1228],{},[1156,1927,1231],{"encoding":1158},[1573,1929,1871,1930],{},[1115,1931,1933],{"className":1932},[1133],[1135,1934,1935],{"xmlns":1137},[1139,1936,1937,1945],{},[1142,1938,1939,1941,1943],{},[1152,1940,1176],{},[1495,1942,1885],{},[1148,1944,1262],{},[1156,1946,1947],{"encoding":1158},"1-\\beta",[1110,1949,1950,1953,1954,1967],{},[1399,1951,1952],{},"Hladina významnosti"," ",[1115,1955,1957],{"className":1956},[1133],[1135,1958,1959],{"xmlns":1137},[1139,1960,1961,1965],{},[1142,1962,1963],{},[1148,1964,1228],{},[1156,1966,1231],{"encoding":1158}," 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.",[1110,1969,1970],{},[1971,1972],"img",{"alt":1973,"className":1974,"src":1976},"mask-th-chyba-i-ii",[1343,1975],"wikilink-broken","\u002Fwiki-assets\u002Fmask-th-chyba-i-ii.png",[1110,1978,1979,1980,1994,1995,2008,2009,2022,2023,2036,2037,2050,2051,1335],{},"Obrázek ukazuje, proč jde o kompromis: posunutí kritické hodnoty ",[1115,1981,1983],{"className":1982},[1133],[1135,1984,1985],{"xmlns":1137},[1139,1986,1987,1992],{},[1142,1988,1989],{},[1148,1990,1991],{},"c",[1156,1993,1991],{"encoding":1158}," doleva zmenší ",[1115,1996,1998],{"className":1997},[1133],[1135,1999,2000],{"xmlns":1137},[1139,2001,2002,2006],{},[1142,2003,2004],{},[1148,2005,1262],{},[1156,2007,1265],{"encoding":1158},", ale zvětší ",[1115,2010,2012],{"className":2011},[1133],[1135,2013,2014],{"xmlns":1137},[1139,2015,2016,2020],{},[1142,2017,2018],{},[1148,2019,1228],{},[1156,2021,1231],{"encoding":1158},", a naopak. Pro danou hladinu ",[1115,2024,2026],{"className":2025},[1133],[1135,2027,2028],{"xmlns":1137},[1139,2029,2030,2034],{},[1142,2031,2032],{},[1148,2033,1228],{},[1156,2035,1231],{"encoding":1158}," je ",[1115,2038,2040],{"className":2039},[1133],[1135,2041,2042],{"xmlns":1137},[1139,2043,2044,2048],{},[1142,2045,2046],{},[1148,2047,1991],{},[1156,2049,1991],{"encoding":1158}," jednoznačně určena rozdělením kritéria za platnosti ",[1115,2052,2054],{"className":2053},[1133],[1135,2055,2056],{"xmlns":1137},[1139,2057,2058,2066],{},[1142,2059,2060],{},[1145,2061,2062,2064],{},[1148,2063,1150],{},[1152,2065,1154],{},[1156,2067,1159],{"encoding":1158},[1695,2069,2071],{"id":2070},"testové-kritérium-a-kritický-obor","Testové kritérium a kritický obor",[1110,2073,2074,1953,2077,2091,2092,1335],{},[1399,2075,2076],{},"Testové kritérium",[1115,2078,2080],{"className":2079},[1133],[1135,2081,2082],{"xmlns":1137},[1139,2083,2084,2089],{},[1142,2085,2086],{},[1148,2087,2088],{},"T",[1156,2090,2088],{"encoding":1158}," je statistika spočtená z výběru; aby bylo možné test provést, musí být známo jeho rozdělení za platnosti ",[1115,2093,2095],{"className":2094},[1133],[1135,2096,2097],{"xmlns":1137},[1139,2098,2099,2107],{},[1142,2100,2101],{},[1145,2102,2103,2105],{},[1148,2104,1150],{},[1152,2106,1154],{},[1156,2108,1159],{"encoding":1158},[1110,2110,2111,1953,2114,2127,2128,2145],{},[1399,2112,2113],{},"Kritický obor",[1115,2115,2117],{"className":2116},[1133],[1135,2118,2119],{"xmlns":1137},[1139,2120,2121,2125],{},[1142,2122,2123],{},[1148,2124,1192],{},[1156,2126,1192],{"encoding":1158}," je množina hodnot svědčících pro ",[1115,2129,2131],{"className":2130},[1133],[1135,2132,2133],{"xmlns":1137},[1139,2134,2135,2143],{},[1142,2136,2137],{},[1145,2138,2139,2141],{},[1148,2140,1150],{},[1152,2142,1176],{},[1156,2144,1179],{"encoding":1158},". Je zkonstruován tak, aby",[1115,2147,2149],{"className":2148},[1133],[1135,2150,2152],{"xmlns":1137,"display":2151},"block",[1139,2153,2154,2189],{},[1142,2155,2156,2159,2163,2165,2168,2170,2173,2179,2182,2184,2186],{},[1148,2157,2158],{},"P",[1495,2160,2162],{"stretchy":2161},"false","(",[1148,2164,2088],{},[1495,2166,2167],{},"∈",[1148,2169,1192],{},[1495,2171,2172],{},"∣",[1145,2174,2175,2177],{},[1148,2176,1150],{},[1152,2178,1154],{},[1495,2180,2181],{"stretchy":2161},")",[1495,2183,1503],{},[1148,2185,1228],{},[1495,2187,2188],{"separator":1121},",",[1156,2190,2191],{"encoding":1158},"P(T \\in W \\mid H_0) = \\alpha,",[1110,2193,2194,2195,2208,2209,2226],{},"tedy aby pravděpodobnost, že výběr dá hodnotu kritéria v ",[1115,2196,2198],{"className":2197},[1133],[1135,2199,2200],{"xmlns":1137},[1139,2201,2202,2206],{},[1142,2203,2204],{},[1148,2205,1192],{},[1156,2207,1192],{"encoding":1158}," i při platné ",[1115,2210,2212],{"className":2211},[1133],[1135,2213,2214],{"xmlns":1137},[1139,2215,2216,2224],{},[1142,2217,2218],{},[1145,2219,2220,2222],{},[1148,2221,1150],{},[1152,2223,1154],{},[1156,2225,1159],{"encoding":1158},", byla rovna zvolené hladině významnosti.",[1695,2228,2230],{"id":2229},"postup-testování-hypotézy","Postup testování hypotézy",[1110,2232,2233],{},[1971,2234],{"alt":2235,"className":2236,"src":2237},"mask-ilu-postup-testovani",[1343,1975],"\u002Fwiki-assets\u002Fmask-ilu-postup-testovani.png",[2239,2240,2241,2279,2282,2298],"ol",{},[1127,2242,2243,2244,2261,2262,1335],{},"Formulace hypotéz ",[1115,2245,2247],{"className":2246},[1133],[1135,2248,2249],{"xmlns":1137},[1139,2250,2251,2259],{},[1142,2252,2253],{},[1145,2254,2255,2257],{},[1148,2256,1150],{},[1152,2258,1154],{},[1156,2260,1159],{"encoding":1158}," a ",[1115,2263,2265],{"className":2264},[1133],[1135,2266,2267],{"xmlns":1137},[1139,2268,2269,2277],{},[1142,2270,2271],{},[1145,2272,2273,2275],{},[1148,2274,1150],{},[1152,2276,1176],{},[1156,2278,1179],{"encoding":1158},[1127,2280,2281],{},"Volba testového kritéria a výpočet jeho hodnoty.",[1127,2283,2284,2285,1335],{},"Volba hladiny významnosti a sestrojení příslušného kritického oboru ",[1115,2286,2288],{"className":2287},[1133],[1135,2289,2290],{"xmlns":1137},[1139,2291,2292,2296],{},[1142,2293,2294],{},[1148,2295,1192],{},[1156,2297,1192],{"encoding":1158},[1127,2299,2300,2301],{},"Formulace závěru:\n",[1124,2302,2303,2386],{},[1127,2304,2305,2306,2324,2325,2342,2343,2367,2368,2385],{},"pokud ",[1115,2307,2309],{"className":2308},[1133],[1135,2310,2311],{"xmlns":1137},[1139,2312,2313,2321],{},[1142,2314,2315,2317,2319],{},[1148,2316,2088],{},[1495,2318,2167],{},[1148,2320,1192],{},[1156,2322,2323],{"encoding":1158},"T \\in W",": ",[1115,2326,2328],{"className":2327},[1133],[1135,2329,2330],{"xmlns":1137},[1139,2331,2332,2340],{},[1142,2333,2334],{},[1145,2335,2336,2338],{},[1148,2337,1150],{},[1152,2339,1176],{},[1156,2341,1179],{"encoding":1158}," je testem prokázána na hladině významnosti ",[1115,2344,2346],{"className":2345},[1133],[1135,2347,2348],{"xmlns":1137},[1139,2349,2350,2364],{},[1142,2351,2352,2355,2357,2361],{},[1152,2353,2354],{},"100",[1148,2356,1228],{},[2358,2359,2360],"mtext",{}," ",[1148,2362,2363],{"mathvariant":1599},"%",[1156,2365,2366],{"encoding":1158},"100\\alpha\\,\\%"," (zamítáme ",[1115,2369,2371],{"className":2370},[1133],[1135,2372,2373],{"xmlns":1137},[1139,2374,2375,2383],{},[1142,2376,2377],{},[1145,2378,2379,2381],{},[1148,2380,1150],{},[1152,2382,1154],{},[1156,2384,1159],{"encoding":1158},");",[1127,2387,2305,2388,2324,2407,2424,2425,2444,2445,2462],{},[1115,2389,2391],{"className":2390},[1133],[1135,2392,2393],{"xmlns":1137},[1139,2394,2395,2404],{},[1142,2396,2397,2399,2402],{},[1148,2398,2088],{},[1495,2400,2401],{"mathvariant":1599},"∉",[1148,2403,1192],{},[1156,2405,2406],{"encoding":1158},"T \\notin W",[1115,2408,2410],{"className":2409},[1133],[1135,2411,2412],{"xmlns":1137},[1139,2413,2414,2422],{},[1142,2415,2416],{},[1145,2417,2418,2420],{},[1148,2419,1150],{},[1152,2421,1176],{},[1156,2423,1179],{"encoding":1158}," není testem prokázána na hladině významnosti ",[1115,2426,2428],{"className":2427},[1133],[1135,2429,2430],{"xmlns":1137},[1139,2431,2432,2442],{},[1142,2433,2434,2436,2438,2440],{},[1152,2435,2354],{},[1148,2437,1228],{},[2358,2439,2360],{},[1148,2441,2363],{"mathvariant":1599},[1156,2443,2366],{"encoding":1158}," ; ",[1115,2446,2448],{"className":2447},[1133],[1135,2449,2450],{"xmlns":1137},[1139,2451,2452,2460],{},[1142,2453,2454],{},[1145,2455,2456,2458],{},[1148,2457,1150],{},[1152,2459,1154],{},[1156,2461,1159],{"encoding":1158}," nezamítáme.",[1110,2464,2465,2466,2469,2470,2487,2488,2505,2506,2528,2529,2546,2547,1953,2567,2584],{},"Rovnocennou alternativou je ",[1399,2467,2468],{},"p-hodnota",": udává, nakolik jsou data slučitelná s ",[1115,2471,2473],{"className":2472},[1133],[1135,2474,2475],{"xmlns":1137},[1139,2476,2477,2485],{},[1142,2478,2479],{},[1145,2480,2481,2483],{},[1148,2482,1150],{},[1152,2484,1154],{},[1156,2486,1159],{"encoding":1158},". Čím menší p-hodnota, tím více data svědčí proti ",[1115,2489,2491],{"className":2490},[1133],[1135,2492,2493],{"xmlns":1137},[1139,2494,2495,2503],{},[1142,2496,2497],{},[1145,2498,2499,2501],{},[1148,2500,1150],{},[1152,2502,1154],{},[1156,2504,1159],{"encoding":1158},". Rozhodovací pravidlo: ",[1115,2507,2509],{"className":2508},[1133],[1135,2510,2511],{"xmlns":1137},[1139,2512,2513,2525],{},[1142,2514,2515,2517,2520,2522],{},[1148,2516,1110],{},[1495,2518,2519],{},"≤",[1148,2521,1228],{},[1495,2523,2524],{},"⇒",[1156,2526,2527],{"encoding":1158},"p \\le \\alpha \\Rightarrow"," zamítáme ",[1115,2530,2532],{"className":2531},[1133],[1135,2533,2534],{"xmlns":1137},[1139,2535,2536,2544],{},[1142,2537,2538],{},[1145,2539,2540,2542],{},[1148,2541,1150],{},[1152,2543,1154],{},[1156,2545,1159],{"encoding":1158},"; ",[1115,2548,2550],{"className":2549},[1133],[1135,2551,2552],{"xmlns":1137},[1139,2553,2554,2564],{},[1142,2555,2556,2558,2560,2562],{},[1148,2557,1110],{},[1495,2559,1641],{},[1148,2561,1228],{},[1495,2563,2524],{},[1156,2565,2566],{"encoding":1158},"p > \\alpha \\Rightarrow",[1115,2568,2570],{"className":2569},[1133],[1135,2571,2572],{"xmlns":1137},[1139,2573,2574,2582],{},[1142,2575,2576],{},[1145,2577,2578,2580],{},[1148,2579,1150],{},[1152,2581,1154],{},[1156,2583,1159],{"encoding":1158}," nezamítáme. Obě cesty — kritický obor i p-hodnota — vedou vždy ke stejnému závěru; R u všech testů vrací p-hodnotu přímo.",[1392,2586,2588],{"id":2587},"jednovýběrový-t-test","Jednovýběrový t-test",[1110,2590,2591,2592,2606,2607,2645,2646,2660,2661,2261,2682,2701,2702,2720,2721,2734],{},"Test o střední hodnotě ",[1115,2593,2595],{"className":2594},[1133],[1135,2596,2597],{"xmlns":1137},[1139,2598,2599,2603],{},[1142,2600,2601],{},[1148,2602,1500],{},[1156,2604,2605],{"encoding":1158},"\\mu"," rozdělení ",[1115,2608,2610],{"className":2609},[1133],[1135,2611,2612],{"xmlns":1137},[1139,2613,2614,2642],{},[1142,2615,2616,2619,2622,2625,2627,2629,2631,2640],{},[1148,2617,2618],{},"X",[1495,2620,2621],{},"∼",[1148,2623,2624],{},"N",[1495,2626,2162],{"stretchy":2161},[1148,2628,1500],{},[1495,2630,2188],{"separator":1121},[2632,2633,2634,2637],"msup",{},[1148,2635,2636],{},"σ",[1152,2638,2639],{},"2",[1495,2641,2181],{"stretchy":2161},[1156,2643,2644],{"encoding":1158},"X \\sim N(\\mu, \\sigma^2)",". Z výběru o rozsahu ",[1115,2647,2649],{"className":2648},[1133],[1135,2650,2651],{"xmlns":1137},[1139,2652,2653,2658],{},[1142,2654,2655],{},[1148,2656,2657],{},"n",[1156,2659,2657],{"encoding":1158}," se určí charakteristiky ",[1115,2662,2664],{"className":2663},[1133],[1135,2665,2666],{"xmlns":1137},[1139,2667,2668,2679],{},[1142,2669,2670],{},[2671,2672,2673,2676],"mover",{"accent":1121},[1148,2674,2675],{},"x",[1495,2677,2678],{},"ˉ",[1156,2680,2681],{"encoding":1158},"\\bar{x}",[1115,2683,2685],{"className":2684},[1133],[1135,2686,2687],{"xmlns":1137},[1139,2688,2689,2698],{},[1142,2690,2691],{},[2632,2692,2693,2696],{},[1148,2694,2695],{},"s",[1152,2697,2639],{},[1156,2699,2700],{"encoding":1158},"s^2","; testem se posuzuje vztah mezi zvoleným číslem ",[1115,2703,2705],{"className":2704},[1133],[1135,2706,2707],{"xmlns":1137},[1139,2708,2709,2717],{},[1142,2710,2711],{},[1145,2712,2713,2715],{},[1148,2714,1500],{},[1152,2716,1154],{},[1156,2718,2719],{"encoding":1158},"\\mu_0"," a neznámou hodnotou ",[1115,2722,2724],{"className":2723},[1133],[1135,2725,2726],{"xmlns":1137},[1139,2727,2728,2732],{},[1142,2729,2730],{},[1148,2731,1500],{},[1156,2733,2605],{"encoding":1158},". Testové kritérium",[1115,2736,2738],{"className":2737},[1133],[1135,2739,2740],{"xmlns":1137,"display":2151},[1139,2741,2742,2788],{},[1142,2743,2744,2746,2748,2769,2774,2776],{},[1148,2745,2088],{},[1495,2747,1503],{},[2749,2750,2751,2767],"mfrac",{},[1142,2752,2753,2759,2761],{},[2671,2754,2755,2757],{"accent":1121},[1148,2756,2675],{},[1495,2758,2678],{},[1495,2760,1885],{},[1145,2762,2763,2765],{},[1148,2764,1500],{},[1152,2766,1154],{},[1148,2768,2695],{},[2770,2771,2772],"msqrt",{},[1148,2773,2657],{},[1495,2775,2621],{},[1145,2777,2778,2780],{},[1148,2779,1373],{},[1142,2781,2782,2784,2786],{},[1148,2783,2657],{},[1495,2785,1885],{},[1152,2787,1176],{},[1156,2789,2790],{"encoding":1158},"T = \\frac{\\bar{x} - \\mu_0}{s}\\sqrt{n} \\sim t_{n-1}",[1110,2792,2793,2794,2812],{},"má Studentovo rozdělení o ",[1115,2795,2797],{"className":2796},[1133],[1135,2798,2799],{"xmlns":1137},[1139,2800,2801,2809],{},[1142,2802,2803,2805,2807],{},[1148,2804,2657],{},[1495,2806,1885],{},[1152,2808,1176],{},[1156,2810,2811],{"encoding":1158},"n-1"," stupních volnosti.",[1532,2814,2815,2873],{},[1535,2816,2817],{},[1538,2818,2819,2838,2857],{},[1541,2820,2821],{},[1115,2822,2824],{"className":2823},[1133],[1135,2825,2826],{"xmlns":1137},[1139,2827,2828,2836],{},[1142,2829,2830],{},[1145,2831,2832,2834],{},[1148,2833,1150],{},[1152,2835,1154],{},[1156,2837,1159],{"encoding":1158},[1541,2839,2840],{},[1115,2841,2843],{"className":2842},[1133],[1135,2844,2845],{"xmlns":1137},[1139,2846,2847,2855],{},[1142,2848,2849],{},[1145,2850,2851,2853],{},[1148,2852,1150],{},[1152,2854,1176],{},[1156,2856,1179],{"encoding":1158},[1541,2858,2859,2860],{},"Kritický obor ",[1115,2861,2863],{"className":2862},[1133],[1135,2864,2865],{"xmlns":1137},[1139,2866,2867,2871],{},[1142,2868,2869],{},[1148,2870,1192],{},[1156,2872,1192],{"encoding":1158},[1568,2874,2875,2966,3065],{},[1538,2876,2877,2901,2925],{},[1573,2878,2879],{},[1115,2880,2882],{"className":2881},[1133],[1135,2883,2884],{"xmlns":1137},[1139,2885,2886,2898],{},[1142,2887,2888,2890,2892],{},[1148,2889,1500],{},[1495,2891,2519],{},[1145,2893,2894,2896],{},[1148,2895,1500],{},[1152,2897,1154],{},[1156,2899,2900],{"encoding":1158},"\\mu \\le \\mu_0",[1573,2902,2903],{},[1115,2904,2906],{"className":2905},[1133],[1135,2907,2908],{"xmlns":1137},[1139,2909,2910,2922],{},[1142,2911,2912,2914,2916],{},[1148,2913,1500],{},[1495,2915,1641],{},[1145,2917,2918,2920],{},[1148,2919,1500],{},[1152,2921,1154],{},[1156,2923,2924],{"encoding":1158},"\\mu > \\mu_0",[1573,2926,2927],{},[1115,2928,2930],{"className":2929},[1133],[1135,2931,2932],{"xmlns":1137},[1139,2933,2934,2963],{},[1142,2935,2936,2938,2941,2953,2955,2957,2959,2961],{},[1148,2937,1373],{},[1495,2939,2940],{},"≥",[1145,2942,2943,2945],{},[1148,2944,1373],{},[1142,2946,2947,2949,2951],{},[1152,2948,1176],{},[1495,2950,1885],{},[1148,2952,1228],{},[1495,2954,2162],{"stretchy":2161},[1148,2956,2657],{},[1495,2958,1885],{},[1152,2960,1176],{},[1495,2962,2181],{"stretchy":2161},[1156,2964,2965],{"encoding":1158},"t \\ge t_{1-\\alpha}(n-1)",[1538,2967,2968,2992,3016],{},[1573,2969,2970],{},[1115,2971,2973],{"className":2972},[1133],[1135,2974,2975],{"xmlns":1137},[1139,2976,2977,2989],{},[1142,2978,2979,2981,2983],{},[1148,2980,1500],{},[1495,2982,1503],{},[1145,2984,2985,2987],{},[1148,2986,1500],{},[1152,2988,1154],{},[1156,2990,2991],{"encoding":1158},"\\mu = \\mu_0",[1573,2993,2994],{},[1115,2995,2997],{"className":2996},[1133],[1135,2998,2999],{"xmlns":1137},[1139,3000,3001,3013],{},[1142,3002,3003,3005,3007],{},[1148,3004,1500],{},[1495,3006,1600],{"mathvariant":1599},[1145,3008,3009,3011],{},[1148,3010,1500],{},[1152,3012,1154],{},[1156,3014,3015],{"encoding":1158},"\\mu \\neq \\mu_0",[1573,3017,3018],{},[1115,3019,3021],{"className":3020},[1133],[1135,3022,3023],{"xmlns":1137},[1139,3024,3025,3062],{},[1142,3026,3027,3029,3031,3033,3035,3052,3054,3056,3058,3060],{},[1495,3028,2172],{"stretchy":2161},[1148,3030,1373],{},[1495,3032,2172],{"stretchy":2161},[1495,3034,2940],{},[1145,3036,3037,3039],{},[1148,3038,1373],{},[1142,3040,3041,3043,3045,3047,3050],{},[1152,3042,1176],{},[1495,3044,1885],{},[1148,3046,1228],{},[1148,3048,3049],{"mathvariant":1599},"\u002F",[1152,3051,2639],{},[1495,3053,2162],{"stretchy":2161},[1148,3055,2657],{},[1495,3057,1885],{},[1152,3059,1176],{},[1495,3061,2181],{"stretchy":2161},[1156,3063,3064],{"encoding":1158},"\\lvert t \\rvert \\ge t_{1-\\alpha\u002F2}(n-1)",[1538,3066,3067,3091,3115],{},[1573,3068,3069],{},[1115,3070,3072],{"className":3071},[1133],[1135,3073,3074],{"xmlns":1137},[1139,3075,3076,3088],{},[1142,3077,3078,3080,3082],{},[1148,3079,1500],{},[1495,3081,2940],{},[1145,3083,3084,3086],{},[1148,3085,1500],{},[1152,3087,1154],{},[1156,3089,3090],{"encoding":1158},"\\mu \\ge \\mu_0",[1573,3092,3093],{},[1115,3094,3096],{"className":3095},[1133],[1135,3097,3098],{"xmlns":1137},[1139,3099,3100,3112],{},[1142,3101,3102,3104,3106],{},[1148,3103,1500],{},[1495,3105,1682],{},[1145,3107,3108,3110],{},[1148,3109,1500],{},[1152,3111,1154],{},[1156,3113,3114],{"encoding":1158},"\\mu \u003C \\mu_0",[1573,3116,3117],{},[1115,3118,3120],{"className":3119},[1133],[1135,3121,3122],{"xmlns":1137},[1139,3123,3124,3154],{},[1142,3125,3126,3128,3130,3132,3144,3146,3148,3150,3152],{},[1148,3127,1373],{},[1495,3129,2519],{},[1495,3131,1885],{},[1145,3133,3134,3136],{},[1148,3135,1373],{},[1142,3137,3138,3140,3142],{},[1152,3139,1176],{},[1495,3141,1885],{},[1148,3143,1228],{},[1495,3145,2162],{"stretchy":2161},[1148,3147,2657],{},[1495,3149,1885],{},[1152,3151,1176],{},[1495,3153,2181],{"stretchy":2161},[1156,3155,3156],{"encoding":1158},"t \\le -t_{1-\\alpha}(n-1)",[1110,3158,3159,3160,3164],{},"V R test provádí ",[3161,3162,3163],"code",{},"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?",[3166,3167,3171],"pre",{"className":3168,"code":3169,"language":71,"meta":3170,"style":3170},"language-r shiki shiki-themes github-light github-light github-dark","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","",[3161,3172,3173,3236],{"__ignoreMap":3170},[1115,3174,3176,3179,3183,3187,3190,3194,3196,3199,3201,3204,3206,3209,3211,3214,3216,3219,3221,3223,3225,3228,3230,3233],{"class":3175,"line":10},"line",[1115,3177,2675],{"class":3178},"sP4rz",[1115,3180,3182],{"class":3181},"s8jYJ"," \u003C-",[1115,3184,3186],{"class":3185},"snPdu"," c",[1115,3188,2162],{"class":3189},"sxrX7",[1115,3191,3193],{"class":3192},"sBjJW","12.5",[1115,3195,2188],{"class":3181},[1115,3197,3198],{"class":3192}," 13.5",[1115,3200,2188],{"class":3181},[1115,3202,3203],{"class":3192}," 11.9",[1115,3205,2188],{"class":3181},[1115,3207,3208],{"class":3192}," 12.2",[1115,3210,2188],{"class":3181},[1115,3212,3213],{"class":3192}," 13.0",[1115,3215,2188],{"class":3181},[1115,3217,3218],{"class":3192}," 14.3",[1115,3220,2188],{"class":3181},[1115,3222,3208],{"class":3192},[1115,3224,2188],{"class":3181},[1115,3226,3227],{"class":3192}," 11.8",[1115,3229,2188],{"class":3181},[1115,3231,3232],{"class":3192}," 14.0",[1115,3234,3235],{"class":3189},")\n",[1115,3237,3238,3241,3243,3245,3247,3250,3253,3256,3258,3261,3263,3267],{"class":3175,"line":27},[1115,3239,3240],{"class":3185},"t.test",[1115,3242,2162],{"class":3189},[1115,3244,2675],{"class":3178},[1115,3246,2188],{"class":3181},[1115,3248,3249],{"class":3178}," mu",[1115,3251,3252],{"class":3181}," =",[1115,3254,3255],{"class":3192}," 12",[1115,3257,2188],{"class":3181},[1115,3259,3260],{"class":3178}," alternative",[1115,3262,3252],{"class":3181},[1115,3264,3266],{"class":3265},"sIIMD"," \"two.sided\"",[1115,3268,3235],{"class":3189},[3166,3270,3275],{"className":3271,"code":3273,"language":3274,"meta":3170},[3272],"language-text","    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","text",[3161,3276,3273],{"__ignoreMap":3170},[1110,3278,3279,3281,3282,3285,3286,3289,3290,3293,3294,3318],{},[3161,3280,1373],{}," je testové kritérium, ",[3161,3283,3284],{},"df"," stupně volnosti, ",[3161,3287,3288],{},"p-value"," p-hodnota pro zvolenou alternativu a ",[3161,3291,3292],{},"mean of x"," výběrový průměr. Zde ",[1115,3295,3297],{"className":3296},[1133],[1135,3298,3299],{"xmlns":1137},[1139,3300,3301,3315],{},[1142,3302,3303,3305,3307,3310,3312],{},[1148,3304,1110],{},[1495,3306,1503],{},[1152,3308,3309],{},"0,02843",[1495,3311,1682],{},[1152,3313,3314],{},"0,05",[1156,3316,3317],{"encoding":1158},"p = 0{,}02843 \u003C 0{,}05",": úprava trasy průměrnou dobu jízdy (původně 12 minut) statisticky významně změnila.",[1103,3320,3324,3332,3423,3479,3577],{"className":3321,"dataCallout":3323},[1106,3322],"callout-example","example",[1110,3325,3327,3331],{"className":3326},[1113],[1115,3328],{"className":3329,"ariaHidden":1121},[1118,3330,1120],"i-lucide:flask-conical","Příklad: Kontrola objemu lahví",[1110,3333,3334,3335,3358,3359,3378,3379,3402,3403,3422],{},"Pivovar plní lahve, deklarovaný objem je ",[1115,3336,3338],{"className":3337},[1133],[1135,3339,3340],{"xmlns":1137},[1139,3341,3342,3355],{},[1142,3343,3344,3350,3352],{},[1145,3345,3346,3348],{},[1148,3347,1500],{},[1152,3349,1154],{},[1495,3351,1503],{},[1152,3353,3354],{},"0,5",[1156,3356,3357],{"encoding":1158},"\\mu_0 = 0{,}5"," l. Náhodný výběr ",[1115,3360,3362],{"className":3361},[1133],[1135,3363,3364],{"xmlns":1137},[1139,3365,3366,3375],{},[1142,3367,3368,3370,3372],{},[1148,3369,2657],{},[1495,3371,1503],{},[1152,3373,3374],{},"20",[1156,3376,3377],{"encoding":1158},"n = 20"," lahví dal ",[1115,3380,3382],{"className":3381},[1133],[1135,3383,3384],{"xmlns":1137},[1139,3385,3386,3399],{},[1142,3387,3388,3394,3396],{},[2671,3389,3390,3392],{"accent":1121},[1148,3391,2675],{},[1495,3393,2678],{},[1495,3395,1503],{},[1152,3397,3398],{},"0,492",[1156,3400,3401],{"encoding":1158},"\\bar{x} = 0{,}492"," l, ",[1115,3404,3406],{"className":3405},[1133],[1135,3407,3408],{"xmlns":1137},[1139,3409,3410,3419],{},[1142,3411,3412,3414,3416],{},[1148,3413,2695],{},[1495,3415,1503],{},[1152,3417,3418],{},"0,015",[1156,3420,3421],{"encoding":1158},"s = 0{,}015"," l. Na hladině významnosti 5 % ověřte podezření, že pivovar lahve nedoplňuje.",[1110,3424,3425,3451,3452,3478],{},[1115,3426,3428],{"className":3427},[1133],[1135,3429,3430],{"xmlns":1137},[1139,3431,3432,3448],{},[1142,3433,3434,3440,3442,3444,3446],{},[1145,3435,3436,3438],{},[1148,3437,1150],{},[1152,3439,1154],{},[1495,3441,1497],{},[1148,3443,1500],{},[1495,3445,2940],{},[1152,3447,3354],{},[1156,3449,3450],{"encoding":1158},"H_0: \\mu \\ge 0{,}5"," l (objem je v pořádku nebo větší), ",[1115,3453,3455],{"className":3454},[1133],[1135,3456,3457],{"xmlns":1137},[1139,3458,3459,3475],{},[1142,3460,3461,3467,3469,3471,3473],{},[1145,3462,3463,3465],{},[1148,3464,1150],{},[1152,3466,1176],{},[1495,3468,1497],{},[1148,3470,1500],{},[1495,3472,1682],{},[1152,3474,3354],{},[1156,3476,3477],{"encoding":1158},"H_1: \\mu \u003C 0{,}5"," l (lahve jsou nedoplněné).",[1110,3480,3481],{},[1115,3482,3484],{"className":3483},[1133],[1135,3485,3486],{"xmlns":1137},[1139,3487,3488,3574],{},[1142,3489,3490,3492,3494,3506,3510,3512,3514,3517,3519,3523,3525,3527,3530,3532,3534,3536,3549,3551,3554,3556,3559,3561,3563,3565,3567,3569,3572],{},[1148,3491,1373],{},[1495,3493,1503],{},[2749,3495,3496,3504],{},[1142,3497,3498,3500,3502],{},[1152,3499,3398],{},[1495,3501,1885],{},[1152,3503,3354],{},[1152,3505,3418],{},[2770,3507,3508],{},[1152,3509,3374],{},[1495,3511,1503],{},[1495,3513,1885],{},[1152,3515,3516],{},"2,385",[1495,3518,2188],{"separator":1121},[3520,3521],"mspace",{"width":3522},"2em",[1148,3524,1192],{},[1495,3526,1503],{},[1495,3528,3529],{"stretchy":2161},"{",[1148,3531,1373],{},[1495,3533,2519],{},[1495,3535,1885],{},[1145,3537,3538,3540],{},[1148,3539,1373],{},[1142,3541,3542,3544,3546],{},[1152,3543,1154],{},[1495,3545,2188],{"separator":1121},[1152,3547,3548],{},"95",[1495,3550,2162],{"stretchy":2161},[1152,3552,3553],{},"19",[1495,3555,2181],{"stretchy":2161},[1495,3557,3558],{"stretchy":2161},"}",[1495,3560,1503],{},[1495,3562,3529],{"stretchy":2161},[1148,3564,1373],{},[1495,3566,2519],{},[1495,3568,1885],{},[1152,3570,3571],{},"1,729",[1495,3573,3558],{"stretchy":2161},[1156,3575,3576],{"encoding":1158},"t = \\frac{0{,}492 - 0{,}5}{0{,}015}\\sqrt{20} = -2{,}385, \\qquad W = \\{t \\le -t_{0,95}(19)\\} = \\{t \\le -1{,}729\\}",[1110,3578,3579,3580,3598,3599,3616],{},"Protože ",[1115,3581,3583],{"className":3582},[1133],[1135,3584,3585],{"xmlns":1137},[1139,3586,3587,3595],{},[1142,3588,3589,3591,3593],{},[1148,3590,1373],{},[1495,3592,2167],{},[1148,3594,1192],{},[1156,3596,3597],{"encoding":1158},"t \\in W",", zamítáme ",[1115,3600,3602],{"className":3601},[1133],[1135,3603,3604],{"xmlns":1137},[1139,3605,3606,3614],{},[1142,3607,3608],{},[1145,3609,3610,3612],{},[1148,3611,1150],{},[1152,3613,1154],{},[1156,3615,1159],{"encoding":1158},": na hladině významnosti 5 % se potvrdilo, že pivovar plní lahve pod deklarovaný objem.",[1110,3618,3619,3620,3622,3623,1497],{},"Ze souhrnných charakteristik bez surových dat ",[3161,3621,3163],{}," spustit nelze — kritérium a kritická hodnota se dopočítají přímo z definice pomocí ",[3161,3624,3625],{},"qt()",[3166,3627,3629],{"className":3168,"code":3628,"language":71,"meta":3170,"style":3170},"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",[3161,3630,3631,3669,3706,3738,3743],{"__ignoreMap":3170},[1115,3632,3633,3636,3638,3641,3643,3645,3647,3650,3652,3654,3656,3659,3661,3664,3666],{"class":3175,"line":10},[1115,3634,3635],{"class":3178},"xbar",[1115,3637,3182],{"class":3181},[1115,3639,3640],{"class":3192}," 0.492",[1115,3642,2546],{"class":3189},[1115,3644,2695],{"class":3178},[1115,3646,3182],{"class":3181},[1115,3648,3649],{"class":3192}," 0.015",[1115,3651,2546],{"class":3189},[1115,3653,2657],{"class":3178},[1115,3655,3182],{"class":3181},[1115,3657,3658],{"class":3192}," 20",[1115,3660,2546],{"class":3189},[1115,3662,3663],{"class":3178},"mu0",[1115,3665,3182],{"class":3181},[1115,3667,3668],{"class":3192}," 0.5\n",[1115,3670,3671,3673,3675,3678,3680,3683,3686,3689,3691,3694,3697,3700,3702,3704],{"class":3175,"line":27},[1115,3672,1373],{"class":3178},[1115,3674,3182],{"class":3181},[1115,3676,3677],{"class":3189}," (",[1115,3679,3635],{"class":3178},[1115,3681,3682],{"class":3181}," -",[1115,3684,3685],{"class":3178}," mu0",[1115,3687,3688],{"class":3189},") ",[1115,3690,3049],{"class":3181},[1115,3692,3693],{"class":3178}," s",[1115,3695,3696],{"class":3181}," *",[1115,3698,3699],{"class":3185}," sqrt",[1115,3701,2162],{"class":3189},[1115,3703,2657],{"class":3178},[1115,3705,3235],{"class":3189},[1115,3707,3708,3711,3713,3716,3718,3721,3723,3726,3728,3731,3733,3736],{"class":3175,"line":148},[1115,3709,3710],{"class":3178},"t_krit",[1115,3712,3182],{"class":3181},[1115,3714,3715],{"class":3185}," qt",[1115,3717,2162],{"class":3189},[1115,3719,3720],{"class":3192},"0.05",[1115,3722,2188],{"class":3181},[1115,3724,3725],{"class":3178}," df",[1115,3727,3252],{"class":3181},[1115,3729,3730],{"class":3178}," n",[1115,3732,3682],{"class":3181},[1115,3734,3735],{"class":3192}," 1",[1115,3737,3235],{"class":3189},[1115,3739,3740],{"class":3175,"line":111},[1115,3741,3742],{"class":3178},"t\n",[1115,3744,3745],{"class":3175,"line":96},[1115,3746,3747],{"class":3178},"t_krit\n",[3166,3749,3752],{"className":3750,"code":3751,"language":3274,"meta":3170},[3272],"[1] -2.385139\n[1] -1.729133\n",[3161,3753,3751],{"__ignoreMap":3170},[1110,3755,3756],{},[1971,3757],{"alt":3758,"className":3759,"src":3760},"mask-th-t-jednostranny",[1343,1975],"\u002Fwiki-assets\u002Fmask-th-t-jednostranny.png",[1110,3762,3763,3764,1497],{},"Další dva příklady mají k dispozici surová data, takže je lze otestovat přímo ",[3161,3765,3163],{},[1110,3767,3768,3771],{},[1399,3769,3770],{},"Životnost baterií."," Výrobce udává průměrnou životnost 10 hodin, na 11 bateriích byly naměřeny hodnoty v hodinách.",[3166,3773,3775],{"className":3168,"code":3774,"language":71,"meta":3170,"style":3170},"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",[3161,3776,3777,3840],{"__ignoreMap":3170},[1115,3778,3779,3782,3784,3786,3788,3791,3793,3796,3798,3801,3803,3806,3808,3811,3813,3816,3818,3820,3822,3825,3827,3829,3831,3834,3836,3838],{"class":3175,"line":10},[1115,3780,3781],{"class":3178},"x2",[1115,3783,3182],{"class":3181},[1115,3785,3186],{"class":3185},[1115,3787,2162],{"class":3189},[1115,3789,3790],{"class":3192},"9.5",[1115,3792,2188],{"class":3181},[1115,3794,3795],{"class":3192}," 10.5",[1115,3797,2188],{"class":3181},[1115,3799,3800],{"class":3192}," 8.9",[1115,3802,2188],{"class":3181},[1115,3804,3805],{"class":3192}," 9.2",[1115,3807,2188],{"class":3181},[1115,3809,3810],{"class":3192}," 10.0",[1115,3812,2188],{"class":3181},[1115,3814,3815],{"class":3192}," 8.5",[1115,3817,2188],{"class":3181},[1115,3819,3805],{"class":3192},[1115,3821,2188],{"class":3181},[1115,3823,3824],{"class":3192}," 8.8",[1115,3826,2188],{"class":3181},[1115,3828,3810],{"class":3192},[1115,3830,2188],{"class":3181},[1115,3832,3833],{"class":3192}," 9.5",[1115,3835,2188],{"class":3181},[1115,3837,3805],{"class":3192},[1115,3839,3235],{"class":3189},[1115,3841,3842,3844,3846,3848,3850,3852,3854,3857,3859,3861,3863,3865],{"class":3175,"line":27},[1115,3843,3240],{"class":3185},[1115,3845,2162],{"class":3189},[1115,3847,3781],{"class":3178},[1115,3849,2188],{"class":3181},[1115,3851,3249],{"class":3178},[1115,3853,3252],{"class":3181},[1115,3855,3856],{"class":3192}," 10",[1115,3858,2188],{"class":3181},[1115,3860,3260],{"class":3178},[1115,3862,3252],{"class":3181},[1115,3864,3266],{"class":3265},[1115,3866,3235],{"class":3189},[3166,3868,3871],{"className":3869,"code":3870,"language":3274,"meta":3170},[3272],"    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",[3161,3872,3870],{"__ignoreMap":3170},[1110,3874,3875,3898],{},[1115,3876,3878],{"className":3877},[1133],[1135,3879,3880],{"xmlns":1137},[1139,3881,3882,3895],{},[1142,3883,3884,3886,3888,3891,3893],{},[1148,3885,1110],{},[1495,3887,1503],{},[1152,3889,3890],{},"0,006548",[1495,3892,1682],{},[1152,3894,3314],{},[1156,3896,3897],{"encoding":1158},"p = 0{,}006548 \u003C 0{,}05",": skutečná životnost se od deklarovaných 10 hodin statisticky významně liší (baterie vydrží méně).",[1110,3900,3901,3904],{},[1399,3902,3903],{},"Odpad materiálu."," Na deseti obráběných kusech byl naměřen odpad materiálu v procentech; testuje se rozdíl proti 4 % a zároveň normalita dat.",[3166,3906,3908],{"className":3168,"code":3907,"language":71,"meta":3170,"style":3170},"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",[3161,3909,3910,3967,3994],{"__ignoreMap":3170},[1115,3911,3912,3915,3917,3919,3921,3924,3926,3929,3931,3934,3936,3939,3941,3943,3945,3947,3949,3952,3954,3957,3959,3961,3963,3965],{"class":3175,"line":10},[1115,3913,3914],{"class":3178},"x3",[1115,3916,3182],{"class":3181},[1115,3918,3186],{"class":3185},[1115,3920,2162],{"class":3189},[1115,3922,3923],{"class":3192},"4.1",[1115,3925,2188],{"class":3181},[1115,3927,3928],{"class":3192}," 4.0",[1115,3930,2188],{"class":3181},[1115,3932,3933],{"class":3192}," 3.8",[1115,3935,2188],{"class":3181},[1115,3937,3938],{"class":3192}," 3.9",[1115,3940,2188],{"class":3181},[1115,3942,3933],{"class":3192},[1115,3944,2188],{"class":3181},[1115,3946,3933],{"class":3192},[1115,3948,2188],{"class":3181},[1115,3950,3951],{"class":3192}," 3.5",[1115,3953,2188],{"class":3181},[1115,3955,3956],{"class":3192}," 3.7",[1115,3958,2188],{"class":3181},[1115,3960,3928],{"class":3192},[1115,3962,2188],{"class":3181},[1115,3964,3928],{"class":3192},[1115,3966,3235],{"class":3189},[1115,3968,3969,3971,3973,3975,3977,3979,3981,3984,3986,3988,3990,3992],{"class":3175,"line":27},[1115,3970,3240],{"class":3185},[1115,3972,2162],{"class":3189},[1115,3974,3914],{"class":3178},[1115,3976,2188],{"class":3181},[1115,3978,3249],{"class":3178},[1115,3980,3252],{"class":3181},[1115,3982,3983],{"class":3192}," 4",[1115,3985,2188],{"class":3181},[1115,3987,3260],{"class":3178},[1115,3989,3252],{"class":3181},[1115,3991,3266],{"class":3265},[1115,3993,3235],{"class":3189},[1115,3995,3996,3999,4001,4003],{"class":3175,"line":148},[1115,3997,3998],{"class":3185},"shapiro.test",[1115,4000,2162],{"class":3189},[1115,4002,3914],{"class":3178},[1115,4004,3235],{"class":3189},[3166,4006,4009],{"className":4007,"code":4008,"language":3274,"meta":3170},[3272],"    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",[3161,4010,4008],{"__ignoreMap":3170},[1110,4012,4013,4036,4037,4060],{},[1115,4014,4016],{"className":4015},[1133],[1135,4017,4018],{"xmlns":1137},[1139,4019,4020,4033],{},[1142,4021,4022,4024,4026,4029,4031],{},[1148,4023,1110],{},[1495,4025,1503],{},[1152,4027,4028],{},"0,0343",[1495,4030,1682],{},[1152,4032,3314],{},[1156,4034,4035],{"encoding":1158},"p = 0{,}0343 \u003C 0{,}05",": průměrný odpad se od 4 % statisticky významně liší (výběrový průměr 3,86 %). Shapiro-Wilkův test dává ",[1115,4038,4040],{"className":4039},[1133],[1135,4041,4042],{"xmlns":1137},[1139,4043,4044,4057],{},[1142,4045,4046,4048,4050,4053,4055],{},[1148,4047,1110],{},[1495,4049,1503],{},[1152,4051,4052],{},"0,4634",[1495,4054,1641],{},[1152,4056,3314],{},[1156,4058,4059],{"encoding":1158},"p = 0{,}4634 > 0{,}05",", předpoklad normality pro t-test je v pořádku.",[1392,4062,4064],{"id":4063},"párový-t-test","Párový t-test",[1110,4066,4067,4068,4100,4101,4136,4137,4176,4177,4190,4191,2261,4210,4230,4231,4248,4249,2734],{},"Používá se, když jsou měření závislá — na stejných objektech se měří dvě hodnoty ",[1115,4069,4071],{"className":4070},[1133],[1135,4072,4073],{"xmlns":1137},[1139,4074,4075,4097],{},[1142,4076,4077,4079,4086,4088,4095],{},[1495,4078,2162],{"stretchy":2161},[1145,4080,4081,4083],{},[1148,4082,2618],{},[1148,4084,4085],{},"i",[1495,4087,2188],{"separator":1121},[1145,4089,4090,4093],{},[1148,4091,4092],{},"Y",[1148,4094,4085],{},[1495,4096,2181],{"stretchy":2161},[1156,4098,4099],{"encoding":1158},"(X_i, Y_i)"," a vyhodnocují se jejich diference ",[1115,4102,4104],{"className":4103},[1133],[1135,4105,4106],{"xmlns":1137},[1139,4107,4108,4133],{},[1142,4109,4110,4117,4119,4125,4127],{},[1145,4111,4112,4115],{},[1148,4113,4114],{},"D",[1148,4116,4085],{},[1495,4118,1503],{},[1145,4120,4121,4123],{},[1148,4122,2618],{},[1148,4124,4085],{},[1495,4126,1885],{},[1145,4128,4129,4131],{},[1148,4130,4092],{},[1148,4132,4085],{},[1156,4134,4135],{"encoding":1158},"D_i = X_i - Y_i",", kde ",[1115,4138,4140],{"className":4139},[1133],[1135,4141,4142],{"xmlns":1137},[1139,4143,4144,4173],{},[1142,4145,4146,4148,4150,4152,4154,4160,4162,4171],{},[1148,4147,4114],{},[1495,4149,2621],{},[1148,4151,2624],{},[1495,4153,2162],{"stretchy":2161},[1145,4155,4156,4158],{},[1148,4157,1500],{},[1148,4159,4114],{},[1495,4161,2188],{"separator":1121},[4163,4164,4165,4167,4169],"msubsup",{},[1148,4166,2636],{},[1148,4168,4114],{},[1152,4170,2639],{},[1495,4172,2181],{"stretchy":2161},[1156,4174,4175],{"encoding":1158},"D \\sim N(\\mu_D, \\sigma_D^2)",". Z ",[1115,4178,4180],{"className":4179},[1133],[1135,4181,4182],{"xmlns":1137},[1139,4183,4184,4188],{},[1142,4185,4186],{},[1148,4187,2657],{},[1156,4189,2657],{"encoding":1158}," dvojic se určí ",[1115,4192,4194],{"className":4193},[1133],[1135,4195,4196],{"xmlns":1137},[1139,4197,4198,4207],{},[1142,4199,4200],{},[2671,4201,4202,4205],{"accent":1121},[1148,4203,4204],{},"d",[1495,4206,2678],{},[1156,4208,4209],{"encoding":1158},"\\bar{d}",[1115,4211,4213],{"className":4212},[1133],[1135,4214,4215],{"xmlns":1137},[1139,4216,4217,4227],{},[1142,4218,4219],{},[4163,4220,4221,4223,4225],{},[1148,4222,2695],{},[1148,4224,4204],{},[1152,4226,2639],{},[1156,4228,4229],{"encoding":1158},"s_d^2","; testuje se vztah mezi zvoleným číslem ",[1115,4232,4234],{"className":4233},[1133],[1135,4235,4236],{"xmlns":1137},[1139,4237,4238,4246],{},[1142,4239,4240],{},[1145,4241,4242,4244],{},[1148,4243,1500],{},[1152,4245,1154],{},[1156,4247,2719],{"encoding":1158}," (obvykle 0) a ",[1115,4250,4252],{"className":4251},[1133],[1135,4253,4254],{"xmlns":1137},[1139,4255,4256,4264],{},[1142,4257,4258],{},[1145,4259,4260,4262],{},[1148,4261,1500],{},[1148,4263,4114],{},[1156,4265,4266],{"encoding":1158},"\\mu_D",[1115,4268,4270],{"className":4269},[1133],[1135,4271,4272],{"xmlns":1137,"display":2151},[1139,4273,4274,4324],{},[1142,4275,4276,4278,4280,4304,4308,4310,4322],{},[1148,4277,2088],{},[1495,4279,1503],{},[2749,4281,4282,4298],{},[1142,4283,4284,4290,4292],{},[2671,4285,4286,4288],{"accent":1121},[1148,4287,4204],{},[1495,4289,2678],{},[1495,4291,1885],{},[1145,4293,4294,4296],{},[1148,4295,1500],{},[1152,4297,1154],{},[1145,4299,4300,4302],{},[1148,4301,2695],{},[1148,4303,4204],{},[2770,4305,4306],{},[1148,4307,2657],{},[1495,4309,2621],{},[1145,4311,4312,4314],{},[1148,4313,1373],{},[1142,4315,4316,4318,4320],{},[1148,4317,2657],{},[1495,4319,1885],{},[1152,4321,1176],{},[1148,4323,1335],{"mathvariant":1599},[1156,4325,4326],{"encoding":1158},"T = \\frac{\\bar{d} - \\mu_0}{s_d}\\sqrt{n} \\sim t_{n-1}.",[1532,4328,4329,4386],{},[1535,4330,4331],{},[1538,4332,4333,4352,4371],{},[1541,4334,4335],{},[1115,4336,4338],{"className":4337},[1133],[1135,4339,4340],{"xmlns":1137},[1139,4341,4342,4350],{},[1142,4343,4344],{},[1145,4345,4346,4348],{},[1148,4347,1150],{},[1152,4349,1154],{},[1156,4351,1159],{"encoding":1158},[1541,4353,4354],{},[1115,4355,4357],{"className":4356},[1133],[1135,4358,4359],{"xmlns":1137},[1139,4360,4361,4369],{},[1142,4362,4363],{},[1145,4364,4365,4367],{},[1148,4366,1150],{},[1152,4368,1176],{},[1156,4370,1179],{"encoding":1158},[1541,4372,2859,4373],{},[1115,4374,4376],{"className":4375},[1133],[1135,4377,4378],{"xmlns":1137},[1139,4379,4380,4384],{},[1142,4381,4382],{},[1148,4383,1192],{},[1156,4385,1192],{"encoding":1158},[1568,4387,4388,4485,4590],{},[1538,4389,4390,4418,4446],{},[1573,4391,4392],{},[1115,4393,4395],{"className":4394},[1133],[1135,4396,4397],{"xmlns":1137},[1139,4398,4399,4415],{},[1142,4400,4401,4407,4409],{},[1145,4402,4403,4405],{},[1148,4404,1500],{},[1148,4406,4114],{},[1495,4408,2519],{},[1145,4410,4411,4413],{},[1148,4412,1500],{},[1152,4414,1154],{},[1156,4416,4417],{"encoding":1158},"\\mu_D \\le \\mu_0",[1573,4419,4420],{},[1115,4421,4423],{"className":4422},[1133],[1135,4424,4425],{"xmlns":1137},[1139,4426,4427,4443],{},[1142,4428,4429,4435,4437],{},[1145,4430,4431,4433],{},[1148,4432,1500],{},[1148,4434,4114],{},[1495,4436,1641],{},[1145,4438,4439,4441],{},[1148,4440,1500],{},[1152,4442,1154],{},[1156,4444,4445],{"encoding":1158},"\\mu_D > \\mu_0",[1573,4447,4448],{},[1115,4449,4451],{"className":4450},[1133],[1135,4452,4453],{"xmlns":1137},[1139,4454,4455,4483],{},[1142,4456,4457,4459,4461,4473,4475,4477,4479,4481],{},[1148,4458,1373],{},[1495,4460,2940],{},[1145,4462,4463,4465],{},[1148,4464,1373],{},[1142,4466,4467,4469,4471],{},[1152,4468,1176],{},[1495,4470,1885],{},[1148,4472,1228],{},[1495,4474,2162],{"stretchy":2161},[1148,4476,2657],{},[1495,4478,1885],{},[1152,4480,1176],{},[1495,4482,2181],{"stretchy":2161},[1156,4484,2965],{"encoding":1158},[1538,4486,4487,4515,4543],{},[1573,4488,4489],{},[1115,4490,4492],{"className":4491},[1133],[1135,4493,4494],{"xmlns":1137},[1139,4495,4496,4512],{},[1142,4497,4498,4504,4506],{},[1145,4499,4500,4502],{},[1148,4501,1500],{},[1148,4503,4114],{},[1495,4505,1503],{},[1145,4507,4508,4510],{},[1148,4509,1500],{},[1152,4511,1154],{},[1156,4513,4514],{"encoding":1158},"\\mu_D = \\mu_0",[1573,4516,4517],{},[1115,4518,4520],{"className":4519},[1133],[1135,4521,4522],{"xmlns":1137},[1139,4523,4524,4540],{},[1142,4525,4526,4532,4534],{},[1145,4527,4528,4530],{},[1148,4529,1500],{},[1148,4531,4114],{},[1495,4533,1600],{"mathvariant":1599},[1145,4535,4536,4538],{},[1148,4537,1500],{},[1152,4539,1154],{},[1156,4541,4542],{"encoding":1158},"\\mu_D \\neq \\mu_0",[1573,4544,4545],{},[1115,4546,4548],{"className":4547},[1133],[1135,4549,4550],{"xmlns":1137},[1139,4551,4552,4588],{},[1142,4553,4554,4556,4558,4560,4562,4578,4580,4582,4584,4586],{},[1495,4555,2172],{"stretchy":2161},[1148,4557,1373],{},[1495,4559,2172],{"stretchy":2161},[1495,4561,2940],{},[1145,4563,4564,4566],{},[1148,4565,1373],{},[1142,4567,4568,4570,4572,4574,4576],{},[1152,4569,1176],{},[1495,4571,1885],{},[1148,4573,1228],{},[1148,4575,3049],{"mathvariant":1599},[1152,4577,2639],{},[1495,4579,2162],{"stretchy":2161},[1148,4581,2657],{},[1495,4583,1885],{},[1152,4585,1176],{},[1495,4587,2181],{"stretchy":2161},[1156,4589,3064],{"encoding":1158},[1538,4591,4592,4620,4648],{},[1573,4593,4594],{},[1115,4595,4597],{"className":4596},[1133],[1135,4598,4599],{"xmlns":1137},[1139,4600,4601,4617],{},[1142,4602,4603,4609,4611],{},[1145,4604,4605,4607],{},[1148,4606,1500],{},[1148,4608,4114],{},[1495,4610,2940],{},[1145,4612,4613,4615],{},[1148,4614,1500],{},[1152,4616,1154],{},[1156,4618,4619],{"encoding":1158},"\\mu_D \\ge \\mu_0",[1573,4621,4622],{},[1115,4623,4625],{"className":4624},[1133],[1135,4626,4627],{"xmlns":1137},[1139,4628,4629,4645],{},[1142,4630,4631,4637,4639],{},[1145,4632,4633,4635],{},[1148,4634,1500],{},[1148,4636,4114],{},[1495,4638,1682],{},[1145,4640,4641,4643],{},[1148,4642,1500],{},[1152,4644,1154],{},[1156,4646,4647],{"encoding":1158},"\\mu_D \u003C \\mu_0",[1573,4649,4650],{},[1115,4651,4653],{"className":4652},[1133],[1135,4654,4655],{"xmlns":1137},[1139,4656,4657,4687],{},[1142,4658,4659,4661,4663,4665,4677,4679,4681,4683,4685],{},[1148,4660,1373],{},[1495,4662,2519],{},[1495,4664,1885],{},[1145,4666,4667,4669],{},[1148,4668,1373],{},[1142,4670,4671,4673,4675],{},[1152,4672,1176],{},[1495,4674,1885],{},[1148,4676,1228],{},[1495,4678,2162],{"stretchy":2161},[1148,4680,2657],{},[1495,4682,1885],{},[1152,4684,1176],{},[1495,4686,2181],{"stretchy":2161},[1156,4688,3156],{"encoding":1158},[1103,4690,4692,4699,4842,4906,4993],{"className":4691,"dataCallout":3323},[1106,3322],[1110,4693,4695,4698],{"className":4694},[1113],[1115,4696],{"className":4697,"ariaHidden":1121},[1118,3330,1120],"Příklad: Snížení spotřeby paliva aditivem",[1110,4700,4701,4702,4721,4722,4740,4741,4759,4760,4793,4794,4817,4818,4841],{},"U ",[1115,4703,4705],{"className":4704},[1133],[1135,4706,4707],{"xmlns":1137},[1139,4708,4709,4718],{},[1142,4710,4711,4713,4715],{},[1148,4712,2657],{},[1495,4714,1503],{},[1152,4716,4717],{},"10",[1156,4719,4720],{"encoding":1158},"n = 10"," vozů se změřila spotřeba před přidáním aditiva (",[1115,4723,4725],{"className":4724},[1133],[1135,4726,4727],{"xmlns":1137},[1139,4728,4729,4737],{},[1142,4730,4731],{},[1145,4732,4733,4735],{},[1148,4734,2618],{},[1148,4736,4085],{},[1156,4738,4739],{"encoding":1158},"X_i",") a po něm (",[1115,4742,4744],{"className":4743},[1133],[1135,4745,4746],{"xmlns":1137},[1139,4747,4748,4756],{},[1142,4749,4750],{},[1145,4751,4752,4754],{},[1148,4753,4092],{},[1148,4755,4085],{},[1156,4757,4758],{"encoding":1158},"Y_i","), diference ",[1115,4761,4763],{"className":4762},[1133],[1135,4764,4765],{"xmlns":1137},[1139,4766,4767,4791],{},[1142,4768,4769,4775,4777,4783,4785],{},[1145,4770,4771,4773],{},[1148,4772,4114],{},[1148,4774,4085],{},[1495,4776,1503],{},[1145,4778,4779,4781],{},[1148,4780,2618],{},[1148,4782,4085],{},[1495,4784,1885],{},[1145,4786,4787,4789],{},[1148,4788,4092],{},[1148,4790,4085],{},[1156,4792,4135],{"encoding":1158}," představují úsporu paliva. Z dat vyšla průměrná úspora ",[1115,4795,4797],{"className":4796},[1133],[1135,4798,4799],{"xmlns":1137},[1139,4800,4801,4814],{},[1142,4802,4803,4809,4811],{},[2671,4804,4805,4807],{"accent":1121},[1148,4806,4204],{},[1495,4808,2678],{},[1495,4810,1503],{},[1152,4812,4813],{},"0,4",[1156,4815,4816],{"encoding":1158},"\\bar{d} = 0{,}4"," l\u002F100 km, ",[1115,4819,4821],{"className":4820},[1133],[1135,4822,4823],{"xmlns":1137},[1139,4824,4825,4838],{},[1142,4826,4827,4833,4835],{},[1145,4828,4829,4831],{},[1148,4830,2695],{},[1148,4832,4204],{},[1495,4834,1503],{},[1152,4836,4837],{},"0,35",[1156,4839,4840],{"encoding":1158},"s_d = 0{,}35"," l\u002F100 km. Ověřte, že aditivum spotřebu statisticky významně snižuje.",[1110,4843,4844,4874,4875,4905],{},[1115,4845,4847],{"className":4846},[1133],[1135,4848,4849],{"xmlns":1137},[1139,4850,4851,4871],{},[1142,4852,4853,4859,4861,4867,4869],{},[1145,4854,4855,4857],{},[1148,4856,1150],{},[1152,4858,1154],{},[1495,4860,1497],{},[1145,4862,4863,4865],{},[1148,4864,1500],{},[1148,4866,4114],{},[1495,4868,2519],{},[1152,4870,1154],{},[1156,4872,4873],{"encoding":1158},"H_0: \\mu_D \\le 0"," (aditivum nemá vliv nebo spotřebu zvyšuje), ",[1115,4876,4878],{"className":4877},[1133],[1135,4879,4880],{"xmlns":1137},[1139,4881,4882,4902],{},[1142,4883,4884,4890,4892,4898,4900],{},[1145,4885,4886,4888],{},[1148,4887,1150],{},[1152,4889,1176],{},[1495,4891,1497],{},[1145,4893,4894,4896],{},[1148,4895,1500],{},[1148,4897,4114],{},[1495,4899,1641],{},[1152,4901,1154],{},[1156,4903,4904],{"encoding":1158},"H_1: \\mu_D > 0"," (aditivum spotřebu snižuje).",[1110,4907,4908],{},[1115,4909,4911],{"className":4910},[1133],[1135,4912,4913],{"xmlns":1137},[1139,4914,4915,4990],{},[1142,4916,4917,4919,4921,4933,4937,4939,4942,4944,4946,4948,4950,4952,4954,4956,4968,4970,4973,4975,4977,4979,4981,4983,4985,4988],{},[1148,4918,1373],{},[1495,4920,1503],{},[2749,4922,4923,4931],{},[1142,4924,4925,4927,4929],{},[1152,4926,4813],{},[1495,4928,1885],{},[1152,4930,1154],{},[1152,4932,4837],{},[2770,4934,4935],{},[1152,4936,4717],{},[1495,4938,1503],{},[1152,4940,4941],{},"3,614",[1495,4943,2188],{"separator":1121},[3520,4945],{"width":3522},[1148,4947,1192],{},[1495,4949,1503],{},[1495,4951,3529],{"stretchy":2161},[1148,4953,1373],{},[1495,4955,2940],{},[1145,4957,4958,4960],{},[1148,4959,1373],{},[1142,4961,4962,4964,4966],{},[1152,4963,1154],{},[1495,4965,2188],{"separator":1121},[1152,4967,3548],{},[1495,4969,2162],{"stretchy":2161},[1152,4971,4972],{},"9",[1495,4974,2181],{"stretchy":2161},[1495,4976,3558],{"stretchy":2161},[1495,4978,1503],{},[1495,4980,3529],{"stretchy":2161},[1148,4982,1373],{},[1495,4984,2940],{},[1152,4986,4987],{},"1,833",[1495,4989,3558],{"stretchy":2161},[1156,4991,4992],{"encoding":1158},"t = \\frac{0{,}4 - 0}{0{,}35}\\sqrt{10} = 3{,}614, \\qquad W = \\{t \\ge t_{0,95}(9)\\} = \\{t \\ge 1{,}833\\}",[1110,4994,3579,4995,3598,5012,5029],{},[1115,4996,4998],{"className":4997},[1133],[1135,4999,5000],{"xmlns":1137},[1139,5001,5002,5010],{},[1142,5003,5004,5006,5008],{},[1148,5005,1373],{},[1495,5007,2167],{},[1148,5009,1192],{},[1156,5011,3597],{"encoding":1158},[1115,5013,5015],{"className":5014},[1133],[1135,5016,5017],{"xmlns":1137},[1139,5018,5019,5027],{},[1142,5020,5021],{},[1145,5022,5023,5025],{},[1148,5024,1150],{},[1152,5026,1154],{},[1156,5028,1159],{"encoding":1158},": aditivum prokazatelně snižuje průměrnou spotřebu paliva.",[3166,5031,5033],{"className":3168,"code":5032,"language":71,"meta":3170,"style":3170},"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",[3161,5034,5035,5064,5096,5123,5127],{"__ignoreMap":3170},[1115,5036,5037,5040,5042,5045,5047,5050,5052,5055,5057,5059,5061],{"class":3175,"line":10},[1115,5038,5039],{"class":3178},"dbar",[1115,5041,3182],{"class":3181},[1115,5043,5044],{"class":3192}," 0.4",[1115,5046,2546],{"class":3189},[1115,5048,5049],{"class":3178},"sd_d",[1115,5051,3182],{"class":3181},[1115,5053,5054],{"class":3192}," 0.35",[1115,5056,2546],{"class":3189},[1115,5058,2657],{"class":3178},[1115,5060,3182],{"class":3181},[1115,5062,5063],{"class":3192}," 10\n",[1115,5065,5066,5068,5070,5072,5074,5076,5079,5081,5083,5086,5088,5090,5092,5094],{"class":3175,"line":27},[1115,5067,1373],{"class":3178},[1115,5069,3182],{"class":3181},[1115,5071,3677],{"class":3189},[1115,5073,5039],{"class":3178},[1115,5075,3682],{"class":3181},[1115,5077,5078],{"class":3192}," 0",[1115,5080,3688],{"class":3189},[1115,5082,3049],{"class":3181},[1115,5084,5085],{"class":3178}," sd_d",[1115,5087,3696],{"class":3181},[1115,5089,3699],{"class":3185},[1115,5091,2162],{"class":3189},[1115,5093,2657],{"class":3178},[1115,5095,3235],{"class":3189},[1115,5097,5098,5100,5102,5104,5106,5109,5111,5113,5115,5117,5119,5121],{"class":3175,"line":148},[1115,5099,3710],{"class":3178},[1115,5101,3182],{"class":3181},[1115,5103,3715],{"class":3185},[1115,5105,2162],{"class":3189},[1115,5107,5108],{"class":3192},"0.95",[1115,5110,2188],{"class":3181},[1115,5112,3725],{"class":3178},[1115,5114,3252],{"class":3181},[1115,5116,3730],{"class":3178},[1115,5118,3682],{"class":3181},[1115,5120,3735],{"class":3192},[1115,5122,3235],{"class":3189},[1115,5124,5125],{"class":3175,"line":111},[1115,5126,3742],{"class":3178},[1115,5128,5129],{"class":3175,"line":96},[1115,5130,3747],{"class":3178},[3166,5132,5135],{"className":5133,"code":5134,"language":3274,"meta":3170},[3272],"[1] 3.614032\n[1] 1.833113\n",[3161,5136,5134],{"__ignoreMap":3170},[1103,5138,5142,5150,5153,5299,5305],{"className":5139,"dataCallout":5141},[1106,5140],"callout-warning","warning",[1110,5143,5145,5149],{"className":5144},[1113],[1115,5146],{"className":5147,"ariaHidden":1121},[1118,5148,1120],"i-lucide:triangle-alert","Ověřte normalitu diferencí, ne jen výsledek testu",[1110,5151,5152],{},"Realitní kancelář nechala dva odhadce ocenit osm nemovitostí (tisíce Kč):",[3166,5154,5156],{"className":3168,"code":5155,"language":71,"meta":3170,"style":3170},"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",[3161,5157,5158,5209,5260,5285],{"__ignoreMap":3170},[1115,5159,5160,5163,5165,5167,5169,5172,5174,5177,5179,5182,5184,5187,5189,5192,5194,5197,5199,5202,5204,5207],{"class":3175,"line":10},[1115,5161,5162],{"class":3178},"estA",[1115,5164,3182],{"class":3181},[1115,5166,3186],{"class":3185},[1115,5168,2162],{"class":3189},[1115,5170,5171],{"class":3192},"3282",[1115,5173,2188],{"class":3181},[1115,5175,5176],{"class":3192}," 2506",[1115,5178,2188],{"class":3181},[1115,5180,5181],{"class":3192}," 2812",[1115,5183,2188],{"class":3181},[1115,5185,5186],{"class":3192}," 5453",[1115,5188,2188],{"class":3181},[1115,5190,5191],{"class":3192}," 3263",[1115,5193,2188],{"class":3181},[1115,5195,5196],{"class":3192}," 4571",[1115,5198,2188],{"class":3181},[1115,5200,5201],{"class":3192}," 3121",[1115,5203,2188],{"class":3181},[1115,5205,5206],{"class":3192}," 2963",[1115,5208,3235],{"class":3189},[1115,5210,5211,5214,5216,5218,5220,5223,5225,5228,5230,5233,5235,5238,5240,5243,5245,5248,5250,5253,5255,5258],{"class":3175,"line":27},[1115,5212,5213],{"class":3178},"estB",[1115,5215,3182],{"class":3181},[1115,5217,3186],{"class":3185},[1115,5219,2162],{"class":3189},[1115,5221,5222],{"class":3192},"3271",[1115,5224,2188],{"class":3181},[1115,5226,5227],{"class":3192}," 2531",[1115,5229,2188],{"class":3181},[1115,5231,5232],{"class":3192}," 2799",[1115,5234,2188],{"class":3181},[1115,5236,5237],{"class":3192}," 5471",[1115,5239,2188],{"class":3181},[1115,5241,5242],{"class":3192}," 3285",[1115,5244,2188],{"class":3181},[1115,5246,5247],{"class":3192}," 4557",[1115,5249,2188],{"class":3181},[1115,5251,5252],{"class":3192}," 3139",[1115,5254,2188],{"class":3181},[1115,5256,5257],{"class":3192}," 2976",[1115,5259,3235],{"class":3189},[1115,5261,5262,5264,5266,5268,5270,5273,5275,5278,5280,5283],{"class":3175,"line":148},[1115,5263,3240],{"class":3185},[1115,5265,2162],{"class":3189},[1115,5267,5162],{"class":3178},[1115,5269,2188],{"class":3181},[1115,5271,5272],{"class":3178}," estB",[1115,5274,2188],{"class":3181},[1115,5276,5277],{"class":3178}," paired",[1115,5279,3252],{"class":3181},[1115,5281,5282],{"class":3192}," TRUE",[1115,5284,3235],{"class":3189},[1115,5286,5287,5289,5291,5293,5295,5297],{"class":3175,"line":111},[1115,5288,3998],{"class":3185},[1115,5290,2162],{"class":3189},[1115,5292,5162],{"class":3178},[1115,5294,3682],{"class":3181},[1115,5296,5272],{"class":3178},[1115,5298,3235],{"class":3189},[3166,5300,5303],{"className":5301,"code":5302,"language":3274,"meta":3170},[3272],"    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",[3161,5304,5302],{"__ignoreMap":3170},[1110,5306,5307,5308,3677,5325,5344,5345,5368],{},"Párový t-test sám nezamítá ",[1115,5309,5311],{"className":5310},[1133],[1135,5312,5313],{"xmlns":1137},[1139,5314,5315,5323],{},[1142,5316,5317],{},[1145,5318,5319,5321],{},[1148,5320,1150],{},[1152,5322,1154],{},[1156,5324,1159],{"encoding":1158},[1115,5326,5328],{"className":5327},[1133],[1135,5329,5330],{"xmlns":1137},[1139,5331,5332,5341],{},[1142,5333,5334,5336,5338],{},[1148,5335,1110],{},[1495,5337,1503],{},[1152,5339,5340],{},"0,2635",[1156,5342,5343],{"encoding":1158},"p = 0{,}2635","): odhadci se podle něj neliší. Shapiro-Wilkův test na diferencích ale dává ",[1115,5346,5348],{"className":5347},[1133],[1135,5349,5350],{"xmlns":1137},[1139,5351,5352,5365],{},[1142,5353,5354,5356,5358,5361,5363],{},[1148,5355,1110],{},[1495,5357,1503],{},[1152,5359,5360],{},"0,03203",[1495,5362,1682],{},[1152,5364,3314],{},[1156,5366,5367],{"encoding":1158},"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).",[1392,5370,5372],{"id":5371},"testy-o-dvou-základních-souborech","Testy o dvou základních souborech",[1110,5374,5375,5376,5403,5404,5442,5443,2261,5461,5442,5499,5517,5518,2261,5550,5582,5583,5609,5610,1335],{},"Uvažují se dva nezávislé základní soubory ",[1115,5377,5379],{"className":5378},[1133],[1135,5380,5381],{"xmlns":1137},[1139,5382,5383,5400],{},[1142,5384,5385,5392,5394],{},[1145,5386,5387,5390],{},[1148,5388,5389],{},"Z",[1152,5391,1176],{},[1495,5393,2188],{"separator":1121},[1145,5395,5396,5398],{},[1148,5397,5389],{},[1152,5399,2639],{},[1156,5401,5402],{"encoding":1158},"Z_1, Z_2"," se znakem ",[1115,5405,5407],{"className":5406},[1133],[1135,5408,5409],{"xmlns":1137},[1139,5410,5411,5439],{},[1142,5412,5413,5415,5417,5419,5421,5427,5429,5437],{},[1148,5414,2618],{},[1495,5416,2621],{},[1148,5418,2624],{},[1495,5420,2162],{"stretchy":2161},[1145,5422,5423,5425],{},[1148,5424,1500],{},[1152,5426,1176],{},[1495,5428,2188],{"separator":1121},[4163,5430,5431,5433,5435],{},[1148,5432,2636],{},[1152,5434,1176],{},[1152,5436,2639],{},[1495,5438,2181],{"stretchy":2161},[1156,5440,5441],{"encoding":1158},"X \\sim N(\\mu_1, \\sigma_1^2)"," v ",[1115,5444,5446],{"className":5445},[1133],[1135,5447,5448],{"xmlns":1137},[1139,5449,5450,5458],{},[1142,5451,5452],{},[1145,5453,5454,5456],{},[1148,5455,5389],{},[1152,5457,1176],{},[1156,5459,5460],{"encoding":1158},"Z_1",[1115,5462,5464],{"className":5463},[1133],[1135,5465,5466],{"xmlns":1137},[1139,5467,5468,5496],{},[1142,5469,5470,5472,5474,5476,5478,5484,5486,5494],{},[1148,5471,2618],{},[1495,5473,2621],{},[1148,5475,2624],{},[1495,5477,2162],{"stretchy":2161},[1145,5479,5480,5482],{},[1148,5481,1500],{},[1152,5483,2639],{},[1495,5485,2188],{"separator":1121},[4163,5487,5488,5490,5492],{},[1148,5489,2636],{},[1152,5491,2639],{},[1152,5493,2639],{},[1495,5495,2181],{"stretchy":2161},[1156,5497,5498],{"encoding":1158},"X \\sim N(\\mu_2, \\sigma_2^2)",[1115,5500,5502],{"className":5501},[1133],[1135,5503,5504],{"xmlns":1137},[1139,5505,5506,5514],{},[1142,5507,5508],{},[1145,5509,5510,5512],{},[1148,5511,5389],{},[1152,5513,2639],{},[1156,5515,5516],{"encoding":1158},"Z_2",". Z výběrů se určí ",[1115,5519,5521],{"className":5520},[1133],[1135,5522,5523],{"xmlns":1137},[1139,5524,5525,5547],{},[1142,5526,5527,5537,5539],{},[1145,5528,5529,5535],{},[2671,5530,5531,5533],{"accent":1121},[1148,5532,2675],{},[1495,5534,2678],{},[1152,5536,1176],{},[1495,5538,2188],{"separator":1121},[4163,5540,5541,5543,5545],{},[1148,5542,2695],{},[1152,5544,1176],{},[1152,5546,2639],{},[1156,5548,5549],{"encoding":1158},"\\bar{x}_1, s_1^2",[1115,5551,5553],{"className":5552},[1133],[1135,5554,5555],{"xmlns":1137},[1139,5556,5557,5579],{},[1142,5558,5559,5569,5571],{},[1145,5560,5561,5567],{},[2671,5562,5563,5565],{"accent":1121},[1148,5564,2675],{},[1495,5566,2678],{},[1152,5568,2639],{},[1495,5570,2188],{"separator":1121},[4163,5572,5573,5575,5577],{},[1148,5574,2695],{},[1152,5576,2639],{},[1152,5578,2639],{},[1156,5580,5581],{"encoding":1158},"\\bar{x}_2, s_2^2",". Testují se varianty vztahů mezi ",[1115,5584,5586],{"className":5585},[1133],[1135,5587,5588],{"xmlns":1137},[1139,5589,5590,5606],{},[1142,5591,5592,5598,5600],{},[1145,5593,5594,5596],{},[1148,5595,1500],{},[1152,5597,1176],{},[1495,5599,2188],{"separator":1121},[1145,5601,5602,5604],{},[1148,5603,1500],{},[1152,5605,2639],{},[1156,5607,5608],{"encoding":1158},"\\mu_1, \\mu_2",", resp. mezi ",[1115,5611,5613],{"className":5612},[1133],[1135,5614,5615],{"xmlns":1137},[1139,5616,5617,5637],{},[1142,5618,5619,5627,5629],{},[4163,5620,5621,5623,5625],{},[1148,5622,2636],{},[1152,5624,1176],{},[1152,5626,2639],{},[1495,5628,2188],{"separator":1121},[4163,5630,5631,5633,5635],{},[1148,5632,2636],{},[1152,5634,2639],{},[1152,5636,2639],{},[1156,5638,5639],{"encoding":1158},"\\sigma_1^2, \\sigma_2^2",[1695,5641,5643],{"id":5642},"f-test-o-rozptylech","F-test o rozptylech",[1110,5645,5646],{},"Statistika",[1115,5648,5650],{"className":5649},[1133],[1135,5651,5652],{"xmlns":1137,"display":2151},[1139,5653,5654,5710],{},[1142,5655,5656,5658,5660,5678,5680],{},[1148,5657,1387],{},[1495,5659,1503],{},[2749,5661,5662,5670],{},[4163,5663,5664,5666,5668],{},[1148,5665,2695],{},[1152,5667,1176],{},[1152,5669,2639],{},[4163,5671,5672,5674,5676],{},[1148,5673,2695],{},[1152,5675,2639],{},[1152,5677,2639],{},[1495,5679,2621],{},[1145,5681,5682,5684],{},[1148,5683,1387],{},[1142,5685,5686,5692,5694,5696,5698,5700,5706,5708],{},[1145,5687,5688,5690],{},[1148,5689,2657],{},[1152,5691,1176],{},[1495,5693,1885],{},[1152,5695,1176],{},[1495,5697,2188],{"separator":1121},[2358,5699,2360],{},[1145,5701,5702,5704],{},[1148,5703,2657],{},[1152,5705,2639],{},[1495,5707,1885],{},[1152,5709,1176],{},[1156,5711,5712],{"encoding":1158},"F = \\frac{s_1^2}{s_2^2} \\sim F_{n_1-1,\\,n_2-1}",[1110,5714,5715,5716,2261,5738,2812],{},"má Fisherovo-Snedecorovo rozdělení o ",[1115,5717,5719],{"className":5718},[1133],[1135,5720,5721],{"xmlns":1137},[1139,5722,5723,5735],{},[1142,5724,5725,5731,5733],{},[1145,5726,5727,5729],{},[1148,5728,2657],{},[1152,5730,1176],{},[1495,5732,1885],{},[1152,5734,1176],{},[1156,5736,5737],{"encoding":1158},"n_1-1",[1115,5739,5741],{"className":5740},[1133],[1135,5742,5743],{"xmlns":1137},[1139,5744,5745,5757],{},[1142,5746,5747,5753,5755],{},[1145,5748,5749,5751],{},[1148,5750,2657],{},[1152,5752,2639],{},[1495,5754,1885],{},[1152,5756,1176],{},[1156,5758,5759],{"encoding":1158},"n_2-1",[1532,5761,5762,5819],{},[1535,5763,5764],{},[1538,5765,5766,5785,5804],{},[1541,5767,5768],{},[1115,5769,5771],{"className":5770},[1133],[1135,5772,5773],{"xmlns":1137},[1139,5774,5775,5783],{},[1142,5776,5777],{},[1145,5778,5779,5781],{},[1148,5780,1150],{},[1152,5782,1154],{},[1156,5784,1159],{"encoding":1158},[1541,5786,5787],{},[1115,5788,5790],{"className":5789},[1133],[1135,5791,5792],{"xmlns":1137},[1139,5793,5794,5802],{},[1142,5795,5796],{},[1145,5797,5798,5800],{},[1148,5799,1150],{},[1152,5801,1176],{},[1156,5803,1179],{"encoding":1158},[1541,5805,2859,5806],{},[1115,5807,5809],{"className":5808},[1133],[1135,5810,5811],{"xmlns":1137},[1139,5812,5813,5817],{},[1142,5814,5815],{},[1148,5816,1192],{},[1156,5818,1192],{"encoding":1158},[1568,5820,5821,5935,6108],{},[1538,5822,5823,5851,5879],{},[1573,5824,5825],{},[1115,5826,5828],{"className":5827},[1133],[1135,5829,5830],{"xmlns":1137},[1139,5831,5832,5848],{},[1142,5833,5834,5840,5842],{},[1145,5835,5836,5838],{},[1148,5837,2636],{},[1152,5839,1176],{},[1495,5841,2519],{},[1145,5843,5844,5846],{},[1148,5845,2636],{},[1152,5847,2639],{},[1156,5849,5850],{"encoding":1158},"\\sigma_1 \\le \\sigma_2",[1573,5852,5853],{},[1115,5854,5856],{"className":5855},[1133],[1135,5857,5858],{"xmlns":1137},[1139,5859,5860,5876],{},[1142,5861,5862,5868,5870],{},[1145,5863,5864,5866],{},[1148,5865,2636],{},[1152,5867,1176],{},[1495,5869,1641],{},[1145,5871,5872,5874],{},[1148,5873,2636],{},[1152,5875,2639],{},[1156,5877,5878],{"encoding":1158},"\\sigma_1 > \\sigma_2",[1573,5880,5881],{},[1115,5882,5884],{"className":5883},[1133],[1135,5885,5886],{"xmlns":1137},[1139,5887,5888,5932],{},[1142,5889,5890,5892,5894,5906,5908,5914,5916,5918,5920,5926,5928,5930],{},[1148,5891,1387],{},[1495,5893,2940],{},[1145,5895,5896,5898],{},[1148,5897,1387],{},[1142,5899,5900,5902,5904],{},[1152,5901,1176],{},[1495,5903,1885],{},[1148,5905,1228],{},[1495,5907,2162],{"stretchy":2161},[1145,5909,5910,5912],{},[1148,5911,2657],{},[1152,5913,1176],{},[1495,5915,1885],{},[1152,5917,1176],{},[1495,5919,2188],{"separator":1121},[1145,5921,5922,5924],{},[1148,5923,2657],{},[1152,5925,2639],{},[1495,5927,1885],{},[1152,5929,1176],{},[1495,5931,2181],{"stretchy":2161},[1156,5933,5934],{"encoding":1158},"F \\ge F_{1-\\alpha}(n_1-1, n_2-1)",[1538,5936,5937,5965,5993],{},[1573,5938,5939],{},[1115,5940,5942],{"className":5941},[1133],[1135,5943,5944],{"xmlns":1137},[1139,5945,5946,5962],{},[1142,5947,5948,5954,5956],{},[1145,5949,5950,5952],{},[1148,5951,2636],{},[1152,5953,1176],{},[1495,5955,1503],{},[1145,5957,5958,5960],{},[1148,5959,2636],{},[1152,5961,2639],{},[1156,5963,5964],{"encoding":1158},"\\sigma_1 = \\sigma_2",[1573,5966,5967],{},[1115,5968,5970],{"className":5969},[1133],[1135,5971,5972],{"xmlns":1137},[1139,5973,5974,5990],{},[1142,5975,5976,5982,5984],{},[1145,5977,5978,5980],{},[1148,5979,2636],{},[1152,5981,1176],{},[1495,5983,1600],{"mathvariant":1599},[1145,5985,5986,5988],{},[1148,5987,2636],{},[1152,5989,2639],{},[1156,5991,5992],{"encoding":1158},"\\sigma_1 \\neq \\sigma_2",[1573,5994,5995,6049,6050],{},[1115,5996,5998],{"className":5997},[1133],[1135,5999,6000],{"xmlns":1137},[1139,6001,6002,6046],{},[1142,6003,6004,6006,6008,6020,6022,6028,6030,6032,6034,6040,6042,6044],{},[1148,6005,1387],{},[1495,6007,2519],{},[1145,6009,6010,6012],{},[1148,6011,1387],{},[1142,6013,6014,6016,6018],{},[1148,6015,1228],{},[1148,6017,3049],{"mathvariant":1599},[1152,6019,2639],{},[1495,6021,2162],{"stretchy":2161},[1145,6023,6024,6026],{},[1148,6025,2657],{},[1152,6027,1176],{},[1495,6029,1885],{},[1152,6031,1176],{},[1495,6033,2188],{"separator":1121},[1145,6035,6036,6038],{},[1148,6037,2657],{},[1152,6039,2639],{},[1495,6041,1885],{},[1152,6043,1176],{},[1495,6045,2181],{"stretchy":2161},[1156,6047,6048],{"encoding":1158},"F \\le F_{\\alpha\u002F2}(n_1-1, n_2-1)"," nebo ",[1115,6051,6053],{"className":6052},[1133],[1135,6054,6055],{"xmlns":1137},[1139,6056,6057,6105],{},[1142,6058,6059,6061,6063,6079,6081,6087,6089,6091,6093,6099,6101,6103],{},[1148,6060,1387],{},[1495,6062,2940],{},[1145,6064,6065,6067],{},[1148,6066,1387],{},[1142,6068,6069,6071,6073,6075,6077],{},[1152,6070,1176],{},[1495,6072,1885],{},[1148,6074,1228],{},[1148,6076,3049],{"mathvariant":1599},[1152,6078,2639],{},[1495,6080,2162],{"stretchy":2161},[1145,6082,6083,6085],{},[1148,6084,2657],{},[1152,6086,1176],{},[1495,6088,1885],{},[1152,6090,1176],{},[1495,6092,2188],{"separator":1121},[1145,6094,6095,6097],{},[1148,6096,2657],{},[1152,6098,2639],{},[1495,6100,1885],{},[1152,6102,1176],{},[1495,6104,2181],{"stretchy":2161},[1156,6106,6107],{"encoding":1158},"F \\ge F_{1-\\alpha\u002F2}(n_1-1, n_2-1)",[1538,6109,6110,6138,6166],{},[1573,6111,6112],{},[1115,6113,6115],{"className":6114},[1133],[1135,6116,6117],{"xmlns":1137},[1139,6118,6119,6135],{},[1142,6120,6121,6127,6129],{},[1145,6122,6123,6125],{},[1148,6124,2636],{},[1152,6126,1176],{},[1495,6128,2940],{},[1145,6130,6131,6133],{},[1148,6132,2636],{},[1152,6134,2639],{},[1156,6136,6137],{"encoding":1158},"\\sigma_1 \\ge \\sigma_2",[1573,6139,6140],{},[1115,6141,6143],{"className":6142},[1133],[1135,6144,6145],{"xmlns":1137},[1139,6146,6147,6163],{},[1142,6148,6149,6155,6157],{},[1145,6150,6151,6153],{},[1148,6152,2636],{},[1152,6154,1176],{},[1495,6156,1682],{},[1145,6158,6159,6161],{},[1148,6160,2636],{},[1152,6162,2639],{},[1156,6164,6165],{"encoding":1158},"\\sigma_1 \u003C \\sigma_2",[1573,6167,6168],{},[1115,6169,6171],{"className":6170},[1133],[1135,6172,6173],{"xmlns":1137},[1139,6174,6175,6213],{},[1142,6176,6177,6179,6181,6187,6189,6195,6197,6199,6201,6207,6209,6211],{},[1148,6178,1387],{},[1495,6180,2519],{},[1145,6182,6183,6185],{},[1148,6184,1387],{},[1148,6186,1228],{},[1495,6188,2162],{"stretchy":2161},[1145,6190,6191,6193],{},[1148,6192,2657],{},[1152,6194,1176],{},[1495,6196,1885],{},[1152,6198,1176],{},[1495,6200,2188],{"separator":1121},[1145,6202,6203,6205],{},[1148,6204,2657],{},[1152,6206,2639],{},[1495,6208,1885],{},[1152,6210,1176],{},[1495,6212,2181],{"stretchy":2161},[1156,6214,6215],{"encoding":1158},"F \\le F_{\\alpha}(n_1-1, n_2-1)",[1695,6217,6219],{"id":6218},"dvouvýběrový-t-test-o-středních-hodnotách","Dvouvýběrový t-test o středních hodnotách",[1110,6221,6222],{},"Volba statistiky závisí na tom, zda jsou rozptyly považovány za shodné:",[1115,6224,6226],{"className":6225},[1133],[1135,6227,6228],{"xmlns":1137,"display":2151},[1139,6229,6230,6408],{},[1142,6231,6232,6238,6240,6317,6365,6367,6369,6378,6380,6386,6388,6394,6396,6402,6404,6406],{},[1145,6233,6234,6236],{},[1148,6235,2088],{},[1152,6237,1176],{},[1495,6239,1503],{},[2749,6241,6242,6266],{},[1142,6243,6244,6254,6256],{},[1145,6245,6246,6252],{},[2671,6247,6248,6250],{"accent":1121},[1148,6249,2675],{},[1495,6251,2678],{},[1152,6253,1176],{},[1495,6255,1885],{},[1145,6257,6258,6264],{},[2671,6259,6260,6262],{"accent":1121},[1148,6261,2675],{},[1495,6263,2678],{},[1152,6265,2639],{},[2770,6267,6268],{},[1142,6269,6270,6272,6278,6280,6282,6284,6292,6295,6297,6303,6305,6307,6309],{},[1495,6271,2162],{"stretchy":2161},[1145,6273,6274,6276],{},[1148,6275,2657],{},[1152,6277,1176],{},[1495,6279,1885],{},[1152,6281,1176],{},[1495,6283,2181],{"stretchy":2161},[4163,6285,6286,6288,6290],{},[1148,6287,2695],{},[1152,6289,1176],{},[1152,6291,2639],{},[1495,6293,6294],{},"+",[1495,6296,2162],{"stretchy":2161},[1145,6298,6299,6301],{},[1148,6300,2657],{},[1152,6302,2639],{},[1495,6304,1885],{},[1152,6306,1176],{},[1495,6308,2181],{"stretchy":2161},[4163,6310,6311,6313,6315],{},[1148,6312,2695],{},[1152,6314,2639],{},[1152,6316,2639],{},[2770,6318,6319],{},[2749,6320,6321,6341],{},[1142,6322,6323,6329,6331,6337,6339],{},[1145,6324,6325,6327],{},[1148,6326,2657],{},[1152,6328,1176],{},[1495,6330,6294],{},[1145,6332,6333,6335],{},[1148,6334,2657],{},[1152,6336,2639],{},[1495,6338,1885],{},[1152,6340,2639],{},[1142,6342,6343,6353,6355],{},[2749,6344,6345,6347],{},[1152,6346,1176],{},[1145,6348,6349,6351],{},[1148,6350,2657],{},[1152,6352,1176],{},[1495,6354,6294],{},[2749,6356,6357,6359],{},[1152,6358,1176],{},[1145,6360,6361,6363],{},[1148,6362,2657],{},[1152,6364,2639],{},[1495,6366,2188],{"separator":1121},[3520,6368],{"width":3522},[4163,6370,6371,6373,6375],{},[1148,6372,1373],{},[1148,6374,1110],{},[1495,6376,6377],{},"∗",[1495,6379,1503],{},[1145,6381,6382,6384],{},[1148,6383,1373],{},[1148,6385,1110],{},[1495,6387,2162],{"stretchy":2161},[1145,6389,6390,6392],{},[1148,6391,2657],{},[1152,6393,1176],{},[1495,6395,6294],{},[1145,6397,6398,6400],{},[1148,6399,2657],{},[1152,6401,2639],{},[1495,6403,1885],{},[1152,6405,2639],{},[1495,6407,2181],{"stretchy":2161},[1156,6409,6410],{"encoding":1158},"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)",[1110,6412,6413,6414,6443],{},"se použije, pokud jsou rozptyly ",[1115,6415,6417],{"className":6416},[1133],[1135,6418,6419],{"xmlns":1137},[1139,6420,6421,6441],{},[1142,6422,6423,6431,6433],{},[4163,6424,6425,6427,6429],{},[1148,6426,2636],{},[1152,6428,1176],{},[1152,6430,2639],{},[1495,6432,2188],{"separator":1121},[4163,6434,6435,6437,6439],{},[1148,6436,2636],{},[1152,6438,2639],{},[1152,6440,2639],{},[1156,6442,5639],{"encoding":1158}," alespoň přibližně shodné; při rozdílných rozptylech",[1115,6445,6447],{"className":6446},[1133],[1135,6448,6449],{"xmlns":1137,"display":2151},[1139,6450,6451,6664],{},[1142,6452,6453,6459,6461,6525,6527,6529,6537,6539,6662],{},[1145,6454,6455,6457],{},[1148,6456,2088],{},[1152,6458,2639],{},[1495,6460,1503],{},[2749,6462,6463,6487],{},[1142,6464,6465,6475,6477],{},[1145,6466,6467,6473],{},[2671,6468,6469,6471],{"accent":1121},[1148,6470,2675],{},[1495,6472,2678],{},[1152,6474,1176],{},[1495,6476,1885],{},[1145,6478,6479,6485],{},[2671,6480,6481,6483],{"accent":1121},[1148,6482,2675],{},[1495,6484,2678],{},[1152,6486,2639],{},[2770,6488,6489],{},[1142,6490,6491,6499,6501,6507,6509,6517,6519],{},[4163,6492,6493,6495,6497],{},[1148,6494,2695],{},[1152,6496,1176],{},[1152,6498,2639],{},[1148,6500,3049],{"mathvariant":1599},[1145,6502,6503,6505],{},[1148,6504,2657],{},[1152,6506,1176],{},[1495,6508,6294],{},[4163,6510,6511,6513,6515],{},[1148,6512,2695],{},[1152,6514,2639],{},[1152,6516,2639],{},[1148,6518,3049],{"mathvariant":1599},[1145,6520,6521,6523],{},[1148,6522,2657],{},[1152,6524,2639],{},[1495,6526,2188],{"separator":1121},[3520,6528],{"width":3522},[4163,6530,6531,6533,6535],{},[1148,6532,1373],{},[1148,6534,1110],{},[1495,6536,6377],{},[1495,6538,1503],{},[2749,6540,6541,6622],{},[1142,6542,6543,6562,6568,6570,6576,6578,6580,6582,6584,6602,6608,6610,6616,6618,6620],{},[6544,6545,6546],"mstyle",{"scriptlevel":1154,"displaystyle":1121},[2749,6547,6548,6556],{},[4163,6549,6550,6552,6554],{},[1148,6551,2695],{},[1152,6553,1176],{},[1152,6555,2639],{},[1145,6557,6558,6560],{},[1148,6559,2657],{},[1152,6561,1176],{},[1145,6563,6564,6566],{},[1148,6565,1373],{},[1148,6567,1110],{},[1495,6569,2162],{"stretchy":2161},[1145,6571,6572,6574],{},[1148,6573,2657],{},[1152,6575,1176],{},[1495,6577,1885],{},[1152,6579,1176],{},[1495,6581,2181],{"stretchy":2161},[1495,6583,6294],{},[6544,6585,6586],{"scriptlevel":1154,"displaystyle":1121},[2749,6587,6588,6596],{},[4163,6589,6590,6592,6594],{},[1148,6591,2695],{},[1152,6593,2639],{},[1152,6595,2639],{},[1145,6597,6598,6600],{},[1148,6599,2657],{},[1152,6601,2639],{},[1145,6603,6604,6606],{},[1148,6605,1373],{},[1148,6607,1110],{},[1495,6609,2162],{"stretchy":2161},[1145,6611,6612,6614],{},[1148,6613,2657],{},[1152,6615,2639],{},[1495,6617,1885],{},[1152,6619,1176],{},[1495,6621,2181],{"stretchy":2161},[1142,6623,6624,6642,6644],{},[6544,6625,6626],{"scriptlevel":1154,"displaystyle":1121},[2749,6627,6628,6636],{},[4163,6629,6630,6632,6634],{},[1148,6631,2695],{},[1152,6633,1176],{},[1152,6635,2639],{},[1145,6637,6638,6640],{},[1148,6639,2657],{},[1152,6641,1176],{},[1495,6643,6294],{},[6544,6645,6646],{"scriptlevel":1154,"displaystyle":1121},[2749,6647,6648,6656],{},[4163,6649,6650,6652,6654],{},[1148,6651,2695],{},[1152,6653,2639],{},[1152,6655,2639],{},[1145,6657,6658,6660],{},[1148,6659,2657],{},[1152,6661,2639],{},[1148,6663,1335],{"mathvariant":1599},[1156,6665,6666],{"encoding":1158},"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}}.",[1532,6668,6669,6726],{},[1535,6670,6671],{},[1538,6672,6673,6692,6711],{},[1541,6674,6675],{},[1115,6676,6678],{"className":6677},[1133],[1135,6679,6680],{"xmlns":1137},[1139,6681,6682,6690],{},[1142,6683,6684],{},[1145,6685,6686,6688],{},[1148,6687,1150],{},[1152,6689,1154],{},[1156,6691,1159],{"encoding":1158},[1541,6693,6694],{},[1115,6695,6697],{"className":6696},[1133],[1135,6698,6699],{"xmlns":1137},[1139,6700,6701,6709],{},[1142,6702,6703],{},[1145,6704,6705,6707],{},[1148,6706,1150],{},[1152,6708,1176],{},[1156,6710,1179],{"encoding":1158},[1541,6712,2859,6713],{},[1115,6714,6716],{"className":6715},[1133],[1135,6717,6718],{"xmlns":1137},[1139,6719,6720,6724],{},[1142,6721,6722],{},[1148,6723,1192],{},[1156,6725,1192],{"encoding":1158},[1568,6727,6728,6812,6900],{},[1538,6729,6730,6758,6786],{},[1573,6731,6732],{},[1115,6733,6735],{"className":6734},[1133],[1135,6736,6737],{"xmlns":1137},[1139,6738,6739,6755],{},[1142,6740,6741,6747,6749],{},[1145,6742,6743,6745],{},[1148,6744,1500],{},[1152,6746,1176],{},[1495,6748,2519],{},[1145,6750,6751,6753],{},[1148,6752,1500],{},[1152,6754,2639],{},[1156,6756,6757],{"encoding":1158},"\\mu_1 \\le \\mu_2",[1573,6759,6760],{},[1115,6761,6763],{"className":6762},[1133],[1135,6764,6765],{"xmlns":1137},[1139,6766,6767,6783],{},[1142,6768,6769,6775,6777],{},[1145,6770,6771,6773],{},[1148,6772,1500],{},[1152,6774,1176],{},[1495,6776,1641],{},[1145,6778,6779,6781],{},[1148,6780,1500],{},[1152,6782,2639],{},[1156,6784,6785],{"encoding":1158},"\\mu_1 > \\mu_2",[1573,6787,6788],{},[1115,6789,6791],{"className":6790},[1133],[1135,6792,6793],{"xmlns":1137},[1139,6794,6795,6809],{},[1142,6796,6797,6799,6801],{},[1148,6798,1373],{},[1495,6800,2940],{},[4163,6802,6803,6805,6807],{},[1148,6804,1373],{},[1148,6806,1110],{},[1495,6808,6377],{},[1156,6810,6811],{"encoding":1158},"t \\ge t_p^*",[1538,6813,6814,6842,6870],{},[1573,6815,6816],{},[1115,6817,6819],{"className":6818},[1133],[1135,6820,6821],{"xmlns":1137},[1139,6822,6823,6839],{},[1142,6824,6825,6831,6833],{},[1145,6826,6827,6829],{},[1148,6828,1500],{},[1152,6830,1176],{},[1495,6832,1503],{},[1145,6834,6835,6837],{},[1148,6836,1500],{},[1152,6838,2639],{},[1156,6840,6841],{"encoding":1158},"\\mu_1 = \\mu_2",[1573,6843,6844],{},[1115,6845,6847],{"className":6846},[1133],[1135,6848,6849],{"xmlns":1137},[1139,6850,6851,6867],{},[1142,6852,6853,6859,6861],{},[1145,6854,6855,6857],{},[1148,6856,1500],{},[1152,6858,1176],{},[1495,6860,1600],{"mathvariant":1599},[1145,6862,6863,6865],{},[1148,6864,1500],{},[1152,6866,2639],{},[1156,6868,6869],{"encoding":1158},"\\mu_1 \\neq \\mu_2",[1573,6871,6872],{},[1115,6873,6875],{"className":6874},[1133],[1135,6876,6877],{"xmlns":1137},[1139,6878,6879,6897],{},[1142,6880,6881,6883,6885,6887,6889],{},[1495,6882,2172],{"stretchy":2161},[1148,6884,1373],{},[1495,6886,2172],{"stretchy":2161},[1495,6888,2940],{},[4163,6890,6891,6893,6895],{},[1148,6892,1373],{},[1148,6894,1110],{},[1495,6896,6377],{},[1156,6898,6899],{"encoding":1158},"\\lvert t \\rvert \\ge t_p^*",[1538,6901,6902,6930,6958],{},[1573,6903,6904],{},[1115,6905,6907],{"className":6906},[1133],[1135,6908,6909],{"xmlns":1137},[1139,6910,6911,6927],{},[1142,6912,6913,6919,6921],{},[1145,6914,6915,6917],{},[1148,6916,1500],{},[1152,6918,1176],{},[1495,6920,2940],{},[1145,6922,6923,6925],{},[1148,6924,1500],{},[1152,6926,2639],{},[1156,6928,6929],{"encoding":1158},"\\mu_1 \\ge \\mu_2",[1573,6931,6932],{},[1115,6933,6935],{"className":6934},[1133],[1135,6936,6937],{"xmlns":1137},[1139,6938,6939,6955],{},[1142,6940,6941,6947,6949],{},[1145,6942,6943,6945],{},[1148,6944,1500],{},[1152,6946,1176],{},[1495,6948,1682],{},[1145,6950,6951,6953],{},[1148,6952,1500],{},[1152,6954,2639],{},[1156,6956,6957],{"encoding":1158},"\\mu_1 \u003C \\mu_2",[1573,6959,6960],{},[1115,6961,6963],{"className":6962},[1133],[1135,6964,6965],{"xmlns":1137},[1139,6966,6967,6983],{},[1142,6968,6969,6971,6973,6975],{},[1148,6970,1373],{},[1495,6972,2519],{},[1495,6974,1885],{},[4163,6976,6977,6979,6981],{},[1148,6978,1373],{},[1148,6980,1110],{},[1495,6982,6377],{},[1156,6984,6985],{"encoding":1158},"t \\le -t_p^*",[1110,6987,6988,6989,6049,7007,1335],{},"Postup je dvoukrokový: nejprve F-test rozhodne o shodě rozptylů, pak se podle výsledku zvolí ",[1115,6990,6992],{"className":6991},[1133],[1135,6993,6994],{"xmlns":1137},[1139,6995,6996,7004],{},[1142,6997,6998],{},[1145,6999,7000,7002],{},[1148,7001,2088],{},[1152,7003,1176],{},[1156,7005,7006],{"encoding":1158},"T_1",[1115,7008,7010],{"className":7009},[1133],[1135,7011,7012],{"xmlns":1137},[1139,7013,7014,7022],{},[1142,7015,7016],{},[1145,7017,7018,7020],{},[1148,7019,2088],{},[1152,7021,2639],{},[1156,7023,7024],{"encoding":1158},"T_2",[1110,7026,7027],{},[1971,7028],{"alt":7029,"className":7030,"src":7031},"mask-th-f-kriticky-obor",[1343,1975],"\u002Fwiki-assets\u002Fmask-th-f-kriticky-obor.png",[1103,7033,7035,7042,7197,7278,7408,7446,7519,7662],{"className":7034,"dataCallout":3323},[1106,3322],[1110,7036,7038,7041],{"className":7037},[1113],[1115,7039],{"className":7040,"ariaHidden":1121},[1118,3330,1120],"Příklad: Porovnání dvou dodavatelů součástek",[1110,7043,7044,7045,1195,7067,7094,7095,7120,7121,1195,7144,7094,7171,7196],{},"Pevnost plastových dílů: dodavatel A (",[1115,7046,7048],{"className":7047},[1133],[1135,7049,7050],{"xmlns":1137},[1139,7051,7052,7064],{},[1142,7053,7054,7060,7062],{},[1145,7055,7056,7058],{},[1148,7057,2657],{},[1152,7059,1176],{},[1495,7061,1503],{},[1152,7063,4717],{},[1156,7065,7066],{"encoding":1158},"n_1 = 10",[1115,7068,7070],{"className":7069},[1133],[1135,7071,7072],{"xmlns":1137},[1139,7073,7074,7091],{},[1142,7075,7076,7086,7088],{},[1145,7077,7078,7084],{},[2671,7079,7080,7082],{"accent":1121},[1148,7081,2675],{},[1495,7083,2678],{},[1152,7085,1176],{},[1495,7087,1503],{},[1152,7089,7090],{},"82",[1156,7092,7093],{"encoding":1158},"\\bar{x}_1 = 82"," MPa, ",[1115,7096,7098],{"className":7097},[1133],[1135,7099,7100],{"xmlns":1137},[1139,7101,7102,7117],{},[1142,7103,7104,7112,7114],{},[4163,7105,7106,7108,7110],{},[1148,7107,2695],{},[1152,7109,1176],{},[1152,7111,2639],{},[1495,7113,1503],{},[1152,7115,7116],{},"25",[1156,7118,7119],{"encoding":1158},"s_1^2 = 25","), dodavatel B (",[1115,7122,7124],{"className":7123},[1133],[1135,7125,7126],{"xmlns":1137},[1139,7127,7128,7141],{},[1142,7129,7130,7136,7138],{},[1145,7131,7132,7134],{},[1148,7133,2657],{},[1152,7135,2639],{},[1495,7137,1503],{},[1152,7139,7140],{},"12",[1156,7142,7143],{"encoding":1158},"n_2 = 12",[1115,7145,7147],{"className":7146},[1133],[1135,7148,7149],{"xmlns":1137},[1139,7150,7151,7168],{},[1142,7152,7153,7163,7165],{},[1145,7154,7155,7161],{},[2671,7156,7157,7159],{"accent":1121},[1148,7158,2675],{},[1495,7160,2678],{},[1152,7162,2639],{},[1495,7164,1503],{},[1152,7166,7167],{},"75",[1156,7169,7170],{"encoding":1158},"\\bar{x}_2 = 75",[1115,7172,7174],{"className":7173},[1133],[1135,7175,7176],{"xmlns":1137},[1139,7177,7178,7193],{},[1142,7179,7180,7188,7190],{},[4163,7181,7182,7184,7186],{},[1148,7183,2695],{},[1152,7185,2639],{},[1152,7187,2639],{},[1495,7189,1503],{},[1152,7191,7192],{},"16",[1156,7194,7195],{"encoding":1158},"s_2^2 = 16","). Předpokládá se normalita obou rozdělení.",[1110,7198,7199,1953,7202,1195,7240,1335],{},[1399,7200,7201],{},"Krok 1 — F-test rozptylů.",[1115,7203,7205],{"className":7204},[1133],[1135,7206,7207],{"xmlns":1137},[1139,7208,7209,7237],{},[1142,7210,7211,7217,7219,7227,7229],{},[1145,7212,7213,7215],{},[1148,7214,1150],{},[1152,7216,1154],{},[1495,7218,1497],{},[4163,7220,7221,7223,7225],{},[1148,7222,2636],{},[1152,7224,1176],{},[1152,7226,2639],{},[1495,7228,1503],{},[4163,7230,7231,7233,7235],{},[1148,7232,2636],{},[1152,7234,2639],{},[1152,7236,2639],{},[1156,7238,7239],{"encoding":1158},"H_0: \\sigma_1^2 = \\sigma_2^2",[1115,7241,7243],{"className":7242},[1133],[1135,7244,7245],{"xmlns":1137},[1139,7246,7247,7275],{},[1142,7248,7249,7255,7257,7265,7267],{},[1145,7250,7251,7253],{},[1148,7252,1150],{},[1152,7254,1176],{},[1495,7256,1497],{},[4163,7258,7259,7261,7263],{},[1148,7260,2636],{},[1152,7262,1176],{},[1152,7264,2639],{},[1495,7266,1600],{"mathvariant":1599},[4163,7268,7269,7271,7273],{},[1148,7270,2636],{},[1152,7272,2639],{},[1152,7274,2639],{},[1156,7276,7277],{"encoding":1158},"H_1: \\sigma_1^2 \\neq \\sigma_2^2",[1110,7279,7280],{},[1115,7281,7283],{"className":7282},[1133],[1135,7284,7285],{"xmlns":1137},[1139,7286,7287,7405],{},[1142,7288,7289,7291,7293,7299,7301,7304,7306,7308,7310,7312,7314,7316,7318,7331,7333,7335,7337,7340,7342,7345,7348,7350,7352,7354,7367,7369,7371,7373,7375,7377,7379,7381,7383,7385,7387,7390,7392,7394,7396,7398,7400,7403],{},[1148,7290,1387],{},[1495,7292,1503],{},[2749,7294,7295,7297],{},[1152,7296,7116],{},[1152,7298,7192],{},[1495,7300,1503],{},[1152,7302,7303],{},"1,5625",[1495,7305,2188],{"separator":1121},[3520,7307],{"width":3522},[1148,7309,1192],{},[1495,7311,1503],{},[1495,7313,3529],{"stretchy":2161},[1148,7315,1387],{},[1495,7317,2519],{},[1145,7319,7320,7322],{},[1148,7321,1387],{},[1142,7323,7324,7326,7328],{},[1152,7325,1154],{},[1495,7327,2188],{"separator":1121},[1152,7329,7330],{},"025",[1495,7332,2162],{"stretchy":2161},[1152,7334,4972],{},[1495,7336,2188],{"separator":1121},[1152,7338,7339],{},"11",[1495,7341,2181],{"stretchy":2161},[2358,7343,7344],{},"  ",[2358,7346,7347],{},"nebo",[2358,7349,7344],{},[1148,7351,1387],{},[1495,7353,2940],{},[1145,7355,7356,7358],{},[1148,7357,1387],{},[1142,7359,7360,7362,7364],{},[1152,7361,1154],{},[1495,7363,2188],{"separator":1121},[1152,7365,7366],{},"975",[1495,7368,2162],{"stretchy":2161},[1152,7370,4972],{},[1495,7372,2188],{"separator":1121},[1152,7374,7339],{},[1495,7376,2181],{"stretchy":2161},[1495,7378,3558],{"stretchy":2161},[1495,7380,1503],{},[1495,7382,3529],{"stretchy":2161},[1148,7384,1387],{},[1495,7386,2519],{},[1152,7388,7389],{},"0,256",[2358,7391,7344],{},[2358,7393,7347],{},[2358,7395,7344],{},[1148,7397,1387],{},[1495,7399,2940],{},[1152,7401,7402],{},"3,588",[1495,7404,3558],{"stretchy":2161},[1156,7406,7407],{"encoding":1158},"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\\}",[1110,7409,7410,7428,7429,1335],{},[1115,7411,7413],{"className":7412},[1133],[1135,7414,7415],{"xmlns":1137},[1139,7416,7417,7425],{},[1142,7418,7419,7421,7423],{},[1148,7420,1387],{},[1495,7422,2401],{"mathvariant":1599},[1148,7424,1192],{},[1156,7426,7427],{"encoding":1158},"F \\notin W",", rozptyly nezamítáme jako shodné — pro t-test se použije ",[1115,7430,7432],{"className":7431},[1133],[1135,7433,7434],{"xmlns":1137},[1139,7435,7436,7444],{},[1142,7437,7438],{},[1145,7439,7440,7442],{},[1148,7441,2088],{},[1152,7443,1176],{},[1156,7445,7006],{"encoding":1158},[1110,7447,7448,1953,7451,1195,7485,1335],{},[1399,7449,7450],{},"Krok 2 — dvouvýběrový t-test středních hodnot.",[1115,7452,7454],{"className":7453},[1133],[1135,7455,7456],{"xmlns":1137},[1139,7457,7458,7482],{},[1142,7459,7460,7466,7468,7474,7476],{},[1145,7461,7462,7464],{},[1148,7463,1150],{},[1152,7465,1154],{},[1495,7467,1497],{},[1145,7469,7470,7472],{},[1148,7471,1500],{},[1152,7473,1176],{},[1495,7475,1503],{},[1145,7477,7478,7480],{},[1148,7479,1500],{},[1152,7481,2639],{},[1156,7483,7484],{"encoding":1158},"H_0: \\mu_1 = \\mu_2",[1115,7486,7488],{"className":7487},[1133],[1135,7489,7490],{"xmlns":1137},[1139,7491,7492,7516],{},[1142,7493,7494,7500,7502,7508,7510],{},[1145,7495,7496,7498],{},[1148,7497,1150],{},[1152,7499,1176],{},[1495,7501,1497],{},[1145,7503,7504,7506],{},[1148,7505,1500],{},[1152,7507,1176],{},[1495,7509,1600],{"mathvariant":1599},[1145,7511,7512,7514],{},[1148,7513,1500],{},[1152,7515,2639],{},[1156,7517,7518],{"encoding":1158},"H_1: \\mu_1 \\neq \\mu_2",[1110,7520,7521],{},[1115,7522,7524],{"className":7523},[1133],[1135,7525,7526],{"xmlns":1137},[1139,7527,7528,7659],{},[1142,7529,7530,7538,7540,7561,7563,7566,7568,7570,7572,7574,7588,7598,7601,7604,7606,7608,7610,7612,7614,7616,7618,7620,7622,7634,7636,7638,7640,7642,7644,7646,7648,7650,7652,7654,7657],{},[4163,7531,7532,7534,7536],{},[1148,7533,2695],{},[1148,7535,1110],{},[1152,7537,2639],{},[1495,7539,1503],{},[2749,7541,7542,7559],{},[1142,7543,7544,7546,7549,7551,7553,7555,7557],{},[1152,7545,4972],{},[1495,7547,7548],{},"⋅",[1152,7550,7116],{},[1495,7552,6294],{},[1152,7554,7339],{},[1495,7556,7548],{},[1152,7558,7192],{},[1152,7560,3374],{},[1495,7562,1503],{},[1152,7564,7565],{},"20,05",[1495,7567,2188],{"separator":1121},[3520,7569],{"width":3522},[1148,7571,1373],{},[1495,7573,1503],{},[2749,7575,7576,7584],{},[1142,7577,7578,7580,7582],{},[1152,7579,7090],{},[1495,7581,1885],{},[1152,7583,7167],{},[2770,7585,7586],{},[1152,7587,7565],{},[2770,7589,7590],{},[2749,7591,7592,7595],{},[1152,7593,7594],{},"120",[1152,7596,7597],{},"22",[1495,7599,7600],{},"≈",[1152,7602,7603],{},"3,651",[1495,7605,2188],{"separator":1121},[3520,7607],{"width":3522},[1148,7609,1192],{},[1495,7611,1503],{},[1495,7613,3529],{"stretchy":2161},[1495,7615,2172],{"stretchy":2161},[1148,7617,1373],{},[1495,7619,2172],{"stretchy":2161},[1495,7621,2940],{},[1145,7623,7624,7626],{},[1148,7625,1373],{},[1142,7627,7628,7630,7632],{},[1152,7629,1154],{},[1495,7631,2188],{"separator":1121},[1152,7633,7366],{},[1495,7635,2162],{"stretchy":2161},[1152,7637,3374],{},[1495,7639,2181],{"stretchy":2161},[1495,7641,3558],{"stretchy":2161},[1495,7643,1503],{},[1495,7645,3529],{"stretchy":2161},[1495,7647,2172],{"stretchy":2161},[1148,7649,1373],{},[1495,7651,2172],{"stretchy":2161},[1495,7653,2940],{},[1152,7655,7656],{},"2,086",[1495,7658,3558],{"stretchy":2161},[1156,7660,7661],{"encoding":1158},"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\\}",[1110,7663,7664,3598,7681,7698],{},[1115,7665,7667],{"className":7666},[1133],[1135,7668,7669],{"xmlns":1137},[1139,7670,7671,7679],{},[1142,7672,7673,7675,7677],{},[1148,7674,1373],{},[1495,7676,2167],{},[1148,7678,1192],{},[1156,7680,3597],{"encoding":1158},[1115,7682,7684],{"className":7683},[1133],[1135,7685,7686],{"xmlns":1137},[1139,7687,7688,7696],{},[1142,7689,7690],{},[1145,7691,7692,7694],{},[1148,7693,1150],{},[1152,7695,1154],{},[1156,7697,1159],{"encoding":1158},": pevnost součástek od obou dodavatelů se statisticky významně liší.",[3166,7700,7702],{"className":3168,"code":7701,"language":71,"meta":3170,"style":3170},"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",[3161,7703,7704,7723,7743,7759,7794,7826,7831,7836],{"__ignoreMap":3170},[1115,7705,7706,7709,7711,7714,7716,7719,7721],{"class":3175,"line":10},[1115,7707,7708],{"class":3178},"s1",[1115,7710,3182],{"class":3181},[1115,7712,7713],{"class":3192}," 25",[1115,7715,2546],{"class":3189},[1115,7717,7718],{"class":3178},"n1",[1115,7720,3182],{"class":3181},[1115,7722,5063],{"class":3192},[1115,7724,7725,7728,7730,7733,7735,7738,7740],{"class":3175,"line":27},[1115,7726,7727],{"class":3178},"s2",[1115,7729,3182],{"class":3181},[1115,7731,7732],{"class":3192}," 16",[1115,7734,2546],{"class":3189},[1115,7736,7737],{"class":3178},"n2",[1115,7739,3182],{"class":3181},[1115,7741,7742],{"class":3192}," 12\n",[1115,7744,7745,7748,7750,7753,7756],{"class":3175,"line":148},[1115,7746,7747],{"class":3178},"Fstat",[1115,7749,3182],{"class":3181},[1115,7751,7752],{"class":3178}," s1",[1115,7754,7755],{"class":3181}," \u002F",[1115,7757,7758],{"class":3178}," s2\n",[1115,7760,7761,7764,7766,7769,7771,7774,7776,7779,7781,7783,7785,7788,7790,7792],{"class":3175,"line":111},[1115,7762,7763],{"class":3178},"F_dolni",[1115,7765,3182],{"class":3181},[1115,7767,7768],{"class":3185}," qf",[1115,7770,2162],{"class":3189},[1115,7772,7773],{"class":3192},"0.025",[1115,7775,2188],{"class":3181},[1115,7777,7778],{"class":3178}," n1",[1115,7780,3682],{"class":3181},[1115,7782,3735],{"class":3192},[1115,7784,2188],{"class":3181},[1115,7786,7787],{"class":3178}," n2",[1115,7789,3682],{"class":3181},[1115,7791,3735],{"class":3192},[1115,7793,3235],{"class":3189},[1115,7795,7796,7799,7801,7803,7805,7808,7810,7812,7814,7816,7818,7820,7822,7824],{"class":3175,"line":96},[1115,7797,7798],{"class":3178},"F_horni",[1115,7800,3182],{"class":3181},[1115,7802,7768],{"class":3185},[1115,7804,2162],{"class":3189},[1115,7806,7807],{"class":3192},"0.975",[1115,7809,2188],{"class":3181},[1115,7811,7778],{"class":3178},[1115,7813,3682],{"class":3181},[1115,7815,3735],{"class":3192},[1115,7817,2188],{"class":3181},[1115,7819,7787],{"class":3178},[1115,7821,3682],{"class":3181},[1115,7823,3735],{"class":3192},[1115,7825,3235],{"class":3189},[1115,7827,7828],{"class":3175,"line":89},[1115,7829,7830],{"class":3178},"Fstat\n",[1115,7832,7833],{"class":3175,"line":82},[1115,7834,7835],{"class":3178},"F_dolni\n",[1115,7837,7838],{"class":3175,"line":75},[1115,7839,7840],{"class":3178},"F_horni\n",[3166,7842,7845],{"className":7843,"code":7844,"language":3274,"meta":3170},[3272],"[1] 1.5625\n[1] 0.2556189\n[1] 3.587899\n",[3161,7846,7844],{"__ignoreMap":3170},[3166,7848,7850],{"className":3168,"code":7849,"language":71,"meta":3170,"style":3170},"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",[3161,7851,7852,7912,7964,7994,7999,8003],{"__ignoreMap":3170},[1115,7853,7854,7857,7859,7862,7864,7866,7868,7870,7873,7875,7878,7880,7882,7884,7886,7888,7890,7893,7895,7897,7899,7901,7903,7905,7907,7910],{"class":3175,"line":10},[1115,7855,7856],{"class":3178},"sp2",[1115,7858,3182],{"class":3181},[1115,7860,7861],{"class":3189}," ((",[1115,7863,7718],{"class":3178},[1115,7865,3682],{"class":3181},[1115,7867,3735],{"class":3192},[1115,7869,3688],{"class":3189},[1115,7871,7872],{"class":3181},"*",[1115,7874,7752],{"class":3178},[1115,7876,7877],{"class":3181}," +",[1115,7879,3677],{"class":3189},[1115,7881,7737],{"class":3178},[1115,7883,3682],{"class":3181},[1115,7885,3735],{"class":3192},[1115,7887,3688],{"class":3189},[1115,7889,7872],{"class":3181},[1115,7891,7892],{"class":3178}," s2",[1115,7894,3688],{"class":3189},[1115,7896,3049],{"class":3181},[1115,7898,3677],{"class":3189},[1115,7900,7718],{"class":3178},[1115,7902,7877],{"class":3181},[1115,7904,7787],{"class":3178},[1115,7906,3682],{"class":3181},[1115,7908,7909],{"class":3192}," 2",[1115,7911,3235],{"class":3189},[1115,7913,7914,7916,7918,7920,7922,7924,7927,7929,7931,7933,7935,7937,7939,7941,7943,7945,7947,7949,7951,7953,7955,7957,7959,7961],{"class":3175,"line":27},[1115,7915,1373],{"class":3178},[1115,7917,3182],{"class":3181},[1115,7919,3677],{"class":3189},[1115,7921,7090],{"class":3192},[1115,7923,3682],{"class":3181},[1115,7925,7926],{"class":3192}," 75",[1115,7928,3688],{"class":3189},[1115,7930,3049],{"class":3181},[1115,7932,3699],{"class":3185},[1115,7934,2162],{"class":3189},[1115,7936,7856],{"class":3178},[1115,7938,3688],{"class":3189},[1115,7940,7872],{"class":3181},[1115,7942,3699],{"class":3185},[1115,7944,2162],{"class":3189},[1115,7946,7718],{"class":3178},[1115,7948,3696],{"class":3181},[1115,7950,7787],{"class":3178},[1115,7952,7755],{"class":3181},[1115,7954,3677],{"class":3189},[1115,7956,7718],{"class":3178},[1115,7958,7877],{"class":3181},[1115,7960,7787],{"class":3178},[1115,7962,7963],{"class":3189},"))\n",[1115,7965,7966,7968,7970,7972,7974,7976,7978,7980,7982,7984,7986,7988,7990,7992],{"class":3175,"line":148},[1115,7967,3710],{"class":3178},[1115,7969,3182],{"class":3181},[1115,7971,3715],{"class":3185},[1115,7973,2162],{"class":3189},[1115,7975,7807],{"class":3192},[1115,7977,2188],{"class":3181},[1115,7979,3725],{"class":3178},[1115,7981,3252],{"class":3181},[1115,7983,7778],{"class":3178},[1115,7985,7877],{"class":3181},[1115,7987,7787],{"class":3178},[1115,7989,3682],{"class":3181},[1115,7991,7909],{"class":3192},[1115,7993,3235],{"class":3189},[1115,7995,7996],{"class":3175,"line":111},[1115,7997,7998],{"class":3178},"sp2\n",[1115,8000,8001],{"class":3175,"line":96},[1115,8002,3742],{"class":3178},[1115,8004,8005],{"class":3175,"line":89},[1115,8006,3747],{"class":3178},[3166,8008,8011],{"className":8009,"code":8010,"language":3274,"meta":3170},[3272],"[1] 20.05\n[1] 3.65107\n[1] 2.085963\n",[3161,8012,8010],{"__ignoreMap":3170},[1110,8014,8015],{},[1971,8016],{"alt":8017,"className":8018,"src":8019},"mask-th-t-dvoustranny",[1343,1975],"\u002Fwiki-assets\u002Fmask-th-t-dvoustranny.png",[1110,8021,8022,8023,2261,8026,8028,8029,8032,8033,2261,8050,2324,8067,8070,8071,8074],{},"V R provede obě kroky ",[3161,8024,8025],{},"var.test()",[3161,8027,3163],{},". Parametr ",[3161,8030,8031],{},"var.equal"," nastavuje volbu mezi ",[1115,8034,8036],{"className":8035},[1133],[1135,8037,8038],{"xmlns":1137},[1139,8039,8040,8048],{},[1142,8041,8042],{},[1145,8043,8044,8046],{},[1148,8045,2088],{},[1152,8047,1176],{},[1156,8049,7006],{"encoding":1158},[1115,8051,8053],{"className":8052},[1133],[1135,8054,8055],{"xmlns":1137},[1139,8056,8057,8065],{},[1142,8058,8059],{},[1145,8060,8061,8063],{},[1148,8062,2088],{},[1152,8064,2639],{},[1156,8066,7024],{"encoding":1158},[3161,8068,8069],{},"TRUE"," znamená předpoklad shodných rozptylů (podle výsledku F-testu), ",[3161,8072,8073],{},"FALSE"," předpoklad rozdílných rozptylů.",[1110,8076,8077,8080],{},[1399,8078,8079],{},"Kabely A\u002FB."," Pevnost v tahu dvou výrobců (MPa, 12 kabelů od každého):",[3166,8082,8084],{"className":3168,"code":8083,"language":71,"meta":3170,"style":3170},"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",[3161,8085,8086,8155,8219,8235],{"__ignoreMap":3170},[1115,8087,8088,8091,8093,8095,8097,8100,8102,8105,8107,8110,8112,8115,8117,8120,8122,8125,8127,8130,8132,8135,8137,8140,8142,8144,8146,8149,8151,8153],{"class":3175,"line":10},[1115,8089,8090],{"class":3178},"A",[1115,8092,3182],{"class":3181},[1115,8094,3186],{"class":3185},[1115,8096,2162],{"class":3189},[1115,8098,8099],{"class":3192},"313",[1115,8101,2188],{"class":3181},[1115,8103,8104],{"class":3192}," 299",[1115,8106,2188],{"class":3181},[1115,8108,8109],{"class":3192}," 315",[1115,8111,2188],{"class":3181},[1115,8113,8114],{"class":3192}," 312",[1115,8116,2188],{"class":3181},[1115,8118,8119],{"class":3192}," 310",[1115,8121,2188],{"class":3181},[1115,8123,8124],{"class":3192}," 308",[1115,8126,2188],{"class":3181},[1115,8128,8129],{"class":3192}," 314",[1115,8131,2188],{"class":3181},[1115,8133,8134],{"class":3192}," 313",[1115,8136,2188],{"class":3181},[1115,8138,8139],{"class":3192}," 305",[1115,8141,2188],{"class":3181},[1115,8143,8119],{"class":3192},[1115,8145,2188],{"class":3181},[1115,8147,8148],{"class":3192}," 309",[1115,8150,2188],{"class":3181},[1115,8152,8129],{"class":3192},[1115,8154,3235],{"class":3189},[1115,8156,8157,8160,8162,8164,8166,8169,8171,8174,8176,8178,8180,8182,8184,8187,8189,8192,8194,8196,8198,8200,8202,8204,8206,8209,8211,8213,8215,8217],{"class":3175,"line":27},[1115,8158,8159],{"class":3178},"B",[1115,8161,3182],{"class":3181},[1115,8163,3186],{"class":3185},[1115,8165,2162],{"class":3189},[1115,8167,8168],{"class":3192},"307",[1115,8170,2188],{"class":3181},[1115,8172,8173],{"class":3192}," 322",[1115,8175,2188],{"class":3181},[1115,8177,8134],{"class":3192},[1115,8179,2188],{"class":3181},[1115,8181,8134],{"class":3192},[1115,8183,2188],{"class":3181},[1115,8185,8186],{"class":3192}," 311",[1115,8188,2188],{"class":3181},[1115,8190,8191],{"class":3192}," 316",[1115,8193,2188],{"class":3181},[1115,8195,8109],{"class":3192},[1115,8197,2188],{"class":3181},[1115,8199,8129],{"class":3192},[1115,8201,2188],{"class":3181},[1115,8203,8124],{"class":3192},[1115,8205,2188],{"class":3181},[1115,8207,8208],{"class":3192}," 319",[1115,8210,2188],{"class":3181},[1115,8212,8134],{"class":3192},[1115,8214,2188],{"class":3181},[1115,8216,8114],{"class":3192},[1115,8218,3235],{"class":3189},[1115,8220,8221,8224,8226,8228,8230,8233],{"class":3175,"line":148},[1115,8222,8223],{"class":3185},"var.test",[1115,8225,2162],{"class":3189},[1115,8227,8090],{"class":3178},[1115,8229,2188],{"class":3181},[1115,8231,8232],{"class":3178}," B",[1115,8234,3235],{"class":3189},[1115,8236,8237,8239,8241,8243,8245,8247,8249,8252,8254,8256],{"class":3175,"line":111},[1115,8238,3240],{"class":3185},[1115,8240,2162],{"class":3189},[1115,8242,8090],{"class":3178},[1115,8244,2188],{"class":3181},[1115,8246,8232],{"class":3178},[1115,8248,2188],{"class":3181},[1115,8250,8251],{"class":3178}," var.equal",[1115,8253,3252],{"class":3181},[1115,8255,5282],{"class":3192},[1115,8257,3235],{"class":3189},[3166,8259,8262],{"className":8260,"code":8261,"language":3274,"meta":3170},[3272],"    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",[3161,8263,8261],{"__ignoreMap":3170},[1110,8265,8266,8267,8286,8287,8290,8291,8310,8311,8328],{},"F-test shodu rozptylů nezamítá (",[1115,8268,8270],{"className":8269},[1133],[1135,8271,8272],{"xmlns":1137},[1139,8273,8274,8283],{},[1142,8275,8276,8278,8280],{},[1148,8277,1110],{},[1495,8279,1503],{},[1152,8281,8282],{},"0,7776",[1156,8284,8285],{"encoding":1158},"p = 0{,}7776","), proto ",[3161,8288,8289],{},"var.equal = TRUE",". Výsledný t-test dává ",[1115,8292,8294],{"className":8293},[1133],[1135,8295,8296],{"xmlns":1137},[1139,8297,8298,8307],{},[1142,8299,8300,8302,8304],{},[1148,8301,1110],{},[1495,8303,1503],{},[1152,8305,8306],{},"0,06932",[1156,8308,8309],{"encoding":1158},"p = 0{,}06932"," — na hladině 5 % se ",[1115,8312,8314],{"className":8313},[1133],[1135,8315,8316],{"xmlns":1137},[1139,8317,8318,8326],{},[1142,8319,8320],{},[1145,8321,8322,8324],{},[1148,8323,1150],{},[1152,8325,1154],{},[1156,8327,1159],{"encoding":1158}," nezamítá, ale hodnota je těsně nad hranicí.",[1110,8330,8331],{},[1399,8332,8333],{},"Výšky chlapců a dívek v páté třídě:",[3166,8335,8337],{"className":3168,"code":8336,"language":71,"meta":3170,"style":3170},"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",[3161,8338,8339,8422,8486,8501],{"__ignoreMap":3170},[1115,8340,8341,8344,8346,8348,8350,8353,8355,8358,8360,8363,8365,8368,8370,8373,8375,8378,8380,8383,8385,8388,8390,8392,8394,8396,8398,8401,8403,8406,8408,8411,8413,8415,8417,8420],{"class":3175,"line":10},[1115,8342,8343],{"class":3178},"boys",[1115,8345,3182],{"class":3181},[1115,8347,3186],{"class":3185},[1115,8349,2162],{"class":3189},[1115,8351,8352],{"class":3192},"130",[1115,8354,2188],{"class":3181},[1115,8356,8357],{"class":3192}," 140",[1115,8359,2188],{"class":3181},[1115,8361,8362],{"class":3192}," 136",[1115,8364,2188],{"class":3181},[1115,8366,8367],{"class":3192}," 141",[1115,8369,2188],{"class":3181},[1115,8371,8372],{"class":3192}," 139",[1115,8374,2188],{"class":3181},[1115,8376,8377],{"class":3192}," 133",[1115,8379,2188],{"class":3181},[1115,8381,8382],{"class":3192}," 149",[1115,8384,2188],{"class":3181},[1115,8386,8387],{"class":3192}," 151",[1115,8389,2188],{"class":3181},[1115,8391,8372],{"class":3192},[1115,8393,2188],{"class":3181},[1115,8395,8362],{"class":3192},[1115,8397,2188],{"class":3181},[1115,8399,8400],{"class":3192}," 138",[1115,8402,2188],{"class":3181},[1115,8404,8405],{"class":3192}," 142",[1115,8407,2188],{"class":3181},[1115,8409,8410],{"class":3192}," 127",[1115,8412,2188],{"class":3181},[1115,8414,8372],{"class":3192},[1115,8416,2188],{"class":3181},[1115,8418,8419],{"class":3192}," 147",[1115,8421,3235],{"class":3189},[1115,8423,8424,8427,8429,8431,8433,8436,8438,8440,8442,8445,8447,8450,8452,8455,8457,8459,8461,8463,8465,8467,8469,8471,8473,8476,8478,8480,8482,8484],{"class":3175,"line":27},[1115,8425,8426],{"class":3178},"girls",[1115,8428,3182],{"class":3181},[1115,8430,3186],{"class":3185},[1115,8432,2162],{"class":3189},[1115,8434,8435],{"class":3192},"135",[1115,8437,2188],{"class":3181},[1115,8439,8367],{"class":3192},[1115,8441,2188],{"class":3181},[1115,8443,8444],{"class":3192}," 143",[1115,8446,2188],{"class":3181},[1115,8448,8449],{"class":3192}," 132",[1115,8451,2188],{"class":3181},[1115,8453,8454],{"class":3192}," 146",[1115,8456,2188],{"class":3181},[1115,8458,8454],{"class":3192},[1115,8460,2188],{"class":3181},[1115,8462,8387],{"class":3192},[1115,8464,2188],{"class":3181},[1115,8466,8367],{"class":3192},[1115,8468,2188],{"class":3181},[1115,8470,8367],{"class":3192},[1115,8472,2188],{"class":3181},[1115,8474,8475],{"class":3192}," 131",[1115,8477,2188],{"class":3181},[1115,8479,8405],{"class":3192},[1115,8481,2188],{"class":3181},[1115,8483,8367],{"class":3192},[1115,8485,3235],{"class":3189},[1115,8487,8488,8490,8492,8494,8496,8499],{"class":3175,"line":148},[1115,8489,8223],{"class":3185},[1115,8491,2162],{"class":3189},[1115,8493,8343],{"class":3178},[1115,8495,2188],{"class":3181},[1115,8497,8498],{"class":3178}," girls",[1115,8500,3235],{"class":3189},[1115,8502,8503,8505,8507,8509,8511,8513,8515,8517,8519,8521],{"class":3175,"line":111},[1115,8504,3240],{"class":3185},[1115,8506,2162],{"class":3189},[1115,8508,8343],{"class":3178},[1115,8510,2188],{"class":3181},[1115,8512,8498],{"class":3178},[1115,8514,2188],{"class":3181},[1115,8516,8251],{"class":3178},[1115,8518,3252],{"class":3181},[1115,8520,5282],{"class":3192},[1115,8522,3235],{"class":3189},[3166,8524,8527],{"className":8525,"code":8526,"language":3274,"meta":3170},[3272],"    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",[3161,8528,8526],{"__ignoreMap":3170},[1110,8530,8266,8531,8550,8551,8553,8554,8573],{},[1115,8532,8534],{"className":8533},[1133],[1135,8535,8536],{"xmlns":1137},[1139,8537,8538,8547],{},[1142,8539,8540,8542,8544],{},[1148,8541,1110],{},[1495,8543,1503],{},[1152,8545,8546],{},"0,6977",[1156,8548,8549],{"encoding":1158},"p = 0{,}6977","), t-test s ",[3161,8552,8289],{}," dává ",[1115,8555,8557],{"className":8556},[1133],[1135,8558,8559],{"xmlns":1137},[1139,8560,8561,8570],{},[1142,8562,8563,8565,8567],{},[1148,8564,1110],{},[1495,8566,1503],{},[1152,8568,8569],{},"0,4883",[1156,8571,8572],{"encoding":1158},"p = 0{,}4883",": na hladině 5 % se rozdíl průměrných výšek chlapců a dívek neprokázal.",[1392,8575,8577],{"id":8576},"testy-dobré-shody-a-normalita","Testy dobré shody a normalita",[1110,8579,8580],{},"Testy dobré shody ověřují, zda datový soubor pochází ze základního souboru s určitým typem rozdělení (normální, exponenciální apod.).",[1695,8582,8584],{"id":8583},"kolmogorovův-smirnovův-test","Kolmogorovův-Smirnovův test",[1110,8586,8587,8588,8612,8613,8633],{},"Univerzální test pro spojitá rozdělení. Porovnává empirickou distribuční funkci ",[1115,8589,8591],{"className":8590},[1133],[1135,8592,8593],{"xmlns":1137},[1139,8594,8595,8609],{},[1142,8596,8597,8603,8605,8607],{},[1145,8598,8599,8601],{},[1148,8600,1387],{},[1148,8602,2657],{},[1495,8604,2162],{"stretchy":2161},[1148,8606,2675],{},[1495,8608,2181],{"stretchy":2161},[1156,8610,8611],{"encoding":1158},"F_n(x)"," s teoretickou distribuční funkcí ",[1115,8614,8616],{"className":8615},[1133],[1135,8617,8618],{"xmlns":1137},[1139,8619,8620,8630],{},[1142,8621,8622,8624,8626,8628],{},[1148,8623,1387],{},[1495,8625,2162],{"stretchy":2161},[1148,8627,2675],{},[1495,8629,2181],{"stretchy":2161},[1156,8631,8632],{"encoding":1158},"F(x)"," testovaného rozdělení.",[1124,8635,8636,8699,8719,8776],{},[1127,8637,8638,8655,8656,2261,8679,8698],{},[1115,8639,8641],{"className":8640},[1133],[1135,8642,8643],{"xmlns":1137},[1139,8644,8645,8653],{},[1142,8646,8647],{},[1145,8648,8649,8651],{},[1148,8650,1150],{},[1152,8652,1154],{},[1156,8654,1159],{"encoding":1158},": odchylky mezi ",[1115,8657,8659],{"className":8658},[1133],[1135,8660,8661],{"xmlns":1137},[1139,8662,8663,8677],{},[1142,8664,8665,8671,8673,8675],{},[1145,8666,8667,8669],{},[1148,8668,1387],{},[1148,8670,2657],{},[1495,8672,2162],{"stretchy":2161},[1148,8674,2675],{},[1495,8676,2181],{"stretchy":2161},[1156,8678,8611],{"encoding":1158},[1115,8680,8682],{"className":8681},[1133],[1135,8683,8684],{"xmlns":1137},[1139,8685,8686,8696],{},[1142,8687,8688,8690,8692,8694],{},[1148,8689,1387],{},[1495,8691,2162],{"stretchy":2161},[1148,8693,2675],{},[1495,8695,2181],{"stretchy":2161},[1156,8697,8632],{"encoding":1158}," jsou náhodné (data mají dané rozdělení).",[1127,8700,8701,8718],{},[1115,8702,8704],{"className":8703},[1133],[1135,8705,8706],{"xmlns":1137},[1139,8707,8708,8716],{},[1142,8709,8710],{},[1145,8711,8712,8714],{},[1148,8713,1150],{},[1152,8715,1176],{},[1156,8717,1179],{"encoding":1158},": data nemají dané rozdělení.",[1127,8720,8721,8722,1335],{},"Testové kritérium: ",[1115,8723,8725],{"className":8724},[1133],[1135,8726,8727],{"xmlns":1137},[1139,8728,8729,8773],{},[1142,8730,8731,8733,8735,8747,8749,8755,8757,8759,8761,8763,8765,8767,8769,8771],{},[1148,8732,4114],{},[1495,8734,1503],{},[1145,8736,8737,8745],{},[1142,8738,8739,8742],{},[1148,8740,8741],{},"sup",[1495,8743,8744],{},"⁡",[1148,8746,2675],{},[1495,8748,2172],{"stretchy":2161},[1145,8750,8751,8753],{},[1148,8752,1387],{},[1148,8754,2657],{},[1495,8756,2162],{"stretchy":2161},[1148,8758,2675],{},[1495,8760,2181],{"stretchy":2161},[1495,8762,1885],{},[1148,8764,1387],{},[1495,8766,2162],{"stretchy":2161},[1148,8768,2675],{},[1495,8770,2181],{"stretchy":2161},[1495,8772,2172],{"stretchy":2161},[1156,8774,8775],{"encoding":1158},"D = \\sup_x \\lvert F_n(x) - F(x) \\rvert",[1127,8777,8778,8779,8823,8824,8843,8844,1335],{},"Kritický obor: ",[1115,8780,8782],{"className":8781},[1133],[1135,8783,8784],{"xmlns":1137},[1139,8785,8786,8820],{},[1142,8787,8788,8794,8796,8798,8800,8802,8804,8806,8812,8814,8816,8818],{},[1145,8789,8790,8792],{},[1148,8791,1192],{},[1148,8793,1228],{},[1495,8795,1503],{},[1495,8797,3529],{"stretchy":2161},[1148,8799,4204],{},[1495,8801,1497],{},[1148,8803,4204],{},[1495,8805,1641],{},[1145,8807,8808,8810],{},[1148,8809,4114],{},[1148,8811,1228],{},[1495,8813,2162],{"stretchy":2161},[1148,8815,2657],{},[1495,8817,2181],{"stretchy":2161},[1495,8819,3558],{"stretchy":2161},[1156,8821,8822],{"encoding":1158},"W_\\alpha = \\{d : d > D_\\alpha(n)\\}","; pro ",[1115,8825,8827],{"className":8826},[1133],[1135,8828,8829],{"xmlns":1137},[1139,8830,8831,8840],{},[1142,8832,8833,8835,8837],{},[1148,8834,2657],{},[1495,8836,1641],{},[1152,8838,8839],{},"30",[1156,8841,8842],{"encoding":1158},"n>30"," se kritická hodnota aproximuje zlomkem ",[1115,8845,8847],{"className":8846},[1133],[1135,8848,8849],{"xmlns":1137},[1139,8850,8851,8862],{},[1142,8852,8853,8856,8858],{},[1152,8854,8855],{},"1,36",[1148,8857,3049],{"mathvariant":1599},[2770,8859,8860],{},[1148,8861,2657],{},[1156,8863,8864],{"encoding":1158},"1{,}36\u002F\\sqrt{n}",[1110,8866,3159,8867,8870,8871,8873,8874,1195,8877,8880],{},[3161,8868,8869],{},"ks.test()",", kde se za ",[3161,8872,8632],{}," dosadí příslušná distribuční funkce (",[3161,8875,8876],{},"\"pnorm\"",[3161,8878,8879],{},"\"pexp\"",", …) s jejími parametry:",[3166,8882,8884],{"className":3168,"code":8883,"language":71,"meta":3170,"style":3170},"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",[3161,8885,8886,8936],{"__ignoreMap":3170},[1115,8887,8888,8890,8892,8894,8896,8898,8900,8902,8904,8906,8908,8910,8912,8914,8916,8918,8920,8922,8924,8926,8928,8930,8932,8934],{"class":3175,"line":10},[1115,8889,3914],{"class":3178},[1115,8891,3182],{"class":3181},[1115,8893,3186],{"class":3185},[1115,8895,2162],{"class":3189},[1115,8897,3923],{"class":3192},[1115,8899,2188],{"class":3181},[1115,8901,3928],{"class":3192},[1115,8903,2188],{"class":3181},[1115,8905,3933],{"class":3192},[1115,8907,2188],{"class":3181},[1115,8909,3938],{"class":3192},[1115,8911,2188],{"class":3181},[1115,8913,3933],{"class":3192},[1115,8915,2188],{"class":3181},[1115,8917,3933],{"class":3192},[1115,8919,2188],{"class":3181},[1115,8921,3951],{"class":3192},[1115,8923,2188],{"class":3181},[1115,8925,3956],{"class":3192},[1115,8927,2188],{"class":3181},[1115,8929,3928],{"class":3192},[1115,8931,2188],{"class":3181},[1115,8933,3928],{"class":3192},[1115,8935,3235],{"class":3189},[1115,8937,8938,8941,8943,8945,8947,8950,8952,8955,8957,8959,8961,8963,8966,8968,8970],{"class":3175,"line":27},[1115,8939,8940],{"class":3185},"ks.test",[1115,8942,2162],{"class":3189},[1115,8944,3914],{"class":3178},[1115,8946,2188],{"class":3181},[1115,8948,8949],{"class":3265}," \"pnorm\"",[1115,8951,2188],{"class":3181},[1115,8953,8954],{"class":3185}," mean",[1115,8956,2162],{"class":3189},[1115,8958,3914],{"class":3178},[1115,8960,2181],{"class":3189},[1115,8962,2188],{"class":3181},[1115,8964,8965],{"class":3185}," sd",[1115,8967,2162],{"class":3189},[1115,8969,3914],{"class":3178},[1115,8971,7963],{"class":3189},[3166,8973,8976],{"className":8974,"code":8975,"language":3274,"meta":3170},[3272],"    Asymptotic one-sample Kolmogorov-Smirnov test\n\ndata:  x3\nD = 0.18469, p-value = 0.8847\nalternative hypothesis: two-sided\n",[3161,8977,8975],{"__ignoreMap":3170},[1110,8979,8980,9003],{},[1115,8981,8983],{"className":8982},[1133],[1135,8984,8985],{"xmlns":1137},[1139,8986,8987,9000],{},[1142,8988,8989,8991,8993,8996,8998],{},[1148,8990,1110],{},[1495,8992,1503],{},[1152,8994,8995],{},"0,8847",[1495,8997,1641],{},[1152,8999,3314],{},[1156,9001,9002],{"encoding":1158},"p = 0{,}8847 > 0{,}05",": odpad materiálu je slučitelný s normálním rozdělením se stejným průměrem a směrodatnou odchylkou.",[1695,9005,9007],{"id":9006},"shapiro-wilkův-test","Shapiro-Wilkův test",[1110,9009,9010],{},"Nejpoužívanější a nejsilnější obecný test normality, citlivý na odchylky v šikmosti i špičatosti. Využívá korelaci mezi uspořádanými hodnotami výběru a jejich očekávanými hodnotami v normálním rozdělení.",[1124,9012,9013,9033,9053],{},[1127,9014,9015,9032],{},[1115,9016,9018],{"className":9017},[1133],[1135,9019,9020],{"xmlns":1137},[1139,9021,9022,9030],{},[1142,9023,9024],{},[1145,9025,9026,9028],{},[1148,9027,1150],{},[1152,9029,1154],{},[1156,9031,1159],{"encoding":1158},": data mají normální rozdělení.",[1127,9034,9035,9052],{},[1115,9036,9038],{"className":9037},[1133],[1135,9039,9040],{"xmlns":1137},[1139,9041,9042,9050],{},[1142,9043,9044],{},[1145,9045,9046,9048],{},[1148,9047,1150],{},[1152,9049,1176],{},[1156,9051,1179],{"encoding":1158},": data nemají normální rozdělení.",[1127,9054,9055,9056,9084],{},"Testová statistika ",[1115,9057,9059],{"className":9058},[1133],[1135,9060,9061],{"xmlns":1137},[1139,9062,9063,9081],{},[1142,9064,9065,9067,9069,9072,9074,9076,9078],{},[1148,9066,1192],{},[1495,9068,2167],{},[1495,9070,9071],{"stretchy":2161},"⟨",[1152,9073,1154],{},[1495,9075,2188],{"separator":1121},[1152,9077,1176],{},[1495,9079,9080],{"stretchy":2161},"⟩",[1156,9082,9083],{"encoding":1158},"W \\in \\langle 0,1 \\rangle","; hodnoty blízké 1 indikují shodu s normalitou.",[1110,9086,9087,9088,9101,9102,1953,9122,9139,9140,1953,9160,9177],{},"Na rozdíl od ostatních testů v této kapitole se Shapiro-Wilkův test v praxi vyhodnocuje pouze přes p-hodnotu (tabulka kritických hodnot pro ",[1115,9089,9091],{"className":9090},[1133],[1135,9092,9093],{"xmlns":1137},[1139,9094,9095,9099],{},[1142,9096,9097],{},[1148,9098,1192],{},[1156,9100,1192],{"encoding":1158}," se běžně neudává): ",[1115,9103,9105],{"className":9104},[1133],[1135,9106,9107],{"xmlns":1137},[1139,9108,9109,9119],{},[1142,9110,9111,9113,9115,9117],{},[1148,9112,1110],{},[1495,9114,2940],{},[1148,9116,1228],{},[1495,9118,2524],{},[1156,9120,9121],{"encoding":1158},"p \\ge \\alpha \\Rightarrow",[1115,9123,9125],{"className":9124},[1133],[1135,9126,9127],{"xmlns":1137},[1139,9128,9129,9137],{},[1142,9130,9131],{},[1145,9132,9133,9135],{},[1148,9134,1150],{},[1152,9136,1154],{},[1156,9138,1159],{"encoding":1158}," nezamítáme (normalitu lze předpokládat); ",[1115,9141,9143],{"className":9142},[1133],[1135,9144,9145],{"xmlns":1137},[1139,9146,9147,9157],{},[1142,9148,9149,9151,9153,9155],{},[1148,9150,1110],{},[1495,9152,1682],{},[1148,9154,1228],{},[1495,9156,2524],{},[1156,9158,9159],{"encoding":1158},"p \u003C \\alpha \\Rightarrow",[1115,9161,9163],{"className":9162},[1133],[1135,9164,9165],{"xmlns":1137},[1139,9166,9167,9175],{},[1142,9168,9169],{},[1145,9170,9171,9173],{},[1148,9172,1150],{},[1152,9174,1154],{},[1156,9176,1159],{"encoding":1158}," zamítáme (předpoklad normality je porušen).",[3166,9179,9181],{"className":3168,"code":9180,"language":71,"meta":3170,"style":3170},"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",[3161,9182,9183,9237],{"__ignoreMap":3170},[1115,9184,9185,9187,9189,9191,9193,9195,9197,9199,9201,9203,9205,9207,9209,9211,9213,9215,9217,9219,9221,9223,9225,9227,9229,9231,9233,9235],{"class":3175,"line":10},[1115,9186,3781],{"class":3178},[1115,9188,3182],{"class":3181},[1115,9190,3186],{"class":3185},[1115,9192,2162],{"class":3189},[1115,9194,3790],{"class":3192},[1115,9196,2188],{"class":3181},[1115,9198,3795],{"class":3192},[1115,9200,2188],{"class":3181},[1115,9202,3800],{"class":3192},[1115,9204,2188],{"class":3181},[1115,9206,3805],{"class":3192},[1115,9208,2188],{"class":3181},[1115,9210,3810],{"class":3192},[1115,9212,2188],{"class":3181},[1115,9214,3815],{"class":3192},[1115,9216,2188],{"class":3181},[1115,9218,3805],{"class":3192},[1115,9220,2188],{"class":3181},[1115,9222,3824],{"class":3192},[1115,9224,2188],{"class":3181},[1115,9226,3810],{"class":3192},[1115,9228,2188],{"class":3181},[1115,9230,3833],{"class":3192},[1115,9232,2188],{"class":3181},[1115,9234,3805],{"class":3192},[1115,9236,3235],{"class":3189},[1115,9238,9239,9241,9243,9245],{"class":3175,"line":27},[1115,9240,3998],{"class":3185},[1115,9242,2162],{"class":3189},[1115,9244,3781],{"class":3178},[1115,9246,3235],{"class":3189},[3166,9248,9251],{"className":9249,"code":9250,"language":3274,"meta":3170},[3272],"    Shapiro-Wilk normality test\n\ndata:  x2\nW = 0.96022, p-value = 0.7744\n",[3161,9252,9250],{"__ignoreMap":3170},[1110,9254,9255,9256,9275],{},"U dat o životnosti baterií se normalita nezamítá (",[1115,9257,9259],{"className":9258},[1133],[1135,9260,9261],{"xmlns":1137},[1139,9262,9263,9272],{},[1142,9264,9265,9267,9269],{},[1148,9266,1110],{},[1495,9268,1503],{},[1152,9270,9271],{},"0,7744",[1156,9273,9274],{"encoding":1158},"p = 0{,}7744","), předpoklad t-testu je tedy splněn.",[1103,9277,9279,9286,9289,9712,9718],{"className":9278,"dataCallout":3323},[1106,3322],[1110,9280,9282,9285],{"className":9281},[1113],[1115,9283],{"className":9284,"ariaHidden":1121},[1118,3330,1120],"Příklad: Doba do poruchy výrobku",[1110,9287,9288],{},"Zkoušky životnosti nového výrobku daly soubor 68 hodnot doby do poruchy (v minutách). Odhadněte charakteristiky a zákon rozdělení.",[3166,9290,9292],{"className":3168,"code":9291,"language":71,"meta":3170,"style":3170},"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",[3161,9293,9294,9401,9494,9597,9636,9647,9658,9669,9679],{"__ignoreMap":3170},[1115,9295,9296,9299,9301,9303,9305,9308,9310,9313,9315,9318,9320,9323,9325,9327,9329,9331,9333,9335,9337,9340,9342,9345,9347,9350,9352,9355,9357,9360,9362,9365,9367,9370,9372,9375,9377,9380,9382,9384,9386,9389,9391,9394,9396,9398],{"class":3175,"line":10},[1115,9297,9298],{"class":3178},"x9",[1115,9300,3182],{"class":3181},[1115,9302,3186],{"class":3185},[1115,9304,2162],{"class":3189},[1115,9306,9307],{"class":3192},"101",[1115,9309,2188],{"class":3181},[1115,9311,9312],{"class":3192}," 338",[1115,9314,2188],{"class":3181},[1115,9316,9317],{"class":3192}," 150",[1115,9319,2188],{"class":3181},[1115,9321,9322],{"class":3192}," 47",[1115,9324,2188],{"class":3181},[1115,9326,3856],{"class":3192},[1115,9328,2188],{"class":3181},[1115,9330,7909],{"class":3192},[1115,9332,2188],{"class":3181},[1115,9334,3255],{"class":3192},[1115,9336,2188],{"class":3181},[1115,9338,9339],{"class":3192}," 392",[1115,9341,2188],{"class":3181},[1115,9343,9344],{"class":3192}," 5",[1115,9346,2188],{"class":3181},[1115,9348,9349],{"class":3192}," 73",[1115,9351,2188],{"class":3181},[1115,9353,9354],{"class":3192}," 367",[1115,9356,2188],{"class":3181},[1115,9358,9359],{"class":3192}," 54",[1115,9361,2188],{"class":3181},[1115,9363,9364],{"class":3192}," 114",[1115,9366,2188],{"class":3181},[1115,9368,9369],{"class":3192}," 213",[1115,9371,2188],{"class":3181},[1115,9373,9374],{"class":3192}," 71",[1115,9376,2188],{"class":3181},[1115,9378,9379],{"class":3192}," 341",[1115,9381,2188],{"class":3181},[1115,9383,8134],{"class":3192},[1115,9385,2188],{"class":3181},[1115,9387,9388],{"class":3192}," 112",[1115,9390,2188],{"class":3181},[1115,9392,9393],{"class":3192}," 343",[1115,9395,2188],{"class":3181},[1115,9397,8387],{"class":3192},[1115,9399,9400],{"class":3181},",\n",[1115,9402,9403,9406,9408,9411,9413,9416,9418,9421,9423,9426,9428,9430,9432,9435,9437,9439,9441,9444,9446,9449,9451,9453,9455,9458,9460,9463,9465,9467,9469,9472,9474,9477,9479,9482,9484,9487,9489,9492],{"class":3175,"line":27},[1115,9404,9405],{"class":3192},"        9",[1115,9407,2188],{"class":3181},[1115,9409,9410],{"class":3192}," 160",[1115,9412,2188],{"class":3181},[1115,9414,9415],{"class":3192}," 18",[1115,9417,2188],{"class":3181},[1115,9419,9420],{"class":3192}," 113",[1115,9422,2188],{"class":3181},[1115,9424,9425],{"class":3192}," 77",[1115,9427,2188],{"class":3181},[1115,9429,9374],{"class":3192},[1115,9431,2188],{"class":3181},[1115,9433,9434],{"class":3192}," 159",[1115,9436,2188],{"class":3181},[1115,9438,3255],{"class":3192},[1115,9440,2188],{"class":3181},[1115,9442,9443],{"class":3192}," 119",[1115,9445,2188],{"class":3181},[1115,9447,9448],{"class":3192}," 130",[1115,9450,2188],{"class":3181},[1115,9452,8357],{"class":3192},[1115,9454,2188],{"class":3181},[1115,9456,9457],{"class":3192}," 161",[1115,9459,2188],{"class":3181},[1115,9461,9462],{"class":3192}," 379",[1115,9464,2188],{"class":3181},[1115,9466,9359],{"class":3192},[1115,9468,2188],{"class":3181},[1115,9470,9471],{"class":3192}," 373",[1115,9473,2188],{"class":3181},[1115,9475,9476],{"class":3192}," 168",[1115,9478,2188],{"class":3181},[1115,9480,9481],{"class":3192}," 365",[1115,9483,2188],{"class":3181},[1115,9485,9486],{"class":3192}," 110",[1115,9488,2188],{"class":3181},[1115,9490,9491],{"class":3192}," 145",[1115,9493,9400],{"class":3181},[1115,9495,9496,9499,9501,9504,9506,9509,9511,9514,9516,9519,9521,9524,9526,9528,9530,9533,9535,9538,9540,9543,9545,9548,9550,9553,9555,9558,9560,9563,9565,9568,9570,9573,9575,9577,9579,9581,9583,9585,9587,9590,9592,9595],{"class":3175,"line":148},[1115,9497,9498],{"class":3192},"        88",[1115,9500,2188],{"class":3181},[1115,9502,9503],{"class":3192}," 74",[1115,9505,2188],{"class":3181},[1115,9507,9508],{"class":3192}," 46",[1115,9510,2188],{"class":3181},[1115,9512,9513],{"class":3192}," 246",[1115,9515,2188],{"class":3181},[1115,9517,9518],{"class":3192}," 259",[1115,9520,2188],{"class":3181},[1115,9522,9523],{"class":3192}," 19",[1115,9525,2188],{"class":3181},[1115,9527,9443],{"class":3192},[1115,9529,2188],{"class":3181},[1115,9531,9532],{"class":3192}," 48",[1115,9534,2188],{"class":3181},[1115,9536,9537],{"class":3192}," 3",[1115,9539,2188],{"class":3181},[1115,9541,9542],{"class":3192}," 163",[1115,9544,2188],{"class":3181},[1115,9546,9547],{"class":3192}," 179",[1115,9549,2188],{"class":3181},[1115,9551,9552],{"class":3192}," 194",[1115,9554,2188],{"class":3181},[1115,9556,9557],{"class":3192}," 33",[1115,9559,2188],{"class":3181},[1115,9561,9562],{"class":3192}," 49",[1115,9564,2188],{"class":3181},[1115,9566,9567],{"class":3192}," 501",[1115,9569,2188],{"class":3181},[1115,9571,9572],{"class":3192}," 193",[1115,9574,2188],{"class":3181},[1115,9576,9523],{"class":3192},[1115,9578,2188],{"class":3181},[1115,9580,9344],{"class":3192},[1115,9582,2188],{"class":3181},[1115,9584,7909],{"class":3192},[1115,9586,2188],{"class":3181},[1115,9588,9589],{"class":3192}," 221",[1115,9591,2188],{"class":3181},[1115,9593,9594],{"class":3192}," 300",[1115,9596,9400],{"class":3181},[1115,9598,9599,9601,9603,9606,9608,9611,9613,9616,9618,9620,9622,9625,9627,9629,9631,9634],{"class":3175,"line":111},[1115,9600,9498],{"class":3192},[1115,9602,2188],{"class":3181},[1115,9604,9605],{"class":3192}," 13",[1115,9607,2188],{"class":3181},[1115,9609,9610],{"class":3192}," 428",[1115,9612,2188],{"class":3181},[1115,9614,9615],{"class":3192}," 249",[1115,9617,2188],{"class":3181},[1115,9619,7713],{"class":3192},[1115,9621,2188],{"class":3181},[1115,9623,9624],{"class":3192}," 209",[1115,9626,2188],{"class":3181},[1115,9628,9359],{"class":3192},[1115,9630,2188],{"class":3181},[1115,9632,9633],{"class":3192}," 91",[1115,9635,3235],{"class":3189},[1115,9637,9638,9641,9643,9645],{"class":3175,"line":96},[1115,9639,9640],{"class":3185},"mean",[1115,9642,2162],{"class":3189},[1115,9644,9298],{"class":3178},[1115,9646,3235],{"class":3189},[1115,9648,9649,9652,9654,9656],{"class":3175,"line":89},[1115,9650,9651],{"class":3185},"sd",[1115,9653,2162],{"class":3189},[1115,9655,9298],{"class":3178},[1115,9657,3235],{"class":3189},[1115,9659,9660,9663,9665,9667],{"class":3175,"line":82},[1115,9661,9662],{"class":3185},"median",[1115,9664,2162],{"class":3189},[1115,9666,9298],{"class":3178},[1115,9668,3235],{"class":3189},[1115,9670,9671,9673,9675,9677],{"class":3175,"line":75},[1115,9672,3998],{"class":3185},[1115,9674,2162],{"class":3189},[1115,9676,9298],{"class":3178},[1115,9678,3235],{"class":3189},[1115,9680,9682,9684,9686,9688,9690,9693,9695,9698,9700,9702,9704,9706,9708,9710],{"class":3175,"line":9681},9,[1115,9683,8940],{"class":3185},[1115,9685,2162],{"class":3189},[1115,9687,9298],{"class":3178},[1115,9689,2188],{"class":3181},[1115,9691,9692],{"class":3265}," \"pexp\"",[1115,9694,2188],{"class":3181},[1115,9696,9697],{"class":3178}," rate",[1115,9699,3252],{"class":3181},[1115,9701,3735],{"class":3192},[1115,9703,7755],{"class":3181},[1115,9705,8954],{"class":3185},[1115,9707,2162],{"class":3189},[1115,9709,9298],{"class":3178},[1115,9711,7963],{"class":3189},[3166,9713,9716],{"className":9714,"code":9715,"language":3274,"meta":3170},[3272],"[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",[3161,9717,9715],{"__ignoreMap":3170},[1110,9719,9720,9721,9740,9741,9758,9759,9778],{},"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 (",[1115,9722,9724],{"className":9723},[1133],[1135,9725,9726],{"xmlns":1137},[1139,9727,9728,9737],{},[1142,9729,9730,9732,9734],{},[1148,9731,1110],{},[1495,9733,1682],{},[1152,9735,9736],{},"0,0001",[1156,9738,9739],{"encoding":1158},"p \u003C 0{,}0001","), zatímco Kolmogorov-Smirnovův test proti exponenciálnímu rozdělení se střední hodnotou ",[1115,9742,9744],{"className":9743},[1133],[1135,9745,9746],{"xmlns":1137},[1139,9747,9748,9756],{},[1142,9749,9750],{},[2671,9751,9752,9754],{"accent":1121},[1148,9753,2675],{},[1495,9755,2678],{},[1156,9757,2681],{"encoding":1158}," shodu nezamítá (",[1115,9760,9762],{"className":9761},[1133],[1135,9763,9764],{"xmlns":1137},[1139,9765,9766,9775],{},[1142,9767,9768,9770,9772],{},[1148,9769,1110],{},[1495,9771,1503],{},[1152,9773,9774],{},"0,8421",[1156,9776,9777],{"encoding":1158},"p = 0{,}8421","): data odpovídají spíše exponenciálnímu rozdělení než normálnímu.",[1110,9780,9781],{},[1971,9782],{"alt":9783,"className":9784,"src":9785},"mask-th-exponencialni-shoda",[1343,1975],"\u002Fwiki-assets\u002Fmask-th-exponencialni-shoda.png",[1392,9787,9789],{"id":9788},"neparametrické-testy","Neparametrické testy",[1110,9791,9792,9793,3677,9796,9821],{},"Když předpoklad normality neplatí, nahrazují t-testy jejich neparametrické obdoby — Wilcoxonovy testy posuzují ",[1399,9794,9795],{},"medián",[1115,9797,9799],{"className":9798},[1133],[1135,9800,9801],{"xmlns":1137},[1139,9802,9803,9818],{},[1142,9804,9805],{},[1145,9806,9807,9809],{},[1148,9808,2675],{},[1142,9810,9811,9813,9815],{},[1152,9812,1154],{},[1495,9814,2188],{"separator":1121},[1152,9816,9817],{},"5",[1156,9819,9820],{"encoding":1158},"x_{0,5}",") místo střední hodnoty a nevyžadují normalitu dat.",[1695,9823,9825],{"id":9824},"wilcoxonovy-testy","Wilcoxonovy testy",[1532,9827,9828,9873],{},[1535,9829,9830],{},[1538,9831,9832,9851,9870],{},[1541,9833,9834],{},[1115,9835,9837],{"className":9836},[1133],[1135,9838,9839],{"xmlns":1137},[1139,9840,9841,9849],{},[1142,9842,9843],{},[1145,9844,9845,9847],{},[1148,9846,1150],{},[1152,9848,1154],{},[1156,9850,1159],{"encoding":1158},[1541,9852,9853],{},[1115,9854,9856],{"className":9855},[1133],[1135,9857,9858],{"xmlns":1137},[1139,9859,9860,9868],{},[1142,9861,9862],{},[1145,9863,9864,9866],{},[1148,9865,1150],{},[1152,9867,1176],{},[1156,9869,1179],{"encoding":1158},[1541,9871,9872],{},"Příkaz v R",[1568,9874,9875,9942,10009],{},[1538,9876,9877,9907,9937],{},[1573,9878,9879],{},[1115,9880,9882],{"className":9881},[1133],[1135,9883,9884],{"xmlns":1137},[1139,9885,9886,9904],{},[1142,9887,9888,9900,9902],{},[1145,9889,9890,9892],{},[1148,9891,2675],{},[1142,9893,9894,9896,9898],{},[1152,9895,1154],{},[1495,9897,2188],{"separator":1121},[1152,9899,9817],{},[1495,9901,2519],{},[1148,9903,1991],{},[1156,9905,9906],{"encoding":1158},"x_{0,5} \\le c",[1573,9908,9909],{},[1115,9910,9912],{"className":9911},[1133],[1135,9913,9914],{"xmlns":1137},[1139,9915,9916,9934],{},[1142,9917,9918,9930,9932],{},[1145,9919,9920,9922],{},[1148,9921,2675],{},[1142,9923,9924,9926,9928],{},[1152,9925,1154],{},[1495,9927,2188],{"separator":1121},[1152,9929,9817],{},[1495,9931,1641],{},[1148,9933,1991],{},[1156,9935,9936],{"encoding":1158},"x_{0,5} > c",[1573,9938,9939],{},[3161,9940,9941],{},"wilcox.test(x, alternative = \"greater\", mu = c)",[1538,9943,9944,9974,10004],{},[1573,9945,9946],{},[1115,9947,9949],{"className":9948},[1133],[1135,9950,9951],{"xmlns":1137},[1139,9952,9953,9971],{},[1142,9954,9955,9967,9969],{},[1145,9956,9957,9959],{},[1148,9958,2675],{},[1142,9960,9961,9963,9965],{},[1152,9962,1154],{},[1495,9964,2188],{"separator":1121},[1152,9966,9817],{},[1495,9968,1503],{},[1148,9970,1991],{},[1156,9972,9973],{"encoding":1158},"x_{0,5} = c",[1573,9975,9976],{},[1115,9977,9979],{"className":9978},[1133],[1135,9980,9981],{"xmlns":1137},[1139,9982,9983,10001],{},[1142,9984,9985,9997,9999],{},[1145,9986,9987,9989],{},[1148,9988,2675],{},[1142,9990,9991,9993,9995],{},[1152,9992,1154],{},[1495,9994,2188],{"separator":1121},[1152,9996,9817],{},[1495,9998,1600],{"mathvariant":1599},[1148,10000,1991],{},[1156,10002,10003],{"encoding":1158},"x_{0,5} \\neq c",[1573,10005,10006],{},[3161,10007,10008],{},"wilcox.test(x, alternative = \"two.sided\", mu = c)",[1538,10010,10011,10041,10071],{},[1573,10012,10013],{},[1115,10014,10016],{"className":10015},[1133],[1135,10017,10018],{"xmlns":1137},[1139,10019,10020,10038],{},[1142,10021,10022,10034,10036],{},[1145,10023,10024,10026],{},[1148,10025,2675],{},[1142,10027,10028,10030,10032],{},[1152,10029,1154],{},[1495,10031,2188],{"separator":1121},[1152,10033,9817],{},[1495,10035,2940],{},[1148,10037,1991],{},[1156,10039,10040],{"encoding":1158},"x_{0,5} \\ge c",[1573,10042,10043],{},[1115,10044,10046],{"className":10045},[1133],[1135,10047,10048],{"xmlns":1137},[1139,10049,10050,10068],{},[1142,10051,10052,10064,10066],{},[1145,10053,10054,10056],{},[1148,10055,2675],{},[1142,10057,10058,10060,10062],{},[1152,10059,1154],{},[1495,10061,2188],{"separator":1121},[1152,10063,9817],{},[1495,10065,1682],{},[1148,10067,1991],{},[1156,10069,10070],{"encoding":1158},"x_{0,5} \u003C c",[1573,10072,10073],{},[3161,10074,10075],{},"wilcox.test(x, alternative = \"less\", mu = c)",[1110,10077,10078,10082,10083,1335],{},[10079,10080,10081],"em",{},"Jednovýběrový Wilcoxonův test"," (obdoba t-testu) posuzuje odchylku mediánu od konstanty ",[1115,10084,10086],{"className":10085},[1133],[1135,10087,10088],{"xmlns":1137},[1139,10089,10090,10094],{},[1142,10091,10092],{},[1148,10093,1991],{},[1156,10095,1991],{"encoding":1158},[1110,10097,10098,10101,10102,10141,10142,10155,10156,1335],{},[10079,10099,10100],{},"Jednovýběrový Wilcoxonův test na diferencích"," (obdoba párového t-testu) posuzuje odchylku mediánu rozdílu ",[1115,10103,10105],{"className":10104},[1133],[1135,10106,10107],{"xmlns":1137},[1139,10108,10109,10138],{},[1142,10110,10111,10123,10125],{},[1145,10112,10113,10115],{},[1148,10114,2675],{},[1142,10116,10117,10119,10121],{},[1152,10118,1154],{},[1495,10120,2188],{"separator":1121},[1152,10122,9817],{},[1495,10124,1885],{},[1145,10126,10127,10130],{},[1148,10128,10129],{},"y",[1142,10131,10132,10134,10136],{},[1152,10133,1154],{},[1495,10135,2188],{"separator":1121},[1152,10137,9817],{},[1156,10139,10140],{"encoding":1158},"x_{0,5}-y_{0,5}"," od ",[1115,10143,10145],{"className":10144},[1133],[1135,10146,10147],{"xmlns":1137},[1139,10148,10149,10153],{},[1142,10150,10151],{},[1148,10152,1991],{},[1156,10154,1991],{"encoding":1158},"; v R se volá se stejnými argumenty jako výše a navíc ",[3161,10157,10158],{},"paired = TRUE",[1110,10160,10161,10164,10165,10168],{},[10079,10162,10163],{},"Dvouvýběrový Wilcoxonův test"," (obdoba dvouvýběrového t-testu) posuzuje odchylku mediánů dvou nezávislých výběrů; argument ",[3161,10166,10167],{},"mu"," odpadá. Pro výšky chlapců a dívek z příkladu výše:",[3166,10170,10172],{"className":3168,"code":10171,"language":71,"meta":3170,"style":3170},"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",[3161,10173,10174,10244,10302],{"__ignoreMap":3170},[1115,10175,10176,10178,10180,10182,10184,10186,10188,10190,10192,10194,10196,10198,10200,10202,10204,10206,10208,10210,10212,10214,10216,10218,10220,10222,10224,10226,10228,10230,10232,10234,10236,10238,10240,10242],{"class":3175,"line":10},[1115,10177,8343],{"class":3178},[1115,10179,3182],{"class":3181},[1115,10181,3186],{"class":3185},[1115,10183,2162],{"class":3189},[1115,10185,8352],{"class":3192},[1115,10187,2188],{"class":3181},[1115,10189,8357],{"class":3192},[1115,10191,2188],{"class":3181},[1115,10193,8362],{"class":3192},[1115,10195,2188],{"class":3181},[1115,10197,8367],{"class":3192},[1115,10199,2188],{"class":3181},[1115,10201,8372],{"class":3192},[1115,10203,2188],{"class":3181},[1115,10205,8377],{"class":3192},[1115,10207,2188],{"class":3181},[1115,10209,8382],{"class":3192},[1115,10211,2188],{"class":3181},[1115,10213,8387],{"class":3192},[1115,10215,2188],{"class":3181},[1115,10217,8372],{"class":3192},[1115,10219,2188],{"class":3181},[1115,10221,8362],{"class":3192},[1115,10223,2188],{"class":3181},[1115,10225,8400],{"class":3192},[1115,10227,2188],{"class":3181},[1115,10229,8405],{"class":3192},[1115,10231,2188],{"class":3181},[1115,10233,8410],{"class":3192},[1115,10235,2188],{"class":3181},[1115,10237,8372],{"class":3192},[1115,10239,2188],{"class":3181},[1115,10241,8419],{"class":3192},[1115,10243,3235],{"class":3189},[1115,10245,10246,10248,10250,10252,10254,10256,10258,10260,10262,10264,10266,10268,10270,10272,10274,10276,10278,10280,10282,10284,10286,10288,10290,10292,10294,10296,10298,10300],{"class":3175,"line":27},[1115,10247,8426],{"class":3178},[1115,10249,3182],{"class":3181},[1115,10251,3186],{"class":3185},[1115,10253,2162],{"class":3189},[1115,10255,8435],{"class":3192},[1115,10257,2188],{"class":3181},[1115,10259,8367],{"class":3192},[1115,10261,2188],{"class":3181},[1115,10263,8444],{"class":3192},[1115,10265,2188],{"class":3181},[1115,10267,8449],{"class":3192},[1115,10269,2188],{"class":3181},[1115,10271,8454],{"class":3192},[1115,10273,2188],{"class":3181},[1115,10275,8454],{"class":3192},[1115,10277,2188],{"class":3181},[1115,10279,8387],{"class":3192},[1115,10281,2188],{"class":3181},[1115,10283,8367],{"class":3192},[1115,10285,2188],{"class":3181},[1115,10287,8367],{"class":3192},[1115,10289,2188],{"class":3181},[1115,10291,8475],{"class":3192},[1115,10293,2188],{"class":3181},[1115,10295,8405],{"class":3192},[1115,10297,2188],{"class":3181},[1115,10299,8367],{"class":3192},[1115,10301,3235],{"class":3189},[1115,10303,10304,10307,10309,10311,10313,10315,10317,10319,10321,10323],{"class":3175,"line":148},[1115,10305,10306],{"class":3185},"wilcox.test",[1115,10308,2162],{"class":3189},[1115,10310,8343],{"class":3178},[1115,10312,2188],{"class":3181},[1115,10314,8498],{"class":3178},[1115,10316,2188],{"class":3181},[1115,10318,3260],{"class":3178},[1115,10320,3252],{"class":3181},[1115,10322,3266],{"class":3265},[1115,10324,3235],{"class":3189},[3166,10326,10329],{"className":10327,"code":10328,"language":3274,"meta":3170},[3272],"    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",[3161,10330,10328],{"__ignoreMap":3170},[1110,10332,10333,10356],{},[1115,10334,10336],{"className":10335},[1133],[1135,10337,10338],{"xmlns":1137},[1139,10339,10340,10353],{},[1142,10341,10342,10344,10346,10349,10351],{},[1148,10343,1110],{},[1495,10345,1503],{},[1152,10347,10348],{},"0,315",[1495,10350,1641],{},[1152,10352,3314],{},[1156,10354,10355],{"encoding":1158},"p = 0{,}315 > 0{,}05",": mediány výšek chlapců a dívek se statisticky významně neliší — stejný závěr jako u dvouvýběrového t-testu.",[1103,10358,10360,10367,10389,10500,10506],{"className":10359,"dataCallout":3323},[1106,3322],[1110,10361,10363,10366],{"className":10362},[1113],[1115,10364],{"className":10365,"ariaHidden":1121},[1118,3330,1120],"Příklad: Realitní odhadci — neparametrická alternativa",[1110,10368,10369,10370,10388],{},"U odhadů cen z párového t-testu výše normalita diferencí neplatí (",[1115,10371,10373],{"className":10372},[1133],[1135,10374,10375],{"xmlns":1137},[1139,10376,10377,10385],{},[1142,10378,10379,10381,10383],{},[1148,10380,1110],{},[1495,10382,1503],{},[1152,10384,5360],{},[1156,10386,10387],{"encoding":1158},"p = 0{,}03203","). Správnou volbou je párový Wilcoxonův test:",[3166,10390,10392],{"className":3168,"code":10391,"language":71,"meta":3170,"style":3170},"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",[3161,10393,10394,10436,10478],{"__ignoreMap":3170},[1115,10395,10396,10398,10400,10402,10404,10406,10408,10410,10412,10414,10416,10418,10420,10422,10424,10426,10428,10430,10432,10434],{"class":3175,"line":10},[1115,10397,5162],{"class":3178},[1115,10399,3182],{"class":3181},[1115,10401,3186],{"class":3185},[1115,10403,2162],{"class":3189},[1115,10405,5171],{"class":3192},[1115,10407,2188],{"class":3181},[1115,10409,5176],{"class":3192},[1115,10411,2188],{"class":3181},[1115,10413,5181],{"class":3192},[1115,10415,2188],{"class":3181},[1115,10417,5186],{"class":3192},[1115,10419,2188],{"class":3181},[1115,10421,5191],{"class":3192},[1115,10423,2188],{"class":3181},[1115,10425,5196],{"class":3192},[1115,10427,2188],{"class":3181},[1115,10429,5201],{"class":3192},[1115,10431,2188],{"class":3181},[1115,10433,5206],{"class":3192},[1115,10435,3235],{"class":3189},[1115,10437,10438,10440,10442,10444,10446,10448,10450,10452,10454,10456,10458,10460,10462,10464,10466,10468,10470,10472,10474,10476],{"class":3175,"line":27},[1115,10439,5213],{"class":3178},[1115,10441,3182],{"class":3181},[1115,10443,3186],{"class":3185},[1115,10445,2162],{"class":3189},[1115,10447,5222],{"class":3192},[1115,10449,2188],{"class":3181},[1115,10451,5227],{"class":3192},[1115,10453,2188],{"class":3181},[1115,10455,5232],{"class":3192},[1115,10457,2188],{"class":3181},[1115,10459,5237],{"class":3192},[1115,10461,2188],{"class":3181},[1115,10463,5242],{"class":3192},[1115,10465,2188],{"class":3181},[1115,10467,5247],{"class":3192},[1115,10469,2188],{"class":3181},[1115,10471,5252],{"class":3192},[1115,10473,2188],{"class":3181},[1115,10475,5257],{"class":3192},[1115,10477,3235],{"class":3189},[1115,10479,10480,10482,10484,10486,10488,10490,10492,10494,10496,10498],{"class":3175,"line":148},[1115,10481,10306],{"class":3185},[1115,10483,2162],{"class":3189},[1115,10485,5162],{"class":3178},[1115,10487,2188],{"class":3181},[1115,10489,5272],{"class":3178},[1115,10491,2188],{"class":3181},[1115,10493,5277],{"class":3178},[1115,10495,3252],{"class":3181},[1115,10497,5282],{"class":3192},[1115,10499,3235],{"class":3189},[3166,10501,10504],{"className":10502,"code":10503,"language":3274,"meta":3170},[3272],"    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",[3161,10505,10503],{"__ignoreMap":3170},[1110,10507,10508,10531],{},[1115,10509,10511],{"className":10510},[1133],[1135,10512,10513],{"xmlns":1137},[1139,10514,10515,10528],{},[1142,10516,10517,10519,10521,10524,10526],{},[1148,10518,1110],{},[1495,10520,1503],{},[1152,10522,10523],{},"0,1484",[1495,10525,1641],{},[1152,10527,3314],{},[1156,10529,10530],{"encoding":1158},"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.",[1695,10533,10535],{"id":10534},"kruskalův-wallisův-test","Kruskalův-Wallisův test",[1110,10537,10538,10539,10556],{},"Zobecnění dvouvýběrového Wilcoxonova testu, neparametrická obdoba analýzy rozptylu jednoduchého třídění. ",[1115,10540,10542],{"className":10541},[1133],[1135,10543,10544],{"xmlns":1137},[1139,10545,10546,10554],{},[1142,10547,10548],{},[1145,10549,10550,10552],{},[1148,10551,1150],{},[1152,10553,1154],{},[1156,10555,1159],{"encoding":1158},": všechny výběry pocházejí ze stejného rozdělení.",[3166,10558,10560],{"className":3168,"code":10559,"language":71,"meta":3170,"style":3170},"kruskal.test(kvantitativní_proměnná ~ faktor, data = soubor)\n",[3161,10561,10562],{"__ignoreMap":3170},[1115,10563,10564,10567,10569,10572,10575,10578,10580,10583,10585,10588],{"class":3175,"line":10},[1115,10565,10566],{"class":3185},"kruskal.test",[1115,10568,2162],{"class":3189},[1115,10570,10571],{"class":3178},"kvantitativní_proměnná",[1115,10573,10574],{"class":3181}," ~",[1115,10576,10577],{"class":3178}," faktor",[1115,10579,2188],{"class":3181},[1115,10581,10582],{"class":3178}," data",[1115,10584,3252],{"class":3181},[1115,10586,10587],{"class":3178}," soubor",[1115,10589,3235],{"class":3189},[1695,10591,10593],{"id":10592},"mediánový-test","Mediánový test",[1110,10595,10596,10597,10614,10615,1497],{},"Má stejný účel jako Kruskalův-Wallisův test (obdoba analýzy rozptylu jednoduchého třídění, ",[1115,10598,10600],{"className":10599},[1133],[1135,10601,10602],{"xmlns":1137},[1139,10603,10604,10612],{},[1142,10605,10606],{},[1145,10607,10608,10610],{},[1148,10609,1150],{},[1152,10611,1154],{},[1156,10613,1159],{"encoding":1158},": všechny výběry pocházejí ze stejného rozdělení) a je součástí balíčku ",[3161,10616,10617],{},"agricolae",[3166,10619,10621],{"className":3168,"code":10620,"language":71,"meta":3170,"style":3170},"library(agricolae)\nMedian.test(kvantitativní_proměnná, faktor)\n",[3161,10622,10623,10634],{"__ignoreMap":3170},[1115,10624,10625,10628,10630,10632],{"class":3175,"line":10},[1115,10626,10627],{"class":3181},"library",[1115,10629,2162],{"class":3189},[1115,10631,10617],{"class":3178},[1115,10633,3235],{"class":3189},[1115,10635,10636,10639,10641,10643,10645,10647],{"class":3175,"line":27},[1115,10637,10638],{"class":3185},"Median.test",[1115,10640,2162],{"class":3189},[1115,10642,10571],{"class":3178},[1115,10644,2188],{"class":3181},[1115,10646,10577],{"class":3178},[1115,10648,3235],{"class":3189},[1695,10650,10652],{"id":10651},"friedmanův-test","Friedmanův test",[1110,10654,10655,10656,10673,10674,10714],{},"Neparametrická obdoba analýzy rozptylu dvojného třídění s jedním pozorováním v každé podtřídě. ",[1115,10657,10659],{"className":10658},[1133],[1135,10660,10661],{"xmlns":1137},[1139,10662,10663,10671],{},[1142,10664,10665],{},[1145,10666,10667,10669],{},[1148,10668,1150],{},[1152,10670,1154],{},[1156,10672,1159],{"encoding":1158},": distribuční funkce veličin ",[1115,10675,10677],{"className":10676},[1133],[1135,10678,10679],{"xmlns":1137},[1139,10680,10681,10711],{},[1142,10682,10683,10693,10695,10698,10700],{},[1145,10684,10685,10687],{},[1148,10686,2618],{},[1142,10688,10689,10691],{},[1148,10690,4085],{},[1152,10692,1176],{},[1495,10694,2188],{"separator":1121},[1495,10696,10697],{},"…",[1495,10699,2188],{"separator":1121},[1145,10701,10702,10704],{},[1148,10703,2618],{},[1142,10705,10706,10708],{},[1148,10707,4085],{},[1148,10709,10710],{},"k",[1156,10712,10713],{"encoding":1158},"X_{i1}, \\dots, X_{ik}"," jsou totožné.",[3166,10716,10718],{"className":3168,"code":10717,"language":71,"meta":3170,"style":3170},"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",[3161,10719,10720,10750,10756],{"__ignoreMap":3170},[1115,10721,10722,10725,10727,10729,10731,10734,10737,10740,10742,10744,10746,10748],{"class":3175,"line":10},[1115,10723,10724],{"class":3185},"friedman.test",[1115,10726,2162],{"class":3189},[1115,10728,10571],{"class":3178},[1115,10730,10574],{"class":3181},[1115,10732,10733],{"class":3178}," faktor_A",[1115,10735,10736],{"class":3181}," |",[1115,10738,10739],{"class":3178}," faktor_B",[1115,10741,2188],{"class":3181},[1115,10743,10582],{"class":3178},[1115,10745,3252],{"class":3181},[1115,10747,10587],{"class":3178},[1115,10749,3235],{"class":3189},[1115,10751,10752],{"class":3175,"line":27},[1115,10753,10755],{"class":10754},"sCsY4","# jsou-li proměnné samostatné vektory (bez argumentu data):\n",[1115,10757,10758,10760,10762,10764,10766,10768,10770,10772],{"class":3175,"line":148},[1115,10759,10724],{"class":3185},[1115,10761,2162],{"class":3189},[1115,10763,10571],{"class":3178},[1115,10765,2188],{"class":3181},[1115,10767,10733],{"class":3178},[1115,10769,2188],{"class":3181},[1115,10771,10739],{"class":3178},[1115,10773,3235],{"class":3189},[1392,10775,10777],{"id":10776},"přehled-testů","Přehled testů",[1110,10779,10780],{},[1971,10781],{"alt":10782,"className":10783,"src":10784},"mask-ilu-volba-testu",[1343,1975],"\u002Fwiki-assets\u002Fmask-ilu-volba-testu.png",[1532,10786,10787,10800],{},[1535,10788,10789],{},[1538,10790,10791,10794,10797],{},[1541,10792,10793],{},"Situace",[1541,10795,10796],{},"Test",[1541,10798,10799],{},"R funkce",[1568,10801,10802,10815,10828,10841,10854,10869,10881,10894,10907,10920,10932,10948],{},[1538,10803,10804,10807,10810],{},[1573,10805,10806],{},"Jedna střední hodnota vs. zadané číslo, normální data",[1573,10808,10809],{},"jednovýběrový t-test",[1573,10811,10812],{},[3161,10813,10814],{},"t.test(x, mu = ..., alternative = ...)",[1538,10816,10817,10820,10823],{},[1573,10818,10819],{},"Rozdíl dvou závislých měření, diference normální",[1573,10821,10822],{},"párový t-test",[1573,10824,10825],{},[3161,10826,10827],{},"t.test(x, y, paired = TRUE)",[1538,10829,10830,10833,10836],{},[1573,10831,10832],{},"Shoda rozptylů dvou nezávislých normálních výběrů",[1573,10834,10835],{},"F-test",[1573,10837,10838],{},[3161,10839,10840],{},"var.test(x, y)",[1538,10842,10843,10846,10849],{},[1573,10844,10845],{},"Shoda středních hodnot dvou nezávislých normálních výběrů",[1573,10847,10848],{},"dvouvýběrový t-test",[1573,10850,10851],{},[3161,10852,10853],{},"t.test(x, y, var.equal = TRUE\u002FFALSE)",[1538,10855,10856,10859,10861],{},[1573,10857,10858],{},"Shoda dat se zadaným typem rozdělení (normální, exponenciální, …)",[1573,10860,8584],{},[1573,10862,10863,1195,10866],{},[3161,10864,10865],{},"ks.test(x, \"pnorm\", mu, sigma)",[3161,10867,10868],{},"ks.test(x, \"pexp\", 1\u002Fdelta)",[1538,10870,10871,10874,10876],{},[1573,10872,10873],{},"Normalita dat",[1573,10875,9007],{},[1573,10877,10878],{},[3161,10879,10880],{},"shapiro.test(x)",[1538,10882,10883,10886,10889],{},[1573,10884,10885],{},"Medián jednoho výběru vs. konstanta, data nejsou normální",[1573,10887,10888],{},"jednovýběrový Wilcoxonův test",[1573,10890,10891],{},[3161,10892,10893],{},"wilcox.test(x, mu = c, alternative = ...)",[1538,10895,10896,10899,10902],{},[1573,10897,10898],{},"Medián diferencí dvou závislých měření, data nejsou normální",[1573,10900,10901],{},"párový Wilcoxonův test",[1573,10903,10904],{},[3161,10905,10906],{},"wilcox.test(x, y, paired = TRUE, mu = c)",[1538,10908,10909,10912,10915],{},[1573,10910,10911],{},"Mediány dvou nezávislých výběrů, data nejsou normální",[1573,10913,10914],{},"dvouvýběrový Wilcoxonův test",[1573,10916,10917],{},[3161,10918,10919],{},"wilcox.test(x, y)",[1538,10921,10922,10925,10927],{},[1573,10923,10924],{},"Více než dva nezávislé výběry, data nejsou normální",[1573,10926,10535],{},[1573,10928,10929],{},[3161,10930,10931],{},"kruskal.test(y ~ faktor, data)",[1538,10933,10934,10937,10940],{},[1573,10935,10936],{},"Více než dva nezávislé výběry, data nejsou normální (alternativa)",[1573,10938,10939],{},"mediánový test",[1573,10941,10942,10945,10946],{},[3161,10943,10944],{},"Median.test(y, faktor)"," z balíčku ",[3161,10947,10617],{},[1538,10949,10950,10953,10955],{},[1573,10951,10952],{},"Více než dva závislé výběry (dvojné třídění, jedno pozorování na podtřídu)",[1573,10954,10652],{},[1573,10956,10957],{},[3161,10958,10959],{},"friedman.test(y ~ A | B, data)",[1392,10961,10963],{"id":10962},"časté-chyby","Časté chyby",[1124,10965,10966,11043,11049,11066,11097],{},[1127,10967,10968,11007,11008,8310,11025,11042],{},[1399,10969,10970,10971,10988,10989,11006],{},"Nezamítnutí ",[1115,10972,10974],{"className":10973},[1133],[1135,10975,10976],{"xmlns":1137},[1139,10977,10978,10986],{},[1142,10979,10980],{},[1145,10981,10982,10984],{},[1148,10983,1150],{},[1152,10985,1154],{},[1156,10987,1159],{"encoding":1158}," není důkaz, že ",[1115,10990,10992],{"className":10991},[1133],[1135,10993,10994],{"xmlns":1137},[1139,10995,10996,11004],{},[1142,10997,10998],{},[1145,10999,11000,11002],{},[1148,11001,1150],{},[1152,11003,1154],{},[1156,11005,1159],{"encoding":1158}," platí."," U kabelů A\u002FB vyšlo ",[1115,11009,11011],{"className":11010},[1133],[1135,11012,11013],{"xmlns":1137},[1139,11014,11015,11023],{},[1142,11016,11017,11019,11021],{},[1148,11018,1110],{},[1495,11020,1503],{},[1152,11022,8306],{},[1156,11024,8309],{"encoding":1158},[1115,11026,11028],{"className":11027},[1133],[1135,11029,11030],{"xmlns":1137},[1139,11031,11032,11040],{},[1142,11033,11034],{},[1145,11035,11036,11038],{},[1148,11037,1150],{},[1152,11039,1154],{},[1156,11041,1159],{"encoding":1158}," nezamítá, ale hodnota je blízko hranice; správná interpretace je „data rovnost průměrů nevyvracejí“, ne „rovnost je prokázána“.",[1127,11044,11045,11048],{},[1399,11046,11047],{},"Před párovým nebo dvouvýběrovým t-testem ověřte normalitu."," U realitních odhadců vycházel párový t-test bez varování, ale Shapiro-Wilkův test na diferencích normalitu zamítl — správným testem byl párový Wilcoxonův test.",[1127,11050,11051,11058,11059,11062,11063,11065],{},[1399,11052,11053,5442,11055,11057],{},[3161,11054,8031],{},[3161,11056,3163],{}," se volí podle F-testu, ne podle výchozí hodnoty."," Výchozí nastavení R je ",[3161,11060,11061],{},"var.equal = FALSE"," (Welchova varianta); pokud F-test potvrdí shodné rozptyly, je třeba explicitně napsat ",[3161,11064,8289],{},", jinak se použije jiná statistika a jiné stupně volnosti.",[1127,11067,11068,11071,11072,11075,11076,11093,11094,1335],{},[1399,11069,11070],{},"Jednostranná vs. dvoustranná alternativa mění kritický obor i závěr."," Volba ",[3161,11073,11074],{},"alternative = \"greater\"\u002F\"less\"\u002F\"two.sided\""," musí odpovídat formulaci ",[1115,11077,11079],{"className":11078},[1133],[1135,11080,11081],{"xmlns":1137},[1139,11082,11083,11091],{},[1142,11084,11085],{},[1145,11086,11087,11089],{},[1148,11088,1150],{},[1152,11090,1176],{},[1156,11092,1179],{"encoding":1158}," v zadání, ne být ponechána na výchozí hodnotě ",[3161,11095,11096],{},"\"two.sided\"",[1127,11098,11099,11102,11103,11116],{},[1399,11100,11101],{},"Shapiro-Wilkův test se vyhodnocuje jen přes p-hodnotu",", ne porovnáním ",[1115,11104,11106],{"className":11105},[1133],[1135,11107,11108],{"xmlns":1137},[1139,11109,11110,11114],{},[1142,11111,11112],{},[1148,11113,1192],{},[1156,11115,1192],{"encoding":1158}," s tabulkovou kritickou hodnotou jako u ostatních testů v této kapitole.",[1392,11118,11120],{"id":11119},"související-stránky","Související stránky",[1124,11122,11123,11129,11135,11141,11149,11157,11165],{},[1127,11124,11125],{},[1340,11126,11128],{"className":11127,"dataFsResolvedFilePath":1344,"href":1345},[1343],"Metody aplikované statistiky",[1127,11130,11131],{},[1340,11132,11134],{"className":11133,"dataFsResolvedFilePath":1358,"href":1359},[1343],"Náhodné veličiny a rozdělení pravděpodobnosti",[1127,11136,11137],{},[1340,11138,11140],{"className":11139,"dataFsResolvedFilePath":1351,"href":1352},[1343],"Popisná statistika a datové soubory",[1127,11142,11143],{},[1340,11144,11148],{"className":11145,"dataFsResolvedFilePath":11146,"href":11147},[1343],"topics\u002Fregresni-a-korelacni-analyza.md","\u002Fwiki\u002Fregresni-a-korelacni-analyza","Regresní a korelační analýza",[1127,11150,11151],{},[1340,11152,11156],{"className":11153,"dataFsResolvedFilePath":11154,"href":11155},[1343],"topics\u002Fkontingencni-tabulky.md","\u002Fwiki\u002Fkontingencni-tabulky","Kontingenční tabulky",[1127,11158,11159],{},[1340,11160,11164],{"className":11161,"dataFsResolvedFilePath":11162,"href":11163},[1343],"topics\u002Fregulacni-diagramy-a-indexy-zpusobilosti.md","\u002Fwiki\u002Fregulacni-diagramy-a-indexy-zpusobilosti","Regulační diagramy a indexy způsobilosti",[1127,11166,11167],{},[1340,11168,11172],{"className":11169,"dataFsResolvedFilePath":11170,"href":11171},[1343],"outputs\u002Fmask-r-tahak.md","\u002Fwiki\u002Fmask-r-tahak","Tahák pro R",[1392,11174,11175],{"id":934},"Reference",[1110,11177,11178,11179,11182],{},"KROPÁČ, J. ",[10079,11180,11181],{},"Statistika A",". 4. vyd. Brno: Fakulta podnikatelská VUT, 2011.",[11184,11185,11186],"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: 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tabulka zaznamenává ",[1399,11257,11258],{},"simultánní četnosti"," dvou kvalitativních znaků naměřených na stejném souboru.",[1127,11261,11262,11265,11266,11283,11284,11303,11304,11317],{},[1399,11263,11264],{},"Test nezávislosti"," srovnává pozorované četnosti s očekávanými za platnosti ",[1115,11267,11269],{"className":11268},[1133],[1135,11270,11271],{"xmlns":1137},[1139,11272,11273,11281],{},[1142,11274,11275],{},[1145,11276,11277,11279],{},[1148,11278,1150],{},[1152,11280,1154],{},[1156,11282,1159],{"encoding":1158}," pomocí statistiky ",[1115,11285,11287],{"className":11286},[1133],[1135,11288,11289],{"xmlns":1137},[1139,11290,11291,11300],{},[1142,11292,11293],{},[2632,11294,11295,11298],{},[1148,11296,11297],{},"χ",[1152,11299,2639],{},[1156,11301,11302],{"encoding":1158},"\\chi^2","; rozhoduje kritický obor ",[1115,11305,11307],{"className":11306},[1133],[1135,11308,11309],{"xmlns":1137},[1139,11310,11311,11315],{},[1142,11312,11313],{},[1148,11314,1192],{},[1156,11316,1192],{"encoding":1158},", prakticky p-hodnota.",[1127,11319,11320,11321,11338],{},"Aproximace ",[1115,11322,11324],{"className":11323},[1133],[1135,11325,11326],{"xmlns":1137},[1139,11327,11328,11336],{},[1142,11329,11330],{},[2632,11331,11332,11334],{},[1148,11333,11297],{},[1152,11335,2639],{},[1156,11337,11302],{"encoding":1158}," rozdělením platí jen tehdy, když jsou očekávané četnosti dostatečně velké — proto se vždy kontrolují.",[1127,11340,11341,11342,11359,11360,1953,11363,1335],{},"Zamítnutí ",[1115,11343,11345],{"className":11344},[1133],[1135,11346,11347],{"xmlns":1137},[1139,11348,11349,11357],{},[1142,11350,11351],{},[1145,11352,11353,11355],{},[1148,11354,1150],{},[1152,11356,1154],{},[1156,11358,1159],{"encoding":1158}," samo o sobě neříká, jak silná závislost je — na to slouží ",[1399,11361,11362],{},"Cramérův koeficient kontingence",[1115,11364,11366],{"className":11365},[1133],[1135,11367,11368],{"xmlns":1137},[1139,11369,11370,11375],{},[1142,11371,11372],{},[1148,11373,11374],{},"V",[1156,11376,11374],{"encoding":1158},[1127,11378,11379,11382,11383,1335],{},[1399,11380,11381],{},"Čtyřpolní tabulka"," (2×2) je speciální případ s vlastním zjednodušeným vzorcem pro ",[1115,11384,11386],{"className":11385},[1133],[1135,11387,11388],{"xmlns":1137},[1139,11389,11390,11399],{},[1142,11391,11392,11394,11396],{},[1148,11393,2657],{},[1495,11395,1641],{},[1152,11397,11398],{},"40",[1156,11400,11401],{"encoding":1158},"n>40",[1127,11403,1478,11404,11407,11408,11411],{},[1399,11405,11406],{},"párová data"," (stejné prvky měřené dvakrát, např. před\u002Fpo zásahu) se používá ",[1399,11409,11410],{},"McNemarův test",", ne obyčejný test nezávislosti.",[1392,11413,11415],{"id":11414},"kontingenční-tabulka","Kontingenční tabulka",[1110,11417,11418,11419,11422,11423,11429,11430,11433],{},"V rámci ",[1340,11420,11128],{"className":11421,"dataFsResolvedFilePath":1344,"href":1345},[1343]," navazují kontingenční tabulky na\n",[1340,11424,11428],{"className":11425,"dataFsResolvedFilePath":11426,"href":11427},[1343],"topics\u002Ftestovani-hypotez.md","\u002Fwiki\u002Ftestovani-hypotez","testování statistických hypotéz",": místo jedné náhodné veličiny teď sledujeme dva\n",[1399,11431,11432],{},"kvalitativní"," (kategoriální) znaky současně a ptáme se, zda spolu souvisí.",[1110,11435,11436,11437,11440,11441,11443,11444,11447,11448,11451],{},"Znak je ",[1399,11438,11439],{},"kvantitativní",", pokud nabývá číselných hodnot (stáří, stav tachometru), a ",[1399,11442,11432],{},"\n(kategoriální), pokud nabývá slovních variant (vzdělání, kuřák\u002Fnekuřák). Kvalitativní znaky dále dělíme na\n",[1399,11445,11446],{},"alternativní"," (dvě varianty, např. vada ano\u002Fne) a ",[1399,11449,11450],{},"množné"," (více než dvě varianty, např. svobodný\u002Frozvedený\u002Fženatý).",[1110,11453,11454,11455,11468,11469,11482,11483,11513,11514,11527,11528,11558,11559,11562,11563,2036,11586,1953,11589,11611,11612,11630,11631,11649,11650,1497],{},"Mějme ",[1115,11456,11458],{"className":11457},[1133],[1135,11459,11460],{"xmlns":1137},[1139,11461,11462,11466],{},[1142,11463,11464],{},[1148,11465,2657],{},[1156,11467,2657],{"encoding":1158}," opakování pokusu, při nichž sledujeme dva kvalitativní znaky ",[1115,11470,11472],{"className":11471},[1133],[1135,11473,11474],{"xmlns":1137},[1139,11475,11476,11480],{},[1142,11477,11478],{},[1148,11479,8090],{},[1156,11481,8090],{"encoding":1158}," (varianty ",[1115,11484,11486],{"className":11485},[1133],[1135,11487,11488],{"xmlns":1137},[1139,11489,11490,11510],{},[1142,11491,11492,11498,11500,11502,11504],{},[1145,11493,11494,11496],{},[1148,11495,8090],{},[1152,11497,1176],{},[1495,11499,2188],{"separator":1121},[1495,11501,10697],{},[1495,11503,2188],{"separator":1121},[1145,11505,11506,11508],{},[1148,11507,8090],{},[1148,11509,71],{},[1156,11511,11512],{"encoding":1158},"A_1,\\dots,A_r",") a ",[1115,11515,11517],{"className":11516},[1133],[1135,11518,11519],{"xmlns":1137},[1139,11520,11521,11525],{},[1142,11522,11523],{},[1148,11524,8159],{},[1156,11526,8159],{"encoding":1158},"\n(varianty ",[1115,11529,11531],{"className":11530},[1133],[1135,11532,11533],{"xmlns":1137},[1139,11534,11535,11555],{},[1142,11536,11537,11543,11545,11547,11549],{},[1145,11538,11539,11541],{},[1148,11540,8159],{},[1152,11542,1176],{},[1495,11544,2188],{"separator":1121},[1495,11546,10697],{},[1495,11548,2188],{"separator":1121},[1145,11550,11551,11553],{},[1148,11552,8159],{},[1148,11554,2695],{},[1156,11556,11557],{"encoding":1158},"B_1,\\dots,B_s","). Výsledky zapíšeme do ",[1399,11560,11561],{},"kontingenční tabulky",": v políčku ",[1115,11564,11566],{"className":11565},[1133],[1135,11567,11568],{"xmlns":1137},[1139,11569,11570,11583],{},[1142,11571,11572,11574,11576,11578,11581],{},[1495,11573,2162],{"stretchy":2161},[1148,11575,4085],{},[1495,11577,2188],{"separator":1121},[1148,11579,11580],{},"j",[1495,11582,2181],{"stretchy":2161},[1156,11584,11585],{"encoding":1158},"(i,j)",[1399,11587,11588],{},"simultánní\nčetnost",[1115,11590,11592],{"className":11591},[1133],[1135,11593,11594],{"xmlns":1137},[1139,11595,11596,11608],{},[1142,11597,11598],{},[1145,11599,11600,11602],{},[1148,11601,2657],{},[1142,11603,11604,11606],{},[1148,11605,4085],{},[1148,11607,11580],{},[1156,11609,11610],{"encoding":1158},"n_{ij}",", tedy počet pokusů s variantou ",[1115,11613,11615],{"className":11614},[1133],[1135,11616,11617],{"xmlns":1137},[1139,11618,11619,11627],{},[1142,11620,11621],{},[1145,11622,11623,11625],{},[1148,11624,8090],{},[1148,11626,4085],{},[1156,11628,11629],{"encoding":1158},"A_i"," zároveň s variantou ",[1115,11632,11634],{"className":11633},[1133],[1135,11635,11636],{"xmlns":1137},[1139,11637,11638,11646],{},[1142,11639,11640],{},[1145,11641,11642,11644],{},[1148,11643,8159],{},[1148,11645,11580],{},[1156,11647,11648],{"encoding":1158},"B_j",". Řádkové a sloupcové součty\njsou ",[1399,11651,11652],{},"marginální četnosti",[1115,11654,11656],{"className":11655},[1133],[1135,11657,11658],{"xmlns":1137,"display":2151},[1139,11659,11660,11787],{},[1142,11661,11662,11673,11675,11691,11701,11703,11705,11715,11717,11731,11741,11743,11745,11747,11749,11763,11777],{},[1145,11663,11664,11666],{},[1148,11665,2657],{},[1142,11667,11668,11670],{},[1148,11669,4085],{},[1495,11671,11672],{},"∙",[1495,11674,1503],{},[11676,11677,11678,11681,11689],"munderover",{},[1495,11679,11680],{},"∑",[1142,11682,11683,11685,11687],{},[1148,11684,11580],{},[1495,11686,1503],{},[1152,11688,1176],{},[1148,11690,2695],{},[1145,11692,11693,11695],{},[1148,11694,2657],{},[1142,11696,11697,11699],{},[1148,11698,4085],{},[1148,11700,11580],{},[1495,11702,2188],{"separator":1121},[3520,11704],{"width":3522},[1145,11706,11707,11709],{},[1148,11708,2657],{},[1142,11710,11711,11713],{},[1495,11712,11672],{},[1148,11714,11580],{},[1495,11716,1503],{},[11676,11718,11719,11721,11729],{},[1495,11720,11680],{},[1142,11722,11723,11725,11727],{},[1148,11724,4085],{},[1495,11726,1503],{},[1152,11728,1176],{},[1148,11730,71],{},[1145,11732,11733,11735],{},[1148,11734,2657],{},[1142,11736,11737,11739],{},[1148,11738,4085],{},[1148,11740,11580],{},[1495,11742,2188],{"separator":1121},[3520,11744],{"width":3522},[1148,11746,2657],{},[1495,11748,1503],{},[11676,11750,11751,11753,11761],{},[1495,11752,11680],{},[1142,11754,11755,11757,11759],{},[1148,11756,4085],{},[1495,11758,1503],{},[1152,11760,1176],{},[1148,11762,71],{},[11676,11764,11765,11767,11775],{},[1495,11766,11680],{},[1142,11768,11769,11771,11773],{},[1148,11770,11580],{},[1495,11772,1503],{},[1152,11774,1176],{},[1148,11776,2695],{},[1145,11778,11779,11781],{},[1148,11780,2657],{},[1142,11782,11783,11785],{},[1148,11784,4085],{},[1148,11786,11580],{},[1156,11788,11789],{"encoding":1158},"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}",[1532,11791,11792,11903],{},[1535,11793,11794],{},[1538,11795,11796,11817,11837,11857,11859,11879],{},[1541,11797,11798],{},[1115,11799,11801],{"className":11800},[1133],[1135,11802,11803],{"xmlns":1137},[1139,11804,11805,11814],{},[1142,11806,11807,11809,11812],{},[1148,11808,8090],{},[1148,11810,11811],{"mathvariant":1599},"\\",[1148,11813,8159],{},[1156,11815,11816],{"encoding":1158},"A \\backslash B",[1541,11818,11819],{},[1115,11820,11822],{"className":11821},[1133],[1135,11823,11824],{"xmlns":1137},[1139,11825,11826,11834],{},[1142,11827,11828],{},[1145,11829,11830,11832],{},[1148,11831,8159],{},[1152,11833,1176],{},[1156,11835,11836],{"encoding":1158},"B_1",[1541,11838,11839],{},[1115,11840,11842],{"className":11841},[1133],[1135,11843,11844],{"xmlns":1137},[1139,11845,11846,11854],{},[1142,11847,11848],{},[1145,11849,11850,11852],{},[1148,11851,8159],{},[1152,11853,2639],{},[1156,11855,11856],{"encoding":1158},"B_2",[1541,11858,10697],{},[1541,11860,11861],{},[1115,11862,11864],{"className":11863},[1133],[1135,11865,11866],{"xmlns":1137},[1139,11867,11868,11876],{},[1142,11869,11870],{},[1145,11871,11872,11874],{},[1148,11873,8159],{},[1148,11875,2695],{},[1156,11877,11878],{"encoding":1158},"B_s",[1541,11880,11881],{},[1115,11882,11884],{"className":11883},[1133],[1135,11885,11886],{"xmlns":1137},[1139,11887,11888,11900],{},[1142,11889,11890],{},[1145,11891,11892,11894],{},[1148,11893,2657],{},[1142,11895,11896,11898],{},[1148,11897,4085],{},[1495,11899,11672],{},[1156,11901,11902],{"encoding":1158},"n_{i\\bullet}",[1568,11904,11905,12017,12130,12146,12266],{},[1538,11906,11907,11927,11947,11967,11969,11993],{},[1573,11908,11909],{},[1115,11910,11912],{"className":11911},[1133],[1135,11913,11914],{"xmlns":1137},[1139,11915,11916,11924],{},[1142,11917,11918],{},[1145,11919,11920,11922],{},[1148,11921,8090],{},[1152,11923,1176],{},[1156,11925,11926],{"encoding":1158},"A_1",[1573,11928,11929],{},[1115,11930,11932],{"className":11931},[1133],[1135,11933,11934],{"xmlns":1137},[1139,11935,11936,11944],{},[1142,11937,11938],{},[1145,11939,11940,11942],{},[1148,11941,2657],{},[1152,11943,7339],{},[1156,11945,11946],{"encoding":1158},"n_{11}",[1573,11948,11949],{},[1115,11950,11952],{"className":11951},[1133],[1135,11953,11954],{"xmlns":1137},[1139,11955,11956,11964],{},[1142,11957,11958],{},[1145,11959,11960,11962],{},[1148,11961,2657],{},[1152,11963,7140],{},[1156,11965,11966],{"encoding":1158},"n_{12}",[1573,11968,10697],{},[1573,11970,11971],{},[1115,11972,11974],{"className":11973},[1133],[1135,11975,11976],{"xmlns":1137},[1139,11977,11978,11990],{},[1142,11979,11980],{},[1145,11981,11982,11984],{},[1148,11983,2657],{},[1142,11985,11986,11988],{},[1152,11987,1176],{},[1148,11989,2695],{},[1156,11991,11992],{"encoding":1158},"n_{1s}",[1573,11994,11995],{},[1115,11996,11998],{"className":11997},[1133],[1135,11999,12000],{"xmlns":1137},[1139,12001,12002,12014],{},[1142,12003,12004],{},[1145,12005,12006,12008],{},[1148,12007,2657],{},[1142,12009,12010,12012],{},[1152,12011,1176],{},[1495,12013,11672],{},[1156,12015,12016],{"encoding":1158},"n_{1\\bullet}",[1538,12018,12019,12039,12060,12080,12082,12106],{},[1573,12020,12021],{},[1115,12022,12024],{"className":12023},[1133],[1135,12025,12026],{"xmlns":1137},[1139,12027,12028,12036],{},[1142,12029,12030],{},[1145,12031,12032,12034],{},[1148,12033,8090],{},[1152,12035,2639],{},[1156,12037,12038],{"encoding":1158},"A_2",[1573,12040,12041],{},[1115,12042,12044],{"className":12043},[1133],[1135,12045,12046],{"xmlns":1137},[1139,12047,12048,12057],{},[1142,12049,12050],{},[1145,12051,12052,12054],{},[1148,12053,2657],{},[1152,12055,12056],{},"21",[1156,12058,12059],{"encoding":1158},"n_{21}",[1573,12061,12062],{},[1115,12063,12065],{"className":12064},[1133],[1135,12066,12067],{"xmlns":1137},[1139,12068,12069,12077],{},[1142,12070,12071],{},[1145,12072,12073,12075],{},[1148,12074,2657],{},[1152,12076,7597],{},[1156,12078,12079],{"encoding":1158},"n_{22}",[1573,12081,10697],{},[1573,12083,12084],{},[1115,12085,12087],{"className":12086},[1133],[1135,12088,12089],{"xmlns":1137},[1139,12090,12091,12103],{},[1142,12092,12093],{},[1145,12094,12095,12097],{},[1148,12096,2657],{},[1142,12098,12099,12101],{},[1152,12100,2639],{},[1148,12102,2695],{},[1156,12104,12105],{"encoding":1158},"n_{2s}",[1573,12107,12108],{},[1115,12109,12111],{"className":12110},[1133],[1135,12112,12113],{"xmlns":1137},[1139,12114,12115,12127],{},[1142,12116,12117],{},[1145,12118,12119,12121],{},[1148,12120,2657],{},[1142,12122,12123,12125],{},[1152,12124,2639],{},[1495,12126,11672],{},[1156,12128,12129],{"encoding":1158},"n_{2\\bullet}",[1538,12131,12132,12135,12137,12139,12142,12144],{},[1573,12133,12134],{},"⋮",[1573,12136,12134],{},[1573,12138,12134],{},[1573,12140,12141],{},"⋱",[1573,12143,12134],{},[1573,12145,12134],{},[1538,12147,12148,12168,12192,12216,12218,12242],{},[1573,12149,12150],{},[1115,12151,12153],{"className":12152},[1133],[1135,12154,12155],{"xmlns":1137},[1139,12156,12157,12165],{},[1142,12158,12159],{},[1145,12160,12161,12163],{},[1148,12162,8090],{},[1148,12164,71],{},[1156,12166,12167],{"encoding":1158},"A_r",[1573,12169,12170],{},[1115,12171,12173],{"className":12172},[1133],[1135,12174,12175],{"xmlns":1137},[1139,12176,12177,12189],{},[1142,12178,12179],{},[1145,12180,12181,12183],{},[1148,12182,2657],{},[1142,12184,12185,12187],{},[1148,12186,71],{},[1152,12188,1176],{},[1156,12190,12191],{"encoding":1158},"n_{r1}",[1573,12193,12194],{},[1115,12195,12197],{"className":12196},[1133],[1135,12198,12199],{"xmlns":1137},[1139,12200,12201,12213],{},[1142,12202,12203],{},[1145,12204,12205,12207],{},[1148,12206,2657],{},[1142,12208,12209,12211],{},[1148,12210,71],{},[1152,12212,2639],{},[1156,12214,12215],{"encoding":1158},"n_{r2}",[1573,12217,10697],{},[1573,12219,12220],{},[1115,12221,12223],{"className":12222},[1133],[1135,12224,12225],{"xmlns":1137},[1139,12226,12227,12239],{},[1142,12228,12229],{},[1145,12230,12231,12233],{},[1148,12232,2657],{},[1142,12234,12235,12237],{},[1148,12236,71],{},[1148,12238,2695],{},[1156,12240,12241],{"encoding":1158},"n_{rs}",[1573,12243,12244],{},[1115,12245,12247],{"className":12246},[1133],[1135,12248,12249],{"xmlns":1137},[1139,12250,12251,12263],{},[1142,12252,12253],{},[1145,12254,12255,12257],{},[1148,12256,2657],{},[1142,12258,12259,12261],{},[1148,12260,71],{},[1495,12262,11672],{},[1156,12264,12265],{"encoding":1158},"n_{r\\bullet}",[1538,12267,12268,12292,12316,12340,12342,12366],{},[1573,12269,12270],{},[1115,12271,12273],{"className":12272},[1133],[1135,12274,12275],{"xmlns":1137},[1139,12276,12277,12289],{},[1142,12278,12279],{},[1145,12280,12281,12283],{},[1148,12282,2657],{},[1142,12284,12285,12287],{},[1495,12286,11672],{},[1148,12288,11580],{},[1156,12290,12291],{"encoding":1158},"n_{\\bullet j}",[1573,12293,12294],{},[1115,12295,12297],{"className":12296},[1133],[1135,12298,12299],{"xmlns":1137},[1139,12300,12301,12313],{},[1142,12302,12303],{},[1145,12304,12305,12307],{},[1148,12306,2657],{},[1142,12308,12309,12311],{},[1495,12310,11672],{},[1152,12312,1176],{},[1156,12314,12315],{"encoding":1158},"n_{\\bullet 1}",[1573,12317,12318],{},[1115,12319,12321],{"className":12320},[1133],[1135,12322,12323],{"xmlns":1137},[1139,12324,12325,12337],{},[1142,12326,12327],{},[1145,12328,12329,12331],{},[1148,12330,2657],{},[1142,12332,12333,12335],{},[1495,12334,11672],{},[1152,12336,2639],{},[1156,12338,12339],{"encoding":1158},"n_{\\bullet 2}",[1573,12341,10697],{},[1573,12343,12344],{},[1115,12345,12347],{"className":12346},[1133],[1135,12348,12349],{"xmlns":1137},[1139,12350,12351,12363],{},[1142,12352,12353],{},[1145,12354,12355,12357],{},[1148,12356,2657],{},[1142,12358,12359,12361],{},[1495,12360,11672],{},[1148,12362,2695],{},[1156,12364,12365],{"encoding":1158},"n_{\\bullet s}",[1573,12367,12368],{},[1115,12369,12371],{"className":12370},[1133],[1135,12372,12373],{"xmlns":1137},[1139,12374,12375,12379],{},[1142,12376,12377],{},[1148,12378,2657],{},[1156,12380,2657],{"encoding":1158},[1110,12382,12383,12384,12397],{},"Vydělením četností počtem opakování ",[1115,12385,12387],{"className":12386},[1133],[1135,12388,12389],{"xmlns":1137},[1139,12390,12391,12395],{},[1142,12392,12393],{},[1148,12394,2657],{},[1156,12396,2657],{"encoding":1158}," dostaneme odhady pravděpodobností:",[1115,12399,12401],{"className":12400},[1133],[1135,12402,12403],{"xmlns":1137,"display":2151},[1139,12404,12405,12506],{},[1142,12406,12407,12422,12424,12438,12440,12442,12456,12458,12472,12474,12476,12490,12492],{},[1145,12408,12409,12416],{},[2671,12410,12411,12413],{"accent":1121},[1148,12412,1110],{},[1495,12414,12415],{},"^",[1142,12417,12418,12420],{},[1148,12419,4085],{},[1148,12421,11580],{},[1495,12423,1503],{},[2749,12425,12426,12436],{},[1145,12427,12428,12430],{},[1148,12429,2657],{},[1142,12431,12432,12434],{},[1148,12433,4085],{},[1148,12435,11580],{},[1148,12437,2657],{},[1495,12439,2188],{"separator":1121},[3520,12441],{"width":3522},[1145,12443,12444,12450],{},[2671,12445,12446,12448],{"accent":1121},[1148,12447,1110],{},[1495,12449,12415],{},[1142,12451,12452,12454],{},[1148,12453,4085],{},[1495,12455,11672],{},[1495,12457,1503],{},[2749,12459,12460,12470],{},[1145,12461,12462,12464],{},[1148,12463,2657],{},[1142,12465,12466,12468],{},[1148,12467,4085],{},[1495,12469,11672],{},[1148,12471,2657],{},[1495,12473,2188],{"separator":1121},[3520,12475],{"width":3522},[1145,12477,12478,12484],{},[2671,12479,12480,12482],{"accent":1121},[1148,12481,1110],{},[1495,12483,12415],{},[1142,12485,12486,12488],{},[1495,12487,11672],{},[1148,12489,11580],{},[1495,12491,1503],{},[2749,12493,12494,12504],{},[1145,12495,12496,12498],{},[1148,12497,2657],{},[1142,12499,12500,12502],{},[1495,12501,11672],{},[1148,12503,11580],{},[1148,12505,2657],{},[1156,12507,12508],{"encoding":1158},"\\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}",[1392,12510,12512],{"id":12511},"test-nezávislosti-dvou-kvalitativních-znaků","Test nezávislosti dvou kvalitativních znaků",[1110,12514,12515,12516,12529,12530,12543],{},"Test ověřuje, zda varianty znaku ",[1115,12517,12519],{"className":12518},[1133],[1135,12520,12521],{"xmlns":1137},[1139,12522,12523,12527],{},[1142,12524,12525],{},[1148,12526,8090],{},[1156,12528,8090],{"encoding":1158}," a varianty znaku ",[1115,12531,12533],{"className":12532},[1133],[1135,12534,12535],{"xmlns":1137},[1139,12536,12537,12541],{},[1142,12538,12539],{},[1148,12540,8159],{},[1156,12542,8159],{"encoding":1158}," jsou na sobě nezávislé, tedy zda simultánní\npravděpodobnost je součinem marginálních pravděpodobností.",[1110,12545,12546],{},[1399,12547,12548],{},"Postup testu:",[2239,12550,12551,12679,12994,13070],{},[1127,12552,12553,12607,12608,1195,12634,12660,12661,12678],{},[1115,12554,12556],{"className":12555},[1133],[1135,12557,12558],{"xmlns":1137},[1139,12559,12560,12604],{},[1142,12561,12562,12568,12570,12580,12582,12592,12594],{},[1145,12563,12564,12566],{},[1148,12565,1150],{},[1152,12567,1154],{},[1495,12569,1497],{},[1145,12571,12572,12574],{},[1148,12573,1110],{},[1142,12575,12576,12578],{},[1148,12577,4085],{},[1148,12579,11580],{},[1495,12581,1503],{},[1145,12583,12584,12586],{},[1148,12585,1110],{},[1142,12587,12588,12590],{},[1148,12589,4085],{},[1495,12591,11672],{},[2358,12593,2360],{},[1145,12595,12596,12598],{},[1148,12597,1110],{},[1142,12599,12600,12602],{},[1495,12601,11672],{},[1148,12603,11580],{},[1156,12605,12606],{"encoding":1158},"H_0: p_{ij} = p_{i\\bullet}\\,p_{\\bullet j}"," pro všechna ",[1115,12609,12611],{"className":12610},[1133],[1135,12612,12613],{"xmlns":1137},[1139,12614,12615,12631],{},[1142,12616,12617,12619,12621,12623,12625,12627,12629],{},[1148,12618,4085],{},[1495,12620,1503],{},[1152,12622,1176],{},[1495,12624,2188],{"separator":1121},[1495,12626,10697],{},[1495,12628,2188],{"separator":1121},[1148,12630,71],{},[1156,12632,12633],{"encoding":1158},"i = 1,\\dots,r",[1115,12635,12637],{"className":12636},[1133],[1135,12638,12639],{"xmlns":1137},[1139,12640,12641,12657],{},[1142,12642,12643,12645,12647,12649,12651,12653,12655],{},[1148,12644,11580],{},[1495,12646,1503],{},[1152,12648,1176],{},[1495,12650,2188],{"separator":1121},[1495,12652,10697],{},[1495,12654,2188],{"separator":1121},[1148,12656,2695],{},[1156,12658,12659],{"encoding":1158},"j = 1,\\dots,s"," (znaky jsou na sobě\nnezávislé) proti ",[1115,12662,12664],{"className":12663},[1133],[1135,12665,12666],{"xmlns":1137},[1139,12667,12668,12676],{},[1142,12669,12670],{},[1145,12671,12672,12674],{},[1148,12673,1150],{},[1152,12675,1176],{},[1156,12677,1179],{"encoding":1158},": znaky jsou závislé.",[1127,12680,2076,12681,12837,12840,12841,12858,12859,12891,12892,2036,12950,12953,12954,12975,12976,12993],{},[1115,12682,12684],{"className":12683},[1133],[1135,12685,12686],{"xmlns":1137,"display":2151},[1139,12687,12688,12834],{},[1142,12689,12690,12696,12698,12712,12726,12784,12786,12788,12802,12804,12818,12820],{},[2632,12691,12692,12694],{},[1148,12693,11297],{},[1152,12695,2639],{},[1495,12697,1503],{},[11676,12699,12700,12702,12710],{},[1495,12701,11680],{},[1142,12703,12704,12706,12708],{},[1148,12705,4085],{},[1495,12707,1503],{},[1152,12709,1176],{},[1148,12711,71],{},[11676,12713,12714,12716,12724],{},[1495,12715,11680],{},[1142,12717,12718,12720,12722],{},[1148,12719,11580],{},[1495,12721,1503],{},[1152,12723,1176],{},[1148,12725,2695],{},[2749,12727,12728,12766],{},[1142,12729,12730,12732,12742,12744,12746,12760],{},[1495,12731,2162],{"stretchy":2161},[1145,12733,12734,12736],{},[1148,12735,2657],{},[1142,12737,12738,12740],{},[1148,12739,4085],{},[1148,12741,11580],{},[1495,12743,1885],{},[1148,12745,2657],{},[1145,12747,12748,12754],{},[2671,12749,12750,12752],{"accent":1121},[1148,12751,1110],{},[1495,12753,12415],{},[1142,12755,12756,12758],{},[1148,12757,4085],{},[1148,12759,11580],{},[2632,12761,12762,12764],{},[1495,12763,2181],{"stretchy":2161},[1152,12765,2639],{},[1142,12767,12768,12770],{},[1148,12769,2657],{},[1145,12771,12772,12778],{},[2671,12773,12774,12776],{"accent":1121},[1148,12775,1110],{},[1495,12777,12415],{},[1142,12779,12780,12782],{},[1148,12781,4085],{},[1148,12783,11580],{},[1495,12785,2188],{"separator":1121},[3520,12787],{"width":3522},[1145,12789,12790,12796],{},[2671,12791,12792,12794],{"accent":1121},[1148,12793,1110],{},[1495,12795,12415],{},[1142,12797,12798,12800],{},[1148,12799,4085],{},[1148,12801,11580],{},[1495,12803,1503],{},[1145,12805,12806,12812],{},[2671,12807,12808,12810],{"accent":1121},[1148,12809,1110],{},[1495,12811,12415],{},[1142,12813,12814,12816],{},[1148,12815,4085],{},[1495,12817,11672],{},[2358,12819,2360],{},[1145,12821,12822,12828],{},[2671,12823,12824,12826],{"accent":1121},[1148,12825,1110],{},[1495,12827,12415],{},[1142,12829,12830,12832],{},[1495,12831,11672],{},[1148,12833,11580],{},[1156,12835,12836],{"encoding":1158},"\\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}",[12838,12839],"br",{},"má asymptoticky Pearsonovo (",[1115,12842,12844],{"className":12843},[1133],[1135,12845,12846],{"xmlns":1137},[1139,12847,12848,12856],{},[1142,12849,12850],{},[2632,12851,12852,12854],{},[1148,12853,11297],{},[1152,12855,2639],{},[1156,12857,11302],{"encoding":1158},") rozdělení o ",[1115,12860,12862],{"className":12861},[1133],[1135,12863,12864],{"xmlns":1137},[1139,12865,12866,12888],{},[1142,12867,12868,12870,12872,12874,12876,12878,12880,12882,12884,12886],{},[1495,12869,2162],{"stretchy":2161},[1148,12871,71],{},[1495,12873,1885],{},[1152,12875,1176],{},[1495,12877,2181],{"stretchy":2161},[1495,12879,2162],{"stretchy":2161},[1148,12881,2695],{},[1495,12883,1885],{},[1152,12885,1176],{},[1495,12887,2181],{"stretchy":2161},[1156,12889,12890],{"encoding":1158},"(r-1)(s-1)"," stupních volnosti. Hodnota ",[1115,12893,12895],{"className":12894},[1133],[1135,12896,12897],{"xmlns":1137},[1139,12898,12899,12947],{},[1142,12900,12901,12903,12917,12919],{},[1148,12902,2657],{},[1145,12904,12905,12911],{},[2671,12906,12907,12909],{"accent":1121},[1148,12908,1110],{},[1495,12910,12415],{},[1142,12912,12913,12915],{},[1148,12914,4085],{},[1148,12916,11580],{},[1495,12918,1503],{},[6544,12920,12921],{"scriptlevel":1154,"displaystyle":1121},[2749,12922,12923,12945],{},[1142,12924,12925,12935],{},[1145,12926,12927,12929],{},[1148,12928,2657],{},[1142,12930,12931,12933],{},[1148,12932,4085],{},[1495,12934,11672],{},[1145,12936,12937,12939],{},[1148,12938,2657],{},[1142,12940,12941,12943],{},[1495,12942,11672],{},[1148,12944,11580],{},[1148,12946,2657],{},[1156,12948,12949],{"encoding":1158},"n\\hat p_{ij} = \\dfrac{n_{i\\bullet}n_{\\bullet j}}{n}",[1399,12951,12952],{},"očekávaná četnost"," políčka ",[1115,12955,12957],{"className":12956},[1133],[1135,12958,12959],{"xmlns":1137},[1139,12960,12961,12973],{},[1142,12962,12963,12965,12967,12969,12971],{},[1495,12964,2162],{"stretchy":2161},[1148,12966,4085],{},[1495,12968,2188],{"separator":1121},[1148,12970,11580],{},[1495,12972,2181],{"stretchy":2161},[1156,12974,11585],{"encoding":1158}," — četnost, kterou bychom čekali, kdyby ",[1115,12977,12979],{"className":12978},[1133],[1135,12980,12981],{"xmlns":1137},[1139,12982,12983,12991],{},[1142,12984,12985],{},[1145,12986,12987,12989],{},[1148,12988,1150],{},[1152,12990,1154],{},[1156,12992,1159],{"encoding":1158}," platila.",[1127,12995,8778,12996,1335],{},[1115,12997,12999],{"className":12998},[1133],[1135,13000,13001],{"xmlns":1137},[1139,13002,13003,13067],{},[1142,13004,13005,13007,13009,13011,13017,13019,13025,13027,13041,13043,13045,13047,13049,13051,13053,13055,13057,13059,13061,13063,13065],{},[1148,13006,1192],{},[1495,13008,1503],{},[1495,13010,3529],{"stretchy":2161},[2632,13012,13013,13015],{},[1148,13014,11297],{},[1152,13016,2639],{},[1495,13018,1497],{},[2632,13020,13021,13023],{},[1148,13022,11297],{},[1152,13024,2639],{},[1495,13026,2940],{},[4163,13028,13029,13031,13039],{},[1148,13030,11297],{},[1142,13032,13033,13035,13037],{},[1152,13034,1176],{},[1495,13036,1885],{},[1148,13038,1228],{},[1152,13040,2639],{},[1495,13042,2162],{"stretchy":2161},[1495,13044,2162],{"stretchy":2161},[1148,13046,71],{},[1495,13048,1885],{},[1152,13050,1176],{},[1495,13052,2181],{"stretchy":2161},[1495,13054,2162],{"stretchy":2161},[1148,13056,2695],{},[1495,13058,1885],{},[1152,13060,1176],{},[1495,13062,2181],{"stretchy":2161},[1495,13064,2181],{"stretchy":2161},[1495,13066,3558],{"stretchy":2161},[1156,13068,13069],{"encoding":1158},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}((r-1)(s-1))\\}",[1127,13071,13072,13073,13086,13087,13100,13101,13118,13119,13136],{},"Padne-li testové kritérium do ",[1115,13074,13076],{"className":13075},[1133],[1135,13077,13078],{"xmlns":1137},[1139,13079,13080,13084],{},[1142,13081,13082],{},[1148,13083,1192],{},[1156,13085,1192],{"encoding":1158},", zamítáme na hladině ",[1115,13088,13090],{"className":13089},[1133],[1135,13091,13092],{"xmlns":1137},[1139,13093,13094,13098],{},[1142,13095,13096],{},[1148,13097,1228],{},[1156,13099,1231],{"encoding":1158}," nulovou hypotézu o nezávislosti a přijímáme\n",[1115,13102,13104],{"className":13103},[1133],[1135,13105,13106],{"xmlns":1137},[1139,13107,13108,13116],{},[1142,13109,13110],{},[1145,13111,13112,13114],{},[1148,13113,1150],{},[1152,13115,1176],{},[1156,13117,1179],{"encoding":1158},"; jinak nemáme důvod ",[1115,13120,13122],{"className":13121},[1133],[1135,13123,13124],{"xmlns":1137},[1139,13125,13126,13134],{},[1142,13127,13128],{},[1145,13129,13130,13132],{},[1148,13131,1150],{},[1152,13133,1154],{},[1156,13135,1159],{"encoding":1158}," zamítnout.",[1110,13138,13139,13140,1335],{},"V R počítá test i očekávané četnosti funkce ",[3161,13141,13142],{},"chisq.test()",[1103,13144,13146,13153,13156,13159,13303],{"className":13145,"dataCallout":3323},[1106,3322],[1110,13147,13149,13152],{"className":13148},[1113],[1115,13150],{"className":13151,"ariaHidden":1121},[1118,3330,1120],"Příklad: nákup potravin na internetu a vzdělání",[1110,13154,13155],{},"Testujte hypotézu, zda se vzájemně ovlivňuje zkušenost s nákupem potravin na internetu a vzdělání respondenta\n(n = 385 respondentů).",[1110,13157,13158],{},"Základní soubor: respondenti; výběrový soubor: respondenti, kteří odpověděli; měřený znak A: vzdělání, měřený\nznak B: způsob nákupu.",[1532,13160,13161,13200],{},[1535,13162,13163],{},[1538,13164,13165,13168,13171,13174,13177],{},[1541,13166,13167],{},"vzdělání \\ nákup",[1541,13169,13170],{},"ano",[1541,13172,13173],{},"ne, ale plánuji",[1541,13175,13176],{},"ne, neplánuji",[1541,13178,13179],{},[1115,13180,13182],{"className":13181},[1133],[1135,13183,13184],{"xmlns":1137},[1139,13185,13186,13198],{},[1142,13187,13188],{},[1145,13189,13190,13192],{},[1148,13191,2657],{},[1142,13193,13194,13196],{},[1148,13195,4085],{},[1495,13197,11672],{},[1156,13199,11902],{"encoding":1158},[1568,13201,13202,13218,13235,13252,13267],{},[1538,13203,13204,13207,13210,13213,13215],{},[1573,13205,13206],{},"SŠ bez maturity",[1573,13208,13209],{},"4",[1573,13211,13212],{},"13",[1573,13214,7140],{},[1573,13216,13217],{},"29",[1538,13219,13220,13223,13226,13229,13232],{},[1573,13221,13222],{},"SŠ s maturitou, VOŠ",[1573,13224,13225],{},"31",[1573,13227,13228],{},"62",[1573,13230,13231],{},"71",[1573,13233,13234],{},"164",[1538,13236,13237,13240,13243,13246,13249],{},[1573,13238,13239],{},"VŠ",[1573,13241,13242],{},"44",[1573,13244,13245],{},"58",[1573,13247,13248],{},"66",[1573,13250,13251],{},"168",[1538,13253,13254,13257,13260,13262,13264],{},[1573,13255,13256],{},"ZŠ",[1573,13258,13259],{},"3",[1573,13261,4972],{},[1573,13263,7140],{},[1573,13265,13266],{},"24",[1538,13268,13269,13292,13294,13297,13300],{},[1573,13270,13271],{},[1115,13272,13274],{"className":13273},[1133],[1135,13275,13276],{"xmlns":1137},[1139,13277,13278,13290],{},[1142,13279,13280],{},[1145,13281,13282,13284],{},[1148,13283,2657],{},[1142,13285,13286,13288],{},[1495,13287,11672],{},[1148,13289,11580],{},[1156,13291,12291],{"encoding":1158},[1573,13293,7090],{},[1573,13295,13296],{},"142",[1573,13298,13299],{},"161",[1573,13301,13302],{},"385",[1110,13304,13305,13357],{},[1115,13306,13308],{"className":13307},[1133],[1135,13309,13310],{"xmlns":1137},[1139,13311,13312,13354],{},[1142,13313,13314,13320,13322,13332,13334,13344],{},[1145,13315,13316,13318],{},[1148,13317,1150],{},[1152,13319,1154],{},[1495,13321,1497],{},[1145,13323,13324,13326],{},[1148,13325,1110],{},[1142,13327,13328,13330],{},[1148,13329,4085],{},[1148,13331,11580],{},[1495,13333,1503],{},[1145,13335,13336,13338],{},[1148,13337,1110],{},[1142,13339,13340,13342],{},[1148,13341,4085],{},[1495,13343,11672],{},[1145,13345,13346,13348],{},[1148,13347,1110],{},[1142,13349,13350,13352],{},[1495,13351,11672],{},[1148,13353,11580],{},[1156,13355,13356],{"encoding":1158},"H_0: p_{ij} = p_{i\\bullet}p_{\\bullet j}"," — vzdělání a způsob nákupu jsou na sobě nezávislé.",[3166,13359,13361],{"className":3168,"code":13360,"language":71,"meta":3170,"style":3170},"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",[3161,13362,13363,13391,13407,13424,13442,13462,13475,13508,13536,13547],{"__ignoreMap":3170},[1115,13364,13365,13368,13370,13373,13375,13377,13379,13381,13383,13385,13387,13389],{"class":3175,"line":10},[1115,13366,13367],{"class":3178},"tab1",[1115,13369,3182],{"class":3181},[1115,13371,13372],{"class":3185}," matrix",[1115,13374,2162],{"class":3189},[1115,13376,1991],{"class":3185},[1115,13378,2162],{"class":3189},[1115,13380,13209],{"class":3192},[1115,13382,2188],{"class":3181},[1115,13384,9605],{"class":3192},[1115,13386,2188],{"class":3181},[1115,13388,3255],{"class":3192},[1115,13390,9400],{"class":3181},[1115,13392,13393,13396,13398,13401,13403,13405],{"class":3175,"line":27},[1115,13394,13395],{"class":3192},"                 31",[1115,13397,2188],{"class":3181},[1115,13399,13400],{"class":3192}," 62",[1115,13402,2188],{"class":3181},[1115,13404,9374],{"class":3192},[1115,13406,9400],{"class":3181},[1115,13408,13409,13412,13414,13417,13419,13422],{"class":3175,"line":148},[1115,13410,13411],{"class":3192},"                 44",[1115,13413,2188],{"class":3181},[1115,13415,13416],{"class":3192}," 58",[1115,13418,2188],{"class":3181},[1115,13420,13421],{"class":3192}," 66",[1115,13423,9400],{"class":3181},[1115,13425,13426,13429,13431,13434,13436,13438,13440],{"class":3175,"line":111},[1115,13427,13428],{"class":3192},"                 3",[1115,13430,2188],{"class":3181},[1115,13432,13433],{"class":3192},"  9",[1115,13435,2188],{"class":3181},[1115,13437,3255],{"class":3192},[1115,13439,2181],{"class":3189},[1115,13441,9400],{"class":3181},[1115,13443,13444,13447,13449,13451,13453,13456,13458,13460],{"class":3175,"line":96},[1115,13445,13446],{"class":3178},"               nrow",[1115,13448,3252],{"class":3181},[1115,13450,3983],{"class":3192},[1115,13452,2188],{"class":3181},[1115,13454,13455],{"class":3178}," byrow",[1115,13457,3252],{"class":3181},[1115,13459,5282],{"class":3192},[1115,13461,9400],{"class":3181},[1115,13463,13464,13467,13469,13472],{"class":3175,"line":89},[1115,13465,13466],{"class":3178},"               dimnames",[1115,13468,3252],{"class":3181},[1115,13470,13471],{"class":3185}," list",[1115,13473,13474],{"class":3189},"(\n",[1115,13476,13477,13480,13482,13484,13486,13489,13491,13494,13496,13499,13501,13504,13506],{"class":3175,"line":82},[1115,13478,13479],{"class":3178},"                 vzdelani",[1115,13481,3252],{"class":3181},[1115,13483,3186],{"class":3185},[1115,13485,2162],{"class":3189},[1115,13487,13488],{"class":3265},"\"SS bez maturity\"",[1115,13490,2188],{"class":3181},[1115,13492,13493],{"class":3265}," \"SS s maturitou nebo VOS\"",[1115,13495,2188],{"class":3181},[1115,13497,13498],{"class":3265}," \"VS\"",[1115,13500,2188],{"class":3181},[1115,13502,13503],{"class":3265}," \"ZS\"",[1115,13505,2181],{"class":3189},[1115,13507,9400],{"class":3181},[1115,13509,13510,13513,13516,13518,13520,13523,13525,13528,13530,13533],{"class":3175,"line":75},[1115,13511,13512],{"class":3178},"                 nakup",[1115,13514,13515],{"class":3181},"    =",[1115,13517,3186],{"class":3185},[1115,13519,2162],{"class":3189},[1115,13521,13522],{"class":3265},"\"ano\"",[1115,13524,2188],{"class":3181},[1115,13526,13527],{"class":3265}," \"ne, ale planuji\"",[1115,13529,2188],{"class":3181},[1115,13531,13532],{"class":3265}," \"ne, neplanuji\"",[1115,13534,13535],{"class":3189},")))\n",[1115,13537,13538,13541,13543,13545],{"class":3175,"line":9681},[1115,13539,13540],{"class":3185},"chisq.test",[1115,13542,2162],{"class":3189},[1115,13544,13367],{"class":3178},[1115,13546,3235],{"class":3189},[1115,13548,13549,13551,13553,13555,13557,13560],{"class":3175,"line":72},[1115,13550,13540],{"class":3185},[1115,13552,2162],{"class":3189},[1115,13554,13367],{"class":3178},[1115,13556,2181],{"class":3189},[1115,13558,13559],{"class":3181},"$",[1115,13561,13562],{"class":3178},"expected\n",[3166,13564,13567],{"className":13565,"code":13566,"language":3274,"meta":3170},[3272],"    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",[3161,13568,13566],{"__ignoreMap":3170},[1110,13570,13571,13572,13595,13596,13610,13611,2324,13630,13647],{},"Všechny očekávané četnosti jsou nad 5, aproximace je v pořádku. Testové kritérium ",[1115,13573,13575],{"className":13574},[1133],[1135,13576,13577],{"xmlns":1137},[1139,13578,13579,13592],{},[1142,13580,13581,13587,13589],{},[2632,13582,13583,13585],{},[1148,13584,11297],{},[1152,13586,2639],{},[1495,13588,1503],{},[1152,13590,13591],{},"5,49",[1156,13593,13594],{"encoding":1158},"\\chi^2 = 5{,}49"," s ",[1115,13597,13599],{"className":13598},[1133],[1135,13600,13601],{"xmlns":1137},[1139,13602,13603,13608],{},[1142,13604,13605],{},[1152,13606,13607],{},"6",[1156,13609,13607],{"encoding":1158}," stupni\nvolnosti dává p-hodnotu ",[1115,13612,13614],{"className":13613},[1133],[1135,13615,13616],{"xmlns":1137},[1139,13617,13618,13627],{},[1142,13619,13620,13623,13625],{},[1152,13621,13622],{},"0,483",[1495,13624,1641],{},[1152,13626,3314],{},[1156,13628,13629],{"encoding":1158},"0{,}483 > 0{,}05",[1115,13631,13633],{"className":13632},[1133],[1135,13634,13635],{"xmlns":1137},[1139,13636,13637,13645],{},[1142,13638,13639],{},[1145,13640,13641,13643],{},[1148,13642,1150],{},[1152,13644,1154],{},[1156,13646,1159],{"encoding":1158}," nezamítáme, závislost mezi zkušeností s nákupem potravin na\ninternetu a vzděláním respondenta se neprokázala.",[1103,13649,13651,13658,13661,13704],{"className":13650,"dataCallout":3323},[1106,3322],[1110,13652,13654,13657],{"className":13653},[1113],[1115,13655],{"className":13656,"ariaHidden":1121},[1118,3330,1120],"Příklad: vzdělání a zveřejňování citlivých údajů na Facebooku",[1110,13659,13660],{},"Mezi 221 osobami bylo zaznamenáno vzdělání a zda zveřejňují na Facebooku citlivé údaje. Proveďte test\nnezávislosti.",[1532,13662,13663,13677],{},[1535,13664,13665],{},[1538,13666,13667,13670,13673,13675],{},[1541,13668,13669],{},"zveřejňuje \\ vzdělání",[1541,13671,13672],{},"SŠ",[1541,13674,13239],{},[1541,13676,13256],{},[1568,13678,13679,13692],{},[1538,13680,13681,13684,13686,13689],{},[1573,13682,13683],{},"ne",[1573,13685,3374],{},[1573,13687,13688],{},"33",[1573,13690,13691],{},"39",[1538,13693,13694,13696,13698,13701],{},[1573,13695,13170],{},[1573,13697,7116],{},[1573,13699,13700],{},"28",[1573,13702,13703],{},"76",[1110,13705,13706,13757],{},[1115,13707,13709],{"className":13708},[1133],[1135,13710,13711],{"xmlns":1137},[1139,13712,13713,13755],{},[1142,13714,13715,13721,13723,13733,13735,13745],{},[1145,13716,13717,13719],{},[1148,13718,1150],{},[1152,13720,1154],{},[1495,13722,1497],{},[1145,13724,13725,13727],{},[1148,13726,1110],{},[1142,13728,13729,13731],{},[1148,13730,4085],{},[1148,13732,11580],{},[1495,13734,1503],{},[1145,13736,13737,13739],{},[1148,13738,1110],{},[1142,13740,13741,13743],{},[1148,13742,4085],{},[1495,13744,11672],{},[1145,13746,13747,13749],{},[1148,13748,1110],{},[1142,13750,13751,13753],{},[1495,13752,11672],{},[1148,13754,11580],{},[1156,13756,13356],{"encoding":1158}," — vzdělání a zveřejňování citlivých údajů jsou na sobě nezávislé.",[3166,13759,13761],{"className":3168,"code":13760,"language":71,"meta":3170,"style":3170},"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",[3161,13762,13763,13791,13810,13828,13838,13861,13885,13895],{"__ignoreMap":3170},[1115,13764,13765,13768,13770,13772,13774,13776,13778,13780,13782,13784,13786,13789],{"class":3175,"line":10},[1115,13766,13767],{"class":3178},"tab2",[1115,13769,3182],{"class":3181},[1115,13771,13372],{"class":3185},[1115,13773,2162],{"class":3189},[1115,13775,1991],{"class":3185},[1115,13777,2162],{"class":3189},[1115,13779,3374],{"class":3192},[1115,13781,2188],{"class":3181},[1115,13783,9557],{"class":3192},[1115,13785,2188],{"class":3181},[1115,13787,13788],{"class":3192}," 39",[1115,13790,9400],{"class":3181},[1115,13792,13793,13796,13798,13801,13803,13806,13808],{"class":3175,"line":27},[1115,13794,13795],{"class":3192},"                 25",[1115,13797,2188],{"class":3181},[1115,13799,13800],{"class":3192}," 28",[1115,13802,2188],{"class":3181},[1115,13804,13805],{"class":3192}," 76",[1115,13807,2181],{"class":3189},[1115,13809,9400],{"class":3181},[1115,13811,13812,13814,13816,13818,13820,13822,13824,13826],{"class":3175,"line":148},[1115,13813,13446],{"class":3178},[1115,13815,3252],{"class":3181},[1115,13817,7909],{"class":3192},[1115,13819,2188],{"class":3181},[1115,13821,13455],{"class":3178},[1115,13823,3252],{"class":3181},[1115,13825,5282],{"class":3192},[1115,13827,9400],{"class":3181},[1115,13829,13830,13832,13834,13836],{"class":3175,"line":111},[1115,13831,13466],{"class":3178},[1115,13833,3252],{"class":3181},[1115,13835,13471],{"class":3185},[1115,13837,13474],{"class":3189},[1115,13839,13840,13843,13845,13847,13849,13852,13854,13857,13859],{"class":3175,"line":96},[1115,13841,13842],{"class":3178},"                 zverejnuje",[1115,13844,3252],{"class":3181},[1115,13846,3186],{"class":3185},[1115,13848,2162],{"class":3189},[1115,13850,13851],{"class":3265},"\"ne\"",[1115,13853,2188],{"class":3181},[1115,13855,13856],{"class":3265}," \"ano\"",[1115,13858,2181],{"class":3189},[1115,13860,9400],{"class":3181},[1115,13862,13863,13865,13868,13870,13872,13875,13877,13879,13881,13883],{"class":3175,"line":89},[1115,13864,13479],{"class":3178},[1115,13866,13867],{"class":3181},"   =",[1115,13869,3186],{"class":3185},[1115,13871,2162],{"class":3189},[1115,13873,13874],{"class":3265},"\"SS\"",[1115,13876,2188],{"class":3181},[1115,13878,13498],{"class":3265},[1115,13880,2188],{"class":3181},[1115,13882,13503],{"class":3265},[1115,13884,13535],{"class":3189},[1115,13886,13887,13889,13891,13893],{"class":3175,"line":82},[1115,13888,13540],{"class":3185},[1115,13890,2162],{"class":3189},[1115,13892,13767],{"class":3178},[1115,13894,3235],{"class":3189},[1115,13896,13897,13899,13901,13903,13905,13907],{"class":3175,"line":75},[1115,13898,13540],{"class":3185},[1115,13900,2162],{"class":3189},[1115,13902,13767],{"class":3178},[1115,13904,2181],{"class":3189},[1115,13906,13559],{"class":3181},[1115,13908,13562],{"class":3178},[3166,13910,13913],{"className":13911,"code":13912,"language":3274,"meta":3170},[3272],"    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",[3161,13914,13912],{"__ignoreMap":3170},[1110,13916,13917,13918,13595,13941,13954,13955,2324,13974,13991,13992,1335],{},"I zde jsou všechny očekávané četnosti nad 5. Testové kritérium ",[1115,13919,13921],{"className":13920},[1133],[1135,13922,13923],{"xmlns":1137},[1139,13924,13925,13938],{},[1142,13926,13927,13933,13935],{},[2632,13928,13929,13931],{},[1148,13930,11297],{},[1152,13932,2639],{},[1495,13934,1503],{},[1152,13936,13937],{},"6,87",[1156,13939,13940],{"encoding":1158},"\\chi^2 = 6{,}87",[1115,13942,13944],{"className":13943},[1133],[1135,13945,13946],{"xmlns":1137},[1139,13947,13948,13952],{},[1142,13949,13950],{},[1152,13951,2639],{},[1156,13953,2639],{"encoding":1158}," stupni volnosti dává\np-hodnotu ",[1115,13956,13958],{"className":13957},[1133],[1135,13959,13960],{"xmlns":1137},[1139,13961,13962,13971],{},[1142,13963,13964,13967,13969],{},[1152,13965,13966],{},"0,032",[1495,13968,1682],{},[1152,13970,3314],{},[1156,13972,13973],{"encoding":1158},"0{,}032 \u003C 0{,}05",[1115,13975,13977],{"className":13976},[1133],[1135,13978,13979],{"xmlns":1137},[1139,13980,13981,13989],{},[1142,13982,13983],{},[1145,13984,13985,13987],{},[1148,13986,1150],{},[1152,13988,1154],{},[1156,13990,1159],{"encoding":1158}," zamítáme — na rozdíl od předchozího příkladu tady vzdělání a zveřejňování\ncitlivých údajů na Facebooku na sobě ",[1399,13993,13994],{},"závisí",[1110,13996,13997,13998,14015],{},"Srovnání pozorovaných a očekávaných četností ukazuje, proč jeden příklad ",[1115,13999,14001],{"className":14000},[1133],[1135,14002,14003],{"xmlns":1137},[1139,14004,14005,14013],{},[1142,14006,14007],{},[1145,14008,14009,14011],{},[1148,14010,1150],{},[1152,14012,1154],{},[1156,14014,1159],{"encoding":1158}," nezamítá a druhý ano — ve druhém\nse pozorované sloupce (zejména u ZŠ) systematicky odchylují od očekávaných, v prvním kolísají jen náhodně kolem nich:",[1110,14017,14018],{},[1971,14019],{"alt":14020,"className":14021,"src":14022},"mask-kt-observed-expected",[1343,1975],"\u002Fwiki-assets\u002Fmask-kt-observed-expected.png",[1110,14024,14025,14026,14043,14044,1497],{},"Totéž je vidět na rozdělení testového kritéria: u prvního příkladu leží ",[1115,14027,14029],{"className":14028},[1133],[1135,14030,14031],{"xmlns":1137},[1139,14032,14033,14041],{},[1142,14034,14035],{},[2632,14036,14037,14039],{},[1148,14038,11297],{},[1152,14040,2639],{},[1156,14042,11302],{"encoding":1158}," hluboko pod kritickou hodnotou,\nu druhého uvnitř kritického oboru ",[1115,14045,14047],{"className":14046},[1133],[1135,14048,14049],{"xmlns":1137},[1139,14050,14051,14055],{},[1142,14052,14053],{},[1148,14054,1192],{},[1156,14056,1192],{"encoding":1158},[1110,14058,14059],{},[1971,14060],{"alt":14061,"className":14062,"src":14063},"mask-kt-chi2-kriticky-obor",[1343,1975],"\u002Fwiki-assets\u002Fmask-kt-chi2-kriticky-obor.png",[1392,14065,11362],{"id":14066},"cramérův-koeficient-kontingence",[1110,14068,14069,14070,1497],{},"Test nezávislosti pouze rozhodne, zda jsou znaky závislé, nebo ne. Sílu závislosti měří ",[1399,14071,14072],{},"Cramérův koeficient\nkontingence",[1115,14074,14076],{"className":14075},[1133],[1135,14077,14078],{"xmlns":1137,"display":2151},[1139,14079,14080,14134],{},[1142,14081,14082,14084,14086,14111,14113,14115,14117,14119,14122,14124,14126,14128,14130,14132],{},[1148,14083,11374],{},[1495,14085,1503],{},[2770,14087,14088],{},[2749,14089,14090,14096],{},[2632,14091,14092,14094],{},[1148,14093,11297],{},[1152,14095,2639],{},[1142,14097,14098,14100,14102,14105,14107,14109],{},[1148,14099,2657],{},[1495,14101,2162],{"stretchy":2161},[1148,14103,14104],{},"m",[1495,14106,1885],{},[1152,14108,1176],{},[1495,14110,2181],{"stretchy":2161},[1495,14112,2188],{"separator":1121},[3520,14114],{"width":3522},[1148,14116,14104],{},[1495,14118,1503],{},[1148,14120,14121],{},"min",[1495,14123,8744],{},[1495,14125,2162],{"stretchy":2161},[1148,14127,71],{},[1495,14129,2188],{"separator":1121},[1148,14131,2695],{},[1495,14133,2181],{"stretchy":2161},[1156,14135,14136],{"encoding":1158},"V = \\sqrt{\\frac{\\chi^2}{n(m-1)}}, \\qquad m = \\min(r, s)",[1110,14138,14139,14140,14157,14158,14176,14177,14195],{},"kde ",[1115,14141,14143],{"className":14142},[1133],[1135,14144,14145],{"xmlns":1137},[1139,14146,14147,14155],{},[1142,14148,14149],{},[2632,14150,14151,14153],{},[1148,14152,11297],{},[1152,14154,2639],{},[1156,14156,11302],{"encoding":1158}," je hodnota testového kritéria z testu nezávislosti. ",[1115,14159,14161],{"className":14160},[1133],[1135,14162,14163],{"xmlns":1137},[1139,14164,14165,14173],{},[1142,14166,14167,14169,14171],{},[1148,14168,11374],{},[1495,14170,1503],{},[1152,14172,1154],{},[1156,14174,14175],{"encoding":1158},"V = 0"," odpovídá úplné nezávislosti znaků,\n",[1115,14178,14180],{"className":14179},[1133],[1135,14181,14182],{"xmlns":1137},[1139,14183,14184,14192],{},[1142,14185,14186,14188,14190],{},[1148,14187,11374],{},[1495,14189,1503],{},[1152,14191,1176],{},[1156,14193,14194],{"encoding":1158},"V = 1"," jejich úplné závislosti.",[3166,14197,14199],{"className":3168,"code":14198,"language":71,"meta":3170,"style":3170},"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",[3161,14200,14201,14270,14333,14338],{"__ignoreMap":3170},[1115,14202,14203,14206,14208,14210,14212,14215,14217,14219,14221,14223,14225,14227,14230,14232,14234,14236,14239,14241,14243,14245,14247,14249,14251,14253,14256,14258,14260,14263,14266,14268],{"class":3175,"line":10},[1115,14204,14205],{"class":3178},"V1",[1115,14207,3182],{"class":3181},[1115,14209,3699],{"class":3185},[1115,14211,2162],{"class":3189},[1115,14213,14214],{"class":3185},"as.numeric",[1115,14216,2162],{"class":3189},[1115,14218,13540],{"class":3185},[1115,14220,2162],{"class":3189},[1115,14222,13367],{"class":3178},[1115,14224,2181],{"class":3189},[1115,14226,13559],{"class":3181},[1115,14228,14229],{"class":3178},"statistic",[1115,14231,3688],{"class":3189},[1115,14233,3049],{"class":3181},[1115,14235,3677],{"class":3189},[1115,14237,14238],{"class":3185},"sum",[1115,14240,2162],{"class":3189},[1115,14242,13367],{"class":3178},[1115,14244,3688],{"class":3189},[1115,14246,7872],{"class":3181},[1115,14248,3677],{"class":3189},[1115,14250,14121],{"class":3185},[1115,14252,2162],{"class":3189},[1115,14254,14255],{"class":3185},"dim",[1115,14257,2162],{"class":3189},[1115,14259,13367],{"class":3178},[1115,14261,14262],{"class":3189},")) ",[1115,14264,14265],{"class":3181},"-",[1115,14267,3735],{"class":3192},[1115,14269,13535],{"class":3189},[1115,14271,14272,14275,14277,14279,14281,14283,14285,14287,14289,14291,14293,14295,14297,14299,14301,14303,14305,14307,14309,14311,14313,14315,14317,14319,14321,14323,14325,14327,14329,14331],{"class":3175,"line":27},[1115,14273,14274],{"class":3178},"V2",[1115,14276,3182],{"class":3181},[1115,14278,3699],{"class":3185},[1115,14280,2162],{"class":3189},[1115,14282,14214],{"class":3185},[1115,14284,2162],{"class":3189},[1115,14286,13540],{"class":3185},[1115,14288,2162],{"class":3189},[1115,14290,13767],{"class":3178},[1115,14292,2181],{"class":3189},[1115,14294,13559],{"class":3181},[1115,14296,14229],{"class":3178},[1115,14298,3688],{"class":3189},[1115,14300,3049],{"class":3181},[1115,14302,3677],{"class":3189},[1115,14304,14238],{"class":3185},[1115,14306,2162],{"class":3189},[1115,14308,13767],{"class":3178},[1115,14310,3688],{"class":3189},[1115,14312,7872],{"class":3181},[1115,14314,3677],{"class":3189},[1115,14316,14121],{"class":3185},[1115,14318,2162],{"class":3189},[1115,14320,14255],{"class":3185},[1115,14322,2162],{"class":3189},[1115,14324,13767],{"class":3178},[1115,14326,14262],{"class":3189},[1115,14328,14265],{"class":3181},[1115,14330,3735],{"class":3192},[1115,14332,13535],{"class":3189},[1115,14334,14335],{"class":3175,"line":148},[1115,14336,14337],{"class":3178},"V1\n",[1115,14339,14340],{"class":3175,"line":111},[1115,14341,14342],{"class":3178},"V2\n",[3166,14344,14347],{"className":14345,"code":14346,"language":3274,"meta":3170},[3272],"[1] 0.08441958\n[1] 0.1762822\n",[3161,14348,14346],{"__ignoreMap":3170},[1110,14350,14351],{},[1971,14352],{"alt":14353,"className":14354,"src":14355},"mask-kt-cramerovo-v",[1343,1975],"\u002Fwiki-assets\u002Fmask-kt-cramerovo-v.png",[1110,14357,14358,14359,14378,14379,14396,14397,2324,14416,14433],{},"U nákupu potravin je ",[1115,14360,14362],{"className":14361},[1133],[1135,14363,14364],{"xmlns":1137},[1139,14365,14366,14375],{},[1142,14367,14368,14370,14372],{},[1148,14369,11374],{},[1495,14371,1503],{},[1152,14373,14374],{},"0,084",[1156,14376,14377],{"encoding":1158},"V = 0{,}084"," zanedbatelné — ostatně ",[1115,14380,14382],{"className":14381},[1133],[1135,14383,14384],{"xmlns":1137},[1139,14385,14386,14394],{},[1142,14387,14388],{},[1145,14389,14390,14392],{},[1148,14391,1150],{},[1152,14393,1154],{},[1156,14395,1159],{"encoding":1158}," jsme ani nezamítli. U zveřejňování údajů je ",[1115,14398,14400],{"className":14399},[1133],[1135,14401,14402],{"xmlns":1137},[1139,14403,14404,14413],{},[1142,14405,14406,14408,14410],{},[1148,14407,11374],{},[1495,14409,1503],{},[1152,14411,14412],{},"0,176",[1156,14414,14415],{"encoding":1158},"V = 0{,}176",[1115,14417,14419],{"className":14418},[1133],[1135,14420,14421],{"xmlns":1137},[1139,14422,14423,14431],{},[1142,14424,14425],{},[1145,14426,14427,14429],{},[1148,14428,1150],{},[1152,14430,1154],{},[1156,14432,1159],{"encoding":1158},"\njsme zamítli, ale samotná závislost je stále slabá.",[1392,14435,11381],{"id":14436},"čtyřpolní-tabulka",[1110,14438,14439,14441,14442,14455,14456,14469,14470,14492],{},[1399,14440,11381],{}," je speciální případ kontingenční tabulky, kdy oba znaky ",[1115,14443,14445],{"className":14444},[1133],[1135,14446,14447],{"xmlns":1137},[1139,14448,14449,14453],{},[1142,14450,14451],{},[1148,14452,8090],{},[1156,14454,8090],{"encoding":1158}," i ",[1115,14457,14459],{"className":14458},[1133],[1135,14460,14461],{"xmlns":1137},[1139,14462,14463,14467],{},[1142,14464,14465],{},[1148,14466,8159],{},[1156,14468,8159],{"encoding":1158}," mají jen dvě varianty\n(",[1115,14471,14473],{"className":14472},[1133],[1135,14474,14475],{"xmlns":1137},[1139,14476,14477,14489],{},[1142,14478,14479,14481,14483,14485,14487],{},[1148,14480,71],{},[1495,14482,1503],{},[1148,14484,2695],{},[1495,14486,1503],{},[1152,14488,2639],{},[1156,14490,14491],{"encoding":1158},"r = s = 2","):",[1532,14494,14495,14579],{},[1535,14496,14497],{},[1538,14498,14499,14518,14537,14556],{},[1541,14500,14501],{},[1115,14502,14504],{"className":14503},[1133],[1135,14505,14506],{"xmlns":1137},[1139,14507,14508,14516],{},[1142,14509,14510,14512,14514],{},[1148,14511,8090],{},[1148,14513,11811],{"mathvariant":1599},[1148,14515,8159],{},[1156,14517,11816],{"encoding":1158},[1541,14519,14520],{},[1115,14521,14523],{"className":14522},[1133],[1135,14524,14525],{"xmlns":1137},[1139,14526,14527,14535],{},[1142,14528,14529],{},[1145,14530,14531,14533],{},[1148,14532,8159],{},[1152,14534,1176],{},[1156,14536,11836],{"encoding":1158},[1541,14538,14539],{},[1115,14540,14542],{"className":14541},[1133],[1135,14543,14544],{"xmlns":1137},[1139,14545,14546,14554],{},[1142,14547,14548],{},[1145,14549,14550,14552],{},[1148,14551,8159],{},[1152,14553,2639],{},[1156,14555,11856],{"encoding":1158},[1541,14557,14558],{},[1115,14559,14561],{"className":14560},[1133],[1135,14562,14563],{"xmlns":1137},[1139,14564,14565,14577],{},[1142,14566,14567],{},[1145,14568,14569,14571],{},[1148,14570,2657],{},[1142,14572,14573,14575],{},[1148,14574,4085],{},[1495,14576,11672],{},[1156,14578,11902],{"encoding":1158},[1568,14580,14581,14663,14745],{},[1538,14582,14583,14602,14621,14640],{},[1573,14584,14585],{},[1115,14586,14588],{"className":14587},[1133],[1135,14589,14590],{"xmlns":1137},[1139,14591,14592,14600],{},[1142,14593,14594],{},[1145,14595,14596,14598],{},[1148,14597,8090],{},[1152,14599,1176],{},[1156,14601,11926],{"encoding":1158},[1573,14603,14604],{},[1115,14605,14607],{"className":14606},[1133],[1135,14608,14609],{"xmlns":1137},[1139,14610,14611,14619],{},[1142,14612,14613],{},[1145,14614,14615,14617],{},[1148,14616,2657],{},[1152,14618,7339],{},[1156,14620,11946],{"encoding":1158},[1573,14622,14623],{},[1115,14624,14626],{"className":14625},[1133],[1135,14627,14628],{"xmlns":1137},[1139,14629,14630,14638],{},[1142,14631,14632],{},[1145,14633,14634,14636],{},[1148,14635,2657],{},[1152,14637,7140],{},[1156,14639,11966],{"encoding":1158},[1573,14641,14642],{},[1115,14643,14645],{"className":14644},[1133],[1135,14646,14647],{"xmlns":1137},[1139,14648,14649,14661],{},[1142,14650,14651],{},[1145,14652,14653,14655],{},[1148,14654,2657],{},[1142,14656,14657,14659],{},[1152,14658,1176],{},[1495,14660,11672],{},[1156,14662,12016],{"encoding":1158},[1538,14664,14665,14684,14703,14722],{},[1573,14666,14667],{},[1115,14668,14670],{"className":14669},[1133],[1135,14671,14672],{"xmlns":1137},[1139,14673,14674,14682],{},[1142,14675,14676],{},[1145,14677,14678,14680],{},[1148,14679,8090],{},[1152,14681,2639],{},[1156,14683,12038],{"encoding":1158},[1573,14685,14686],{},[1115,14687,14689],{"className":14688},[1133],[1135,14690,14691],{"xmlns":1137},[1139,14692,14693,14701],{},[1142,14694,14695],{},[1145,14696,14697,14699],{},[1148,14698,2657],{},[1152,14700,12056],{},[1156,14702,12059],{"encoding":1158},[1573,14704,14705],{},[1115,14706,14708],{"className":14707},[1133],[1135,14709,14710],{"xmlns":1137},[1139,14711,14712,14720],{},[1142,14713,14714],{},[1145,14715,14716,14718],{},[1148,14717,2657],{},[1152,14719,7597],{},[1156,14721,12079],{"encoding":1158},[1573,14723,14724],{},[1115,14725,14727],{"className":14726},[1133],[1135,14728,14729],{"xmlns":1137},[1139,14730,14731,14743],{},[1142,14732,14733],{},[1145,14734,14735,14737],{},[1148,14736,2657],{},[1142,14738,14739,14741],{},[1152,14740,2639],{},[1495,14742,11672],{},[1156,14744,12129],{"encoding":1158},[1538,14746,14747,14770,14793,14816],{},[1573,14748,14749],{},[1115,14750,14752],{"className":14751},[1133],[1135,14753,14754],{"xmlns":1137},[1139,14755,14756,14768],{},[1142,14757,14758],{},[1145,14759,14760,14762],{},[1148,14761,2657],{},[1142,14763,14764,14766],{},[1495,14765,11672],{},[1148,14767,11580],{},[1156,14769,12291],{"encoding":1158},[1573,14771,14772],{},[1115,14773,14775],{"className":14774},[1133],[1135,14776,14777],{"xmlns":1137},[1139,14778,14779,14791],{},[1142,14780,14781],{},[1145,14782,14783,14785],{},[1148,14784,2657],{},[1142,14786,14787,14789],{},[1495,14788,11672],{},[1152,14790,1176],{},[1156,14792,12315],{"encoding":1158},[1573,14794,14795],{},[1115,14796,14798],{"className":14797},[1133],[1135,14799,14800],{"xmlns":1137},[1139,14801,14802,14814],{},[1142,14803,14804],{},[1145,14805,14806,14808],{},[1148,14807,2657],{},[1142,14809,14810,14812],{},[1495,14811,11672],{},[1152,14813,2639],{},[1156,14815,12339],{"encoding":1158},[1573,14817,14818],{},[1115,14819,14821],{"className":14820},[1133],[1135,14822,14823],{"xmlns":1137},[1139,14824,14825,14829],{},[1142,14826,14827],{},[1148,14828,2657],{},[1156,14830,2657],{"encoding":1158},[1110,14832,1478,14833,14851],{},[1115,14834,14836],{"className":14835},[1133],[1135,14837,14838],{"xmlns":1137},[1139,14839,14840,14848],{},[1142,14841,14842,14844,14846],{},[1148,14843,2657],{},[1495,14845,1641],{},[1152,14847,11398],{},[1156,14849,14850],{"encoding":1158},"n > 40"," se místo obecného vzorce používá zjednodušená varianta testového kritéria:",[1115,14853,14855],{"className":14854},[1133],[1135,14856,14857],{"xmlns":1137,"display":2151},[1139,14858,14859,14953],{},[1142,14860,14861,14867,14869,14871,14873],{},[2632,14862,14863,14865],{},[1148,14864,11297],{},[1152,14866,2639],{},[1495,14868,1503],{},[1148,14870,2657],{},[2358,14872,2360],{},[2749,14874,14875,14911],{},[1142,14876,14877,14879,14885,14891,14893,14899,14905],{},[1495,14878,2162],{"stretchy":2161},[1145,14880,14881,14883],{},[1148,14882,2657],{},[1152,14884,7339],{},[1145,14886,14887,14889],{},[1148,14888,2657],{},[1152,14890,7597],{},[1495,14892,1885],{},[1145,14894,14895,14897],{},[1148,14896,2657],{},[1152,14898,7140],{},[1145,14900,14901,14903],{},[1148,14902,2657],{},[1152,14904,12056],{},[2632,14906,14907,14909],{},[1495,14908,2181],{"stretchy":2161},[1152,14910,2639],{},[1142,14912,14913,14923,14933,14943],{},[1145,14914,14915,14917],{},[1148,14916,2657],{},[1142,14918,14919,14921],{},[1152,14920,1176],{},[1495,14922,11672],{},[1145,14924,14925,14927],{},[1148,14926,2657],{},[1142,14928,14929,14931],{},[1152,14930,2639],{},[1495,14932,11672],{},[1145,14934,14935,14937],{},[1148,14936,2657],{},[1142,14938,14939,14941],{},[1495,14940,11672],{},[1152,14942,1176],{},[1145,14944,14945,14947],{},[1148,14946,2657],{},[1142,14948,14949,14951],{},[1495,14950,11672],{},[1152,14952,2639],{},[1156,14954,14955],{"encoding":1158},"\\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}}",[1110,14957,14958,14959,15019,15020,15056,15057,15060,15061,15064],{},"s kritickým oborem ",[1115,14960,14962],{"className":14961},[1133],[1135,14963,14964],{"xmlns":1137},[1139,14965,14966,15016],{},[1142,14967,14968,14974,14976,14978,14984,14986,14992,14994,15008,15010,15012,15014],{},[1145,14969,14970,14972],{},[1148,14971,1192],{},[1148,14973,1228],{},[1495,14975,1503],{},[1495,14977,3529],{"stretchy":2161},[2632,14979,14980,14982],{},[1148,14981,11297],{},[1152,14983,2639],{},[1495,14985,1497],{},[2632,14987,14988,14990],{},[1148,14989,11297],{},[1152,14991,2639],{},[1495,14993,2940],{},[4163,14995,14996,14998,15006],{},[1148,14997,11297],{},[1142,14999,15000,15002,15004],{},[1152,15001,1176],{},[1495,15003,1885],{},[1148,15005,1228],{},[1152,15007,2639],{},[1495,15009,2162],{"stretchy":2161},[1152,15011,1176],{},[1495,15013,2181],{"stretchy":2161},[1495,15015,3558],{"stretchy":2161},[1156,15017,15018],{"encoding":1158},"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 ",[1115,15021,15023],{"className":15022},[1133],[1135,15024,15025],{"xmlns":1137},[1139,15026,15027,15053],{},[1142,15028,15029,15031,15033,15035,15037,15039,15041,15043,15045,15047,15049,15051],{},[1495,15030,2162],{"stretchy":2161},[1148,15032,71],{},[1495,15034,1885],{},[1152,15036,1176],{},[1495,15038,2181],{"stretchy":2161},[1495,15040,2162],{"stretchy":2161},[1148,15042,2695],{},[1495,15044,1885],{},[1152,15046,1176],{},[1495,15048,2181],{"stretchy":2161},[1495,15050,1503],{},[1152,15052,1176],{},[1156,15054,15055],{"encoding":1158},"(r-1)(s-1) = 1"," stupeň volnosti. V R dává tuto hodnotu ",[3161,15058,15059],{},"chisq.test(tab, correct = FALSE)",". Bez ",[3161,15062,15063],{},"correct = FALSE"," R u tabulky 2 × 2 použije Yatesovu korekci na kontinuitu a testové kritérium vyjde menší.",[1392,15066,11410],{"id":15067},"mcnemarův-test",[1110,15069,15070,15071,15074,15075,15077,15078,15081,15082,15085,15086,15088],{},"Čtyřpolní tabulka z předchozí sekce porovnává dva ",[1399,15072,15073],{},"různé"," znaky na stejném souboru. ",[1399,15076,11410],{}," řeší\njinou situaci: na prvcích základního souboru se měří ",[1399,15079,15080],{},"jeden"," alternativní znak, a to ",[1399,15083,15084],{},"dvakrát"," — před a po\nnějakém zásahu. Cílem je zjistit, zda zásah změnil pravděpodobnostní rozdělení variant tohoto znaku. Jde tedy o\n",[1399,15087,11406],{}," (stejné prvky měřené opakovaně), ne o dva nezávisle naměřené znaky.",[1110,15090,15091],{},"Kontingenční tabulka před\u002Fpo má tvar:",[1532,15093,15094,15128],{},[1535,15095,15096],{},[1538,15097,15098,15101,15103,15105],{},[1541,15099,15100],{},"před \\ po",[1541,15102,6294],{},[1541,15104,1885],{},[1541,15106,15107],{},[1115,15108,15110],{"className":15109},[1133],[1135,15111,15112],{"xmlns":1137},[1139,15113,15114,15126],{},[1142,15115,15116],{},[1145,15117,15118,15120],{},[1148,15119,2657],{},[1142,15121,15122,15124],{},[1148,15123,4085],{},[1495,15125,11672],{},[1156,15127,11902],{"encoding":1158},[1568,15129,15130,15195,15260],{},[1538,15131,15132,15134,15153,15172],{},[1573,15133,6294],{},[1573,15135,15136],{},[1115,15137,15139],{"className":15138},[1133],[1135,15140,15141],{"xmlns":1137},[1139,15142,15143,15151],{},[1142,15144,15145],{},[1145,15146,15147,15149],{},[1148,15148,2657],{},[1152,15150,7339],{},[1156,15152,11946],{"encoding":1158},[1573,15154,15155],{},[1115,15156,15158],{"className":15157},[1133],[1135,15159,15160],{"xmlns":1137},[1139,15161,15162,15170],{},[1142,15163,15164],{},[1145,15165,15166,15168],{},[1148,15167,2657],{},[1152,15169,7140],{},[1156,15171,11966],{"encoding":1158},[1573,15173,15174],{},[1115,15175,15177],{"className":15176},[1133],[1135,15178,15179],{"xmlns":1137},[1139,15180,15181,15193],{},[1142,15182,15183],{},[1145,15184,15185,15187],{},[1148,15186,2657],{},[1142,15188,15189,15191],{},[1152,15190,1176],{},[1495,15192,11672],{},[1156,15194,12016],{"encoding":1158},[1538,15196,15197,15199,15218,15237],{},[1573,15198,1885],{},[1573,15200,15201],{},[1115,15202,15204],{"className":15203},[1133],[1135,15205,15206],{"xmlns":1137},[1139,15207,15208,15216],{},[1142,15209,15210],{},[1145,15211,15212,15214],{},[1148,15213,2657],{},[1152,15215,12056],{},[1156,15217,12059],{"encoding":1158},[1573,15219,15220],{},[1115,15221,15223],{"className":15222},[1133],[1135,15224,15225],{"xmlns":1137},[1139,15226,15227,15235],{},[1142,15228,15229],{},[1145,15230,15231,15233],{},[1148,15232,2657],{},[1152,15234,7597],{},[1156,15236,12079],{"encoding":1158},[1573,15238,15239],{},[1115,15240,15242],{"className":15241},[1133],[1135,15243,15244],{"xmlns":1137},[1139,15245,15246,15258],{},[1142,15247,15248],{},[1145,15249,15250,15252],{},[1148,15251,2657],{},[1142,15253,15254,15256],{},[1152,15255,2639],{},[1495,15257,11672],{},[1156,15259,12129],{"encoding":1158},[1538,15261,15262,15285,15308,15331],{},[1573,15263,15264],{},[1115,15265,15267],{"className":15266},[1133],[1135,15268,15269],{"xmlns":1137},[1139,15270,15271,15283],{},[1142,15272,15273],{},[1145,15274,15275,15277],{},[1148,15276,2657],{},[1142,15278,15279,15281],{},[1495,15280,11672],{},[1148,15282,11580],{},[1156,15284,12291],{"encoding":1158},[1573,15286,15287],{},[1115,15288,15290],{"className":15289},[1133],[1135,15291,15292],{"xmlns":1137},[1139,15293,15294,15306],{},[1142,15295,15296],{},[1145,15297,15298,15300],{},[1148,15299,2657],{},[1142,15301,15302,15304],{},[1495,15303,11672],{},[1152,15305,1176],{},[1156,15307,12315],{"encoding":1158},[1573,15309,15310],{},[1115,15311,15313],{"className":15312},[1133],[1135,15314,15315],{"xmlns":1137},[1139,15316,15317,15329],{},[1142,15318,15319],{},[1145,15320,15321,15323],{},[1148,15322,2657],{},[1142,15324,15325,15327],{},[1495,15326,11672],{},[1152,15328,2639],{},[1156,15330,12339],{"encoding":1158},[1573,15332,15333],{},[1115,15334,15336],{"className":15335},[1133],[1135,15337,15338],{"xmlns":1137},[1139,15339,15340,15344],{},[1142,15341,15342],{},[1148,15343,2657],{},[1156,15345,2657],{"encoding":1158},[1110,15347,15348,15349,2261,15366,15383,15384,15387,15388,2261,15405,15422,15423,15426],{},"Pole ",[1115,15350,15352],{"className":15351},[1133],[1135,15353,15354],{"xmlns":1137},[1139,15355,15356,15364],{},[1142,15357,15358],{},[1145,15359,15360,15362],{},[1148,15361,2657],{},[1152,15363,7339],{},[1156,15365,11946],{"encoding":1158},[1115,15367,15369],{"className":15368},[1133],[1135,15370,15371],{"xmlns":1137},[1139,15372,15373,15381],{},[1142,15374,15375],{},[1145,15376,15377,15379],{},[1148,15378,2657],{},[1152,15380,7597],{},[1156,15382,12079],{"encoding":1158}," jsou ",[1399,15385,15386],{},"shodná"," (prvek zůstal ve stejné variantě), pole ",[1115,15389,15391],{"className":15390},[1133],[1135,15392,15393],{"xmlns":1137},[1139,15394,15395,15403],{},[1142,15396,15397],{},[1145,15398,15399,15401],{},[1148,15400,2657],{},[1152,15402,7140],{},[1156,15404,11966],{"encoding":1158},[1115,15406,15408],{"className":15407},[1133],[1135,15409,15410],{"xmlns":1137},[1139,15411,15412,15420],{},[1142,15413,15414],{},[1145,15415,15416,15418],{},[1148,15417,2657],{},[1152,15419,12056],{},[1156,15421,12059],{"encoding":1158}," jsou\n",[1399,15424,15425],{},"diskordantní"," (prvek mezi měřeními variantu změnil) — jen ta rozhodují o výsledku testu:",[1110,15428,15429],{},[1971,15430],{"alt":15431,"className":15432,"src":15433},"mask-kt-mcnemar-tabulka",[1343,1975],"\u002Fwiki-assets\u002Fmask-kt-mcnemar-tabulka.png",[1110,15435,15436],{},[1399,15437,12548],{},[2239,15439,15440,15477,15558,15616],{},[1127,15441,15442,15476],{},[1115,15443,15445],{"className":15444},[1133],[1135,15446,15447],{"xmlns":1137},[1139,15448,15449,15473],{},[1142,15450,15451,15457,15459,15465,15467],{},[1145,15452,15453,15455],{},[1148,15454,1150],{},[1152,15456,1154],{},[1495,15458,1497],{},[1145,15460,15461,15463],{},[1148,15462,1110],{},[1152,15464,7140],{},[1495,15466,1503],{},[1145,15468,15469,15471],{},[1148,15470,1110],{},[1152,15472,12056],{},[1156,15474,15475],{"encoding":1158},"H_0: p_{12} = p_{21}"," — pravděpodobnost přechodu z varianty (+) do (−) je stejná jako pravděpodobnost\npřechodu z (−) do (+); zásah tedy nemá na rozdělení variant žádný vliv.",[1127,15478,2076,15479,15541,15543,15544,15557],{},[1115,15480,15482],{"className":15481},[1133],[1135,15483,15484],{"xmlns":1137,"display":2151},[1139,15485,15486,15538],{},[1142,15487,15488,15494,15496],{},[2632,15489,15490,15492],{},[1148,15491,11297],{},[1152,15493,2639],{},[1495,15495,1503],{},[2749,15497,15498,15522],{},[1142,15499,15500,15502,15508,15510,15516],{},[1495,15501,2162],{"stretchy":2161},[1145,15503,15504,15506],{},[1148,15505,2657],{},[1152,15507,7140],{},[1495,15509,1885],{},[1145,15511,15512,15514],{},[1148,15513,2657],{},[1152,15515,12056],{},[2632,15517,15518,15520],{},[1495,15519,2181],{"stretchy":2161},[1152,15521,2639],{},[1142,15523,15524,15530,15532],{},[1145,15525,15526,15528],{},[1148,15527,2657],{},[1152,15529,7140],{},[1495,15531,6294],{},[1145,15533,15534,15536],{},[1148,15535,2657],{},[1152,15537,12056],{},[1156,15539,15540],{"encoding":1158},"\\chi^2 = \\frac{(n_{12} - n_{21})^2}{n_{12} + n_{21}}",[12838,15542],{},"má asymptoticky Pearsonovo rozdělení o ",[1115,15545,15547],{"className":15546},[1133],[1135,15548,15549],{"xmlns":1137},[1139,15550,15551,15555],{},[1142,15552,15553],{},[1152,15554,1176],{},[1156,15556,1176],{"encoding":1158}," stupni volnosti.",[1127,15559,8778,15560,1335],{},[1115,15561,15563],{"className":15562},[1133],[1135,15564,15565],{"xmlns":1137},[1139,15566,15567,15613],{},[1142,15568,15569,15571,15573,15575,15581,15583,15589,15591,15605,15607,15609,15611],{},[1148,15570,1192],{},[1495,15572,1503],{},[1495,15574,3529],{"stretchy":2161},[2632,15576,15577,15579],{},[1148,15578,11297],{},[1152,15580,2639],{},[1495,15582,1497],{},[2632,15584,15585,15587],{},[1148,15586,11297],{},[1152,15588,2639],{},[1495,15590,2940],{},[4163,15592,15593,15595,15603],{},[1148,15594,11297],{},[1142,15596,15597,15599,15601],{},[1152,15598,1176],{},[1495,15600,1885],{},[1148,15602,1228],{},[1152,15604,2639],{},[1495,15606,2162],{"stretchy":2161},[1152,15608,1176],{},[1495,15610,2181],{"stretchy":2161},[1495,15612,3558],{"stretchy":2161},[1156,15614,15615],{"encoding":1158},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}(1)\\}",[1127,15617,13072,15618,3598,15631,15648,15649,15666],{},[1115,15619,15621],{"className":15620},[1133],[1135,15622,15623],{"xmlns":1137},[1139,15624,15625,15629],{},[1142,15626,15627],{},[1148,15628,1192],{},[1156,15630,1192],{"encoding":1158},[1115,15632,15634],{"className":15633},[1133],[1135,15635,15636],{"xmlns":1137},[1139,15637,15638,15646],{},[1142,15639,15640],{},[1145,15641,15642,15644],{},[1148,15643,1150],{},[1152,15645,1154],{},[1156,15647,1159],{"encoding":1158}," a přijímáme ",[1115,15650,15652],{"className":15651},[1133],[1135,15653,15654],{"xmlns":1137},[1139,15655,15656,15664],{},[1142,15657,15658],{},[1145,15659,15660,15662],{},[1148,15661,1150],{},[1152,15663,1176],{},[1156,15665,1179],{"encoding":1158},": zásah rozdělení variant změnil.",[1110,15668,15669,15670,15673,15674,15677,15678,15680],{},"V R počítá tento test funkce ",[3161,15671,15672],{},"mcnemar.test()",". Vzorec výše ",[1399,15675,15676],{},"neobsahuje korekci na kontinuitu"," — aby R vrátilo\npřesně tuto hodnotu, musí se volat s ",[3161,15679,15063],{}," (viz Časté chyby níže).",[1103,15682,15684,15691,15694,15697,15794],{"className":15683,"dataCallout":3323},[1106,3322],[1110,15685,15687,15690],{"className":15686},[1113],[1115,15688],{"className":15689,"ariaHidden":1121},[1118,3330,1120],"Příklad: informační kampaň a zveřejňování na Facebooku",[1110,15692,15693],{},"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.",[1110,15695,15696],{},"Základní soubor: všichni studenti; výběrový soubor: vybraní studenti; měřený znak: zveřejňování (ano \u002F ne).",[1532,15698,15699,15734],{},[1535,15700,15701],{},[1538,15702,15703,15705,15708,15711],{},[1541,15704,15100],{},[1541,15706,15707],{},"nezveřejňuje",[1541,15709,15710],{},"zveřejňuje",[1541,15712,15713],{},[1115,15714,15716],{"className":15715},[1133],[1135,15717,15718],{"xmlns":1137},[1139,15719,15720,15732],{},[1142,15721,15722],{},[1145,15723,15724,15726],{},[1148,15725,2657],{},[1142,15727,15728,15730],{},[1148,15729,4085],{},[1495,15731,11672],{},[1156,15733,11902],{"encoding":1158},[1568,15735,15736,15748,15760],{},[1538,15737,15738,15740,15742,15745],{},[1573,15739,15707],{},[1573,15741,13266],{},[1573,15743,15744],{},"68",[1573,15746,15747],{},"92",[1538,15749,15750,15752,15754,15757],{},[1573,15751,15710],{},[1573,15753,13700],{},[1573,15755,15756],{},"50",[1573,15758,15759],{},"78",[1538,15761,15762,15785,15788,15791],{},[1573,15763,15764],{},[1115,15765,15767],{"className":15766},[1133],[1135,15768,15769],{"xmlns":1137},[1139,15770,15771,15783],{},[1142,15772,15773],{},[1145,15774,15775,15777],{},[1148,15776,2657],{},[1142,15778,15779,15781],{},[1495,15780,11672],{},[1148,15782,11580],{},[1156,15784,12291],{"encoding":1158},[1573,15786,15787],{},"52",[1573,15789,15790],{},"118",[1573,15792,15793],{},"170",[1110,15795,15796,15829],{},[1115,15797,15799],{"className":15798},[1133],[1135,15800,15801],{"xmlns":1137},[1139,15802,15803,15827],{},[1142,15804,15805,15811,15813,15819,15821],{},[1145,15806,15807,15809],{},[1148,15808,1150],{},[1152,15810,1154],{},[1495,15812,1497],{},[1145,15814,15815,15817],{},[1148,15816,1110],{},[1152,15818,7140],{},[1495,15820,1503],{},[1145,15822,15823,15825],{},[1148,15824,1110],{},[1152,15826,12056],{},[1156,15828,15475],{"encoding":1158}," — informační kampaň nemá na chování vliv.",[3166,15831,15833],{"className":3168,"code":15832,"language":71,"meta":3170,"style":3170},"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",[3161,15834,15835,15859,15873,15891,15901,15924,15943],{"__ignoreMap":3170},[1115,15836,15837,15840,15842,15844,15846,15848,15850,15852,15854,15857],{"class":3175,"line":10},[1115,15838,15839],{"class":3178},"tab3",[1115,15841,3182],{"class":3181},[1115,15843,13372],{"class":3185},[1115,15845,2162],{"class":3189},[1115,15847,1991],{"class":3185},[1115,15849,2162],{"class":3189},[1115,15851,13266],{"class":3192},[1115,15853,2188],{"class":3181},[1115,15855,15856],{"class":3192}," 68",[1115,15858,9400],{"class":3181},[1115,15860,15861,15864,15866,15869,15871],{"class":3175,"line":27},[1115,15862,15863],{"class":3192},"                 28",[1115,15865,2188],{"class":3181},[1115,15867,15868],{"class":3192}," 50",[1115,15870,2181],{"class":3189},[1115,15872,9400],{"class":3181},[1115,15874,15875,15877,15879,15881,15883,15885,15887,15889],{"class":3175,"line":148},[1115,15876,13446],{"class":3178},[1115,15878,3252],{"class":3181},[1115,15880,7909],{"class":3192},[1115,15882,2188],{"class":3181},[1115,15884,13455],{"class":3178},[1115,15886,3252],{"class":3181},[1115,15888,5282],{"class":3192},[1115,15890,9400],{"class":3181},[1115,15892,15893,15895,15897,15899],{"class":3175,"line":111},[1115,15894,13466],{"class":3178},[1115,15896,3252],{"class":3181},[1115,15898,13471],{"class":3185},[1115,15900,13474],{"class":3189},[1115,15902,15903,15906,15908,15910,15912,15915,15917,15920,15922],{"class":3175,"line":96},[1115,15904,15905],{"class":3178},"                 pred",[1115,15907,3252],{"class":3181},[1115,15909,3186],{"class":3185},[1115,15911,2162],{"class":3189},[1115,15913,15914],{"class":3265},"\"nezverejnuje\"",[1115,15916,2188],{"class":3181},[1115,15918,15919],{"class":3265}," \"zverejnuje\"",[1115,15921,2181],{"class":3189},[1115,15923,9400],{"class":3181},[1115,15925,15926,15929,15931,15933,15935,15937,15939,15941],{"class":3175,"line":89},[1115,15927,15928],{"class":3178},"                 po",[1115,15930,13867],{"class":3181},[1115,15932,3186],{"class":3185},[1115,15934,2162],{"class":3189},[1115,15936,15914],{"class":3265},[1115,15938,2188],{"class":3181},[1115,15940,15919],{"class":3265},[1115,15942,13535],{"class":3189},[1115,15944,15945,15948,15950,15952,15954,15957,15959,15962],{"class":3175,"line":82},[1115,15946,15947],{"class":3185},"mcnemar.test",[1115,15949,2162],{"class":3189},[1115,15951,15839],{"class":3178},[1115,15953,2188],{"class":3181},[1115,15955,15956],{"class":3178}," correct",[1115,15958,3252],{"class":3181},[1115,15960,15961],{"class":3192}," FALSE",[1115,15963,3235],{"class":3189},[3166,15965,15968],{"className":15966,"code":15967,"language":3274,"meta":3170},[3272],"    McNemar's Chi-squared test\n\ndata:  tab3\nMcNemar's chi-squared = 16.667, df = 1, p-value = 4.456e-05\n",[3161,15969,15967],{"__ignoreMap":3170},[1110,15971,15972,15973,2324,15992,16009,16010,16027],{},"P-hodnota ",[1115,15974,15976],{"className":15975},[1133],[1135,15977,15978],{"xmlns":1137},[1139,15979,15980,15989],{},[1142,15981,15982,15985,15987],{},[1152,15983,15984],{},"0,00004456",[1495,15986,1682],{},[1152,15988,3314],{},[1156,15990,15991],{"encoding":1158},"0{,}00004456 \u003C 0{,}05",[1115,15993,15995],{"className":15994},[1133],[1135,15996,15997],{"xmlns":1137},[1139,15998,15999,16007],{},[1142,16000,16001],{},[1145,16002,16003,16005],{},[1148,16004,1150],{},[1152,16006,1154],{},[1156,16008,1159],{"encoding":1158}," zamítáme, přijímáme ",[1115,16011,16013],{"className":16012},[1133],[1135,16014,16015],{"xmlns":1137},[1139,16016,16017,16025],{},[1142,16018,16019],{},[1145,16020,16021,16023],{},[1148,16022,1150],{},[1152,16024,1176],{},[1156,16026,1179],{"encoding":1158}," — informační kampaň měla vliv na změnu\nchování studentů ve zveřejňování údajů na Facebooku.",[1392,16029,10963],{"id":10962},[1103,16031,16033,16040],{"className":16032,"dataCallout":5141},[1106,5140],[1110,16034,16036,16039],{"className":16035},[1113],[1115,16037],{"className":16038,"ariaHidden":1121},[1118,5148,1120],"Test nezávislosti na párovaných datech",[1110,16041,16042,16043,16045],{},"Tabulka před\u002Fpo vypadá jako obyčejná kontingenční tabulka, ale ",[3161,16044,13142],{}," 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.",[3166,16047,16049],{"className":3168,"code":16048,"language":71,"meta":3170,"style":3170},"chisq.test(tab3)\n",[3161,16050,16051],{"__ignoreMap":3170},[1115,16052,16053,16055,16057,16059],{"class":3175,"line":10},[1115,16054,13540],{"class":3185},[1115,16056,2162],{"class":3189},[1115,16058,15839],{"class":3178},[1115,16060,3235],{"class":3189},[3166,16062,16065],{"className":16063,"code":16064,"language":3274,"meta":3170},[3272],"    Pearson's Chi-squared test with Yates' continuity correction\n\ndata:  tab3\nX-squared = 1.4793, df = 1, p-value = 0.2239\n",[3161,16066,16064],{"__ignoreMap":3170},[1110,16068,15972,16069,16088,16089,16106,16107,16109,16110,1335],{},[1115,16070,16072],{"className":16071},[1133],[1135,16073,16074],{"xmlns":1137},[1139,16075,16076,16085],{},[1142,16077,16078,16081,16083],{},[1152,16079,16080],{},"0,224",[1495,16082,1641],{},[1152,16084,3314],{},[1156,16086,16087],{"encoding":1158},"0{,}224 > 0{,}05"," by vedla k nezamítnutí ",[1115,16090,16092],{"className":16091},[1133],[1135,16093,16094],{"xmlns":1137},[1139,16095,16096,16104],{},[1142,16097,16098],{},[1145,16099,16100,16102],{},[1148,16101,1150],{},[1152,16103,1154],{},[1156,16105,1159],{"encoding":1158}," — opačný závěr než správný McNemarův test. Na\npárovaná data (stejné prvky měřené dvakrát) vždy patří ",[3161,16108,15672],{},", nikdy ",[3161,16111,13142],{},[1103,16113,16115,16124],{"className":16114,"dataCallout":5141},[1106,5140],[1110,16116,16118,16121,16122],{"className":16117},[1113],[1115,16119],{"className":16120,"ariaHidden":1121},[1118,5148,1120],"Výchozí korekce na kontinuitu v ",[3161,16123,15672],{},[1110,16125,16126,16127,16130],{},"Bez argumentu ",[3161,16128,16129],{},"correct"," R ve výchozím nastavení použije Yatesovu korekci na kontinuitu, která dá jinou\np-hodnotu než nekorigovaný vzorec uvedený výše.",[3166,16132,16134],{"className":3168,"code":16133,"language":71,"meta":3170,"style":3170},"mcnemar.test(tab3)\n",[3161,16135,16136],{"__ignoreMap":3170},[1115,16137,16138,16140,16142,16144],{"class":3175,"line":10},[1115,16139,15947],{"class":3185},[1115,16141,2162],{"class":3189},[1115,16143,15839],{"class":3178},[1115,16145,3235],{"class":3189},[3166,16147,16150],{"className":16148,"code":16149,"language":3274,"meta":3170},[3272],"    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",[3161,16151,16149],{"__ignoreMap":3170},[1110,16153,16154,16155,16173,16174,16193,16194,16207,16208,1335],{},"Oproti nekorigované hodnotě ",[1115,16156,16158],{"className":16157},[1133],[1135,16159,16160],{"xmlns":1137},[1139,16161,16162,16170],{},[1142,16163,16164,16166,16168],{},[1148,16165,1110],{},[1495,16167,1503],{},[1152,16169,15984],{},[1156,16171,16172],{"encoding":1158},"p = 0{,}00004456"," vyjde ",[1115,16175,16177],{"className":16176},[1133],[1135,16178,16179],{"xmlns":1137},[1139,16180,16181,16190],{},[1142,16182,16183,16185,16187],{},[1148,16184,1110],{},[1495,16186,1503],{},[1152,16188,16189],{},"0,00006879",[1156,16191,16192],{"encoding":1158},"p = 0{,}00006879"," — v tomto příkladu obě vedou ke\nstejnému rozhodnutí, ale u hodnot blíž hranici ",[1115,16195,16197],{"className":16196},[1133],[1135,16198,16199],{"xmlns":1137},[1139,16200,16201,16205],{},[1142,16202,16203],{},[1148,16204,1228],{},[1156,16206,1231],{"encoding":1158}," by korekce mohla rozhodnutí změnit. Aby R reprodukovalo\nnekorigovaný vzorec, je třeba vždy volat ",[3161,16209,16210],{},"mcnemar.test(x, correct = FALSE)",[1392,16212,11120],{"id":11119},[1124,16214,16215,16220,16225,16230,16235,16240,16245],{},[1127,16216,16217],{},[1340,16218,11128],{"className":16219,"dataFsResolvedFilePath":1344,"href":1345},[1343],[1127,16221,16222],{},[1340,16223,1094],{"className":16224,"dataFsResolvedFilePath":11426,"href":11427},[1343],[1127,16226,16227],{},[1340,16228,11140],{"className":16229,"dataFsResolvedFilePath":1351,"href":1352},[1343],[1127,16231,16232],{},[1340,16233,11134],{"className":16234,"dataFsResolvedFilePath":1358,"href":1359},[1343],[1127,16236,16237],{},[1340,16238,11148],{"className":16239,"dataFsResolvedFilePath":11146,"href":11147},[1343],[1127,16241,16242],{},[1340,16243,11164],{"className":16244,"dataFsResolvedFilePath":11162,"href":11163},[1343],[1127,16246,16247],{},[1340,16248,11172],{"className":16249,"dataFsResolvedFilePath":11170,"href":11171},[1343],[1392,16251,11175],{"id":934},[1110,16253,11178,16254,11182],{},[10079,16255,11181],{},[11184,16257,16258],{},"html pre.shiki 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05.docx","topics\u002Fkontingencni-tabulky",[23,67,714,486,768,71],"E-gDO0c3LOdVy6YB6I-h8KKMQKlrqjomMSQWFmOANZE",{"id":16279,"title":11134,"body":16280,"course":23,"courses":11214,"created":11215,"description":3170,"extension":11216,"meta":20688,"navigation":11218,"path":20689,"seo":20690,"sources":20691,"stem":20694,"tags":20695,"type":11231,"updated":11215,"__hash__":20696},"topics\u002Ftopics\u002Fnahodne-veliciny-a-rozdeleni.md",{"type":1096,"value":16281,"toc":20676},[16282,16285,16563,16567,16795,16798,16865,16869,16876,16883,17040,17079,17082,17315,17318,17395,17449,17547,17551,17653,17656,17660,17666,17721,17724,17732,17882,17889,17941,17971,18088,18091,18139,18301,18356,18363,18468,18529,18533,18635,18638,18674,18680,18739,18787,18794,18828,18834,18837,18885,18892,18954,18960,18963,19026,19033,19070,19076,19079,19083,19107,19438,19476,19530,19656,19662,19666,19673,19692,19798,19842,19861,19956,19973,20015,20190,20197,20200,20203,20357,20360,20433,20439,20441,20626,20628,20667,20669,20673],[1099,16283,11134],{"id":16284},"náhodné-veličiny-a-rozdělení-pravděpodobnosti",[1103,16286,16288,16294],{"className":16287,"dataCallout":1108},[1106,1107],[1110,16289,16291,1122],{"className":16290},[1113],[1115,16292],{"className":16293,"ariaHidden":1121},[1118,1119,1120],[1124,16295,16296,16307,16406,16473,16551],{},[1127,16297,16298,16299,16302,16303,16306],{},"Náhodná veličina je funkce, která výsledkům pokusu přiřazuje reálná čísla; rozlišujeme ",[1399,16300,16301],{},"diskrétní"," (izolované hodnoty s nenulovou pravděpodobností) a ",[1399,16304,16305],{},"spojité"," (hodnoty z intervalu, každý bod má nulovou pravděpodobnost).",[1127,16308,16309,16310,1953,16313,16347,16348,4136,16385,16405],{},"Každou náhodnou veličinu popisuje ",[1399,16311,16312],{},"distribuční funkce",[1115,16314,16316],{"className":16315},[1133],[1135,16317,16318],{"xmlns":1137},[1139,16319,16320,16344],{},[1142,16321,16322,16324,16326,16328,16330,16332,16334,16336,16338,16340,16342],{},[1148,16323,1387],{},[1495,16325,2162],{"stretchy":2161},[1148,16327,2675],{},[1495,16329,2181],{"stretchy":2161},[1495,16331,1503],{},[1148,16333,2158],{},[1495,16335,2162],{"stretchy":2161},[1148,16337,2618],{},[1495,16339,2519],{},[1148,16341,2675],{},[1495,16343,2181],{"stretchy":2161},[1156,16345,16346],{"encoding":1158},"F(x) = P(X \\le x)","; u spojité veličiny platí ",[1115,16349,16351],{"className":16350},[1133],[1135,16352,16353],{"xmlns":1137},[1139,16354,16355,16382],{},[1142,16356,16357,16365,16367,16369,16371,16373,16376,16378,16380],{},[2632,16358,16359,16361],{},[1148,16360,1387],{},[1495,16362,16364],{"mathvariant":1599,"lspace":16363,"rspace":16363},"0em","′",[1495,16366,2162],{"stretchy":2161},[1148,16368,2675],{},[1495,16370,2181],{"stretchy":2161},[1495,16372,1503],{},[1148,16374,16375],{},"f",[1495,16377,2162],{"stretchy":2161},[1148,16379,2675],{},[1495,16381,2181],{"stretchy":2161},[1156,16383,16384],{"encoding":1158},"F'(x) = f(x)",[1115,16386,16388],{"className":16387},[1133],[1135,16389,16390],{"xmlns":1137},[1139,16391,16392,16402],{},[1142,16393,16394,16396,16398,16400],{},[1148,16395,16375],{},[1495,16397,2162],{"stretchy":2161},[1148,16399,2675],{},[1495,16401,2181],{"stretchy":2161},[1156,16403,16404],{"encoding":1158},"f(x)"," je hustota pravděpodobnosti.",[1127,16407,16408,16409,1335],{},"Pravděpodobnost na intervalu se počítá jako ",[1115,16410,16412],{"className":16411},[1133],[1135,16413,16414],{"xmlns":1137},[1139,16415,16416,16470],{},[1142,16417,16418,16420,16422,16428,16430,16432,16434,16440,16442,16444,16446,16448,16454,16456,16458,16460,16462,16468],{},[1148,16419,2158],{},[1495,16421,2162],{"stretchy":2161},[1145,16423,16424,16426],{},[1148,16425,2675],{},[1152,16427,1176],{},[1495,16429,1682],{},[1148,16431,2618],{},[1495,16433,1682],{},[1145,16435,16436,16438],{},[1148,16437,2675],{},[1152,16439,2639],{},[1495,16441,2181],{"stretchy":2161},[1495,16443,1503],{},[1148,16445,1387],{},[1495,16447,2162],{"stretchy":2161},[1145,16449,16450,16452],{},[1148,16451,2675],{},[1152,16453,2639],{},[1495,16455,2181],{"stretchy":2161},[1495,16457,1885],{},[1148,16459,1387],{},[1495,16461,2162],{"stretchy":2161},[1145,16463,16464,16466],{},[1148,16465,2675],{},[1152,16467,1176],{},[1495,16469,2181],{"stretchy":2161},[1156,16471,16472],{"encoding":1158},"P(x_1 \u003C X \u003C x_2) = F(x_2) - F(x_1)",[1127,16474,16475,1953,16478,16507,16508,1195,16511,1195,16514,16517,16518,16532,16533,1335],{},[1399,16476,16477],{},"Normální rozdělení",[1115,16479,16481],{"className":16480},[1133],[1135,16482,16483],{"xmlns":1137},[1139,16484,16485,16504],{},[1142,16486,16487,16489,16491,16493,16496,16502],{},[1148,16488,2624],{},[1495,16490,2162],{"stretchy":2161},[1148,16492,1500],{},[1495,16494,16495],{"separator":1121},";",[2632,16497,16498,16500],{},[1148,16499,2636],{},[1152,16501,2639],{},[1495,16503,2181],{"stretchy":2161},[1156,16505,16506],{"encoding":1158},"N(\\mu; \\sigma^2)"," je nejdůležitější spojité rozdělení; v R ho počítáme funkcemi ",[3161,16509,16510],{},"dnorm",[3161,16512,16513],{},"pnorm",[3161,16515,16516],{},"qnorm"," — R jako parametr očekává směrodatnou odchylku ",[1115,16519,16521],{"className":16520},[1133],[1135,16522,16523],{"xmlns":1137},[1139,16524,16525,16529],{},[1142,16526,16527],{},[1148,16528,2636],{},[1156,16530,16531],{"encoding":1158},"\\sigma",", ne rozptyl ",[1115,16534,16536],{"className":16535},[1133],[1135,16537,16538],{"xmlns":1137},[1139,16539,16540,16548],{},[1142,16541,16542],{},[2632,16543,16544,16546],{},[1148,16545,2636],{},[1152,16547,2639],{},[1156,16549,16550],{"encoding":1158},"\\sigma^2",[1127,16552,16553,1195,16556,2261,16559,16562],{},[1399,16554,16555],{},"Studentovo",[1399,16557,16558],{},"Pearsonovo (χ²)",[1399,16560,16561],{},"Fisherovo-Snedecorovo"," rozdělení slouží jako nástroj pro pozdější konstrukci intervalů spolehlivosti a testování hypotéz.",[1392,16564,16566],{"id":16565},"náhodná-veličina","Náhodná veličina",[1110,16568,16569,16572,16573,16588,16589,1953,16591,16604,16605,16624,16625,4136,16638,16662,16663,1195,16676,1195,16689,16702,16703,1195,16716,1195,16729,16742,16743,16756,16757,16770,16771,1335],{},[1340,16570,11128],{"className":16571,"dataFsResolvedFilePath":1344,"href":1345},[1343]," pracuje s veličinami, jejichž hodnota závisí na náhodě. Formálně: uvažujeme základní prostor ",[1115,16574,16576],{"className":16575},[1133],[1135,16577,16578],{"xmlns":1137},[1139,16579,16580,16585],{},[1142,16581,16582],{},[1148,16583,16584],{"mathvariant":1599},"Ω",[1156,16586,16587],{"encoding":1158},"\\Omega"," přiřazený výsledkům pokusu. ",[1399,16590,16566],{},[1115,16592,16594],{"className":16593},[1133],[1135,16595,16596],{"xmlns":1137},[1139,16597,16598,16602],{},[1142,16599,16600],{},[1148,16601,2618],{},[1156,16603,2618],{"encoding":1158}," je funkce, která prvkům ",[1115,16606,16608],{"className":16607},[1133],[1135,16609,16610],{"xmlns":1137},[1139,16611,16612,16621],{},[1142,16613,16614,16617,16619],{},[1148,16615,16616],{},"ω",[1495,16618,2167],{},[1148,16620,16584],{"mathvariant":1599},[1156,16622,16623],{"encoding":1158},"\\omega \\in \\Omega"," přiřazuje reálná čísla ",[1115,16626,16628],{"className":16627},[1133],[1135,16629,16630],{"xmlns":1137},[1139,16631,16632,16636],{},[1142,16633,16634],{},[1148,16635,2675],{},[1156,16637,2675],{"encoding":1158},[1115,16639,16641],{"className":16640},[1133],[1135,16642,16643],{"xmlns":1137},[1139,16644,16645,16659],{},[1142,16646,16647,16649,16651,16653,16655,16657],{},[1148,16648,2675],{},[1495,16650,1503],{},[1148,16652,2618],{},[1495,16654,2162],{"stretchy":2161},[1148,16656,16616],{},[1495,16658,2181],{"stretchy":2161},[1156,16660,16661],{"encoding":1158},"x = X(\\omega)",". Náhodné veličiny značíme velkými písmeny (",[1115,16664,16666],{"className":16665},[1133],[1135,16667,16668],{"xmlns":1137},[1139,16669,16670,16674],{},[1142,16671,16672],{},[1148,16673,2618],{},[1156,16675,2618],{"encoding":1158},[1115,16677,16679],{"className":16678},[1133],[1135,16680,16681],{"xmlns":1137},[1139,16682,16683,16687],{},[1142,16684,16685],{},[1148,16686,4092],{},[1156,16688,4092],{"encoding":1158},[1115,16690,16692],{"className":16691},[1133],[1135,16693,16694],{"xmlns":1137},[1139,16695,16696,16700],{},[1142,16697,16698],{},[1148,16699,2088],{},[1156,16701,2088],{"encoding":1158},"), jejich konkrétní hodnoty odpovídajícími malými písmeny (",[1115,16704,16706],{"className":16705},[1133],[1135,16707,16708],{"xmlns":1137},[1139,16709,16710,16714],{},[1142,16711,16712],{},[1148,16713,2675],{},[1156,16715,2675],{"encoding":1158},[1115,16717,16719],{"className":16718},[1133],[1135,16720,16721],{"xmlns":1137},[1139,16722,16723,16727],{},[1142,16724,16725],{},[1148,16726,10129],{},[1156,16728,10129],{"encoding":1158},[1115,16730,16732],{"className":16731},[1133],[1135,16733,16734],{"xmlns":1137},[1139,16735,16736,16740],{},[1142,16737,16738],{},[1148,16739,1373],{},[1156,16741,1373],{"encoding":1158},"); pravděpodobnost, že ",[1115,16744,16746],{"className":16745},[1133],[1135,16747,16748],{"xmlns":1137},[1139,16749,16750,16754],{},[1142,16751,16752],{},[1148,16753,2618],{},[1156,16755,2618],{"encoding":1158}," nabyla hodnoty ",[1115,16758,16760],{"className":16759},[1133],[1135,16761,16762],{"xmlns":1137},[1139,16763,16764,16768],{},[1142,16765,16766],{},[1148,16767,2675],{},[1156,16769,2675],{"encoding":1158},", zapisujeme ",[1115,16772,16774],{"className":16773},[1133],[1135,16775,16776],{"xmlns":1137},[1139,16777,16778,16792],{},[1142,16779,16780,16782,16784,16786,16788,16790],{},[1148,16781,2158],{},[1495,16783,2162],{"stretchy":2161},[1148,16785,2618],{},[1495,16787,1503],{},[1148,16789,2675],{},[1495,16791,2181],{"stretchy":2161},[1156,16793,16794],{"encoding":1158},"P(X = x)",[1110,16796,16797],{},"Podle typu hodnot, kterých náhodná veličina nabývá, rozlišujeme dva typy:",[1124,16799,16800,16859],{},[1127,16801,16802,16805,16806,16819,16820,16858],{},[1399,16803,16804],{},"Diskrétní náhodná veličina"," — prvky ",[1115,16807,16809],{"className":16808},[1133],[1135,16810,16811],{"xmlns":1137},[1139,16812,16813,16817],{},[1142,16814,16815],{},[1148,16816,16584],{"mathvariant":1599},[1156,16818,16587],{"encoding":1158}," se zobrazí na osu reálných čísel jako izolované body ",[1115,16821,16823],{"className":16822},[1133],[1135,16824,16825],{"xmlns":1137},[1139,16826,16827,16855],{},[1142,16828,16829,16835,16837,16843,16845,16847,16849],{},[1145,16830,16831,16833],{},[1148,16832,2675],{},[1152,16834,1176],{},[1495,16836,2188],{"separator":1121},[1145,16838,16839,16841],{},[1148,16840,2675],{},[1152,16842,2639],{},[1495,16844,2188],{"separator":1121},[1495,16846,10697],{},[1495,16848,2188],{"separator":1121},[1145,16850,16851,16853],{},[1148,16852,2675],{},[1148,16854,10710],{},[1156,16856,16857],{"encoding":1158},"x_1, x_2, \\dots, x_k",", přičemž každý z nich má nenulovou pravděpodobnost. Příklad: počet bodů při hodu kostkou, počet studentů na cvičení.",[1127,16860,16861,16864],{},[1399,16862,16863],{},"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.",[1392,16866,16868],{"id":16867},"distribuční-funkce","Distribuční funkce",[1110,16870,16871,16872,16875],{},"Náhodná veličina nabývá při pokusu určité hodnoty, aniž bychom předem věděli, které. Při opakování pokusu se ale projevují zákonitosti, které popisují ",[1399,16873,16874],{},"zákony rozdělení",". Nejobecnějším z nich je distribuční funkce.",[1110,16877,16878],{},[1971,16879],{"alt":16880,"className":16881,"src":16882},"mask-nv-distribucni-funkce",[1343,1975],"\u002Fwiki-assets\u002Fmask-nv-distribucni-funkce.png",[1103,16884,16887,16894],{"className":16885,"dataCallout":654},[1106,16886],"callout-info",[1110,16888,16890,16893],{"className":16889},[1113],[1115,16891],{"className":16892,"ariaHidden":1121},[1118,1119,1120],"Definice",[1110,16895,16896,16897,16910,16911,16930,16931,16944,16945,16981,17000,17001,17014,17015,1335],{},"Distribuční funkcí náhodné veličiny ",[1115,16898,16900],{"className":16899},[1133],[1135,16901,16902],{"xmlns":1137},[1139,16903,16904,16908],{},[1142,16905,16906],{},[1148,16907,2618],{},[1156,16909,2618],{"encoding":1158}," nazýváme reálnou funkci ",[1115,16912,16914],{"className":16913},[1133],[1135,16915,16916],{"xmlns":1137},[1139,16917,16918,16928],{},[1142,16919,16920,16922,16924,16926],{},[1148,16921,1387],{},[1495,16923,2162],{"stretchy":2161},[1148,16925,2675],{},[1495,16927,2181],{"stretchy":2161},[1156,16929,8632],{"encoding":1158}," definovanou pro každé reálné číslo ",[1115,16932,16934],{"className":16933},[1133],[1135,16935,16936],{"xmlns":1137},[1139,16937,16938,16942],{},[1142,16939,16940],{},[1148,16941,2675],{},[1156,16943,2675],{"encoding":1158}," jako\n",[1115,16946,16948],{"className":16947},[1133],[1135,16949,16950],{"xmlns":1137},[1139,16951,16952,16978],{},[1142,16953,16954,16956,16958,16960,16962,16964,16966,16968,16970,16972,16974,16976],{},[1148,16955,1387],{},[1495,16957,2162],{"stretchy":2161},[1148,16959,2675],{},[1495,16961,2181],{"stretchy":2161},[1495,16963,1503],{},[1148,16965,2158],{},[1495,16967,2162],{"stretchy":2161},[1148,16969,2618],{},[1495,16971,2519],{},[1148,16973,2675],{},[1495,16975,2181],{"stretchy":2161},[1148,16977,1335],{"mathvariant":1599},[1156,16979,16980],{"encoding":1158},"F(x) = P(X \\le x).",[1115,16982,16984],{"className":16983},[1133],[1135,16985,16986],{"xmlns":1137},[1139,16987,16988,16998],{},[1142,16989,16990,16992,16994,16996],{},[1148,16991,1387],{},[1495,16993,2162],{"stretchy":2161},[1148,16995,2675],{},[1495,16997,2181],{"stretchy":2161},[1156,16999,8632],{"encoding":1158}," tedy vyjadřuje pravděpodobnost, s jakou ",[1115,17002,17004],{"className":17003},[1133],[1135,17005,17006],{"xmlns":1137},[1139,17007,17008,17012],{},[1142,17009,17010],{},[1148,17011,2618],{},[1156,17013,2618],{"encoding":1158}," nabude hodnoty z intervalu ",[1115,17016,17018],{"className":17017},[1133],[1135,17019,17020],{"xmlns":1137},[1139,17021,17022,17037],{},[1142,17023,17024,17026,17028,17031,17033,17035],{},[1495,17025,2162],{"stretchy":2161},[1495,17027,1885],{},[1148,17029,17030],{"mathvariant":1599},"∞",[1495,17032,2188],{"separator":1121},[1148,17034,2675],{},[1495,17036,9080],{"stretchy":2161},[1156,17038,17039],{"encoding":1158},"(-\\infty, x\\rangle",[1110,17041,17042,17043,17056,17057,17078],{},"Značí-li například ",[1115,17044,17046],{"className":17045},[1133],[1135,17047,17048],{"xmlns":1137},[1139,17049,17050,17054],{},[1142,17051,17052],{},[1148,17053,2618],{},[1156,17055,2618],{"encoding":1158}," výšku mužů v populaci, pak ",[1115,17058,17060],{"className":17059},[1133],[1135,17061,17062],{"xmlns":1137},[1139,17063,17064,17075],{},[1142,17065,17066,17068,17070,17073],{},[1148,17067,1387],{},[1495,17069,2162],{"stretchy":2161},[1152,17071,17072],{},"175",[1495,17074,2181],{"stretchy":2161},[1156,17076,17077],{"encoding":1158},"F(175)"," je pravděpodobnost, že muž měří nejvýše 175 cm.",[1110,17080,17081],{},"Pro distribuční funkci vždy platí:",[1124,17083,17084,17114,17171,17231],{},[1127,17085,17086,2188],{},[1115,17087,17089],{"className":17088},[1133],[1135,17090,17091],{"xmlns":1137},[1139,17092,17093,17111],{},[1142,17094,17095,17097,17099,17101,17103,17105,17107,17109],{},[1152,17096,1154],{},[1495,17098,2519],{},[1148,17100,1387],{},[1495,17102,2162],{"stretchy":2161},[1148,17104,2675],{},[1495,17106,2181],{"stretchy":2161},[1495,17108,2519],{},[1152,17110,1176],{},[1156,17112,17113],{"encoding":1158},"0 \\le F(x) \\le 1",[1127,17115,17116,17117,2188],{},"je neklesající: ",[1115,17118,17120],{"className":17119},[1133],[1135,17121,17122],{"xmlns":1137},[1139,17123,17124,17168],{},[1142,17125,17126,17132,17134,17140,17142,17144,17146,17152,17154,17156,17158,17160,17166],{},[1145,17127,17128,17130],{},[1148,17129,2675],{},[1152,17131,1176],{},[1495,17133,2519],{},[1145,17135,17136,17138],{},[1148,17137,2675],{},[1152,17139,2639],{},[1495,17141,2524],{},[1148,17143,1387],{},[1495,17145,2162],{"stretchy":2161},[1145,17147,17148,17150],{},[1148,17149,2675],{},[1152,17151,1176],{},[1495,17153,2181],{"stretchy":2161},[1495,17155,2519],{},[1148,17157,1387],{},[1495,17159,2162],{"stretchy":2161},[1145,17161,17162,17164],{},[1148,17163,2675],{},[1152,17165,2639],{},[1495,17167,2181],{"stretchy":2161},[1156,17169,17170],{"encoding":1158},"x_1 \\le x_2 \\Rightarrow F(x_1) \\le F(x_2)",[1127,17172,17173,17174,2188],{},"je spojitá zprava: ",[1115,17175,17177],{"className":17176},[1133],[1135,17178,17179],{"xmlns":1137},[1139,17180,17181,17228],{},[1142,17182,17183,17206,17208,17210,17212,17214,17216,17218,17220,17222,17224,17226],{},[1145,17184,17185,17192],{},[1142,17186,17187,17190],{},[1148,17188,17189],{},"lim",[1495,17191,8744],{},[1142,17193,17194,17197,17200],{},[1148,17195,17196],{},"h",[1495,17198,17199],{},"→",[2632,17201,17202,17204],{},[1152,17203,1154],{},[1495,17205,6294],{},[1148,17207,1387],{},[1495,17209,2162],{"stretchy":2161},[1148,17211,2675],{},[1495,17213,6294],{},[1148,17215,17196],{},[1495,17217,2181],{"stretchy":2161},[1495,17219,1503],{},[1148,17221,1387],{},[1495,17223,2162],{"stretchy":2161},[1148,17225,2675],{},[1495,17227,2181],{"stretchy":2161},[1156,17229,17230],{"encoding":1158},"\\lim_{h \\to 0^+} F(x+h) = F(x)",[1127,17232,17233,1195,17275,1335],{},[1115,17234,17236],{"className":17235},[1133],[1135,17237,17238],{"xmlns":1137},[1139,17239,17240,17272],{},[1142,17241,17242,17260,17262,17264,17266,17268,17270],{},[1145,17243,17244,17250],{},[1142,17245,17246,17248],{},[1148,17247,17189],{},[1495,17249,8744],{},[1142,17251,17252,17254,17256,17258],{},[1148,17253,2675],{},[1495,17255,17199],{},[1495,17257,1885],{},[1148,17259,17030],{"mathvariant":1599},[1148,17261,1387],{},[1495,17263,2162],{"stretchy":2161},[1148,17265,2675],{},[1495,17267,2181],{"stretchy":2161},[1495,17269,1503],{},[1152,17271,1154],{},[1156,17273,17274],{"encoding":1158},"\\lim_{x \\to -\\infty} F(x) = 0",[1115,17276,17278],{"className":17277},[1133],[1135,17279,17280],{"xmlns":1137},[1139,17281,17282,17312],{},[1142,17283,17284,17300,17302,17304,17306,17308,17310],{},[1145,17285,17286,17292],{},[1142,17287,17288,17290],{},[1148,17289,17189],{},[1495,17291,8744],{},[1142,17293,17294,17296,17298],{},[1148,17295,2675],{},[1495,17297,17199],{},[1148,17299,17030],{"mathvariant":1599},[1148,17301,1387],{},[1495,17303,2162],{"stretchy":2161},[1148,17305,2675],{},[1495,17307,2181],{"stretchy":2161},[1495,17309,1503],{},[1152,17311,1176],{},[1156,17313,17314],{"encoding":1158},"\\lim_{x \\to \\infty} F(x) = 1",[1110,17316,17317],{},"U spojité náhodné veličiny je distribuční funkce svázaná s hustotou pravděpodobnosti vztahem",[1115,17319,17321],{"className":17320},[1133],[1135,17322,17323],{"xmlns":1137,"display":2151},[1139,17324,17325,17392],{},[1142,17326,17327,17333,17335,17337,17339,17341,17343,17345,17347,17349,17351,17353,17355,17357,17359,17361,17363,17376,17378,17380,17382,17384,17386,17388,17390],{},[2632,17328,17329,17331],{},[1148,17330,1387],{},[1495,17332,16364],{"mathvariant":1599,"lspace":16363,"rspace":16363},[1495,17334,2162],{"stretchy":2161},[1148,17336,2675],{},[1495,17338,2181],{"stretchy":2161},[1495,17340,1503],{},[1148,17342,16375],{},[1495,17344,2162],{"stretchy":2161},[1148,17346,2675],{},[1495,17348,2181],{"stretchy":2161},[1495,17350,2188],{"separator":1121},[3520,17352],{"width":3522},[1148,17354,1387],{},[1495,17356,2162],{"stretchy":2161},[1148,17358,2675],{},[1495,17360,2181],{"stretchy":2161},[1495,17362,1503],{},[4163,17364,17365,17368,17374],{},[1495,17366,17367],{},"∫",[1142,17369,17370,17372],{},[1495,17371,1885],{},[1148,17373,17030],{"mathvariant":1599},[1148,17375,2675],{},[1148,17377,16375],{},[1495,17379,2162],{"stretchy":2161},[1148,17381,1373],{},[1495,17383,2181],{"stretchy":2161},[2358,17385,2360],{},[1148,17387,4204],{},[1148,17389,1373],{},[1148,17391,1335],{"mathvariant":1599},[1156,17393,17394],{"encoding":1158},"F'(x) = f(x), \\qquad F(x) = \\int_{-\\infty}^{x} f(t)\\,dt.",[1110,17396,17397,17398,17411,17412,2261,17430,17448],{},"Pravděpodobnost, že ",[1115,17399,17401],{"className":17400},[1133],[1135,17402,17403],{"xmlns":1137},[1139,17404,17405,17409],{},[1142,17406,17407],{},[1148,17408,2618],{},[1156,17410,2618],{"encoding":1158}," padne mezi body ",[1115,17413,17415],{"className":17414},[1133],[1135,17416,17417],{"xmlns":1137},[1139,17418,17419,17427],{},[1142,17420,17421],{},[1145,17422,17423,17425],{},[1148,17424,2675],{},[1152,17426,1176],{},[1156,17428,17429],{"encoding":1158},"x_1",[1115,17431,17433],{"className":17432},[1133],[1135,17434,17435],{"xmlns":1137},[1139,17436,17437,17445],{},[1142,17438,17439],{},[1145,17440,17441,17443],{},[1148,17442,2675],{},[1152,17444,2639],{},[1156,17446,17447],{"encoding":1158},"x_2",", se pak počítá jako",[1115,17450,17452],{"className":17451},[1133],[1135,17453,17454],{"xmlns":1137,"display":2151},[1139,17455,17456,17544],{},[1142,17457,17458,17460,17462,17468,17470,17472,17474,17480,17482,17484,17500,17502,17504,17506,17508,17510,17512,17514,17516,17518,17520,17526,17528,17530,17532,17534,17540,17542],{},[1148,17459,2158],{},[1495,17461,2162],{"stretchy":2161},[1145,17463,17464,17466],{},[1148,17465,2675],{},[1152,17467,1176],{},[1495,17469,1682],{},[1148,17471,2618],{},[1495,17473,1682],{},[1145,17475,17476,17478],{},[1148,17477,2675],{},[1152,17479,2639],{},[1495,17481,2181],{"stretchy":2161},[1495,17483,1503],{},[4163,17485,17486,17488,17494],{},[1495,17487,17367],{},[1145,17489,17490,17492],{},[1148,17491,2675],{},[1152,17493,1176],{},[1145,17495,17496,17498],{},[1148,17497,2675],{},[1152,17499,2639],{},[1148,17501,16375],{},[1495,17503,2162],{"stretchy":2161},[1148,17505,1373],{},[1495,17507,2181],{"stretchy":2161},[2358,17509,2360],{},[1148,17511,4204],{},[1148,17513,1373],{},[1495,17515,1503],{},[1148,17517,1387],{},[1495,17519,2162],{"stretchy":2161},[1145,17521,17522,17524],{},[1148,17523,2675],{},[1152,17525,2639],{},[1495,17527,2181],{"stretchy":2161},[1495,17529,1885],{},[1148,17531,1387],{},[1495,17533,2162],{"stretchy":2161},[1145,17535,17536,17538],{},[1148,17537,2675],{},[1152,17539,1176],{},[1495,17541,2181],{"stretchy":2161},[1148,17543,1335],{"mathvariant":1599},[1156,17545,17546],{"encoding":1158},"P(x_1 \u003C X \u003C x_2) = \\int_{x_1}^{x_2} f(t)\\,dt = F(x_2) - F(x_1).",[1392,17548,17550],{"id":17549},"hustota-pravděpodobnosti","Hustota pravděpodobnosti",[1103,17552,17554,17560],{"className":17553,"dataCallout":654},[1106,16886],[1110,17555,17557,16893],{"className":17556},[1113],[1115,17558],{"className":17559,"ariaHidden":1121},[1118,1119,1120],[1110,17561,17562,17563,17582,17583,17596,17597,17610,17611,1335],{},"Hustota pravděpodobnosti ",[1115,17564,17566],{"className":17565},[1133],[1135,17567,17568],{"xmlns":1137},[1139,17569,17570,17580],{},[1142,17571,17572,17574,17576,17578],{},[1148,17573,16375],{},[1495,17575,2162],{"stretchy":2161},[1148,17577,2675],{},[1495,17579,2181],{"stretchy":2161},[1156,17581,16404],{"encoding":1158}," určuje, jak jsou hodnoty spojité náhodné veličiny ",[1115,17584,17586],{"className":17585},[1133],[1135,17587,17588],{"xmlns":1137},[1139,17589,17590,17594],{},[1142,17591,17592],{},[1148,17593,2618],{},[1156,17595,2618],{"encoding":1158}," nahuštěny v okolí bodu ",[1115,17598,17600],{"className":17599},[1133],[1135,17601,17602],{"xmlns":1137},[1139,17603,17604,17608],{},[1142,17605,17606],{},[1148,17607,2675],{},[1156,17609,2675],{"encoding":1158},". Je vždy nezáporná a platí pro ni ",[1115,17612,17614],{"className":17613},[1133],[1135,17615,17616],{"xmlns":1137},[1139,17617,17618,17650],{},[1142,17619,17620,17632,17634,17636,17638,17640,17642,17644,17646,17648],{},[4163,17621,17622,17624,17630],{},[1495,17623,17367],{},[1142,17625,17626,17628],{},[1495,17627,1885],{},[1148,17629,17030],{"mathvariant":1599},[1148,17631,17030],{"mathvariant":1599},[1148,17633,16375],{},[1495,17635,2162],{"stretchy":2161},[1148,17637,2675],{},[1495,17639,2181],{"stretchy":2161},[2358,17641,2360],{},[1148,17643,4204],{},[1148,17645,2675],{},[1495,17647,1503],{},[1152,17649,1176],{},[1156,17651,17652],{"encoding":1158},"\\int_{-\\infty}^{\\infty} f(x)\\,dx = 1",[1110,17654,17655],{},"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.",[1392,17657,17659],{"id":17658},"charakteristiky-spojité-náhodné-veličiny","Charakteristiky spojité náhodné veličiny",[1110,17661,17662,17665],{},[1399,17663,17664],{},"Střední hodnota"," je nejdůležitější charakteristika náhodné veličiny:",[1115,17667,17669],{"className":17668},[1133],[1135,17670,17671],{"xmlns":1137,"display":2151},[1139,17672,17673,17718],{},[1142,17674,17675,17678,17680,17682,17684,17686,17698,17700,17702,17704,17706,17708,17710,17712,17714,17716],{},[1148,17676,17677],{},"E",[1495,17679,2162],{"stretchy":2161},[1148,17681,2618],{},[1495,17683,2181],{"stretchy":2161},[1495,17685,1503],{},[4163,17687,17688,17690,17696],{},[1495,17689,17367],{},[1142,17691,17692,17694],{},[1495,17693,1885],{},[1148,17695,17030],{"mathvariant":1599},[1148,17697,17030],{"mathvariant":1599},[1148,17699,2675],{},[1495,17701,7548],{},[1148,17703,16375],{},[1495,17705,2162],{"stretchy":2161},[1148,17707,2675],{},[1495,17709,2181],{"stretchy":2161},[2358,17711,2360],{},[1148,17713,4204],{},[1148,17715,2675],{},[1148,17717,1335],{"mathvariant":1599},[1156,17719,17720],{"encoding":1158},"E(X) = \\int_{-\\infty}^{\\infty} x \\cdot f(x)\\,dx.",[1110,17722,17723],{},"Je to číslo, kolem něhož kolísají výběrové průměry vypočtené ze sérií pozorovaných hodnot náhodné veličiny.",[1110,17725,17726,2261,17729,1497],{},[1399,17727,17728],{},"Rozptyl",[1399,17730,17731],{},"směrodatná odchylka",[1115,17733,17735],{"className":17734},[1133],[1135,17736,17737],{"xmlns":1137,"display":2151},[1139,17738,17739,17879],{},[1142,17740,17741,17743,17745,17747,17749,17751,17763,17766,17768,17770,17772,17774,17776,17778,17785,17787,17789,17791,17793,17795,17797,17799,17801,17813,17819,17821,17823,17825,17827,17829,17831,17833,17835,17837,17839,17841,17843,17845,17851,17853,17855,17857,17859,17861,17863,17865,17877],{},[1148,17742,4114],{},[1495,17744,2162],{"stretchy":2161},[1148,17746,2618],{},[1495,17748,2181],{"stretchy":2161},[1495,17750,1503],{},[4163,17752,17753,17755,17761],{},[1495,17754,17367],{},[1142,17756,17757,17759],{},[1495,17758,1885],{},[1148,17760,17030],{"mathvariant":1599},[1148,17762,17030],{"mathvariant":1599},[1495,17764,17765],{"stretchy":2161},"[",[1148,17767,2675],{},[1495,17769,1885],{},[1148,17771,17677],{},[1495,17773,2162],{"stretchy":2161},[1148,17775,2618],{},[1495,17777,2181],{"stretchy":2161},[2632,17779,17780,17783],{},[1495,17781,17782],{"stretchy":2161},"]",[1152,17784,2639],{},[1148,17786,16375],{},[1495,17788,2162],{"stretchy":2161},[1148,17790,2675],{},[1495,17792,2181],{"stretchy":2161},[2358,17794,2360],{},[1148,17796,4204],{},[1148,17798,2675],{},[1495,17800,1503],{},[4163,17802,17803,17805,17811],{},[1495,17804,17367],{},[1142,17806,17807,17809],{},[1495,17808,1885],{},[1148,17810,17030],{"mathvariant":1599},[1148,17812,17030],{"mathvariant":1599},[2632,17814,17815,17817],{},[1148,17816,2675],{},[1152,17818,2639],{},[1148,17820,16375],{},[1495,17822,2162],{"stretchy":2161},[1148,17824,2675],{},[1495,17826,2181],{"stretchy":2161},[2358,17828,2360],{},[1148,17830,4204],{},[1148,17832,2675],{},[1495,17834,1885],{},[1495,17836,17765],{"stretchy":2161},[1148,17838,17677],{},[1495,17840,2162],{"stretchy":2161},[1148,17842,2618],{},[1495,17844,2181],{"stretchy":2161},[2632,17846,17847,17849],{},[1495,17848,17782],{"stretchy":2161},[1152,17850,2639],{},[1495,17852,2188],{"separator":1121},[3520,17854],{"width":3522},[1148,17856,2636],{},[1495,17858,2162],{"stretchy":2161},[1148,17860,2618],{},[1495,17862,2181],{"stretchy":2161},[1495,17864,1503],{},[2770,17866,17867],{},[1142,17868,17869,17871,17873,17875],{},[1148,17870,4114],{},[1495,17872,2162],{"stretchy":2161},[1148,17874,2618],{},[1495,17876,2181],{"stretchy":2161},[1148,17878,1335],{"mathvariant":1599},[1156,17880,17881],{"encoding":1158},"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)}.",[1110,17883,17884,17885,17888],{},"Směrodatná odchylka udává, jak moc jsou hodnoty náhodné veličiny rozptýlené kolem střední hodnoty. (Pro odhad těchto charakteristik z naměřených dat viz empirické protějšky v ",[1340,17886,886],{"className":17887,"dataFsResolvedFilePath":1351,"href":1352},[1343],".)",[1110,17890,17891,17894,17895,17908,17909,17927,17928,1841],{},[1399,17892,17893],{},"Kvantily"," udávají, jak jsou hodnoty náhodné veličiny ",[1115,17896,17898],{"className":17897},[1133],[1135,17899,17900],{"xmlns":1137},[1139,17901,17902,17906],{},[1142,17903,17904],{},[1148,17905,2618],{},[1156,17907,2618],{"encoding":1158}," rozděleny na ose reálných čísel v určitém pravděpodobnostním poměru. 100p%-ní kvantil ",[1115,17910,17912],{"className":17911},[1133],[1135,17913,17914],{"xmlns":1137},[1139,17915,17916,17924],{},[1142,17917,17918],{},[1145,17919,17920,17922],{},[1148,17921,2675],{},[1148,17923,1110],{},[1156,17925,17926],{"encoding":1158},"x_p"," je číslo, pro které při zvolené pravděpodobnosti ",[1115,17929,17931],{"className":17930},[1133],[1135,17932,17933],{"xmlns":1137},[1139,17934,17935,17939],{},[1142,17936,17937],{},[1148,17938,1110],{},[1156,17940,1110],{"encoding":1158},[1115,17942,17944],{"className":17943},[1133],[1135,17945,17946],{"xmlns":1137,"display":2151},[1139,17947,17948,17968],{},[1142,17949,17950,17952,17954,17960,17962,17964,17966],{},[1148,17951,1387],{},[1495,17953,2162],{"stretchy":2161},[1145,17955,17956,17958],{},[1148,17957,2675],{},[1148,17959,1110],{},[1495,17961,2181],{"stretchy":2161},[1495,17963,1503],{},[1148,17965,1110],{},[1148,17967,1335],{"mathvariant":1599},[1156,17969,17970],{"encoding":1158},"F(x_p) = p.",[1110,17972,17973,17974,18002,18003,18029,18030,18048,18049,18068,18069,1335],{},"V intervalu ",[1115,17975,17977],{"className":17976},[1133],[1135,17978,17979],{"xmlns":1137},[1139,17980,17981,17999],{},[1142,17982,17983,17985,17987,17989,17991,17997],{},[1495,17984,2162],{"stretchy":2161},[1495,17986,1885],{},[1148,17988,17030],{"mathvariant":1599},[1495,17990,16495],{"separator":1121},[1145,17992,17993,17995],{},[1148,17994,2675],{},[1148,17996,1110],{},[1495,17998,2181],{"stretchy":2161},[1156,18000,18001],{"encoding":1158},"(-\\infty; x_p)"," leží 100p % hodnot, v intervalu ",[1115,18004,18006],{"className":18005},[1133],[1135,18007,18008],{"xmlns":1137},[1139,18009,18010,18026],{},[1142,18011,18012,18014,18020,18022,18024],{},[1495,18013,9071],{"stretchy":2161},[1145,18015,18016,18018],{},[1148,18017,2675],{},[1148,18019,1110],{},[1495,18021,16495],{"separator":1121},[1148,18023,17030],{"mathvariant":1599},[1495,18025,2181],{"stretchy":2161},[1156,18027,18028],{"encoding":1158},"\\langle x_p; \\infty)"," leží 100(1-p) % hodnot. Nejdůležitější kvantily jsou medián ",[1115,18031,18033],{"className":18032},[1133],[1135,18034,18035],{"xmlns":1137},[1139,18036,18037,18045],{},[1142,18038,18039],{},[1145,18040,18041,18043],{},[1148,18042,2675],{},[1152,18044,3354],{},[1156,18046,18047],{"encoding":1158},"x_{0{,}5}",", dolní kvartil ",[1115,18050,18052],{"className":18051},[1133],[1135,18053,18054],{"xmlns":1137},[1139,18055,18056,18065],{},[1142,18057,18058],{},[1145,18059,18060,18062],{},[1148,18061,2675],{},[1152,18063,18064],{},"0,25",[1156,18066,18067],{"encoding":1158},"x_{0{,}25}"," a horní kvartil ",[1115,18070,18072],{"className":18071},[1133],[1135,18073,18074],{"xmlns":1137},[1139,18075,18076,18085],{},[1142,18077,18078],{},[1145,18079,18080,18082],{},[1148,18081,2675],{},[1152,18083,18084],{},"0,75",[1156,18086,18087],{"encoding":1158},"x_{0{,}75}",[1392,18089,16477],{"id":18090},"normální-rozdělení",[1110,18092,18093,18094,18107,18108,1953,18111,18138],{},"Spojitá náhodná veličina ",[1115,18095,18097],{"className":18096},[1133],[1135,18098,18099],{"xmlns":1137},[1139,18100,18101,18105],{},[1142,18102,18103],{},[1148,18104,2618],{},[1156,18106,2618],{"encoding":1158}," má ",[1399,18109,18110],{},"normální rozdělení",[1115,18112,18114],{"className":18113},[1133],[1135,18115,18116],{"xmlns":1137},[1139,18117,18118,18136],{},[1142,18119,18120,18122,18124,18126,18128,18134],{},[1148,18121,2624],{},[1495,18123,2162],{"stretchy":2161},[1148,18125,1500],{},[1495,18127,16495],{"separator":1121},[2632,18129,18130,18132],{},[1148,18131,2636],{},[1152,18133,2639],{},[1495,18135,2181],{"stretchy":2161},[1156,18137,16506],{"encoding":1158},", jestliže její hustota pravděpodobnosti a distribuční funkce jsou dány předpisy",[1115,18140,18142],{"className":18141},[1133],[1135,18143,18144],{"xmlns":1137,"display":2151},[1139,18145,18146,18298],{},[1142,18147,18148,18150,18152,18154,18156,18158,18175,18212,18214,18216,18218,18220,18222,18224,18226,18242,18254,18290,18292,18294,18296],{},[1148,18149,16375],{},[1495,18151,2162],{"stretchy":2161},[1148,18153,2675],{},[1495,18155,2181],{"stretchy":2161},[1495,18157,1503],{},[2749,18159,18160,18162],{},[1152,18161,1176],{},[1142,18163,18164,18166],{},[1148,18165,2636],{},[2770,18167,18168],{},[1142,18169,18170,18172],{},[1152,18171,2639],{},[1148,18173,18174],{},"π",[2632,18176,18177,18180],{},[1148,18178,18179],{},"e",[1142,18181,18182,18184],{},[1495,18183,1885],{},[2749,18185,18186,18202],{},[1142,18187,18188,18190,18192,18194,18196],{},[1495,18189,2162],{"stretchy":2161},[1148,18191,2675],{},[1495,18193,1885],{},[1148,18195,1500],{},[2632,18197,18198,18200],{},[1495,18199,2181],{"stretchy":2161},[1152,18201,2639],{},[1142,18203,18204,18206],{},[1152,18205,2639],{},[2632,18207,18208,18210],{},[1148,18209,2636],{},[1152,18211,2639],{},[1495,18213,2188],{"separator":1121},[3520,18215],{"width":3522},[1148,18217,1387],{},[1495,18219,2162],{"stretchy":2161},[1148,18221,2675],{},[1495,18223,2181],{"stretchy":2161},[1495,18225,1503],{},[2749,18227,18228,18230],{},[1152,18229,1176],{},[1142,18231,18232,18234],{},[1148,18233,2636],{},[2770,18235,18236],{},[1142,18237,18238,18240],{},[1152,18239,2639],{},[1148,18241,18174],{},[4163,18243,18244,18246,18252],{},[1495,18245,17367],{},[1142,18247,18248,18250],{},[1495,18249,1885],{},[1148,18251,17030],{"mathvariant":1599},[1148,18253,2675],{},[2632,18255,18256,18258],{},[1148,18257,18179],{},[1142,18259,18260,18262],{},[1495,18261,1885],{},[2749,18263,18264,18280],{},[1142,18265,18266,18268,18270,18272,18274],{},[1495,18267,2162],{"stretchy":2161},[1148,18269,1373],{},[1495,18271,1885],{},[1148,18273,1500],{},[2632,18275,18276,18278],{},[1495,18277,2181],{"stretchy":2161},[1152,18279,2639],{},[1142,18281,18282,18284],{},[1152,18283,2639],{},[2632,18285,18286,18288],{},[1148,18287,2636],{},[1152,18289,2639],{},[2358,18291,2360],{},[1148,18293,4204],{},[1148,18295,1373],{},[1495,18297,2188],{"separator":1121},[1156,18299,18300],{"encoding":1158},"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,",[1110,18302,18303,18304,1195,18328,1335],{},"přičemž ",[1115,18305,18307],{"className":18306},[1133],[1135,18308,18309],{"xmlns":1137},[1139,18310,18311,18325],{},[1142,18312,18313,18315,18317,18319,18321,18323],{},[1148,18314,17677],{},[1495,18316,2162],{"stretchy":2161},[1148,18318,2618],{},[1495,18320,2181],{"stretchy":2161},[1495,18322,1503],{},[1148,18324,1500],{},[1156,18326,18327],{"encoding":1158},"E(X) = \\mu",[1115,18329,18331],{"className":18330},[1133],[1135,18332,18333],{"xmlns":1137},[1139,18334,18335,18353],{},[1142,18336,18337,18339,18341,18343,18345,18347],{},[1148,18338,4114],{},[1495,18340,2162],{"stretchy":2161},[1148,18342,2618],{},[1495,18344,2181],{"stretchy":2161},[1495,18346,1503],{},[2632,18348,18349,18351],{},[1148,18350,2636],{},[1152,18352,2639],{},[1156,18354,18355],{"encoding":1158},"D(X) = \\sigma^2",[1110,18357,18358],{},[1971,18359],{"alt":18360,"className":18361,"src":18362},"mask-nv-normalni",[1343,1975],"\u002Fwiki-assets\u002Fmask-nv-normalni.png",[1110,18364,18365,18366,18369,18370,18383,18384,18403,18404,10141,18420,18433,18434,1335],{},"Křivka hustoty se nazývá ",[1399,18367,18368],{},"Gaussova křivka",": je symetrická kolem svislé přímky procházející ",[1115,18371,18373],{"className":18372},[1133],[1135,18374,18375],{"xmlns":1137},[1139,18376,18377,18381],{},[1142,18378,18379],{},[1148,18380,1500],{},[1156,18382,2605],{"encoding":1158},", kde má ",[1115,18385,18387],{"className":18386},[1133],[1135,18388,18389],{"xmlns":1137},[1139,18390,18391,18401],{},[1142,18392,18393,18395,18397,18399],{},[1148,18394,16375],{},[1495,18396,2162],{"stretchy":2161},[1148,18398,2675],{},[1495,18400,2181],{"stretchy":2161},[1156,18402,16404],{"encoding":1158}," globální maximum, a ve vzdálenosti ",[1115,18405,18407],{"className":18406},[1133],[1135,18408,18409],{"xmlns":1137},[1139,18410,18411,18417],{},[1142,18412,18413,18415],{},[1152,18414,13259],{},[1148,18416,2636],{},[1156,18418,18419],{"encoding":1158},"3\\sigma",[1115,18421,18423],{"className":18422},[1133],[1135,18424,18425],{"xmlns":1137},[1139,18426,18427,18431],{},[1142,18428,18429],{},[1148,18430,1500],{},[1156,18432,2605],{"encoding":1158}," se téměř dotýká osy x — zhruba 99,73 % hodnot leží v intervalu ",[1115,18435,18437],{"className":18436},[1133],[1135,18438,18439],{"xmlns":1137},[1139,18440,18441,18465],{},[1142,18442,18443,18445,18447,18449,18451,18453,18455,18457,18459,18461,18463],{},[1495,18444,2162],{"stretchy":2161},[1148,18446,1500],{},[1495,18448,1885],{},[1152,18450,13259],{},[1148,18452,2636],{},[1495,18454,16495],{"separator":1121},[1148,18456,1500],{},[1495,18458,6294],{},[1152,18460,13259],{},[1148,18462,2636],{},[1495,18464,2181],{"stretchy":2161},[1156,18466,18467],{"encoding":1158},"(\\mu - 3\\sigma; \\mu + 3\\sigma)",[1110,18469,18470,18471,1953,18474,18498,18499,1335],{},"Zvláštní postavení má ",[1399,18472,18473],{},"normované normální rozdělení",[1115,18475,18477],{"className":18476},[1133],[1135,18478,18479],{"xmlns":1137},[1139,18480,18481,18495],{},[1142,18482,18483,18485,18487,18489,18491,18493],{},[1148,18484,2624],{},[1495,18486,2162],{"stretchy":2161},[1152,18488,1154],{},[1495,18490,16495],{"separator":1121},[1152,18492,1176],{},[1495,18494,2181],{"stretchy":2161},[1156,18496,18497],{"encoding":1158},"N(0; 1)",", na které se dá libovolné normální rozdělení převést standardizací ",[1115,18500,18502],{"className":18501},[1133],[1135,18503,18504],{"xmlns":1137},[1139,18505,18506,18526],{},[1142,18507,18508,18510,18512,18514,18516,18518,18520,18522,18524],{},[1148,18509,5389],{},[1495,18511,1503],{},[1495,18513,2162],{"stretchy":2161},[1148,18515,2618],{},[1495,18517,1885],{},[1148,18519,1500],{},[1495,18521,2181],{"stretchy":2161},[1148,18523,3049],{"mathvariant":1599},[1148,18525,2636],{},[1156,18527,18528],{"encoding":1158},"Z = (X-\\mu)\u002F\\sigma",[18530,18531],"graph-mount",{"spec":18532},"{\"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\"}]}",[1103,18534,18536,18543],{"className":18535,"dataCallout":5141},[1106,5140],[1110,18537,18539,18542],{"className":18538},[1113],[1115,18540],{"className":18541,"ariaHidden":1121},[1118,5148,1120],"R očekává směrodatnou odchylku, ne rozptyl",[1110,18544,18545,18546,18573,18574,18577,18578,1195,18580,2261,18582,18584,18585,1953,18588,18601,18602,18627,18628,18631,18632,1335],{},"Zápis ",[1115,18547,18549],{"className":18548},[1133],[1135,18550,18551],{"xmlns":1137},[1139,18552,18553,18571],{},[1142,18554,18555,18557,18559,18561,18563,18569],{},[1148,18556,2624],{},[1495,18558,2162],{"stretchy":2161},[1148,18560,1500],{},[1495,18562,16495],{"separator":1121},[2632,18564,18565,18567],{},[1148,18566,2636],{},[1152,18568,2639],{},[1495,18570,2181],{"stretchy":2161},[1156,18572,16506],{"encoding":1158}," v definici používá ",[1399,18575,18576],{},"rozptyl",". Funkce ",[3161,18579,16510],{},[3161,18581,16513],{},[3161,18583,16516],{}," v R ale jako třetí argument berou ",[1399,18586,18587],{},"směrodatnou odchylku",[1115,18589,18591],{"className":18590},[1133],[1135,18592,18593],{"xmlns":1137},[1139,18594,18595,18599],{},[1142,18596,18597],{},[1148,18598,2636],{},[1156,18600,16531],{"encoding":1158},". Má-li náhodná veličina rozdělení ",[1115,18603,18605],{"className":18604},[1133],[1135,18606,18607],{"xmlns":1137},[1139,18608,18609,18624],{},[1142,18610,18611,18613,18615,18617,18619,18622],{},[1148,18612,2624],{},[1495,18614,2162],{"stretchy":2161},[1152,18616,4717],{},[1495,18618,16495],{"separator":1121},[1152,18620,18621],{},"0,12",[1495,18623,2181],{"stretchy":2161},[1156,18625,18626],{"encoding":1158},"N(10; 0{,}12)",", je ",[3161,18629,18630],{},"sd = sqrt(0.12)",", ne ",[3161,18633,18634],{},"sd = 0.12",[1110,18636,18637],{},"V R:",[3166,18639,18641],{"className":3168,"code":18640,"language":71,"meta":3170,"style":3170},"dnorm(0)\npnorm(1.96)\nqnorm(0.975)\n",[3161,18642,18643,18653,18664],{"__ignoreMap":3170},[1115,18644,18645,18647,18649,18651],{"class":3175,"line":10},[1115,18646,16510],{"class":3185},[1115,18648,2162],{"class":3189},[1115,18650,1154],{"class":3192},[1115,18652,3235],{"class":3189},[1115,18654,18655,18657,18659,18662],{"class":3175,"line":27},[1115,18656,16513],{"class":3185},[1115,18658,2162],{"class":3189},[1115,18660,18661],{"class":3192},"1.96",[1115,18663,3235],{"class":3189},[1115,18665,18666,18668,18670,18672],{"class":3175,"line":148},[1115,18667,16516],{"class":3185},[1115,18669,2162],{"class":3189},[1115,18671,7807],{"class":3192},[1115,18673,3235],{"class":3189},[3166,18675,18678],{"className":18676,"code":18677,"language":3274,"meta":3170},[3272],"[1] 0.3989423\n[1] 0.9750021\n[1] 1.959964\n",[3161,18679,18677],{"__ignoreMap":3170},[1110,18681,18682,18685,18686,18710,18711,2036,18714,2261,18735,18738],{},[3161,18683,18684],{},"dnorm(0)"," je hodnota hustoty ",[1115,18687,18689],{"className":18688},[1133],[1135,18690,18691],{"xmlns":1137},[1139,18692,18693,18707],{},[1142,18694,18695,18697,18699,18701,18703,18705],{},[1148,18696,2624],{},[1495,18698,2162],{"stretchy":2161},[1152,18700,1154],{},[1495,18702,16495],{"separator":1121},[1152,18704,1176],{},[1495,18706,2181],{"stretchy":2161},[1156,18708,18709],{"encoding":1158},"N(0;1)"," v bodě 0, ",[3161,18712,18713],{},"pnorm(1.96)",[1115,18715,18717],{"className":18716},[1133],[1135,18718,18719],{"xmlns":1137},[1139,18720,18721,18732],{},[1142,18722,18723,18725,18727,18730],{},[1148,18724,1387],{},[1495,18726,2162],{"stretchy":2161},[1152,18728,18729],{},"1,96",[1495,18731,2181],{"stretchy":2161},[1156,18733,18734],{"encoding":1158},"F(1{,}96)",[3161,18736,18737],{},"qnorm(0.975)"," je 97,5%-ní kvantil — hodnota, pod kterou leží 97,5 % pravděpodobnosti.",[1103,18740,18742,18749],{"className":18741,"dataCallout":3323},[1106,3322],[1110,18743,18745,18748],{"className":18744},[1113],[1115,18746],{"className":18747,"ariaHidden":1121},[1118,3330,1120],"Příklad: Návštěvnost zábavního parku",[1110,18750,18751,18752,18786],{},"Denní návštěvnost zábavního parku je náhodná veličina s normálním rozdělením, průměrnou hodnotou 230 a směrodatnou odchylkou 27,5 návštěvníků: ",[1115,18753,18755],{"className":18754},[1133],[1135,18756,18757],{"xmlns":1137},[1139,18758,18759,18783],{},[1142,18760,18761,18763,18765,18767,18769,18772,18774,18781],{},[1148,18762,2618],{},[1495,18764,2621],{},[1148,18766,2624],{},[1495,18768,2162],{"stretchy":2161},[1152,18770,18771],{},"230",[1495,18773,16495],{"separator":1121},[2632,18775,18776,18779],{},[1152,18777,18778],{},"27,5",[1152,18780,2639],{},[1495,18782,2181],{"stretchy":2161},[1156,18784,18785],{"encoding":1158},"X \\sim N(230; 27{,}5^2)",". Přijde-li za den méně než 180 návštěvníků, je park ztrátový. Kolik procent dní je ztrátových?",[1110,18788,18789],{},[1971,18790],{"alt":18791,"className":18792,"src":18793},"mask-nv-priklad-park",[1343,1975],"\u002Fwiki-assets\u002Fmask-nv-priklad-park.png",[3166,18795,18797],{"className":3168,"code":18796,"language":71,"meta":3170,"style":3170},"pnorm(180, mean = 230, sd = 27.5)\n",[3161,18798,18799],{"__ignoreMap":3170},[1115,18800,18801,18803,18805,18808,18810,18812,18814,18817,18819,18821,18823,18826],{"class":3175,"line":10},[1115,18802,16513],{"class":3185},[1115,18804,2162],{"class":3189},[1115,18806,18807],{"class":3192},"180",[1115,18809,2188],{"class":3181},[1115,18811,8954],{"class":3178},[1115,18813,3252],{"class":3181},[1115,18815,18816],{"class":3192}," 230",[1115,18818,2188],{"class":3181},[1115,18820,8965],{"class":3178},[1115,18822,3252],{"class":3181},[1115,18824,18825],{"class":3192}," 27.5",[1115,18827,3235],{"class":3189},[3166,18829,18832],{"className":18830,"code":18831,"language":3274,"meta":3170},[3272],"[1] 0.03451817\n",[3161,18833,18831],{"__ignoreMap":3170},[1110,18835,18836],{},"Park je ztrátový přibližně v 3,45 % dní.",[1103,18838,18840,18847],{"className":18839,"dataCallout":3323},[1106,3322],[1110,18841,18843,18846],{"className":18842},[1113],[1115,18844],{"className":18845,"ariaHidden":1121},[1118,3330,1120],"Příklad: Délka výrobku",[1110,18848,18849,18850,18884],{},"Automat je seřízen tak, aby střední hodnota délky výrobku byla 42 mm, s přesností charakterizovanou směrodatnou odchylkou 1,2 mm: ",[1115,18851,18853],{"className":18852},[1133],[1135,18854,18855],{"xmlns":1137},[1139,18856,18857,18881],{},[1142,18858,18859,18861,18863,18865,18867,18870,18872,18879],{},[1148,18860,2618],{},[1495,18862,2621],{},[1148,18864,2624],{},[1495,18866,2162],{"stretchy":2161},[1152,18868,18869],{},"42",[1495,18871,16495],{"separator":1121},[2632,18873,18874,18877],{},[1152,18875,18876],{},"1,2",[1152,18878,2639],{},[1495,18880,2181],{"stretchy":2161},[1156,18882,18883],{"encoding":1158},"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?",[1110,18886,18887],{},[1971,18888],{"alt":18889,"className":18890,"src":18891},"mask-nv-priklad-delka",[1343,1975],"\u002Fwiki-assets\u002Fmask-nv-priklad-delka.png",[3166,18893,18895],{"className":3168,"code":18894,"language":71,"meta":3170,"style":3170},"pnorm(43, mean = 42, sd = 1.2) - pnorm(41, mean = 42, sd = 1.2)\n",[3161,18896,18897],{"__ignoreMap":3170},[1115,18898,18899,18901,18903,18906,18908,18910,18912,18915,18917,18919,18921,18924,18926,18928,18931,18933,18936,18938,18940,18942,18944,18946,18948,18950,18952],{"class":3175,"line":10},[1115,18900,16513],{"class":3185},[1115,18902,2162],{"class":3189},[1115,18904,18905],{"class":3192},"43",[1115,18907,2188],{"class":3181},[1115,18909,8954],{"class":3178},[1115,18911,3252],{"class":3181},[1115,18913,18914],{"class":3192}," 42",[1115,18916,2188],{"class":3181},[1115,18918,8965],{"class":3178},[1115,18920,3252],{"class":3181},[1115,18922,18923],{"class":3192}," 1.2",[1115,18925,3688],{"class":3189},[1115,18927,14265],{"class":3181},[1115,18929,18930],{"class":3185}," pnorm",[1115,18932,2162],{"class":3189},[1115,18934,18935],{"class":3192},"41",[1115,18937,2188],{"class":3181},[1115,18939,8954],{"class":3178},[1115,18941,3252],{"class":3181},[1115,18943,18914],{"class":3192},[1115,18945,2188],{"class":3181},[1115,18947,8965],{"class":3178},[1115,18949,3252],{"class":3181},[1115,18951,18923],{"class":3192},[1115,18953,3235],{"class":3189},[3166,18955,18958],{"className":18956,"code":18957,"language":3274,"meta":3170},[3272],"[1] 0.5953432\n",[3161,18959,18957],{"__ignoreMap":3170},[1110,18961,18962],{},"Do 1. jakostní třídy spadá přibližně 59,53 % výrobků.",[1103,18964,18966,18973],{"className":18965,"dataCallout":3323},[1106,3322],[1110,18967,18969,18972],{"className":18968},[1113],[1115,18970],{"className":18971,"ariaHidden":1121},[1118,3330,1120],"Příklad: Obsah ampulky",[1110,18974,18975,18976,18999,19000,19025],{},"Obsah ampulky s lékem (v cm³) má rozdělení ",[1115,18977,18979],{"className":18978},[1133],[1135,18980,18981],{"xmlns":1137},[1139,18982,18983,18997],{},[1142,18984,18985,18987,18989,18991,18993,18995],{},[1148,18986,2624],{},[1495,18988,2162],{"stretchy":2161},[1152,18990,4717],{},[1495,18992,16495],{"separator":1121},[1152,18994,18621],{},[1495,18996,2181],{"stretchy":2161},[1156,18998,18626],{"encoding":1158},", tedy střední hodnota 10 a rozptyl 0,12 (",[1115,19001,19003],{"className":19002},[1133],[1135,19004,19005],{"xmlns":1137},[1139,19006,19007,19022],{},[1142,19008,19009,19011,19013,19017,19019],{},[1148,19010,2636],{},[1495,19012,1503],{},[2770,19014,19015],{},[1152,19016,18621],{},[1495,19018,7600],{},[1152,19020,19021],{},"0,346",[1156,19023,19024],{"encoding":1158},"\\sigma = \\sqrt{0{,}12} \\approx 0{,}346","). Kolik procent ampulek má obsah menší než 9,8 cm³?",[1110,19027,19028],{},[1971,19029],{"alt":19030,"className":19031,"src":19032},"mask-nv-priklad-ampulka",[1343,1975],"\u002Fwiki-assets\u002Fmask-nv-priklad-ampulka.png",[3166,19034,19036],{"className":3168,"code":19035,"language":71,"meta":3170,"style":3170},"pnorm(9.8, mean = 10, sd = sqrt(0.12))\n",[3161,19037,19038],{"__ignoreMap":3170},[1115,19039,19040,19042,19044,19047,19049,19051,19053,19055,19057,19059,19061,19063,19065,19068],{"class":3175,"line":10},[1115,19041,16513],{"class":3185},[1115,19043,2162],{"class":3189},[1115,19045,19046],{"class":3192},"9.8",[1115,19048,2188],{"class":3181},[1115,19050,8954],{"class":3178},[1115,19052,3252],{"class":3181},[1115,19054,3856],{"class":3192},[1115,19056,2188],{"class":3181},[1115,19058,8965],{"class":3178},[1115,19060,3252],{"class":3181},[1115,19062,3699],{"class":3185},[1115,19064,2162],{"class":3189},[1115,19066,19067],{"class":3192},"0.12",[1115,19069,7963],{"class":3189},[3166,19071,19074],{"className":19072,"code":19073,"language":3274,"meta":3170},[3272],"[1] 0.2818514\n",[3161,19075,19073],{"__ignoreMap":3170},[1110,19077,19078],{},"Obsah menší než 9,8 cm³ má přibližně 28,19 % ampulek.",[1392,19080,19082],{"id":19081},"další-rozdělení-dostupná-v-r","Další rozdělení dostupná v R",[1110,19084,19085,19086,19089,19090,19093,19094,19097,19098,3049,19100,19102,19103,19106],{},"Vedle normálního rozdělení R přímo nabízí hustotu, distribuční funkci a kvantilovou funkci i pro další běžná rozdělení. Pojmenování funkcí je jednotné: ",[3161,19087,19088],{},"d*"," je hustota\u002Fpravděpodobnostní funkce, ",[3161,19091,19092],{},"p*"," distribuční funkce (s ",[3161,19095,19096],{},"lower.tail = FALSE",", případně čtvrtým argumentem ",[3161,19099,8069],{},[3161,19101,8073],{},", pro horní chvost) a ",[3161,19104,19105],{},"q*"," kvantilová funkce.",[1532,19108,19109,19215],{},[1535,19110,19111],{},[1538,19112,19113,19116,19162,19188],{},[1541,19114,19115],{},"Rozdělení",[1541,19117,19118,19142,19143],{},[1115,19119,19121],{"className":19120},[1133],[1135,19122,19123],{"xmlns":1137},[1139,19124,19125,19139],{},[1142,19126,19127,19129,19131,19133,19135,19137],{},[1148,19128,2158],{},[1495,19130,2162],{"stretchy":2161},[1148,19132,2618],{},[1495,19134,1503],{},[1148,19136,10710],{},[1495,19138,2181],{"stretchy":2161},[1156,19140,19141],{"encoding":1158},"P(X=k)"," \u002F ",[1115,19144,19146],{"className":19145},[1133],[1135,19147,19148],{"xmlns":1137},[1139,19149,19150,19160],{},[1142,19151,19152,19154,19156,19158],{},[1148,19153,16375],{},[1495,19155,2162],{"stretchy":2161},[1148,19157,2675],{},[1495,19159,2181],{"stretchy":2161},[1156,19161,16404],{"encoding":1158},[1541,19163,19164],{},[1115,19165,19167],{"className":19166},[1133],[1135,19168,19169],{"xmlns":1137},[1139,19170,19171,19185],{},[1142,19172,19173,19175,19177,19179,19181,19183],{},[1148,19174,2158],{},[1495,19176,2162],{"stretchy":2161},[1148,19178,2618],{},[1495,19180,2519],{},[1148,19182,10710],{},[1495,19184,2181],{"stretchy":2161},[1156,19186,19187],{"encoding":1158},"P(X \\le k)",[1541,19189,19190,19191],{},"horní chvost ",[1115,19192,19194],{"className":19193},[1133],[1135,19195,19196],{"xmlns":1137},[1139,19197,19198,19212],{},[1142,19199,19200,19202,19204,19206,19208,19210],{},[1148,19201,2158],{},[1495,19203,2162],{"stretchy":2161},[1148,19205,2618],{},[1495,19207,1641],{},[1148,19209,10710],{},[1495,19211,2181],{"stretchy":2161},[1156,19213,19214],{"encoding":1158},"P(X>k)",[1568,19216,19217,19263,19307,19348,19397],{},[1538,19218,19219,19248,19253,19258],{},[1573,19220,19221,19222],{},"Binomické ",[1115,19223,19225],{"className":19224},[1133],[1135,19226,19227],{"xmlns":1137},[1139,19228,19229,19245],{},[1142,19230,19231,19233,19235,19237,19239,19241,19243],{},[1148,19232,8159],{},[1148,19234,4085],{},[1495,19236,2162],{"stretchy":2161},[1148,19238,2657],{},[1495,19240,2188],{"separator":1121},[1148,19242,1110],{},[1495,19244,2181],{"stretchy":2161},[1156,19246,19247],{"encoding":1158},"Bi(n,p)",[1573,19249,19250],{},[3161,19251,19252],{},"dbinom(k, n, p)",[1573,19254,19255],{},[3161,19256,19257],{},"pbinom(k, n, p)",[1573,19259,19260],{},[3161,19261,19262],{},"pbinom(k, n, p, FALSE)",[1538,19264,19265,19292,19297,19302],{},[1573,19266,19267,19268],{},"Poissonovo ",[1115,19269,19271],{"className":19270},[1133],[1135,19272,19273],{"xmlns":1137},[1139,19274,19275,19289],{},[1142,19276,19277,19279,19282,19284,19287],{},[1148,19278,2158],{},[1148,19280,19281],{},"o",[1495,19283,2162],{"stretchy":2161},[1148,19285,19286],{},"λ",[1495,19288,2181],{"stretchy":2161},[1156,19290,19291],{"encoding":1158},"Po(\\lambda)",[1573,19293,19294],{},[3161,19295,19296],{},"dpois(k, lambda)",[1573,19298,19299],{},[3161,19300,19301],{},"ppois(k, lambda)",[1573,19303,19304],{},[3161,19305,19306],{},"ppois(k, lambda, FALSE)",[1538,19308,19309,19333,19338,19343],{},[1573,19310,19311,19312],{},"Geometrické ",[1115,19313,19315],{"className":19314},[1133],[1135,19316,19317],{"xmlns":1137},[1139,19318,19319,19330],{},[1142,19320,19321,19324,19326,19328],{},[1148,19322,19323],{},"G",[1495,19325,2162],{"stretchy":2161},[1148,19327,1110],{},[1495,19329,2181],{"stretchy":2161},[1156,19331,19332],{"encoding":1158},"G(p)",[1573,19334,19335],{},[3161,19336,19337],{},"dgeom(k, p)",[1573,19339,19340],{},[3161,19341,19342],{},"pgeom(k, p)",[1573,19344,19345],{},[3161,19346,19347],{},"pgeom(k, p, FALSE)",[1538,19349,19350,19382,19387,19392],{},[1573,19351,19352,19353],{},"Hypergeometrické ",[1115,19354,19356],{"className":19355},[1133],[1135,19357,19358],{"xmlns":1137},[1139,19359,19360,19379],{},[1142,19361,19362,19364,19366,19368,19370,19373,19375,19377],{},[1148,19363,1150],{},[1495,19365,2162],{"stretchy":2161},[1148,19367,2624],{},[1495,19369,2188],{"separator":1121},[1148,19371,19372],{},"M",[1495,19374,2188],{"separator":1121},[1148,19376,2657],{},[1495,19378,2181],{"stretchy":2161},[1156,19380,19381],{"encoding":1158},"H(N,M,n)",[1573,19383,19384],{},[3161,19385,19386],{},"dhyper(k, M, N-M, n)",[1573,19388,19389],{},[3161,19390,19391],{},"phyper(k, M, N-M, n)",[1573,19393,19394],{},[3161,19395,19396],{},"phyper(k, M, N-M, n, FALSE)",[1538,19398,19399,19423,19428,19433],{},[1573,19400,19401,19402],{},"Exponenciální ",[1115,19403,19405],{"className":19404},[1133],[1135,19406,19407],{"xmlns":1137},[1139,19408,19409,19420],{},[1142,19410,19411,19413,19415,19418],{},[1148,19412,17677],{},[1495,19414,2162],{"stretchy":2161},[1148,19416,19417],{},"δ",[1495,19419,2181],{"stretchy":2161},[1156,19421,19422],{"encoding":1158},"E(\\delta)",[1573,19424,19425],{},[3161,19426,19427],{},"dexp(k, 1\u002Fdelta)",[1573,19429,19430],{},[3161,19431,19432],{},"pexp(k, 1\u002Fdelta)",[1573,19434,19435],{},[3161,19436,19437],{},"pexp(k, 1\u002Fdelta, FALSE)",[1103,19439,19441,19448],{"className":19440,"dataCallout":5141},[1106,5140],[1110,19442,19444,19447],{"className":19443},[1113],[1115,19445],{"className":19446,"ariaHidden":1121},[1118,5148,1120],"Exponenciální rozdělení: R bere intenzitu, ne střední hodnotu",[1110,19449,19450,19451,19454,19455,19469,19470,18631,19473,1335],{},"R parametrizuje exponenciální rozdělení intenzitou (",[3161,19452,19453],{},"rate","). Je-li ",[1115,19456,19458],{"className":19457},[1133],[1135,19459,19460],{"xmlns":1137},[1139,19461,19462,19466],{},[1142,19463,19464],{},[1148,19465,19417],{},[1156,19467,19468],{"encoding":1158},"\\delta"," střední doba do události, do R se dosazuje ",[3161,19471,19472],{},"1\u002Fdelta",[3161,19474,19475],{},"delta",[1110,19477,19478,19479,19510,19511,19529],{},"V R (pravděpodobnostní a distribuční funkce diskrétní náhodné veličiny ",[1115,19480,19482],{"className":19481},[1133],[1135,19483,19484],{"xmlns":1137},[1139,19485,19486,19507],{},[1142,19487,19488,19490,19492,19494,19496,19498,19500,19502,19505],{},[1148,19489,2618],{},[1495,19491,2621],{},[1148,19493,8159],{},[1148,19495,4085],{},[1495,19497,2162],{"stretchy":2161},[1152,19499,9817],{},[1495,19501,16495],{"separator":1121},[1152,19503,19504],{},"0,95",[1495,19506,2181],{"stretchy":2161},[1156,19508,19509],{"encoding":1158},"X \\sim Bi(5; 0{,}95)",", a pravděpodobnost, že u exponenciálního rozdělení se střední hodnotou ",[1115,19512,19514],{"className":19513},[1133],[1135,19515,19516],{"xmlns":1137},[1139,19517,19518,19526],{},[1142,19519,19520,19522,19524],{},[1148,19521,19417],{},[1495,19523,1503],{},[1152,19525,9817],{},[1156,19527,19528],{"encoding":1158},"\\delta = 5"," nastane událost do 3 jednotek času):",[3166,19531,19533],{"className":3168,"code":19532,"language":71,"meta":3170,"style":3170},"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",[3161,19534,19535,19548,19579,19608,19613,19622],{"__ignoreMap":3170},[1115,19536,19537,19539,19541,19543,19545],{"class":3175,"line":10},[1115,19538,2675],{"class":3178},[1115,19540,3182],{"class":3181},[1115,19542,5078],{"class":3192},[1115,19544,1497],{"class":3181},[1115,19546,19547],{"class":3192},"5\n",[1115,19549,19550,19553,19555,19558,19560,19562,19564,19566,19568,19571,19573,19575,19577],{"class":3175,"line":27},[1115,19551,19552],{"class":3185},"round",[1115,19554,2162],{"class":3189},[1115,19556,19557],{"class":3185},"dbinom",[1115,19559,2162],{"class":3189},[1115,19561,2675],{"class":3178},[1115,19563,2188],{"class":3181},[1115,19565,9344],{"class":3192},[1115,19567,2188],{"class":3181},[1115,19569,19570],{"class":3192}," 0.95",[1115,19572,2181],{"class":3189},[1115,19574,2188],{"class":3181},[1115,19576,3983],{"class":3192},[1115,19578,3235],{"class":3189},[1115,19580,19581,19583,19585,19588,19590,19592,19594,19596,19598,19600,19602,19604,19606],{"class":3175,"line":148},[1115,19582,19552],{"class":3185},[1115,19584,2162],{"class":3189},[1115,19586,19587],{"class":3185},"pbinom",[1115,19589,2162],{"class":3189},[1115,19591,2675],{"class":3178},[1115,19593,2188],{"class":3181},[1115,19595,9344],{"class":3192},[1115,19597,2188],{"class":3181},[1115,19599,19570],{"class":3192},[1115,19601,2181],{"class":3189},[1115,19603,2188],{"class":3181},[1115,19605,3983],{"class":3192},[1115,19607,3235],{"class":3189},[1115,19609,19610],{"class":3175,"line":111},[1115,19611,19612],{"emptyLinePlaceholder":11218},"\n",[1115,19614,19615,19617,19619],{"class":3175,"line":96},[1115,19616,19475],{"class":3178},[1115,19618,3182],{"class":3181},[1115,19620,19621],{"class":3192}," 5\n",[1115,19623,19624,19626,19628,19631,19633,19635,19637,19639,19641,19643,19645,19648,19650,19652,19654],{"class":3175,"line":89},[1115,19625,19552],{"class":3185},[1115,19627,2162],{"class":3189},[1115,19629,19630],{"class":3185},"pexp",[1115,19632,2162],{"class":3189},[1115,19634,13259],{"class":3192},[1115,19636,2188],{"class":3181},[1115,19638,9697],{"class":3178},[1115,19640,3252],{"class":3181},[1115,19642,3735],{"class":3192},[1115,19644,7755],{"class":3181},[1115,19646,19647],{"class":3178}," delta",[1115,19649,2181],{"class":3189},[1115,19651,2188],{"class":3181},[1115,19653,3983],{"class":3192},[1115,19655,3235],{"class":3189},[3166,19657,19660],{"className":19658,"code":19659,"language":3274,"meta":3170},[3272],"[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",[3161,19661,19659],{"__ignoreMap":3170},[1392,19663,19665],{"id":19664},"studentovo-pearsonovo-a-fisherovo-snedecorovo-rozdělení","Studentovo, Pearsonovo a Fisherovo-Snedecorovo rozdělení",[1110,19667,19668,19669,19672],{},"Tato tři rozdělení mají statistiky, které se dále používají při konstrukci intervalů spolehlivosti a testování hypotéz (viz ",[1340,19670,141],{"className":19671,"dataFsResolvedFilePath":11426,"href":11427},[1343],") — na rozdíl od normálního rozdělení se v příkladech této kapitoly samostatně nepočítají, jsou to nástroje pro další kapitoly.",[1110,19674,19675,13595,19678,19691],{},[1399,19676,19677],{},"Studentovo rozdělení",[1115,19679,19681],{"className":19680},[1133],[1135,19682,19683],{"xmlns":1137},[1139,19684,19685,19689],{},[1142,19686,19687],{},[1148,19688,10710],{},[1156,19690,10710],{"encoding":1158}," stupni volnosti má hustotu pravděpodobnosti",[1115,19693,19695],{"className":19694},[1133],[1135,19696,19697],{"xmlns":1137,"display":2151},[1139,19698,19699,19795],{},[1142,19700,19701,19703,19705,19707,19709,19711,19743,19781,19783,19785,19787,19789,19793],{},[1148,19702,16375],{},[1495,19704,2162],{"stretchy":2161},[1148,19706,2675],{},[1495,19708,2181],{"stretchy":2161},[1495,19710,1503],{},[2749,19712,19713,19715],{},[1152,19714,1176],{},[1142,19716,19717,19719,19739],{},[1148,19718,8159],{},[1142,19720,19721,19723,19729,19731,19737],{},[1495,19722,2162],{"fence":1121},[2749,19724,19725,19727],{},[1152,19726,1176],{},[1152,19728,2639],{},[1495,19730,2188],{"separator":1121},[2749,19732,19733,19735],{},[1148,19734,10710],{},[1152,19736,2639],{},[1495,19738,2181],{"fence":1121},[2770,19740,19741],{},[1148,19742,10710],{},[2632,19744,19745,19765],{},[1142,19746,19747,19749,19751,19753,19763],{},[1495,19748,2162],{"fence":1121},[1152,19750,1176],{},[1495,19752,6294],{},[2749,19754,19755,19761],{},[2632,19756,19757,19759],{},[1148,19758,2675],{},[1152,19760,2639],{},[1148,19762,10710],{},[1495,19764,2181],{"fence":1121},[1142,19766,19767,19769],{},[1495,19768,1885],{},[2749,19770,19771,19779],{},[1142,19772,19773,19775,19777],{},[1148,19774,10710],{},[1495,19776,6294],{},[1152,19778,1176],{},[1152,19780,2639],{},[1495,19782,2188],{"separator":1121},[3520,19784],{"width":3522},[1148,19786,2675],{},[1495,19788,2167],{},[1148,19790,19792],{"mathvariant":19791},"double-struck","R",[1495,19794,2188],{"separator":1121},[1156,19796,19797],{"encoding":1158},"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},",[1110,19799,14139,19800,19813,19814,19827,19828,19841],{},[1115,19801,19803],{"className":19802},[1133],[1135,19804,19805],{"xmlns":1137},[1139,19806,19807,19811],{},[1142,19808,19809],{},[1148,19810,8159],{},[1156,19812,8159],{"encoding":1158}," je funkce beta. Je symetrické kolem nuly; číslo ",[1115,19815,19817],{"className":19816},[1133],[1135,19818,19819],{"xmlns":1137},[1139,19820,19821,19825],{},[1142,19822,19823],{},[1148,19824,10710],{},[1156,19826,10710],{"encoding":1158}," určuje tvar křivky — s rostoucím ",[1115,19829,19831],{"className":19830},[1133],[1135,19832,19833],{"xmlns":1137},[1139,19834,19835,19839],{},[1142,19836,19837],{},[1148,19838,10710],{},[1156,19840,10710],{"encoding":1158}," se rozdělení blíží normálnímu.",[1110,19843,19844,13595,19847,19860],{},[1399,19845,19846],{},"Pearsonovo (chí-kvadrát) rozdělení",[1115,19848,19850],{"className":19849},[1133],[1135,19851,19852],{"xmlns":1137},[1139,19853,19854,19858],{},[1142,19855,19856],{},[1148,19857,10710],{},[1156,19859,10710],{"encoding":1158}," stupni volnosti:",[1115,19862,19864],{"className":19863},[1133],[1135,19865,19866],{"xmlns":1137,"display":2151},[1139,19867,19868,19953],{},[1142,19869,19870,19872,19874,19876,19878,19880,19911,19927,19941,19943,19945,19947,19949,19951],{},[1148,19871,16375],{},[1495,19873,2162],{"stretchy":2161},[1148,19875,2675],{},[1495,19877,2181],{"stretchy":2161},[1495,19879,1503],{},[2749,19881,19882,19884],{},[1152,19883,1176],{},[1142,19885,19886,19898,19901,19903,19905,19907,19909],{},[2632,19887,19888,19890],{},[1152,19889,2639],{},[1142,19891,19892,19894,19896],{},[1148,19893,10710],{},[1148,19895,3049],{"mathvariant":1599},[1152,19897,2639],{},[1148,19899,19900],{"mathvariant":1599},"Γ",[1495,19902,2162],{"stretchy":2161},[1148,19904,10710],{},[1148,19906,3049],{"mathvariant":1599},[1152,19908,2639],{},[1495,19910,2181],{"stretchy":2161},[2632,19912,19913,19915],{},[1148,19914,2675],{},[1142,19916,19917,19919,19921,19923,19925],{},[1148,19918,10710],{},[1148,19920,3049],{"mathvariant":1599},[1152,19922,2639],{},[1495,19924,1885],{},[1152,19926,1176],{},[2632,19928,19929,19931],{},[1148,19930,18179],{},[1142,19932,19933,19935,19937,19939],{},[1495,19934,1885],{},[1148,19936,2675],{},[1148,19938,3049],{"mathvariant":1599},[1152,19940,2639],{},[1495,19942,2188],{"separator":1121},[3520,19944],{"width":3522},[1148,19946,2675],{},[1495,19948,1641],{},[1152,19950,1154],{},[1495,19952,2188],{"separator":1121},[1156,19954,19955],{"encoding":1158},"f(x) = \\frac{1}{2^{k\u002F2}\\Gamma(k\u002F2)} x^{k\u002F2-1} e^{-x\u002F2}, \\qquad x > 0,",[1110,19957,14139,19958,19972],{},[1115,19959,19961],{"className":19960},[1133],[1135,19962,19963],{"xmlns":1137},[1139,19964,19965,19969],{},[1142,19966,19967],{},[1148,19968,19900],{"mathvariant":1599},[1156,19970,19971],{"encoding":1158},"\\Gamma"," je funkce gama.",[1110,19974,19975,19978,19979,2261,19997,1497],{},[1399,19976,19977],{},"Fisherovo-Snedecorovo rozdělení"," se stupni volnosti ",[1115,19980,19982],{"className":19981},[1133],[1135,19983,19984],{"xmlns":1137},[1139,19985,19986,19994],{},[1142,19987,19988],{},[1145,19989,19990,19992],{},[1148,19991,10710],{},[1152,19993,1176],{},[1156,19995,19996],{"encoding":1158},"k_1",[1115,19998,20000],{"className":19999},[1133],[1135,20001,20002],{"xmlns":1137},[1139,20003,20004,20012],{},[1142,20005,20006],{},[1145,20007,20008,20010],{},[1148,20009,10710],{},[1152,20011,2639],{},[1156,20013,20014],{"encoding":1158},"k_2",[1115,20016,20018],{"className":20017},[1133],[1135,20019,20020],{"xmlns":1137,"display":2151},[1139,20021,20022,20187],{},[1142,20023,20024,20026,20028,20030,20032,20034,20070,20104,20124,20176,20178,20180,20182,20184],{},[1148,20025,16375],{},[1495,20027,2162],{"stretchy":2161},[1148,20029,2675],{},[1495,20031,2181],{"stretchy":2161},[1495,20033,1503],{},[2749,20035,20036,20038],{},[1152,20037,1176],{},[1142,20039,20040,20042],{},[1148,20041,8159],{},[1142,20043,20044,20046,20056,20058,20068],{},[1495,20045,2162],{"fence":1121},[2749,20047,20048,20054],{},[1145,20049,20050,20052],{},[1148,20051,10710],{},[1152,20053,1176],{},[1152,20055,2639],{},[1495,20057,2188],{"separator":1121},[2749,20059,20060,20066],{},[1145,20061,20062,20064],{},[1148,20063,10710],{},[1152,20065,2639],{},[1152,20067,2639],{},[1495,20069,2181],{"fence":1121},[2632,20071,20072,20092],{},[1142,20073,20074,20076,20090],{},[1495,20075,2162],{"fence":1121},[2749,20077,20078,20084],{},[1145,20079,20080,20082],{},[1148,20081,10710],{},[1152,20083,1176],{},[1145,20085,20086,20088],{},[1148,20087,10710],{},[1152,20089,2639],{},[1495,20091,2181],{"fence":1121},[1142,20093,20094,20100,20102],{},[1145,20095,20096,20098],{},[1148,20097,10710],{},[1152,20099,1176],{},[1148,20101,3049],{"mathvariant":1599},[1152,20103,2639],{},[2632,20105,20106,20108],{},[1148,20107,2675],{},[1142,20109,20110,20116,20118,20120,20122],{},[1145,20111,20112,20114],{},[1148,20113,10710],{},[1152,20115,1176],{},[1148,20117,3049],{"mathvariant":1599},[1152,20119,2639],{},[1495,20121,1885],{},[1152,20123,1176],{},[2632,20125,20126,20152],{},[1142,20127,20128,20130,20132,20134,20148,20150],{},[1495,20129,2162],{"fence":1121},[1152,20131,1176],{},[1495,20133,6294],{},[2749,20135,20136,20142],{},[1145,20137,20138,20140],{},[1148,20139,10710],{},[1152,20141,1176],{},[1145,20143,20144,20146],{},[1148,20145,10710],{},[1152,20147,2639],{},[1148,20149,2675],{},[1495,20151,2181],{"fence":1121},[1142,20153,20154,20156],{},[1495,20155,1885],{},[2749,20157,20158,20174],{},[1142,20159,20160,20166,20168],{},[1145,20161,20162,20164],{},[1148,20163,10710],{},[1152,20165,1176],{},[1495,20167,6294],{},[1145,20169,20170,20172],{},[1148,20171,10710],{},[1152,20173,2639],{},[1152,20175,2639],{},[1495,20177,2188],{"separator":1121},[3520,20179],{"width":3522},[1148,20181,2675],{},[1495,20183,1641],{},[1152,20185,20186],{},"0.",[1156,20188,20189],{"encoding":1158},"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.",[1110,20191,20192],{},[1971,20193],{"alt":20194,"className":20195,"src":20196},"mask-nv-specialni-rozdeleni",[1343,1975],"\u002Fwiki-assets\u002Fmask-nv-specialni-rozdeleni.png",[18530,20198],{"spec":20199},"{\"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\":[]}",[1110,20201,20202],{},"R funkce pro tato tři rozdělení:",[1532,20204,20205,20219],{},[1535,20206,20207],{},[1538,20208,20209,20211,20214,20216],{},[1541,20210,19115],{},[1541,20212,20213],{},"hustota",[1541,20215,16312],{},[1541,20217,20218],{},"kvantil",[1568,20220,20221,20261,20305],{},[1538,20222,20223,20246,20251,20256],{},[1573,20224,20225,20226],{},"Studentovo ",[1115,20227,20229],{"className":20228},[1133],[1135,20230,20231],{"xmlns":1137},[1139,20232,20233,20243],{},[1142,20234,20235,20237,20239,20241],{},[1148,20236,1373],{},[1495,20238,2162],{"stretchy":2161},[1148,20240,10710],{},[1495,20242,2181],{"stretchy":2161},[1156,20244,20245],{"encoding":1158},"t(k)",[1573,20247,20248],{},[3161,20249,20250],{},"dt(x, df = k)",[1573,20252,20253],{},[3161,20254,20255],{},"pt(x, df = k)",[1573,20257,20258],{},[3161,20259,20260],{},"qt(p, df = k)",[1538,20262,20263,20290,20295,20300],{},[1573,20264,20265,20266],{},"Pearsonovo ",[1115,20267,20269],{"className":20268},[1133],[1135,20270,20271],{"xmlns":1137},[1139,20272,20273,20287],{},[1142,20274,20275,20281,20283,20285],{},[2632,20276,20277,20279],{},[1148,20278,11297],{},[1152,20280,2639],{},[1495,20282,2162],{"stretchy":2161},[1148,20284,10710],{},[1495,20286,2181],{"stretchy":2161},[1156,20288,20289],{"encoding":1158},"\\chi^2(k)",[1573,20291,20292],{},[3161,20293,20294],{},"dchisq(x, df = k)",[1573,20296,20297],{},[3161,20298,20299],{},"pchisq(x, df = k)",[1573,20301,20302],{},[3161,20303,20304],{},"qchisq(p, df = k)",[1538,20306,20307,20342,20347,20352],{},[1573,20308,20309,20310],{},"Fisherovo-Snedecorovo ",[1115,20311,20313],{"className":20312},[1133],[1135,20314,20315],{"xmlns":1137},[1139,20316,20317,20339],{},[1142,20318,20319,20321,20323,20329,20331,20337],{},[1148,20320,1387],{},[1495,20322,2162],{"stretchy":2161},[1145,20324,20325,20327],{},[1148,20326,10710],{},[1152,20328,1176],{},[1495,20330,2188],{"separator":1121},[1145,20332,20333,20335],{},[1148,20334,10710],{},[1152,20336,2639],{},[1495,20338,2181],{"stretchy":2161},[1156,20340,20341],{"encoding":1158},"F(k_1, k_2)",[1573,20343,20344],{},[3161,20345,20346],{},"df(x, df1 = k1, df2 = k2)",[1573,20348,20349],{},[3161,20350,20351],{},"pf(x, df1 = k1, df2 = k2)",[1573,20353,20354],{},[3161,20355,20356],{},"qf(p, df1 = k1, df2 = k2)",[1110,20358,20359],{},"V R (97,5%-ní kvantil Studentova rozdělení s 9 stupni volnosti, 95%-ní kvantily Pearsonova a Fisherova-Snedecorova rozdělení):",[3166,20361,20363],{"className":3168,"code":20362,"language":71,"meta":3170,"style":3170},"qt(0.975, df = 9)\nqchisq(0.95, df = 9)\nqf(0.95, df1 = 3, df2 = 10)\n",[3161,20364,20365,20385,20404],{"__ignoreMap":3170},[1115,20366,20367,20370,20372,20374,20376,20378,20380,20383],{"class":3175,"line":10},[1115,20368,20369],{"class":3185},"qt",[1115,20371,2162],{"class":3189},[1115,20373,7807],{"class":3192},[1115,20375,2188],{"class":3181},[1115,20377,3725],{"class":3178},[1115,20379,3252],{"class":3181},[1115,20381,20382],{"class":3192}," 9",[1115,20384,3235],{"class":3189},[1115,20386,20387,20390,20392,20394,20396,20398,20400,20402],{"class":3175,"line":27},[1115,20388,20389],{"class":3185},"qchisq",[1115,20391,2162],{"class":3189},[1115,20393,5108],{"class":3192},[1115,20395,2188],{"class":3181},[1115,20397,3725],{"class":3178},[1115,20399,3252],{"class":3181},[1115,20401,20382],{"class":3192},[1115,20403,3235],{"class":3189},[1115,20405,20406,20409,20411,20413,20415,20418,20420,20422,20424,20427,20429,20431],{"class":3175,"line":148},[1115,20407,20408],{"class":3185},"qf",[1115,20410,2162],{"class":3189},[1115,20412,5108],{"class":3192},[1115,20414,2188],{"class":3181},[1115,20416,20417],{"class":3178}," df1",[1115,20419,3252],{"class":3181},[1115,20421,9537],{"class":3192},[1115,20423,2188],{"class":3181},[1115,20425,20426],{"class":3178}," df2",[1115,20428,3252],{"class":3181},[1115,20430,3856],{"class":3192},[1115,20432,3235],{"class":3189},[3166,20434,20437],{"className":20435,"code":20436,"language":3274,"meta":3170},[3272],"[1] 2.262157\n[1] 16.91898\n[1] 3.708265\n",[3161,20438,20436],{"__ignoreMap":3170},[1392,20440,10963],{"id":10962},[1124,20442,20443,20528,20578],{},[1127,20444,20445,20448,20449,20476,20477,3049,20479,3049,20481,20483,20484,20504,20505,20527],{},[1399,20446,20447],{},"Rozptyl vs. směrodatná odchylka v R."," Zápis ",[1115,20450,20452],{"className":20451},[1133],[1135,20453,20454],{"xmlns":1137},[1139,20455,20456,20474],{},[1142,20457,20458,20460,20462,20464,20466,20472],{},[1148,20459,2624],{},[1495,20461,2162],{"stretchy":2161},[1148,20463,1500],{},[1495,20465,16495],{"separator":1121},[2632,20467,20468,20470],{},[1148,20469,2636],{},[1152,20471,2639],{},[1495,20473,2181],{"stretchy":2161},[1156,20475,16506],{"encoding":1158}," používá rozptyl, ale ",[3161,20478,16510],{},[3161,20480,16513],{},[3161,20482,16516],{}," očekávají směrodatnou odchylku. Dosazení rozptylu místo ",[1115,20485,20487],{"className":20486},[1133],[1135,20488,20489],{"xmlns":1137},[1139,20490,20491,20501],{},[1142,20492,20493],{},[2770,20494,20495],{},[2632,20496,20497,20499],{},[1148,20498,2636],{},[1152,20500,2639],{},[1156,20502,20503],{"encoding":1158},"\\sqrt{\\sigma^2}"," dává jiný — a pro ",[1115,20506,20508],{"className":20507},[1133],[1135,20509,20510],{"xmlns":1137},[1139,20511,20512,20524],{},[1142,20513,20514,20520,20522],{},[2632,20515,20516,20518],{},[1148,20517,2636],{},[1152,20519,2639],{},[1495,20521,1600],{"mathvariant":1599},[1152,20523,1176],{},[1156,20525,20526],{"encoding":1158},"\\sigma^2 \\ne 1"," výrazně odlišný — výsledek (viz příklad s ampulkou).",[1127,20529,20530,20557,20558,20577],{},[1399,20531,20532,20556],{},[1115,20533,20535],{"className":20534},[1133],[1135,20536,20537],{"xmlns":1137},[1139,20538,20539,20553],{},[1142,20540,20541,20543,20545,20547,20549,20551],{},[1148,20542,2158],{},[1495,20544,2162],{"stretchy":2161},[1148,20546,2618],{},[1495,20548,1503],{},[1148,20550,2675],{},[1495,20552,2181],{"stretchy":2161},[1156,20554,20555],{"encoding":1158},"P(X=x)"," u spojité veličiny je vždy 0."," Hustota ",[1115,20559,20561],{"className":20560},[1133],[1135,20562,20563],{"xmlns":1137},[1139,20564,20565,20575],{},[1142,20566,20567,20569,20571,20573],{},[1148,20568,16375],{},[1495,20570,2162],{"stretchy":2161},[1148,20572,2675],{},[1495,20574,2181],{"stretchy":2161},[1156,20576,16404],{"encoding":1158}," sama o sobě pravděpodobnost neudává — pravděpodobnost dává až plocha pod křivkou na intervalu.",[1127,20579,20580,1953,20583,20600,20601,20618,20619,20622,20623,1335],{},[1399,20581,20582],{},"Záměna stupňů volnosti u Fisherova-Snedecorova rozdělení.",[1115,20584,20586],{"className":20585},[1133],[1135,20587,20588],{"xmlns":1137},[1139,20589,20590,20598],{},[1142,20591,20592],{},[1145,20593,20594,20596],{},[1148,20595,10710],{},[1152,20597,1176],{},[1156,20599,19996],{"encoding":1158}," (čitatel) a ",[1115,20602,20604],{"className":20603},[1133],[1135,20605,20606],{"xmlns":1137},[1139,20607,20608,20616],{},[1142,20609,20610],{},[1145,20611,20612,20614],{},[1148,20613,10710],{},[1152,20615,2639],{},[1156,20617,20014],{"encoding":1158}," (jmenovatel) nejsou zaměnitelné — ",[3161,20620,20621],{},"qf(p, df1, df2)"," dá jiný výsledek než ",[3161,20624,20625],{},"qf(p, df2, df1)",[1392,20627,11120],{"id":11119},[1124,20629,20630,20635,20640,20645,20651,20656,20662],{},[1127,20631,20632],{},[1340,20633,11128],{"className":20634,"dataFsResolvedFilePath":1344,"href":1345},[1343],[1127,20636,20637],{},[1340,20638,886],{"className":20639,"dataFsResolvedFilePath":1351,"href":1352},[1343],[1127,20641,20642],{},[1340,20643,141],{"className":20644,"dataFsResolvedFilePath":11426,"href":11427},[1343],[1127,20646,20647],{},[1340,20648,20650],{"className":20649,"dataFsResolvedFilePath":11146,"href":11147},[1343],"regresni-a-korelacni-analyza",[1127,20652,20653],{},[1340,20654,716],{"className":20655,"dataFsResolvedFilePath":11154,"href":11155},[1343],[1127,20657,20658],{},[1340,20659,20661],{"className":20660,"dataFsResolvedFilePath":11162,"href":11163},[1343],"regulacni-diagramy-a-indexy-zpusobilosti",[1127,20663,20664],{},[1340,20665,11172],{"className":20666,"dataFsResolvedFilePath":11170,"href":11171},[1343],[1392,20668,11175],{"id":934},[1110,20670,11178,20671,11182],{},[10079,20672,11181],{},[11184,20674,20675],{},"html 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R.pdf","topics\u002Fnahodne-veliciny-a-rozdeleni",[23,67,812,332,532,71],"y7MCWBwmskoGgsMoqVPhRRaL6YYTo3Cf-R4Yf-89eMs",{"id":20698,"title":11140,"body":20699,"course":23,"courses":11214,"created":11215,"description":3170,"extension":11216,"meta":25380,"navigation":11218,"path":25381,"seo":25382,"sources":25383,"stem":25389,"tags":25390,"type":11231,"updated":11215,"__hash__":25391},"topics\u002Ftopics\u002Fpopisna-statistika.md",{"type":1096,"value":20700,"toc":25371},[20701,20704,20797,20801,20811,20937,20944,20955,20959,21002,21007,21108,21117,21122,21261,21337,21341,21440,21521,21528,21592,21610,21612,21826,21832,21842,21849,21852,21906,21912,21922,21935,22081,22084,22097,22415,22421,22424,22428,22507,22541,22570,22572,22650,22656,22717,22724,22737,22814,22930,22980,22993,23148,23154,23181,23185,23210,23213,23426,23494,23595,23602,23615,24070,24076,24108,24365,24518,24629,24658,24664,24671,24677,24690,25118,25124,25127,25129,25323,25325,25362,25364,25368],[1099,20702,11140],{"id":20703},"popisná-statistika-a-datové-soubory",[1103,20705,20707,20713],{"className":20706,"dataCallout":1108},[1106,1107],[1110,20708,20710,1122],{"className":20709},[1113],[1115,20711],{"className":20712,"ariaHidden":1121},[1118,1119,1120],[1124,20714,20715,20718,20721,20747,20794],{},[1127,20716,20717],{},"Rozlišit základní a výběrový soubor, typ statistického znaku (kvantitativní\u002Fkvalitativní, diskrétní\u002Fspojitý) a požadavek reprezentativity a nezávislého výběru.",[1127,20719,20720],{},"Spočítat výběrový průměr, rozptyl, směrodatnou odchylku a variační rozpětí; interpretovat je jako bodové odhady charakteristik náhodné veličiny.",[1127,20722,20723,20724,1335],{},"Určit medián a kvartily a číst empirickou distribuční funkci ",[1115,20725,20727],{"className":20726},[1133],[1135,20728,20729],{"xmlns":1137},[1139,20730,20731,20745],{},[1142,20732,20733,20739,20741,20743],{},[1145,20734,20735,20737],{},[1148,20736,1387],{},[1148,20738,2657],{},[1495,20740,2162],{"stretchy":2161},[1148,20742,2675],{},[1495,20744,2181],{"stretchy":2161},[1156,20746,8611],{"encoding":1158},[1127,20748,20749,20750,20793],{},"Roztřídit velký datový soubor do tříd (intervalové rozdělení četností), sestavit tabulku ",[1115,20751,20753],{"className":20752},[1133],[1135,20754,20755],{"xmlns":1137},[1139,20756,20757,20790],{},[1142,20758,20759,20766,20768,20774,20776,20782,20784],{},[1145,20760,20761,20764],{},[1148,20762,20763],{},"I",[1148,20765,11580],{},[1495,20767,2188],{"separator":1121},[1145,20769,20770,20772],{},[1148,20771,5389],{},[1148,20773,11580],{},[1495,20775,2188],{"separator":1121},[1145,20777,20778,20780],{},[1148,20779,16375],{},[1148,20781,11580],{},[1495,20783,2188],{"separator":1121},[1145,20785,20786,20788],{},[1148,20787,1110],{},[1148,20789,11580],{},[1156,20791,20792],{"encoding":1158},"I_j, Z_j, f_j, p_j"," a nakreslit histogram.",[1127,20795,20796],{},"Z histogramu odhadnout zákon rozdělení dat; formální test shody patří do testování hypotéz.",[1392,20798,20800],{"id":20799},"základní-pojmy","Základní pojmy",[1110,20802,20803,20806,20807,20810],{},[1340,20804,11128],{"className":20805,"dataFsResolvedFilePath":1344,"href":1345},[1343]," pracuje s ",[1399,20808,20809],{},"datovými soubory"," — konkrétními hodnotami, které popisují vlastnost zkoumaných prvků.",[1124,20812,20813,20819,20843,20849,20924],{},[1127,20814,20815,20818],{},[1399,20816,20817],{},"Základní soubor"," — množina prvků, na nichž provádíme šetření (např. všichni výdělečně činní obyvatelé ČR).",[1127,20820,20821,20824,20825],{},[1399,20822,20823],{},"Statistický znak"," — funkce, která vyjadřuje určitou vlastnost prvku (např. velikost platu). Znaky dělíme na:\n",[1124,20826,20827,20838],{},[1127,20828,20829,20831,20832,20834,20835,20837],{},[1399,20830,11439],{}," (vyjádřitelné číslem) — dále ",[1399,20833,16301],{}," (spočetně mnoho hodnot) nebo ",[1399,20836,16305],{}," (libovolná hodnota v intervalu);",[1127,20839,20840,20842],{},[1399,20841,11432],{}," (vyjádřitelné slovně).",[1127,20844,20845,20848],{},[1399,20846,20847],{},"Výběrový soubor"," — podmnožina prvků základního souboru, na níž znak skutečně zjišťujeme (např. 5 náhodně vybraných obyvatel).",[1127,20850,20851,20854,20855,1335],{},[1399,20852,20853],{},"Datový soubor"," — n-tice naměřených hodnot zkoumaného znaku, např. ",[1115,20856,20858],{"className":20857},[1133],[1135,20859,20860],{"xmlns":1137},[1139,20861,20862,20921],{},[1142,20863,20864,20866,20868,20870,20873,20875,20878,20881,20883,20886,20888,20890,20893,20895,20898,20900,20902,20904,20906,20908,20910,20912,20914,20916,20919],{},[1495,20865,2162],{"stretchy":2161},[1152,20867,13217],{},[2358,20869,2360],{},[1152,20871,20872],{},"500",[1495,20874,2188],{"separator":1121},[2358,20876,20877],{}," ",[1152,20879,20880],{},"38",[2358,20882,2360],{},[1152,20884,20885],{},"000",[1495,20887,2188],{"separator":1121},[2358,20889,20877],{},[1152,20891,20892],{},"37",[2358,20894,2360],{},[1152,20896,20897],{},"800",[1495,20899,2188],{"separator":1121},[2358,20901,20877],{},[1152,20903,18935],{},[2358,20905,2360],{},[1152,20907,20885],{},[1495,20909,2188],{"separator":1121},[2358,20911,20877],{},[1152,20913,13225],{},[2358,20915,2360],{},[1152,20917,20918],{},"200",[1495,20920,2181],{"stretchy":2161},[1156,20922,20923],{"encoding":1158},"(29\\,500,\\ 38\\,000,\\ 37\\,800,\\ 41\\,000,\\ 31\\,200)",[1127,20925,20926,20927,1195,20930,2261,20933,20936],{},"Podle počtu sledovaných znaků rozlišujeme ",[1399,20928,20929],{},"jednorozměrné",[1399,20931,20932],{},"dvourozměrné",[1399,20934,20935],{},"vícerozměrné"," datové soubory.",[1110,20938,20939],{},[1971,20940],{"alt":20941,"className":20942,"src":20943},"mask-ilu-zakladni-soubor-vyber",[1343,1975],"\u002Fwiki-assets\u002Fmask-ilu-zakladni-soubor-vyber.png",[1110,20945,20946,20947,20950,20951,20954],{},"Aby výběrový soubor dobře vypovídal o základním souboru, měl by být ",[1399,20948,20949],{},"reprezentativní"," (podobný základnímu souboru svým složením). Není-li to možné zajistit přímo, volí se prvky do výběru náhodně — ",[1399,20952,20953],{},"nezávislý výběr",". Bez náhodnosti výběru nelze vlastnosti základního souboru správně vystihnout.",[1392,20956,20958],{"id":20957},"empirické-charakteristiky","Empirické charakteristiky",[1110,20960,20961,20962,20965,20966,20969,20970,20983,20984,20987,20988,21001],{},"Zpracováním datového souboru získáme ",[1399,20963,20964],{},"empirické charakteristiky"," a odhad ",[1399,20967,20968],{},"zákona rozdělení"," zkoumané náhodné veličiny ",[1115,20971,20973],{"className":20972},[1133],[1135,20974,20975],{"xmlns":1137},[1139,20976,20977,20981],{},[1142,20978,20979],{},[1148,20980,2618],{},[1156,20982,2618],{"encoding":1158},". Jde o ",[1399,20985,20986],{},"bodové odhady"," charakteristik ",[1115,20989,20991],{"className":20990},[1133],[1135,20992,20993],{"xmlns":1137},[1139,20994,20995,20999],{},[1142,20996,20997],{},[1148,20998,2618],{},[1156,21000,2618],{"encoding":1158},"; ruční výpočet podle vzorců níže je potřeba jen bez dostupného softwaru.",[1110,21003,21004],{},[1399,21005,21006],{},"Míry polohy",[1115,21008,21010],{"className":21009},[1133],[1135,21011,21012],{"xmlns":1137,"display":2151},[1139,21013,21014,21105],{},[1142,21015,21016,21022,21024,21030,21044,21050,21052],{},[2671,21017,21018,21020],{"accent":1121},[1148,21019,2675],{},[1495,21021,2678],{},[1495,21023,1503],{},[2749,21025,21026,21028],{},[1152,21027,1176],{},[1148,21029,2657],{},[11676,21031,21032,21034,21042],{},[1495,21033,11680],{},[1142,21035,21036,21038,21040],{},[1148,21037,4085],{},[1495,21039,1503],{},[1152,21041,1176],{},[1148,21043,2657],{},[1145,21045,21046,21048],{},[1148,21047,2675],{},[1148,21049,4085],{},[3520,21051],{"width":3522},[1142,21053,21054,21057,21064,21067,21074,21077,21083,21086,21094,21096,21102],{},[2358,21055,21056],{},"(v",[2671,21058,21059,21061],{"accent":1121},[2358,21060,10129],{},[1495,21062,21063],{},"ˊ",[2358,21065,21066],{},"b",[2671,21068,21069,21071],{"accent":1121},[2358,21070,18179],{},[1495,21072,21073],{},"ˇ",[2358,21075,21076],{},"rov",[2671,21078,21079,21081],{"accent":1121},[2358,21080,10129],{},[1495,21082,21063],{},[2358,21084,21085],{}," pr",[2671,21087,21088,21091],{"accent":1121},[2358,21089,21090],{},"u",[1495,21092,21093],{},"˚",[2358,21095,14104],{},[2671,21097,21098,21100],{"accent":1121},[2358,21099,18179],{},[1495,21101,21073],{},[2358,21103,21104],{},"r)",[1156,21106,21107],{"encoding":1158},"\\bar{x} = \\frac{1}{n}\\sum_{i=1}^{n} x_i \\qquad \\text{(výběrový průměr)}",[1110,21109,21110,21111,2261,21113,21116],{},"Dalšími mírami polohy jsou ",[1399,21112,9795],{},[1399,21114,21115],{},"modus"," (nejčetnější hodnota výběru).",[1110,21118,21119],{},[1399,21120,21121],{},"Míry variability",[1115,21123,21125],{"className":21124},[1133],[1135,21126,21127],{"xmlns":1137,"display":2151},[1139,21128,21129,21258],{},[1142,21130,21131,21137,21139,21151,21193,21195,21197,21199,21201,21209,21211],{},[2632,21132,21133,21135],{},[1148,21134,2695],{},[1152,21136,2639],{},[1495,21138,1503],{},[2749,21140,21141,21143],{},[1152,21142,1176],{},[1142,21144,21145,21147,21149],{},[1148,21146,2657],{},[1495,21148,1885],{},[1152,21150,1176],{},[1142,21152,21153,21155,21169,21177,21179,21181,21191],{},[1495,21154,2162],{"fence":1121},[11676,21156,21157,21159,21167],{},[1495,21158,11680],{},[1142,21160,21161,21163,21165],{},[1148,21162,4085],{},[1495,21164,1503],{},[1152,21166,1176],{},[1148,21168,2657],{},[4163,21170,21171,21173,21175],{},[1148,21172,2675],{},[1148,21174,4085],{},[1152,21176,2639],{},[1495,21178,1885],{},[1148,21180,2657],{},[2632,21182,21183,21189],{},[2671,21184,21185,21187],{"accent":1121},[1148,21186,2675],{},[1495,21188,2678],{},[1152,21190,2639],{},[1495,21192,2181],{"fence":1121},[1495,21194,2188],{"separator":1121},[3520,21196],{"width":3522},[1148,21198,2695],{},[1495,21200,1503],{},[2770,21202,21203],{},[2632,21204,21205,21207],{},[1148,21206,2695],{},[1152,21208,2639],{},[3520,21210],{"width":3522},[1142,21212,21213,21215,21221,21223,21229,21231,21237,21240,21246,21249,21255],{},[2358,21214,21056],{},[2671,21216,21217,21219],{"accent":1121},[2358,21218,10129],{},[1495,21220,21063],{},[2358,21222,21066],{},[2671,21224,21225,21227],{"accent":1121},[2358,21226,18179],{},[1495,21228,21073],{},[2358,21230,21076],{},[2671,21232,21233,21235],{"accent":1121},[2358,21234,10129],{},[1495,21236,21063],{},[2358,21238,21239],{}," rozptyl, sm",[2671,21241,21242,21244],{"accent":1121},[2358,21243,18179],{},[1495,21245,21073],{},[2358,21247,21248],{},"rodatn",[2671,21250,21251,21253],{"accent":1121},[2358,21252,1340],{},[1495,21254,21063],{},[2358,21256,21257],{}," odchylka)",[1156,21259,21260],{"encoding":1158},"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)}",[1115,21262,21264],{"className":21263},[1133],[1135,21265,21266],{"xmlns":1137,"display":2151},[1139,21267,21268,21334],{},[1142,21269,21270,21272,21274,21283,21285,21293,21295],{},[1148,21271,19792],{},[1495,21273,1503],{},[1145,21275,21276,21278,21281],{},[1148,21277,2675],{},[1148,21279,21280],{},"max",[1495,21282,8744],{},[1495,21284,1885],{},[1145,21286,21287,21289,21291],{},[1148,21288,2675],{},[1148,21290,14121],{},[1495,21292,8744],{},[3520,21294],{"width":3522},[1142,21296,21297,21300,21306,21308,21315,21318,21324,21326,21332],{},[2358,21298,21299],{},"(varia",[2671,21301,21302,21304],{"accent":1121},[2358,21303,1991],{},[1495,21305,21073],{},[2358,21307,2657],{},[2671,21309,21310,21313],{"accent":1121},[2358,21311,21312],{},"ı",[1495,21314,21063],{},[2358,21316,21317],{}," rozp",[2671,21319,21320,21322],{"accent":1121},[2358,21321,18179],{},[1495,21323,21073],{},[2358,21325,1373],{},[2671,21327,21328,21330],{"accent":1121},[2358,21329,21312],{},[1495,21331,21063],{},[2358,21333,2181],{},[1156,21335,21336],{"encoding":1158},"R = x_{\\max} - x_{\\min} \\qquad \\text{(variační rozpětí)}",[1110,21338,21339],{},[1399,21340,17893],{},[1110,21342,21343,21344,21367,21368,21388,21389,21410,21411,21439],{},"Kvantil ",[1115,21345,21347],{"className":21346},[1133],[1135,21348,21349],{"xmlns":1137},[1139,21350,21351,21364],{},[1142,21352,21353],{},[1145,21354,21355,21362],{},[2671,21356,21357,21359],{"accent":1121},[1148,21358,2675],{},[1495,21360,21361],{},"~",[1148,21363,1110],{},[1156,21365,21366],{"encoding":1158},"\\tilde{x}_p"," dělí hodnoty datového souboru na dvě části: ",[1115,21369,21371],{"className":21370},[1133],[1135,21372,21373],{"xmlns":1137},[1139,21374,21375,21385],{},[1142,21376,21377,21379,21381,21383],{},[1152,21378,2354],{},[1148,21380,1110],{},[2358,21382,2360],{},[1148,21384,2363],{"mathvariant":1599},[1156,21386,21387],{"encoding":1158},"100p\\,\\%"," hodnot je menších nebo rovných ",[1115,21390,21392],{"className":21391},[1133],[1135,21393,21394],{"xmlns":1137},[1139,21395,21396,21408],{},[1142,21397,21398],{},[1145,21399,21400,21406],{},[2671,21401,21402,21404],{"accent":1121},[1148,21403,2675],{},[1495,21405,21361],{},[1148,21407,1110],{},[1156,21409,21366],{"encoding":1158},", zbylých ",[1115,21412,21414],{"className":21413},[1133],[1135,21415,21416],{"xmlns":1137},[1139,21417,21418,21436],{},[1142,21419,21420,21422,21424,21426,21428,21430,21432,21434],{},[1152,21421,2354],{},[1495,21423,2162],{"stretchy":2161},[1152,21425,1176],{},[1495,21427,1885],{},[1148,21429,1110],{},[1495,21431,2181],{"stretchy":2161},[2358,21433,2360],{},[1148,21435,2363],{"mathvariant":1599},[1156,21437,21438],{"encoding":1158},"100(1-p)\\,\\%"," je větších. Nejdůležitější kvantily:",[1124,21441,21442,21469],{},[1127,21443,21444,1953,21446,21468],{},[1399,21445,9795],{},[1115,21447,21449],{"className":21448},[1133],[1135,21450,21451],{"xmlns":1137},[1139,21452,21453,21465],{},[1142,21454,21455],{},[1145,21456,21457,21463],{},[2671,21458,21459,21461],{"accent":1121},[1148,21460,2675],{},[1495,21462,21361],{},[1152,21464,3354],{},[1156,21466,21467],{"encoding":1158},"\\tilde{x}_{0{,}5}"," — pro lichý počet prvků uspořádaného souboru prostřední prvek, pro sudý počet průměr dvou prostředních prvků;",[1127,21470,21471,1953,21474,2261,21496,1953,21499,1335],{},[1399,21472,21473],{},"dolní kvartil",[1115,21475,21477],{"className":21476},[1133],[1135,21478,21479],{"xmlns":1137},[1139,21480,21481,21493],{},[1142,21482,21483],{},[1145,21484,21485,21491],{},[2671,21486,21487,21489],{"accent":1121},[1148,21488,2675],{},[1495,21490,21361],{},[1152,21492,18064],{},[1156,21494,21495],{"encoding":1158},"\\tilde{x}_{0{,}25}",[1399,21497,21498],{},"horní kvartil",[1115,21500,21502],{"className":21501},[1133],[1135,21503,21504],{"xmlns":1137},[1139,21505,21506,21518],{},[1142,21507,21508],{},[1145,21509,21510,21516],{},[2671,21511,21512,21514],{"accent":1121},[1148,21513,2675],{},[1495,21515,21361],{},[1152,21517,18084],{},[1156,21519,21520],{"encoding":1158},"\\tilde{x}_{0{,}75}",[1110,21522,21523,21524,21527],{},"Datový soubor se do R zadává buď přímo (",[3161,21525,21526],{},"x \u003C- c(...)","), nebo načtením ze souboru:",[3166,21529,21531],{"className":3168,"code":21530,"language":71,"meta":3170,"style":3170},"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",[3161,21532,21533,21587],{"__ignoreMap":3170},[1115,21534,21535,21537,21539,21541,21543,21545,21547,21549,21551,21553,21555,21557,21559,21561,21563,21565,21567,21569,21571,21573,21575,21577,21579,21581,21584],{"class":3175,"line":10},[1115,21536,2675],{"class":3178},[1115,21538,3182],{"class":3181},[1115,21540,3186],{"class":3185},[1115,21542,2162],{"class":3189},[1115,21544,3923],{"class":3192},[1115,21546,2188],{"class":3181},[1115,21548,3928],{"class":3192},[1115,21550,2188],{"class":3181},[1115,21552,3933],{"class":3192},[1115,21554,2188],{"class":3181},[1115,21556,3938],{"class":3192},[1115,21558,2188],{"class":3181},[1115,21560,3933],{"class":3192},[1115,21562,2188],{"class":3181},[1115,21564,3933],{"class":3192},[1115,21566,2188],{"class":3181},[1115,21568,3951],{"class":3192},[1115,21570,2188],{"class":3181},[1115,21572,3956],{"class":3192},[1115,21574,2188],{"class":3181},[1115,21576,3928],{"class":3192},[1115,21578,2188],{"class":3181},[1115,21580,3928],{"class":3192},[1115,21582,21583],{"class":3189},")   ",[1115,21585,21586],{"class":10754},"# přímé zadání hodnot\n",[1115,21588,21589],{"class":3175,"line":27},[1115,21590,21591],{"class":10754},"# x \u003C- read.table(\"data.txt\")[, 1]                       # načtení prvního sloupce ze souboru\n",[1110,21593,21594,21595,21598,21599,21602,21603,8286,21606,21609],{},"Řádek s načtením ze souboru je zakomentovaný znakem ",[3161,21596,21597],{},"#",": soubor musí ležet v pracovním adresáři R. ",[3161,21600,21601],{},"read.table()"," vrací datovou tabulku (",[3161,21604,21605],{},"data.frame",[3161,21607,21608],{},"[, 1]"," vybere její první sloupec jako vektor.",[1110,21611,18637],{},[3166,21613,21615],{"className":3168,"code":21614,"language":71,"meta":3170,"style":3170},"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",[3161,21616,21617,21674,21685,21695,21706,21716,21754,21780,21803],{"__ignoreMap":3170},[1115,21618,21619,21621,21623,21625,21627,21630,21632,21635,21637,21640,21642,21645,21647,21649,21651,21654,21656,21658,21660,21663,21665,21668,21670,21672],{"class":3175,"line":10},[1115,21620,2675],{"class":3178},[1115,21622,3182],{"class":3181},[1115,21624,3186],{"class":3185},[1115,21626,2162],{"class":3189},[1115,21628,21629],{"class":3192},"11.1",[1115,21631,2188],{"class":3181},[1115,21633,21634],{"class":3192}," 12.7",[1115,21636,2188],{"class":3181},[1115,21638,21639],{"class":3192}," 10.8",[1115,21641,2188],{"class":3181},[1115,21643,21644],{"class":3192}," 13.2",[1115,21646,2188],{"class":3181},[1115,21648,21634],{"class":3192},[1115,21650,2188],{"class":3181},[1115,21652,21653],{"class":3192}," 13.4",[1115,21655,2188],{"class":3181},[1115,21657,21634],{"class":3192},[1115,21659,2188],{"class":3181},[1115,21661,21662],{"class":3192}," 14.4",[1115,21664,2188],{"class":3181},[1115,21666,21667],{"class":3192}," 14.7",[1115,21669,2188],{"class":3181},[1115,21671,21662],{"class":3192},[1115,21673,3235],{"class":3189},[1115,21675,21676,21679,21681,21683],{"class":3175,"line":27},[1115,21677,21678],{"class":3185},"length",[1115,21680,2162],{"class":3189},[1115,21682,2675],{"class":3178},[1115,21684,3235],{"class":3189},[1115,21686,21687,21689,21691,21693],{"class":3175,"line":148},[1115,21688,9640],{"class":3185},[1115,21690,2162],{"class":3189},[1115,21692,2675],{"class":3178},[1115,21694,3235],{"class":3189},[1115,21696,21697,21700,21702,21704],{"class":3175,"line":111},[1115,21698,21699],{"class":3185},"var",[1115,21701,2162],{"class":3189},[1115,21703,2675],{"class":3178},[1115,21705,3235],{"class":3189},[1115,21707,21708,21710,21712,21714],{"class":3175,"line":96},[1115,21709,9651],{"class":3185},[1115,21711,2162],{"class":3189},[1115,21713,2675],{"class":3178},[1115,21715,3235],{"class":3189},[1115,21717,21718,21720,21722,21724,21727,21729,21731,21733,21735,21737,21739,21741,21743,21745,21748,21750,21752],{"class":3175,"line":89},[1115,21719,14121],{"class":3185},[1115,21721,2162],{"class":3189},[1115,21723,2675],{"class":3178},[1115,21725,21726],{"class":3189},"); ",[1115,21728,21280],{"class":3185},[1115,21730,2162],{"class":3189},[1115,21732,2675],{"class":3178},[1115,21734,21726],{"class":3189},[1115,21736,21280],{"class":3185},[1115,21738,2162],{"class":3189},[1115,21740,2675],{"class":3178},[1115,21742,3688],{"class":3189},[1115,21744,14265],{"class":3181},[1115,21746,21747],{"class":3185}," min",[1115,21749,2162],{"class":3189},[1115,21751,2675],{"class":3178},[1115,21753,3235],{"class":3189},[1115,21755,21756,21759,21761,21763,21765,21768,21770,21773,21775,21778],{"class":3175,"line":82},[1115,21757,21758],{"class":3185},"quantile",[1115,21760,2162],{"class":3189},[1115,21762,2675],{"class":3178},[1115,21764,2188],{"class":3181},[1115,21766,21767],{"class":3192}," 0.5",[1115,21769,2188],{"class":3181},[1115,21771,21772],{"class":3178}," type",[1115,21774,3252],{"class":3181},[1115,21776,21777],{"class":3192}," 6",[1115,21779,3235],{"class":3189},[1115,21781,21782,21784,21786,21788,21790,21793,21795,21797,21799,21801],{"class":3175,"line":75},[1115,21783,21758],{"class":3185},[1115,21785,2162],{"class":3189},[1115,21787,2675],{"class":3178},[1115,21789,2188],{"class":3181},[1115,21791,21792],{"class":3192}," 0.25",[1115,21794,2188],{"class":3181},[1115,21796,21772],{"class":3178},[1115,21798,3252],{"class":3181},[1115,21800,21777],{"class":3192},[1115,21802,3235],{"class":3189},[1115,21804,21805,21807,21809,21811,21813,21816,21818,21820,21822,21824],{"class":3175,"line":9681},[1115,21806,21758],{"class":3185},[1115,21808,2162],{"class":3189},[1115,21810,2675],{"class":3178},[1115,21812,2188],{"class":3181},[1115,21814,21815],{"class":3192}," 0.75",[1115,21817,2188],{"class":3181},[1115,21819,21772],{"class":3178},[1115,21821,3252],{"class":3181},[1115,21823,21777],{"class":3192},[1115,21825,3235],{"class":3189},[3166,21827,21830],{"className":21828,"code":21829,"language":3274,"meta":3170},[3272],"[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",[3161,21831,21829],{"__ignoreMap":3170},[1110,21833,21834,21837,21838,21841],{},[3161,21835,21836],{},"quantile(x, p, type = 6)"," je potřeba zadat explicitně — výchozí typ v R (",[3161,21839,21840],{},"type = 7",") by u některých souborů dal mírně odlišné hodnoty kvantilů než ruční výpočet použitý v této kapitole.",[1110,21843,21844],{},[1971,21845],{"alt":21846,"className":21847,"src":21848},"mask-ps-kvantily",[1343,1975],"\u002Fwiki-assets\u002Fmask-ps-kvantily.png",[1110,21850,21851],{},"Seřazení souboru a krabicový graf:",[3166,21853,21855],{"className":3168,"code":21854,"language":71,"meta":3170,"style":3170},"sort(x)                     # vzestupně\nsort(x, decreasing = TRUE)  # sestupně\nboxplot(x)\n",[3161,21856,21857,21872,21895],{"__ignoreMap":3170},[1115,21858,21859,21862,21864,21866,21869],{"class":3175,"line":10},[1115,21860,21861],{"class":3185},"sort",[1115,21863,2162],{"class":3189},[1115,21865,2675],{"class":3178},[1115,21867,21868],{"class":3189},")                     ",[1115,21870,21871],{"class":10754},"# vzestupně\n",[1115,21873,21874,21876,21878,21880,21882,21885,21887,21889,21892],{"class":3175,"line":27},[1115,21875,21861],{"class":3185},[1115,21877,2162],{"class":3189},[1115,21879,2675],{"class":3178},[1115,21881,2188],{"class":3181},[1115,21883,21884],{"class":3178}," decreasing",[1115,21886,3252],{"class":3181},[1115,21888,5282],{"class":3192},[1115,21890,21891],{"class":3189},")  ",[1115,21893,21894],{"class":10754},"# sestupně\n",[1115,21896,21897,21900,21902,21904],{"class":3175,"line":148},[1115,21898,21899],{"class":3185},"boxplot",[1115,21901,2162],{"class":3189},[1115,21903,2675],{"class":3178},[1115,21905,3235],{"class":3189},[3166,21907,21910],{"className":21908,"code":21909,"language":3274,"meta":3170},[3272]," [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",[3161,21911,21909],{"__ignoreMap":3170},[1110,21913,21914,21917,21918,21921],{},[3161,21915,21916],{},"boxplot()"," kreslí krabici mezi hodnotami ",[3161,21919,21920],{},"fivenum(x)"," (zde 12,7 a 14,4), které se od kvartilů typu 6 mohou mírně lišit.",[1103,21923,21925,21932],{"className":21924,"dataCallout":3323},[1106,3322],[1110,21926,21928,21931],{"className":21927},[1113],[1115,21929],{"className":21930,"ariaHidden":1121},[1118,3330,1120],"Příklad: Empirické charakteristiky",[1110,21933,21934],{},"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.",[1110,21936,21937,21938,1195,21961,1195,21984,1195,22003,22022,22023,18048,22050,22065,22066,1335],{},"Výstup R kódu výše dává ",[1115,21939,21941],{"className":21940},[1133],[1135,21942,21943],{"xmlns":1137},[1139,21944,21945,21958],{},[1142,21946,21947,21953,21955],{},[2671,21948,21949,21951],{"accent":1121},[1148,21950,2675],{},[1495,21952,2678],{},[1495,21954,1503],{},[1152,21956,21957],{},"13,01",[1156,21959,21960],{"encoding":1158},"\\bar{x}=13{,}01",[1115,21962,21964],{"className":21963},[1133],[1135,21965,21966],{"xmlns":1137},[1139,21967,21968,21981],{},[1142,21969,21970,21976,21978],{},[2632,21971,21972,21974],{},[1148,21973,2695],{},[1152,21975,2639],{},[1495,21977,1503],{},[1152,21979,21980],{},"1,75",[1156,21982,21983],{"encoding":1158},"s^2=1{,}75",[1115,21985,21987],{"className":21986},[1133],[1135,21988,21989],{"xmlns":1137},[1139,21990,21991,22000],{},[1142,21992,21993,21995,21997],{},[1148,21994,2695],{},[1495,21996,1503],{},[1152,21998,21999],{},"1,32",[1156,22001,22002],{"encoding":1158},"s=1{,}32",[1115,22004,22006],{"className":22005},[1133],[1135,22007,22008],{"xmlns":1137},[1139,22009,22010,22019],{},[1142,22011,22012,22014,22016],{},[1148,22013,19792],{},[1495,22015,1503],{},[1152,22017,22018],{},"3,9",[1156,22020,22021],{"encoding":1158},"R=3{,}9",", medián ",[1115,22024,22026],{"className":22025},[1133],[1135,22027,22028],{"xmlns":1137},[1139,22029,22030,22047],{},[1142,22031,22032,22042,22044],{},[1145,22033,22034,22040],{},[2671,22035,22036,22038],{"accent":1121},[1148,22037,2675],{},[1495,22039,21361],{},[1152,22041,3354],{},[1495,22043,1503],{},[1152,22045,22046],{},"12,95",[1156,22048,22049],{"encoding":1158},"\\tilde{x}_{0{,}5}=12{,}95",[1115,22051,22053],{"className":22052},[1133],[1135,22054,22055],{"xmlns":1137},[1139,22056,22057,22062],{},[1142,22058,22059],{},[1152,22060,22061],{},"12,3",[1156,22063,22064],{"encoding":1158},"12{,}3",", horní kvartil ",[1115,22067,22069],{"className":22068},[1133],[1135,22070,22071],{"xmlns":1137},[1139,22072,22073,22078],{},[1142,22074,22075],{},[1152,22076,22077],{},"14,4",[1156,22079,22080],{"encoding":1158},"14{,}4",[1110,22082,22083],{},"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.",[1103,22085,22087,22094],{"className":22086,"dataCallout":3323},[1106,3322],[1110,22088,22090,22093],{"className":22089},[1113],[1115,22091],{"className":22092,"ariaHidden":1121},[1118,3330,1120],"Příklad: Doba oprav televizorů",[1110,22095,22096],{},"Při 50 opravách určité závady televizoru byly naměřeny časy (v minutách). Určete empirické charakteristiky.",[3166,22098,22100],{"className":3168,"code":22099,"language":71,"meta":3170,"style":3170},"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",[3161,22101,22102,22162,22213,22260,22307,22355,22365,22375,22385,22405],{"__ignoreMap":3170},[1115,22103,22104,22107,22109,22111,22113,22115,22117,22120,22122,22125,22127,22130,22132,22135,22137,22140,22142,22145,22147,22150,22152,22155,22157,22160],{"class":3175,"line":10},[1115,22105,22106],{"class":3178},"x6",[1115,22108,3182],{"class":3181},[1115,22110,3186],{"class":3185},[1115,22112,2162],{"class":3189},[1115,22114,13242],{"class":3192},[1115,22116,2188],{"class":3181},[1115,22118,22119],{"class":3192}," 40.2",[1115,22121,2188],{"class":3181},[1115,22123,22124],{"class":3192}," 41.9",[1115,22126,2188],{"class":3181},[1115,22128,22129],{"class":3192}," 43.4",[1115,22131,2188],{"class":3181},[1115,22133,22134],{"class":3192}," 42.8",[1115,22136,2188],{"class":3181},[1115,22138,22139],{"class":3192}," 42.3",[1115,22141,2188],{"class":3181},[1115,22143,22144],{"class":3192}," 43.2",[1115,22146,2188],{"class":3181},[1115,22148,22149],{"class":3192}," 45",[1115,22151,2188],{"class":3181},[1115,22153,22154],{"class":3192}," 41.5",[1115,22156,2188],{"class":3181},[1115,22158,22159],{"class":3192}," 42.7",[1115,22161,9400],{"class":3181},[1115,22163,22164,22167,22169,22172,22174,22177,22179,22182,22184,22187,22189,22192,22194,22197,22199,22202,22204,22206,22208,22211],{"class":3175,"line":27},[1115,22165,22166],{"class":3192},"        43.9",[1115,22168,2188],{"class":3181},[1115,22170,22171],{"class":3192}," 40.1",[1115,22173,2188],{"class":3181},[1115,22175,22176],{"class":3192}," 43.3",[1115,22178,2188],{"class":3181},[1115,22180,22181],{"class":3192}," 41.1",[1115,22183,2188],{"class":3181},[1115,22185,22186],{"class":3192}," 42.5",[1115,22188,2188],{"class":3181},[1115,22190,22191],{"class":3192}," 42.4",[1115,22193,2188],{"class":3181},[1115,22195,22196],{"class":3192}," 41.4",[1115,22198,2188],{"class":3181},[1115,22200,22201],{"class":3192}," 40.8",[1115,22203,2188],{"class":3181},[1115,22205,18914],{"class":3192},[1115,22207,2188],{"class":3181},[1115,22209,22210],{"class":3192}," 44.7",[1115,22212,9400],{"class":3181},[1115,22214,22215,22218,22220,22222,22224,22226,22228,22231,22233,22236,22238,22241,22243,22245,22247,22250,22252,22254,22256,22258],{"class":3175,"line":148},[1115,22216,22217],{"class":3192},"        41.2",[1115,22219,2188],{"class":3181},[1115,22221,22124],{"class":3192},[1115,22223,2188],{"class":3181},[1115,22225,22191],{"class":3192},[1115,22227,2188],{"class":3181},[1115,22229,22230],{"class":3192}," 44.4",[1115,22232,2188],{"class":3181},[1115,22234,22235],{"class":3192}," 40.5",[1115,22237,2188],{"class":3181},[1115,22239,22240],{"class":3192}," 39.7",[1115,22242,2188],{"class":3181},[1115,22244,22181],{"class":3192},[1115,22246,2188],{"class":3181},[1115,22248,22249],{"class":3192}," 41",[1115,22251,2188],{"class":3181},[1115,22253,22124],{"class":3192},[1115,22255,2188],{"class":3181},[1115,22257,22201],{"class":3192},[1115,22259,9400],{"class":3181},[1115,22261,22262,22265,22267,22269,22271,22274,22276,22278,22280,22282,22284,22287,22289,22292,22294,22296,22298,22301,22303,22305],{"class":3175,"line":111},[1115,22263,22264],{"class":3192},"        43",[1115,22266,2188],{"class":3181},[1115,22268,22134],{"class":3192},[1115,22270,2188],{"class":3181},[1115,22272,22273],{"class":3192}," 42.9",[1115,22275,2188],{"class":3181},[1115,22277,22159],{"class":3192},[1115,22279,2188],{"class":3181},[1115,22281,22176],{"class":3192},[1115,22283,2188],{"class":3181},[1115,22285,22286],{"class":3192}," 42.2",[1115,22288,2188],{"class":3181},[1115,22290,22291],{"class":3192}," 39.2",[1115,22293,2188],{"class":3181},[1115,22295,22154],{"class":3192},[1115,22297,2188],{"class":3181},[1115,22299,22300],{"class":3192}," 41.6",[1115,22302,2188],{"class":3181},[1115,22304,22159],{"class":3192},[1115,22306,9400],{"class":3181},[1115,22308,22309,22312,22314,22316,22318,22321,22323,22325,22327,22330,22332,22335,22337,22340,22342,22344,22346,22349,22351,22353],{"class":3175,"line":96},[1115,22310,22311],{"class":3192},"        45",[1115,22313,2188],{"class":3181},[1115,22315,22139],{"class":3192},[1115,22317,2188],{"class":3181},[1115,22319,22320],{"class":3192}," 43.6",[1115,22322,2188],{"class":3181},[1115,22324,22144],{"class":3192},[1115,22326,2188],{"class":3181},[1115,22328,22329],{"class":3192}," 38.8",[1115,22331,2188],{"class":3181},[1115,22333,22334],{"class":3192}," 43",[1115,22336,2188],{"class":3181},[1115,22338,22339],{"class":3192}," 44.2",[1115,22341,2188],{"class":3181},[1115,22343,22334],{"class":3192},[1115,22345,2188],{"class":3181},[1115,22347,22348],{"class":3192}," 40",[1115,22350,2188],{"class":3181},[1115,22352,22230],{"class":3192},[1115,22354,3235],{"class":3189},[1115,22356,22357,22359,22361,22363],{"class":3175,"line":89},[1115,22358,21678],{"class":3185},[1115,22360,2162],{"class":3189},[1115,22362,22106],{"class":3178},[1115,22364,3235],{"class":3189},[1115,22366,22367,22369,22371,22373],{"class":3175,"line":82},[1115,22368,9640],{"class":3185},[1115,22370,2162],{"class":3189},[1115,22372,22106],{"class":3178},[1115,22374,3235],{"class":3189},[1115,22376,22377,22379,22381,22383],{"class":3175,"line":75},[1115,22378,9651],{"class":3185},[1115,22380,2162],{"class":3189},[1115,22382,22106],{"class":3178},[1115,22384,3235],{"class":3189},[1115,22386,22387,22389,22391,22393,22395,22397,22399,22401,22403],{"class":3175,"line":9681},[1115,22388,21280],{"class":3185},[1115,22390,2162],{"class":3189},[1115,22392,22106],{"class":3178},[1115,22394,3688],{"class":3189},[1115,22396,14265],{"class":3181},[1115,22398,21747],{"class":3185},[1115,22400,2162],{"class":3189},[1115,22402,22106],{"class":3178},[1115,22404,3235],{"class":3189},[1115,22406,22407,22409,22411,22413],{"class":3175,"line":72},[1115,22408,9662],{"class":3185},[1115,22410,2162],{"class":3189},[1115,22412,22106],{"class":3178},[1115,22414,3235],{"class":3189},[3166,22416,22419],{"className":22417,"code":22418,"language":3274,"meta":3170},[3272],"[1] 50\n[1] 42.27\n[1] 1.48052\n[1] 6.2\n[1] 42.4\n",[3161,22420,22418],{"__ignoreMap":3170},[1110,22422,22423],{},"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.",[1392,22425,22427],{"id":22426},"empirická-distribuční-funkce","Empirická distribuční funkce",[1110,22429,22430,22431,22444,22445,1953,22448,22471,22472,22506],{},"Pro libovolný rozsah datového souboru, diskrétní i spojitou náhodnou veličinu ",[1115,22432,22434],{"className":22433},[1133],[1135,22435,22436],{"xmlns":1137},[1139,22437,22438,22442],{},[1142,22439,22440],{},[1148,22441,2618],{},[1156,22443,2618],{"encoding":1158},", lze sestrojit ",[1399,22446,22447],{},"empirickou distribuční funkci",[1115,22449,22451],{"className":22450},[1133],[1135,22452,22453],{"xmlns":1137},[1139,22454,22455,22469],{},[1142,22456,22457,22463,22465,22467],{},[1145,22458,22459,22461],{},[1148,22460,1387],{},[1148,22462,2657],{},[1495,22464,2162],{"stretchy":2161},[1148,22466,2675],{},[1495,22468,2181],{"stretchy":2161},[1156,22470,8611],{"encoding":1158},". Pro datový soubor ",[1115,22473,22475],{"className":22474},[1133],[1135,22476,22477],{"xmlns":1137},[1139,22478,22479,22503],{},[1142,22480,22481,22483,22489,22491,22493,22495,22501],{},[1495,22482,2162],{"stretchy":2161},[1145,22484,22485,22487],{},[1148,22486,2675],{},[1152,22488,1176],{},[1495,22490,2188],{"separator":1121},[1495,22492,10697],{},[1495,22494,2188],{"separator":1121},[1145,22496,22497,22499],{},[1148,22498,2675],{},[1148,22500,2657],{},[1495,22502,2181],{"stretchy":2161},[1156,22504,22505],{"encoding":1158},"(x_1,\\dots,x_n)"," je",[1115,22508,22510],{"className":22509},[1133],[1135,22511,22512],{"xmlns":1137,"display":2151},[1139,22513,22514,22538],{},[1142,22515,22516,22522,22524,22526,22528,22530,22536],{},[1145,22517,22518,22520],{},[1148,22519,1387],{},[1148,22521,2657],{},[1495,22523,2162],{"stretchy":2161},[1148,22525,2675],{},[1495,22527,2181],{"stretchy":2161},[1495,22529,1503],{},[2749,22531,22532,22534],{},[1148,22533,10710],{},[1148,22535,2657],{},[1495,22537,2188],{"separator":1121},[1156,22539,22540],{"encoding":1158},"F_n(x) = \\frac{k}{n},",[1110,22542,14139,22543,22556,22557,1335],{},[1115,22544,22546],{"className":22545},[1133],[1135,22547,22548],{"xmlns":1137},[1139,22549,22550,22554],{},[1142,22551,22552],{},[1148,22553,10710],{},[1156,22555,10710],{"encoding":1158}," je počet prvků datového souboru menších nebo rovných číslu ",[1115,22558,22560],{"className":22559},[1133],[1135,22561,22562],{"xmlns":1137},[1139,22563,22564,22568],{},[1142,22565,22566],{},[1148,22567,2675],{},[1156,22569,2675],{"encoding":1158},[1110,22571,18637],{},[3166,22573,22575],{"className":3168,"code":22574,"language":71,"meta":3170,"style":3170},"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",[3161,22576,22577,22592,22607,22625,22639],{"__ignoreMap":3170},[1115,22578,22579,22581,22583,22586,22588,22590],{"class":3175,"line":10},[1115,22580,16375],{"class":3178},[1115,22582,3182],{"class":3181},[1115,22584,22585],{"class":3185}," ecdf",[1115,22587,2162],{"class":3189},[1115,22589,2675],{"class":3178},[1115,22591,3235],{"class":3189},[1115,22593,22594,22597,22599,22601,22604],{"class":3175,"line":27},[1115,22595,22596],{"class":3185},"knots",[1115,22598,2162],{"class":3189},[1115,22600,16375],{"class":3178},[1115,22602,22603],{"class":3189},")        ",[1115,22605,22606],{"class":10754},"# vzestupně seřazené různé hodnoty datového souboru\n",[1115,22608,22609,22611,22613,22615,22617,22619,22622],{"class":3175,"line":148},[1115,22610,16375],{"class":3185},[1115,22612,2162],{"class":3189},[1115,22614,22596],{"class":3185},[1115,22616,2162],{"class":3189},[1115,22618,16375],{"class":3178},[1115,22620,22621],{"class":3189},"))      ",[1115,22623,22624],{"class":10754},"# hodnoty Fn(x) v těchto bodech\n",[1115,22626,22627,22629,22631,22633,22636],{"class":3175,"line":111},[1115,22628,16375],{"class":3185},[1115,22630,2162],{"class":3189},[1115,22632,13212],{"class":3192},[1115,22634,22635],{"class":3189},")            ",[1115,22637,22638],{"class":10754},"# Fn v libovolném bodě\n",[1115,22640,22641,22644,22646,22648],{"class":3175,"line":96},[1115,22642,22643],{"class":3185},"plot",[1115,22645,2162],{"class":3189},[1115,22647,16375],{"class":3178},[1115,22649,3235],{"class":3189},[3166,22651,22654],{"className":22652,"code":22653,"language":3274,"meta":3170},[3272],"[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",[3161,22655,22653],{"__ignoreMap":3170},[1110,22657,22658,22661,22662,22680,22681,22684,22685,22698,22699,1335],{},[3161,22659,22660],{},"knots()"," vrací jen různé hodnoty (opakující se hodnota 12,7 je ve výpočtu ",[1115,22663,22665],{"className":22664},[1133],[1135,22666,22667],{"xmlns":1137},[1139,22668,22669,22677],{},[1142,22670,22671],{},[1145,22672,22673,22675],{},[1148,22674,1387],{},[1148,22676,2657],{},[1156,22678,22679],{"encoding":1158},"F_n"," započtena třikrát, v seznamu uzlů je ale jen jednou); ",[3161,22682,22683],{},"plot(f)"," nakreslí schodovitý graf, který v každém uzlu skáče o ",[1115,22686,22688],{"className":22687},[1133],[1135,22689,22690],{"xmlns":1137},[1139,22691,22692,22696],{},[1142,22693,22694],{},[1148,22695,10710],{},[1156,22697,10710],{"encoding":1158},"-násobek ",[1115,22700,22702],{"className":22701},[1133],[1135,22703,22704],{"xmlns":1137},[1139,22705,22706,22714],{},[1142,22707,22708,22710,22712],{},[1152,22709,1176],{},[1148,22711,3049],{"mathvariant":1599},[1148,22713,2657],{},[1156,22715,22716],{"encoding":1158},"1\u002Fn",[1110,22718,22719],{},[1971,22720],{"alt":22721,"className":22722,"src":22723},"mask-ps-ecdf",[1343,1975],"\u002Fwiki-assets\u002Fmask-ps-ecdf.png",[1103,22725,22727,22734],{"className":22726,"dataCallout":3323},[1106,3322],[1110,22728,22730,22733],{"className":22729},[1113],[1115,22731],{"className":22732,"ariaHidden":1121},[1118,3330,1120],"Příklad: Empirická distribuční funkce",[1110,22735,22736],{},"Pro předchozí datový soubor (doba opravy součástky) určete empirickou distribuční funkci.",[1110,22738,22739,22740,1335],{},"Uspořádaný soubor je ",[1115,22741,22743],{"className":22742},[1133],[1135,22744,22745],{"xmlns":1137},[1139,22746,22747,22811],{},[1142,22748,22749,22752,22754,22756,22759,22761,22763,22766,22768,22770,22772,22774,22776,22778,22780,22782,22785,22787,22789,22792,22794,22796,22798,22800,22802,22804,22806,22808],{},[1152,22750,22751],{},"10,8",[1495,22753,16495],{"separator":1121},[2358,22755,20877],{},[1152,22757,22758],{},"11,1",[1495,22760,16495],{"separator":1121},[2358,22762,20877],{},[1152,22764,22765],{},"12,7",[1495,22767,16495],{"separator":1121},[2358,22769,20877],{},[1152,22771,22765],{},[1495,22773,16495],{"separator":1121},[2358,22775,20877],{},[1152,22777,22765],{},[1495,22779,16495],{"separator":1121},[2358,22781,20877],{},[1152,22783,22784],{},"13,2",[1495,22786,16495],{"separator":1121},[2358,22788,20877],{},[1152,22790,22791],{},"13,4",[1495,22793,16495],{"separator":1121},[2358,22795,20877],{},[1152,22797,22077],{},[1495,22799,16495],{"separator":1121},[2358,22801,20877],{},[1152,22803,22077],{},[1495,22805,16495],{"separator":1121},[2358,22807,20877],{},[1152,22809,22810],{},"14,7",[1156,22812,22813],{"encoding":1158},"10{,}8;\\ 11{,}1;\\ 12{,}7;\\ 12{,}7;\\ 12{,}7;\\ 13{,}2;\\ 13{,}4;\\ 14{,}4;\\ 14{,}4;\\ 14{,}7",[1532,22815,22816,22849],{},[1535,22817,22818],{},[1538,22819,22820,22835,22837,22839,22841,22843,22845,22847],{},[1541,22821,22822],{},[1115,22823,22825],{"className":22824},[1133],[1135,22826,22827],{"xmlns":1137},[1139,22828,22829,22833],{},[1142,22830,22831],{},[1148,22832,2675],{},[1156,22834,2675],{"encoding":1158},[1541,22836,22751],{},[1541,22838,22758],{},[1541,22840,22765],{},[1541,22842,22784],{},[1541,22844,22791],{},[1541,22846,22077],{},[1541,22848,22810],{},[1568,22850,22851,22883],{},[1538,22852,22853,22868,22870,22872,22874,22876,22879,22881],{},[1573,22854,22855],{},[1115,22856,22858],{"className":22857},[1133],[1135,22859,22860],{"xmlns":1137},[1139,22861,22862,22866],{},[1142,22863,22864],{},[1148,22865,10710],{},[1156,22867,10710],{"encoding":1158},[1573,22869,1176],{},[1573,22871,2639],{},[1573,22873,9817],{},[1573,22875,13607],{},[1573,22877,22878],{},"7",[1573,22880,4972],{},[1573,22882,4717],{},[1538,22884,22885,22910,22913,22916,22918,22921,22924,22927],{},[1573,22886,22887],{},[1115,22888,22890],{"className":22889},[1133],[1135,22891,22892],{"xmlns":1137},[1139,22893,22894,22908],{},[1142,22895,22896,22902,22904,22906],{},[1145,22897,22898,22900],{},[1148,22899,1387],{},[1148,22901,2657],{},[1495,22903,2162],{"stretchy":2161},[1148,22905,2675],{},[1495,22907,2181],{"stretchy":2161},[1156,22909,8611],{"encoding":1158},[1573,22911,22912],{},"0,1",[1573,22914,22915],{},"0,2",[1573,22917,3354],{},[1573,22919,22920],{},"0,6",[1573,22922,22923],{},"0,7",[1573,22925,22926],{},"0,9",[1573,22928,22929],{},"1,0",[1110,22931,22932,22933,22955,22956,22979],{},"Graf (levý panel výše) odpovídá tabulce: funkce je nulová pod 10,8, skáče o ",[1115,22934,22936],{"className":22935},[1133],[1135,22937,22938],{"xmlns":1137},[1139,22939,22940,22952],{},[1142,22941,22942,22944,22946,22948,22950],{},[1152,22943,1176],{},[1148,22945,3049],{"mathvariant":1599},[1148,22947,2657],{},[1495,22949,1503],{},[1152,22951,22912],{},[1156,22953,22954],{"encoding":1158},"1\u002Fn = 0{,}1"," v každé jednoduché hodnotě a o ",[1115,22957,22959],{"className":22958},[1133],[1135,22960,22961],{"xmlns":1137},[1139,22962,22963,22976],{},[1142,22964,22965,22967,22969,22971,22973],{},[1152,22966,13259],{},[1148,22968,3049],{"mathvariant":1599},[1148,22970,2657],{},[1495,22972,1503],{},[1152,22974,22975],{},"0,3",[1156,22977,22978],{"encoding":1158},"3\u002Fn = 0{,}3"," v bodě 12,7, kde se hodnota opakuje třikrát.",[1103,22981,22983,22990],{"className":22982,"dataCallout":3323},[1106,3322],[1110,22984,22986,22989],{"className":22985},[1113],[1115,22987],{"className":22988,"ariaHidden":1121},[1118,3330,1120],"Příklad: Odpad materiálu",[1110,22991,22992],{},"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.",[3166,22994,22996],{"className":3168,"code":22995,"language":71,"meta":3170,"style":3170},"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",[3161,22997,22998,23049,23059,23069,23079,23099,23109,23124,23134],{"__ignoreMap":3170},[1115,22999,23000,23003,23005,23007,23009,23011,23013,23015,23017,23019,23021,23023,23025,23027,23029,23031,23033,23035,23037,23039,23041,23043,23045,23047],{"class":3175,"line":10},[1115,23001,23002],{"class":3178},"x4",[1115,23004,3182],{"class":3181},[1115,23006,3186],{"class":3185},[1115,23008,2162],{"class":3189},[1115,23010,3923],{"class":3192},[1115,23012,2188],{"class":3181},[1115,23014,3928],{"class":3192},[1115,23016,2188],{"class":3181},[1115,23018,3933],{"class":3192},[1115,23020,2188],{"class":3181},[1115,23022,3938],{"class":3192},[1115,23024,2188],{"class":3181},[1115,23026,3933],{"class":3192},[1115,23028,2188],{"class":3181},[1115,23030,3933],{"class":3192},[1115,23032,2188],{"class":3181},[1115,23034,3951],{"class":3192},[1115,23036,2188],{"class":3181},[1115,23038,3956],{"class":3192},[1115,23040,2188],{"class":3181},[1115,23042,3928],{"class":3192},[1115,23044,2188],{"class":3181},[1115,23046,3928],{"class":3192},[1115,23048,3235],{"class":3189},[1115,23050,23051,23053,23055,23057],{"class":3175,"line":27},[1115,23052,21678],{"class":3185},[1115,23054,2162],{"class":3189},[1115,23056,23002],{"class":3178},[1115,23058,3235],{"class":3189},[1115,23060,23061,23063,23065,23067],{"class":3175,"line":148},[1115,23062,9640],{"class":3185},[1115,23064,2162],{"class":3189},[1115,23066,23002],{"class":3178},[1115,23068,3235],{"class":3189},[1115,23070,23071,23073,23075,23077],{"class":3175,"line":111},[1115,23072,9651],{"class":3185},[1115,23074,2162],{"class":3189},[1115,23076,23002],{"class":3178},[1115,23078,3235],{"class":3189},[1115,23080,23081,23083,23085,23087,23089,23091,23093,23095,23097],{"class":3175,"line":96},[1115,23082,21280],{"class":3185},[1115,23084,2162],{"class":3189},[1115,23086,23002],{"class":3178},[1115,23088,3688],{"class":3189},[1115,23090,14265],{"class":3181},[1115,23092,21747],{"class":3185},[1115,23094,2162],{"class":3189},[1115,23096,23002],{"class":3178},[1115,23098,3235],{"class":3189},[1115,23100,23101,23103,23105,23107],{"class":3175,"line":89},[1115,23102,9662],{"class":3185},[1115,23104,2162],{"class":3189},[1115,23106,23002],{"class":3178},[1115,23108,3235],{"class":3189},[1115,23110,23111,23114,23116,23118,23120,23122],{"class":3175,"line":82},[1115,23112,23113],{"class":3178},"f4",[1115,23115,3182],{"class":3181},[1115,23117,22585],{"class":3185},[1115,23119,2162],{"class":3189},[1115,23121,23002],{"class":3178},[1115,23123,3235],{"class":3189},[1115,23125,23126,23128,23130,23132],{"class":3175,"line":75},[1115,23127,22596],{"class":3185},[1115,23129,2162],{"class":3189},[1115,23131,23113],{"class":3178},[1115,23133,3235],{"class":3189},[1115,23135,23136,23138,23140,23142,23144,23146],{"class":3175,"line":9681},[1115,23137,23113],{"class":3185},[1115,23139,2162],{"class":3189},[1115,23141,22596],{"class":3185},[1115,23143,2162],{"class":3189},[1115,23145,23113],{"class":3178},[1115,23147,7963],{"class":3189},[3166,23149,23152],{"className":23150,"code":23151,"language":3274,"meta":3170},[3272],"[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",[3161,23153,23151],{"__ignoreMap":3170},[1110,23155,23156,23157,23180],{},"Průměrný odpad je 3,86 % se směrodatnou odchylkou 0,18 % a mediánem 3,85 %. Pravý panel obrázku výše ukazuje tvar ",[1115,23158,23160],{"className":23159},[1133],[1135,23161,23162],{"xmlns":1137},[1139,23163,23164,23178],{},[1142,23165,23166,23172,23174,23176],{},[1145,23167,23168,23170],{},[1148,23169,1387],{},[1148,23171,2657],{},[1495,23173,2162],{"stretchy":2161},[1148,23175,2675],{},[1495,23177,2181],{"stretchy":2161},[1156,23179,8611],{"encoding":1158},": hodnota 3,8 se v souboru opakuje třikrát, proto zde funkce skáče o 0,3 najednou, stejně jako hodnota 4,0.",[1392,23182,23184],{"id":23183},"třídění-datového-souboru-do-tříd","Třídění datového souboru do tříd",[1110,23186,23187,23188,23191,23192,23205,23206,23209],{},"Je-li rozsah datového souboru velký (řádově přes 30 až 50 pozorování), hodnoty se před dalším zpracováním ",[1399,23189,23190],{},"roztřídí",": variační rozpětí ",[1115,23193,23195],{"className":23194},[1133],[1135,23196,23197],{"xmlns":1137},[1139,23198,23199,23203],{},[1142,23200,23201],{},[1148,23202,19792],{},[1156,23204,19792],{"encoding":1158}," se rozdělí na určitý počet ",[1399,23207,23208],{},"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.",[1110,23211,23212],{},"Výsledkem je tabulka četností se sloupci:",[1124,23214,23215,23295,23316,23337],{},[1127,23216,23217,23235,23236,23249,23250,23294],{},[1115,23218,23220],{"className":23219},[1133],[1135,23221,23222],{"xmlns":1137},[1139,23223,23224,23232],{},[1142,23225,23226],{},[1145,23227,23228,23230],{},[1148,23229,20763],{},[1148,23231,11580],{},[1156,23233,23234],{"encoding":1158},"I_j"," — ",[1115,23237,23239],{"className":23238},[1133],[1135,23240,23241],{"xmlns":1137},[1139,23242,23243,23247],{},[1142,23244,23245],{},[1148,23246,11580],{},[1156,23248,11580],{"encoding":1158},"-tý interval (v této kapitole vždy zleva uzavřený a zprava otevřený, ",[1115,23251,23253],{"className":23252},[1133],[1135,23254,23255],{"xmlns":1137},[1139,23256,23257,23291],{},[1142,23258,23259,23265,23267,23269,23275,23277,23289],{},[1145,23260,23261,23263],{},[1148,23262,20763],{},[1148,23264,11580],{},[1495,23266,1503],{},[1495,23268,9071],{"stretchy":2161},[1145,23270,23271,23273],{},[1148,23272,1991],{},[1148,23274,11580],{},[1495,23276,16495],{"separator":1121},[1145,23278,23279,23281],{},[1148,23280,1991],{},[1142,23282,23283,23285,23287],{},[1148,23284,11580],{},[1495,23286,6294],{},[1152,23288,1176],{},[1495,23290,2181],{"stretchy":2161},[1156,23292,23293],{"encoding":1158},"I_j = \\langle c_j; c_{j+1})","),",[1127,23296,23297,23315],{},[1115,23298,23300],{"className":23299},[1133],[1135,23301,23302],{"xmlns":1137},[1139,23303,23304,23312],{},[1142,23305,23306],{},[1145,23307,23308,23310],{},[1148,23309,5389],{},[1148,23311,11580],{},[1156,23313,23314],{"encoding":1158},"Z_j"," — střed (reprezentant) intervalu,",[1127,23317,23318,23336],{},[1115,23319,23321],{"className":23320},[1133],[1135,23322,23323],{"xmlns":1137},[1139,23324,23325,23333],{},[1142,23326,23327],{},[1145,23328,23329,23331],{},[1148,23330,16375],{},[1148,23332,11580],{},[1156,23334,23335],{"encoding":1158},"f_j"," — četnost, počet hodnot v intervalu,",[1127,23338,23339,23369,23370,2261,23398,1335],{},[1115,23340,23342],{"className":23341},[1133],[1135,23343,23344],{"xmlns":1137},[1139,23345,23346,23366],{},[1142,23347,23348,23354,23356,23362,23364],{},[1145,23349,23350,23352],{},[1148,23351,1110],{},[1148,23353,11580],{},[1495,23355,1503],{},[1145,23357,23358,23360],{},[1148,23359,16375],{},[1148,23361,11580],{},[1148,23363,3049],{"mathvariant":1599},[1148,23365,2657],{},[1156,23367,23368],{"encoding":1158},"p_j = f_j\u002Fn"," — relativní četnost, přičemž ",[1115,23371,23373],{"className":23372},[1133],[1135,23374,23375],{"xmlns":1137},[1139,23376,23377,23395],{},[1142,23378,23379,23385,23391,23393],{},[1145,23380,23381,23383],{},[1495,23382,11680],{},[1148,23384,11580],{},[1145,23386,23387,23389],{},[1148,23388,16375],{},[1148,23390,11580],{},[1495,23392,1503],{},[1148,23394,2657],{},[1156,23396,23397],{"encoding":1158},"\\sum_j f_j = n",[1115,23399,23401],{"className":23400},[1133],[1135,23402,23403],{"xmlns":1137},[1139,23404,23405,23423],{},[1142,23406,23407,23413,23419,23421],{},[1145,23408,23409,23411],{},[1495,23410,11680],{},[1148,23412,11580],{},[1145,23414,23415,23417],{},[1148,23416,1110],{},[1148,23418,11580],{},[1495,23420,1503],{},[1152,23422,1176],{},[1156,23424,23425],{"encoding":1158},"\\sum_j p_j = 1",[1110,23427,23428,23429,23432,23433,23436,23437,23440,23441,23444,23445,3677,23448,23465,23466,23469,23470,3677,23473,11513,23490,23493],{},"V R se třídění provádí příkazem ",[3161,23430,23431],{},"hist()"," — buď necháme R zvolit třídy samo (",[3161,23434,23435],{},"hist(x)","), nebo zadáme hranice přímo (",[3161,23438,23439],{},"hist(x, br = seq(0, 550, by = 50))","). Uložením výsledku do proměnné (",[3161,23442,23443],{},"y \u003C- hist(...)",") získáme jednotlivé sloupce tabulky: ",[3161,23446,23447],{},"y$counts",[1115,23449,23451],{"className":23450},[1133],[1135,23452,23453],{"xmlns":1137},[1139,23454,23455,23463],{},[1142,23456,23457],{},[1145,23458,23459,23461],{},[1148,23460,16375],{},[1148,23462,11580],{},[1156,23464,23335],{"encoding":1158},"), ",[3161,23467,23468],{},"y$breaks"," (hranice tříd), ",[3161,23471,23472],{},"y$mids",[1115,23474,23476],{"className":23475},[1133],[1135,23477,23478],{"xmlns":1137},[1139,23479,23480,23488],{},[1142,23481,23482],{},[1145,23483,23484,23486],{},[1148,23485,5389],{},[1148,23487,11580],{},[1156,23489,23314],{"encoding":1158},[3161,23491,23492],{},"y$density"," (relativní četnosti na škále hustoty).",[1110,23495,23496,23497,23514,23515,23517,23518,23554,23555,23558,23559,1335],{},"Interval ",[1115,23498,23500],{"className":23499},[1133],[1135,23501,23502],{"xmlns":1137},[1139,23503,23504,23512],{},[1142,23505,23506],{},[1145,23507,23508,23510],{},[1148,23509,20763],{},[1148,23511,11580],{},[1156,23513,23234],{"encoding":1158}," je ve výchozím nastavení ",[3161,23516,23431],{}," zleva otevřený a zprava uzavřený, ",[1115,23519,23521],{"className":23520},[1133],[1135,23522,23523],{"xmlns":1137},[1139,23524,23525,23551],{},[1142,23526,23527,23529,23535,23537,23549],{},[1495,23528,2162],{"stretchy":2161},[1145,23530,23531,23533],{},[1148,23532,1991],{},[1148,23534,11580],{},[1495,23536,16495],{"separator":1121},[1145,23538,23539,23541],{},[1148,23540,1991],{},[1142,23542,23543,23545,23547],{},[1148,23544,11580],{},[1495,23546,6294],{},[1152,23548,1176],{},[1495,23550,9080],{"stretchy":2161},[1156,23552,23553],{"encoding":1158},"(c_j; c_{j+1}\\rangle"," — opačně, než jak třídy zapisujeme v této kapitole. Parametr ",[3161,23556,23557],{},"right = FALSE"," třídy obrátí na ",[1115,23560,23562],{"className":23561},[1133],[1135,23563,23564],{"xmlns":1137},[1139,23565,23566,23592],{},[1142,23567,23568,23570,23576,23578,23590],{},[1495,23569,9071],{"stretchy":2161},[1145,23571,23572,23574],{},[1148,23573,1991],{},[1148,23575,11580],{},[1495,23577,16495],{"separator":1121},[1145,23579,23580,23582],{},[1148,23581,1991],{},[1142,23583,23584,23586,23588],{},[1148,23585,11580],{},[1495,23587,6294],{},[1152,23589,1176],{},[1495,23591,2181],{"stretchy":2161},[1156,23593,23594],{"encoding":1158},"\\langle c_j; c_{j+1})",[1110,23596,23597],{},[1971,23598],{"alt":23599,"className":23600,"src":23601},"mask-ps-histogram-trideni",[1343,1975],"\u002Fwiki-assets\u002Fmask-ps-histogram-trideni.png",[1103,23603,23605,23612],{"className":23604,"dataCallout":3323},[1106,3322],[1110,23606,23608,23611],{"className":23607},[1113],[1115,23609],{"className":23610,"ariaHidden":1121},[1118,3330,1120],"Příklad: Třídění datového souboru",[1110,23613,23614],{},"Byly provedeny zkoušky životnosti nového výrobku. Datový soubor obsahuje 68 hodnot doby do poruchy (v minutách). Určete odhady charakteristik a zákona rozdělení.",[3166,23616,23618],{"className":3168,"code":23617,"language":71,"meta":3170,"style":3170},"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",[3161,23619,23620,23670,23713,23755,23799,23842,23885,23919,23929,23949,24013,24022,24052],{"__ignoreMap":3170},[1115,23621,23622,23624,23626,23628,23630,23632,23634,23636,23638,23640,23642,23644,23646,23648,23650,23652,23654,23656,23658,23660,23662,23664,23666,23668],{"class":3175,"line":10},[1115,23623,9298],{"class":3178},[1115,23625,3182],{"class":3181},[1115,23627,3186],{"class":3185},[1115,23629,2162],{"class":3189},[1115,23631,9307],{"class":3192},[1115,23633,2188],{"class":3181},[1115,23635,9312],{"class":3192},[1115,23637,2188],{"class":3181},[1115,23639,9317],{"class":3192},[1115,23641,2188],{"class":3181},[1115,23643,9322],{"class":3192},[1115,23645,2188],{"class":3181},[1115,23647,3856],{"class":3192},[1115,23649,2188],{"class":3181},[1115,23651,7909],{"class":3192},[1115,23653,2188],{"class":3181},[1115,23655,3255],{"class":3192},[1115,23657,2188],{"class":3181},[1115,23659,9339],{"class":3192},[1115,23661,2188],{"class":3181},[1115,23663,9344],{"class":3192},[1115,23665,2188],{"class":3181},[1115,23667,9349],{"class":3192},[1115,23669,9400],{"class":3181},[1115,23671,23672,23675,23677,23679,23681,23683,23685,23687,23689,23691,23693,23695,23697,23699,23701,23703,23705,23707,23709,23711],{"class":3175,"line":27},[1115,23673,23674],{"class":3192},"        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hist",[1115,23960,2162],{"class":3189},[1115,23962,9298],{"class":3178},[1115,23964,2188],{"class":3181},[1115,23966,23967],{"class":3178}," br",[1115,23969,3252],{"class":3181},[1115,23971,23972],{"class":3185}," seq",[1115,23974,2162],{"class":3189},[1115,23976,1154],{"class":3192},[1115,23978,2188],{"class":3181},[1115,23980,23981],{"class":3192}," 550",[1115,23983,2188],{"class":3181},[1115,23985,23986],{"class":3178}," by",[1115,23988,3252],{"class":3181},[1115,23990,15868],{"class":3192},[1115,23992,2181],{"class":3189},[1115,23994,2188],{"class":3181},[1115,23996,23997],{"class":3178}," right",[1115,23999,3252],{"class":3181},[1115,24001,15961],{"class":3192},[1115,24003,2188],{"class":3181},[1115,24005,24006],{"class":3178}," plot",[1115,24008,3252],{"class":3181},[1115,24010,15961],{"class":3192},[1115,24012,3235],{"class":3189},[1115,24014,24015,24017,24019],{"class":3175,"line":25},[1115,24016,23953],{"class":3178},[1115,24018,13559],{"class":3181},[1115,24020,24021],{"class":3178},"counts\n",[1115,24023,24024,24026,24028,24030,24032,24035,24037,24040,24042,24044,24046,24048,24050],{"class":3175,"line":65},[1115,24025,19552],{"class":3185},[1115,24027,2162],{"class":3189},[1115,24029,23953],{"class":3178},[1115,24031,13559],{"class":3181},[1115,24033,24034],{"class":3178},"counts",[1115,24036,7755],{"class":3181},[1115,24038,24039],{"class":3185}," length",[1115,24041,2162],{"class":3189},[1115,24043,9298],{"class":3178},[1115,24045,2181],{"class":3189},[1115,24047,2188],{"class":3181},[1115,24049,9537],{"class":3192},[1115,24051,3235],{"class":3189},[1115,24053,24054,24056,24058,24060,24062,24064,24066,24068],{"class":3175,"line":63},[1115,24055,9640],{"class":3185},[1115,24057,2162],{"class":3189},[1115,24059,9298],{"class":3178},[1115,24061,21726],{"class":3189},[1115,24063,9651],{"class":3185},[1115,24065,2162],{"class":3189},[1115,24067,9298],{"class":3178},[1115,24069,3235],{"class":3189},[3166,24071,24074],{"className":24072,"code":24073,"language":3274,"meta":3170},[3272],"[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",[3161,24075,24073],{"__ignoreMap":3170},[1110,24077,24078,24079,24107],{},"Variační rozpětí je ",[1115,24080,24082],{"className":24081},[1133],[1135,24083,24084],{"xmlns":1137},[1139,24085,24086,24104],{},[1142,24087,24088,24090,24092,24095,24097,24099,24101],{},[1148,24089,19792],{},[1495,24091,1503],{},[1152,24093,24094],{},"501",[1495,24096,1885],{},[1152,24098,2639],{},[1495,24100,1503],{},[1152,24102,24103],{},"499",[1156,24105,24106],{"encoding":1158},"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:",[1532,24109,24110,24206],{},[1535,24111,24112],{},[1538,24113,24114,24129,24148,24167,24186],{},[1541,24115,24116],{},[1115,24117,24119],{"className":24118},[1133],[1135,24120,24121],{"xmlns":1137},[1139,24122,24123,24127],{},[1142,24124,24125],{},[1148,24126,11580],{},[1156,24128,11580],{"encoding":1158},[1541,24130,24131],{},[1115,24132,24134],{"className":24133},[1133],[1135,24135,24136],{"xmlns":1137},[1139,24137,24138,24146],{},[1142,24139,24140],{},[1145,24141,24142,24144],{},[1148,24143,20763],{},[1148,24145,11580],{},[1156,24147,23234],{"encoding":1158},[1541,24149,24150],{},[1115,24151,24153],{"className":24152},[1133],[1135,24154,24155],{"xmlns":1137},[1139,24156,24157,24165],{},[1142,24158,24159],{},[1145,24160,24161,24163],{},[1148,24162,5389],{},[1148,24164,11580],{},[1156,24166,23314],{"encoding":1158},[1541,24168,24169],{},[1115,24170,24172],{"className":24171},[1133],[1135,24173,24174],{"xmlns":1137},[1139,24175,24176,24184],{},[1142,24177,24178],{},[1145,24179,24180,24182],{},[1148,24181,16375],{},[1148,24183,11580],{},[1156,24185,23335],{"encoding":1158},[1541,24187,24188],{},[1115,24189,24191],{"className":24190},[1133],[1135,24192,24193],{"xmlns":1137},[1139,24194,24195,24203],{},[1142,24196,24197],{},[1145,24198,24199,24201],{},[1148,24200,1110],{},[1148,24202,11580],{},[1156,24204,24205],{"encoding":1158},"p_j",[1568,24207,24208,24222,24236,24251,24264,24279,24293,24307,24322,24336,24351],{},[1538,24209,24210,24212,24215,24217,24219],{},[1573,24211,1176],{},[1573,24213,24214],{},"⟨0; 50)",[1573,24216,7116],{},[1573,24218,3553],{},[1573,24220,24221],{},"0,279",[1538,24223,24224,24226,24229,24231,24233],{},[1573,24225,2639],{},[1573,24227,24228],{},"⟨50; 100)",[1573,24230,7167],{},[1573,24232,7339],{},[1573,24234,24235],{},"0,162",[1538,24237,24238,24240,24243,24246,24248],{},[1573,24239,13259],{},[1573,24241,24242],{},"⟨100; 150)",[1573,24244,24245],{},"125",[1573,24247,4717],{},[1573,24249,24250],{},"0,147",[1538,24252,24253,24255,24258,24260,24262],{},[1573,24254,13209],{},[1573,24256,24257],{},"⟨150; 200)",[1573,24259,17072],{},[1573,24261,4717],{},[1573,24263,24250],{},[1538,24265,24266,24268,24271,24274,24276],{},[1573,24267,9817],{},[1573,24269,24270],{},"⟨200; 250)",[1573,24272,24273],{},"225",[1573,24275,9817],{},[1573,24277,24278],{},"0,074",[1538,24280,24281,24283,24286,24289,24291],{},[1573,24282,13607],{},[1573,24284,24285],{},"⟨250; 300)",[1573,24287,24288],{},"275",[1573,24290,1176],{},[1573,24292,3418],{},[1538,24294,24295,24297,24300,24303,24305],{},[1573,24296,22878],{},[1573,24298,24299],{},"⟨300; 350)",[1573,24301,24302],{},"325",[1573,24304,9817],{},[1573,24306,24278],{},[1538,24308,24309,24312,24315,24318,24320],{},[1573,24310,24311],{},"8",[1573,24313,24314],{},"⟨350; 400)",[1573,24316,24317],{},"375",[1573,24319,9817],{},[1573,24321,24278],{},[1538,24323,24324,24326,24329,24332,24334],{},[1573,24325,4972],{},[1573,24327,24328],{},"⟨400; 450)",[1573,24330,24331],{},"425",[1573,24333,1176],{},[1573,24335,3418],{},[1538,24337,24338,24340,24343,24346,24348],{},[1573,24339,4717],{},[1573,24341,24342],{},"⟨450; 500)",[1573,24344,24345],{},"475",[1573,24347,1154],{},[1573,24349,24350],{},"0,000",[1538,24352,24353,24355,24358,24361,24363],{},[1573,24354,7339],{},[1573,24356,24357],{},"⟨500; ∞)",[1573,24359,24360],{},"525",[1573,24362,1176],{},[1573,24364,3418],{},[1110,24366,24367,24368,24385,24386,24403,24404,1195,24427,1195,24455,24474,24475,1195,24498,24517],{},"Asi 27,9 % výrobků vydrželo méně než 50 minut, jen asi 1,5 % mezi 250 a 300 minutami. Charakteristiky spočtené ze středů tříd ",[1115,24369,24371],{"className":24370},[1133],[1135,24372,24373],{"xmlns":1137},[1139,24374,24375,24383],{},[1142,24376,24377],{},[1145,24378,24379,24381],{},[1148,24380,5389],{},[1148,24382,11580],{},[1156,24384,23314],{"encoding":1158}," (vážený průměr a rozptyl se střední hodnotou nahrazenou ",[1115,24387,24389],{"className":24388},[1133],[1135,24390,24391],{"xmlns":1137},[1139,24392,24393,24401],{},[1142,24394,24395],{},[1145,24396,24397,24399],{},[1148,24398,5389],{},[1148,24400,11580],{},[1156,24402,23314],{"encoding":1158},") vycházejí ",[1115,24405,24407],{"className":24406},[1133],[1135,24408,24409],{"xmlns":1137},[1139,24410,24411,24424],{},[1142,24412,24413,24419,24421],{},[2671,24414,24415,24417],{"accent":1121},[1148,24416,2675],{},[1495,24418,2678],{},[1495,24420,7600],{},[1152,24422,24423],{},"149,26",[1156,24425,24426],{"encoding":1158},"\\bar{x} \\approx 149{,}26",[1115,24428,24430],{"className":24429},[1133],[1135,24431,24432],{"xmlns":1137},[1139,24433,24434,24452],{},[1142,24435,24436,24442,24444,24447,24449],{},[2632,24437,24438,24440],{},[1148,24439,2695],{},[1152,24441,2639],{},[1495,24443,7600],{},[1152,24445,24446],{},"15",[2358,24448,2360],{},[1152,24450,24451],{},"484,5",[1156,24453,24454],{"encoding":1158},"s^2 \\approx 15\\,484{,}5",[1115,24456,24458],{"className":24457},[1133],[1135,24459,24460],{"xmlns":1137},[1139,24461,24462,24471],{},[1142,24463,24464,24466,24468],{},[1148,24465,2695],{},[1495,24467,7600],{},[1152,24469,24470],{},"124,44",[1156,24472,24473],{"encoding":1158},"s \\approx 124{,}44"," — blízko hodnotám ",[1115,24476,24478],{"className":24477},[1133],[1135,24479,24480],{"xmlns":1137},[1139,24481,24482,24495],{},[1142,24483,24484,24490,24492],{},[2671,24485,24486,24488],{"accent":1121},[1148,24487,2675],{},[1495,24489,2678],{},[1495,24491,1503],{},[1152,24493,24494],{},"145,44",[1156,24496,24497],{"encoding":1158},"\\bar{x}=145{,}44",[1115,24499,24501],{"className":24500},[1133],[1135,24502,24503],{"xmlns":1137},[1139,24504,24505,24514],{},[1142,24506,24507,24509,24511],{},[1148,24508,2695],{},[1495,24510,1503],{},[1152,24512,24513],{},"126,13",[1156,24515,24516],{"encoding":1158},"s=126{,}13"," spočteným přímo z nerozdělených dat; malý rozdíl vzniká tím, že třídění nahrazuje skutečné hodnoty středy tříd.",[1110,24519,24520,24521,24524,24525,24561,24562,24580,24581,24595,24596,24622,24623,24625,24626,14492],{},"Tvar histogramu — vysoká četnost u krátkých dob, rychlý pokles — odpovídá ",[1399,24522,24523],{},"exponenciálnímu rozdělení",", které se pro dobu do poruchy používá nejčastěji. Jeho hustota je ",[1115,24526,24528],{"className":24527},[1133],[1135,24529,24530],{"xmlns":1137},[1139,24531,24532,24558],{},[1142,24533,24534,24536,24538,24540,24542,24544,24546],{},[1148,24535,16375],{},[1495,24537,2162],{"stretchy":2161},[1148,24539,2675],{},[1495,24541,2181],{"stretchy":2161},[1495,24543,1503],{},[1148,24545,19286],{},[2632,24547,24548,24550],{},[1148,24549,18179],{},[1142,24551,24552,24554,24556],{},[1495,24553,1885],{},[1148,24555,19286],{},[1148,24557,2675],{},[1156,24559,24560],{"encoding":1158},"f(x) = \\lambda e^{-\\lambda x}"," pro ",[1115,24563,24565],{"className":24564},[1133],[1135,24566,24567],{"xmlns":1137},[1139,24568,24569,24577],{},[1142,24570,24571,24573,24575],{},[1148,24572,2675],{},[1495,24574,2940],{},[1152,24576,1154],{},[1156,24578,24579],{"encoding":1158},"x \\ge 0",", s parametrem ",[1115,24582,24584],{"className":24583},[1133],[1135,24585,24586],{"xmlns":1137},[1139,24587,24588,24592],{},[1142,24589,24590],{},[1148,24591,19286],{},[1156,24593,24594],{"encoding":1158},"\\lambda"," odhadnutým jako ",[1115,24597,24599],{"className":24598},[1133],[1135,24600,24601],{"xmlns":1137},[1139,24602,24603,24619],{},[1142,24604,24605,24607,24609,24611,24613],{},[1148,24606,19286],{},[1495,24608,1503],{},[1152,24610,1176],{},[1148,24612,3049],{"mathvariant":1599},[2671,24614,24615,24617],{"accent":1121},[1148,24616,2675],{},[1495,24618,2678],{},[1156,24620,24621],{"encoding":1158},"\\lambda = 1\u002F\\bar{x}"," (v R je ",[3161,24624,19453],{}," parametrem ",[3161,24627,24628],{},"dexp()",[3166,24630,24632],{"className":3168,"code":24631,"language":71,"meta":3170,"style":3170},"rate9 \u003C- 1 \u002F mean(x9)\nrate9\n",[3161,24633,24634,24653],{"__ignoreMap":3170},[1115,24635,24636,24639,24641,24643,24645,24647,24649,24651],{"class":3175,"line":10},[1115,24637,24638],{"class":3178},"rate9",[1115,24640,3182],{"class":3181},[1115,24642,3735],{"class":3192},[1115,24644,7755],{"class":3181},[1115,24646,8954],{"class":3185},[1115,24648,2162],{"class":3189},[1115,24650,9298],{"class":3178},[1115,24652,3235],{"class":3189},[1115,24654,24655],{"class":3175,"line":27},[1115,24656,24657],{"class":3178},"rate9\n",[3166,24659,24662],{"className":24660,"code":24661,"language":3274,"meta":3170},[3272],"[1] 0.006875632\n",[3161,24663,24661],{"__ignoreMap":3170},[1110,24665,24666],{},[1971,24667],{"alt":24668,"className":24669,"src":24670},"mask-ps-hustota-fit",[1343,1975],"\u002Fwiki-assets\u002Fmask-ps-hustota-fit.png",[1110,24672,24673,24674,1335],{},"Proložená křivka dobře sleduje tvar sloupců. Zda data odpovídají exponenciálnímu rozdělení formálně, posuzuje test dobré shody popsaný v ",[1340,24675,1094],{"className":24676,"dataFsResolvedFilePath":11426,"href":11427},[1343],[1103,24678,24680,24687],{"className":24679,"dataCallout":3323},[1106,3322],[1110,24681,24683,24686],{"className":24682},[1113],[1115,24684],{"className":24685,"ariaHidden":1121},[1118,3330,1120],"Příklad: Doba života výrobku",[1110,24688,24689],{},"Sledováním doby života výrobku bylo naměřeno 50 hodnot (v minutách). Určete empirické charakteristiky, roztřiďte datový soubor a nakreslete histogram četností.",[3166,24691,24693],{"className":3168,"code":24692,"language":71,"meta":3170,"style":3170},"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",[3161,24694,24695,24756,24807,24857,24907,24959,24969,24995,25015,25073,25082,25090],{"__ignoreMap":3170},[1115,24696,24697,24700,24702,24704,24706,24709,24711,24714,24716,24719,24721,24724,24726,24729,24731,24734,24736,24739,24741,24744,24746,24749,24751,24754],{"class":3175,"line":10},[1115,24698,24699],{"class":3178},"x5",[1115,24701,3182],{"class":3181},[1115,24703,3186],{"class":3185},[1115,24705,2162],{"class":3189},[1115,24707,24708],{"class":3192},"63",[1115,24710,2188],{"class":3181},[1115,24712,24713],{"class":3192}," 156",[1115,24715,2188],{"class":3181},[1115,24717,24718],{"class":3192}," 184",[1115,24720,2188],{"class":3181},[1115,24722,24723],{"class":3192}," 786",[1115,24725,2188],{"class":3181},[1115,24727,24728],{"class":3192}," 822",[1115,24730,2188],{"class":3181},[1115,24732,24733],{"class":3192}," 278",[1115,24735,2188],{"class":3181},[1115,24737,24738],{"class":3192}," 15",[1115,24740,2188],{"class":3181},[1115,24742,24743],{"class":3192}," 561",[1115,24745,2188],{"class":3181},[1115,24747,24748],{"class":3192}," 229",[1115,24750,2188],{"class":3181},[1115,24752,24753],{"class":3192}," 8",[1115,24755,9400],{"class":3181},[1115,24757,24758,24761,24763,24766,24768,24770,24772,24775,24777,24780,24782,24785,24787,24790,24792,24795,24797,24800,24802,24805],{"class":3175,"line":27},[1115,24759,24760],{"class":3192},"        4",[1115,24762,2188],{"class":3181},[1115,24764,24765],{"class":3192}," 35",[1115,24767,2188],{"class":3181},[1115,24769,9349],{"class":3192},[1115,24771,2188],{"class":3181},[1115,24773,24774],{"class":3192}," 203",[1115,24776,2188],{"class":3181},[1115,24778,24779],{"class":3192}," 178",[1115,24781,2188],{"class":3181},[1115,24783,24784],{"class":3192}," 323",[1115,24786,2188],{"class":3181},[1115,24788,24789],{"class":3192}," 275",[1115,24791,2188],{"class":3181},[1115,24793,24794],{"class":3192}," 176",[1115,24796,2188],{"class":3181},[1115,24798,24799],{"class":3192}," 427",[1115,24801,2188],{"class":3181},[1115,24803,24804],{"class":3192}," 196",[1115,24806,9400],{"class":3181},[1115,24808,24809,24812,24814,24816,24818,24821,24823,24826,24828,24831,24833,24836,24838,24841,24843,24845,24847,24850,24852,24855],{"class":3175,"line":148},[1115,24810,24811],{"class":3192},"        415",[1115,24813,2188],{"class":3181},[1115,24815,8357],{"class":3192},[1115,24817,2188],{"class":3181},[1115,24819,24820],{"class":3192}," 17",[1115,24822,2188],{"class":3181},[1115,24824,24825],{"class":3192}," 293",[1115,24827,2188],{"class":3181},[1115,24829,24830],{"class":3192}," 991",[1115,24832,2188],{"class":3181},[1115,24834,24835],{"class":3192}," 100",[1115,24837,2188],{"class":3181},[1115,24839,24840],{"class":3192}," 189",[1115,24842,2188],{"class":3181},[1115,24844,24794],{"class":3192},[1115,24846,2188],{"class":3181},[1115,24848,24849],{"class":3192}," 672",[1115,24851,2188],{"class":3181},[1115,24853,24854],{"class":3192}," 134",[1115,24856,9400],{"class":3181},[1115,24858,24859,24862,24864,24866,24868,24871,24873,24876,24878,24880,24882,24885,24887,24890,24892,24895,24897,24900,24902,24905],{"class":3175,"line":111},[1115,24860,24861],{"class":3192},"        529",[1115,24863,2188],{"class":3181},[1115,24865,8119],{"class":3192},[1115,24867,2188],{"class":3181},[1115,24869,24870],{"class":3192}," 22",[1115,24872,2188],{"class":3181},[1115,24874,24875],{"class":3192}," 69",[1115,24877,2188],{"class":3181},[1115,24879,9448],{"class":3192},[1115,24881,2188],{"class":3181},[1115,24883,24884],{"class":3192}," 272",[1115,24886,2188],{"class":3181},[1115,24888,24889],{"class":3192}," 117",[1115,24891,2188],{"class":3181},[1115,24893,24894],{"class":3192}," 169",[1115,24896,2188],{"class":3181},[1115,24898,24899],{"class":3192}," 466",[1115,24901,2188],{"class":3181},[1115,24903,24904],{"class":3192}," 286",[1115,24906,9400],{"class":3181},[1115,24908,24909,24912,24914,24917,24919,24922,24924,24927,24929,24932,24934,24937,24939,24942,24944,24947,24949,24952,24954,24957],{"class":3175,"line":96},[1115,24910,24911],{"class":3192},"        46",[1115,24913,2188],{"class":3181},[1115,24915,24916],{"class":3192}," 236",[1115,24918,2188],{"class":3181},[1115,24920,24921],{"class":3192}," 387",[1115,24923,2188],{"class":3181},[1115,24925,24926],{"class":3192}," 92",[1115,24928,2188],{"class":3181},[1115,24930,24931],{"class":3192}," 177",[1115,24933,2188],{"class":3181},[1115,24935,24936],{"class":3192}," 188",[1115,24938,2188],{"class":3181},[1115,24940,24941],{"class":3192}," 124",[1115,24943,2188],{"class":3181},[1115,24945,24946],{"class":3192}," 385",[1115,24948,2188],{"class":3181},[1115,24950,24951],{"class":3192}," 174",[1115,24953,2188],{"class":3181},[1115,24955,24956],{"class":3192}," 23",[1115,24958,3235],{"class":3189},[1115,24960,24961,24963,24965,24967],{"class":3175,"line":89},[1115,24962,21678],{"class":3185},[1115,24964,2162],{"class":3189},[1115,24966,24699],{"class":3178},[1115,24968,3235],{"class":3189},[1115,24970,24971,24973,24975,24977,24979,24981,24983,24985,24987,24989,24991,24993],{"class":3175,"line":82},[1115,24972,9640],{"class":3185},[1115,24974,2162],{"class":3189},[1115,24976,24699],{"class":3178},[1115,24978,21726],{"class":3189},[1115,24980,9651],{"class":3185},[1115,24982,2162],{"class":3189},[1115,24984,24699],{"class":3178},[1115,24986,21726],{"class":3189},[1115,24988,9662],{"class":3185},[1115,24990,2162],{"class":3189},[1115,24992,24699],{"class":3178},[1115,24994,3235],{"class":3189},[1115,24996,24997,24999,25001,25003,25005,25007,25009,25011,25013],{"class":3175,"line":75},[1115,24998,21280],{"class":3185},[1115,25000,2162],{"class":3189},[1115,25002,24699],{"class":3178},[1115,25004,3688],{"class":3189},[1115,25006,14265],{"class":3181},[1115,25008,21747],{"class":3185},[1115,25010,2162],{"class":3189},[1115,25012,24699],{"class":3178},[1115,25014,3235],{"class":3189},[1115,25016,25017,25020,25022,25024,25026,25028,25030,25032,25034,25036,25038,25040,25042,25045,25047,25049,25051,25053,25055,25057,25059,25061,25063,25065,25067,25069,25071],{"class":3175,"line":9681},[1115,25018,25019],{"class":3178},"y5",[1115,25021,3182],{"class":3181},[1115,25023,23958],{"class":3185},[1115,25025,2162],{"class":3189},[1115,25027,24699],{"class":3178},[1115,25029,2188],{"class":3181},[1115,25031,23967],{"class":3178},[1115,25033,3252],{"class":3181},[1115,25035,23972],{"class":3185},[1115,25037,2162],{"class":3189},[1115,25039,1154],{"class":3192},[1115,25041,2188],{"class":3181},[1115,25043,25044],{"class":3192}," 1050",[1115,25046,2188],{"class":3181},[1115,25048,23986],{"class":3178},[1115,25050,3252],{"class":3181},[1115,25052,9317],{"class":3192},[1115,25054,2181],{"class":3189},[1115,25056,2188],{"class":3181},[1115,25058,23997],{"class":3178},[1115,25060,3252],{"class":3181},[1115,25062,15961],{"class":3192},[1115,25064,2188],{"class":3181},[1115,25066,24006],{"class":3178},[1115,25068,3252],{"class":3181},[1115,25070,15961],{"class":3192},[1115,25072,3235],{"class":3189},[1115,25074,25075,25077,25079],{"class":3175,"line":72},[1115,25076,25019],{"class":3178},[1115,25078,13559],{"class":3181},[1115,25080,25081],{"class":3178},"mids\n",[1115,25083,25084,25086,25088],{"class":3175,"line":25},[1115,25085,25019],{"class":3178},[1115,25087,13559],{"class":3181},[1115,25089,24021],{"class":3178},[1115,25091,25092,25094,25096,25098,25100,25102,25104,25106,25108,25110,25112,25114,25116],{"class":3175,"line":65},[1115,25093,19552],{"class":3185},[1115,25095,2162],{"class":3189},[1115,25097,25019],{"class":3178},[1115,25099,13559],{"class":3181},[1115,25101,24034],{"class":3178},[1115,25103,7755],{"class":3181},[1115,25105,24039],{"class":3185},[1115,25107,2162],{"class":3189},[1115,25109,24699],{"class":3178},[1115,25111,2181],{"class":3189},[1115,25113,2188],{"class":3181},[1115,25115,9537],{"class":3192},[1115,25117,3235],{"class":3189},[3166,25119,25122],{"className":25120,"code":25121,"language":3274,"meta":3170},[3272],"[1] 50\n[1] 246.42\n[1] 220.0209\n[1] 181\n[1] 987\n[1]   75 225 375 525 675 825 975\n[1] 18 19  6  3  1  2  1\n[1] 0.36 0.38 0.12 0.06 0.02 0.04 0.02\n",[3161,25123,25121],{"__ignoreMap":3170},[1110,25125,25126],{},"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.",[1392,25128,10963],{"id":10962},[1124,25130,25131,25149,25250,25317],{},[1127,25132,25133,1953,25136,25139,25140,25143,25144,25146,25147,1335],{},[1399,25134,25135],{},"Výchozí typ kvantilu v R.",[3161,25137,25138],{},"quantile()"," bez argumentu ",[3161,25141,25142],{},"type"," používá jiný výpočetní vzorec (",[3161,25145,21840],{},") než ruční postup v této kapitole — u některých souborů se hodnoty liší. Pro shodu s ručním výpočtem zadávejte ",[3161,25148,21836],{},[1127,25150,25151,25156,25157,25159,25160,25195,25196,25231,25232,25249],{},[1399,25152,25153,25154,1335],{},"Výchozí ohraničení tříd v ",[3161,25155,23431],{}," Bez ",[3161,25158,23557],{}," jsou třídy zprava uzavřené, ",[1115,25161,25163],{"className":25162},[1133],[1135,25164,25165],{"xmlns":1137},[1139,25166,25167,25193],{},[1142,25168,25169,25171,25177,25179,25191],{},[1495,25170,2162],{"stretchy":2161},[1145,25172,25173,25175],{},[1148,25174,1991],{},[1148,25176,11580],{},[1495,25178,16495],{"separator":1121},[1145,25180,25181,25183],{},[1148,25182,1991],{},[1142,25184,25185,25187,25189],{},[1148,25186,11580],{},[1495,25188,6294],{},[1152,25190,1176],{},[1495,25192,9080],{"stretchy":2161},[1156,25194,23553],{"encoding":1158}," — opačně než konvence ",[1115,25197,25199],{"className":25198},[1133],[1135,25200,25201],{"xmlns":1137},[1139,25202,25203,25229],{},[1142,25204,25205,25207,25213,25215,25227],{},[1495,25206,9071],{"stretchy":2161},[1145,25208,25209,25211],{},[1148,25210,1991],{},[1148,25212,11580],{},[1495,25214,16495],{"separator":1121},[1145,25216,25217,25219],{},[1148,25218,1991],{},[1142,25220,25221,25223,25225],{},[1148,25222,11580],{},[1495,25224,6294],{},[1152,25226,1176],{},[1495,25228,2181],{"stretchy":2161},[1156,25230,23594],{"encoding":1158}," použitá v tabulkách výše. Hodnota ležící přesně na hranici pak spadne do jiné třídy a četnosti ",[1115,25233,25235],{"className":25234},[1133],[1135,25236,25237],{"xmlns":1137},[1139,25238,25239,25247],{},[1142,25240,25241],{},[1145,25242,25243,25245],{},[1148,25244,16375],{},[1148,25246,11580],{},[1156,25248,23335],{"encoding":1158}," vyjdou jinak.",[1127,25251,25252,1953,25255,25272,25273,25286,25287,18631,25300,1335],{},[1399,25253,25254],{},"Rozptyl vs. směrodatná odchylka.",[1115,25256,25258],{"className":25257},[1133],[1135,25259,25260],{"xmlns":1137},[1139,25261,25262,25270],{},[1142,25263,25264],{},[2632,25265,25266,25268],{},[1148,25267,2695],{},[1152,25269,2639],{},[1156,25271,2700],{"encoding":1158}," se udává v jednotkách znaku na druhou, ",[1115,25274,25276],{"className":25275},[1133],[1135,25277,25278],{"xmlns":1137},[1139,25279,25280,25284],{},[1142,25281,25282],{},[1148,25283,2695],{},[1156,25285,2695],{"encoding":1158}," ve stejných jednotkách jako data — pro interpretaci (např. „kolísání kolem průměru\") patří vždy ",[1115,25288,25290],{"className":25289},[1133],[1135,25291,25292],{"xmlns":1137},[1139,25293,25294,25298],{},[1142,25295,25296],{},[1148,25297,2695],{},[1156,25299,2695],{"encoding":1158},[1115,25301,25303],{"className":25302},[1133],[1135,25304,25305],{"xmlns":1137},[1139,25306,25307,25315],{},[1142,25308,25309],{},[2632,25310,25311,25313],{},[1148,25312,2695],{},[1152,25314,2639],{},[1156,25316,2700],{"encoding":1158},[1127,25318,25319,25322],{},[1399,25320,25321],{},"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.",[1392,25324,11120],{"id":11119},[1124,25326,25327,25332,25337,25342,25347,25352,25357],{},[1127,25328,25329],{},[1340,25330,11128],{"className":25331,"dataFsResolvedFilePath":1344,"href":1345},[1343],[1127,25333,25334],{},[1340,25335,11134],{"className":25336,"dataFsResolvedFilePath":1358,"href":1359},[1343],[1127,25338,25339],{},[1340,25340,1094],{"className":25341,"dataFsResolvedFilePath":11426,"href":11427},[1343],[1127,25343,25344],{},[1340,25345,11148],{"className":25346,"dataFsResolvedFilePath":11146,"href":11147},[1343],[1127,25348,25349],{},[1340,25350,11156],{"className":25351,"dataFsResolvedFilePath":11154,"href":11155},[1343],[1127,25353,25354],{},[1340,25355,11164],{"className":25356,"dataFsResolvedFilePath":11162,"href":11163},[1343],[1127,25358,25359],{},[1340,25360,11172],{"className":25361,"dataFsResolvedFilePath":11170,"href":11171},[1343],[1392,25363,11175],{"id":934},[1110,25365,11178,25366,11182],{},[10079,25367,11181],{},[11184,25369,25370],{},"html 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příkladům\u002F6.txt","topics\u002Fpopisna-statistika",[23,67,886,624,732,71],"S7Mr0W_asypsa_HGrO-Qlzv4HzQm_pC2nyjSomTKbnk",{"id":25393,"title":11148,"body":25394,"course":23,"courses":11214,"created":11215,"description":3170,"extension":11216,"meta":30075,"navigation":11218,"path":30076,"seo":30077,"sources":30078,"stem":30081,"tags":30082,"type":11231,"updated":11215,"__hash__":30083},"topics\u002Ftopics\u002Fregresni-a-korelacni-analyza.md",{"type":1096,"value":25395,"toc":30048},[25396,25399,25626,25628,25696,25702,25705,25783,25794,25798,26016,26023,26083,26086,26093,26115,26119,26125,26187,26237,26241,26252,26364,26370,26500,26503,26541,26547,26666,26683,26810,26816,26860,26864,26877,26904,26910,26967,26994,27000,27056,27075,27081,27102,27109,27112,27351,27355,27467,27787,27844,27886,27893,27897,27903,28025,28031,28080,28084,28090,28150,28156,28195,28239,28245,28338,28342,28348,28390,28396,28456,28567,28673,28677,28682,28760,28795,28826,28886,28923,28930,28993,28996,29017,29023,29053,29096,29100,29117,29237,29241,29263,29267,29278,29379,29383,29455,29462,29465,29468,29479,29546,29549,29553,29576,29579,29582,29785,29794,29824,29826,29961,29974,29987,30000,30002,30039,30041,30045],[1099,25397,11148],{"id":25398},"regresní-a-korelační-analýza",[1103,25400,25402,25408],{"className":25401,"dataCallout":1108},[1106,1107],[1110,25403,25405,1122],{"className":25404},[1113],[1115,25406],{"className":25407,"ariaHidden":1121},[1118,1119,1120],[1124,25409,25410,25448,25495,25573,25587,25593],{},[1127,25411,25412,25415,25416,25429,25430,25443,25444,25447],{},[1399,25413,25414],{},"Regresní analýza"," zkoumá jednostrannou závislost vysvětlované proměnné ",[1115,25417,25419],{"className":25418},[1133],[1135,25420,25421],{"xmlns":1137},[1139,25422,25423,25427],{},[1142,25424,25425],{},[1148,25426,10129],{},[1156,25428,10129],{"encoding":1158}," na vysvětlujících proměnných ",[1115,25431,25433],{"className":25432},[1133],[1135,25434,25435],{"xmlns":1137},[1139,25436,25437,25441],{},[1142,25438,25439],{},[1148,25440,2675],{},[1156,25442,2675],{"encoding":1158}," (příčina → následek); ",[1399,25445,25446],{},"korelační analýza"," měří intenzitu (těsnost) vzájemné závislosti.",[1127,25449,25450,25451,25454,25455,1335],{},"Parametry regresní funkce se odhadují ",[1399,25452,25453],{},"metodou nejmenších čtverců"," — minimalizací součtu čtverců reziduí ",[1115,25456,25458],{"className":25457},[1133],[1135,25459,25460],{"xmlns":1137},[1139,25461,25462,25492],{},[1142,25463,25464,25466,25468,25474,25476,25486],{},[1495,25465,11680],{},[1495,25467,2162],{"stretchy":2161},[1145,25469,25470,25472],{},[1148,25471,10129],{},[1148,25473,4085],{},[1495,25475,1885],{},[1145,25477,25478,25484],{},[2671,25479,25480,25482],{"accent":1121},[1148,25481,10129],{},[1495,25483,12415],{},[1148,25485,4085],{},[2632,25487,25488,25490],{},[1495,25489,2181],{"stretchy":2161},[1152,25491,2639],{},[1156,25493,25494],{"encoding":1158},"\\sum(y_i-\\hat y_i)^2",[1127,25496,25497,25498,1953,25501,25519,25520,1953,25523,25547,25548,1953,25551,1335],{},"Kvalitu fitu měří ",[1399,25499,25500],{},"index determinace",[1115,25502,25504],{"className":25503},[1133],[1135,25505,25506],{"xmlns":1137},[1139,25507,25508,25516],{},[1142,25509,25510],{},[2632,25511,25512,25514],{},[1148,25513,19792],{},[1152,25515,2639],{},[1156,25517,25518],{"encoding":1158},"R^2","; obecnou těsnost závislosti ",[1399,25521,25522],{},"index korelace",[1115,25524,25526],{"className":25525},[1133],[1135,25527,25528],{"xmlns":1137},[1139,25529,25530,25544],{},[1142,25531,25532,25534,25536],{},[1148,25533,20763],{},[1495,25535,1503],{},[2770,25537,25538],{},[2632,25539,25540,25542],{},[1148,25541,19792],{},[1152,25543,2639],{},[1156,25545,25546],{"encoding":1158},"I=\\sqrt{R^2}",", který je pro regresní přímku roven ",[1399,25549,25550],{},"koeficientu korelace",[1115,25552,25554],{"className":25553},[1133],[1135,25555,25556],{"xmlns":1137},[1139,25557,25558,25570],{},[1142,25559,25560],{},[1145,25561,25562,25564],{},[1148,25563,71],{},[1142,25565,25566,25568],{},[1148,25567,2675],{},[1148,25569,10129],{},[1156,25571,25572],{"encoding":1158},"r_{xy}",[1127,25574,25575,25576,25579,25580,25583,25584,1390],{},"Když přímka nestačí, volí se ",[1399,25577,25578],{},"parabolická, polynomická, hyperbolická nebo logaritmická"," regrese (stále lineární v parametrech, odhad metodou nejmenších čtverců) nebo ",[1399,25581,25582],{},"exponenciální"," regrese (nelineární v parametrech, odhad přes ",[3161,25585,25586],{},"nls2",[1127,25588,25589,25592],{},[1399,25590,25591],{},"Vícenásobná regrese"," rozšiřuje model o více regresorů; vyžaduje výběr proměnných (ENTER\u002Fstepwise), ověření šesti předpokladů modelu a kontrolu multikolinearity přes VIF.",[1127,25594,25595,25596,1195,25599,1195,25602,1195,25605,1195,25608,1195,25611,1195,25614,1195,25617,1195,25620,1195,25623,1335],{},"V R: ",[3161,25597,25598],{},"lm()",[3161,25600,25601],{},"nls2()",[3161,25603,25604],{},"summary()",[3161,25606,25607],{},"confint()",[3161,25609,25610],{},"predict()",[3161,25612,25613],{},"step()",[3161,25615,25616],{},"car::vif()",[3161,25618,25619],{},"lmtest::dwtest()",[3161,25621,25622],{},"whitestrap::white_test()",[3161,25624,25625],{},"shapiro.test()",[1392,25627,20800],{"id":20799},[1110,25629,25630,25633,25634,2261,25647,25660,25661,25663,25664,25677,25678,25691,25692,25695],{},[1340,25631,11128],{"className":25632,"dataFsResolvedFilePath":1344,"href":1345},[1343]," pracuje se dvěma znaky ",[1115,25635,25637],{"className":25636},[1133],[1135,25638,25639],{"xmlns":1137},[1139,25640,25641,25645],{},[1142,25642,25643],{},[1148,25644,2675],{},[1156,25646,2675],{"encoding":1158},[1115,25648,25650],{"className":25649},[1133],[1135,25651,25652],{"xmlns":1137},[1139,25653,25654,25658],{},[1142,25655,25656],{},[1148,25657,10129],{},[1156,25659,10129],{"encoding":1158}," zjištěnými na stejných jednotkách. ",[1399,25662,25414],{}," se zabývá jednostrannými závislostmi, kdy proti sobě stojí vysvětlující (nezávisle) proměnná ",[1115,25665,25667],{"className":25666},[1133],[1135,25668,25669],{"xmlns":1137},[1139,25670,25671,25675],{},[1142,25672,25673],{},[1148,25674,2675],{},[1156,25676,2675],{"encoding":1158}," v úloze příčiny a vysvětlovaná (závisle) proměnná ",[1115,25679,25681],{"className":25680},[1133],[1135,25682,25683],{"xmlns":1137},[1139,25684,25685,25689],{},[1142,25686,25687],{},[1148,25688,10129],{},[1156,25690,10129],{"encoding":1158}," v úloze následku. ",[1399,25693,25694],{},"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.",[1110,25697,25698,25699,1390],{},"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 (",[1399,25700,25701],{},"regresní funkce",[1110,25703,25704],{},"Druh regresní analýzy určuje struktura datového souboru:",[1124,25706,25707,25744],{},[1127,25708,25709,25712,25713,25726,25727,25740,25741,2188],{},[1399,25710,25711],{},"dvourozměrný datový soubor"," (jedna ",[1115,25714,25716],{"className":25715},[1133],[1135,25717,25718],{"xmlns":1137},[1139,25719,25720,25724],{},[1142,25721,25722],{},[1148,25723,2675],{},[1156,25725,2675],{"encoding":1158},", jedna ",[1115,25728,25730],{"className":25729},[1133],[1135,25731,25732],{"xmlns":1137},[1139,25733,25734,25738],{},[1142,25735,25736],{},[1148,25737,10129],{},[1156,25739,10129],{"encoding":1158},") → ",[1399,25742,25743],{},"regresní analýza dvou proměnných",[1127,25745,25746,25749,25750,25740,25780,1335],{},[1399,25747,25748],{},"vícerozměrný datový soubor"," (více ",[1115,25751,25753],{"className":25752},[1133],[1135,25754,25755],{"xmlns":1137},[1139,25756,25757,25777],{},[1142,25758,25759,25765,25767,25769,25771],{},[1145,25760,25761,25763],{},[1148,25762,2675],{},[1152,25764,1176],{},[1495,25766,2188],{"separator":1121},[1495,25768,10697],{},[1495,25770,2188],{"separator":1121},[1145,25772,25773,25775],{},[1148,25774,2675],{},[1148,25776,1110],{},[1156,25778,25779],{"encoding":1158},"x_1,\\dots,x_p",[1399,25781,25782],{},"vícenásobná regresní analýza",[1110,25784,25785,25786,25789,25790,25793],{},"Volba konkrétní regresní funkce by měla vycházet jak z ",[1399,25787,25788],{},"ekonomické teorie"," (ta napovídá, zda závislost roste, nebo klesá, zda je přímková, nebo zakřivená), tak z ",[1399,25791,25792],{},"grafické a matematicko-statistické analýzy"," dat — oba přístupy je vhodné kombinovat.",[1392,25795,25797],{"id":25796},"metoda-nejmenších-čtverců","Metoda nejmenších čtverců",[1110,25799,25800,25801,1953,25804,25857,25858,25876,25877,1953,25880,25936,25937,25955,25956,25973,25974,26012,26013,1335],{},"Rozlišují se ",[1399,25802,25803],{},"teoretická regresní funkce",[1115,25805,25807],{"className":25806},[1133],[1135,25808,25809],{"xmlns":1137},[1139,25810,25811,25854],{},[1142,25812,25813,25816,25818,25820,25822,25824,25826,25832,25834,25840,25842,25844,25846,25852],{},[1148,25814,25815],{},"η",[1495,25817,1503],{},[1148,25819,16375],{},[1495,25821,2162],{"stretchy":2161},[1148,25823,2675],{},[1495,25825,16495],{"separator":1121},[1145,25827,25828,25830],{},[1148,25829,1262],{},[1152,25831,1154],{},[1495,25833,2188],{"separator":1121},[1145,25835,25836,25838],{},[1148,25837,1262],{},[1152,25839,1176],{},[1495,25841,2188],{"separator":1121},[1495,25843,10697],{},[1495,25845,2188],{"separator":1121},[1145,25847,25848,25850],{},[1148,25849,1262],{},[1148,25851,1110],{},[1495,25853,2181],{"stretchy":2161},[1156,25855,25856],{"encoding":1158},"\\eta = f(x;\\beta_0,\\beta_1,\\dots,\\beta_p)"," — neznámá, populační, daná neznámými parametry ",[1115,25859,25861],{"className":25860},[1133],[1135,25862,25863],{"xmlns":1137},[1139,25864,25865,25873],{},[1142,25866,25867],{},[1145,25868,25869,25871],{},[1148,25870,1262],{},[1148,25872,4085],{},[1156,25874,25875],{"encoding":1158},"\\beta_i"," — a ",[1399,25878,25879],{},"empirická regresní funkce",[1115,25881,25883],{"className":25882},[1133],[1135,25884,25885],{"xmlns":1137},[1139,25886,25887,25933],{},[1142,25888,25889,25895,25897,25899,25901,25903,25905,25911,25913,25919,25921,25923,25925,25931],{},[2671,25890,25891,25893],{"accent":1121},[1148,25892,10129],{},[1495,25894,12415],{},[1495,25896,1503],{},[1148,25898,16375],{},[1495,25900,2162],{"stretchy":2161},[1148,25902,2675],{},[1495,25904,16495],{"separator":1121},[1145,25906,25907,25909],{},[1148,25908,21066],{},[1152,25910,1154],{},[1495,25912,2188],{"separator":1121},[1145,25914,25915,25917],{},[1148,25916,21066],{},[1152,25918,1176],{},[1495,25920,2188],{"separator":1121},[1495,25922,10697],{},[1495,25924,2188],{"separator":1121},[1145,25926,25927,25929],{},[1148,25928,21066],{},[1148,25930,1110],{},[1495,25932,2181],{"stretchy":2161},[1156,25934,25935],{"encoding":1158},"\\hat y = f(x; b_0,b_1,\\dots,b_p)",", jejíž odhadnuté parametry ",[1115,25938,25940],{"className":25939},[1133],[1135,25941,25942],{"xmlns":1137},[1139,25943,25944,25952],{},[1142,25945,25946],{},[1145,25947,25948,25950],{},[1148,25949,21066],{},[1148,25951,4085],{},[1156,25953,25954],{"encoding":1158},"b_i"," jsou odhadem ",[1115,25957,25959],{"className":25958},[1133],[1135,25960,25961],{"xmlns":1137},[1139,25962,25963,25971],{},[1142,25964,25965],{},[1145,25966,25967,25969],{},[1148,25968,1262],{},[1148,25970,4085],{},[1156,25972,25875],{"encoding":1158}," vypočteným z konkrétních dat. Odchylky skutečných hodnot od empirické funkce, ",[1115,25975,25977],{"className":25976},[1133],[1135,25978,25979],{"xmlns":1137},[1139,25980,25981,26009],{},[1142,25982,25983,25989,25991,25997,25999],{},[1145,25984,25985,25987],{},[1148,25986,18179],{},[1148,25988,4085],{},[1495,25990,1503],{},[1145,25992,25993,25995],{},[1148,25994,10129],{},[1148,25996,4085],{},[1495,25998,1885],{},[1145,26000,26001,26007],{},[2671,26002,26003,26005],{"accent":1121},[1148,26004,10129],{},[1495,26006,12415],{},[1148,26008,4085],{},[1156,26010,26011],{"encoding":1158},"e_i=y_i-\\hat y_i",", se nazývají ",[1399,26014,26015],{},"rezidua",[1110,26017,26018,26019,26022],{},"Nejpoužívanější metodou odhadu parametrů je ",[1399,26020,26021],{},"metoda nejmenších čtverců (OLS)",": hledají se takové parametry, pro které je součet čtverců reziduí minimální,",[1115,26024,26026],{"className":26025},[1133],[1135,26027,26028],{"xmlns":1137,"display":2151},[1139,26029,26030,26080],{},[1142,26031,26032,26046,26048,26054,26056,26066,26072,26074,26076,26078],{},[11676,26033,26034,26036,26044],{},[1495,26035,11680],{},[1142,26037,26038,26040,26042],{},[1148,26039,4085],{},[1495,26041,1503],{},[1152,26043,1176],{},[1148,26045,2657],{},[1495,26047,2162],{"stretchy":2161},[1145,26049,26050,26052],{},[1148,26051,10129],{},[1148,26053,4085],{},[1495,26055,1885],{},[1145,26057,26058,26064],{},[2671,26059,26060,26062],{"accent":1121},[1148,26061,10129],{},[1495,26063,12415],{},[1148,26065,4085],{},[2632,26067,26068,26070],{},[1495,26069,2181],{"stretchy":2161},[1152,26071,2639],{},[1495,26073,17199],{},[1148,26075,14121],{},[1495,26077,8744],{},[1148,26079,1335],{"mathvariant":1599},[1156,26081,26082],{"encoding":1158},"\\sum_{i=1}^n (y_i - \\hat y_i)^2 \\to \\min.",[1110,26084,26085],{},"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.",[1110,26087,26088],{},[1971,26089],{"alt":26090,"className":26091,"src":26092},"mask-ra-primka-rezidua",[1343,1975],"\u002Fwiki-assets\u002Fmask-ra-primka-rezidua.png",[1110,26094,26095,26096,26114],{},"Obrázek ukazuje přesně to, co metoda minimalizuje: délky červených úseček jsou rezidua ",[1115,26097,26099],{"className":26098},[1133],[1135,26100,26101],{"xmlns":1137},[1139,26102,26103,26111],{},[1142,26104,26105],{},[1145,26106,26107,26109],{},[1148,26108,18179],{},[1148,26110,4085],{},[1156,26112,26113],{"encoding":1158},"e_i",", metoda nejmenších čtverců volí přímku tak, aby součet jejich čtverců byl nejmenší možný.",[1392,26116,26118],{"id":26117},"regresní-přímka","Regresní přímka",[1110,26120,26121,26122,1497],{},"Nejjednodušší regresní funkcí je ",[1399,26123,26124],{},"regresní přímka",[1115,26126,26128],{"className":26127},[1133],[1135,26129,26130],{"xmlns":1137,"display":2151},[1139,26131,26132,26184],{},[1142,26133,26134,26136,26138,26144,26146,26152,26154,26156,26158,26164,26166,26172,26174,26180,26182],{},[1148,26135,25815],{},[1495,26137,1503],{},[1145,26139,26140,26142],{},[1148,26141,1262],{},[1152,26143,1154],{},[1495,26145,6294],{},[1145,26147,26148,26150],{},[1148,26149,1262],{},[1152,26151,1176],{},[1148,26153,2675],{},[1495,26155,2188],{"separator":1121},[3520,26157],{"width":3522},[2671,26159,26160,26162],{"accent":1121},[1148,26161,10129],{},[1495,26163,12415],{},[1495,26165,1503],{},[1145,26167,26168,26170],{},[1148,26169,21066],{},[1152,26171,1154],{},[1495,26173,6294],{},[1145,26175,26176,26178],{},[1148,26177,21066],{},[1152,26179,1176],{},[1148,26181,2675],{},[1148,26183,1335],{"mathvariant":1599},[1156,26185,26186],{"encoding":1158},"\\eta = \\beta_0 + \\beta_1 x, \\qquad \\hat y = b_0 + b_1 x.",[1110,26188,26189,26190,26208,26209,26222,26223,26236],{},"Koeficient ",[1115,26191,26193],{"className":26192},[1133],[1135,26194,26195],{"xmlns":1137},[1139,26196,26197,26205],{},[1142,26198,26199],{},[1145,26200,26201,26203],{},[1148,26202,21066],{},[1152,26204,1176],{},[1156,26206,26207],{"encoding":1158},"b_1"," udává změnu průměru ",[1115,26210,26212],{"className":26211},[1133],[1135,26213,26214],{"xmlns":1137},[1139,26215,26216,26220],{},[1142,26217,26218],{},[1148,26219,10129],{},[1156,26221,10129],{"encoding":1158}," při jednotkové změně ",[1115,26224,26226],{"className":26225},[1133],[1135,26227,26228],{"xmlns":1137},[1139,26229,26230,26234],{},[1142,26231,26232],{},[1148,26233,2675],{},[1156,26235,2675],{"encoding":1158},"; jeho znaménko určuje, zda je závislost přímá, nebo nepřímá.",[1695,26238,26240],{"id":26239},"v-r","V R",[1110,26242,26243,26244,26247,26248,26251],{},"Vstupní data se nahrají buď ze souboru (",[3161,26245,26246],{},"d \u003C- read.table(\"data.txt\")",", případně ",[3161,26249,26250],{},"d \u003C- read.table(file.choose())","), nebo zapíší přímo jako vektory. Na šesti domácnostech sledujeme počet členů domácnosti a jejich týdenní výdaje:",[3166,26253,26255],{"className":3168,"code":26254,"language":71,"meta":3170,"style":3170},"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",[3161,26256,26257,26292,26333,26353],{"__ignoreMap":3170},[1115,26258,26259,26262,26264,26266,26268,26270,26272,26274,26276,26278,26280,26282,26284,26286,26288,26290],{"class":3175,"line":10},[1115,26260,26261],{"class":3178},"pocet_clenu",[1115,26263,3182],{"class":3181},[1115,26265,3186],{"class":3185},[1115,26267,2162],{"class":3189},[1115,26269,1176],{"class":3192},[1115,26271,2188],{"class":3181},[1115,26273,7909],{"class":3192},[1115,26275,2188],{"class":3181},[1115,26277,9537],{"class":3192},[1115,26279,2188],{"class":3181},[1115,26281,3983],{"class":3192},[1115,26283,2188],{"class":3181},[1115,26285,9344],{"class":3192},[1115,26287,2188],{"class":3181},[1115,26289,21777],{"class":3192},[1115,26291,3235],{"class":3189},[1115,26293,26294,26297,26299,26301,26303,26306,26308,26311,26313,26316,26318,26321,26323,26326,26328,26331],{"class":3175,"line":27},[1115,26295,26296],{"class":3178},"tydenni_vydaje",[1115,26298,3182],{"class":3181},[1115,26300,3186],{"class":3185},[1115,26302,2162],{"class":3189},[1115,26304,26305],{"class":3192},"490",[1115,26307,2188],{"class":3181},[1115,26309,26310],{"class":3192}," 820",[1115,26312,2188],{"class":3181},[1115,26314,26315],{"class":3192}," 1230",[1115,26317,2188],{"class":3181},[1115,26319,26320],{"class":3192}," 1570",[1115,26322,2188],{"class":3181},[1115,26324,26325],{"class":3192}," 1950",[1115,26327,2188],{"class":3181},[1115,26329,26330],{"class":3192}," 2320",[1115,26332,3235],{"class":3189},[1115,26334,26335,26337,26339,26342,26344,26346,26348,26351],{"class":3175,"line":148},[1115,26336,786],{"class":3178},[1115,26338,3182],{"class":3181},[1115,26340,26341],{"class":3185}," lm",[1115,26343,2162],{"class":3189},[1115,26345,26296],{"class":3178},[1115,26347,10574],{"class":3181},[1115,26349,26350],{"class":3178}," pocet_clenu",[1115,26352,3235],{"class":3189},[1115,26354,26355,26358,26360,26362],{"class":3175,"line":111},[1115,26356,26357],{"class":3185},"summary",[1115,26359,2162],{"class":3189},[1115,26361,786],{"class":3178},[1115,26363,3235],{"class":3189},[3166,26365,26368],{"className":26366,"code":26367,"language":3274,"meta":3170},[3272],"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",[3161,26369,26367],{"__ignoreMap":3170},[1110,26371,26372,26373,26405,26406,26409,26410,26440,26441,26471,26472,26475,26476,26499],{},"Odhadnutý model je ",[1115,26374,26376],{"className":26375},[1133],[1135,26377,26378],{"xmlns":1137},[1139,26379,26380,26402],{},[1142,26381,26382,26388,26390,26393,26395,26398,26400],{},[2671,26383,26384,26386],{"accent":1121},[1148,26385,10129],{},[1495,26387,12415],{},[1495,26389,1503],{},[1152,26391,26392],{},"108,7",[1495,26394,6294],{},[1152,26396,26397],{},"368,0",[2358,26399,2360],{},[1148,26401,2675],{},[1156,26403,26404],{"encoding":1158},"\\hat y = 108{,}7 + 368{,}0\\,x",". Sloupec ",[3161,26407,26408],{},"Pr(>|t|)"," je p-hodnota t-testu ",[1115,26411,26413],{"className":26412},[1133],[1135,26414,26415],{"xmlns":1137},[1139,26416,26417,26437],{},[1142,26418,26419,26425,26427,26433,26435],{},[1145,26420,26421,26423],{},[1148,26422,1150],{},[1152,26424,1154],{},[1495,26426,1497],{},[1145,26428,26429,26431],{},[1148,26430,1262],{},[1148,26432,4085],{},[1495,26434,1503],{},[1152,26436,1154],{},[1156,26438,26439],{"encoding":1158},"H_0:\\beta_i=0"," proti ",[1115,26442,26444],{"className":26443},[1133],[1135,26445,26446],{"xmlns":1137},[1139,26447,26448,26468],{},[1142,26449,26450,26456,26458,26464,26466],{},[1145,26451,26452,26454],{},[1148,26453,1150],{},[1152,26455,1176],{},[1495,26457,1497],{},[1145,26459,26460,26462],{},[1148,26461,1262],{},[1148,26463,4085],{},[1495,26465,1600],{"mathvariant":1599},[1152,26467,1154],{},[1156,26469,26470],{"encoding":1158},"H_1:\\beta_i\\neq0"," pro každý parametr — obě p-hodnoty jsou hluboko pod 0,05, oba parametry jsou tedy statisticky významné. ",[3161,26473,26474],{},"Multiple R-squared"," je index determinace ",[1115,26477,26479],{"className":26478},[1133],[1135,26480,26481],{"xmlns":1137},[1139,26482,26483,26496],{},[1142,26484,26485,26491,26493],{},[2632,26486,26487,26489],{},[1148,26488,19792],{},[1152,26490,2639],{},[1495,26492,1503],{},[1152,26494,26495],{},"0,9995",[1156,26497,26498],{"encoding":1158},"R^2=0{,}9995",": model vysvětluje 99,95 % rozptylu výdajů.",[1110,26501,26502],{},"Pro doplňkový přehled slouží přímé přístupové funkce:",[3166,26504,26506],{"className":3168,"code":26505,"language":71,"meta":3170,"style":3170},"coef(model)\nfitted(model)\nresiduals(model)\n",[3161,26507,26508,26519,26530],{"__ignoreMap":3170},[1115,26509,26510,26513,26515,26517],{"class":3175,"line":10},[1115,26511,26512],{"class":3185},"coef",[1115,26514,2162],{"class":3189},[1115,26516,786],{"class":3178},[1115,26518,3235],{"class":3189},[1115,26520,26521,26524,26526,26528],{"class":3175,"line":27},[1115,26522,26523],{"class":3185},"fitted",[1115,26525,2162],{"class":3189},[1115,26527,786],{"class":3178},[1115,26529,3235],{"class":3189},[1115,26531,26532,26535,26537,26539],{"class":3175,"line":148},[1115,26533,26534],{"class":3185},"residuals",[1115,26536,2162],{"class":3189},[1115,26538,786],{"class":3178},[1115,26540,3235],{"class":3189},[3166,26542,26545],{"className":26543,"code":26544,"language":3274,"meta":3170},[3272],"(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",[3161,26546,26544],{"__ignoreMap":3170},[1110,26548,26549,26552,26553,1195,26579,26582,26583,26605,26606,1195,26624,26627,26628,26665],{},[3161,26550,26551],{},"coef()"," vrací odhadnuté parametry ",[1115,26554,26556],{"className":26555},[1133],[1135,26557,26558],{"xmlns":1137},[1139,26559,26560,26576],{},[1142,26561,26562,26568,26570],{},[1145,26563,26564,26566],{},[1148,26565,21066],{},[1152,26567,1154],{},[1495,26569,2188],{"separator":1121},[1145,26571,26572,26574],{},[1148,26573,21066],{},[1152,26575,1176],{},[1156,26577,26578],{"encoding":1158},"b_0,b_1",[3161,26580,26581],{},"fitted()"," predikce ",[1115,26584,26586],{"className":26585},[1133],[1135,26587,26588],{"xmlns":1137},[1139,26589,26590,26602],{},[1142,26591,26592],{},[1145,26593,26594,26600],{},[2671,26595,26596,26598],{"accent":1121},[1148,26597,10129],{},[1495,26599,12415],{},[1148,26601,4085],{},[1156,26603,26604],{"encoding":1158},"\\hat y_i"," pro pozorované ",[1115,26607,26609],{"className":26608},[1133],[1135,26610,26611],{"xmlns":1137},[1139,26612,26613,26621],{},[1142,26614,26615],{},[1145,26616,26617,26619],{},[1148,26618,2675],{},[1148,26620,4085],{},[1156,26622,26623],{"encoding":1158},"x_i",[3161,26625,26626],{},"residuals()"," rezidua ",[1115,26629,26631],{"className":26630},[1133],[1135,26632,26633],{"xmlns":1137},[1139,26634,26635,26663],{},[1142,26636,26637,26643,26645,26651,26653],{},[1145,26638,26639,26641],{},[1148,26640,18179],{},[1148,26642,4085],{},[1495,26644,1503],{},[1145,26646,26647,26649],{},[1148,26648,10129],{},[1148,26650,4085],{},[1495,26652,1885],{},[1145,26654,26655,26661],{},[2671,26656,26657,26659],{"accent":1121},[1148,26658,10129],{},[1495,26660,12415],{},[1148,26662,4085],{},[1156,26664,26011],{"encoding":1158}," — stejná čísla, která na obrázku výše tvoří délky červených úseček.",[1110,26667,26668,26669,26682],{},"Intervaly spolehlivosti pro parametry a pro predikci v nových bodech ",[1115,26670,26672],{"className":26671},[1133],[1135,26673,26674],{"xmlns":1137},[1139,26675,26676,26680],{},[1142,26677,26678],{},[1148,26679,2675],{},[1156,26681,2675],{"encoding":1158}," (zde 7 a 8 členů domácnosti):",[3166,26684,26686],{"className":3168,"code":26685,"language":71,"meta":3170,"style":3170},"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",[3161,26687,26688,26708,26736,26775],{"__ignoreMap":3170},[1115,26689,26690,26693,26695,26697,26699,26702,26704,26706],{"class":3175,"line":10},[1115,26691,26692],{"class":3185},"confint",[1115,26694,2162],{"class":3189},[1115,26696,786],{"class":3178},[1115,26698,2188],{"class":3181},[1115,26700,26701],{"class":3178}," level",[1115,26703,3252],{"class":3181},[1115,26705,19570],{"class":3192},[1115,26707,3235],{"class":3189},[1115,26709,26710,26713,26715,26718,26720,26722,26724,26726,26728,26730,26732,26734],{"class":3175,"line":27},[1115,26711,26712],{"class":3178},"nove",[1115,26714,3182],{"class":3181},[1115,26716,26717],{"class":3185}," data.frame",[1115,26719,2162],{"class":3189},[1115,26721,26261],{"class":3178},[1115,26723,3252],{"class":3181},[1115,26725,3186],{"class":3185},[1115,26727,2162],{"class":3189},[1115,26729,22878],{"class":3192},[1115,26731,2188],{"class":3181},[1115,26733,24753],{"class":3192},[1115,26735,7963],{"class":3189},[1115,26737,26738,26741,26743,26745,26747,26750,26752,26755,26757,26760,26762,26765,26767,26769,26771,26773],{"class":3175,"line":148},[1115,26739,26740],{"class":3185},"predict",[1115,26742,2162],{"class":3189},[1115,26744,786],{"class":3178},[1115,26746,2188],{"class":3181},[1115,26748,26749],{"class":3178}," newdata",[1115,26751,3252],{"class":3181},[1115,26753,26754],{"class":3178}," nove",[1115,26756,2188],{"class":3181},[1115,26758,26759],{"class":3178}," interval",[1115,26761,3252],{"class":3181},[1115,26763,26764],{"class":3265}," \"confidence\"",[1115,26766,2188],{"class":3181},[1115,26768,26701],{"class":3178},[1115,26770,3252],{"class":3181},[1115,26772,19570],{"class":3192},[1115,26774,3235],{"class":3189},[1115,26776,26777,26779,26781,26783,26785,26787,26789,26791,26793,26795,26797,26800,26802,26804,26806,26808],{"class":3175,"line":111},[1115,26778,26740],{"class":3185},[1115,26780,2162],{"class":3189},[1115,26782,786],{"class":3178},[1115,26784,2188],{"class":3181},[1115,26786,26749],{"class":3178},[1115,26788,3252],{"class":3181},[1115,26790,26754],{"class":3178},[1115,26792,2188],{"class":3181},[1115,26794,26759],{"class":3178},[1115,26796,3252],{"class":3181},[1115,26798,26799],{"class":3265}," \"prediction\"",[1115,26801,2188],{"class":3181},[1115,26803,26701],{"class":3178},[1115,26805,3252],{"class":3181},[1115,26807,19570],{"class":3192},[1115,26809,3235],{"class":3189},[3166,26811,26814],{"className":26812,"code":26813,"language":3274,"meta":3170},[3272],"                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",[3161,26815,26813],{"__ignoreMap":3170},[1110,26817,26818,26821,26822,1953,26825,26838,26839,1195,26852,26855,26856,26859],{},[3161,26819,26820],{},"interval = \"confidence\""," dává interval spolehlivosti pro ",[1399,26823,26824],{},"střední hodnotu",[1115,26826,26828],{"className":26827},[1133],[1135,26829,26830],{"xmlns":1137},[1139,26831,26832,26836],{},[1142,26833,26834],{},[1148,26835,10129],{},[1156,26837,10129],{"encoding":1158}," při daném ",[1115,26840,26842],{"className":26841},[1133],[1135,26843,26844],{"xmlns":1137},[1139,26845,26846,26850],{},[1142,26847,26848],{},[1148,26849,2675],{},[1156,26851,2675],{"encoding":1158},[3161,26853,26854],{},"interval = \"prediction\""," širší interval pro ",[1399,26857,26858],{},"jednotlivé budoucí pozorování"," — ten musí zahrnout i rozptyl kolem regresní přímky, proto je vždy širší.",[1695,26861,26863],{"id":26862},"diagnostika-modelu","Diagnostika modelu",[1110,26865,26866,26867,1195,26870,2261,26873,26876],{},"Platnost závěrů z regresní přímky stojí na předpokladech o reziduích: ",[1399,26868,26869],{},"absenci autokorelace",[1399,26871,26872],{},"stálosti rozptylu (homoskedasticitě)",[1399,26874,26875],{},"normalitě",". V R se ověřují takto:",[3166,26878,26880],{"className":3168,"code":26879,"language":71,"meta":3170,"style":3170},"library(lmtest)\ndwtest(model)\n",[3161,26881,26882,26893],{"__ignoreMap":3170},[1115,26883,26884,26886,26888,26891],{"class":3175,"line":10},[1115,26885,10627],{"class":3181},[1115,26887,2162],{"class":3189},[1115,26889,26890],{"class":3178},"lmtest",[1115,26892,3235],{"class":3189},[1115,26894,26895,26898,26900,26902],{"class":3175,"line":27},[1115,26896,26897],{"class":3185},"dwtest",[1115,26899,2162],{"class":3189},[1115,26901,786],{"class":3178},[1115,26903,3235],{"class":3189},[3166,26905,26908],{"className":26906,"code":26907,"language":3274,"meta":3170},[3272],"    Durbin-Watson test\n\ndata:  model\nDW = 3.4121, p-value = 0.9555\nalternative hypothesis: true autocorrelation is greater than 0\n",[3161,26909,26907],{"__ignoreMap":3170},[1110,26911,26912,26913,26930,26931,26948,26949,26966],{},"Durbinův–Watsonův test má ",[1115,26914,26916],{"className":26915},[1133],[1135,26917,26918],{"xmlns":1137},[1139,26919,26920,26928],{},[1142,26921,26922],{},[1145,26923,26924,26926],{},[1148,26925,1150],{},[1152,26927,1154],{},[1156,26929,1159],{"encoding":1158},": v modelu není problém s autokorelací, proti ",[1115,26932,26934],{"className":26933},[1133],[1135,26935,26936],{"xmlns":1137},[1139,26937,26938,26946],{},[1142,26939,26940],{},[1145,26941,26942,26944],{},[1148,26943,1150],{},[1152,26945,1176],{},[1156,26947,1179],{"encoding":1158},": 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, ",[1115,26950,26952],{"className":26951},[1133],[1135,26953,26954],{"xmlns":1137},[1139,26955,26956,26964],{},[1142,26957,26958],{},[1145,26959,26960,26962],{},[1148,26961,1150],{},[1152,26963,1154],{},[1156,26965,1159],{"encoding":1158}," se nezamítá.",[3166,26968,26970],{"className":3168,"code":26969,"language":71,"meta":3170,"style":3170},"library(whitestrap)\nwhite_test(model)\n",[3161,26971,26972,26983],{"__ignoreMap":3170},[1115,26973,26974,26976,26978,26981],{"class":3175,"line":10},[1115,26975,10627],{"class":3181},[1115,26977,2162],{"class":3189},[1115,26979,26980],{"class":3178},"whitestrap",[1115,26982,3235],{"class":3189},[1115,26984,26985,26988,26990,26992],{"class":3175,"line":27},[1115,26986,26987],{"class":3185},"white_test",[1115,26989,2162],{"class":3189},[1115,26991,786],{"class":3178},[1115,26993,3235],{"class":3189},[3166,26995,26998],{"className":26996,"code":26997,"language":3274,"meta":3170},[3272],"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",[3161,26999,26997],{"__ignoreMap":3170},[1110,27001,27002,27003,27020,27021,27038,27039,26966],{},"Whiteův test má ",[1115,27004,27006],{"className":27005},[1133],[1135,27007,27008],{"xmlns":1137},[1139,27009,27010,27018],{},[1142,27011,27012],{},[1145,27013,27014,27016],{},[1148,27015,1150],{},[1152,27017,1154],{},[1156,27019,1159],{"encoding":1158},": rozptyl reziduí je stálý (homoskedasticita), proti ",[1115,27022,27024],{"className":27023},[1133],[1135,27025,27026],{"xmlns":1137},[1139,27027,27028,27036],{},[1142,27029,27030],{},[1145,27031,27032,27034],{},[1148,27033,1150],{},[1152,27035,1176],{},[1156,27037,1179],{"encoding":1158},": rozptyl není stálý (heteroskedasticita). P-hodnota 0,21 je nad 0,05, ",[1115,27040,27042],{"className":27041},[1133],[1135,27043,27044],{"xmlns":1137},[1139,27045,27046,27054],{},[1142,27047,27048],{},[1145,27049,27050,27052],{},[1148,27051,1150],{},[1152,27053,1154],{},[1156,27055,1159],{"encoding":1158},[3166,27057,27059],{"className":3168,"code":27058,"language":71,"meta":3170,"style":3170},"shapiro.test(residuals(model))\n",[3161,27060,27061],{"__ignoreMap":3170},[1115,27062,27063,27065,27067,27069,27071,27073],{"class":3175,"line":10},[1115,27064,3998],{"class":3185},[1115,27066,2162],{"class":3189},[1115,27068,26534],{"class":3185},[1115,27070,2162],{"class":3189},[1115,27072,786],{"class":3178},[1115,27074,7963],{"class":3189},[3166,27076,27079],{"className":27077,"code":27078,"language":3274,"meta":3170},[3272],"    Shapiro-Wilk normality test\n\ndata:  residuals(model)\nW = 0.94818, p-value = 0.7255\n",[3161,27080,27078],{"__ignoreMap":3170},[1110,27082,27083,27084,27101],{},"Shapiro–Wilkův test má ",[1115,27085,27087],{"className":27086},[1133],[1135,27088,27089],{"xmlns":1137},[1139,27090,27091,27099],{},[1142,27092,27093],{},[1145,27094,27095,27097],{},[1148,27096,1150],{},[1152,27098,1154],{},[1156,27100,1159],{"encoding":1158},": rezidua pocházejí z normálního rozdělení. P-hodnota 0,73 opět nevede k zamítnutí — všechny tři předpoklady model splňuje.",[1110,27103,27104],{},[1971,27105],{"alt":27106,"className":27107,"src":27108},"mask-ra-diagnostika-rezidui",[1343,1975],"\u002Fwiki-assets\u002Fmask-ra-diagnostika-rezidui.png",[1110,27110,27111],{},"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.",[1103,27113,27115,27122,27153,27188,27253],{"className":27114,"dataCallout":3323},[1106,3322],[1110,27116,27118,27121],{"className":27117},[1113],[1115,27119],{"className":27120,"ariaHidden":1121},[1118,3330,1120],"Příklad: Regresní přímka",[1110,27123,27124,27125,27138,27139,27152],{},"V souboru s údaji o hodnotě produkce (v milionech Kč, proměnná ",[1115,27126,27128],{"className":27127},[1133],[1135,27129,27130],{"xmlns":1137},[1139,27131,27132,27136],{},[1142,27133,27134],{},[1148,27135,10129],{},[1156,27137,10129],{"encoding":1158},") a výši investic (ve stovkách tisíc Kč, proměnná ",[1115,27140,27142],{"className":27141},[1133],[1135,27143,27144],{"xmlns":1137},[1139,27145,27146,27150],{},[1142,27147,27148],{},[1148,27149,2675],{},[1156,27151,2675],{"encoding":1158},") 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.",[1110,27154,27155,27156,1335],{},"Výsledek: ",[1115,27157,27159],{"className":27158},[1133],[1135,27160,27161],{"xmlns":1137},[1139,27162,27163,27185],{},[1142,27164,27165,27171,27173,27176,27178,27181,27183],{},[2671,27166,27167,27169],{"accent":1121},[1148,27168,10129],{},[1495,27170,12415],{},[1495,27172,1503],{},[1152,27174,27175],{},"32,74",[1495,27177,6294],{},[1152,27179,27180],{},"2,15",[2358,27182,2360],{},[1148,27184,2675],{},[1156,27186,27187],{"encoding":1158},"\\hat y = 32{,}74 + 2{,}15\\,x",[1110,27189,26189,27190,27212,27213,27252],{},[1115,27191,27193],{"className":27192},[1133],[1135,27194,27195],{"xmlns":1137},[1139,27196,27197,27209],{},[1142,27198,27199,27205,27207],{},[1145,27200,27201,27203],{},[1148,27202,21066],{},[1152,27204,1176],{},[1495,27206,1503],{},[1152,27208,27180],{},[1156,27210,27211],{"encoding":1158},"b_1=2{,}15"," říká, že se zvýšením investic o 100 000 Kč vzroste produkce v průměru o ",[1115,27214,27216],{"className":27215},[1133],[1135,27217,27218],{"xmlns":1137},[1139,27219,27220,27249],{},[1142,27221,27222,27224,27226,27228,27230,27232,27234,27236,27238,27240,27242,27245,27247],{},[1152,27223,27180],{},[1495,27225,7548],{},[1152,27227,1176],{},[2358,27229,2360],{},[1152,27231,20885],{},[2358,27233,2360],{},[1152,27235,20885],{},[1495,27237,1503],{},[1152,27239,2639],{},[2358,27241,2360],{},[1152,27243,27244],{},"150",[2358,27246,2360],{},[1152,27248,20885],{},[1156,27250,27251],{"encoding":1158},"2{,}15\\cdot 1\\,000\\,000=2\\,150\\,000"," Kč.",[1110,27254,27255,27256,2324,27275,27323,27324,1390],{},"Dosazením libovolné hodnoty investic do empirické regresní funkce dostaneme predikci produkce, například pro třináctou firmu s investicemi ",[1115,27257,27259],{"className":27258},[1133],[1135,27260,27261],{"xmlns":1137},[1139,27262,27263,27272],{},[1142,27264,27265,27267,27269],{},[1148,27266,2675],{},[1495,27268,1503],{},[1152,27270,27271],{},"34",[1156,27273,27274],{"encoding":1158},"x=34",[1115,27276,27278],{"className":27277},[1133],[1135,27279,27280],{"xmlns":1137},[1139,27281,27282,27320],{},[1142,27283,27284,27294,27296,27302,27304,27310,27312,27314,27317],{},[1145,27285,27286,27292],{},[2671,27287,27288,27290],{"accent":1121},[1148,27289,10129],{},[1495,27291,12415],{},[1152,27293,13212],{},[1495,27295,1503],{},[1145,27297,27298,27300],{},[1148,27299,21066],{},[1152,27301,1154],{},[1495,27303,6294],{},[1145,27305,27306,27308],{},[1148,27307,21066],{},[1152,27309,1176],{},[1495,27311,7548],{},[1152,27313,27271],{},[1495,27315,27316],{},"≐",[1152,27318,27319],{},"105,81",[1156,27321,27322],{"encoding":1158},"\\hat y_{13} = b_0 + b_1\\cdot 34 \\doteq 105{,}81"," milionu Kč (se zaokrouhlenými koeficienty ",[1115,27325,27327],{"className":27326},[1133],[1135,27328,27329],{"xmlns":1137},[1139,27330,27331,27348],{},[1142,27332,27333,27335,27337,27339,27341,27343,27345],{},[1152,27334,27175],{},[1495,27336,6294],{},[1152,27338,27180],{},[1495,27340,7548],{},[1152,27342,27271],{},[1495,27344,27316],{},[1152,27346,27347],{},"105,8",[1156,27349,27350],{"encoding":1158},"32{,}74 + 2{,}15\\cdot 34 \\doteq 105{,}8",[1392,27352,27354],{"id":27353},"nelineární-a-vyšší-řády-regresních-funkcí","Nelineární a vyšší řády regresních funkcí",[1110,27356,27357,27358,27361,27362,27429,27430,27448,27449,27466],{},"Když přímka závislost nevystihuje, nabízí se další ",[1399,27359,27360],{},"lineární funkce"," — tedy funkce lineární ve svých parametrech, zapsatelné ve tvaru ",[1115,27363,27365],{"className":27364},[1133],[1135,27366,27367],{"xmlns":1137},[1139,27368,27369,27426],{},[1142,27370,27371,27373,27375,27381,27383,27389,27395,27397,27399,27401,27403,27406,27408,27414,27420,27422,27424],{},[1148,27372,25815],{},[1495,27374,1503],{},[1145,27376,27377,27379],{},[1148,27378,1262],{},[1152,27380,1154],{},[1495,27382,6294],{},[1145,27384,27385,27387],{},[1148,27386,1262],{},[1152,27388,1176],{},[1145,27390,27391,27393],{},[1148,27392,16375],{},[1152,27394,1176],{},[1495,27396,2162],{"stretchy":2161},[1148,27398,2675],{},[1495,27400,2181],{"stretchy":2161},[1495,27402,6294],{},[1495,27404,27405],{},"⋯",[1495,27407,6294],{},[1145,27409,27410,27412],{},[1148,27411,1262],{},[1148,27413,1110],{},[1145,27415,27416,27418],{},[1148,27417,16375],{},[1148,27419,1110],{},[1495,27421,2162],{"stretchy":2161},[1148,27423,2675],{},[1495,27425,2181],{"stretchy":2161},[1156,27427,27428],{"encoding":1158},"\\eta=\\beta_0+\\beta_1 f_1(x)+\\dots+\\beta_p f_p(x)"," se známými funkcemi ",[1115,27431,27433],{"className":27432},[1133],[1135,27434,27435],{"xmlns":1137},[1139,27436,27437,27445],{},[1142,27438,27439],{},[1145,27440,27441,27443],{},[1148,27442,16375],{},[1148,27444,4085],{},[1156,27446,27447],{"encoding":1158},"f_i"," a neznámými parametry ",[1115,27450,27452],{"className":27451},[1133],[1135,27453,27454],{"xmlns":1137},[1139,27455,27456,27464],{},[1142,27457,27458],{},[1145,27459,27460,27462],{},[1148,27461,1262],{},[1148,27463,4085],{},[1156,27465,25875],{"encoding":1158},". I tyto parametry se odhadují metodou nejmenších čtverců, stejně jako u přímky:",[1115,27468,27470],{"className":27469},[1133],[1135,27471,27472],{"xmlns":1137,"display":2151},[1139,27473,27474,27784],{},[27475,27476,27479,27552,27665,27724],"mtable",{"rowspacing":27477,"columnalign":27478,"columnspacing":16363},"0.25em","right left",[27480,27481,27482,27506],"mtr",{},[27483,27484,27485],"mtd",{},[6544,27486,27487],{"scriptlevel":1154,"displaystyle":1121},[1142,27488,27489,27503],{},[1142,27490,27491,27494,27500],{},[2358,27492,27493],{},"parabolick",[2671,27495,27496,27498],{"accent":1121},[2358,27497,1340],{},[1495,27499,21063],{},[2358,27501,27502],{}," regrese: ",[3520,27504],{"width":27505},"1em",[27483,27507,27508],{},[6544,27509,27510],{"scriptlevel":1154,"displaystyle":1121},[1142,27511,27512,27514,27520,27522,27528,27530,27536,27538,27540,27546],{},[1142,27513],{},[2671,27515,27516,27518],{"accent":1121},[1148,27517,10129],{},[1495,27519,12415],{},[1495,27521,1503],{},[1145,27523,27524,27526],{},[1148,27525,21066],{},[1152,27527,1154],{},[1495,27529,6294],{},[1145,27531,27532,27534],{},[1148,27533,21066],{},[1152,27535,1176],{},[1148,27537,2675],{},[1495,27539,6294],{},[1145,27541,27542,27544],{},[1148,27543,21066],{},[1152,27545,2639],{},[2632,27547,27548,27550],{},[1148,27549,2675],{},[1152,27551,2639],{},[27480,27553,27554,27601],{},[27483,27555,27556],{},[6544,27557,27558],{"scriptlevel":1154,"displaystyle":1121},[1142,27559,27560,27599],{},[1142,27561,27562,27565,27571,27574,27578,27581,27587,27590,27596],{},[2358,27563,27564],{},"polynomick",[2671,27566,27567,27569],{"accent":1121},[2358,27568,1340],{},[1495,27570,21063],{},[2358,27572,27573],{}," regrese ",[6544,27575,27576],{"scriptlevel":1154,"displaystyle":2161},[1148,27577,1110],{},[2358,27579,27580],{},"-t",[2671,27582,27583,27585],{"accent":1121},[2358,27584,18179],{},[1495,27586,21063],{},[2358,27588,27589],{},"ho stupn",[2671,27591,27592,27594],{"accent":1121},[2358,27593,18179],{},[1495,27595,21073],{},[2358,27597,27598],{},": ",[3520,27600],{"width":27505},[27483,27602,27603],{},[6544,27604,27605],{"scriptlevel":1154,"displaystyle":1121},[1142,27606,27607,27609,27615,27617,27623,27625,27631,27633,27635,27641,27647,27649,27651,27653,27659],{},[1142,27608],{},[2671,27610,27611,27613],{"accent":1121},[1148,27612,10129],{},[1495,27614,12415],{},[1495,27616,1503],{},[1145,27618,27619,27621],{},[1148,27620,21066],{},[1152,27622,1154],{},[1495,27624,6294],{},[1145,27626,27627,27629],{},[1148,27628,21066],{},[1152,27630,1176],{},[1148,27632,2675],{},[1495,27634,6294],{},[1145,27636,27637,27639],{},[1148,27638,21066],{},[1152,27640,2639],{},[2632,27642,27643,27645],{},[1148,27644,2675],{},[1152,27646,2639],{},[1495,27648,6294],{},[1495,27650,27405],{},[1495,27652,6294],{},[1145,27654,27655,27657],{},[1148,27656,21066],{},[1148,27658,1110],{},[2632,27660,27661,27663],{},[1148,27662,2675],{},[1148,27664,1110],{},[27480,27666,27667,27688],{},[27483,27668,27669],{},[6544,27670,27671],{"scriptlevel":1154,"displaystyle":1121},[1142,27672,27673,27686],{},[1142,27674,27675,27678,27684],{},[2358,27676,27677],{},"hyperbolick",[2671,27679,27680,27682],{"accent":1121},[2358,27681,1340],{},[1495,27683,21063],{},[2358,27685,27502],{},[3520,27687],{"width":27505},[27483,27689,27690],{},[6544,27691,27692],{"scriptlevel":1154,"displaystyle":1121},[1142,27693,27694,27696,27702,27704,27710,27712,27718],{},[1142,27695],{},[2671,27697,27698,27700],{"accent":1121},[1148,27699,10129],{},[1495,27701,12415],{},[1495,27703,1503],{},[1145,27705,27706,27708],{},[1148,27707,21066],{},[1152,27709,1154],{},[1495,27711,6294],{},[1145,27713,27714,27716],{},[1148,27715,21066],{},[1152,27717,1176],{},[2749,27719,27720,27722],{},[1152,27721,1176],{},[1148,27723,2675],{},[27480,27725,27726,27747],{},[27483,27727,27728],{},[6544,27729,27730],{"scriptlevel":1154,"displaystyle":1121},[1142,27731,27732,27745],{},[1142,27733,27734,27737,27743],{},[2358,27735,27736],{},"logaritmick",[2671,27738,27739,27741],{"accent":1121},[2358,27740,1340],{},[1495,27742,21063],{},[2358,27744,27502],{},[3520,27746],{"width":27505},[27483,27748,27749],{},[6544,27750,27751],{"scriptlevel":1154,"displaystyle":1121},[1142,27752,27753,27755,27761,27763,27769,27771,27777,27780,27782],{},[1142,27754],{},[2671,27756,27757,27759],{"accent":1121},[1148,27758,10129],{},[1495,27760,12415],{},[1495,27762,1503],{},[1145,27764,27765,27767],{},[1148,27766,21066],{},[1152,27768,1154],{},[1495,27770,6294],{},[1145,27772,27773,27775],{},[1148,27774,21066],{},[1152,27776,1176],{},[1148,27778,27779],{},"ln",[1495,27781,8744],{},[1148,27783,2675],{},[1156,27785,27786],{"encoding":1158},"\\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}",[1110,27788,27789,27790,27793,27794,27840,27841,1497],{},"Naproti tomu ",[1399,27791,27792],{},"nelineární funkce"," nelze do tvaru ",[1115,27795,27797],{"className":27796},[1133],[1135,27798,27799],{"xmlns":1137},[1139,27800,27801,27837],{},[1142,27802,27803,27805,27807,27813,27815,27821,27827,27829,27831,27833,27835],{},[1148,27804,25815],{},[1495,27806,1503],{},[1145,27808,27809,27811],{},[1148,27810,1262],{},[1152,27812,1154],{},[1495,27814,6294],{},[1145,27816,27817,27819],{},[1148,27818,1262],{},[1152,27820,1176],{},[1145,27822,27823,27825],{},[1148,27824,16375],{},[1152,27826,1176],{},[1495,27828,2162],{"stretchy":2161},[1148,27830,2675],{},[1495,27832,2181],{"stretchy":2161},[1495,27834,6294],{},[1495,27836,10697],{},[1156,27838,27839],{"encoding":1158},"\\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 ",[1399,27842,27843],{},"exponenciální regrese",[1115,27845,27847],{"className":27846},[1133],[1135,27848,27849],{"xmlns":1137,"display":2151},[1139,27850,27851,27883],{},[1142,27852,27853,27859,27861,27867,27869,27881],{},[2671,27854,27855,27857],{"accent":1121},[1148,27856,10129],{},[1495,27858,12415],{},[1495,27860,1503],{},[1145,27862,27863,27865],{},[1148,27864,21066],{},[1152,27866,1154],{},[1495,27868,7548],{},[4163,27870,27871,27873,27875],{},[1148,27872,21066],{},[1152,27874,1176],{},[1142,27876,27877,27879],{},[2358,27878,2360],{},[1148,27880,2675],{},[1148,27882,1335],{"mathvariant":1599},[1156,27884,27885],{"encoding":1158},"\\hat y = b_0 \\cdot b_1^{\\,x}.",[1110,27887,27888],{},[1971,27889],{"alt":27890,"className":27891,"src":27892},"mask-ra-nelinearni-krivky",[1343,1975],"\u002Fwiki-assets\u002Fmask-ra-nelinearni-krivky.png",[1695,27894,27896],{"id":27895},"v-r-parabolická-regrese","V R — parabolická regrese",[1110,27898,27899,27900,1497],{},"Na ročních ziscích firmy (šest let) se parabolická regrese odhadne přidáním kvadratického členu ",[3161,27901,27902],{},"I(x^2)",[3166,27904,27906],{"className":3168,"code":27905,"language":71,"meta":3170,"style":3170},"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",[3161,27907,27908,27943,27982,28015],{"__ignoreMap":3170},[1115,27909,27910,27913,27915,27917,27919,27921,27923,27925,27927,27929,27931,27933,27935,27937,27939,27941],{"class":3175,"line":10},[1115,27911,27912],{"class":3178},"rok",[1115,27914,3182],{"class":3181},[1115,27916,3186],{"class":3185},[1115,27918,2162],{"class":3189},[1115,27920,1176],{"class":3192},[1115,27922,2188],{"class":3181},[1115,27924,7909],{"class":3192},[1115,27926,2188],{"class":3181},[1115,27928,9537],{"class":3192},[1115,27930,2188],{"class":3181},[1115,27932,3983],{"class":3192},[1115,27934,2188],{"class":3181},[1115,27936,9344],{"class":3192},[1115,27938,2188],{"class":3181},[1115,27940,21777],{"class":3192},[1115,27942,3235],{"class":3189},[1115,27944,27945,27947,27949,27951,27953,27956,27958,27960,27962,27965,27967,27970,27972,27975,27977,27980],{"class":3175,"line":27},[1115,27946,1088],{"class":3178},[1115,27948,3182],{"class":3181},[1115,27950,3186],{"class":3185},[1115,27952,2162],{"class":3189},[1115,27954,27955],{"class":3192},"112",[1115,27957,2188],{"class":3181},[1115,27959,8382],{"class":3192},[1115,27961,2188],{"class":3181},[1115,27963,27964],{"class":3192}," 238",[1115,27966,2188],{"class":3181},[1115,27968,27969],{"class":3192}," 354",[1115,27971,2188],{"class":3181},[1115,27973,27974],{"class":3192}," 580",[1115,27976,2188],{"class":3181},[1115,27978,27979],{"class":3192}," 867",[1115,27981,3235],{"class":3189},[1115,27983,27984,27987,27989,27991,27993,27995,27997,28000,28002,28005,28007,28009,28011,28013],{"class":3175,"line":148},[1115,27985,27986],{"class":3178},"model_parabola",[1115,27988,3182],{"class":3181},[1115,27990,26341],{"class":3185},[1115,27992,2162],{"class":3189},[1115,27994,1088],{"class":3178},[1115,27996,10574],{"class":3181},[1115,27998,27999],{"class":3178}," rok",[1115,28001,7877],{"class":3181},[1115,28003,28004],{"class":3185}," I",[1115,28006,2162],{"class":3189},[1115,28008,27912],{"class":3178},[1115,28010,12415],{"class":3181},[1115,28012,2639],{"class":3192},[1115,28014,7963],{"class":3189},[1115,28016,28017,28019,28021,28023],{"class":3175,"line":111},[1115,28018,26357],{"class":3185},[1115,28020,2162],{"class":3189},[1115,28022,27986],{"class":3178},[1115,28024,3235],{"class":3189},[3166,28026,28029],{"className":28027,"code":28028,"language":3274,"meta":3170},[3272],"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",[3161,28030,28028],{"__ignoreMap":3170},[1110,28032,28033,28034,28079],{},"Odhadnutá parabola ",[1115,28035,28037],{"className":28036},[1133],[1135,28038,28039],{"xmlns":1137},[1139,28040,28041,28076],{},[1142,28042,28043,28049,28051,28054,28056,28059,28061,28063,28065,28068,28070],{},[2671,28044,28045,28047],{"accent":1121},[1148,28046,10129],{},[1495,28048,12415],{},[1495,28050,1503],{},[1152,28052,28053],{},"164,6",[1495,28055,1885],{},[1152,28057,28058],{},"76,6",[2358,28060,2360],{},[1148,28062,2675],{},[1495,28064,6294],{},[1152,28066,28067],{},"32,1",[2358,28069,2360],{},[2632,28071,28072,28074],{},[1148,28073,2675],{},[1152,28075,2639],{},[1156,28077,28078],{"encoding":1158},"\\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.",[1695,28081,28083],{"id":28082},"v-r-exponenciální-regrese","V R — exponenciální regrese",[1110,28085,28086,28087,28089],{},"Nelineární funkce se v R odhadují funkcí ",[3161,28088,25601],{}," ze stejnojmenného balíčku. Bez zadaných počátečních hodnot R upozorní, že parametry nastavil na 1, a odhad dopočítá iteračně:",[3166,28091,28093],{"className":3168,"code":28092,"language":71,"meta":3170,"style":3170},"library(nls2)\nmodel_exp \u003C- nls2(zisk ~ b1 * exp(b2 * rok))\nsummary(model_exp)\n",[3161,28094,28095,28105,28140],{"__ignoreMap":3170},[1115,28096,28097,28099,28101,28103],{"class":3175,"line":10},[1115,28098,10627],{"class":3181},[1115,28100,2162],{"class":3189},[1115,28102,25586],{"class":3178},[1115,28104,3235],{"class":3189},[1115,28106,28107,28110,28112,28115,28117,28119,28121,28124,28126,28129,28131,28134,28136,28138],{"class":3175,"line":27},[1115,28108,28109],{"class":3178},"model_exp",[1115,28111,3182],{"class":3181},[1115,28113,28114],{"class":3185}," nls2",[1115,28116,2162],{"class":3189},[1115,28118,1088],{"class":3178},[1115,28120,10574],{"class":3181},[1115,28122,28123],{"class":3178}," b1",[1115,28125,3696],{"class":3181},[1115,28127,28128],{"class":3185}," exp",[1115,28130,2162],{"class":3189},[1115,28132,28133],{"class":3178},"b2",[1115,28135,3696],{"class":3181},[1115,28137,27999],{"class":3178},[1115,28139,7963],{"class":3189},[1115,28141,28142,28144,28146,28148],{"class":3175,"line":148},[1115,28143,26357],{"class":3185},[1115,28145,2162],{"class":3189},[1115,28147,28109],{"class":3178},[1115,28149,3235],{"class":3189},[3166,28151,28154],{"className":28152,"code":28153,"language":3274,"meta":3170},[3272],"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",[3161,28155,28153],{"__ignoreMap":3170},[1110,28157,28158,28159,1497],{},"Stejnou křivku lze zapsat i v mocninném tvaru ",[1115,28160,28162],{"className":28161},[1133],[1135,28163,28164],{"xmlns":1137},[1139,28165,28166,28192],{},[1142,28167,28168,28174,28176,28182,28184],{},[2671,28169,28170,28172],{"accent":1121},[1148,28171,10129],{},[1495,28173,12415],{},[1495,28175,1503],{},[1145,28177,28178,28180],{},[1148,28179,21066],{},[1152,28181,1176],{},[1495,28183,7548],{},[4163,28185,28186,28188,28190],{},[1148,28187,21066],{},[1152,28189,2639],{},[1148,28191,2675],{},[1156,28193,28194],{"encoding":1158},"\\hat y=b_1\\cdot b_2^{x}",[3166,28196,28198],{"className":3168,"code":28197,"language":71,"meta":3170,"style":3170},"model_pow \u003C- nls2(zisk ~ b1 * (b2^rok))\nsummary(model_pow)\n",[3161,28199,28200,28229],{"__ignoreMap":3170},[1115,28201,28202,28205,28207,28209,28211,28213,28215,28217,28219,28221,28223,28225,28227],{"class":3175,"line":10},[1115,28203,28204],{"class":3178},"model_pow",[1115,28206,3182],{"class":3181},[1115,28208,28114],{"class":3185},[1115,28210,2162],{"class":3189},[1115,28212,1088],{"class":3178},[1115,28214,10574],{"class":3181},[1115,28216,28123],{"class":3178},[1115,28218,3696],{"class":3181},[1115,28220,3677],{"class":3189},[1115,28222,28133],{"class":3178},[1115,28224,12415],{"class":3181},[1115,28226,27912],{"class":3178},[1115,28228,7963],{"class":3189},[1115,28230,28231,28233,28235,28237],{"class":3175,"line":27},[1115,28232,26357],{"class":3185},[1115,28234,2162],{"class":3189},[1115,28236,28204],{"class":3178},[1115,28238,3235],{"class":3189},[3166,28240,28243],{"className":28241,"code":28242,"language":3274,"meta":3170},[3272],"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",[3161,28244,28242],{"__ignoreMap":3170},[1110,28246,28247,28248,28312,28313,28337],{},"Obě varianty popisují stejnou křivku (",[1115,28249,28251],{"className":28250},[1133],[1135,28252,28253],{"xmlns":1137},[1139,28254,28255,28309],{},[1142,28256,28257,28274,28276],{},[4163,28258,28259,28261,28263],{},[1148,28260,21066],{},[1152,28262,2639],{},[1142,28264,28265,28268],{},[2358,28266,28267],{},"mocninn",[2671,28269,28270,28272],{"accent":1121},[2358,28271,10129],{},[1495,28273,21063],{},[1495,28275,1503],{},[2632,28277,28278,28280],{},[1148,28279,18179],{},[1142,28281,28282,28284],{},[2358,28283,2360],{},[4163,28285,28286,28288,28290],{},[1148,28287,21066],{},[1152,28289,2639],{},[1142,28291,28292,28295,28301,28303],{},[2358,28293,28294],{},"exponenci",[2671,28296,28297,28299],{"accent":1121},[2358,28298,1340],{},[1495,28300,21063],{},[2358,28302,27779],{},[2671,28304,28305,28307],{"accent":1121},[2358,28306,21312],{},[1495,28308,21063],{},[1156,28310,28311],{"encoding":1158},"b_2^{\\text{mocninný}} = e^{\\,b_2^{\\text{exponenciální}}}",", zde ",[1115,28314,28316],{"className":28315},[1133],[1135,28317,28318],{"xmlns":1137},[1139,28319,28320,28334],{},[1142,28321,28322,28329,28331],{},[2632,28323,28324,28326],{},[1148,28325,18179],{},[1152,28327,28328],{},"0,4316",[1495,28330,7600],{},[1152,28332,28333],{},"1,540",[1156,28335,28336],{"encoding":1158},"e^{0{,}4316}\\approx 1{,}540",") a mají totožnou reziduální chybu — je to jen otázka parametrizace.",[1695,28339,28341],{"id":28340},"v-r-hyperbolická-regrese","V R — hyperbolická regrese",[1110,28343,28344,28345,1497],{},"Hyperbolická regrese se odhadne jako obyčejná lineární regrese na transformované proměnné ",[3161,28346,28347],{},"I(1\u002Fx)",[3166,28349,28351],{"className":3168,"code":28350,"language":71,"meta":3170,"style":3170},"model_hyperbola \u003C- lm(tydenni_vydaje ~ I(1 \u002F pocet_clenu))\nsummary(model_hyperbola)\n",[3161,28352,28353,28380],{"__ignoreMap":3170},[1115,28354,28355,28358,28360,28362,28364,28366,28368,28370,28372,28374,28376,28378],{"class":3175,"line":10},[1115,28356,28357],{"class":3178},"model_hyperbola",[1115,28359,3182],{"class":3181},[1115,28361,26341],{"class":3185},[1115,28363,2162],{"class":3189},[1115,28365,26296],{"class":3178},[1115,28367,10574],{"class":3181},[1115,28369,28004],{"class":3185},[1115,28371,2162],{"class":3189},[1115,28373,1176],{"class":3192},[1115,28375,7755],{"class":3181},[1115,28377,26350],{"class":3178},[1115,28379,7963],{"class":3189},[1115,28381,28382,28384,28386,28388],{"class":3175,"line":27},[1115,28383,26357],{"class":3185},[1115,28385,2162],{"class":3189},[1115,28387,28357],{"class":3178},[1115,28389,3235],{"class":3189},[3166,28391,28394],{"className":28392,"code":28393,"language":3274,"meta":3170},[3272],"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",[3161,28395,28393],{"__ignoreMap":3170},[1110,28397,28398,28399,28433,28434,28455],{},"Model ",[1115,28400,28402],{"className":28401},[1133],[1135,28403,28404],{"xmlns":1137},[1139,28405,28406,28430],{},[1142,28407,28408,28414,28416,28419,28421],{},[2671,28409,28410,28412],{"accent":1121},[1148,28411,10129],{},[1495,28413,12415],{},[1495,28415,1503],{},[1152,28417,28418],{},"2180,7",[1495,28420,1885],{},[6544,28422,28423],{"scriptlevel":1154,"displaystyle":1121},[2749,28424,28425,28428],{},[1152,28426,28427],{},"1920,0",[1148,28429,2675],{},[1156,28431,28432],{"encoding":1158},"\\hat y = 2180{,}7 - \\dfrac{1920{,}0}{x}"," vysvětluje jen 76,3 % rozptylu — u těchto dat je hyperbola podstatně horší volbou než přímka (",[1115,28435,28437],{"className":28436},[1133],[1135,28438,28439],{"xmlns":1137},[1139,28440,28441,28453],{},[1142,28442,28443,28449,28451],{},[2632,28444,28445,28447],{},[1148,28446,19792],{},[1152,28448,2639],{},[1495,28450,1503],{},[1152,28452,26495],{},[1156,28454,26498],{"encoding":1158},"). Právě k takovému porovnání slouží index determinace: nízká hodnota signalizuje, že zvolený typ funkce k datům nesedí.",[1103,28457,28459,28466,28497,28545],{"className":28458,"dataCallout":3323},[1106,3322],[1110,28460,28462,28465],{"className":28461},[1113],[1115,28463],{"className":28464,"ariaHidden":1121},[1118,3330,1120],"Příklad: Parabolická regrese",[1110,28467,28468,28469,28482,28483,28496],{},"Prodejna počítačových her nechala prodavače absolvovat kurz prodejních dovedností. Při dvaceti měřeních sledovala, kolik zákazníků navštíví prodejnu během prodejní doby (proměnná ",[1115,28470,28472],{"className":28471},[1133],[1135,28473,28474],{"xmlns":1137},[1139,28475,28476,28480],{},[1142,28477,28478],{},[1148,28479,2675],{},[1156,28481,2675],{"encoding":1158},") a jaká je toho dne tržba v tisících Kč (proměnná ",[1115,28484,28486],{"className":28485},[1133],[1135,28487,28488],{"xmlns":1137},[1139,28489,28490,28494],{},[1142,28491,28492],{},[1148,28493,10129],{},[1156,28495,10129],{"encoding":1158},"). Zároveň chtěla zjistit, zda při rostoucím počtu zákazníků stačí stávající počet prodavačů.",[1110,28498,27155,28499,1335],{},[1115,28500,28502],{"className":28501},[1133],[1135,28503,28504],{"xmlns":1137},[1139,28505,28506,28542],{},[1142,28507,28508,28514,28516,28518,28521,28523,28526,28528,28530,28532,28534,28536],{},[2671,28509,28510,28512],{"accent":1121},[1148,28511,10129],{},[1495,28513,12415],{},[1495,28515,1503],{},[1495,28517,1885],{},[1152,28519,28520],{},"60,3",[1495,28522,6294],{},[1152,28524,28525],{},"4,55",[2358,28527,2360],{},[1148,28529,2675],{},[1495,28531,1885],{},[1152,28533,3314],{},[2358,28535,2360],{},[2632,28537,28538,28540],{},[1148,28539,2675],{},[1152,28541,2639],{},[1156,28543,28544],{"encoding":1158},"\\hat y = -60{,}3 + 4{,}55\\,x - 0{,}05\\,x^2",[1110,28546,28547,28548,28566],{},"Záporný koeficient ",[1115,28549,28551],{"className":28550},[1133],[1135,28552,28553],{"xmlns":1137},[1139,28554,28555,28563],{},[1142,28556,28557],{},[1145,28558,28559,28561],{},[1148,28560,21066],{},[1152,28562,2639],{},[1156,28564,28565],{"encoding":1158},"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.",[1103,28568,28570,28577,28607,28652],{"className":28569,"dataCallout":3323},[1106,3322],[1110,28571,28573,28576],{"className":28572},[1113],[1115,28574],{"className":28575,"ariaHidden":1121},[1118,3330,1120],"Příklad: Hyperbolická regrese",[1110,28578,28579,28580,28593,28594,1390],{},"V podniku se podle interního účetnictví sledovala závislost vlastních nákladů na jednotku produkce v Kč (proměnná ",[1115,28581,28583],{"className":28582},[1133],[1135,28584,28585],{"xmlns":1137},[1139,28586,28587,28591],{},[1142,28588,28589],{},[1148,28590,10129],{},[1156,28592,10129],{"encoding":1158},") na objemu produkce v tisících kusů (proměnná ",[1115,28595,28597],{"className":28596},[1133],[1135,28598,28599],{"xmlns":1137},[1139,28600,28601,28605],{},[1142,28602,28603],{},[1148,28604,2675],{},[1156,28606,2675],{"encoding":1158},[1110,28608,27155,28609,1335],{},[1115,28610,28612],{"className":28611},[1133],[1135,28613,28614],{"xmlns":1137},[1139,28615,28616,28649],{},[1142,28617,28618,28624,28626,28628,28631,28633],{},[2671,28619,28620,28622],{"accent":1121},[1148,28621,10129],{},[1495,28623,12415],{},[1495,28625,1503],{},[1495,28627,1885],{},[1152,28629,28630],{},"96,78",[1495,28632,6294],{},[6544,28634,28635],{"scriptlevel":1154,"displaystyle":1121},[2749,28636,28637,28647],{},[1142,28638,28639,28642,28644],{},[1152,28640,28641],{},"250",[2358,28643,2360],{},[1152,28645,28646],{},"528,88",[1148,28648,2675],{},[1156,28650,28651],{"encoding":1158},"\\hat y = -96{,}78 + \\dfrac{250\\,528{,}88}{x}",[1110,28653,28654,28655,28672],{},"Záporná hodnota ",[1115,28656,28658],{"className":28657},[1133],[1135,28659,28660],{"xmlns":1137},[1139,28661,28662,28670],{},[1142,28663,28664],{},[1145,28665,28666,28668],{},[1148,28667,21066],{},[1152,28669,1176],{},[1156,28671,26207],{"encoding":1158}," v čitateli ukazuje klesající náklady na jednotku s rostoucím objemem produkce — typický projev úspor z rozsahu, který hyperbola dobře zachycuje.",[1392,28674,28676],{"id":28675},"kvalita-regresní-funkce-a-korelační-analýza","Kvalita regresní funkce a korelační analýza",[1110,28678,28679,28680,1497],{},"Kvalitu odhadnuté regresní funkce vyjadřuje ",[1399,28681,25500],{},[1115,28683,28685],{"className":28684},[1133],[1135,28686,28687],{"xmlns":1137,"display":2151},[1139,28688,28689,28757],{},[1142,28690,28691,28697,28699,28721,28723,28725,28727,28755],{},[2632,28692,28693,28695],{},[1148,28694,19792],{},[1152,28696,2639],{},[1495,28698,1503],{},[2749,28700,28701,28713],{},[4163,28702,28703,28705,28711],{},[1148,28704,2695],{},[2671,28706,28707,28709],{"accent":1121},[1148,28708,10129],{},[1495,28710,12415],{},[1152,28712,2639],{},[4163,28714,28715,28717,28719],{},[1148,28716,2695],{},[1148,28718,10129],{},[1152,28720,2639],{},[1495,28722,1503],{},[1152,28724,1176],{},[1495,28726,1885],{},[2749,28728,28729,28747],{},[4163,28730,28731,28733,28745],{},[1148,28732,2695],{},[1142,28734,28735,28737,28739],{},[1148,28736,10129],{},[1495,28738,1885],{},[2671,28740,28741,28743],{"accent":1121},[1148,28742,10129],{},[1495,28744,12415],{},[1152,28746,2639],{},[4163,28748,28749,28751,28753],{},[1148,28750,2695],{},[1148,28752,10129],{},[1152,28754,2639],{},[1148,28756,1335],{"mathvariant":1599},[1156,28758,28759],{"encoding":1158},"R^2 = \\frac{s^2_{\\hat y}}{s^2_y} = 1 - \\frac{s^2_{y-\\hat y}}{s^2_y}.",[1110,28761,28762,28763,28780,28781,28794],{},"Čím blíž je ",[1115,28764,28766],{"className":28765},[1133],[1135,28767,28768],{"xmlns":1137},[1139,28769,28770,28778],{},[1142,28771,28772],{},[2632,28773,28774,28776],{},[1148,28775,19792],{},[1152,28777,2639],{},[1156,28779,25518],{"encoding":1158}," k 1, tím silnější je závislost; v procentech udává, jakou část rozptylu závisle proměnné ",[1115,28782,28784],{"className":28783},[1133],[1135,28785,28786],{"xmlns":1137},[1139,28787,28788,28792],{},[1142,28789,28790],{},[1148,28791,10129],{},[1156,28793,10129],{"encoding":1158}," se podařilo vysvětlit zvolenou regresní funkcí. Nízký index determinace může signalizovat špatně zvolený typ regresní funkce, ne nutně absenci závislosti.",[1110,28796,28797,28798,1953,28800,28823,28824,1497],{},"Obecnou mírou těsnosti závislosti — platnou pro libovolný typ regresní funkce — je ",[1399,28799,25522],{},[1115,28801,28803],{"className":28802},[1133],[1135,28804,28805],{"xmlns":1137},[1139,28806,28807,28821],{},[1142,28808,28809,28811,28813],{},[1148,28810,20763],{},[1495,28812,1503],{},[2770,28814,28815],{},[2632,28816,28817,28819],{},[1148,28818,19792],{},[1152,28820,2639],{},[1156,28822,25546],{"encoding":1158},". Je-li zvolenou funkcí regresní přímka, index korelace je roven (až na znaménko) ",[1399,28825,25550],{},[1115,28827,28829],{"className":28828},[1133],[1135,28830,28831],{"xmlns":1137,"display":2151},[1139,28832,28833,28883],{},[1142,28834,28835,28845,28847,28881],{},[1145,28836,28837,28839],{},[1148,28838,71],{},[1142,28840,28841,28843],{},[1148,28842,2675],{},[1148,28844,10129],{},[1495,28846,1503],{},[2749,28848,28849,28859],{},[1145,28850,28851,28853],{},[1148,28852,2695],{},[1142,28854,28855,28857],{},[1148,28856,2675],{},[1148,28858,10129],{},[2770,28860,28861],{},[1142,28862,28863,28871,28873],{},[4163,28864,28865,28867,28869],{},[1148,28866,2695],{},[1148,28868,2675],{},[1152,28870,2639],{},[1495,28872,7548],{},[4163,28874,28875,28877,28879],{},[1148,28876,2695],{},[1148,28878,10129],{},[1152,28880,2639],{},[1148,28882,1335],{"mathvariant":1599},[1156,28884,28885],{"encoding":1158},"r_{xy} = \\frac{s_{xy}}{\\sqrt{s^2_x\\cdot s^2_y}}.",[1110,28887,28888,28889,28905,28906,28922],{},"Koeficient korelace nabývá hodnot od ",[1115,28890,28892],{"className":28891},[1133],[1135,28893,28894],{"xmlns":1137},[1139,28895,28896,28902],{},[1142,28897,28898,28900],{},[1495,28899,1885],{},[1152,28901,1176],{},[1156,28903,28904],{"encoding":1158},"-1"," do ",[1115,28907,28909],{"className":28908},[1133],[1135,28910,28911],{"xmlns":1137},[1139,28912,28913,28919],{},[1142,28914,28915,28917],{},[1495,28916,6294],{},[1152,28918,1176],{},[1156,28920,28921],{"encoding":1158},"+1",": znaménko určuje typ závislosti (pozitivní, nebo negativní), absolutní hodnota její sílu — čím blíž k 0, tím je závislost slabší.",[1110,28924,28925],{},[1971,28926],{"alt":28927,"className":28928,"src":28929},"mask-ra-korelace-sila",[1343,1975],"\u002Fwiki-assets\u002Fmask-ra-korelace-sila.png",[1110,28931,28932,28933,28946,28947,28965,28966,2261,28979,28992],{},"S rostoucí absolutní hodnotou ",[1115,28934,28936],{"className":28935},[1133],[1135,28937,28938],{"xmlns":1137},[1139,28939,28940,28944],{},[1142,28941,28942],{},[1148,28943,71],{},[1156,28945,71],{"encoding":1158}," se body v rozptylovém grafu víc blíží přímce; kolem ",[1115,28948,28950],{"className":28949},[1133],[1135,28951,28952],{"xmlns":1137},[1139,28953,28954,28962],{},[1142,28955,28956,28958,28960],{},[1148,28957,71],{},[1495,28959,7600],{},[1152,28961,1154],{},[1156,28963,28964],{"encoding":1158},"r\\approx 0"," je mezi ",[1115,28967,28969],{"className":28968},[1133],[1135,28970,28971],{"xmlns":1137},[1139,28972,28973,28977],{},[1142,28974,28975],{},[1148,28976,2675],{},[1156,28978,2675],{"encoding":1158},[1115,28980,28982],{"className":28981},[1133],[1135,28983,28984],{"xmlns":1137},[1139,28985,28986,28990],{},[1142,28987,28988],{},[1148,28989,10129],{},[1156,28991,10129],{"encoding":1158}," patrná jen náhodná rozptýlenost bez lineárního trendu.",[1695,28994,26240],{"id":28995},"v-r-1",[3166,28997,28999],{"className":3168,"code":28998,"language":71,"meta":3170,"style":3170},"cor(pocet_clenu, tydenni_vydaje)\n",[3161,29000,29001],{"__ignoreMap":3170},[1115,29002,29003,29006,29008,29010,29012,29015],{"class":3175,"line":10},[1115,29004,29005],{"class":3185},"cor",[1115,29007,2162],{"class":3189},[1115,29009,26261],{"class":3178},[1115,29011,2188],{"class":3181},[1115,29013,29014],{"class":3178}," tydenni_vydaje",[1115,29016,3235],{"class":3189},[3166,29018,29021],{"className":29019,"code":29020,"language":3274,"meta":3170},[3272],"[1] 0.9997441\n",[3161,29022,29020],{"__ignoreMap":3170},[1110,29024,29025,29026,29052],{},"Hodnota 0,9997 odpovídá ",[1115,29027,29029],{"className":29028},[1133],[1135,29030,29031],{"xmlns":1137},[1139,29032,29033,29049],{},[1142,29034,29035,29043,29045],{},[2770,29036,29037],{},[2632,29038,29039,29041],{},[1148,29040,19792],{},[1152,29042,2639],{},[1495,29044,1503],{},[2770,29046,29047],{},[1152,29048,26495],{},[1156,29050,29051],{"encoding":1158},"\\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.",[1103,29054,29056,29063,29066],{"className":29055,"dataCallout":3323},[1106,3322],[1110,29057,29059,29062],{"className":29058},[1113],[1115,29060],{"className":29061,"ariaHidden":1121},[1118,3330,1120],"Příklad: Koeficient korelace",[1110,29064,29065],{},"Pro stejná data o hodnotě produkce a výši investic dvanácti firem jako u regresní přímky byl spočten koeficient korelace mezi oběma proměnnými.",[1110,29067,27155,29068,29095],{},[1115,29069,29071],{"className":29070},[1133],[1135,29072,29073],{"xmlns":1137},[1139,29074,29075,29092],{},[1142,29076,29077,29087,29089],{},[1145,29078,29079,29081],{},[1148,29080,71],{},[1142,29082,29083,29085],{},[1148,29084,2675],{},[1148,29086,10129],{},[1495,29088,1503],{},[1152,29090,29091],{},"0,739",[1156,29093,29094],{"encoding":1158},"r_{xy} = 0{,}739"," — silná kladná závislost hodnoty produkce na výši investic.",[1392,29097,29099],{"id":29098},"vícenásobná-regrese-a-korelace","Vícenásobná regrese a korelace",[1110,29101,29102,29103,29116],{},"Pokud na závisle proměnnou ",[1115,29104,29106],{"className":29105},[1133],[1135,29107,29108],{"xmlns":1137},[1139,29109,29110,29114],{},[1142,29111,29112],{},[1148,29113,10129],{},[1156,29115,10129],{"encoding":1158}," působí víc vysvětlujících proměnných současně, analyzuje se zvlášť vliv každé z nich a výsledná regresní funkce se konstruuje jako součet jednoduchých regresních funkcí:",[1115,29118,29120],{"className":29119},[1133],[1135,29121,29122],{"xmlns":1137,"display":2151},[1139,29123,29124,29234],{},[1142,29125,29126,29128,29130,29136,29138,29144,29150,29152,29158,29164,29166,29168,29170,29176,29182,29184,29186,29192,29194,29200,29202,29208,29214,29216,29218,29220,29226,29232],{},[1148,29127,25815],{},[1495,29129,1503],{},[1145,29131,29132,29134],{},[1148,29133,1262],{},[1152,29135,1154],{},[1495,29137,6294],{},[1145,29139,29140,29142],{},[1148,29141,1262],{},[1152,29143,1176],{},[1145,29145,29146,29148],{},[1148,29147,2675],{},[1152,29149,1176],{},[1495,29151,6294],{},[1145,29153,29154,29156],{},[1148,29155,1262],{},[1152,29157,2639],{},[1145,29159,29160,29162],{},[1148,29161,2675],{},[1152,29163,2639],{},[1495,29165,6294],{},[1495,29167,27405],{},[1495,29169,6294],{},[1145,29171,29172,29174],{},[1148,29173,1262],{},[1148,29175,1110],{},[1145,29177,29178,29180],{},[1148,29179,2675],{},[1148,29181,1110],{},[1495,29183,2188],{"separator":1121},[3520,29185],{"width":3522},[2671,29187,29188,29190],{"accent":1121},[1148,29189,10129],{},[1495,29191,12415],{},[1495,29193,1503],{},[1145,29195,29196,29198],{},[1148,29197,21066],{},[1152,29199,1154],{},[1495,29201,6294],{},[1145,29203,29204,29206],{},[1148,29205,21066],{},[1152,29207,1176],{},[1145,29209,29210,29212],{},[1148,29211,2675],{},[1152,29213,1176],{},[1495,29215,6294],{},[1495,29217,27405],{},[1495,29219,6294],{},[1145,29221,29222,29224],{},[1148,29223,21066],{},[1148,29225,1110],{},[1145,29227,29228,29230],{},[1148,29229,2675],{},[1148,29231,1110],{},[1148,29233,1335],{"mathvariant":1599},[1156,29235,29236],{"encoding":1158},"\\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.",[1695,29238,29240],{"id":29239},"výběr-proměnných","Výběr proměnných",[1124,29242,29243,29249],{},[1127,29244,29245,29248],{},[1399,29246,29247],{},"Metoda ENTER"," — vloží do modelu všechny proměnné najednou. Použije se, když jde o index determinace celého modelu, o vliv každé nezávislé proměnné při kontrole vlivu ostatních, nebo o relativní důležitost proměnných. Vyžaduje poměrně vysoký počet pozorování — aspoň 20 na každou proměnnou.",[1127,29250,29251,29254,29255,29258,29259,29262],{},[1399,29252,29253],{},"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 ",[1399,29256,29257],{},"forward"," proměnné postupně přidává, varianta ",[1399,29260,29261],{},"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.",[1695,29264,29266],{"id":29265},"postup-odhadu","Postup odhadu",[2239,29268,29269,29272,29275],{},[1127,29270,29271],{},"ověření předpokladů regresního modelu,",[1127,29273,29274],{},"samotný odhad parametrů,",[1127,29276,29277],{},"reziduální analýza výsledného modelu.",[1110,29279,29280,29281,29298,29299,2324,29301,29330,29331,29360,29361,29378],{},"Důležitost každého parametru ",[1115,29282,29284],{"className":29283},[1133],[1135,29285,29286],{"xmlns":1137},[1139,29287,29288,29296],{},[1142,29289,29290],{},[1145,29291,29292,29294],{},[1148,29293,21066],{},[1148,29295,4085],{},[1156,29297,25954],{"encoding":1158}," v modelu ověřuje ",[1399,29300,992],{},[1115,29302,29304],{"className":29303},[1133],[1135,29305,29306],{"xmlns":1137},[1139,29307,29308,29328],{},[1142,29309,29310,29316,29318,29324,29326],{},[1145,29311,29312,29314],{},[1148,29313,1150],{},[1152,29315,1154],{},[1495,29317,1497],{},[1145,29319,29320,29322],{},[1148,29321,1262],{},[1148,29323,4085],{},[1495,29325,1503],{},[1152,29327,1154],{},[1156,29329,26439],{"encoding":1158}," (proměnná je v modelu nevýznamná) proti ",[1115,29332,29334],{"className":29333},[1133],[1135,29335,29336],{"xmlns":1137},[1139,29337,29338,29358],{},[1142,29339,29340,29346,29348,29354,29356],{},[1145,29341,29342,29344],{},[1148,29343,1150],{},[1152,29345,1176],{},[1495,29347,1497],{},[1145,29349,29350,29352],{},[1148,29351,1262],{},[1148,29353,4085],{},[1495,29355,1600],{"mathvariant":1599},[1152,29357,1154],{},[1156,29359,26470],{"encoding":1158}," (proměnná je významná). Při nezamítnutí ",[1115,29362,29364],{"className":29363},[1133],[1135,29365,29366],{"xmlns":1137},[1139,29367,29368,29376],{},[1142,29369,29370],{},[1145,29371,29372,29374],{},[1148,29373,1150],{},[1152,29375,1154],{},[1156,29377,1159],{"encoding":1158}," by proměnná — a s ní spojený regresor — v modelu neměla zůstat.",[1695,29380,29382],{"id":29381},"předpoklady-modelu","Předpoklady modelu",[2239,29384,29385,29402,29435,29441,29444,29447],{},[1127,29386,29387,29388,29401],{},"Závisle proměnná ",[1115,29389,29391],{"className":29390},[1133],[1135,29392,29393],{"xmlns":1137},[1139,29394,29395,29399],{},[1142,29396,29397],{},[1148,29398,10129],{},[1156,29400,10129],{"encoding":1158}," musí být aspoň intervalového typu (ne binární, diskrétní s málo hodnotami apod.) — jinak je na místě logistická regrese.",[1127,29403,29404,29405,29434],{},"Nezávislé proměnné ",[1115,29406,29408],{"className":29407},[1133],[1135,29409,29410],{"xmlns":1137},[1139,29411,29412,29432],{},[1142,29413,29414,29420,29422,29424,29426],{},[1145,29415,29416,29418],{},[1148,29417,2675],{},[1152,29419,1176],{},[1495,29421,2188],{"separator":1121},[1495,29423,10697],{},[1495,29425,2188],{"separator":1121},[1145,29427,29428,29430],{},[1148,29429,2675],{},[1148,29431,1110],{},[1156,29433,25779],{"encoding":1158}," jsou rovněž aspoň intervalového typu, mohou být i alternativní.",[1127,29436,29437,29438,1335],{},"Nezávislé proměnné by mezi sebou neměly být příliš vysoce korelované — ",[1399,29439,29440],{},"multikolinearita",[1127,29442,29443],{},"V datech nesmí být odlehlé či extrémní hodnoty; regresní analýza je na ně citlivá a mohou vážně narušit kvalitu odhadů.",[1127,29445,29446],{},"Proměnné musí být ve vzájemně lineárním vztahu — vícenásobná lineární regrese je založená na Pearsonově koeficientu korelace, takže nelineární vztahy mezi proměnnými zůstanou neodhalené.",[1127,29448,29449,29450,29454],{},"Proměnné mají mít ",[1340,29451,29453],{"className":29452,"dataFsResolvedFilePath":1358,"href":1359},[1343],"normální rozložení","; význam tohoto předpokladu ustupuje do pozadí u dostatečně velkého datového souboru díky centrální limitní větě.",[1110,29456,29457,29458,29461],{},"Normalita se u menšího počtu pozorování ověřuje stejnými testy jako u jiných znaků (viz ",[1340,29459,11428],{"className":29460,"dataFsResolvedFilePath":11426,"href":11427},[1343],") — 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.",[1695,29463,29464],{"id":29440},"Multikolinearita",[1110,29466,29467],{},"Multikolinearita vzniká, když vysvětlující proměnné silně závisejí jedna na druhé. Je nežádoucí, protože:",[1124,29469,29470,29473,29476],{},[1127,29471,29472],{},"výsledky regrese jsou pak nespolehlivé,",[1127,29474,29475],{},"zvyšuje pravděpodobnost, že se důležitá proměnná jeví jako statisticky nevýznamná a bude z modelu vyřazena,",[1127,29477,29478],{},"směrodatné odchylky odhadnutých parametrů jsou vysoké, testová kritéria t-testů nízká, p-hodnoty vysoké.",[1110,29480,29481,29482,29485,29486,29509,29510,29528,29529,29545],{},"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 ",[1399,29483,29484],{},"VIF (Variance Inflation Factor)",": hodnoty ",[1115,29487,29489],{"className":29488},[1133],[1135,29490,29491],{"xmlns":1137},[1139,29492,29493,29506],{},[1142,29494,29495,29497,29499,29502,29504],{},[1152,29496,1176],{},[1495,29498,1682],{},[2358,29500,29501],{},"VIF",[1495,29503,1682],{},[1152,29505,9817],{},[1156,29507,29508],{"encoding":1158},"1\u003C\\text{VIF}\u003C5"," jsou varující, ",[1115,29511,29513],{"className":29512},[1133],[1135,29514,29515],{"xmlns":1137},[1139,29516,29517,29525],{},[1142,29518,29519,29521,29523],{},[2358,29520,29501],{},[1495,29522,1641],{},[1152,29524,9817],{},[1156,29526,29527],{"encoding":1158},"\\text{VIF}>5"," (přísněji ",[1115,29530,29532],{"className":29531},[1133],[1135,29533,29534],{"xmlns":1137},[1139,29535,29536,29542],{},[1142,29537,29538,29540],{},[1495,29539,1641],{},[1152,29541,4717],{},[1156,29543,29544],{"encoding":1158},">10",") značí vysokou multikolinearitu.",[1110,29547,29548],{},"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.",[1695,29550,29552],{"id":29551},"další-ukazatele-kvality-modelu","Další ukazatele kvality modelu",[1124,29554,29555,29560,29566],{},[1127,29556,29557,29559],{},[1399,29558,10835],{}," — testuje hypotézu, že všechny regresní koeficienty jsou rovny nule, proti alternativě, že aspoň jeden v modelu být má (celková významnost modelu).",[1127,29561,29562,29565],{},[1399,29563,29564],{},"RMSE"," (odmocnina z reziduálního rozptylu) — absolutní měřítko vhodnosti funkce (na rozdíl od indexu determinace, který je relativní); nižší hodnota znamená lepší fit.",[1127,29567,29568,29571,29572,29575],{},[1399,29569,29570],{},"AIC"," (Akaikeho informační kritérium) a ",[1399,29573,29574],{},"BIC"," (Bayesovo informační kritérium) — čím nižší hodnoty obou kritérií, tím lepší model; používají se hlavně při stepwise výběru proměnných.",[1695,29577,26240],{"id":29578},"v-r-2",[1110,29580,29581],{},"Pro vícenásobnou regresi je postup v R rozšířením postupu pro regresní přímku — přibývá výběr proměnných a kontrola multikolinearity:",[3166,29583,29585],{"className":3168,"code":29584,"language":71,"meta":3170,"style":3170},"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",[3161,29586,29587,29613,29656,29682,29692,29696,29707,29718,29722,29732,29742,29746,29756,29766,29771],{"__ignoreMap":3170},[1115,29588,29589,29592,29594,29597,29599,29602,29604,29607,29609,29611],{"class":3175,"line":10},[1115,29590,29591],{"class":3178},"data",[1115,29593,3182],{"class":3181},[1115,29595,29596],{"class":3185}," read.table",[1115,29598,2162],{"class":3189},[1115,29600,29601],{"class":3265},"\"4_4.txt\"",[1115,29603,2188],{"class":3181},[1115,29605,29606],{"class":3178}," header",[1115,29608,3252],{"class":3181},[1115,29610,5282],{"class":3192},[1115,29612,3235],{"class":3189},[1115,29614,29615,29618,29620,29622,29624,29626,29628,29631,29633,29636,29638,29641,29643,29646,29648,29650,29652,29654],{"class":3175,"line":27},[1115,29616,29617],{"class":3178},"model_plny",[1115,29619,3182],{"class":3181},[1115,29621,26341],{"class":3185},[1115,29623,2162],{"class":3189},[1115,29625,10129],{"class":3178},[1115,29627,10574],{"class":3181},[1115,29629,29630],{"class":3178}," x1",[1115,29632,7877],{"class":3181},[1115,29634,29635],{"class":3178}," x2",[1115,29637,7877],{"class":3181},[1115,29639,29640],{"class":3178}," x3",[1115,29642,7877],{"class":3181},[1115,29644,29645],{"class":3178}," x4",[1115,29647,2188],{"class":3181},[1115,29649,10582],{"class":3178},[1115,29651,3252],{"class":3181},[1115,29653,10582],{"class":3178},[1115,29655,3235],{"class":3189},[1115,29657,29658,29661,29663,29666,29668,29670,29672,29675,29677,29680],{"class":3175,"line":148},[1115,29659,29660],{"class":3178},"model_krok",[1115,29662,3182],{"class":3181},[1115,29664,29665],{"class":3185}," step",[1115,29667,2162],{"class":3189},[1115,29669,29617],{"class":3178},[1115,29671,2188],{"class":3181},[1115,29673,29674],{"class":3178}," direction",[1115,29676,3252],{"class":3181},[1115,29678,29679],{"class":3265}," \"both\"",[1115,29681,3235],{"class":3189},[1115,29683,29684,29686,29688,29690],{"class":3175,"line":111},[1115,29685,26357],{"class":3185},[1115,29687,2162],{"class":3189},[1115,29689,29660],{"class":3178},[1115,29691,3235],{"class":3189},[1115,29693,29694],{"class":3175,"line":96},[1115,29695,19612],{"emptyLinePlaceholder":11218},[1115,29697,29698,29700,29702,29705],{"class":3175,"line":89},[1115,29699,10627],{"class":3181},[1115,29701,2162],{"class":3189},[1115,29703,29704],{"class":3178},"car",[1115,29706,3235],{"class":3189},[1115,29708,29709,29712,29714,29716],{"class":3175,"line":82},[1115,29710,29711],{"class":3185},"vif",[1115,29713,2162],{"class":3189},[1115,29715,29660],{"class":3178},[1115,29717,3235],{"class":3189},[1115,29719,29720],{"class":3175,"line":75},[1115,29721,19612],{"emptyLinePlaceholder":11218},[1115,29723,29724,29726,29728,29730],{"class":3175,"line":9681},[1115,29725,10627],{"class":3181},[1115,29727,2162],{"class":3189},[1115,29729,26890],{"class":3178},[1115,29731,3235],{"class":3189},[1115,29733,29734,29736,29738,29740],{"class":3175,"line":72},[1115,29735,26897],{"class":3185},[1115,29737,2162],{"class":3189},[1115,29739,29660],{"class":3178},[1115,29741,3235],{"class":3189},[1115,29743,29744],{"class":3175,"line":25},[1115,29745,19612],{"emptyLinePlaceholder":11218},[1115,29747,29748,29750,29752,29754],{"class":3175,"line":65},[1115,29749,10627],{"class":3181},[1115,29751,2162],{"class":3189},[1115,29753,26980],{"class":3178},[1115,29755,3235],{"class":3189},[1115,29757,29758,29760,29762,29764],{"class":3175,"line":63},[1115,29759,26987],{"class":3185},[1115,29761,2162],{"class":3189},[1115,29763,29660],{"class":3178},[1115,29765,3235],{"class":3189},[1115,29767,29769],{"class":3175,"line":29768},14,[1115,29770,19612],{"emptyLinePlaceholder":11218},[1115,29772,29773,29775,29777,29779,29781,29783],{"class":3175,"line":60},[1115,29774,3998],{"class":3185},[1115,29776,2162],{"class":3189},[1115,29778,26534],{"class":3185},[1115,29780,2162],{"class":3189},[1115,29782,29660],{"class":3178},[1115,29784,7963],{"class":3189},[1110,29786,29787,29789,29790,29793],{},[3161,29788,25613],{}," provádí stepwise výběr podle AIC, ",[3161,29791,29792],{},"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.",[1103,29795,29797,29804,29807,29810],{"className":29796,"dataCallout":3323},[1106,3322],[1110,29798,29800,29803],{"className":29799},[1113],[1115,29801],{"className":29802,"ariaHidden":1121},[1118,3330,1120],"Příklad: Vícenásobná regrese",[1110,29805,29806],{},"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.",[1110,29808,29809],{},"Postup: odhad plného modelu → stepwise analýza podle AIC → ověření předpokladů.",[1110,29811,29812,29813,29816,29817,29819,29820,29823],{},"Diagnostika odhaleného modelu ukázala tři problémy: (1) ",[1399,29814,29815],{},"nelinearita"," — mezi některými vysvětlujícími proměnnými a cenou je zjevně jiný než lineární vztah, řešením je zkusit u nich druhou mocninu; (2) ",[1399,29818,29440],{}," mezi dvojicí proměnných popisujících vzdálenost (k silnici a ke spalovně) — doporučeno jednu z nich vynechat; (3) ",[1399,29821,29822],{},"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.",[1392,29825,10963],{"id":10962},[1103,29827,29829,29836],{"className":29828,"dataCallout":5141},[1106,5140],[1110,29830,29832,29835],{"className":29831},[1113],[1115,29833],{"className":29834,"ariaHidden":1121},[1118,5148,1120],"Koeficient korelace jen pro přímku",[1110,29837,29838,29839,29895,29896,29913,29914,29934,29935,2261,29948,1335],{},"Vzorec ",[1115,29840,29842],{"className":29841},[1133],[1135,29843,29844],{"xmlns":1137},[1139,29845,29846,29892],{},[1142,29847,29848,29858,29860,29870,29872],{},[1145,29849,29850,29852],{},[1148,29851,71],{},[1142,29853,29854,29856],{},[1148,29855,2675],{},[1148,29857,10129],{},[1495,29859,1503],{},[1145,29861,29862,29864],{},[1148,29863,2695],{},[1142,29865,29866,29868],{},[1148,29867,2675],{},[1148,29869,10129],{},[1148,29871,3049],{"mathvariant":1599},[2770,29873,29874],{},[1142,29875,29876,29884],{},[4163,29877,29878,29880,29882],{},[1148,29879,2695],{},[1148,29881,2675],{},[1152,29883,2639],{},[4163,29885,29886,29888,29890],{},[1148,29887,2695],{},[1148,29889,10129],{},[1152,29891,2639],{},[1156,29893,29894],{"encoding":1158},"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 ",[1115,29897,29899],{"className":29898},[1133],[1135,29900,29901],{"xmlns":1137},[1139,29902,29903,29911],{},[1142,29904,29905],{},[2632,29906,29907,29909],{},[1148,29908,19792],{},[1152,29910,2639],{},[1156,29912,25518],{"encoding":1158},", případně obecným indexem korelace ",[1115,29915,29917],{"className":29916},[1133],[1135,29918,29919],{"xmlns":1137},[1139,29920,29921,29931],{},[1142,29922,29923],{},[2770,29924,29925],{},[2632,29926,29927,29929],{},[1148,29928,19792],{},[1152,29930,2639],{},[1156,29932,29933],{"encoding":1158},"\\sqrt{R^2}"," — ne koeficientem korelace mezi ",[1115,29936,29938],{"className":29937},[1133],[1135,29939,29940],{"xmlns":1137},[1139,29941,29942,29946],{},[1142,29943,29944],{},[1148,29945,2675],{},[1156,29947,2675],{"encoding":1158},[1115,29949,29951],{"className":29950},[1133],[1135,29952,29953],{"xmlns":1137},[1139,29954,29955,29959],{},[1142,29956,29957],{},[1148,29958,10129],{},[1156,29960,10129],{"encoding":1158},[1103,29962,29964,29971],{"className":29963,"dataCallout":5141},[1106,5140],[1110,29965,29967,29970],{"className":29966},[1113],[1115,29968],{"className":29969,"ariaHidden":1121},[1118,5148,1120],"Významný F-test, nevýznamné t-testy",[1110,29972,29973],{},"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.",[1103,29975,29977,29984],{"className":29976,"dataCallout":5141},[1106,5140],[1110,29978,29980,29983],{"className":29979},[1113],[1115,29981],{"className":29982,"ariaHidden":1121},[1118,5148,1120],"Durbin-Watsonova statistika mimo okolí 2",[1110,29985,29986],{},"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.",[1103,29988,29990,29997],{"className":29989,"dataCallout":5141},[1106,5140],[1110,29991,29993,29996],{"className":29992},[1113],[1115,29994],{"className":29995,"ariaHidden":1121},[1118,5148,1120],"Nízký počet pozorování při stepwise výběru",[1110,29998,29999],{},"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.",[1392,30001,11120],{"id":11119},[1124,30003,30004,30009,30014,30019,30024,30029,30034],{},[1127,30005,30006],{},[1340,30007,11128],{"className":30008,"dataFsResolvedFilePath":1344,"href":1345},[1343],[1127,30010,30011],{},[1340,30012,11134],{"className":30013,"dataFsResolvedFilePath":1358,"href":1359},[1343],[1127,30015,30016],{},[1340,30017,11140],{"className":30018,"dataFsResolvedFilePath":1351,"href":1352},[1343],[1127,30020,30021],{},[1340,30022,1094],{"className":30023,"dataFsResolvedFilePath":11426,"href":11427},[1343],[1127,30025,30026],{},[1340,30027,11156],{"className":30028,"dataFsResolvedFilePath":11154,"href":11155},[1343],[1127,30030,30031],{},[1340,30032,11164],{"className":30033,"dataFsResolvedFilePath":11162,"href":11163},[1343],[1127,30035,30036],{},[1340,30037,11172],{"className":30038,"dataFsResolvedFilePath":11170,"href":11171},[1343],[1392,30040,11175],{"id":934},[1110,30042,11178,30043,11182],{},[10079,30044,11181],{},[11184,30046,30047],{},"html pre.shiki 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diagram zobrazuje vývoj variability procesu v čase a dává signál, že na proces začala působit vymezitelná příčina: bod mimo akční meze UCL a LCL.",[1127,30106,30107,30108,1195,30134,2261,30160,1335],{},"Regulace měřením (spojitá veličina s normálním rozdělením): diagramy ",[1115,30109,30111],{"className":30110},[1133],[1135,30112,30113],{"xmlns":1137},[1139,30114,30115,30131],{},[1142,30116,30117,30119,30125,30127,30129],{},[1495,30118,2162],{"stretchy":2161},[2671,30120,30121,30123],{"accent":1121},[1148,30122,2675],{},[1495,30124,2678],{},[1495,30126,2188],{"separator":1121},[1148,30128,19792],{},[1495,30130,2181],{"stretchy":2161},[1156,30132,30133],{"encoding":1158},"(\\bar{x}, R)",[1115,30135,30137],{"className":30136},[1133],[1135,30138,30139],{"xmlns":1137},[1139,30140,30141,30157],{},[1142,30142,30143,30145,30151,30153,30155],{},[1495,30144,2162],{"stretchy":2161},[2671,30146,30147,30149],{"accent":1121},[1148,30148,2675],{},[1495,30150,2678],{},[1495,30152,2188],{"separator":1121},[1148,30154,2695],{},[1495,30156,2181],{"stretchy":2161},[1156,30158,30159],{"encoding":1158},"(\\bar{x}, s)",[1115,30161,30163],{"className":30162},[1133],[1135,30164,30165],{"xmlns":1137},[1139,30166,30167,30196],{},[1142,30168,30169,30171,30177,30179,30194],{},[1495,30170,2162],{"stretchy":2161},[1145,30172,30173,30175],{},[1148,30174,2675],{},[1148,30176,4085],{},[1495,30178,2188],{"separator":1121},[1145,30180,30181,30183],{},[1148,30182,19792],{},[1142,30184,30185,30187,30190,30192],{},[1148,30186,10710],{},[1148,30188,30189],{},"l",[1495,30191,2188],{"separator":1121},[1148,30193,4085],{},[1495,30195,2181],{"stretchy":2161},[1156,30197,30198],{"encoding":1158},"(x_i, R_{kl,i})",[1127,30200,30201,30202,30215,30216,30229,30230,30246,30247,30260],{},"Regulace srovnáváním (diskrétní veličina): počet neshod ",[1115,30203,30205],{"className":30204},[1133],[1135,30206,30207],{"xmlns":1137},[1139,30208,30209,30213],{},[1142,30210,30211],{},[1148,30212,1991],{},[1156,30214,1991],{"encoding":1158}," (konstantní rozsah) a ",[1115,30217,30219],{"className":30218},[1133],[1135,30220,30221],{"xmlns":1137},[1139,30222,30223,30227],{},[1142,30224,30225],{},[1148,30226,21090],{},[1156,30228,21090],{"encoding":1158}," (nekonstantní rozsah), počet neshodných produktů ",[1115,30231,30233],{"className":30232},[1133],[1135,30234,30235],{"xmlns":1137},[1139,30236,30237,30243],{},[1142,30238,30239,30241],{},[1148,30240,2657],{},[1148,30242,1110],{},[1156,30244,30245],{"encoding":1158},"np"," (konstantní rozsah) a jejich podíl ",[1115,30248,30250],{"className":30249},[1133],[1135,30251,30252],{"xmlns":1137},[1139,30253,30254,30258],{},[1142,30255,30256],{},[1148,30257,1110],{},[1156,30259,1110],{"encoding":1158}," (nekonstantní rozsah).",[1127,30262,30263],{},"Podskupiny s vymezitelnou příčinou se po jejím odstranění z výpočtu vyřadí a meze se přepočítají, dokud jsou všechny body uvnitř mezí.",[1127,30265,30266,30267,1195,30286,1195,30308,1195,30330,30354,30355,30376],{},"Indexy způsobilosti ",[1115,30268,30270],{"className":30269},[1133],[1135,30271,30272],{"xmlns":1137},[1139,30273,30274,30283],{},[1142,30275,30276],{},[1145,30277,30278,30281],{},[1148,30279,30280],{},"C",[1148,30282,1110],{},[1156,30284,30285],{"encoding":1158},"C_p",[1115,30287,30289],{"className":30288},[1133],[1135,30290,30291],{"xmlns":1137},[1139,30292,30293,30305],{},[1142,30294,30295],{},[1145,30296,30297,30299],{},[1148,30298,30280],{},[1142,30300,30301,30303],{},[1148,30302,1110],{},[1148,30304,10710],{},[1156,30306,30307],{"encoding":1158},"C_{pk}",[1115,30309,30311],{"className":30310},[1133],[1135,30312,30313],{"xmlns":1137},[1139,30314,30315,30327],{},[1142,30316,30317],{},[1145,30318,30319,30321],{},[1148,30320,30280],{},[1142,30322,30323,30325],{},[1148,30324,1110],{},[1148,30326,14104],{},[1156,30328,30329],{"encoding":1158},"C_{pm}",[1115,30331,30333],{"className":30332},[1133],[1135,30334,30335],{"xmlns":1137},[1139,30336,30337,30351],{},[1142,30338,30339],{},[1145,30340,30341,30343],{},[1148,30342,30280],{},[1142,30344,30345,30347,30349],{},[1148,30346,1110],{},[1148,30348,14104],{},[1148,30350,10710],{},[1156,30352,30353],{"encoding":1158},"C_{pmk}"," posuzují, zda statisticky zvládnutý proces vyhovuje tolerančním mezím; ",[1115,30356,30358],{"className":30357},[1133],[1135,30359,30360],{"xmlns":1137},[1139,30361,30362,30374],{},[1142,30363,30364],{},[1145,30365,30366,30368],{},[1148,30367,30280],{},[1142,30369,30370,30372],{},[1148,30371,1110],{},[1148,30373,10710],{},[1156,30375,30307],{"encoding":1158}," navíc zohledňuje vychýlení střední hodnoty.",[1127,30378,30379,30380,1335],{},"V R diagramy i indexy počítá balíček ",[3161,30381,360],{},[1392,30383,30385],{"id":30384},"statistická-regulace-procesu","Statistická regulace procesu",[1110,30387,30388,30389,30391,30392,1335],{},"Tradiční zabezpečování jakosti kontroluje výrobky až po jejich vyrobení, což je neekonomické. ",[1399,30390,30385],{}," 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 ",[1399,30393,30394],{},"statisticky zvládnutém stavu",[1110,30396,30397,30398,30401],{},"Teorie regulace vychází z ",[1399,30399,30400],{},"variability"," procesu, kterou způsobují dva druhy příčin:",[1532,30403,30404,30416],{},[1535,30405,30406],{},[1538,30407,30408,30410,30413],{},[1541,30409],{},[1541,30411,30412],{},"Náhodné příčiny",[1541,30414,30415],{},"Vymezitelné příčiny",[1568,30417,30418,30429,30440],{},[1538,30419,30420,30423,30426],{},[1573,30421,30422],{},"Povaha",[1573,30424,30425],{},"široká skupina neidentifikovatelných vlivů, každý přispívá k variabilitě malou měrou",[1573,30427,30428],{},"vlivy, které za běžných podmínek na proces nepůsobí; vyvolají nepřirozené kolísání údajů",[1538,30430,30431,30434,30437],{},[1573,30432,30433],{},"Stav procesu",[1573,30435,30436],{},"ustálený, jakost výstupů je předvídatelná, není nutné zasahovat — statisticky zvládnutý",[1573,30438,30439],{},"jakost výstupů není předvídatelná, je nutné zasáhnout — proces není statisticky zvládnutý",[1538,30441,30442,30445,30448],{},[1573,30443,30444],{},"Příklady",[1573,30446,30447],{},"psychický stav pracovníka, chvění stroje, teplota ovzduší",[1573,30449,30450],{},"změna materiálu, nezaškolená obsluha",[1110,30452,30453,30454,30457,30458,30461],{},"Vymezitelné příčiny jsou ",[1399,30455,30456],{},"sporadické"," (vznikají náhle, změny trvají krátce) nebo ",[1399,30459,30460],{},"přetrvávající"," (trvají stále nebo se mění).",[1110,30463,30464],{},[1971,30465],{"alt":30466,"className":30467,"src":30468},"mask-ilu-pricin-variability",[1343,1975],"\u002Fwiki-assets\u002Fmask-ilu-pricin-variability.png",[1110,30470,30471],{},"Regulace probíhá ve třech fázích:",[2239,30473,30474,30484,30490],{},[1127,30475,30476,30479,30480,30483],{},[1399,30477,30478],{},"Fáze přípravná"," — stanoví se sledované znaky jakosti (rozměr, hmotnost, počet vad…), délka časového intervalu mezi měřeními, ",[1399,30481,30482],{},"logická podskupina"," (skupina měření, v níž se předpokládá působení pouze náhodných příčin), typ regulačního diagramu a místa kontroly v procesu.",[1127,30485,30486,30489],{},[1399,30487,30488],{},"Fáze zabezpečování statistické zvládnutosti"," — pomocí regulačních diagramů se identifikují vymezitelné příčiny a odstraní se jejich působení.",[1127,30491,30492,30495],{},[1399,30493,30494],{},"Fáze analýzy a zabezpečení způsobilosti"," — zkoumá se, zda statisticky zvládnutý proces vyhovuje požadavkům zákazníka; k tomu slouží indexy způsobilosti (níže).",[1392,30497,30499],{"id":30498},"princip-regulačního-diagramu","Princip regulačního diagramu",[1110,30501,30502,30505],{},[1399,30503,30504],{},"Regulační diagram"," je grafický prostředek pro zobrazení vývoje variability procesu v čase. Popisuje statistickou zvládnutelnost procesu a dává signál, že na proces začala působit vymezitelná příčina; na jeho základě se do procesu zasáhne s cílem příčinu odstranit.",[1124,30507,30508,30514,30520],{},[1127,30509,30510,30513],{},[1399,30511,30512],{},"CL"," — střední přímka, odpovídá požadované (referenční) hodnotě použité charakteristiky,",[1127,30515,30516,30519],{},[1399,30517,30518],{},"UCL"," — horní akční regulační mez,",[1127,30521,30522,30525],{},[1399,30523,30524],{},"LCL"," — dolní akční regulační mez.",[1110,30527,30528],{},"Akční meze vymezují pásmo působení pouze náhodných příčin variability.",[1110,30530,30531],{},[1971,30532],{"alt":30533,"className":30534,"src":30535},"mask-rd-schema",[1343,1975],"\u002Fwiki-assets\u002Fmask-rd-schema.png",[1110,30537,30538,30541],{},[1399,30539,30540],{},"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.",[1110,30543,30544,30545,30548,30549,30552],{},"Podle charakteru regulované veličiny se diagramy dělí na diagramy pro ",[1399,30546,30547],{},"regulaci měřením"," (regulovaná veličina je spojitá náhodná veličina) a pro ",[1399,30550,30551],{},"regulaci srovnáváním"," (diskrétní náhodná veličina).",[1110,30554,30555],{},"Postup při konstrukci regulačního diagramu:",[2239,30557,30558,30561,30564,30567,30570,30573,30576,30579,30582],{},[1127,30559,30560],{},"volba regulované veličiny,",[1127,30562,30563],{},"sběr a záznam dat,",[1127,30565,30566],{},"ověření požadovaných předpokladů o datech,",[1127,30568,30569],{},"volba rozsahu logických podskupin,",[1127,30571,30572],{},"volba vhodného regulačního diagramu,",[1127,30574,30575],{},"výpočet hodnot zvoleného testového kritéria pro jednotlivé výběry,",[1127,30577,30578],{},"ověření a zajištění statistické zvládnutosti procesu,",[1127,30580,30581],{},"ověření způsobilosti procesu,",[1127,30583,30584],{},"vlastní regulace procesu.",[1392,30586,30588],{"id":30587},"regulace-měřením","Regulace měřením",[1110,30590,30591],{},"Diagramy pro regulaci měřením se používají, když je regulovaná veličina měřitelná. Požaduje se, aby:",[1124,30593,30594,30597],{},[1127,30595,30596],{},"jednotlivá měření byla vzájemně nezávislá,",[1127,30598,30599,30600,30613,30614,30627,30628,30641,30642,30655],{},"regulovaná veličina byla spojitá náhodná veličina s normálním rozdělením se střední hodnotou ",[1115,30601,30603],{"className":30602},[1133],[1135,30604,30605],{"xmlns":1137},[1139,30606,30607,30611],{},[1142,30608,30609],{},[1148,30610,1500],{},[1156,30612,2605],{"encoding":1158}," a směrodatnou odchylkou ",[1115,30615,30617],{"className":30616},[1133],[1135,30618,30619],{"xmlns":1137},[1139,30620,30621,30625],{},[1142,30622,30623],{},[1148,30624,2636],{},[1156,30626,16531],{"encoding":1158}," — tyto dva parametry charakterizují statistickou stabilitu procesu; ",[1115,30629,30631],{"className":30630},[1133],[1135,30632,30633],{"xmlns":1137},[1139,30634,30635,30639],{},[1142,30636,30637],{},[1148,30638,1500],{},[1156,30640,2605],{"encoding":1158}," je hodnota, na niž je proces nastaven, ",[1115,30643,30645],{"className":30644},[1133],[1135,30646,30647],{"xmlns":1137},[1139,30648,30649,30653],{},[1142,30650,30651],{},[1148,30652,2636],{},[1156,30654,16531],{"encoding":1158}," charakterizuje jeho přesnost.",[1110,30657,30658,30659,1195,30684,2261,30709,30746],{},"Jsou-li předpoklady splněny, volí se diagramy, které současně sledují stabilitu polohy i stabilitu rozptylu: ",[1115,30660,30662],{"className":30661},[1133],[1135,30663,30664],{"xmlns":1137},[1139,30665,30666,30682],{},[1142,30667,30668,30670,30676,30678,30680],{},[1495,30669,2162],{"stretchy":2161},[2671,30671,30672,30674],{"accent":1121},[1148,30673,2675],{},[1495,30675,2678],{},[1495,30677,2188],{"separator":1121},[1148,30679,19792],{},[1495,30681,2181],{"stretchy":2161},[1156,30683,30133],{"encoding":1158},[1115,30685,30687],{"className":30686},[1133],[1135,30688,30689],{"xmlns":1137},[1139,30690,30691,30707],{},[1142,30692,30693,30695,30701,30703,30705],{},[1495,30694,2162],{"stretchy":2161},[2671,30696,30697,30699],{"accent":1121},[1148,30698,2675],{},[1495,30700,2678],{},[1495,30702,2188],{"separator":1121},[1148,30704,2695],{},[1495,30706,2181],{"stretchy":2161},[1156,30708,30159],{"encoding":1158},[1115,30710,30712],{"className":30711},[1133],[1135,30713,30714],{"xmlns":1137},[1139,30715,30716,30744],{},[1142,30717,30718,30720,30726,30728,30742],{},[1495,30719,2162],{"stretchy":2161},[1145,30721,30722,30724],{},[1148,30723,2675],{},[1148,30725,4085],{},[1495,30727,2188],{"separator":1121},[1145,30729,30730,30732],{},[1148,30731,19792],{},[1142,30733,30734,30736,30738,30740],{},[1148,30735,10710],{},[1148,30737,30189],{},[1495,30739,2188],{"separator":1121},[1148,30741,4085],{},[1495,30743,2181],{"stretchy":2161},[1156,30745,30198],{"encoding":1158},". Výsledkem jsou vždy dva diagramy.",[1695,30748,30750,30751],{"id":30749},"diagram-xˉrbarx-r","Diagram ",[1115,30752,30754],{"className":30753},[1133],[1135,30755,30756],{"xmlns":1137},[1139,30757,30758,30774],{},[1142,30759,30760,30762,30768,30770,30772],{},[1495,30761,2162],{"stretchy":2161},[2671,30763,30764,30766],{"accent":1121},[1148,30765,2675],{},[1495,30767,2678],{},[1495,30769,2188],{"separator":1121},[1148,30771,19792],{},[1495,30773,2181],{"stretchy":2161},[1156,30775,30133],{"encoding":1158},[1110,30777,30778,30779,30801,30802,30820],{},"Regulované veličiny jsou výběrové průměry ",[1115,30780,30782],{"className":30781},[1133],[1135,30783,30784],{"xmlns":1137},[1139,30785,30786,30798],{},[1142,30787,30788],{},[1145,30789,30790,30796],{},[2671,30791,30792,30794],{"accent":1121},[1148,30793,2675],{},[1495,30795,2678],{},[1148,30797,4085],{},[1156,30799,30800],{"encoding":1158},"\\bar{x}_i"," a výběrová rozpětí ",[1115,30803,30805],{"className":30804},[1133],[1135,30806,30807],{"xmlns":1137},[1139,30808,30809,30817],{},[1142,30810,30811],{},[1145,30812,30813,30815],{},[1148,30814,19792],{},[1148,30816,4085],{},[1156,30818,30819],{"encoding":1158},"R_i"," v logických podskupinách:",[1115,30822,30824],{"className":30823},[1133],[1135,30825,30826],{"xmlns":1137,"display":2151},[1139,30827,30828,30929],{},[1142,30829,30830,30840,30842,30848,30862,30872,30874,30876,30882,30884,30895,30905,30907,30917,30927],{},[1145,30831,30832,30838],{},[2671,30833,30834,30836],{"accent":1121},[1148,30835,2675],{},[1495,30837,2678],{},[1148,30839,4085],{},[1495,30841,1503],{},[2749,30843,30844,30846],{},[1152,30845,1176],{},[1148,30847,2657],{},[11676,30849,30850,30852,30860],{},[1495,30851,11680],{},[1142,30853,30854,30856,30858],{},[1148,30855,11580],{},[1495,30857,1503],{},[1152,30859,1176],{},[1148,30861,2657],{},[1145,30863,30864,30866],{},[1148,30865,2675],{},[1142,30867,30868,30870],{},[1148,30869,4085],{},[1148,30871,11580],{},[1495,30873,2188],{"separator":1121},[3520,30875],{"width":3522},[1145,30877,30878,30880],{},[1148,30879,19792],{},[1148,30881,4085],{},[1495,30883,1503],{},[30885,30886,30887,30893],"munder",{},[1142,30888,30889,30891],{},[1148,30890,21280],{},[1495,30892,8744],{},[1148,30894,11580],{},[1145,30896,30897,30899],{},[1148,30898,2675],{},[1142,30900,30901,30903],{},[1148,30902,4085],{},[1148,30904,11580],{},[1495,30906,1885],{},[30885,30908,30909,30915],{},[1142,30910,30911,30913],{},[1148,30912,14121],{},[1495,30914,8744],{},[1148,30916,11580],{},[1145,30918,30919,30921],{},[1148,30920,2675],{},[1142,30922,30923,30925],{},[1148,30924,4085],{},[1148,30926,11580],{},[1148,30928,1335],{"mathvariant":1599},[1156,30930,30931],{"encoding":1158},"\\bar{x}_i = \\frac{1}{n}\\sum_{j=1}^n x_{ij}, \\qquad R_i = \\max_j x_{ij} - \\min_j x_{ij}.",[1110,30933,30934],{},"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.",[1110,30936,30937,30938,30964,30965,30978,30979,2261,31000,31017,31018,31031,31032,31049,31050,1335],{},"Data se zapisují do tabulky: řádek ",[1115,30939,30941],{"className":30940},[1133],[1135,30942,30943],{"xmlns":1137},[1139,30944,30945,30961],{},[1142,30946,30947,30949,30951,30953,30955,30957,30959],{},[1148,30948,4085],{},[1495,30950,1503],{},[1152,30952,1176],{},[1495,30954,2188],{"separator":1121},[1495,30956,10697],{},[1495,30958,2188],{"separator":1121},[1148,30960,10710],{},[1156,30962,30963],{"encoding":1158},"i = 1, \\dots, k"," je logická podskupina v pořadí, v jakém byla získána, sloupce obsahují ",[1115,30966,30968],{"className":30967},[1133],[1135,30969,30970],{"xmlns":1137},[1139,30971,30972,30976],{},[1142,30973,30974],{},[1148,30975,2657],{},[1156,30977,2657],{"encoding":1158}," naměřených hodnot a poslední dva sloupce ",[1115,30980,30982],{"className":30981},[1133],[1135,30983,30984],{"xmlns":1137},[1139,30985,30986,30998],{},[1142,30987,30988],{},[1145,30989,30990,30996],{},[2671,30991,30992,30994],{"accent":1121},[1148,30993,2675],{},[1495,30995,2678],{},[1148,30997,4085],{},[1156,30999,30800],{"encoding":1158},[1115,31001,31003],{"className":31002},[1133],[1135,31004,31005],{"xmlns":1137},[1139,31006,31007,31015],{},[1142,31008,31009],{},[1145,31010,31011,31013],{},[1148,31012,19792],{},[1148,31014,4085],{},[1156,31016,30819],{"encoding":1158},". Pro sestrojení diagramu je potřeba aspoň 20 podskupin. Nejprve se určí diagram ",[1115,31019,31021],{"className":31020},[1133],[1135,31022,31023],{"xmlns":1137},[1139,31024,31025,31029],{},[1142,31026,31027],{},[1148,31028,19792],{},[1156,31030,19792],{"encoding":1158},", potom diagram ",[1115,31033,31035],{"className":31034},[1133],[1135,31036,31037],{"xmlns":1137},[1139,31038,31039,31047],{},[1142,31040,31041],{},[2671,31042,31043,31045],{"accent":1121},[1148,31044,2675],{},[1495,31046,2678],{},[1156,31048,2681],{"encoding":1158}," — u obou střední přímka a akční meze. V R se diagramy konstruují funkcí ",[3161,31051,31052],{},"qcc()",[1103,31054,31056,31063],{"className":31055,"dataCallout":3323},[1106,3322],[1110,31057,31059,31062],{"className":31058},[1113],[1115,31060],{"className":31061,"ariaHidden":1121},[1118,3330,1120],"Příklad: kontrola rozměru dílu ve 20 logických podskupinách",[1110,31064,31065,31066,31079,31080,1195,31098,31116,31117,1335],{},"Naměřená data znaku jakosti ",[1115,31067,31069],{"className":31068},[1133],[1135,31070,31071],{"xmlns":1137},[1139,31072,31073,31077],{},[1142,31074,31075],{},[1148,31076,2618],{},[1156,31078,2618],{"encoding":1158}," byla získána ve 20 logických podskupinách po 4 měřeních (",[1115,31081,31083],{"className":31082},[1133],[1135,31084,31085],{"xmlns":1137},[1139,31086,31087,31095],{},[1142,31088,31089,31091,31093],{},[1148,31090,10710],{},[1495,31092,1503],{},[1152,31094,3374],{},[1156,31096,31097],{"encoding":1158},"k=20",[1115,31099,31101],{"className":31100},[1133],[1135,31102,31103],{"xmlns":1137},[1139,31104,31105,31113],{},[1142,31106,31107,31109,31111],{},[1148,31108,2657],{},[1495,31110,1503],{},[1152,31112,13209],{},[1156,31114,31115],{"encoding":1158},"n=4","); znak je měřitelný a má normální rozdělení. Sestrojte regulační diagram ",[1115,31118,31120],{"className":31119},[1133],[1135,31121,31122],{"xmlns":1137},[1139,31123,31124,31140],{},[1142,31125,31126,31128,31134,31136,31138],{},[1495,31127,2162],{"stretchy":2161},[2671,31129,31130,31132],{"accent":1121},[1148,31131,2675],{},[1495,31133,2678],{},[1495,31135,2188],{"separator":1121},[1148,31137,19792],{},[1495,31139,2181],{"stretchy":2161},[1156,31141,30133],{"encoding":1158},[1532,31143,31144,31259],{},[1535,31145,31146],{},[1538,31147,31148,31163,31187,31211,31235],{},[1541,31149,31150],{},[1115,31151,31153],{"className":31152},[1133],[1135,31154,31155],{"xmlns":1137},[1139,31156,31157,31161],{},[1142,31158,31159],{},[1148,31160,4085],{},[1156,31162,4085],{"encoding":1158},[1541,31164,31165],{},[1115,31166,31168],{"className":31167},[1133],[1135,31169,31170],{"xmlns":1137},[1139,31171,31172,31184],{},[1142,31173,31174],{},[1145,31175,31176,31178],{},[1148,31177,2675],{},[1142,31179,31180,31182],{},[1148,31181,4085],{},[1152,31183,1176],{},[1156,31185,31186],{"encoding":1158},"x_{i1}",[1541,31188,31189],{},[1115,31190,31192],{"className":31191},[1133],[1135,31193,31194],{"xmlns":1137},[1139,31195,31196,31208],{},[1142,31197,31198],{},[1145,31199,31200,31202],{},[1148,31201,2675],{},[1142,31203,31204,31206],{},[1148,31205,4085],{},[1152,31207,2639],{},[1156,31209,31210],{"encoding":1158},"x_{i2}",[1541,31212,31213],{},[1115,31214,31216],{"className":31215},[1133],[1135,31217,31218],{"xmlns":1137},[1139,31219,31220,31232],{},[1142,31221,31222],{},[1145,31223,31224,31226],{},[1148,31225,2675],{},[1142,31227,31228,31230],{},[1148,31229,4085],{},[1152,31231,13259],{},[1156,31233,31234],{"encoding":1158},"x_{i3}",[1541,31236,31237],{},[1115,31238,31240],{"className":31239},[1133],[1135,31241,31242],{"xmlns":1137},[1139,31243,31244,31256],{},[1142,31245,31246],{},[1145,31247,31248,31250],{},[1148,31249,2675],{},[1142,31251,31252,31254],{},[1148,31253,4085],{},[1152,31255,13209],{},[1156,31257,31258],{"encoding":1158},"x_{i4}",[1568,31260,31261,31275,31289,31305,31319,31331,31345,31357,31369],{},[1538,31262,31263,31265,31268,31271,31273],{},[1573,31264,1176],{},[1573,31266,31267],{},"106",[1573,31269,31270],{},"98",[1573,31272,9307],{},[1573,31274,9307],{},[1538,31276,31277,31279,31281,31284,31287],{},[1573,31278,2639],{},[1573,31280,3548],{},[1573,31282,31283],{},"94",[1573,31285,31286],{},"108",[1573,31288,15747],{},[1538,31290,31291,31293,31296,31299,31302],{},[1573,31292,13259],{},[1573,31294,31295],{},"122",[1573,31297,31298],{},"105",[1573,31300,31301],{},"103",[1573,31303,31304],{},"133",[1538,31306,31307,31309,31312,31314,31317],{},[1573,31308,13209],{},[1573,31310,31311],{},"113",[1573,31313,13231],{},[1573,31315,31316],{},"128",[1573,31318,8435],{},[1538,31320,31321,31323,31325,31327,31329],{},[1573,31322,9817],{},[1573,31324,9307],{},[1573,31326,15747],{},[1573,31328,31301],{},[1573,31330,15747],{},[1538,31332,31333,31335,31337,31339,31342],{},[1573,31334,13607],{},[1573,31336,31270],{},[1573,31338,31301],{},[1573,31340,31341],{},"97",[1573,31343,31344],{},"99",[1538,31346,31347,31349,31351,31353,31355],{},[1573,31348,10697],{},[1573,31350,10697],{},[1573,31352,10697],{},[1573,31354,10697],{},[1573,31356,10697],{},[1538,31358,31359,31361,31363,31365,31367],{},[1573,31360,3553],{},[1573,31362,31316],{},[1573,31364,31304],{},[1573,31366,7594],{},[1573,31368,24245],{},[1538,31370,31371,31373,31375,31377,31379],{},[1573,31372,3374],{},[1573,31374,31270],{},[1573,31376,31301],{},[1573,31378,31341],{},[1573,31380,31344],{},[1110,31382,31383,31384,31405,31406,1497],{},"Pro každou podskupinu se dopočítá výběrový průměr ",[1115,31385,31387],{"className":31386},[1133],[1135,31388,31389],{"xmlns":1137},[1139,31390,31391,31403],{},[1142,31392,31393],{},[1145,31394,31395,31401],{},[2671,31396,31397,31399],{"accent":1121},[1148,31398,2675],{},[1495,31400,2678],{},[1148,31402,4085],{},[1156,31404,30800],{"encoding":1158}," a rozpětí ",[1115,31407,31409],{"className":31408},[1133],[1135,31410,31411],{"xmlns":1137},[1139,31412,31413,31421],{},[1142,31414,31415],{},[1145,31416,31417,31419],{},[1148,31418,19792],{},[1148,31420,4085],{},[1156,31422,30819],{"encoding":1158},[1532,31424,31425,31486],{},[1535,31426,31427],{},[1538,31428,31429,31444,31467],{},[1541,31430,31431],{},[1115,31432,31434],{"className":31433},[1133],[1135,31435,31436],{"xmlns":1137},[1139,31437,31438,31442],{},[1142,31439,31440],{},[1148,31441,4085],{},[1156,31443,4085],{"encoding":1158},[1541,31445,31446],{},[1115,31447,31449],{"className":31448},[1133],[1135,31450,31451],{"xmlns":1137},[1139,31452,31453,31465],{},[1142,31454,31455],{},[1145,31456,31457,31463],{},[2671,31458,31459,31461],{"accent":1121},[1148,31460,2675],{},[1495,31462,2678],{},[1148,31464,4085],{},[1156,31466,30800],{"encoding":1158},[1541,31468,31469],{},[1115,31470,31472],{"className":31471},[1133],[1135,31473,31474],{"xmlns":1137},[1139,31475,31476,31484],{},[1142,31477,31478],{},[1145,31479,31480,31482],{},[1148,31481,19792],{},[1148,31483,4085],{},[1156,31485,30819],{"encoding":1158},[1568,31487,31488,31497,31506,31515,31525,31534,31543,31551,31560],{},[1538,31489,31490,31492,31495],{},[1573,31491,1176],{},[1573,31493,31494],{},"101,50",[1573,31496,24311],{},[1538,31498,31499,31501,31504],{},[1573,31500,2639],{},[1573,31502,31503],{},"97,25",[1573,31505,7192],{},[1538,31507,31508,31510,31513],{},[1573,31509,13259],{},[1573,31511,31512],{},"115,75",[1573,31514,8839],{},[1538,31516,31517,31519,31522],{},[1573,31518,13209],{},[1573,31520,31521],{},"111,75",[1573,31523,31524],{},"64",[1538,31526,31527,31529,31532],{},[1573,31528,9817],{},[1573,31530,31531],{},"97,00",[1573,31533,7339],{},[1538,31535,31536,31538,31541],{},[1573,31537,13607],{},[1573,31539,31540],{},"99,25",[1573,31542,13607],{},[1538,31544,31545,31547,31549],{},[1573,31546,10697],{},[1573,31548,10697],{},[1573,31550,10697],{},[1538,31552,31553,31555,31558],{},[1573,31554,3553],{},[1573,31556,31557],{},"126,50",[1573,31559,13212],{},[1538,31561,31562,31564,31566],{},[1573,31563,3374],{},[1573,31565,31540],{},[1573,31567,13607],{},[1110,31569,31570,31571,31584,31585,1195,31613,1195,31643,31671,31672,31694,31695,1195,31722,1195,31751,31778,31779,1335],{},"Nejprve se posoudí diagram ",[1115,31572,31574],{"className":31573},[1133],[1135,31575,31576],{"xmlns":1137},[1139,31577,31578,31582],{},[1142,31579,31580],{},[1148,31581,19792],{},[1156,31583,19792],{"encoding":1158}," na všech 20 podskupinách: ",[1115,31586,31588],{"className":31587},[1133],[1135,31589,31590],{"xmlns":1137},[1139,31591,31592,31610],{},[1142,31593,31594,31596,31599,31601,31603,31605,31607],{},[1148,31595,30280],{},[1148,31597,31598],{},"L",[1495,31600,2162],{"stretchy":2161},[1148,31602,19792],{},[1495,31604,2181],{"stretchy":2161},[1495,31606,1503],{},[1152,31608,31609],{},"15,8",[1156,31611,31612],{"encoding":1158},"CL(R)=15{,}8",[1115,31614,31616],{"className":31615},[1133],[1135,31617,31618],{"xmlns":1137},[1139,31619,31620,31640],{},[1142,31621,31622,31625,31627,31629,31631,31633,31635,31637],{},[1148,31623,31624],{},"U",[1148,31626,30280],{},[1148,31628,31598],{},[1495,31630,2162],{"stretchy":2161},[1148,31632,19792],{},[1495,31634,2181],{"stretchy":2161},[1495,31636,1503],{},[1152,31638,31639],{},"36,06",[1156,31641,31642],{"encoding":1158},"UCL(R)=36{,}06",[1115,31644,31646],{"className":31645},[1133],[1135,31647,31648],{"xmlns":1137},[1139,31649,31650,31668],{},[1142,31651,31652,31654,31656,31658,31660,31662,31664,31666],{},[1148,31653,31598],{},[1148,31655,30280],{},[1148,31657,31598],{},[1495,31659,2162],{"stretchy":2161},[1148,31661,19792],{},[1495,31663,2181],{"stretchy":2161},[1495,31665,1503],{},[1152,31667,1154],{},[1156,31669,31670],{"encoding":1158},"LCL(R)=0",". Rozpětí čtvrté podskupiny (",[1115,31673,31675],{"className":31674},[1133],[1135,31676,31677],{"xmlns":1137},[1139,31678,31679,31691],{},[1142,31680,31681,31687,31689],{},[1145,31682,31683,31685],{},[1148,31684,19792],{},[1152,31686,13209],{},[1495,31688,1503],{},[1152,31690,31524],{},[1156,31692,31693],{"encoding":1158},"R_4=64",") mez překračuje; po potvrzení vymezitelné příčiny se podskupina 4 z výpočtu vyřadí a meze se přepočítají — ",[1115,31696,31698],{"className":31697},[1133],[1135,31699,31700],{"xmlns":1137},[1139,31701,31702,31719],{},[1142,31703,31704,31706,31708,31710,31712,31714,31716],{},[1148,31705,30280],{},[1148,31707,31598],{},[1495,31709,2162],{"stretchy":2161},[1148,31711,19792],{},[1495,31713,2181],{"stretchy":2161},[1495,31715,1503],{},[1152,31717,31718],{},"13,26",[1156,31720,31721],{"encoding":1158},"CL(R)=13{,}26",[1115,31723,31725],{"className":31724},[1133],[1135,31726,31727],{"xmlns":1137},[1139,31728,31729,31748],{},[1142,31730,31731,31733,31735,31737,31739,31741,31743,31745],{},[1148,31732,31624],{},[1148,31734,30280],{},[1148,31736,31598],{},[1495,31738,2162],{"stretchy":2161},[1148,31740,19792],{},[1495,31742,2181],{"stretchy":2161},[1495,31744,1503],{},[1152,31746,31747],{},"30,27",[1156,31749,31750],{"encoding":1158},"UCL(R)=30{,}27",[1115,31752,31754],{"className":31753},[1133],[1135,31755,31756],{"xmlns":1137},[1139,31757,31758,31776],{},[1142,31759,31760,31762,31764,31766,31768,31770,31772,31774],{},[1148,31761,31598],{},[1148,31763,30280],{},[1148,31765,31598],{},[1495,31767,2162],{"stretchy":2161},[1148,31769,19792],{},[1495,31771,2181],{"stretchy":2161},[1495,31773,1503],{},[1152,31775,1154],{},[1156,31777,31670],{"encoding":1158},". Diagram rozpětí je teď zvládnutý, lze tedy posoudit diagram ",[1115,31780,31782],{"className":31781},[1133],[1135,31783,31784],{"xmlns":1137},[1139,31785,31786,31794],{},[1142,31787,31788],{},[2671,31789,31790,31792],{"accent":1121},[1148,31791,2675],{},[1495,31793,2678],{},[1156,31795,2681],{"encoding":1158},[1110,31797,30750,31798,31815,31816,1195,31847,1195,31880,31913,31914,31927,31928,1195,31955,1195,31984,32011],{},[1115,31799,31801],{"className":31800},[1133],[1135,31802,31803],{"xmlns":1137},[1139,31804,31805,31813],{},[1142,31806,31807],{},[2671,31808,31809,31811],{"accent":1121},[1148,31810,2675],{},[1495,31812,2678],{},[1156,31814,2681],{"encoding":1158}," bez čtvrté podskupiny dává ",[1115,31817,31819],{"className":31818},[1133],[1135,31820,31821],{"xmlns":1137},[1139,31822,31823,31844],{},[1142,31824,31825,31827,31829,31831,31837,31839,31841],{},[1148,31826,30280],{},[1148,31828,31598],{},[1495,31830,2162],{"stretchy":2161},[2671,31832,31833,31835],{"accent":1121},[1148,31834,2675],{},[1495,31836,2678],{},[1495,31838,2181],{"stretchy":2161},[1495,31840,1503],{},[1152,31842,31843],{},"102,01",[1156,31845,31846],{"encoding":1158},"CL(\\bar{x})=102{,}01",[1115,31848,31850],{"className":31849},[1133],[1135,31851,31852],{"xmlns":1137},[1139,31853,31854,31877],{},[1142,31855,31856,31858,31860,31862,31864,31870,31872,31874],{},[1148,31857,31624],{},[1148,31859,30280],{},[1148,31861,31598],{},[1495,31863,2162],{"stretchy":2161},[2671,31865,31866,31868],{"accent":1121},[1148,31867,2675],{},[1495,31869,2678],{},[1495,31871,2181],{"stretchy":2161},[1495,31873,1503],{},[1152,31875,31876],{},"111,68",[1156,31878,31879],{"encoding":1158},"UCL(\\bar{x})=111{,}68",[1115,31881,31883],{"className":31882},[1133],[1135,31884,31885],{"xmlns":1137},[1139,31886,31887,31910],{},[1142,31888,31889,31891,31893,31895,31897,31903,31905,31907],{},[1148,31890,31598],{},[1148,31892,30280],{},[1148,31894,31598],{},[1495,31896,2162],{"stretchy":2161},[2671,31898,31899,31901],{"accent":1121},[1148,31900,2675],{},[1495,31902,2678],{},[1495,31904,2181],{"stretchy":2161},[1495,31906,1503],{},[1152,31908,31909],{},"92,34",[1156,31911,31912],{"encoding":1158},"LCL(\\bar{x})=92{,}34",". Mez teď překračují průměry podskupin 3 a 19. Po potvrzení vymezitelné příčiny se vyřadí obě najednou a meze diagramu ",[1115,31915,31917],{"className":31916},[1133],[1135,31918,31919],{"xmlns":1137},[1139,31920,31921,31925],{},[1142,31922,31923],{},[1148,31924,19792],{},[1156,31926,19792],{"encoding":1158}," se přepočítají bez podskupin 3, 4 a 19: ",[1115,31929,31931],{"className":31930},[1133],[1135,31932,31933],{"xmlns":1137},[1139,31934,31935,31952],{},[1142,31936,31937,31939,31941,31943,31945,31947,31949],{},[1148,31938,30280],{},[1148,31940,31598],{},[1495,31942,2162],{"stretchy":2161},[1148,31944,19792],{},[1495,31946,2181],{"stretchy":2161},[1495,31948,1503],{},[1152,31950,31951],{},"12,29",[1156,31953,31954],{"encoding":1158},"CL(R)=12{,}29",[1115,31956,31958],{"className":31957},[1133],[1135,31959,31960],{"xmlns":1137},[1139,31961,31962,31981],{},[1142,31963,31964,31966,31968,31970,31972,31974,31976,31978],{},[1148,31965,31624],{},[1148,31967,30280],{},[1148,31969,31598],{},[1495,31971,2162],{"stretchy":2161},[1148,31973,19792],{},[1495,31975,2181],{"stretchy":2161},[1495,31977,1503],{},[1152,31979,31980],{},"28,06",[1156,31982,31983],{"encoding":1158},"UCL(R)=28{,}06",[1115,31985,31987],{"className":31986},[1133],[1135,31988,31989],{"xmlns":1137},[1139,31990,31991,32009],{},[1142,31992,31993,31995,31997,31999,32001,32003,32005,32007],{},[1148,31994,31598],{},[1148,31996,30280],{},[1148,31998,31598],{},[1495,32000,2162],{"stretchy":2161},[1148,32002,19792],{},[1495,32004,2181],{"stretchy":2161},[1495,32006,1503],{},[1152,32008,1154],{},[1156,32010,31670],{"encoding":1158}," — žádná z 17 zbývajících podskupin mez nepřekračuje.",[1110,32013,32014,32015,32032,32033,1195,32064,1195,32097,32130],{},"Konečný diagram ",[1115,32016,32018],{"className":32017},[1133],[1135,32019,32020],{"xmlns":1137},[1139,32021,32022,32030],{},[1142,32023,32024],{},[2671,32025,32026,32028],{"accent":1121},[1148,32027,2675],{},[1495,32029,2678],{},[1156,32031,2681],{"encoding":1158}," na stejných 17 podskupinách má ",[1115,32034,32036],{"className":32035},[1133],[1135,32037,32038],{"xmlns":1137},[1139,32039,32040,32061],{},[1142,32041,32042,32044,32046,32048,32054,32056,32058],{},[1148,32043,30280],{},[1148,32045,31598],{},[1495,32047,2162],{"stretchy":2161},[2671,32049,32050,32052],{"accent":1121},[1148,32051,2675],{},[1495,32053,2678],{},[1495,32055,2181],{"stretchy":2161},[1495,32057,1503],{},[1152,32059,32060],{},"99,76",[1156,32062,32063],{"encoding":1158},"CL(\\bar{x})=99{,}76",[1115,32065,32067],{"className":32066},[1133],[1135,32068,32069],{"xmlns":1137},[1139,32070,32071,32094],{},[1142,32072,32073,32075,32077,32079,32081,32087,32089,32091],{},[1148,32074,31624],{},[1148,32076,30280],{},[1148,32078,31598],{},[1495,32080,2162],{"stretchy":2161},[2671,32082,32083,32085],{"accent":1121},[1148,32084,2675],{},[1495,32086,2678],{},[1495,32088,2181],{"stretchy":2161},[1495,32090,1503],{},[1152,32092,32093],{},"108,73",[1156,32095,32096],{"encoding":1158},"UCL(\\bar{x})=108{,}73",[1115,32098,32100],{"className":32099},[1133],[1135,32101,32102],{"xmlns":1137},[1139,32103,32104,32127],{},[1142,32105,32106,32108,32110,32112,32114,32120,32122,32124],{},[1148,32107,31598],{},[1148,32109,30280],{},[1148,32111,31598],{},[1495,32113,2162],{"stretchy":2161},[2671,32115,32116,32118],{"accent":1121},[1148,32117,2675],{},[1495,32119,2678],{},[1495,32121,2181],{"stretchy":2161},[1495,32123,1503],{},[1152,32125,32126],{},"90,80",[1156,32128,32129],{"encoding":1158},"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.",[1110,32132,32133],{},[1971,32134],{"alt":32135,"className":32136,"src":32137},"mask-rd-priklad1-meze",[1343,1975],"\u002Fwiki-assets\u002Fmask-rd-priklad1-meze.png",[1110,32139,32140,32141,10945,32143,32145],{},"V R se diagramy sestrojí funkcí ",[3161,32142,31052],{},[3161,32144,360],{},". Data jsou tabulka, v níž řádek odpovídá logické podskupině a sloupce jednotlivým měřením:",[3166,32147,32149],{"className":3168,"code":32148,"language":71,"meta":3170,"style":3170},"library(qcc)\ndata \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"R\")      # diagram R\nqcc(data, type = \"xbar\")   # diagram x̄\n",[3161,32150,32151,32161,32184,32207],{"__ignoreMap":3170},[1115,32152,32153,32155,32157,32159],{"class":3175,"line":10},[1115,32154,10627],{"class":3181},[1115,32156,2162],{"class":3189},[1115,32158,360],{"class":3178},[1115,32160,3235],{"class":3189},[1115,32162,32163,32165,32167,32169,32171,32174,32176,32178,32180,32182],{"class":3175,"line":27},[1115,32164,29591],{"class":3178},[1115,32166,3182],{"class":3181},[1115,32168,29596],{"class":3185},[1115,32170,2162],{"class":3189},[1115,32172,32173],{"class":3265},"\"3_2.txt\"",[1115,32175,2188],{"class":3181},[1115,32177,29606],{"class":3178},[1115,32179,3252],{"class":3181},[1115,32181,5282],{"class":3192},[1115,32183,3235],{"class":3189},[1115,32185,32186,32188,32190,32192,32194,32196,32198,32201,32204],{"class":3175,"line":148},[1115,32187,360],{"class":3185},[1115,32189,2162],{"class":3189},[1115,32191,29591],{"class":3178},[1115,32193,2188],{"class":3181},[1115,32195,21772],{"class":3178},[1115,32197,3252],{"class":3181},[1115,32199,32200],{"class":3265}," \"R\"",[1115,32202,32203],{"class":3189},")      ",[1115,32205,32206],{"class":10754},"# diagram R\n",[1115,32208,32209,32211,32213,32215,32217,32219,32221,32224,32226],{"class":3175,"line":111},[1115,32210,360],{"class":3185},[1115,32212,2162],{"class":3189},[1115,32214,29591],{"class":3178},[1115,32216,2188],{"class":3181},[1115,32218,21772],{"class":3178},[1115,32220,3252],{"class":3181},[1115,32222,32223],{"class":3265}," \"xbar\"",[1115,32225,21583],{"class":3189},[1115,32227,32228],{"class":10754},"# diagram x̄\n",[1110,32230,32231,32232,32235],{},"Funkce vykreslí diagram se střední přímkou a akčními mezemi a body mimo meze zvýrazní. Podskupina s potvrzenou vymezitelnou příčinou se vyřadí z dat (například ",[3161,32233,32234],{},"data[-4, ]",") a diagram se sestrojí znovu.",[1695,32237,30750,32239],{"id":32238},"diagram-xˉsbarx-s",[1115,32240,32242],{"className":32241},[1133],[1135,32243,32244],{"xmlns":1137},[1139,32245,32246,32262],{},[1142,32247,32248,32250,32256,32258,32260],{},[1495,32249,2162],{"stretchy":2161},[2671,32251,32252,32254],{"accent":1121},[1148,32253,2675],{},[1495,32255,2678],{},[1495,32257,2188],{"separator":1121},[1148,32259,2695],{},[1495,32261,2181],{"stretchy":2161},[1156,32263,30159],{"encoding":1158},[1110,32265,30778,32266,32287,32288,32306,32307,32332],{},[1115,32267,32269],{"className":32268},[1133],[1135,32270,32271],{"xmlns":1137},[1139,32272,32273,32285],{},[1142,32274,32275],{},[1145,32276,32277,32283],{},[2671,32278,32279,32281],{"accent":1121},[1148,32280,2675],{},[1495,32282,2678],{},[1148,32284,4085],{},[1156,32286,30800],{"encoding":1158}," a výběrové směrodatné odchylky ",[1115,32289,32291],{"className":32290},[1133],[1135,32292,32293],{"xmlns":1137},[1139,32294,32295,32303],{},[1142,32296,32297],{},[1145,32298,32299,32301],{},[1148,32300,2695],{},[1148,32302,4085],{},[1156,32304,32305],{"encoding":1158},"s_i"," v logických podskupinách. Podmínky použití jsou stejné jako u ",[1115,32308,32310],{"className":32309},[1133],[1135,32311,32312],{"xmlns":1137},[1139,32313,32314,32330],{},[1142,32315,32316,32318,32324,32326,32328],{},[1495,32317,2162],{"stretchy":2161},[2671,32319,32320,32322],{"accent":1121},[1148,32321,2675],{},[1495,32323,2678],{},[1495,32325,2188],{"separator":1121},[1148,32327,19792],{},[1495,32329,2181],{"stretchy":2161},[1156,32331,30133],{"encoding":1158},", logické podskupiny ale sestávají z většího počtu měření. Data se zapisují do obdobné tabulky.",[3166,32334,32336],{"className":3168,"code":32335,"language":71,"meta":3170,"style":3170},"data \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"S\")      # diagram s\nqcc(data, type = \"xbar\")   # diagram x̄\n",[3161,32337,32338,32360,32382],{"__ignoreMap":3170},[1115,32339,32340,32342,32344,32346,32348,32350,32352,32354,32356,32358],{"class":3175,"line":10},[1115,32341,29591],{"class":3178},[1115,32343,3182],{"class":3181},[1115,32345,29596],{"class":3185},[1115,32347,2162],{"class":3189},[1115,32349,32173],{"class":3265},[1115,32351,2188],{"class":3181},[1115,32353,29606],{"class":3178},[1115,32355,3252],{"class":3181},[1115,32357,5282],{"class":3192},[1115,32359,3235],{"class":3189},[1115,32361,32362,32364,32366,32368,32370,32372,32374,32377,32379],{"class":3175,"line":27},[1115,32363,360],{"class":3185},[1115,32365,2162],{"class":3189},[1115,32367,29591],{"class":3178},[1115,32369,2188],{"class":3181},[1115,32371,21772],{"class":3178},[1115,32373,3252],{"class":3181},[1115,32375,32376],{"class":3265}," \"S\"",[1115,32378,32203],{"class":3189},[1115,32380,32381],{"class":10754},"# diagram s\n",[1115,32383,32384,32386,32388,32390,32392,32394,32396,32398,32400],{"class":3175,"line":148},[1115,32385,360],{"class":3185},[1115,32387,2162],{"class":3189},[1115,32389,29591],{"class":3178},[1115,32391,2188],{"class":3181},[1115,32393,21772],{"class":3178},[1115,32395,3252],{"class":3181},[1115,32397,32223],{"class":3265},[1115,32399,21583],{"class":3189},[1115,32401,32228],{"class":10754},[1695,32403,30750,32405],{"id":32404},"diagram-xirklix_i-r_kli",[1115,32406,32408],{"className":32407},[1133],[1135,32409,32410],{"xmlns":1137},[1139,32411,32412,32440],{},[1142,32413,32414,32416,32422,32424,32438],{},[1495,32415,2162],{"stretchy":2161},[1145,32417,32418,32420],{},[1148,32419,2675],{},[1148,32421,4085],{},[1495,32423,2188],{"separator":1121},[1145,32425,32426,32428],{},[1148,32427,19792],{},[1142,32429,32430,32432,32434,32436],{},[1148,32431,10710],{},[1148,32433,30189],{},[1495,32435,2188],{"separator":1121},[1148,32437,4085],{},[1495,32439,2181],{"stretchy":2161},[1156,32441,30198],{"encoding":1158},[1110,32443,32444,32445,32470,32471,1497],{},"Používá se za stejných podmínek jako ",[1115,32446,32448],{"className":32447},[1133],[1135,32449,32450],{"xmlns":1137},[1139,32451,32452,32468],{},[1142,32453,32454,32456,32462,32464,32466],{},[1495,32455,2162],{"stretchy":2161},[2671,32457,32458,32460],{"accent":1121},[1148,32459,2675],{},[1495,32461,2678],{},[1495,32463,2188],{"separator":1121},[1148,32465,19792],{},[1495,32467,2181],{"stretchy":2161},[1156,32469,30133],{"encoding":1158},", 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 ",[1399,32472,32473],{},"klouzavé rozpětí",[1115,32475,32477],{"className":32476},[1133],[1135,32478,32479],{"xmlns":1137,"display":2151},[1139,32480,32481,32607],{},[1142,32482,32483,32497,32499,32501,32507,32509,32521,32523,32525,32527,32529,32531,32533,32535,32537,32539,32541,32543,32545,32547,32549,32563,32565,32577,32591,32605],{},[1145,32484,32485,32487],{},[1148,32486,19792],{},[1142,32488,32489,32491,32493,32495],{},[1148,32490,10710],{},[1148,32492,30189],{},[1495,32494,2188],{"separator":1121},[1148,32496,4085],{},[1495,32498,1503],{},[1148,32500,2172],{"mathvariant":1599},[1145,32502,32503,32505],{},[1148,32504,2675],{},[1148,32506,4085],{},[1495,32508,1885],{},[1145,32510,32511,32513],{},[1148,32512,2675],{},[1142,32514,32515,32517,32519],{},[1148,32516,4085],{},[1495,32518,1885],{},[1152,32520,1176],{},[1148,32522,2172],{"mathvariant":1599},[1495,32524,2188],{"separator":1121},[3520,32526],{"width":27505},[1148,32528,4085],{},[1495,32530,1503],{},[1152,32532,2639],{},[1495,32534,2188],{"separator":1121},[1152,32536,13259],{},[1495,32538,2188],{"separator":1121},[1495,32540,10697],{},[1495,32542,2188],{"separator":1121},[1148,32544,10710],{},[1495,32546,2188],{"separator":1121},[3520,32548],{"width":3522},[1145,32550,32551,32557],{},[2671,32552,32553,32555],{"accent":1121},[1148,32554,19792],{},[1495,32556,2678],{},[1142,32558,32559,32561],{},[1148,32560,10710],{},[1148,32562,30189],{},[1495,32564,1503],{},[2749,32566,32567,32569],{},[1152,32568,1176],{},[1142,32570,32571,32573,32575],{},[1148,32572,10710],{},[1495,32574,1885],{},[1152,32576,1176],{},[11676,32578,32579,32581,32589],{},[1495,32580,11680],{},[1142,32582,32583,32585,32587],{},[1148,32584,4085],{},[1495,32586,1503],{},[1152,32588,2639],{},[1148,32590,10710],{},[1145,32592,32593,32595],{},[1148,32594,19792],{},[1142,32596,32597,32599,32601,32603],{},[1148,32598,10710],{},[1148,32600,30189],{},[1495,32602,2188],{"separator":1121},[1148,32604,4085],{},[1148,32606,1335],{"mathvariant":1599},[1156,32608,32609],{"encoding":1158},"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}.",[1110,32611,32612,32613,2261,32630,32656,32657,32682,32683,32700],{},"Regulované veličiny jsou hodnoty ",[1115,32614,32616],{"className":32615},[1133],[1135,32617,32618],{"xmlns":1137},[1139,32619,32620,32628],{},[1142,32621,32622],{},[1145,32623,32624,32626],{},[1148,32625,2675],{},[1148,32627,4085],{},[1156,32629,26623],{"encoding":1158},[1115,32631,32633],{"className":32632},[1133],[1135,32634,32635],{"xmlns":1137},[1139,32636,32637,32653],{},[1142,32638,32639],{},[1145,32640,32641,32643],{},[1148,32642,19792],{},[1142,32644,32645,32647,32649,32651],{},[1148,32646,10710],{},[1148,32648,30189],{},[1495,32650,2188],{"separator":1121},[1148,32652,4085],{},[1156,32654,32655],{"encoding":1158},"R_{kl,i}","; nejdříve se určí střední přímka a meze diagramu ",[1115,32658,32660],{"className":32659},[1133],[1135,32661,32662],{"xmlns":1137},[1139,32663,32664,32680],{},[1142,32665,32666],{},[1145,32667,32668,32670],{},[1148,32669,19792],{},[1142,32671,32672,32674,32676,32678],{},[1148,32673,10710],{},[1148,32675,30189],{},[1495,32677,2188],{"separator":1121},[1148,32679,4085],{},[1156,32681,32655],{"encoding":1158},", potom diagramu ",[1115,32684,32686],{"className":32685},[1133],[1135,32687,32688],{"xmlns":1137},[1139,32689,32690,32698],{},[1142,32691,32692],{},[1145,32693,32694,32696],{},[1148,32695,2675],{},[1148,32697,4085],{},[1156,32699,26623],{"encoding":1158},". Data jsou jeden vektor naměřených hodnot:",[3166,32702,32704],{"className":3168,"code":32703,"language":71,"meta":3170,"style":3170},"data \u003C- read.table(\"3_3.txt\", header = TRUE)\nqcc(data[, 1], type = \"xbar.one\")\n",[3161,32705,32706,32729],{"__ignoreMap":3170},[1115,32707,32708,32710,32712,32714,32716,32719,32721,32723,32725,32727],{"class":3175,"line":10},[1115,32709,29591],{"class":3178},[1115,32711,3182],{"class":3181},[1115,32713,29596],{"class":3185},[1115,32715,2162],{"class":3189},[1115,32717,32718],{"class":3265},"\"3_3.txt\"",[1115,32720,2188],{"class":3181},[1115,32722,29606],{"class":3178},[1115,32724,3252],{"class":3181},[1115,32726,5282],{"class":3192},[1115,32728,3235],{"class":3189},[1115,32730,32731,32733,32735,32737,32739,32741,32743,32745,32747,32749,32751,32754],{"class":3175,"line":27},[1115,32732,360],{"class":3185},[1115,32734,2162],{"class":3189},[1115,32736,29591],{"class":3178},[1115,32738,17765],{"class":3189},[1115,32740,2188],{"class":3181},[1115,32742,3735],{"class":3192},[1115,32744,17782],{"class":3189},[1115,32746,2188],{"class":3181},[1115,32748,21772],{"class":3178},[1115,32750,3252],{"class":3181},[1115,32752,32753],{"class":3265}," \"xbar.one\"",[1115,32755,3235],{"class":3189},[1392,32757,32759],{"id":32758},"regulace-srovnáváním","Regulace srovnáváním",[1110,32761,32762],{},"Diagramy pro regulaci srovnáváním se používají, sledují-li se počty neshodných produktů nebo počty neshod na produktech — regulovaná veličina je diskrétní náhodná veličina.",[1532,32764,32765,32778],{},[1535,32766,32767],{},[1538,32768,32769,32772,32775],{},[1541,32770,32771],{},"Sleduje se",[1541,32773,32774],{},"Konstantní rozsah podskupin",[1541,32776,32777],{},"Nekonstantní rozsah podskupin",[1568,32779,32780,32815],{},[1538,32781,32782,32785,32800],{},[1573,32783,32784],{},"počet neshod na produktech (např. vady na stejných tabulích skla)",[1573,32786,32787],{},[1115,32788,32790],{"className":32789},[1133],[1135,32791,32792],{"xmlns":1137},[1139,32793,32794,32798],{},[1142,32795,32796],{},[1148,32797,1991],{},[1156,32799,1991],{"encoding":1158},[1573,32801,32802],{},[1115,32803,32805],{"className":32804},[1133],[1135,32806,32807],{"xmlns":1137},[1139,32808,32809,32813],{},[1142,32810,32811],{},[1148,32812,21090],{},[1156,32814,21090],{"encoding":1158},[1538,32816,32817,32820,32837],{},[1573,32818,32819],{},"počet neshodných produktů ve výběru (např. neshodné kusy ze série na výrobní lince)",[1573,32821,32822],{},[1115,32823,32825],{"className":32824},[1133],[1135,32826,32827],{"xmlns":1137},[1139,32828,32829,32835],{},[1142,32830,32831,32833],{},[1148,32832,2657],{},[1148,32834,1110],{},[1156,32836,30245],{"encoding":1158},[1573,32838,32839],{},[1115,32840,32842],{"className":32841},[1133],[1135,32843,32844],{"xmlns":1137},[1139,32845,32846,32850],{},[1142,32847,32848],{},[1148,32849,1110],{},[1156,32851,1110],{"encoding":1158},[1695,32853,30750,32855],{"id":32854},"diagram-cc",[1115,32856,32858],{"className":32857},[1133],[1135,32859,32860],{"xmlns":1137},[1139,32861,32862,32866],{},[1142,32863,32864],{},[1148,32865,1991],{},[1156,32867,1991],{"encoding":1158},[1110,32869,32870,32871,32889,32890,32903,32904,32929,32930,32943],{},"Regulovanou veličinou ",[1115,32872,32874],{"className":32873},[1133],[1135,32875,32876],{"xmlns":1137},[1139,32877,32878,32886],{},[1142,32879,32880],{},[1145,32881,32882,32884],{},[1148,32883,1991],{},[1148,32885,4085],{},[1156,32887,32888],{"encoding":1158},"c_i"," je počet neshod na produktech v ",[1115,32891,32893],{"className":32892},[1133],[1135,32894,32895],{"xmlns":1137},[1139,32896,32897,32901],{},[1142,32898,32899],{},[1148,32900,4085],{},[1156,32902,4085],{"encoding":1158},"-té logické podskupině, ",[1115,32905,32907],{"className":32906},[1133],[1135,32908,32909],{"xmlns":1137},[1139,32910,32911,32927],{},[1142,32912,32913,32915,32917,32919,32921,32923,32925],{},[1148,32914,4085],{},[1495,32916,1503],{},[1152,32918,1176],{},[1495,32920,2188],{"separator":1121},[1495,32922,10697],{},[1495,32924,2188],{"separator":1121},[1148,32926,10710],{},[1156,32928,30963],{"encoding":1158},"; v každé podskupině je stejný počet ",[1115,32931,32933],{"className":32932},[1133],[1135,32934,32935],{"xmlns":1137},[1139,32936,32937,32941],{},[1142,32938,32939],{},[1148,32940,2657],{},[1156,32942,2657],{"encoding":1158}," 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.",[1103,32945,32947,32954],{"className":32946,"dataCallout":3323},[1106,3322],[1110,32948,32950,32953],{"className":32949},[1113],[1115,32951],{"className":32952,"ariaHidden":1121},[1118,3330,1120],"Příklad: bodové vady na pásech látky",[1110,32955,32956,32957,32974,32975,1335],{},"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 ",[1115,32958,32960],{"className":32959},[1133],[1135,32961,32962],{"xmlns":1137},[1139,32963,32964,32972],{},[1142,32965,32966],{},[1145,32967,32968,32970],{},[1148,32969,1991],{},[1148,32971,4085],{},[1156,32973,32888],{"encoding":1158},". Sestrojte regulační diagram ",[1115,32976,32978],{"className":32977},[1133],[1135,32979,32980],{"xmlns":1137},[1139,32981,32982,32986],{},[1142,32983,32984],{},[1148,32985,1991],{},[1156,32987,1991],{"encoding":1158},[3166,32989,32991],{"className":3168,"code":32990,"language":71,"meta":3170,"style":3170},"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",[3161,32992,32993,33083,33087,33112],{"__ignoreMap":3170},[1115,32994,32995,32997,32999,33001,33003,33005,33007,33009,33011,33013,33015,33017,33019,33021,33023,33025,33027,33029,33031,33033,33035,33037,33039,33041,33043,33045,33047,33049,33051,33053,33055,33057,33059,33061,33063,33065,33067,33069,33071,33073,33075,33077,33079,33081],{"class":3175,"line":10},[1115,32996,32888],{"class":3178},[1115,32998,3182],{"class":3181},[1115,33000,3186],{"class":3185},[1115,33002,2162],{"class":3189},[1115,33004,22878],{"class":3192},[1115,33006,2188],{"class":3181},[1115,33008,3735],{"class":3192},[1115,33010,2188],{"class":3181},[1115,33012,7909],{"class":3192},[1115,33014,2188],{"class":3181},[1115,33016,9344],{"class":3192},[1115,33018,2188],{"class":3181},[1115,33020,5078],{"class":3192},[1115,33022,2188],{"class":3181},[1115,33024,21777],{"class":3192},[1115,33026,2188],{"class":3181},[1115,33028,7909],{"class":3192},[1115,33030,2188],{"class":3181},[1115,33032,5078],{"class":3192},[1115,33034,2188],{"class":3181},[1115,33036,3983],{"class":3192},[1115,33038,2188],{"class":3181},[1115,33040,3983],{"class":3192},[1115,33042,2188],{"class":3181},[1115,33044,21777],{"class":3192},[1115,33046,2188],{"class":3181},[1115,33048,9537],{"class":3192},[1115,33050,2188],{"class":3181},[1115,33052,9537],{"class":3192},[1115,33054,2188],{"class":3181},[1115,33056,9537],{"class":3192},[1115,33058,2188],{"class":3181},[1115,33060,3735],{"class":3192},[1115,33062,2188],{"class":3181},[1115,33064,21777],{"class":3192},[1115,33066,2188],{"class":3181},[1115,33068,9537],{"class":3192},[1115,33070,2188],{"class":3181},[1115,33072,3735],{"class":3192},[1115,33074,2188],{"class":3181},[1115,33076,9344],{"class":3192},[1115,33078,2188],{"class":3181},[1115,33080,21777],{"class":3192},[1115,33082,3235],{"class":3189},[1115,33084,33085],{"class":3175,"line":27},[1115,33086,19612],{"emptyLinePlaceholder":11218},[1115,33088,33089,33092,33094,33097,33099,33101,33103,33105,33107,33110],{"class":3175,"line":148},[1115,33090,33091],{"class":3178},"q_c",[1115,33093,3182],{"class":3181},[1115,33095,33096],{"class":3185}," qcc",[1115,33098,2162],{"class":3189},[1115,33100,32888],{"class":3178},[1115,33102,2188],{"class":3181},[1115,33104,21772],{"class":3178},[1115,33106,3252],{"class":3181},[1115,33108,33109],{"class":3265}," \"c\"",[1115,33111,3235],{"class":3189},[1115,33113,33114,33116,33118,33120],{"class":3175,"line":111},[1115,33115,26357],{"class":3185},[1115,33117,2162],{"class":3189},[1115,33119,33091],{"class":3178},[1115,33121,3235],{"class":3189},[3166,33123,33126],{"className":33124,"code":33125,"language":3274,"meta":3170},[3272],"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",[3161,33127,33125],{"__ignoreMap":3170},[1110,33129,33130,33131,33160,33161,33184,33185,33207],{},"Průměrný počet vad na pás je ",[1115,33132,33134],{"className":33133},[1133],[1135,33135,33136],{"xmlns":1137},[1139,33137,33138,33157],{},[1142,33139,33140,33142,33144,33146,33152,33154],{},[1148,33141,30280],{},[1148,33143,31598],{},[1495,33145,1503],{},[2671,33147,33148,33150],{"accent":1121},[1148,33149,1991],{},[1495,33151,2678],{},[1495,33153,1503],{},[1152,33155,33156],{},"3,4",[1156,33158,33159],{"encoding":1158},"CL = \\bar{c} = 3{,}4",", horní mez ",[1115,33162,33164],{"className":33163},[1133],[1135,33165,33166],{"xmlns":1137},[1139,33167,33168,33181],{},[1142,33169,33170,33172,33174,33176,33178],{},[1148,33171,31624],{},[1148,33173,30280],{},[1148,33175,31598],{},[1495,33177,1503],{},[1152,33179,33180],{},"8,93",[1156,33182,33183],{"encoding":1158},"UCL = 8{,}93"," a dolní mez ",[1115,33186,33188],{"className":33187},[1133],[1135,33189,33190],{"xmlns":1137},[1139,33191,33192,33204],{},[1142,33193,33194,33196,33198,33200,33202],{},[1148,33195,31598],{},[1148,33197,30280],{},[1148,33199,31598],{},[1495,33201,1503],{},[1152,33203,1154],{},[1156,33205,33206],{"encoding":1158},"LCL = 0",". Žádný pás meze nepřekračuje — proces je zvládnutý.",[1110,33209,33210],{},[1971,33211],{"alt":33212,"className":33213,"src":33214},"mask-rd-priklad2-c",[1343,1975],"\u002Fwiki-assets\u002Fmask-rd-priklad2-c.png",[1695,33216,30750,33218],{"id":33217},"diagram-uu",[1115,33219,33221],{"className":33220},[1133],[1135,33222,33223],{"xmlns":1137},[1139,33224,33225,33229],{},[1142,33226,33227],{},[1148,33228,21090],{},[1156,33230,21090],{"encoding":1158},[1110,33232,32870,33233,33267,33268,33286],{},[1115,33234,33236],{"className":33235},[1133],[1135,33237,33238],{"xmlns":1137},[1139,33239,33240,33264],{},[1142,33241,33242,33248,33250,33256,33258],{},[1145,33243,33244,33246],{},[1148,33245,21090],{},[1148,33247,4085],{},[1495,33249,1503],{},[1145,33251,33252,33254],{},[1148,33253,1991],{},[1148,33255,4085],{},[1148,33257,3049],{"mathvariant":1599},[1145,33259,33260,33262],{},[1148,33261,2657],{},[1148,33263,4085],{},[1156,33265,33266],{"encoding":1158},"u_i = c_i\u002Fn_i"," je průměrný počet neshod přepočítaný na jeden produkt z logické podskupiny; rozsah podskupin ",[1115,33269,33271],{"className":33270},[1133],[1135,33272,33273],{"xmlns":1137},[1139,33274,33275,33283],{},[1142,33276,33277],{},[1145,33278,33279,33281],{},[1148,33280,2657],{},[1148,33282,4085],{},[1156,33284,33285],{"encoding":1158},"n_i"," není konstantní, a proto se bod od bodu mění i meze.",[1110,33288,33289,33290,33293],{},"Za ",[3161,33291,33292],{},"sizes"," se dosadí vektor rozsahů jednotlivých logických podskupin, resp. rozměr jejich jednotek:",[3166,33295,33297],{"className":3168,"code":33296,"language":71,"meta":3170,"style":3170},"data \u003C- read.table(\"3_4.txt\", header = TRUE)   # počty suků a rozměry prken\nqcc(data[, 1], type = \"u\", sizes = data[, 2])\n",[3161,33298,33299,33325],{"__ignoreMap":3170},[1115,33300,33301,33303,33305,33307,33309,33312,33314,33316,33318,33320,33322],{"class":3175,"line":10},[1115,33302,29591],{"class":3178},[1115,33304,3182],{"class":3181},[1115,33306,29596],{"class":3185},[1115,33308,2162],{"class":3189},[1115,33310,33311],{"class":3265},"\"3_4.txt\"",[1115,33313,2188],{"class":3181},[1115,33315,29606],{"class":3178},[1115,33317,3252],{"class":3181},[1115,33319,5282],{"class":3192},[1115,33321,21583],{"class":3189},[1115,33323,33324],{"class":10754},"# počty suků a rozměry prken\n",[1115,33326,33327,33329,33331,33333,33335,33337,33339,33341,33343,33345,33347,33350,33352,33355,33357,33359,33361,33363,33365],{"class":3175,"line":27},[1115,33328,360],{"class":3185},[1115,33330,2162],{"class":3189},[1115,33332,29591],{"class":3178},[1115,33334,17765],{"class":3189},[1115,33336,2188],{"class":3181},[1115,33338,3735],{"class":3192},[1115,33340,17782],{"class":3189},[1115,33342,2188],{"class":3181},[1115,33344,21772],{"class":3178},[1115,33346,3252],{"class":3181},[1115,33348,33349],{"class":3265}," \"u\"",[1115,33351,2188],{"class":3181},[1115,33353,33354],{"class":3178}," sizes",[1115,33356,3252],{"class":3181},[1115,33358,10582],{"class":3178},[1115,33360,17765],{"class":3189},[1115,33362,2188],{"class":3181},[1115,33364,7909],{"class":3192},[1115,33366,33367],{"class":3189},"])\n",[1695,33369,30750,33371],{"id":33370},"diagram-npnp",[1115,33372,33374],{"className":33373},[1133],[1135,33375,33376],{"xmlns":1137},[1139,33377,33378,33384],{},[1142,33379,33380,33382],{},[1148,33381,2657],{},[1148,33383,1110],{},[1156,33385,30245],{"encoding":1158},[1110,33387,33388,33389,4136,33404,33417],{},"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 ",[1115,33390,33392],{"className":33391},[1133],[1135,33393,33394],{"xmlns":1137},[1139,33395,33396,33402],{},[1142,33397,33398,33400],{},[1148,33399,2657],{},[1148,33401,1110],{},[1156,33403,30245],{"encoding":1158},[1115,33405,33407],{"className":33406},[1133],[1135,33408,33409],{"xmlns":1137},[1139,33410,33411,33415],{},[1142,33412,33413],{},[1148,33414,1110],{},[1156,33416,1110],{"encoding":1158}," je pravděpodobnost, že vyrobený produkt je neshodný.",[1110,33419,33420,33421,1497],{},"Pro konstantní rozsah ",[1115,33422,33424],{"className":33423},[1133],[1135,33425,33426],{"xmlns":1137},[1139,33427,33428,33432],{},[1142,33429,33430],{},[1148,33431,2657],{},[1156,33433,2657],{"encoding":1158},[3166,33435,33437],{"className":3168,"code":33436,"language":71,"meta":3170,"style":3170},"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",[3161,33438,33439,33465],{"__ignoreMap":3170},[1115,33440,33441,33443,33445,33447,33449,33452,33454,33456,33458,33460,33462],{"class":3175,"line":10},[1115,33442,29591],{"class":3178},[1115,33444,3182],{"class":3181},[1115,33446,29596],{"class":3185},[1115,33448,2162],{"class":3189},[1115,33450,33451],{"class":3265},"\"3_7.txt\"",[1115,33453,2188],{"class":3181},[1115,33455,29606],{"class":3178},[1115,33457,3252],{"class":3181},[1115,33459,5282],{"class":3192},[1115,33461,21583],{"class":3189},[1115,33463,33464],{"class":10754},"# počty vadných tabletů v sériích po 100 kusech\n",[1115,33466,33467,33469,33471,33473,33475,33477,33479,33481,33483,33485,33487,33490,33492,33494,33496,33498],{"class":3175,"line":27},[1115,33468,360],{"class":3185},[1115,33470,2162],{"class":3189},[1115,33472,29591],{"class":3178},[1115,33474,17765],{"class":3189},[1115,33476,2188],{"class":3181},[1115,33478,3735],{"class":3192},[1115,33480,17782],{"class":3189},[1115,33482,2188],{"class":3181},[1115,33484,21772],{"class":3178},[1115,33486,3252],{"class":3181},[1115,33488,33489],{"class":3265}," \"np\"",[1115,33491,2188],{"class":3181},[1115,33493,33354],{"class":3178},[1115,33495,3252],{"class":3181},[1115,33497,24835],{"class":3192},[1115,33499,3235],{"class":3189},[1695,33501,30750,33503],{"id":33502},"diagram-pp",[1115,33504,33506],{"className":33505},[1133],[1135,33507,33508],{"xmlns":1137},[1139,33509,33510,33514],{},[1142,33511,33512],{},[1148,33513,1110],{},[1156,33515,1110],{"encoding":1158},[1110,33517,33518,33519,33555],{},"Regulovanou veličinou je počet neshodných produktů v logické podskupině přepočtený na jednotku, ",[1115,33520,33522],{"className":33521},[1133],[1135,33523,33524],{"xmlns":1137},[1139,33525,33526,33552],{},[1142,33527,33528,33534,33536,33538,33544,33546],{},[1145,33529,33530,33532],{},[1148,33531,1110],{},[1148,33533,4085],{},[1495,33535,1503],{},[1148,33537,2657],{},[1145,33539,33540,33542],{},[1148,33541,1110],{},[1148,33543,4085],{},[1148,33545,3049],{"mathvariant":1599},[1145,33547,33548,33550],{},[1148,33549,2657],{},[1148,33551,4085],{},[1156,33553,33554],{"encoding":1158},"p_i = np_i\u002Fn_i","; rozsahy podskupin nemusí být konstantní.",[1110,33557,33289,33558,33560],{},[3161,33559,33292],{}," se dosadí vektor rozsahů logických podskupin:",[3166,33562,33564],{"className":3168,"code":33563,"language":71,"meta":3170,"style":3170},"data \u003C- read.table(\"3_6.txt\", header = TRUE)   # počty vadných tabletů a rozsahy sérií\nqcc(data[, 1], type = \"p\", sizes = data[, 2])\n",[3161,33565,33566,33592],{"__ignoreMap":3170},[1115,33567,33568,33570,33572,33574,33576,33579,33581,33583,33585,33587,33589],{"class":3175,"line":10},[1115,33569,29591],{"class":3178},[1115,33571,3182],{"class":3181},[1115,33573,29596],{"class":3185},[1115,33575,2162],{"class":3189},[1115,33577,33578],{"class":3265},"\"3_6.txt\"",[1115,33580,2188],{"class":3181},[1115,33582,29606],{"class":3178},[1115,33584,3252],{"class":3181},[1115,33586,5282],{"class":3192},[1115,33588,21583],{"class":3189},[1115,33590,33591],{"class":10754},"# počty vadných tabletů a rozsahy sérií\n",[1115,33593,33594,33596,33598,33600,33602,33604,33606,33608,33610,33612,33614,33617,33619,33621,33623,33625,33627,33629,33631],{"class":3175,"line":27},[1115,33595,360],{"class":3185},[1115,33597,2162],{"class":3189},[1115,33599,29591],{"class":3178},[1115,33601,17765],{"class":3189},[1115,33603,2188],{"class":3181},[1115,33605,3735],{"class":3192},[1115,33607,17782],{"class":3189},[1115,33609,2188],{"class":3181},[1115,33611,21772],{"class":3178},[1115,33613,3252],{"class":3181},[1115,33615,33616],{"class":3265}," \"p\"",[1115,33618,2188],{"class":3181},[1115,33620,33354],{"class":3178},[1115,33622,3252],{"class":3181},[1115,33624,10582],{"class":3178},[1115,33626,17765],{"class":3189},[1115,33628,2188],{"class":3181},[1115,33630,7909],{"class":3192},[1115,33632,33367],{"class":3189},[1392,33634,33636],{"id":33635},"indexy-způsobilosti","Indexy způsobilosti",[1110,33638,33639,33640,33659,33660,33678],{},"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 ",[1115,33641,33643],{"className":33642},[1133],[1135,33644,33645],{"xmlns":1137},[1139,33646,33647,33656],{},[1142,33648,33649,33651,33654],{},[1148,33650,31598],{},[1148,33652,33653],{},"S",[1148,33655,31598],{},[1156,33657,33658],{"encoding":1158},"LSL"," a horní meze ",[1115,33661,33663],{"className":33662},[1133],[1135,33664,33665],{"xmlns":1137},[1139,33666,33667,33675],{},[1142,33668,33669,33671,33673],{},[1148,33670,31624],{},[1148,33672,33653],{},[1148,33674,31598],{},[1156,33676,33677],{"encoding":1158},"USL",". Způsobilost se zkoumá až pro proces, který je podle regulačních diagramů statisticky zvládnutý (třetí fáze regulace).",[1695,33680,33682,33699],{"id":33681},"cpc_p-index-způsobilosti",[1115,33683,33685],{"className":33684},[1133],[1135,33686,33687],{"xmlns":1137},[1139,33688,33689,33697],{},[1142,33690,33691],{},[1145,33692,33693,33695],{},[1148,33694,30280],{},[1148,33696,1110],{},[1156,33698,30285],{"encoding":1158}," — index způsobilosti",[1110,33701,33702,33703,1497],{},"Podíl mezi délkou tolerančního intervalu a délkou intervalu, ve kterém by za normálního rozdělení mělo ležet skoro všech 99,73 % hodnot znaku, tedy ",[1115,33704,33706],{"className":33705},[1133],[1135,33707,33708],{"xmlns":1137},[1139,33709,33710,33716],{},[1142,33711,33712,33714],{},[1152,33713,13607],{},[1148,33715,2636],{},[1156,33717,33718],{"encoding":1158},"6\\sigma",[1115,33720,33722],{"className":33721},[1133],[1135,33723,33724],{"xmlns":1137,"display":2151},[1139,33725,33726,33762],{},[1142,33727,33728,33734,33736,33760],{},[1145,33729,33730,33732],{},[1148,33731,30280],{},[1148,33733,1110],{},[1495,33735,1503],{},[2749,33737,33738,33754],{},[1142,33739,33740,33742,33744,33746,33748,33750,33752],{},[1148,33741,31624],{},[1148,33743,33653],{},[1148,33745,31598],{},[1495,33747,1885],{},[1148,33749,31598],{},[1148,33751,33653],{},[1148,33753,31598],{},[1142,33755,33756,33758],{},[1152,33757,13607],{},[1148,33759,2636],{},[1148,33761,1335],{"mathvariant":1599},[1156,33763,33764],{"encoding":1158},"C_p = \\frac{USL - LSL}{6\\sigma}.",[1110,33766,33767,33784,33785,33798,33799,1335],{},[1115,33768,33770],{"className":33769},[1133],[1135,33771,33772],{"xmlns":1137},[1139,33773,33774,33782],{},[1142,33775,33776],{},[1145,33777,33778,33780],{},[1148,33779,30280],{},[1148,33781,1110],{},[1156,33783,30285],{"encoding":1158}," srovnává jen délky, nevšímá si, kde uprostřed tolerance proces leží — centrovaný i silně vychýlený proces se stejným ",[1115,33786,33788],{"className":33787},[1133],[1135,33789,33790],{"xmlns":1137},[1139,33791,33792,33796],{},[1142,33793,33794],{},[1148,33795,2636],{},[1156,33797,16531],{"encoding":1158}," mají stejné ",[1115,33800,33802],{"className":33801},[1133],[1135,33803,33804],{"xmlns":1137},[1139,33805,33806,33814],{},[1142,33807,33808],{},[1145,33809,33810,33812],{},[1148,33811,30280],{},[1148,33813,1110],{},[1156,33815,30285],{"encoding":1158},[1110,33817,33818],{},"Doplňkové charakteristiky využití tolerančního intervalu:",[1124,33820,33821,33855,33943],{},[1127,33822,33823,2324,33826,33854],{},[1399,33824,33825],{},"míra využití tolerančního intervalu",[1115,33827,33829],{"className":33828},[1133],[1135,33830,33831],{"xmlns":1137},[1139,33832,33833,33851],{},[1142,33834,33835,33847,33849],{},[6544,33836,33837],{"scriptlevel":1154,"displaystyle":1121},[2749,33838,33839,33841],{},[1152,33840,2354],{},[1145,33842,33843,33845],{},[1148,33844,30280],{},[1148,33846,1110],{},[2358,33848,2360],{},[1148,33850,2363],{"mathvariant":1599},[1156,33852,33853],{"encoding":1158},"\\dfrac{100}{C_p}\\,\\%"," — na kolik procent je toleranční interval využíván sledovaným znakem,",[1127,33856,33857,33860,33861,33878,33879,2261,33911,2188],{},[1399,33858,33859],{},"robustnost procesu",": rezerva, kterou máme v tolerančních mezích, než index ",[1115,33862,33864],{"className":33863},[1133],[1135,33865,33866],{"xmlns":1137},[1139,33867,33868,33876],{},[1142,33869,33870],{},[1145,33871,33872,33874],{},[1148,33873,30280],{},[1148,33875,1110],{},[1156,33877,30285],{"encoding":1158}," nabyde hodnotu 1 — rovná se menší hodnotě z výrazů ",[1115,33880,33882],{"className":33881},[1133],[1135,33883,33884],{"xmlns":1137},[1139,33885,33886,33908],{},[1142,33887,33888,33890,33892,33894,33896,33898,33900,33902,33904,33906],{},[1148,33889,31624],{},[1148,33891,33653],{},[1148,33893,31598],{},[1495,33895,1885],{},[1495,33897,2162],{"stretchy":2161},[1148,33899,1500],{},[1495,33901,6294],{},[1152,33903,13259],{},[1148,33905,2636],{},[1495,33907,2181],{"stretchy":2161},[1156,33909,33910],{"encoding":1158},"USL-(\\mu+3\\sigma)",[1115,33912,33914],{"className":33913},[1133],[1135,33915,33916],{"xmlns":1137},[1139,33917,33918,33940],{},[1142,33919,33920,33922,33924,33926,33928,33930,33932,33934,33936,33938],{},[1495,33921,2162],{"stretchy":2161},[1148,33923,1500],{},[1495,33925,1885],{},[1152,33927,13259],{},[1148,33929,2636],{},[1495,33931,2181],{"stretchy":2161},[1495,33933,1885],{},[1148,33935,31598],{},[1148,33937,33653],{},[1148,33939,31598],{},[1156,33941,33942],{"encoding":1158},"(\\mu-3\\sigma)-LSL",[1127,33944,33945,2324,33948,4136,33988,34002],{},[1399,33946,33947],{},"podíl zmetků",[1115,33949,33951],{"className":33950},[1133],[1135,33952,33953],{"xmlns":1137},[1139,33954,33955,33985],{},[1142,33956,33957,33964,33966,33968,33971,33973,33975,33977,33983],{},[1145,33958,33959,33961],{},[1148,33960,2158],{},[1148,33962,33963],{},"z",[1495,33965,1503],{},[1152,33967,2639],{},[1148,33969,33970],{"mathvariant":1599},"Φ",[1495,33972,2162],{"stretchy":2161},[1495,33974,1885],{},[1152,33976,13259],{},[1145,33978,33979,33981],{},[1148,33980,30280],{},[1148,33982,1110],{},[1495,33984,2181],{"stretchy":2161},[1156,33986,33987],{"encoding":1158},"P_z = 2\\Phi(-3C_p)",[1115,33989,33991],{"className":33990},[1133],[1135,33992,33993],{"xmlns":1137},[1139,33994,33995,33999],{},[1142,33996,33997],{},[1148,33998,33970],{"mathvariant":1599},[1156,34000,34001],{"encoding":1158},"\\Phi"," je distribuční funkce normovaného normálního rozdělení.",[1695,34004,34006,34027],{"id":34005},"cpkc_pk-index-způsobilosti-s-ohledem-na-vychýlení",[1115,34007,34009],{"className":34008},[1133],[1135,34010,34011],{"xmlns":1137},[1139,34012,34013,34025],{},[1142,34014,34015],{},[1145,34016,34017,34019],{},[1148,34018,30280],{},[1142,34020,34021,34023],{},[1148,34022,1110],{},[1148,34024,10710],{},[1156,34026,30307],{"encoding":1158}," — index způsobilosti s ohledem na vychýlení",[1110,34029,34030],{},"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:",[1115,34032,34034],{"className":34033},[1133],[1135,34035,34036],{"xmlns":1137,"display":2151},[1139,34037,34038,34108],{},[1142,34039,34040,34050,34052,34054,34056,34106],{},[1145,34041,34042,34044],{},[1148,34043,30280],{},[1142,34045,34046,34048],{},[1148,34047,1110],{},[1148,34049,10710],{},[1495,34051,1503],{},[1148,34053,14121],{},[1495,34055,8744],{},[1142,34057,34058,34060,34080,34082,34084,34104],{},[1495,34059,2162],{"fence":1121},[2749,34061,34062,34074],{},[1142,34063,34064,34066,34068,34070,34072],{},[1148,34065,31624],{},[1148,34067,33653],{},[1148,34069,31598],{},[1495,34071,1885],{},[1148,34073,1500],{},[1142,34075,34076,34078],{},[1152,34077,13259],{},[1148,34079,2636],{},[1495,34081,2188],{"separator":1121},[2358,34083,20877],{},[2749,34085,34086,34098],{},[1142,34087,34088,34090,34092,34094,34096],{},[1148,34089,1500],{},[1495,34091,1885],{},[1148,34093,31598],{},[1148,34095,33653],{},[1148,34097,31598],{},[1142,34099,34100,34102],{},[1152,34101,13259],{},[1148,34103,2636],{},[1495,34105,2181],{"fence":1121},[1148,34107,1335],{"mathvariant":1599},[1156,34109,34110],{"encoding":1158},"C_{pk} = \\min\\left(\\frac{USL-\\mu}{3\\sigma},\\ \\frac{\\mu-LSL}{3\\sigma}\\right).",[1110,34112,34113,34114,34127,34128,34158,34159,34180,34181,1335],{},"Vyjde-li některý z obou podílů záporný, položí se roven nule; to nastane, když střední hodnota ",[1115,34115,34117],{"className":34116},[1133],[1135,34118,34119],{"xmlns":1137},[1139,34120,34121,34125],{},[1142,34122,34123],{},[1148,34124,1500],{},[1156,34126,2605],{"encoding":1158}," leží mimo toleranční interval, a proces pak není pod statistickou kontrolou. U centrovaného procesu jsou oba podíly stejné a ",[1115,34129,34131],{"className":34130},[1133],[1135,34132,34133],{"xmlns":1137},[1139,34134,34135,34155],{},[1142,34136,34137,34147,34149],{},[1145,34138,34139,34141],{},[1148,34140,30280],{},[1142,34142,34143,34145],{},[1148,34144,1110],{},[1148,34146,10710],{},[1495,34148,1503],{},[1145,34150,34151,34153],{},[1148,34152,30280],{},[1148,34154,1110],{},[1156,34156,34157],{"encoding":1158},"C_{pk} = C_p","; čím víc je proces vychýlený, tím víc je ",[1115,34160,34162],{"className":34161},[1133],[1135,34163,34164],{"xmlns":1137},[1139,34165,34166,34178],{},[1142,34167,34168],{},[1145,34169,34170,34172],{},[1148,34171,30280],{},[1142,34173,34174,34176],{},[1148,34175,1110],{},[1148,34177,10710],{},[1156,34179,30307],{"encoding":1158}," menší než ",[1115,34182,34184],{"className":34183},[1133],[1135,34185,34186],{"xmlns":1137},[1139,34187,34188,34196],{},[1142,34189,34190],{},[1145,34191,34192,34194],{},[1148,34193,30280],{},[1148,34195,1110],{},[1156,34197,30285],{"encoding":1158},[1695,34199,34201,2261,34222,34245],{"id":34200},"cpmc_pm-a-cpmkc_pmk-indexy-vztažené-k-cíli",[1115,34202,34204],{"className":34203},[1133],[1135,34205,34206],{"xmlns":1137},[1139,34207,34208,34220],{},[1142,34209,34210],{},[1145,34211,34212,34214],{},[1148,34213,30280],{},[1142,34215,34216,34218],{},[1148,34217,1110],{},[1148,34219,14104],{},[1156,34221,30329],{"encoding":1158},[1115,34223,34225],{"className":34224},[1133],[1135,34226,34227],{"xmlns":1137},[1139,34228,34229,34243],{},[1142,34230,34231],{},[1145,34232,34233,34235],{},[1148,34234,30280],{},[1142,34236,34237,34239,34241],{},[1148,34238,1110],{},[1148,34240,14104],{},[1148,34242,10710],{},[1156,34244,30353],{"encoding":1158}," — indexy vztažené k cíli",[1110,34247,34248,34249,34262,34263,34276,34277,34320,34321,1497],{},"Pokud má proces zadaný cílový střed ",[1115,34250,34252],{"className":34251},[1133],[1135,34253,34254],{"xmlns":1137},[1139,34255,34256,34260],{},[1142,34257,34258],{},[1148,34259,2088],{},[1156,34261,2088],{"encoding":1158}," (ne nutně střed tolerance), nahradí se ",[1115,34264,34266],{"className":34265},[1133],[1135,34267,34268],{"xmlns":1137},[1139,34269,34270,34274],{},[1142,34271,34272],{},[1148,34273,2636],{},[1156,34275,16531],{"encoding":1158}," odmocninou ze střední čtvercové odchylky od cíle ",[1115,34278,34280],{"className":34279},[1133],[1135,34281,34282],{"xmlns":1137},[1139,34283,34284,34317],{},[1142,34285,34286,34289,34291],{},[1148,34287,34288],{},"τ",[1495,34290,1503],{},[2770,34292,34293],{},[1142,34294,34295,34301,34303,34305,34307,34309,34311],{},[2632,34296,34297,34299],{},[1148,34298,2636],{},[1152,34300,2639],{},[1495,34302,6294],{},[1495,34304,2162],{"stretchy":2161},[1148,34306,1500],{},[1495,34308,1885],{},[1148,34310,2088],{},[2632,34312,34313,34315],{},[1495,34314,2181],{"stretchy":2161},[1152,34316,2639],{},[1156,34318,34319],{"encoding":1158},"\\tau = \\sqrt{\\sigma^2+(\\mu-T)^2}",", která trestá i vychýlení od ",[1115,34322,34324],{"className":34323},[1133],[1135,34325,34326],{"xmlns":1137},[1139,34327,34328,34332],{},[1142,34329,34330],{},[1148,34331,2088],{},[1156,34333,2088],{"encoding":1158},[1115,34335,34337],{"className":34336},[1133],[1135,34338,34339],{"xmlns":1137,"display":2151},[1139,34340,34341,34453],{},[1142,34342,34343,34353,34355,34379,34381,34383,34395,34397,34399,34401,34451],{},[1145,34344,34345,34347],{},[1148,34346,30280],{},[1142,34348,34349,34351],{},[1148,34350,1110],{},[1148,34352,14104],{},[1495,34354,1503],{},[2749,34356,34357,34373],{},[1142,34358,34359,34361,34363,34365,34367,34369,34371],{},[1148,34360,31624],{},[1148,34362,33653],{},[1148,34364,31598],{},[1495,34366,1885],{},[1148,34368,31598],{},[1148,34370,33653],{},[1148,34372,31598],{},[1142,34374,34375,34377],{},[1152,34376,13607],{},[1148,34378,34288],{},[1495,34380,2188],{"separator":1121},[3520,34382],{"width":3522},[1145,34384,34385,34387],{},[1148,34386,30280],{},[1142,34388,34389,34391,34393],{},[1148,34390,1110],{},[1148,34392,14104],{},[1148,34394,10710],{},[1495,34396,1503],{},[1148,34398,14121],{},[1495,34400,8744],{},[1142,34402,34403,34405,34425,34427,34429,34449],{},[1495,34404,2162],{"fence":1121},[2749,34406,34407,34419],{},[1142,34408,34409,34411,34413,34415,34417],{},[1148,34410,31624],{},[1148,34412,33653],{},[1148,34414,31598],{},[1495,34416,1885],{},[1148,34418,1500],{},[1142,34420,34421,34423],{},[1152,34422,13259],{},[1148,34424,34288],{},[1495,34426,2188],{"separator":1121},[2358,34428,20877],{},[2749,34430,34431,34443],{},[1142,34432,34433,34435,34437,34439,34441],{},[1148,34434,1500],{},[1495,34436,1885],{},[1148,34438,31598],{},[1148,34440,33653],{},[1148,34442,31598],{},[1142,34444,34445,34447],{},[1152,34446,13259],{},[1148,34448,34288],{},[1495,34450,2181],{"fence":1121},[1148,34452,1335],{"mathvariant":1599},[1156,34454,34455],{"encoding":1158},"C_{pm} = \\frac{USL-LSL}{6\\tau}, \\qquad C_{pmk} = \\min\\left(\\frac{USL-\\mu}{3\\tau},\\ \\frac{\\mu-LSL}{3\\tau}\\right).",[1695,34457,34459],{"id":34458},"interpretace","Interpretace",[1532,34461,34462,34489],{},[1535,34463,34464],{},[1538,34465,34466,34486],{},[1541,34467,34468,34469],{},"Hodnota ",[1115,34470,34472],{"className":34471},[1133],[1135,34473,34474],{"xmlns":1137},[1139,34475,34476,34484],{},[1142,34477,34478],{},[1145,34479,34480,34482],{},[1148,34481,30280],{},[1148,34483,1110],{},[1156,34485,30285],{"encoding":1158},[1541,34487,34488],{},"Způsobilost procesu",[1568,34490,34491,34520,34563],{},[1538,34492,34493,34517],{},[1573,34494,34495],{},[1115,34496,34498],{"className":34497},[1133],[1135,34499,34500],{"xmlns":1137},[1139,34501,34502,34514],{},[1142,34503,34504,34510,34512],{},[1145,34505,34506,34508],{},[1148,34507,30280],{},[1148,34509,1110],{},[1495,34511,1682],{},[1152,34513,1176],{},[1156,34515,34516],{"encoding":1158},"C_p \u003C 1",[1573,34518,34519],{},"dosahovaná přesnost je menší než předepsaná — proces je nezpůsobilý",[1538,34521,34522,34546],{},[1573,34523,34524],{},[1115,34525,34527],{"className":34526},[1133],[1135,34528,34529],{"xmlns":1137},[1139,34530,34531,34543],{},[1142,34532,34533,34539,34541],{},[1145,34534,34535,34537],{},[1148,34536,30280],{},[1148,34538,1110],{},[1495,34540,1503],{},[1152,34542,1176],{},[1156,34544,34545],{"encoding":1158},"C_p = 1",[1573,34547,34548,34549,34562],{},"dosahovaná přesnost je rovna předepsané — proces je způsobilý, ale sebemenší zvětšení ",[1115,34550,34552],{"className":34551},[1133],[1135,34553,34554],{"xmlns":1137},[1139,34555,34556,34560],{},[1142,34557,34558],{},[1148,34559,2636],{},[1156,34561,16531],{"encoding":1158}," jej posune na nezpůsobilý",[1538,34564,34565,34589],{},[1573,34566,34567],{},[1115,34568,34570],{"className":34569},[1133],[1135,34571,34572],{"xmlns":1137},[1139,34573,34574,34586],{},[1142,34575,34576,34582,34584],{},[1145,34577,34578,34580],{},[1148,34579,30280],{},[1148,34581,1110],{},[1495,34583,1641],{},[1152,34585,1176],{},[1156,34587,34588],{"encoding":1158},"C_p > 1",[1573,34590,34591],{},"dosahovaná přesnost je větší než předepsaná — proces je způsobilý",[1110,34593,34594,34595,34616,34617,1335],{},"U indexu ",[1115,34596,34598],{"className":34597},[1133],[1135,34599,34600],{"xmlns":1137},[1139,34601,34602,34614],{},[1142,34603,34604],{},[1145,34605,34606,34608],{},[1148,34607,30280],{},[1142,34609,34610,34612],{},[1148,34611,1110],{},[1148,34613,10710],{},[1156,34615,30307],{"encoding":1158}," se v praxi požaduje víc než jen hodnota nad 1: s rozvojem technologií roste nárok na rezervu, a běžně se dnes vyžaduje hodnota alespoň ",[1115,34618,34620],{"className":34619},[1133],[1135,34621,34622],{"xmlns":1137},[1139,34623,34624,34629],{},[1142,34625,34626],{},[1152,34627,34628],{},"1,5",[1156,34630,34631],{"encoding":1158},"1{,}5",[1110,34633,34634],{},[1971,34635],{"alt":34636,"className":34637,"src":34638},"mask-rd-cp-panely",[1343,1975],"\u002Fwiki-assets\u002Fmask-rd-cp-panely.png",[1110,34640,34641],{},[1971,34642],{"alt":34643,"className":34644,"src":34645},"mask-rd-cpk-off-centre",[1343,1975],"\u002Fwiki-assets\u002Fmask-rd-cpk-off-centre.png",[1695,34647,34649],{"id":34648},"výpočet-v-r","Výpočet v R",[1110,34651,34652,34653,34656,34657,2546,34660,34663,34664,2261,34681,1195,34698,34701,34702,34715],{},"Indexy způsobilosti počítá ",[3161,34654,34655],{},"process.capability()"," z výstupu regulačního diagramu ",[3161,34658,34659],{},"q",[3161,34661,34662],{},"spec.limits"," jsou toleranční meze ",[1115,34665,34667],{"className":34666},[1133],[1135,34668,34669],{"xmlns":1137},[1139,34670,34671,34679],{},[1142,34672,34673,34675,34677],{},[1148,34674,31598],{},[1148,34676,33653],{},[1148,34678,31598],{},[1156,34680,33658],{"encoding":1158},[1115,34682,34684],{"className":34683},[1133],[1135,34685,34686],{"xmlns":1137},[1139,34687,34688,34696],{},[1142,34689,34690,34692,34694],{},[1148,34691,31624],{},[1148,34693,33653],{},[1148,34695,31598],{},[1156,34697,33677],{"encoding":1158},[3161,34699,34700],{},"target"," cílová hodnota ",[1115,34703,34705],{"className":34704},[1133],[1135,34706,34707],{"xmlns":1137},[1139,34708,34709,34713],{},[1142,34710,34711],{},[1148,34712,2088],{},[1156,34714,2088],{"encoding":1158},". Pro velikost výrobku v mm s tolerančními mezemi 100 a 110 mm a cílovou hodnotou 105 mm:",[3166,34717,34719],{"className":3168,"code":34718,"language":71,"meta":3170,"style":3170},"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",[3161,34720,34721,34731,34754,34769,34791],{"__ignoreMap":3170},[1115,34722,34723,34725,34727,34729],{"class":3175,"line":10},[1115,34724,10627],{"class":3181},[1115,34726,2162],{"class":3189},[1115,34728,360],{"class":3178},[1115,34730,3235],{"class":3189},[1115,34732,34733,34735,34737,34739,34741,34744,34746,34748,34750,34752],{"class":3175,"line":27},[1115,34734,29591],{"class":3178},[1115,34736,3182],{"class":3181},[1115,34738,29596],{"class":3185},[1115,34740,2162],{"class":3189},[1115,34742,34743],{"class":3265},"\"3_8.txt\"",[1115,34745,2188],{"class":3181},[1115,34747,29606],{"class":3178},[1115,34749,3252],{"class":3181},[1115,34751,5282],{"class":3192},[1115,34753,3235],{"class":3189},[1115,34755,34756,34758,34760,34763,34765,34767],{"class":3175,"line":148},[1115,34757,2675],{"class":3178},[1115,34759,3182],{"class":3181},[1115,34761,34762],{"class":3185}," as.matrix",[1115,34764,2162],{"class":3189},[1115,34766,29591],{"class":3178},[1115,34768,3235],{"class":3189},[1115,34770,34771,34773,34775,34777,34779,34781,34783,34785,34787,34789],{"class":3175,"line":111},[1115,34772,34659],{"class":3178},[1115,34774,3182],{"class":3181},[1115,34776,33096],{"class":3185},[1115,34778,2162],{"class":3189},[1115,34780,2675],{"class":3178},[1115,34782,2188],{"class":3181},[1115,34784,21772],{"class":3178},[1115,34786,3252],{"class":3181},[1115,34788,32223],{"class":3265},[1115,34790,3235],{"class":3189},[1115,34792,34793,34796,34798,34800,34802,34805,34807,34809,34811,34813,34815,34817,34819,34821,34824,34826,34829,34831,34834,34836,34838,34840,34842],{"class":3175,"line":96},[1115,34794,34795],{"class":3185},"process.capability",[1115,34797,2162],{"class":3189},[1115,34799,34659],{"class":3178},[1115,34801,2188],{"class":3181},[1115,34803,34804],{"class":3178}," spec.limits",[1115,34806,3252],{"class":3181},[1115,34808,3186],{"class":3185},[1115,34810,2162],{"class":3189},[1115,34812,2354],{"class":3192},[1115,34814,2188],{"class":3181},[1115,34816,9486],{"class":3192},[1115,34818,2181],{"class":3189},[1115,34820,2188],{"class":3181},[1115,34822,34823],{"class":3178}," target",[1115,34825,3252],{"class":3181},[1115,34827,34828],{"class":3192}," 105",[1115,34830,2188],{"class":3181},[1115,34832,34833],{"class":3178}," std.dev",[1115,34835,3252],{"class":3181},[1115,34837,8965],{"class":3185},[1115,34839,2162],{"class":3189},[1115,34841,2675],{"class":3178},[1115,34843,7963],{"class":3189},[1110,34845,34846,34847,1195,34850,1195,34853,1195,34856,2261,34859,34862,34863,2261,34865,34867,34868,34889,34890,34913],{},"Výpis obsahuje řádky ",[3161,34848,34849],{},"Cp",[3161,34851,34852],{},"Cp_l",[3161,34854,34855],{},"Cp_u",[3161,34857,34858],{},"Cp_k",[3161,34860,34861],{},"Cpm"," s hodnotou indexu a 95% intervalem spolehlivosti. ",[3161,34864,34852],{},[3161,34866,34855],{}," jsou dílčí poměry k dolní a horní mezi, jejich minimum je ",[1115,34869,34871],{"className":34870},[1133],[1135,34872,34873],{"xmlns":1137},[1139,34874,34875,34887],{},[1142,34876,34877],{},[1145,34878,34879,34881],{},[1148,34880,30280],{},[1142,34882,34883,34885],{},[1148,34884,1110],{},[1148,34886,10710],{},[1156,34888,30307],{"encoding":1158},". Index ",[1115,34891,34893],{"className":34892},[1133],[1135,34894,34895],{"xmlns":1137},[1139,34896,34897,34911],{},[1142,34898,34899],{},[1145,34900,34901,34903],{},[1148,34902,30280],{},[1142,34904,34905,34907,34909],{},[1148,34906,1110],{},[1148,34908,14104],{},[1148,34910,10710],{},[1156,34912,30353],{"encoding":1158}," a doplňkové charakteristiky se dopočítají ze vzorců výše:",[3166,34915,34917],{"className":3168,"code":34916,"language":71,"meta":3170,"style":3170},"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",[3161,34918,34919,34945,34970,35006,35036,35093,35107,35158],{"__ignoreMap":3170},[1115,34920,34921,34923,34925,34927,34929,34931,34933,34935,34937,34939,34941,34943],{"class":3175,"line":10},[1115,34922,10167],{"class":3178},[1115,34924,3182],{"class":3181},[1115,34926,8954],{"class":3185},[1115,34928,2162],{"class":3189},[1115,34930,2675],{"class":3178},[1115,34932,21726],{"class":3189},[1115,34934,380],{"class":3178},[1115,34936,3182],{"class":3181},[1115,34938,8965],{"class":3185},[1115,34940,2162],{"class":3189},[1115,34942,2675],{"class":3178},[1115,34944,3235],{"class":3189},[1115,34946,34947,34949,34951,34953,34955,34957,34959,34961,34963,34965,34967],{"class":3175,"line":27},[1115,34948,33658],{"class":3178},[1115,34950,3182],{"class":3181},[1115,34952,24835],{"class":3192},[1115,34954,2546],{"class":3189},[1115,34956,33677],{"class":3178},[1115,34958,3182],{"class":3181},[1115,34960,9486],{"class":3192},[1115,34962,2546],{"class":3189},[1115,34964,2088],{"class":3178},[1115,34966,3182],{"class":3181},[1115,34968,34969],{"class":3192}," 105\n",[1115,34971,34972,34975,34977,34979,34981,34983,34985,34987,34989,34991,34993,34995,34998,35000,35002,35004],{"class":3175,"line":148},[1115,34973,34974],{"class":3178},"tau",[1115,34976,3182],{"class":3181},[1115,34978,3699],{"class":3185},[1115,34980,2162],{"class":3189},[1115,34982,380],{"class":3178},[1115,34984,12415],{"class":3181},[1115,34986,2639],{"class":3192},[1115,34988,7877],{"class":3181},[1115,34990,3677],{"class":3189},[1115,34992,10167],{"class":3178},[1115,34994,3682],{"class":3181},[1115,34996,34997],{"class":3178}," T",[1115,34999,2181],{"class":3189},[1115,35001,12415],{"class":3181},[1115,35003,2639],{"class":3192},[1115,35005,3235],{"class":3189},[1115,35007,35008,35010,35012,35014,35016,35018,35021,35023,35025,35027,35029,35031,35034],{"class":3175,"line":111},[1115,35009,34849],{"class":3178},[1115,35011,3182],{"class":3181},[1115,35013,3677],{"class":3189},[1115,35015,33677],{"class":3178},[1115,35017,3682],{"class":3181},[1115,35019,35020],{"class":3178}," LSL",[1115,35022,3688],{"class":3189},[1115,35024,3049],{"class":3181},[1115,35026,3677],{"class":3189},[1115,35028,13607],{"class":3192},[1115,35030,3696],{"class":3181},[1115,35032,35033],{"class":3178}," sigma",[1115,35035,3235],{"class":3189},[1115,35037,35038,35041,35043,35045,35048,35050,35052,35054,35056,35058,35060,35062,35064,35067,35069,35071,35073,35075,35077,35079,35081,35083,35085,35087,35089,35091],{"class":3175,"line":96},[1115,35039,35040],{"class":3178},"Cpmk",[1115,35042,3182],{"class":3181},[1115,35044,21747],{"class":3185},[1115,35046,35047],{"class":3189},"((",[1115,35049,33677],{"class":3178},[1115,35051,3682],{"class":3181},[1115,35053,3249],{"class":3178},[1115,35055,3688],{"class":3189},[1115,35057,3049],{"class":3181},[1115,35059,3677],{"class":3189},[1115,35061,13259],{"class":3192},[1115,35063,3696],{"class":3181},[1115,35065,35066],{"class":3178}," tau",[1115,35068,2181],{"class":3189},[1115,35070,2188],{"class":3181},[1115,35072,3677],{"class":3189},[1115,35074,10167],{"class":3178},[1115,35076,3682],{"class":3181},[1115,35078,35020],{"class":3178},[1115,35080,3688],{"class":3189},[1115,35082,3049],{"class":3181},[1115,35084,3677],{"class":3189},[1115,35086,13259],{"class":3192},[1115,35088,3696],{"class":3181},[1115,35090,35066],{"class":3178},[1115,35092,7963],{"class":3189},[1115,35094,35095,35098,35100,35102,35104],{"class":3175,"line":89},[1115,35096,35097],{"class":3178},"miravyuziti",[1115,35099,3182],{"class":3181},[1115,35101,24835],{"class":3192},[1115,35103,7755],{"class":3181},[1115,35105,35106],{"class":3178}," Cp\n",[1115,35108,35109,35112,35114,35116,35118,35120,35122,35124,35126,35128,35130,35132,35134,35136,35138,35140,35142,35144,35146,35148,35150,35152,35154,35156],{"class":3175,"line":82},[1115,35110,35111],{"class":3178},"robustnost",[1115,35113,3182],{"class":3181},[1115,35115,21747],{"class":3185},[1115,35117,2162],{"class":3189},[1115,35119,33677],{"class":3178},[1115,35121,3682],{"class":3181},[1115,35123,3677],{"class":3189},[1115,35125,10167],{"class":3178},[1115,35127,7877],{"class":3181},[1115,35129,9537],{"class":3192},[1115,35131,3696],{"class":3181},[1115,35133,35033],{"class":3178},[1115,35135,2181],{"class":3189},[1115,35137,2188],{"class":3181},[1115,35139,3677],{"class":3189},[1115,35141,10167],{"class":3178},[1115,35143,3682],{"class":3181},[1115,35145,9537],{"class":3192},[1115,35147,3696],{"class":3181},[1115,35149,35033],{"class":3178},[1115,35151,3688],{"class":3189},[1115,35153,14265],{"class":3181},[1115,35155,35020],{"class":3178},[1115,35157,3235],{"class":3189},[1115,35159,35160,35163,35165,35167,35169,35171,35173,35175,35177,35179,35182],{"class":3175,"line":75},[1115,35161,35162],{"class":3178},"Pz",[1115,35164,3182],{"class":3181},[1115,35166,7909],{"class":3192},[1115,35168,3696],{"class":3181},[1115,35170,18930],{"class":3185},[1115,35172,2162],{"class":3189},[1115,35174,14265],{"class":3181},[1115,35176,13259],{"class":3192},[1115,35178,3696],{"class":3181},[1115,35180,35181],{"class":3178}," Cp",[1115,35183,3235],{"class":3189},[1392,35185,10963],{"id":10962},[1124,35187,35188,35191,35251,35342,35408],{},[1127,35189,35190],{},"Počítat indexy způsobilosti pro proces, který není statisticky zvládnutý — způsobilost se zkoumá až ve třetí fázi regulace.",[1127,35192,35193,35194,35211,35212,35229,35230,1335],{},"Posuzovat jen ",[1115,35195,35197],{"className":35196},[1133],[1135,35198,35199],{"xmlns":1137},[1139,35200,35201,35209],{},[1142,35202,35203],{},[1145,35204,35205,35207],{},[1148,35206,30280],{},[1148,35208,1110],{},[1156,35210,30285],{"encoding":1158}," u vychýleného procesu — ",[1115,35213,35215],{"className":35214},[1133],[1135,35216,35217],{"xmlns":1137},[1139,35218,35219,35227],{},[1142,35220,35221],{},[1145,35222,35223,35225],{},[1148,35224,30280],{},[1148,35226,1110],{},[1156,35228,30285],{"encoding":1158}," polohu střední hodnoty nezohledňuje, vychýlení zachytí až ",[1115,35231,35233],{"className":35232},[1133],[1135,35234,35235],{"xmlns":1137},[1139,35236,35237,35249],{},[1142,35238,35239],{},[1145,35240,35241,35243],{},[1148,35242,30280],{},[1142,35244,35245,35247],{},[1148,35246,1110],{},[1148,35248,10710],{},[1156,35250,30307],{"encoding":1158},[1127,35252,35253,35254,35267,35268,35281,35282,35267,35297,35310,35311,35324,35325,35338,35339,35341],{},"Zaměnit diagram ",[1115,35255,35257],{"className":35256},[1133],[1135,35258,35259],{"xmlns":1137},[1139,35260,35261,35265],{},[1142,35262,35263],{},[1148,35264,1991],{},[1156,35266,1991],{"encoding":1158}," s diagramem ",[1115,35269,35271],{"className":35270},[1133],[1135,35272,35273],{"xmlns":1137},[1139,35274,35275,35279],{},[1142,35276,35277],{},[1148,35278,21090],{},[1156,35280,21090],{"encoding":1158}," nebo diagram ",[1115,35283,35285],{"className":35284},[1133],[1135,35286,35287],{"xmlns":1137},[1139,35288,35289,35295],{},[1142,35290,35291,35293],{},[1148,35292,2657],{},[1148,35294,1110],{},[1156,35296,30245],{"encoding":1158},[1115,35298,35300],{"className":35299},[1133],[1135,35301,35302],{"xmlns":1137},[1139,35303,35304,35308],{},[1142,35305,35306],{},[1148,35307,1110],{},[1156,35309,1110],{"encoding":1158}," — při nekonstantním rozsahu podskupin se volí ",[1115,35312,35314],{"className":35313},[1133],[1135,35315,35316],{"xmlns":1137},[1139,35317,35318,35322],{},[1142,35319,35320],{},[1148,35321,21090],{},[1156,35323,21090],{"encoding":1158},", resp. ",[1115,35326,35328],{"className":35327},[1133],[1135,35329,35330],{"xmlns":1137},[1139,35331,35332,35336],{},[1142,35333,35334],{},[1148,35335,1110],{},[1156,35337,1110],{"encoding":1158},", a do ",[3161,35340,33292],{}," se zadává vektor rozsahů.",[1127,35343,35344,35345,35362,35363,35376,35377,35390,35391,1335],{},"Posuzovat diagram ",[1115,35346,35348],{"className":35347},[1133],[1135,35349,35350],{"xmlns":1137},[1139,35351,35352,35360],{},[1142,35353,35354],{},[2671,35355,35356,35358],{"accent":1121},[1148,35357,2675],{},[1495,35359,2678],{},[1156,35361,2681],{"encoding":1158}," dřív než diagram rozpětí — nejprve se určí a stabilizuje diagram ",[1115,35364,35366],{"className":35365},[1133],[1135,35367,35368],{"xmlns":1137},[1139,35369,35370,35374],{},[1142,35371,35372],{},[1148,35373,19792],{},[1156,35375,19792],{"encoding":1158}," (resp. ",[1115,35378,35380],{"className":35379},[1133],[1135,35381,35382],{"xmlns":1137},[1139,35383,35384,35388],{},[1142,35385,35386],{},[1148,35387,2695],{},[1156,35389,2695],{"encoding":1158},"), potom diagram ",[1115,35392,35394],{"className":35393},[1133],[1135,35395,35396],{"xmlns":1137},[1139,35397,35398,35406],{},[1142,35399,35400],{},[2671,35401,35402,35404],{"accent":1121},[1148,35403,2675],{},[1495,35405,2678],{},[1156,35407,2681],{"encoding":1158},[1127,35409,35410],{},"Vyřadit podskupinu jen podle polohy bodu — vyřazuje se až po zjištění a odstranění vymezitelné příčiny.",[1392,35412,11120],{"id":11119},[1124,35414,35415,35420,35425,35431,35436,35441,35446],{},[1127,35416,35417],{},[1340,35418,11128],{"className":35419,"dataFsResolvedFilePath":1344,"href":1345},[1343],[1127,35421,35422],{},[1340,35423,886],{"className":35424,"dataFsResolvedFilePath":1351,"href":1352},[1343],[1127,35426,35427],{},[1340,35428,35430],{"className":35429,"dataFsResolvedFilePath":1358,"href":1359},[1343],"nahodne-veliciny-a-rozdeleni",[1127,35432,35433],{},[1340,35434,141],{"className":35435,"dataFsResolvedFilePath":11426,"href":11427},[1343],[1127,35437,35438],{},[1340,35439,20650],{"className":35440,"dataFsResolvedFilePath":11146,"href":11147},[1343],[1127,35442,35443],{},[1340,35444,716],{"className":35445,"dataFsResolvedFilePath":11154,"href":11155},[1343],[1127,35447,35448],{},[1340,35449,11172],{"className":35450,"dataFsResolvedFilePath":11170,"href":11171},[1343],[1392,35452,11175],{"id":934},[1110,35454,11178,35455,11182],{},[10079,35456,11181],{},[1110,35458,35459,35460,35463],{},"MONTGOMERY, D. C. ",[10079,35461,35462],{},"Introduction to Statistical Quality Control",". 6. vyd. John Wiley & Sons, 2005.",[1110,35465,35466,35467,35470],{},"ČSN ISO 8258. ",[10079,35468,35469],{},"Shewhartovy regulační diagramy",". Praha: Český normalizační institut, 1994.",[1110,35472,35473,35474,35477],{},"KUPKA, K. ",[10079,35475,35476],{},"Statistické řízení jakosti",". Pardubice: TriloByte, 1997.",[11184,35479,35480],{},"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":33635,"depth":27,"text":33636,"children":35504},[35505,35507,35509,35511,35512],{"id":33681,"depth":148,"text":35506},"CpC_p — index způsobilosti",{"id":34005,"depth":148,"text":35508},"CpkC_{pk} — index způsobilosti s ohledem na vychýlení",{"id":34200,"depth":148,"text":35510},"CpmC_{pm} a CpmkC_{pmk} — indexy vztažené k cíli",{"id":34458,"depth":148,"text":34459},{"id":34648,"depth":148,"text":34649},{"id":10962,"depth":27,"text":10963},{"id":11119,"depth":27,"text":11120},{"id":934,"depth":27,"text":11175},{},"\u002Ftopics\u002Fregulacni-diagramy-a-indexy-zpusobilosti",{"title":11164,"description":3170},[35520,35521,35522,35523],"raw\u002Fmask\u002F06 regulační diagramy.pdf","raw\u002Fmask\u002F07 indexy způsobilosti.pdf","raw\u002Fmask\u002Fnávod 06 a 07.pdf","raw\u002Fmask\u002Fpříklady 06 a 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í tabulka V rámci Metody aplikované statistiky navazují kontingenční tabulky na \u003C\u003Ctestovani-hypotez>>: místo jedné náhodné veličiny teď sledujeme dva **kvalitativní** (kategoriální) znaky sou …",{"slug":23,"path":1345,"title":24,"snippet":44647},"… y, kvantily, empirická distribuční funkce, třídění naměřených dat do tříd a histogram. 3. \u003C\u003Ctestovani-hypotez>> — jednovýběrový a párový t-test, F-test, dvouvýběrový t-test, testy normality a jejich ne …",{"slug":44649,"path":44650,"title":44651,"snippet":44652},"mask-detail-predmetu","\u002Fwiki\u002Fmask-detail-predmetu","Detail předmětu — Metody aplikované statistiky","… * — parametrické a neparametrické testy o střední hodnotě, rozptylu a shodě s rozdělením (\u003C\u003Ctestovani-hypotez>>). 4. **Regresní a korelační analýza** — lineární, nelineární a vícenásobná regrese, diagn …",{"slug":44654,"path":44655,"title":44656,"snippet":44657},"mask-prednasky-veliciny-data-testy","\u002Fwiki\u002Fmask-prednasky-veliciny-data-testy","MasK — Náhodné veličiny, datové soubory a testy hypotéz","… zdělení pravděpodobnosti]] - Popisná statistika a datové soubory - \u003C\u003Ctestovani-hypotez>> - masK — Tahák pro R ## Reference KROPÁČ, J. *Statistika A*. 4. vyd. B …",{"slug":44659,"path":11171,"title":44660,"snippet":44661},"mask-r-tahak","masK — Tahák pro R","… ibuční funkce v bodě $k$ | | `knots(f)` | vzestupně seřazené různé hodnoty souboru | ### \u003C\u003Ctestovani-hypotez>> | Funkce | Použití | |---|---| | `t.test(x, mu = ..., alternative = ...)` | jednovýběrov …",{"slug":35430,"path":1359,"title":11134,"snippet":44663},"… , které se dále používají při konstrukci intervalů spolehlivosti a testování hypotéz (viz \u003C\u003Ctestovani-hypotez>>) — na rozdíl od normálního rozdělení se v příkladech této kapitoly samostatně nepočítají, …",{"slug":886,"path":1352,"title":11140,"snippet":44665},"… a data odpovídají exponenciálnímu rozdělení formálně, posuzuje test dobré shody popsaný v \u003C\u003Ctestovani-hypotez>>. > [!example] Příklad: Doba života výrobku > Sledováním doby života výrobku bylo naměřen …",{"slug":20650,"path":11147,"title":11148,"snippet":44667},"… Normalita se u menšího počtu pozorování ověřuje stejnými testy jako u jiných znaků (viz \u003C\u003Ctestovani-hypotez>>) — Shapiro–Wilkovým nebo Kolmogorovovým–Smirnovovým testem — nebo graficky grafem reziduí …",[44669,44670,44671,44672,44673],{"slug":44654,"title":44656,"path":44655,"sharedTags":148},{"slug":44659,"title":44660,"path":11171,"sharedTags":148},{"slug":44649,"title":44651,"path":44650,"sharedTags":27},{"slug":716,"title":11156,"path":11155,"sharedTags":27},{"slug":44674,"title":44675,"path":44676,"sharedTags":27},"mask-prednasky-regrese-kontingence","MasK — Regresní analýza a kontingenční tabulky","\u002Fwiki\u002Fmask-prednasky-regrese-kontingence",{"zapisku":25,"topics":89,"summaries":111,"outputs":10},1791009625487]