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x","–",[1115,1250,1252],{"className":1251},[1138],[1140,1253,1254],{"xmlns":1142},[1144,1255,1256,1261],{},[1147,1257,1258],{},[1153,1259,1260],{},"R",[1159,1262,1260],{"encoding":1161},[1115,1264,1266],{"className":1265},[1138],[1140,1267,1268],{"xmlns":1142},[1144,1269,1270,1278],{},[1147,1271,1272],{},[1236,1273,1274,1276],{"accent":1121},[1153,1275,1240],{},[1242,1277,1244],{},[1159,1279,1247],{"encoding":1161},[1115,1281,1283],{"className":1282},[1138],[1140,1284,1285],{"xmlns":1142},[1144,1286,1287,1292],{},[1147,1288,1289],{},[1153,1290,1291],{},"s",[1159,1293,1291],{"encoding":1161}," pro logické podskupiny, diagram jednotlivých hodnot ",[1115,1296,1298],{"className":1297},[1138],[1140,1299,1300],{"xmlns":1142},[1144,1301,1302,1306],{},[1147,1303,1304],{},[1153,1305,1240],{},[1159,1307,1240],{"encoding":1161},[1115,1309,1311],{"className":1310},[1138],[1140,1312,1313],{"xmlns":1142},[1144,1314,1315,1328],{},[1147,1316,1317],{},[1150,1318,1319,1321],{},[1153,1320,1260],{},[1147,1322,1323,1325],{},[1153,1324,1183],{},[1153,1326,1327],{},"l",[1159,1329,1330],{"encoding":1161},"R_{kl}",", diagramy pro počty neshodných jednotek a vad (",[1115,1333,1335],{"className":1334},[1138],[1140,1336,1337],{"xmlns":1142},[1144,1338,1339,1344],{},[1147,1340,1341],{},[1153,1342,1343],{},"c",[1159,1345,1343],{"encoding":1161},", ",[1115,1348,1350],{"className":1349},[1138],[1140,1351,1352],{"xmlns":1142},[1144,1353,1354,1359],{},[1147,1355,1356],{},[1153,1357,1358],{},"u",[1159,1360,1358],{"encoding":1161},[1115,1362,1364],{"className":1363},[1138],[1140,1365,1366],{"xmlns":1142},[1144,1367,1368,1375],{},[1147,1369,1370,1373],{},[1153,1371,1372],{},"n",[1153,1374,1110],{},[1159,1376,1377],{"encoding":1161},"np",[1115,1379,1381],{"className":1380},[1138],[1140,1382,1383],{"xmlns":1142},[1144,1384,1385,1389],{},[1147,1386,1387],{},[1153,1388,1110],{},[1159,1390,1110],{"encoding":1161},"), hodnocení stavu regulace, indexy způsobilosti ",[1115,1393,1395],{"className":1394},[1138],[1140,1396,1397],{"xmlns":1142},[1144,1398,1399,1407],{},[1147,1400,1401],{},[1150,1402,1403,1405],{},[1153,1404,1155],{},[1153,1406,1110],{},[1159,1408,1162],{"encoding":1161},[1115,1410,1412],{"className":1411},[1138],[1140,1413,1414],{"xmlns":1142},[1144,1415,1416,1428],{},[1147,1417,1418],{},[1150,1419,1420,1422],{},[1153,1421,1155],{},[1147,1423,1424,1426],{},[1153,1425,1110],{},[1153,1427,1183],{},[1159,1429,1186],{"encoding":1161}," vůči mezím specifikace",[1189,1432,1434],{"id":1433},"související-stránky","Související stránky",[1436,1437,1438,1444,1449],"ul",{},[1439,1440,1441],"li",{},[1127,1442,1133],{"className":1443,"dataFsResolvedFilePath":1131,"href":1132},[1130],[1439,1445,1446],{},[1127,1447,1222],{"className":1448,"dataFsResolvedFilePath":1220,"href":1221},[1130],[1439,1450,1451],{},[1127,1452,1456],{"className":1453,"dataFsResolvedFilePath":1454,"href":1455},[1130],"outputs\u002Fmask-r-tahak.md","\u002Fwiki\u002Fmask-r-tahak","masK — Tahák pro R",[1189,1458,1459],{"id":934},"Reference",[1110,1461,1462,1463,1467],{},"KROPÁČ, J. ",[1464,1465,1466],"em",{},"Statistika A",". 4. vyd. Brno: Fakulta podnikatelská VUT, 2011.",[1110,1469,1470,1471,1474],{},"MONTGOMERY, D. C. ",[1464,1472,1473],{},"Introduction to Statistical Quality Control",". 6. vyd. John Wiley & Sons, 2005.",[1110,1476,1477,1478,1481],{},"ČSN ISO 8258. ",[1464,1479,1480],{},"Shewhartovy regulační diagramy",". Praha: Český normalizační institut, 1994.",[1110,1483,1484,1485,1488],{},"KUPKA, K. ",[1464,1486,1487],{},"Statistické řízení jakosti",". Pardubice: TriloByte, 1997.",{"title":1490,"searchDepth":27,"depth":27,"links":1491},"",[1492,1493,1494],{"id":1191,"depth":27,"text":1192},{"id":1433,"depth":27,"text":1434},{"id":934,"depth":27,"text":1459},null,"2026-10-02","md",{},true,"\u002Fsummaries\u002Fmask-prednasky-regulace-zpusobilost",{"title":1094,"description":1490},[1503,1504,1505,1506],"raw\u002Fmask\u002F06 regulační diagramy.pdf","raw\u002Fmask\u002F07 indexy způsobilosti.pdf","raw\u002Fmask\u002Fnávod 06 a 07.pdf","raw\u002Fmask\u002Fpříklady 06 a 07.pdf","summaries\u002Fmask-prednasky-regulace-zpusobilost",[23,67,137,274,360,71],"summary","8DjJRCMFxgFvwn1wsc-UZFaKjpsszi3YeZWYKcfrLMw","summaries",[1513,6672,11137,15901,20603,26040],{"id":1514,"title":1515,"body":1516,"course":23,"courses":1495,"created":1496,"description":1490,"extension":1497,"meta":6662,"navigation":1499,"path":6663,"seo":6664,"sources":6665,"stem":6668,"tags":6669,"type":6670,"updated":1496,"__hash__":6671},"topics\u002Ftopics\u002Fkontingencni-tabulky.md","Kontingenční tabulky",{"type":1096,"value":1517,"toc":6652},[1518,1521,1707,1711,1729,1747,1959,2100,2695,2712,2824,2828,2859,2864,3466,3473,3693,3918,3926,4007,4119,4272,4278,4359,4380,4389,4423,4430,4433,4439,4505,4564,4717,4723,4730,4808,4811,4867,5205,5226,5330,5439,5442,5463,5466,5721,5802,5809,5813,6043,6057,6206,6340,6346,6404,6408,6427,6442,6448,6493,6512,6527,6533,6592,6594,6642,6644,6648],[1099,1519,1515],{"id":1520},"kontingenční-tabulky",[1103,1522,1526,1534],{"className":1523,"dataCallout":1525},[1106,1524],"callout-default","tldr",[1110,1527,1529,1533],{"className":1528},[1113],[1115,1530],{"className":1531,"ariaHidden":1121},[1118,1532,1120],"i-lucide:info","V kostce",[1436,1535,1536,1544,1609,1630,1670,1696],{},[1439,1537,1538,1539,1543],{},"Kontingenční tabulka zaznamenává ",[1540,1541,1542],"strong",{},"simultánní četnosti"," dvou kvalitativních znaků naměřených na stejném souboru.",[1439,1545,1546,1549,1550,1571,1572,1593,1594,1608],{},[1540,1547,1548],{},"Test nezávislosti"," srovnává pozorované četnosti s očekávanými za platnosti ",[1115,1551,1553],{"className":1552},[1138],[1140,1554,1555],{"xmlns":1142},[1144,1556,1557,1568],{},[1147,1558,1559],{},[1150,1560,1561,1564],{},[1153,1562,1563],{},"H",[1565,1566,1567],"mn",{},"0",[1159,1569,1570],{"encoding":1161},"H_0"," pomocí statistiky ",[1115,1573,1575],{"className":1574},[1138],[1140,1576,1577],{"xmlns":1142},[1144,1578,1579,1590],{},[1147,1580,1581],{},[1582,1583,1584,1587],"msup",{},[1153,1585,1586],{},"χ",[1565,1588,1589],{},"2",[1159,1591,1592],{"encoding":1161},"\\chi^2","; rozhoduje kritický obor ",[1115,1595,1597],{"className":1596},[1138],[1140,1598,1599],{"xmlns":1142},[1144,1600,1601,1606],{},[1147,1602,1603],{},[1153,1604,1605],{},"W",[1159,1607,1605],{"encoding":1161},", prakticky p-hodnota.",[1439,1610,1611,1612,1629],{},"Aproximace ",[1115,1613,1615],{"className":1614},[1138],[1140,1616,1617],{"xmlns":1142},[1144,1618,1619,1627],{},[1147,1620,1621],{},[1582,1622,1623,1625],{},[1153,1624,1586],{},[1565,1626,1589],{},[1159,1628,1592],{"encoding":1161}," rozdělením platí jen tehdy, když jsou očekávané četnosti dostatečně velké — proto se vždy kontrolují.",[1439,1631,1632,1633,1650,1651,1654,1655,1669],{},"Zamítnutí ",[1115,1634,1636],{"className":1635},[1138],[1140,1637,1638],{"xmlns":1142},[1144,1639,1640,1648],{},[1147,1641,1642],{},[1150,1643,1644,1646],{},[1153,1645,1563],{},[1565,1647,1567],{},[1159,1649,1570],{"encoding":1161}," samo o sobě neříká, jak silná závislost je — na to slouží ",[1540,1652,1653],{},"Cramérův koeficient kontingence"," ",[1115,1656,1658],{"className":1657},[1138],[1140,1659,1660],{"xmlns":1142},[1144,1661,1662,1667],{},[1147,1663,1664],{},[1153,1665,1666],{},"V",[1159,1668,1666],{"encoding":1161},".",[1439,1671,1672,1675,1676,1669],{},[1540,1673,1674],{},"Čtyřpolní tabulka"," (2×2) je speciální případ s vlastním zjednodušeným vzorcem pro ",[1115,1677,1679],{"className":1678},[1138],[1140,1680,1681],{"xmlns":1142},[1144,1682,1683,1693],{},[1147,1684,1685,1687,1690],{},[1153,1686,1372],{},[1242,1688,1689],{},">",[1565,1691,1692],{},"40",[1159,1694,1695],{"encoding":1161},"n>40",[1439,1697,1698,1699,1702,1703,1706],{},"Pro ",[1540,1700,1701],{},"párová data"," (stejné prvky měřené dvakrát, např. před\u002Fpo zásahu) se používá ",[1540,1704,1705],{},"McNemarův test",", ne obyčejný test nezávislosti.",[1189,1708,1710],{"id":1709},"kontingenční-tabulka","Kontingenční tabulka",[1110,1712,1713,1714,1717,1718,1724,1725,1728],{},"V rámci ",[1127,1715,1133],{"className":1716,"dataFsResolvedFilePath":1131,"href":1132},[1130]," navazují kontingenční tabulky na\n",[1127,1719,1723],{"className":1720,"dataFsResolvedFilePath":1721,"href":1722},[1130],"topics\u002Ftestovani-hypotez.md","\u002Fwiki\u002Ftestovani-hypotez","testování statistických hypotéz",": místo jedné náhodné veličiny teď sledujeme dva\n",[1540,1726,1727],{},"kvalitativní"," (kategoriální) znaky současně a ptáme se, zda spolu souvisí.",[1110,1730,1731,1732,1735,1736,1738,1739,1742,1743,1746],{},"Znak je ",[1540,1733,1734],{},"kvantitativní",", pokud nabývá číselných hodnot (stáří, stav tachometru), a ",[1540,1737,1727],{},"\n(kategoriální), pokud nabývá slovních variant (vzdělání, kuřák\u002Fnekuřák). Kvalitativní znaky dále dělíme na\n",[1540,1740,1741],{},"alternativní"," (dvě varianty, např. vada ano\u002Fne) a ",[1540,1744,1745],{},"množné"," (více než dvě varianty, např. svobodný\u002Frozvedený\u002Fženatý).",[1110,1748,1749,1750,1763,1764,1778,1779,1812,1813,1827,1828,1858,1859,1862,1863,1890,1891,1654,1894,1916,1917,1935,1936,1954,1955,1958],{},"Mějme ",[1115,1751,1753],{"className":1752},[1138],[1140,1754,1755],{"xmlns":1142},[1144,1756,1757,1761],{},[1147,1758,1759],{},[1153,1760,1372],{},[1159,1762,1372],{"encoding":1161}," opakování pokusu, při nichž sledujeme dva kvalitativní znaky ",[1115,1765,1767],{"className":1766},[1138],[1140,1768,1769],{"xmlns":1142},[1144,1770,1771,1776],{},[1147,1772,1773],{},[1153,1774,1775],{},"A",[1159,1777,1775],{"encoding":1161}," (varianty ",[1115,1780,1782],{"className":1781},[1138],[1140,1783,1784],{"xmlns":1142},[1144,1785,1786,1809],{},[1147,1787,1788,1795,1798,1801,1803],{},[1150,1789,1790,1792],{},[1153,1791,1775],{},[1565,1793,1794],{},"1",[1242,1796,1797],{"separator":1121},",",[1242,1799,1800],{},"…",[1242,1802,1797],{"separator":1121},[1150,1804,1805,1807],{},[1153,1806,1775],{},[1153,1808,71],{},[1159,1810,1811],{"encoding":1161},"A_1,\\dots,A_r",") a ",[1115,1814,1816],{"className":1815},[1138],[1140,1817,1818],{"xmlns":1142},[1144,1819,1820,1825],{},[1147,1821,1822],{},[1153,1823,1824],{},"B",[1159,1826,1824],{"encoding":1161},"\n(varianty ",[1115,1829,1831],{"className":1830},[1138],[1140,1832,1833],{"xmlns":1142},[1144,1834,1835,1855],{},[1147,1836,1837,1843,1845,1847,1849],{},[1150,1838,1839,1841],{},[1153,1840,1824],{},[1565,1842,1794],{},[1242,1844,1797],{"separator":1121},[1242,1846,1800],{},[1242,1848,1797],{"separator":1121},[1150,1850,1851,1853],{},[1153,1852,1824],{},[1153,1854,1291],{},[1159,1856,1857],{"encoding":1161},"B_1,\\dots,B_s","). Výsledky zapíšeme do ",[1540,1860,1861],{},"kontingenční tabulky",": v políčku ",[1115,1864,1866],{"className":1865},[1138],[1140,1867,1868],{"xmlns":1142},[1144,1869,1870,1887],{},[1147,1871,1872,1876,1879,1881,1884],{},[1242,1873,1875],{"stretchy":1874},"false","(",[1153,1877,1878],{},"i",[1242,1880,1797],{"separator":1121},[1153,1882,1883],{},"j",[1242,1885,1886],{"stretchy":1874},")",[1159,1888,1889],{"encoding":1161},"(i,j)"," je ",[1540,1892,1893],{},"simultánní\nčetnost",[1115,1895,1897],{"className":1896},[1138],[1140,1898,1899],{"xmlns":1142},[1144,1900,1901,1913],{},[1147,1902,1903],{},[1150,1904,1905,1907],{},[1153,1906,1372],{},[1147,1908,1909,1911],{},[1153,1910,1878],{},[1153,1912,1883],{},[1159,1914,1915],{"encoding":1161},"n_{ij}",", tedy počet pokusů s variantou ",[1115,1918,1920],{"className":1919},[1138],[1140,1921,1922],{"xmlns":1142},[1144,1923,1924,1932],{},[1147,1925,1926],{},[1150,1927,1928,1930],{},[1153,1929,1775],{},[1153,1931,1878],{},[1159,1933,1934],{"encoding":1161},"A_i"," zároveň s variantou ",[1115,1937,1939],{"className":1938},[1138],[1140,1940,1941],{"xmlns":1142},[1144,1942,1943,1951],{},[1147,1944,1945],{},[1150,1946,1947,1949],{},[1153,1948,1824],{},[1153,1950,1883],{},[1159,1952,1953],{"encoding":1161},"B_j",". Řádkové a sloupcové součty\njsou ",[1540,1956,1957],{},"marginální četnosti",":",[1115,1960,1962],{"className":1961},[1138],[1140,1963,1965],{"xmlns":1142,"display":1964},"block",[1144,1966,1967,2097],{},[1147,1968,1969,1980,1983,1999,2009,2011,2015,2025,2027,2041,2051,2053,2055,2057,2059,2073,2087],{},[1150,1970,1971,1973],{},[1153,1972,1372],{},[1147,1974,1975,1977],{},[1153,1976,1878],{},[1242,1978,1979],{},"∙",[1242,1981,1982],{},"=",[1984,1985,1986,1989,1997],"munderover",{},[1242,1987,1988],{},"∑",[1147,1990,1991,1993,1995],{},[1153,1992,1883],{},[1242,1994,1982],{},[1565,1996,1794],{},[1153,1998,1291],{},[1150,2000,2001,2003],{},[1153,2002,1372],{},[1147,2004,2005,2007],{},[1153,2006,1878],{},[1153,2008,1883],{},[1242,2010,1797],{"separator":1121},[2012,2013],"mspace",{"width":2014},"2em",[1150,2016,2017,2019],{},[1153,2018,1372],{},[1147,2020,2021,2023],{},[1242,2022,1979],{},[1153,2024,1883],{},[1242,2026,1982],{},[1984,2028,2029,2031,2039],{},[1242,2030,1988],{},[1147,2032,2033,2035,2037],{},[1153,2034,1878],{},[1242,2036,1982],{},[1565,2038,1794],{},[1153,2040,71],{},[1150,2042,2043,2045],{},[1153,2044,1372],{},[1147,2046,2047,2049],{},[1153,2048,1878],{},[1153,2050,1883],{},[1242,2052,1797],{"separator":1121},[2012,2054],{"width":2014},[1153,2056,1372],{},[1242,2058,1982],{},[1984,2060,2061,2063,2071],{},[1242,2062,1988],{},[1147,2064,2065,2067,2069],{},[1153,2066,1878],{},[1242,2068,1982],{},[1565,2070,1794],{},[1153,2072,71],{},[1984,2074,2075,2077,2085],{},[1242,2076,1988],{},[1147,2078,2079,2081,2083],{},[1153,2080,1883],{},[1242,2082,1982],{},[1565,2084,1794],{},[1153,2086,1291],{},[1150,2088,2089,2091],{},[1153,2090,1372],{},[1147,2092,2093,2095],{},[1153,2094,1878],{},[1153,2096,1883],{},[1159,2098,2099],{"encoding":1161},"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}",[1194,2101,2102,2214],{},[1197,2103,2104],{},[1200,2105,2106,2128,2148,2168,2170,2190],{},[1203,2107,2108],{},[1115,2109,2111],{"className":2110},[1138],[1140,2112,2113],{"xmlns":1142},[1144,2114,2115,2125],{},[1147,2116,2117,2119,2123],{},[1153,2118,1775],{},[1153,2120,2122],{"mathvariant":2121},"normal","\\",[1153,2124,1824],{},[1159,2126,2127],{"encoding":1161},"A \\backslash B",[1203,2129,2130],{},[1115,2131,2133],{"className":2132},[1138],[1140,2134,2135],{"xmlns":1142},[1144,2136,2137,2145],{},[1147,2138,2139],{},[1150,2140,2141,2143],{},[1153,2142,1824],{},[1565,2144,1794],{},[1159,2146,2147],{"encoding":1161},"B_1",[1203,2149,2150],{},[1115,2151,2153],{"className":2152},[1138],[1140,2154,2155],{"xmlns":1142},[1144,2156,2157,2165],{},[1147,2158,2159],{},[1150,2160,2161,2163],{},[1153,2162,1824],{},[1565,2164,1589],{},[1159,2166,2167],{"encoding":1161},"B_2",[1203,2169,1800],{},[1203,2171,2172],{},[1115,2173,2175],{"className":2174},[1138],[1140,2176,2177],{"xmlns":1142},[1144,2178,2179,2187],{},[1147,2180,2181],{},[1150,2182,2183,2185],{},[1153,2184,1824],{},[1153,2186,1291],{},[1159,2188,2189],{"encoding":1161},"B_s",[1203,2191,2192],{},[1115,2193,2195],{"className":2194},[1138],[1140,2196,2197],{"xmlns":1142},[1144,2198,2199,2211],{},[1147,2200,2201],{},[1150,2202,2203,2205],{},[1153,2204,1372],{},[1147,2206,2207,2209],{},[1153,2208,1878],{},[1242,2210,1979],{},[1159,2212,2213],{"encoding":1161},"n_{i\\bullet}",[1210,2215,2216,2330,2444,2460,2580],{},[1200,2217,2218,2238,2259,2280,2282,2306],{},[1215,2219,2220],{},[1115,2221,2223],{"className":2222},[1138],[1140,2224,2225],{"xmlns":1142},[1144,2226,2227,2235],{},[1147,2228,2229],{},[1150,2230,2231,2233],{},[1153,2232,1775],{},[1565,2234,1794],{},[1159,2236,2237],{"encoding":1161},"A_1",[1215,2239,2240],{},[1115,2241,2243],{"className":2242},[1138],[1140,2244,2245],{"xmlns":1142},[1144,2246,2247,2256],{},[1147,2248,2249],{},[1150,2250,2251,2253],{},[1153,2252,1372],{},[1565,2254,2255],{},"11",[1159,2257,2258],{"encoding":1161},"n_{11}",[1215,2260,2261],{},[1115,2262,2264],{"className":2263},[1138],[1140,2265,2266],{"xmlns":1142},[1144,2267,2268,2277],{},[1147,2269,2270],{},[1150,2271,2272,2274],{},[1153,2273,1372],{},[1565,2275,2276],{},"12",[1159,2278,2279],{"encoding":1161},"n_{12}",[1215,2281,1800],{},[1215,2283,2284],{},[1115,2285,2287],{"className":2286},[1138],[1140,2288,2289],{"xmlns":1142},[1144,2290,2291,2303],{},[1147,2292,2293],{},[1150,2294,2295,2297],{},[1153,2296,1372],{},[1147,2298,2299,2301],{},[1565,2300,1794],{},[1153,2302,1291],{},[1159,2304,2305],{"encoding":1161},"n_{1s}",[1215,2307,2308],{},[1115,2309,2311],{"className":2310},[1138],[1140,2312,2313],{"xmlns":1142},[1144,2314,2315,2327],{},[1147,2316,2317],{},[1150,2318,2319,2321],{},[1153,2320,1372],{},[1147,2322,2323,2325],{},[1565,2324,1794],{},[1242,2326,1979],{},[1159,2328,2329],{"encoding":1161},"n_{1\\bullet}",[1200,2331,2332,2352,2373,2394,2396,2420],{},[1215,2333,2334],{},[1115,2335,2337],{"className":2336},[1138],[1140,2338,2339],{"xmlns":1142},[1144,2340,2341,2349],{},[1147,2342,2343],{},[1150,2344,2345,2347],{},[1153,2346,1775],{},[1565,2348,1589],{},[1159,2350,2351],{"encoding":1161},"A_2",[1215,2353,2354],{},[1115,2355,2357],{"className":2356},[1138],[1140,2358,2359],{"xmlns":1142},[1144,2360,2361,2370],{},[1147,2362,2363],{},[1150,2364,2365,2367],{},[1153,2366,1372],{},[1565,2368,2369],{},"21",[1159,2371,2372],{"encoding":1161},"n_{21}",[1215,2374,2375],{},[1115,2376,2378],{"className":2377},[1138],[1140,2379,2380],{"xmlns":1142},[1144,2381,2382,2391],{},[1147,2383,2384],{},[1150,2385,2386,2388],{},[1153,2387,1372],{},[1565,2389,2390],{},"22",[1159,2392,2393],{"encoding":1161},"n_{22}",[1215,2395,1800],{},[1215,2397,2398],{},[1115,2399,2401],{"className":2400},[1138],[1140,2402,2403],{"xmlns":1142},[1144,2404,2405,2417],{},[1147,2406,2407],{},[1150,2408,2409,2411],{},[1153,2410,1372],{},[1147,2412,2413,2415],{},[1565,2414,1589],{},[1153,2416,1291],{},[1159,2418,2419],{"encoding":1161},"n_{2s}",[1215,2421,2422],{},[1115,2423,2425],{"className":2424},[1138],[1140,2426,2427],{"xmlns":1142},[1144,2428,2429,2441],{},[1147,2430,2431],{},[1150,2432,2433,2435],{},[1153,2434,1372],{},[1147,2436,2437,2439],{},[1565,2438,1589],{},[1242,2440,1979],{},[1159,2442,2443],{"encoding":1161},"n_{2\\bullet}",[1200,2445,2446,2449,2451,2453,2456,2458],{},[1215,2447,2448],{},"⋮",[1215,2450,2448],{},[1215,2452,2448],{},[1215,2454,2455],{},"⋱",[1215,2457,2448],{},[1215,2459,2448],{},[1200,2461,2462,2482,2506,2530,2532,2556],{},[1215,2463,2464],{},[1115,2465,2467],{"className":2466},[1138],[1140,2468,2469],{"xmlns":1142},[1144,2470,2471,2479],{},[1147,2472,2473],{},[1150,2474,2475,2477],{},[1153,2476,1775],{},[1153,2478,71],{},[1159,2480,2481],{"encoding":1161},"A_r",[1215,2483,2484],{},[1115,2485,2487],{"className":2486},[1138],[1140,2488,2489],{"xmlns":1142},[1144,2490,2491,2503],{},[1147,2492,2493],{},[1150,2494,2495,2497],{},[1153,2496,1372],{},[1147,2498,2499,2501],{},[1153,2500,71],{},[1565,2502,1794],{},[1159,2504,2505],{"encoding":1161},"n_{r1}",[1215,2507,2508],{},[1115,2509,2511],{"className":2510},[1138],[1140,2512,2513],{"xmlns":1142},[1144,2514,2515,2527],{},[1147,2516,2517],{},[1150,2518,2519,2521],{},[1153,2520,1372],{},[1147,2522,2523,2525],{},[1153,2524,71],{},[1565,2526,1589],{},[1159,2528,2529],{"encoding":1161},"n_{r2}",[1215,2531,1800],{},[1215,2533,2534],{},[1115,2535,2537],{"className":2536},[1138],[1140,2538,2539],{"xmlns":1142},[1144,2540,2541,2553],{},[1147,2542,2543],{},[1150,2544,2545,2547],{},[1153,2546,1372],{},[1147,2548,2549,2551],{},[1153,2550,71],{},[1153,2552,1291],{},[1159,2554,2555],{"encoding":1161},"n_{rs}",[1215,2557,2558],{},[1115,2559,2561],{"className":2560},[1138],[1140,2562,2563],{"xmlns":1142},[1144,2564,2565,2577],{},[1147,2566,2567],{},[1150,2568,2569,2571],{},[1153,2570,1372],{},[1147,2572,2573,2575],{},[1153,2574,71],{},[1242,2576,1979],{},[1159,2578,2579],{"encoding":1161},"n_{r\\bullet}",[1200,2581,2582,2606,2630,2654,2656,2680],{},[1215,2583,2584],{},[1115,2585,2587],{"className":2586},[1138],[1140,2588,2589],{"xmlns":1142},[1144,2590,2591,2603],{},[1147,2592,2593],{},[1150,2594,2595,2597],{},[1153,2596,1372],{},[1147,2598,2599,2601],{},[1242,2600,1979],{},[1153,2602,1883],{},[1159,2604,2605],{"encoding":1161},"n_{\\bullet j}",[1215,2607,2608],{},[1115,2609,2611],{"className":2610},[1138],[1140,2612,2613],{"xmlns":1142},[1144,2614,2615,2627],{},[1147,2616,2617],{},[1150,2618,2619,2621],{},[1153,2620,1372],{},[1147,2622,2623,2625],{},[1242,2624,1979],{},[1565,2626,1794],{},[1159,2628,2629],{"encoding":1161},"n_{\\bullet 1}",[1215,2631,2632],{},[1115,2633,2635],{"className":2634},[1138],[1140,2636,2637],{"xmlns":1142},[1144,2638,2639,2651],{},[1147,2640,2641],{},[1150,2642,2643,2645],{},[1153,2644,1372],{},[1147,2646,2647,2649],{},[1242,2648,1979],{},[1565,2650,1589],{},[1159,2652,2653],{"encoding":1161},"n_{\\bullet 2}",[1215,2655,1800],{},[1215,2657,2658],{},[1115,2659,2661],{"className":2660},[1138],[1140,2662,2663],{"xmlns":1142},[1144,2664,2665,2677],{},[1147,2666,2667],{},[1150,2668,2669,2671],{},[1153,2670,1372],{},[1147,2672,2673,2675],{},[1242,2674,1979],{},[1153,2676,1291],{},[1159,2678,2679],{"encoding":1161},"n_{\\bullet s}",[1215,2681,2682],{},[1115,2683,2685],{"className":2684},[1138],[1140,2686,2687],{"xmlns":1142},[1144,2688,2689,2693],{},[1147,2690,2691],{},[1153,2692,1372],{},[1159,2694,1372],{"encoding":1161},[1110,2696,2697,2698,2711],{},"Vydělením četností počtem opakování ",[1115,2699,2701],{"className":2700},[1138],[1140,2702,2703],{"xmlns":1142},[1144,2704,2705,2709],{},[1147,2706,2707],{},[1153,2708,1372],{},[1159,2710,1372],{"encoding":1161}," dostaneme odhady pravděpodobností:",[1115,2713,2715],{"className":2714},[1138],[1140,2716,2717],{"xmlns":1142,"display":1964},[1144,2718,2719,2821],{},[1147,2720,2721,2736,2738,2753,2755,2757,2771,2773,2787,2789,2791,2805,2807],{},[1150,2722,2723,2730],{},[1236,2724,2725,2727],{"accent":1121},[1153,2726,1110],{},[1242,2728,2729],{},"^",[1147,2731,2732,2734],{},[1153,2733,1878],{},[1153,2735,1883],{},[1242,2737,1982],{},[2739,2740,2741,2751],"mfrac",{},[1150,2742,2743,2745],{},[1153,2744,1372],{},[1147,2746,2747,2749],{},[1153,2748,1878],{},[1153,2750,1883],{},[1153,2752,1372],{},[1242,2754,1797],{"separator":1121},[2012,2756],{"width":2014},[1150,2758,2759,2765],{},[1236,2760,2761,2763],{"accent":1121},[1153,2762,1110],{},[1242,2764,2729],{},[1147,2766,2767,2769],{},[1153,2768,1878],{},[1242,2770,1979],{},[1242,2772,1982],{},[2739,2774,2775,2785],{},[1150,2776,2777,2779],{},[1153,2778,1372],{},[1147,2780,2781,2783],{},[1153,2782,1878],{},[1242,2784,1979],{},[1153,2786,1372],{},[1242,2788,1797],{"separator":1121},[2012,2790],{"width":2014},[1150,2792,2793,2799],{},[1236,2794,2795,2797],{"accent":1121},[1153,2796,1110],{},[1242,2798,2729],{},[1147,2800,2801,2803],{},[1242,2802,1979],{},[1153,2804,1883],{},[1242,2806,1982],{},[2739,2808,2809,2819],{},[1150,2810,2811,2813],{},[1153,2812,1372],{},[1147,2814,2815,2817],{},[1242,2816,1979],{},[1153,2818,1883],{},[1153,2820,1372],{},[1159,2822,2823],{"encoding":1161},"\\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}",[1189,2825,2827],{"id":2826},"test-nezávislosti-dvou-kvalitativních-znaků","Test nezávislosti dvou kvalitativních znaků",[1110,2829,2830,2831,2844,2845,2858],{},"Test ověřuje, zda varianty znaku ",[1115,2832,2834],{"className":2833},[1138],[1140,2835,2836],{"xmlns":1142},[1144,2837,2838,2842],{},[1147,2839,2840],{},[1153,2841,1775],{},[1159,2843,1775],{"encoding":1161}," a varianty znaku ",[1115,2846,2848],{"className":2847},[1138],[1140,2849,2850],{"xmlns":1142},[1144,2851,2852,2856],{},[1147,2853,2854],{},[1153,2855,1824],{},[1159,2857,1824],{"encoding":1161}," jsou na sobě nezávislé, tedy zda simultánní\npravděpodobnost je součinem marginálních pravděpodobností.",[1110,2860,2861],{},[1540,2862,2863],{},"Postup testu:",[2865,2866,2867,2998,3316,3398],"ol",{},[1439,2868,2869,2925,2926,1346,2952,2978,2979,2997],{},[1115,2870,2872],{"className":2871},[1138],[1140,2873,2874],{"xmlns":1142},[1144,2875,2876,2922],{},[1147,2877,2878,2884,2886,2896,2898,2908,2912],{},[1150,2879,2880,2882],{},[1153,2881,1563],{},[1565,2883,1567],{},[1242,2885,1958],{},[1150,2887,2888,2890],{},[1153,2889,1110],{},[1147,2891,2892,2894],{},[1153,2893,1878],{},[1153,2895,1883],{},[1242,2897,1982],{},[1150,2899,2900,2902],{},[1153,2901,1110],{},[1147,2903,2904,2906],{},[1153,2905,1878],{},[1242,2907,1979],{},[2909,2910,2911],"mtext",{}," ",[1150,2913,2914,2916],{},[1153,2915,1110],{},[1147,2917,2918,2920],{},[1242,2919,1979],{},[1153,2921,1883],{},[1159,2923,2924],{"encoding":1161},"H_0: p_{ij} = p_{i\\bullet}\\,p_{\\bullet j}"," pro všechna ",[1115,2927,2929],{"className":2928},[1138],[1140,2930,2931],{"xmlns":1142},[1144,2932,2933,2949],{},[1147,2934,2935,2937,2939,2941,2943,2945,2947],{},[1153,2936,1878],{},[1242,2938,1982],{},[1565,2940,1794],{},[1242,2942,1797],{"separator":1121},[1242,2944,1800],{},[1242,2946,1797],{"separator":1121},[1153,2948,71],{},[1159,2950,2951],{"encoding":1161},"i = 1,\\dots,r",[1115,2953,2955],{"className":2954},[1138],[1140,2956,2957],{"xmlns":1142},[1144,2958,2959,2975],{},[1147,2960,2961,2963,2965,2967,2969,2971,2973],{},[1153,2962,1883],{},[1242,2964,1982],{},[1565,2966,1794],{},[1242,2968,1797],{"separator":1121},[1242,2970,1800],{},[1242,2972,1797],{"separator":1121},[1153,2974,1291],{},[1159,2976,2977],{"encoding":1161},"j = 1,\\dots,s"," (znaky jsou na sobě\nnezávislé) proti ",[1115,2980,2982],{"className":2981},[1138],[1140,2983,2984],{"xmlns":1142},[1144,2985,2986,2994],{},[1147,2987,2988],{},[1150,2989,2990,2992],{},[1153,2991,1563],{},[1565,2993,1794],{},[1159,2995,2996],{"encoding":1161},"H_1",": znaky jsou závislé.",[1439,2999,3000,3001,3158,3161,3162,3179,3180,3212,3213,1890,3272,3275,3276,3297,3298,3315],{},"Testové kritérium",[1115,3002,3004],{"className":3003},[1138],[1140,3005,3006],{"xmlns":1142,"display":1964},[1144,3007,3008,3155],{},[1147,3009,3010,3016,3018,3032,3046,3105,3107,3109,3123,3125,3139,3141],{},[1582,3011,3012,3014],{},[1153,3013,1586],{},[1565,3015,1589],{},[1242,3017,1982],{},[1984,3019,3020,3022,3030],{},[1242,3021,1988],{},[1147,3023,3024,3026,3028],{},[1153,3025,1878],{},[1242,3027,1982],{},[1565,3029,1794],{},[1153,3031,71],{},[1984,3033,3034,3036,3044],{},[1242,3035,1988],{},[1147,3037,3038,3040,3042],{},[1153,3039,1883],{},[1242,3041,1982],{},[1565,3043,1794],{},[1153,3045,1291],{},[2739,3047,3048,3087],{},[1147,3049,3050,3052,3062,3065,3067,3081],{},[1242,3051,1875],{"stretchy":1874},[1150,3053,3054,3056],{},[1153,3055,1372],{},[1147,3057,3058,3060],{},[1153,3059,1878],{},[1153,3061,1883],{},[1242,3063,3064],{},"−",[1153,3066,1372],{},[1150,3068,3069,3075],{},[1236,3070,3071,3073],{"accent":1121},[1153,3072,1110],{},[1242,3074,2729],{},[1147,3076,3077,3079],{},[1153,3078,1878],{},[1153,3080,1883],{},[1582,3082,3083,3085],{},[1242,3084,1886],{"stretchy":1874},[1565,3086,1589],{},[1147,3088,3089,3091],{},[1153,3090,1372],{},[1150,3092,3093,3099],{},[1236,3094,3095,3097],{"accent":1121},[1153,3096,1110],{},[1242,3098,2729],{},[1147,3100,3101,3103],{},[1153,3102,1878],{},[1153,3104,1883],{},[1242,3106,1797],{"separator":1121},[2012,3108],{"width":2014},[1150,3110,3111,3117],{},[1236,3112,3113,3115],{"accent":1121},[1153,3114,1110],{},[1242,3116,2729],{},[1147,3118,3119,3121],{},[1153,3120,1878],{},[1153,3122,1883],{},[1242,3124,1982],{},[1150,3126,3127,3133],{},[1236,3128,3129,3131],{"accent":1121},[1153,3130,1110],{},[1242,3132,2729],{},[1147,3134,3135,3137],{},[1153,3136,1878],{},[1242,3138,1979],{},[2909,3140,2911],{},[1150,3142,3143,3149],{},[1236,3144,3145,3147],{"accent":1121},[1153,3146,1110],{},[1242,3148,2729],{},[1147,3150,3151,3153],{},[1242,3152,1979],{},[1153,3154,1883],{},[1159,3156,3157],{"encoding":1161},"\\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}",[3159,3160],"br",{},"má asymptoticky Pearsonovo (",[1115,3163,3165],{"className":3164},[1138],[1140,3166,3167],{"xmlns":1142},[1144,3168,3169,3177],{},[1147,3170,3171],{},[1582,3172,3173,3175],{},[1153,3174,1586],{},[1565,3176,1589],{},[1159,3178,1592],{"encoding":1161},") rozdělení o ",[1115,3181,3183],{"className":3182},[1138],[1140,3184,3185],{"xmlns":1142},[1144,3186,3187,3209],{},[1147,3188,3189,3191,3193,3195,3197,3199,3201,3203,3205,3207],{},[1242,3190,1875],{"stretchy":1874},[1153,3192,71],{},[1242,3194,3064],{},[1565,3196,1794],{},[1242,3198,1886],{"stretchy":1874},[1242,3200,1875],{"stretchy":1874},[1153,3202,1291],{},[1242,3204,3064],{},[1565,3206,1794],{},[1242,3208,1886],{"stretchy":1874},[1159,3210,3211],{"encoding":1161},"(r-1)(s-1)"," stupních volnosti. Hodnota ",[1115,3214,3216],{"className":3215},[1138],[1140,3217,3218],{"xmlns":1142},[1144,3219,3220,3269],{},[1147,3221,3222,3224,3238,3240],{},[1153,3223,1372],{},[1150,3225,3226,3232],{},[1236,3227,3228,3230],{"accent":1121},[1153,3229,1110],{},[1242,3231,2729],{},[1147,3233,3234,3236],{},[1153,3235,1878],{},[1153,3237,1883],{},[1242,3239,1982],{},[3241,3242,3243],"mstyle",{"scriptlevel":1567,"displaystyle":1121},[2739,3244,3245,3267],{},[1147,3246,3247,3257],{},[1150,3248,3249,3251],{},[1153,3250,1372],{},[1147,3252,3253,3255],{},[1153,3254,1878],{},[1242,3256,1979],{},[1150,3258,3259,3261],{},[1153,3260,1372],{},[1147,3262,3263,3265],{},[1242,3264,1979],{},[1153,3266,1883],{},[1153,3268,1372],{},[1159,3270,3271],{"encoding":1161},"n\\hat p_{ij} = \\dfrac{n_{i\\bullet}n_{\\bullet j}}{n}",[1540,3273,3274],{},"očekávaná četnost"," políčka ",[1115,3277,3279],{"className":3278},[1138],[1140,3280,3281],{"xmlns":1142},[1144,3282,3283,3295],{},[1147,3284,3285,3287,3289,3291,3293],{},[1242,3286,1875],{"stretchy":1874},[1153,3288,1878],{},[1242,3290,1797],{"separator":1121},[1153,3292,1883],{},[1242,3294,1886],{"stretchy":1874},[1159,3296,1889],{"encoding":1161}," — četnost, kterou bychom čekali, kdyby ",[1115,3299,3301],{"className":3300},[1138],[1140,3302,3303],{"xmlns":1142},[1144,3304,3305,3313],{},[1147,3306,3307],{},[1150,3308,3309,3311],{},[1153,3310,1563],{},[1565,3312,1567],{},[1159,3314,1570],{"encoding":1161}," platila.",[1439,3317,3318,3319,1669],{},"Kritický obor: ",[1115,3320,3322],{"className":3321},[1138],[1140,3323,3324],{"xmlns":1142},[1144,3325,3326,3395],{},[1147,3327,3328,3330,3332,3335,3341,3343,3349,3352,3368,3370,3372,3374,3376,3378,3380,3382,3384,3386,3388,3390,3392],{},[1153,3329,1605],{},[1242,3331,1982],{},[1242,3333,3334],{"stretchy":1874},"{",[1582,3336,3337,3339],{},[1153,3338,1586],{},[1565,3340,1589],{},[1242,3342,1958],{},[1582,3344,3345,3347],{},[1153,3346,1586],{},[1565,3348,1589],{},[1242,3350,3351],{},"≥",[3353,3354,3355,3357,3366],"msubsup",{},[1153,3356,1586],{},[1147,3358,3359,3361,3363],{},[1565,3360,1794],{},[1242,3362,3064],{},[1153,3364,3365],{},"α",[1565,3367,1589],{},[1242,3369,1875],{"stretchy":1874},[1242,3371,1875],{"stretchy":1874},[1153,3373,71],{},[1242,3375,3064],{},[1565,3377,1794],{},[1242,3379,1886],{"stretchy":1874},[1242,3381,1875],{"stretchy":1874},[1153,3383,1291],{},[1242,3385,3064],{},[1565,3387,1794],{},[1242,3389,1886],{"stretchy":1874},[1242,3391,1886],{"stretchy":1874},[1242,3393,3394],{"stretchy":1874},"}",[1159,3396,3397],{"encoding":1161},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}((r-1)(s-1))\\}",[1439,3399,3400,3401,3414,3415,3429,3430,3447,3448,3465],{},"Padne-li testové kritérium do ",[1115,3402,3404],{"className":3403},[1138],[1140,3405,3406],{"xmlns":1142},[1144,3407,3408,3412],{},[1147,3409,3410],{},[1153,3411,1605],{},[1159,3413,1605],{"encoding":1161},", zamítáme na hladině ",[1115,3416,3418],{"className":3417},[1138],[1140,3419,3420],{"xmlns":1142},[1144,3421,3422,3426],{},[1147,3423,3424],{},[1153,3425,3365],{},[1159,3427,3428],{"encoding":1161},"\\alpha"," nulovou hypotézu o nezávislosti a přijímáme\n",[1115,3431,3433],{"className":3432},[1138],[1140,3434,3435],{"xmlns":1142},[1144,3436,3437,3445],{},[1147,3438,3439],{},[1150,3440,3441,3443],{},[1153,3442,1563],{},[1565,3444,1794],{},[1159,3446,2996],{"encoding":1161},"; jinak nemáme důvod ",[1115,3449,3451],{"className":3450},[1138],[1140,3452,3453],{"xmlns":1142},[1144,3454,3455,3463],{},[1147,3456,3457],{},[1150,3458,3459,3461],{},[1153,3460,1563],{},[1565,3462,1567],{},[1159,3464,1570],{"encoding":1161}," zamítnout.",[1110,3467,3468,3469,1669],{},"V R počítá test i očekávané četnosti funkce ",[3470,3471,3472],"code",{},"chisq.test()",[1103,3474,3478,3486,3489,3492,3638],{"className":3475,"dataCallout":3477},[1106,3476],"callout-example","example",[1110,3479,3481,3485],{"className":3480},[1113],[1115,3482],{"className":3483,"ariaHidden":1121},[1118,3484,1120],"i-lucide:flask-conical","Příklad: nákup potravin na internetu a vzdělání",[1110,3487,3488],{},"Testujte hypotézu, zda se vzájemně ovlivňuje zkušenost s nákupem potravin na internetu a vzdělání respondenta\n(n = 385 respondentů).",[1110,3490,3491],{},"Základní soubor: respondenti; výběrový soubor: respondenti, kteří odpověděli; měřený znak A: vzdělání, měřený\nznak B: způsob nákupu.",[1194,3493,3494,3533],{},[1197,3495,3496],{},[1200,3497,3498,3501,3504,3507,3510],{},[1203,3499,3500],{},"vzdělání \\ nákup",[1203,3502,3503],{},"ano",[1203,3505,3506],{},"ne, ale plánuji",[1203,3508,3509],{},"ne, neplánuji",[1203,3511,3512],{},[1115,3513,3515],{"className":3514},[1138],[1140,3516,3517],{"xmlns":1142},[1144,3518,3519,3531],{},[1147,3520,3521],{},[1150,3522,3523,3525],{},[1153,3524,1372],{},[1147,3526,3527,3529],{},[1153,3528,1878],{},[1242,3530,1979],{},[1159,3532,2213],{"encoding":1161},[1210,3534,3535,3551,3568,3585,3601],{},[1200,3536,3537,3540,3543,3546,3548],{},[1215,3538,3539],{},"SŠ bez maturity",[1215,3541,3542],{},"4",[1215,3544,3545],{},"13",[1215,3547,2276],{},[1215,3549,3550],{},"29",[1200,3552,3553,3556,3559,3562,3565],{},[1215,3554,3555],{},"SŠ s maturitou, VOŠ",[1215,3557,3558],{},"31",[1215,3560,3561],{},"62",[1215,3563,3564],{},"71",[1215,3566,3567],{},"164",[1200,3569,3570,3573,3576,3579,3582],{},[1215,3571,3572],{},"VŠ",[1215,3574,3575],{},"44",[1215,3577,3578],{},"58",[1215,3580,3581],{},"66",[1215,3583,3584],{},"168",[1200,3586,3587,3590,3593,3596,3598],{},[1215,3588,3589],{},"ZŠ",[1215,3591,3592],{},"3",[1215,3594,3595],{},"9",[1215,3597,2276],{},[1215,3599,3600],{},"24",[1200,3602,3603,3626,3629,3632,3635],{},[1215,3604,3605],{},[1115,3606,3608],{"className":3607},[1138],[1140,3609,3610],{"xmlns":1142},[1144,3611,3612,3624],{},[1147,3613,3614],{},[1150,3615,3616,3618],{},[1153,3617,1372],{},[1147,3619,3620,3622],{},[1242,3621,1979],{},[1153,3623,1883],{},[1159,3625,2605],{"encoding":1161},[1215,3627,3628],{},"82",[1215,3630,3631],{},"142",[1215,3633,3634],{},"161",[1215,3636,3637],{},"385",[1110,3639,3640,3692],{},[1115,3641,3643],{"className":3642},[1138],[1140,3644,3645],{"xmlns":1142},[1144,3646,3647,3689],{},[1147,3648,3649,3655,3657,3667,3669,3679],{},[1150,3650,3651,3653],{},[1153,3652,1563],{},[1565,3654,1567],{},[1242,3656,1958],{},[1150,3658,3659,3661],{},[1153,3660,1110],{},[1147,3662,3663,3665],{},[1153,3664,1878],{},[1153,3666,1883],{},[1242,3668,1982],{},[1150,3670,3671,3673],{},[1153,3672,1110],{},[1147,3674,3675,3677],{},[1153,3676,1878],{},[1242,3678,1979],{},[1150,3680,3681,3683],{},[1153,3682,1110],{},[1147,3684,3685,3687],{},[1242,3686,1979],{},[1153,3688,1883],{},[1159,3690,3691],{"encoding":1161},"H_0: p_{ij} = p_{i\\bullet}p_{\\bullet j}"," — vzdělání a způsob nákupu jsou na sobě nezávislé.",[3694,3695,3698],"pre",{"className":3696,"code":3697,"language":71,"meta":1490,"style":1490},"language-r shiki shiki-themes github-light github-light github-dark","tab1 \u003C- matrix(c(4, 13, 12,\n                 31, 62, 71,\n                 44, 58, 66,\n                 3,  9, 12),\n               nrow = 4, byrow = TRUE,\n               dimnames = list(\n                 vzdelani = c(\"SS bez maturity\", \"SS s maturitou nebo VOS\", \"VS\", \"ZS\"),\n                 nakup    = c(\"ano\", \"ne, ale planuji\", \"ne, neplanuji\")))\nchisq.test(tab1)\nchisq.test(tab1)$expected\n",[3470,3699,3700,3738,3755,3772,3790,3813,3826,3861,3889,3902],{"__ignoreMap":1490},[1115,3701,3703,3707,3711,3715,3718,3720,3722,3725,3727,3730,3732,3735],{"class":3702,"line":10},"line",[1115,3704,3706],{"class":3705},"sP4rz","tab1",[1115,3708,3710],{"class":3709},"s8jYJ"," \u003C-",[1115,3712,3714],{"class":3713},"snPdu"," matrix",[1115,3716,1875],{"class":3717},"sxrX7",[1115,3719,1343],{"class":3713},[1115,3721,1875],{"class":3717},[1115,3723,3542],{"class":3724},"sBjJW",[1115,3726,1797],{"class":3709},[1115,3728,3729],{"class":3724}," 13",[1115,3731,1797],{"class":3709},[1115,3733,3734],{"class":3724}," 12",[1115,3736,3737],{"class":3709},",\n",[1115,3739,3740,3743,3745,3748,3750,3753],{"class":3702,"line":27},[1115,3741,3742],{"class":3724},"                 31",[1115,3744,1797],{"class":3709},[1115,3746,3747],{"class":3724}," 62",[1115,3749,1797],{"class":3709},[1115,3751,3752],{"class":3724}," 71",[1115,3754,3737],{"class":3709},[1115,3756,3757,3760,3762,3765,3767,3770],{"class":3702,"line":148},[1115,3758,3759],{"class":3724},"                 44",[1115,3761,1797],{"class":3709},[1115,3763,3764],{"class":3724}," 58",[1115,3766,1797],{"class":3709},[1115,3768,3769],{"class":3724}," 66",[1115,3771,3737],{"class":3709},[1115,3773,3774,3777,3779,3782,3784,3786,3788],{"class":3702,"line":111},[1115,3775,3776],{"class":3724},"                 3",[1115,3778,1797],{"class":3709},[1115,3780,3781],{"class":3724},"  9",[1115,3783,1797],{"class":3709},[1115,3785,3734],{"class":3724},[1115,3787,1886],{"class":3717},[1115,3789,3737],{"class":3709},[1115,3791,3792,3795,3798,3801,3803,3806,3808,3811],{"class":3702,"line":96},[1115,3793,3794],{"class":3705},"               nrow",[1115,3796,3797],{"class":3709}," =",[1115,3799,3800],{"class":3724}," 4",[1115,3802,1797],{"class":3709},[1115,3804,3805],{"class":3705}," byrow",[1115,3807,3797],{"class":3709},[1115,3809,3810],{"class":3724}," TRUE",[1115,3812,3737],{"class":3709},[1115,3814,3815,3818,3820,3823],{"class":3702,"line":89},[1115,3816,3817],{"class":3705},"               dimnames",[1115,3819,3797],{"class":3709},[1115,3821,3822],{"class":3713}," list",[1115,3824,3825],{"class":3717},"(\n",[1115,3827,3828,3831,3833,3836,3838,3842,3844,3847,3849,3852,3854,3857,3859],{"class":3702,"line":82},[1115,3829,3830],{"class":3705},"                 vzdelani",[1115,3832,3797],{"class":3709},[1115,3834,3835],{"class":3713}," c",[1115,3837,1875],{"class":3717},[1115,3839,3841],{"class":3840},"sIIMD","\"SS bez maturity\"",[1115,3843,1797],{"class":3709},[1115,3845,3846],{"class":3840}," \"SS s maturitou nebo VOS\"",[1115,3848,1797],{"class":3709},[1115,3850,3851],{"class":3840}," \"VS\"",[1115,3853,1797],{"class":3709},[1115,3855,3856],{"class":3840}," \"ZS\"",[1115,3858,1886],{"class":3717},[1115,3860,3737],{"class":3709},[1115,3862,3863,3866,3869,3871,3873,3876,3878,3881,3883,3886],{"class":3702,"line":75},[1115,3864,3865],{"class":3705},"                 nakup",[1115,3867,3868],{"class":3709},"    =",[1115,3870,3835],{"class":3713},[1115,3872,1875],{"class":3717},[1115,3874,3875],{"class":3840},"\"ano\"",[1115,3877,1797],{"class":3709},[1115,3879,3880],{"class":3840}," \"ne, ale planuji\"",[1115,3882,1797],{"class":3709},[1115,3884,3885],{"class":3840}," \"ne, neplanuji\"",[1115,3887,3888],{"class":3717},")))\n",[1115,3890,3892,3895,3897,3899],{"class":3702,"line":3891},9,[1115,3893,3894],{"class":3713},"chisq.test",[1115,3896,1875],{"class":3717},[1115,3898,3706],{"class":3705},[1115,3900,3901],{"class":3717},")\n",[1115,3903,3904,3906,3908,3910,3912,3915],{"class":3702,"line":72},[1115,3905,3894],{"class":3713},[1115,3907,1875],{"class":3717},[1115,3909,3706],{"class":3705},[1115,3911,1886],{"class":3717},[1115,3913,3914],{"class":3709},"$",[1115,3916,3917],{"class":3705},"expected\n",[3694,3919,3924],{"className":3920,"code":3922,"language":3923,"meta":1490},[3921],"language-text","    Pearson's Chi-squared test\n\ndata:  tab1\nX-squared = 5.4875, df = 6, p-value = 0.483\n\n                         nakup\nvzdelani                        ano ne, ale planuji ne, neplanuji\n  SS bez maturity          6.176623       10.696104      12.12727\n  SS s maturitou nebo VOS 34.929870       60.488312      68.58182\n  VS                      35.781818       61.963636      70.25455\n  ZS                       5.111688        8.851948      10.03636\n","text",[3470,3925,3922],{"__ignoreMap":1490},[1110,3927,3928,3929,3952,3953,3967,3968,3988,3989,4006],{},"Všechny očekávané četnosti jsou nad 5, aproximace je v pořádku. Testové kritérium ",[1115,3930,3932],{"className":3931},[1138],[1140,3933,3934],{"xmlns":1142},[1144,3935,3936,3949],{},[1147,3937,3938,3944,3946],{},[1582,3939,3940,3942],{},[1153,3941,1586],{},[1565,3943,1589],{},[1242,3945,1982],{},[1565,3947,3948],{},"5,49",[1159,3950,3951],{"encoding":1161},"\\chi^2 = 5{,}49"," s ",[1115,3954,3956],{"className":3955},[1138],[1140,3957,3958],{"xmlns":1142},[1144,3959,3960,3965],{},[1147,3961,3962],{},[1565,3963,3964],{},"6",[1159,3966,3964],{"encoding":1161}," stupni\nvolnosti dává p-hodnotu ",[1115,3969,3971],{"className":3970},[1138],[1140,3972,3973],{"xmlns":1142},[1144,3974,3975,3985],{},[1147,3976,3977,3980,3982],{},[1565,3978,3979],{},"0,483",[1242,3981,1689],{},[1565,3983,3984],{},"0,05",[1159,3986,3987],{"encoding":1161},"0{,}483 > 0{,}05",": ",[1115,3990,3992],{"className":3991},[1138],[1140,3993,3994],{"xmlns":1142},[1144,3995,3996,4004],{},[1147,3997,3998],{},[1150,3999,4000,4002],{},[1153,4001,1563],{},[1565,4003,1567],{},[1159,4005,1570],{"encoding":1161}," nezamítáme, závislost mezi zkušeností s nákupem potravin na\ninternetu a vzděláním respondenta se neprokázala.",[1103,4008,4010,4017,4020,4065],{"className":4009,"dataCallout":3477},[1106,3476],[1110,4011,4013,4016],{"className":4012},[1113],[1115,4014],{"className":4015,"ariaHidden":1121},[1118,3484,1120],"Příklad: vzdělání a zveřejňování citlivých údajů na Facebooku",[1110,4018,4019],{},"Mezi 221 osobami bylo zaznamenáno vzdělání a zda zveřejňují na Facebooku citlivé údaje. Proveďte test\nnezávislosti.",[1194,4021,4022,4036],{},[1197,4023,4024],{},[1200,4025,4026,4029,4032,4034],{},[1203,4027,4028],{},"zveřejňuje \\ vzdělání",[1203,4030,4031],{},"SŠ",[1203,4033,3572],{},[1203,4035,3589],{},[1210,4037,4038,4052],{},[1200,4039,4040,4043,4046,4049],{},[1215,4041,4042],{},"ne",[1215,4044,4045],{},"20",[1215,4047,4048],{},"33",[1215,4050,4051],{},"39",[1200,4053,4054,4056,4059,4062],{},[1215,4055,3503],{},[1215,4057,4058],{},"25",[1215,4060,4061],{},"28",[1215,4063,4064],{},"76",[1110,4066,4067,4118],{},[1115,4068,4070],{"className":4069},[1138],[1140,4071,4072],{"xmlns":1142},[1144,4073,4074,4116],{},[1147,4075,4076,4082,4084,4094,4096,4106],{},[1150,4077,4078,4080],{},[1153,4079,1563],{},[1565,4081,1567],{},[1242,4083,1958],{},[1150,4085,4086,4088],{},[1153,4087,1110],{},[1147,4089,4090,4092],{},[1153,4091,1878],{},[1153,4093,1883],{},[1242,4095,1982],{},[1150,4097,4098,4100],{},[1153,4099,1110],{},[1147,4101,4102,4104],{},[1153,4103,1878],{},[1242,4105,1979],{},[1150,4107,4108,4110],{},[1153,4109,1110],{},[1147,4111,4112,4114],{},[1242,4113,1979],{},[1153,4115,1883],{},[1159,4117,3691],{"encoding":1161}," — vzdělání a zveřejňování citlivých údajů jsou na sobě nezávislé.",[3694,4120,4122],{"className":3696,"code":4121,"language":71,"meta":1490,"style":1490},"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",[3470,4123,4124,4153,4172,4191,4201,4224,4248,4258],{"__ignoreMap":1490},[1115,4125,4126,4129,4131,4133,4135,4137,4139,4141,4143,4146,4148,4151],{"class":3702,"line":10},[1115,4127,4128],{"class":3705},"tab2",[1115,4130,3710],{"class":3709},[1115,4132,3714],{"class":3713},[1115,4134,1875],{"class":3717},[1115,4136,1343],{"class":3713},[1115,4138,1875],{"class":3717},[1115,4140,4045],{"class":3724},[1115,4142,1797],{"class":3709},[1115,4144,4145],{"class":3724}," 33",[1115,4147,1797],{"class":3709},[1115,4149,4150],{"class":3724}," 39",[1115,4152,3737],{"class":3709},[1115,4154,4155,4158,4160,4163,4165,4168,4170],{"class":3702,"line":27},[1115,4156,4157],{"class":3724},"                 25",[1115,4159,1797],{"class":3709},[1115,4161,4162],{"class":3724}," 28",[1115,4164,1797],{"class":3709},[1115,4166,4167],{"class":3724}," 76",[1115,4169,1886],{"class":3717},[1115,4171,3737],{"class":3709},[1115,4173,4174,4176,4178,4181,4183,4185,4187,4189],{"class":3702,"line":148},[1115,4175,3794],{"class":3705},[1115,4177,3797],{"class":3709},[1115,4179,4180],{"class":3724}," 2",[1115,4182,1797],{"class":3709},[1115,4184,3805],{"class":3705},[1115,4186,3797],{"class":3709},[1115,4188,3810],{"class":3724},[1115,4190,3737],{"class":3709},[1115,4192,4193,4195,4197,4199],{"class":3702,"line":111},[1115,4194,3817],{"class":3705},[1115,4196,3797],{"class":3709},[1115,4198,3822],{"class":3713},[1115,4200,3825],{"class":3717},[1115,4202,4203,4206,4208,4210,4212,4215,4217,4220,4222],{"class":3702,"line":96},[1115,4204,4205],{"class":3705},"                 zverejnuje",[1115,4207,3797],{"class":3709},[1115,4209,3835],{"class":3713},[1115,4211,1875],{"class":3717},[1115,4213,4214],{"class":3840},"\"ne\"",[1115,4216,1797],{"class":3709},[1115,4218,4219],{"class":3840}," \"ano\"",[1115,4221,1886],{"class":3717},[1115,4223,3737],{"class":3709},[1115,4225,4226,4228,4231,4233,4235,4238,4240,4242,4244,4246],{"class":3702,"line":89},[1115,4227,3830],{"class":3705},[1115,4229,4230],{"class":3709},"   =",[1115,4232,3835],{"class":3713},[1115,4234,1875],{"class":3717},[1115,4236,4237],{"class":3840},"\"SS\"",[1115,4239,1797],{"class":3709},[1115,4241,3851],{"class":3840},[1115,4243,1797],{"class":3709},[1115,4245,3856],{"class":3840},[1115,4247,3888],{"class":3717},[1115,4249,4250,4252,4254,4256],{"class":3702,"line":82},[1115,4251,3894],{"class":3713},[1115,4253,1875],{"class":3717},[1115,4255,4128],{"class":3705},[1115,4257,3901],{"class":3717},[1115,4259,4260,4262,4264,4266,4268,4270],{"class":3702,"line":75},[1115,4261,3894],{"class":3713},[1115,4263,1875],{"class":3717},[1115,4265,4128],{"class":3705},[1115,4267,1886],{"class":3717},[1115,4269,3914],{"class":3709},[1115,4271,3917],{"class":3705},[3694,4273,4276],{"className":4274,"code":4275,"language":3923,"meta":1490},[3921],"    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",[3470,4277,4275],{"__ignoreMap":1490},[1110,4279,4280,4281,3952,4304,4317,4318,3988,4338,4355,4356,1669],{},"I zde jsou všechny očekávané četnosti nad 5. Testové kritérium ",[1115,4282,4284],{"className":4283},[1138],[1140,4285,4286],{"xmlns":1142},[1144,4287,4288,4301],{},[1147,4289,4290,4296,4298],{},[1582,4291,4292,4294],{},[1153,4293,1586],{},[1565,4295,1589],{},[1242,4297,1982],{},[1565,4299,4300],{},"6,87",[1159,4302,4303],{"encoding":1161},"\\chi^2 = 6{,}87",[1115,4305,4307],{"className":4306},[1138],[1140,4308,4309],{"xmlns":1142},[1144,4310,4311,4315],{},[1147,4312,4313],{},[1565,4314,1589],{},[1159,4316,1589],{"encoding":1161}," stupni volnosti dává\np-hodnotu ",[1115,4319,4321],{"className":4320},[1138],[1140,4322,4323],{"xmlns":1142},[1144,4324,4325,4335],{},[1147,4326,4327,4330,4333],{},[1565,4328,4329],{},"0,032",[1242,4331,4332],{},"\u003C",[1565,4334,3984],{},[1159,4336,4337],{"encoding":1161},"0{,}032 \u003C 0{,}05",[1115,4339,4341],{"className":4340},[1138],[1140,4342,4343],{"xmlns":1142},[1144,4344,4345,4353],{},[1147,4346,4347],{},[1150,4348,4349,4351],{},[1153,4350,1563],{},[1565,4352,1567],{},[1159,4354,1570],{"encoding":1161}," zamítáme — na rozdíl od předchozího příkladu tady vzdělání a zveřejňování\ncitlivých údajů na Facebooku na sobě ",[1540,4357,4358],{},"závisí",[1110,4360,4361,4362,4379],{},"Srovnání pozorovaných a očekávaných četností ukazuje, proč jeden příklad ",[1115,4363,4365],{"className":4364},[1138],[1140,4366,4367],{"xmlns":1142},[1144,4368,4369,4377],{},[1147,4370,4371],{},[1150,4372,4373,4375],{},[1153,4374,1563],{},[1565,4376,1567],{},[1159,4378,1570],{"encoding":1161}," nezamítá a druhý ano — ve druhém\nse pozorované sloupce (zejména u ZŠ) systematicky odchylují od očekávaných, v prvním kolísají jen náhodně kolem nich:",[1110,4381,4382],{},[4383,4384],"img",{"alt":4385,"className":4386,"src":4388},"mask-kt-observed-expected",[1130,4387],"wikilink-broken","\u002Fwiki-assets\u002Fmask-kt-observed-expected.png",[1110,4390,4391,4392,4409,4410,1958],{},"Totéž je vidět na rozdělení testového kritéria: u prvního příkladu leží ",[1115,4393,4395],{"className":4394},[1138],[1140,4396,4397],{"xmlns":1142},[1144,4398,4399,4407],{},[1147,4400,4401],{},[1582,4402,4403,4405],{},[1153,4404,1586],{},[1565,4406,1589],{},[1159,4408,1592],{"encoding":1161}," hluboko pod kritickou hodnotou,\nu druhého uvnitř kritického oboru ",[1115,4411,4413],{"className":4412},[1138],[1140,4414,4415],{"xmlns":1142},[1144,4416,4417,4421],{},[1147,4418,4419],{},[1153,4420,1605],{},[1159,4422,1605],{"encoding":1161},[1110,4424,4425],{},[4383,4426],{"alt":4427,"className":4428,"src":4429},"mask-kt-chi2-kriticky-obor",[1130,4387],"\u002Fwiki-assets\u002Fmask-kt-chi2-kriticky-obor.png",[1189,4431,1653],{"id":4432},"cramérův-koeficient-kontingence",[1110,4434,4435,4436,1958],{},"Test nezávislosti pouze rozhodne, zda jsou znaky závislé, nebo ne. Sílu závislosti měří ",[1540,4437,4438],{},"Cramérův koeficient\nkontingence",[1115,4440,4442],{"className":4441},[1138],[1140,4443,4444],{"xmlns":1142,"display":1964},[1144,4445,4446,4502],{},[1147,4447,4448,4450,4452,4478,4480,4482,4484,4486,4489,4492,4494,4496,4498,4500],{},[1153,4449,1666],{},[1242,4451,1982],{},[4453,4454,4455],"msqrt",{},[2739,4456,4457,4463],{},[1582,4458,4459,4461],{},[1153,4460,1586],{},[1565,4462,1589],{},[1147,4464,4465,4467,4469,4472,4474,4476],{},[1153,4466,1372],{},[1242,4468,1875],{"stretchy":1874},[1153,4470,4471],{},"m",[1242,4473,3064],{},[1565,4475,1794],{},[1242,4477,1886],{"stretchy":1874},[1242,4479,1797],{"separator":1121},[2012,4481],{"width":2014},[1153,4483,4471],{},[1242,4485,1982],{},[1153,4487,4488],{},"min",[1242,4490,4491],{},"⁡",[1242,4493,1875],{"stretchy":1874},[1153,4495,71],{},[1242,4497,1797],{"separator":1121},[1153,4499,1291],{},[1242,4501,1886],{"stretchy":1874},[1159,4503,4504],{"encoding":1161},"V = \\sqrt{\\frac{\\chi^2}{n(m-1)}}, \\qquad m = \\min(r, s)",[1110,4506,4507,4508,4525,4526,4544,4545,4563],{},"kde ",[1115,4509,4511],{"className":4510},[1138],[1140,4512,4513],{"xmlns":1142},[1144,4514,4515,4523],{},[1147,4516,4517],{},[1582,4518,4519,4521],{},[1153,4520,1586],{},[1565,4522,1589],{},[1159,4524,1592],{"encoding":1161}," je hodnota testového kritéria z testu nezávislosti. ",[1115,4527,4529],{"className":4528},[1138],[1140,4530,4531],{"xmlns":1142},[1144,4532,4533,4541],{},[1147,4534,4535,4537,4539],{},[1153,4536,1666],{},[1242,4538,1982],{},[1565,4540,1567],{},[1159,4542,4543],{"encoding":1161},"V = 0"," odpovídá úplné nezávislosti znaků,\n",[1115,4546,4548],{"className":4547},[1138],[1140,4549,4550],{"xmlns":1142},[1144,4551,4552,4560],{},[1147,4553,4554,4556,4558],{},[1153,4555,1666],{},[1242,4557,1982],{},[1565,4559,1794],{},[1159,4561,4562],{"encoding":1161},"V = 1"," jejich úplné závislosti.",[3694,4565,4567],{"className":3696,"code":4566,"language":71,"meta":1490,"style":1490},"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",[3470,4568,4569,4644,4707,4712],{"__ignoreMap":1490},[1115,4570,4571,4574,4576,4579,4581,4584,4586,4588,4590,4592,4594,4596,4599,4602,4605,4608,4611,4613,4615,4617,4620,4622,4624,4626,4629,4631,4633,4636,4639,4642],{"class":3702,"line":10},[1115,4572,4573],{"class":3705},"V1",[1115,4575,3710],{"class":3709},[1115,4577,4578],{"class":3713}," sqrt",[1115,4580,1875],{"class":3717},[1115,4582,4583],{"class":3713},"as.numeric",[1115,4585,1875],{"class":3717},[1115,4587,3894],{"class":3713},[1115,4589,1875],{"class":3717},[1115,4591,3706],{"class":3705},[1115,4593,1886],{"class":3717},[1115,4595,3914],{"class":3709},[1115,4597,4598],{"class":3705},"statistic",[1115,4600,4601],{"class":3717},") ",[1115,4603,4604],{"class":3709},"\u002F",[1115,4606,4607],{"class":3717}," (",[1115,4609,4610],{"class":3713},"sum",[1115,4612,1875],{"class":3717},[1115,4614,3706],{"class":3705},[1115,4616,4601],{"class":3717},[1115,4618,4619],{"class":3709},"*",[1115,4621,4607],{"class":3717},[1115,4623,4488],{"class":3713},[1115,4625,1875],{"class":3717},[1115,4627,4628],{"class":3713},"dim",[1115,4630,1875],{"class":3717},[1115,4632,3706],{"class":3705},[1115,4634,4635],{"class":3717},")) ",[1115,4637,4638],{"class":3709},"-",[1115,4640,4641],{"class":3724}," 1",[1115,4643,3888],{"class":3717},[1115,4645,4646,4649,4651,4653,4655,4657,4659,4661,4663,4665,4667,4669,4671,4673,4675,4677,4679,4681,4683,4685,4687,4689,4691,4693,4695,4697,4699,4701,4703,4705],{"class":3702,"line":27},[1115,4647,4648],{"class":3705},"V2",[1115,4650,3710],{"class":3709},[1115,4652,4578],{"class":3713},[1115,4654,1875],{"class":3717},[1115,4656,4583],{"class":3713},[1115,4658,1875],{"class":3717},[1115,4660,3894],{"class":3713},[1115,4662,1875],{"class":3717},[1115,4664,4128],{"class":3705},[1115,4666,1886],{"class":3717},[1115,4668,3914],{"class":3709},[1115,4670,4598],{"class":3705},[1115,4672,4601],{"class":3717},[1115,4674,4604],{"class":3709},[1115,4676,4607],{"class":3717},[1115,4678,4610],{"class":3713},[1115,4680,1875],{"class":3717},[1115,4682,4128],{"class":3705},[1115,4684,4601],{"class":3717},[1115,4686,4619],{"class":3709},[1115,4688,4607],{"class":3717},[1115,4690,4488],{"class":3713},[1115,4692,1875],{"class":3717},[1115,4694,4628],{"class":3713},[1115,4696,1875],{"class":3717},[1115,4698,4128],{"class":3705},[1115,4700,4635],{"class":3717},[1115,4702,4638],{"class":3709},[1115,4704,4641],{"class":3724},[1115,4706,3888],{"class":3717},[1115,4708,4709],{"class":3702,"line":148},[1115,4710,4711],{"class":3705},"V1\n",[1115,4713,4714],{"class":3702,"line":111},[1115,4715,4716],{"class":3705},"V2\n",[3694,4718,4721],{"className":4719,"code":4720,"language":3923,"meta":1490},[3921],"[1] 0.08441958\n[1] 0.1762822\n",[3470,4722,4720],{"__ignoreMap":1490},[1110,4724,4725],{},[4383,4726],{"alt":4727,"className":4728,"src":4729},"mask-kt-cramerovo-v",[1130,4387],"\u002Fwiki-assets\u002Fmask-kt-cramerovo-v.png",[1110,4731,4732,4733,4752,4753,4770,4771,3988,4790,4807],{},"U nákupu potravin je ",[1115,4734,4736],{"className":4735},[1138],[1140,4737,4738],{"xmlns":1142},[1144,4739,4740,4749],{},[1147,4741,4742,4744,4746],{},[1153,4743,1666],{},[1242,4745,1982],{},[1565,4747,4748],{},"0,084",[1159,4750,4751],{"encoding":1161},"V = 0{,}084"," zanedbatelné — ostatně ",[1115,4754,4756],{"className":4755},[1138],[1140,4757,4758],{"xmlns":1142},[1144,4759,4760,4768],{},[1147,4761,4762],{},[1150,4763,4764,4766],{},[1153,4765,1563],{},[1565,4767,1567],{},[1159,4769,1570],{"encoding":1161}," jsme ani nezamítli. U zveřejňování údajů je ",[1115,4772,4774],{"className":4773},[1138],[1140,4775,4776],{"xmlns":1142},[1144,4777,4778,4787],{},[1147,4779,4780,4782,4784],{},[1153,4781,1666],{},[1242,4783,1982],{},[1565,4785,4786],{},"0,176",[1159,4788,4789],{"encoding":1161},"V = 0{,}176",[1115,4791,4793],{"className":4792},[1138],[1140,4794,4795],{"xmlns":1142},[1144,4796,4797,4805],{},[1147,4798,4799],{},[1150,4800,4801,4803],{},[1153,4802,1563],{},[1565,4804,1567],{},[1159,4806,1570],{"encoding":1161},"\njsme zamítli, ale samotná závislost je stále slabá.",[1189,4809,1674],{"id":4810},"čtyřpolní-tabulka",[1110,4812,4813,4815,4816,4829,4830,4843,4844,4866],{},[1540,4814,1674],{}," je speciální případ kontingenční tabulky, kdy oba znaky ",[1115,4817,4819],{"className":4818},[1138],[1140,4820,4821],{"xmlns":1142},[1144,4822,4823,4827],{},[1147,4824,4825],{},[1153,4826,1775],{},[1159,4828,1775],{"encoding":1161}," i ",[1115,4831,4833],{"className":4832},[1138],[1140,4834,4835],{"xmlns":1142},[1144,4836,4837,4841],{},[1147,4838,4839],{},[1153,4840,1824],{},[1159,4842,1824],{"encoding":1161}," mají jen dvě varianty\n(",[1115,4845,4847],{"className":4846},[1138],[1140,4848,4849],{"xmlns":1142},[1144,4850,4851,4863],{},[1147,4852,4853,4855,4857,4859,4861],{},[1153,4854,71],{},[1242,4856,1982],{},[1153,4858,1291],{},[1242,4860,1982],{},[1565,4862,1589],{},[1159,4864,4865],{"encoding":1161},"r = s = 2","):",[1194,4868,4869,4953],{},[1197,4870,4871],{},[1200,4872,4873,4892,4911,4930],{},[1203,4874,4875],{},[1115,4876,4878],{"className":4877},[1138],[1140,4879,4880],{"xmlns":1142},[1144,4881,4882,4890],{},[1147,4883,4884,4886,4888],{},[1153,4885,1775],{},[1153,4887,2122],{"mathvariant":2121},[1153,4889,1824],{},[1159,4891,2127],{"encoding":1161},[1203,4893,4894],{},[1115,4895,4897],{"className":4896},[1138],[1140,4898,4899],{"xmlns":1142},[1144,4900,4901,4909],{},[1147,4902,4903],{},[1150,4904,4905,4907],{},[1153,4906,1824],{},[1565,4908,1794],{},[1159,4910,2147],{"encoding":1161},[1203,4912,4913],{},[1115,4914,4916],{"className":4915},[1138],[1140,4917,4918],{"xmlns":1142},[1144,4919,4920,4928],{},[1147,4921,4922],{},[1150,4923,4924,4926],{},[1153,4925,1824],{},[1565,4927,1589],{},[1159,4929,2167],{"encoding":1161},[1203,4931,4932],{},[1115,4933,4935],{"className":4934},[1138],[1140,4936,4937],{"xmlns":1142},[1144,4938,4939,4951],{},[1147,4940,4941],{},[1150,4942,4943,4945],{},[1153,4944,1372],{},[1147,4946,4947,4949],{},[1153,4948,1878],{},[1242,4950,1979],{},[1159,4952,2213],{"encoding":1161},[1210,4954,4955,5037,5119],{},[1200,4956,4957,4976,4995,5014],{},[1215,4958,4959],{},[1115,4960,4962],{"className":4961},[1138],[1140,4963,4964],{"xmlns":1142},[1144,4965,4966,4974],{},[1147,4967,4968],{},[1150,4969,4970,4972],{},[1153,4971,1775],{},[1565,4973,1794],{},[1159,4975,2237],{"encoding":1161},[1215,4977,4978],{},[1115,4979,4981],{"className":4980},[1138],[1140,4982,4983],{"xmlns":1142},[1144,4984,4985,4993],{},[1147,4986,4987],{},[1150,4988,4989,4991],{},[1153,4990,1372],{},[1565,4992,2255],{},[1159,4994,2258],{"encoding":1161},[1215,4996,4997],{},[1115,4998,5000],{"className":4999},[1138],[1140,5001,5002],{"xmlns":1142},[1144,5003,5004,5012],{},[1147,5005,5006],{},[1150,5007,5008,5010],{},[1153,5009,1372],{},[1565,5011,2276],{},[1159,5013,2279],{"encoding":1161},[1215,5015,5016],{},[1115,5017,5019],{"className":5018},[1138],[1140,5020,5021],{"xmlns":1142},[1144,5022,5023,5035],{},[1147,5024,5025],{},[1150,5026,5027,5029],{},[1153,5028,1372],{},[1147,5030,5031,5033],{},[1565,5032,1794],{},[1242,5034,1979],{},[1159,5036,2329],{"encoding":1161},[1200,5038,5039,5058,5077,5096],{},[1215,5040,5041],{},[1115,5042,5044],{"className":5043},[1138],[1140,5045,5046],{"xmlns":1142},[1144,5047,5048,5056],{},[1147,5049,5050],{},[1150,5051,5052,5054],{},[1153,5053,1775],{},[1565,5055,1589],{},[1159,5057,2351],{"encoding":1161},[1215,5059,5060],{},[1115,5061,5063],{"className":5062},[1138],[1140,5064,5065],{"xmlns":1142},[1144,5066,5067,5075],{},[1147,5068,5069],{},[1150,5070,5071,5073],{},[1153,5072,1372],{},[1565,5074,2369],{},[1159,5076,2372],{"encoding":1161},[1215,5078,5079],{},[1115,5080,5082],{"className":5081},[1138],[1140,5083,5084],{"xmlns":1142},[1144,5085,5086,5094],{},[1147,5087,5088],{},[1150,5089,5090,5092],{},[1153,5091,1372],{},[1565,5093,2390],{},[1159,5095,2393],{"encoding":1161},[1215,5097,5098],{},[1115,5099,5101],{"className":5100},[1138],[1140,5102,5103],{"xmlns":1142},[1144,5104,5105,5117],{},[1147,5106,5107],{},[1150,5108,5109,5111],{},[1153,5110,1372],{},[1147,5112,5113,5115],{},[1565,5114,1589],{},[1242,5116,1979],{},[1159,5118,2443],{"encoding":1161},[1200,5120,5121,5144,5167,5190],{},[1215,5122,5123],{},[1115,5124,5126],{"className":5125},[1138],[1140,5127,5128],{"xmlns":1142},[1144,5129,5130,5142],{},[1147,5131,5132],{},[1150,5133,5134,5136],{},[1153,5135,1372],{},[1147,5137,5138,5140],{},[1242,5139,1979],{},[1153,5141,1883],{},[1159,5143,2605],{"encoding":1161},[1215,5145,5146],{},[1115,5147,5149],{"className":5148},[1138],[1140,5150,5151],{"xmlns":1142},[1144,5152,5153,5165],{},[1147,5154,5155],{},[1150,5156,5157,5159],{},[1153,5158,1372],{},[1147,5160,5161,5163],{},[1242,5162,1979],{},[1565,5164,1794],{},[1159,5166,2629],{"encoding":1161},[1215,5168,5169],{},[1115,5170,5172],{"className":5171},[1138],[1140,5173,5174],{"xmlns":1142},[1144,5175,5176,5188],{},[1147,5177,5178],{},[1150,5179,5180,5182],{},[1153,5181,1372],{},[1147,5183,5184,5186],{},[1242,5185,1979],{},[1565,5187,1589],{},[1159,5189,2653],{"encoding":1161},[1215,5191,5192],{},[1115,5193,5195],{"className":5194},[1138],[1140,5196,5197],{"xmlns":1142},[1144,5198,5199,5203],{},[1147,5200,5201],{},[1153,5202,1372],{},[1159,5204,1372],{"encoding":1161},[1110,5206,1698,5207,5225],{},[1115,5208,5210],{"className":5209},[1138],[1140,5211,5212],{"xmlns":1142},[1144,5213,5214,5222],{},[1147,5215,5216,5218,5220],{},[1153,5217,1372],{},[1242,5219,1689],{},[1565,5221,1692],{},[1159,5223,5224],{"encoding":1161},"n > 40"," se místo obecného vzorce používá zjednodušená varianta testového kritéria:",[1115,5227,5229],{"className":5228},[1138],[1140,5230,5231],{"xmlns":1142,"display":1964},[1144,5232,5233,5327],{},[1147,5234,5235,5241,5243,5245,5247],{},[1582,5236,5237,5239],{},[1153,5238,1586],{},[1565,5240,1589],{},[1242,5242,1982],{},[1153,5244,1372],{},[2909,5246,2911],{},[2739,5248,5249,5285],{},[1147,5250,5251,5253,5259,5265,5267,5273,5279],{},[1242,5252,1875],{"stretchy":1874},[1150,5254,5255,5257],{},[1153,5256,1372],{},[1565,5258,2255],{},[1150,5260,5261,5263],{},[1153,5262,1372],{},[1565,5264,2390],{},[1242,5266,3064],{},[1150,5268,5269,5271],{},[1153,5270,1372],{},[1565,5272,2276],{},[1150,5274,5275,5277],{},[1153,5276,1372],{},[1565,5278,2369],{},[1582,5280,5281,5283],{},[1242,5282,1886],{"stretchy":1874},[1565,5284,1589],{},[1147,5286,5287,5297,5307,5317],{},[1150,5288,5289,5291],{},[1153,5290,1372],{},[1147,5292,5293,5295],{},[1565,5294,1794],{},[1242,5296,1979],{},[1150,5298,5299,5301],{},[1153,5300,1372],{},[1147,5302,5303,5305],{},[1565,5304,1589],{},[1242,5306,1979],{},[1150,5308,5309,5311],{},[1153,5310,1372],{},[1147,5312,5313,5315],{},[1242,5314,1979],{},[1565,5316,1794],{},[1150,5318,5319,5321],{},[1153,5320,1372],{},[1147,5322,5323,5325],{},[1242,5324,1979],{},[1565,5326,1589],{},[1159,5328,5329],{"encoding":1161},"\\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}}",[1110,5331,5332,5333,5393,5394,5430,5431,5434,5435,5438],{},"s kritickým oborem ",[1115,5334,5336],{"className":5335},[1138],[1140,5337,5338],{"xmlns":1142},[1144,5339,5340,5390],{},[1147,5341,5342,5348,5350,5352,5358,5360,5366,5368,5382,5384,5386,5388],{},[1150,5343,5344,5346],{},[1153,5345,1605],{},[1153,5347,3365],{},[1242,5349,1982],{},[1242,5351,3334],{"stretchy":1874},[1582,5353,5354,5356],{},[1153,5355,1586],{},[1565,5357,1589],{},[1242,5359,1958],{},[1582,5361,5362,5364],{},[1153,5363,1586],{},[1565,5365,1589],{},[1242,5367,3351],{},[3353,5369,5370,5372,5380],{},[1153,5371,1586],{},[1147,5373,5374,5376,5378],{},[1565,5375,1794],{},[1242,5377,3064],{},[1153,5379,3365],{},[1565,5381,1589],{},[1242,5383,1875],{"stretchy":1874},[1565,5385,1794],{},[1242,5387,1886],{"stretchy":1874},[1242,5389,3394],{"stretchy":1874},[1159,5391,5392],{"encoding":1161},"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 ",[1115,5395,5397],{"className":5396},[1138],[1140,5398,5399],{"xmlns":1142},[1144,5400,5401,5427],{},[1147,5402,5403,5405,5407,5409,5411,5413,5415,5417,5419,5421,5423,5425],{},[1242,5404,1875],{"stretchy":1874},[1153,5406,71],{},[1242,5408,3064],{},[1565,5410,1794],{},[1242,5412,1886],{"stretchy":1874},[1242,5414,1875],{"stretchy":1874},[1153,5416,1291],{},[1242,5418,3064],{},[1565,5420,1794],{},[1242,5422,1886],{"stretchy":1874},[1242,5424,1982],{},[1565,5426,1794],{},[1159,5428,5429],{"encoding":1161},"(r-1)(s-1) = 1"," stupeň volnosti. V R dává tuto hodnotu ",[3470,5432,5433],{},"chisq.test(tab, correct = FALSE)",". Bez ",[3470,5436,5437],{},"correct = FALSE"," R u tabulky 2 × 2 použije Yatesovu korekci na kontinuitu a testové kritérium vyjde menší.",[1189,5440,1705],{"id":5441},"mcnemarův-test",[1110,5443,5444,5445,5448,5449,5451,5452,5455,5456,5459,5460,5462],{},"Čtyřpolní tabulka z předchozí sekce porovnává dva ",[1540,5446,5447],{},"různé"," znaky na stejném souboru. ",[1540,5450,1705],{}," řeší\njinou situaci: na prvcích základního souboru se měří ",[1540,5453,5454],{},"jeden"," alternativní znak, a to ",[1540,5457,5458],{},"dvakrát"," — před a po\nnějakém zásahu. Cílem je zjistit, zda zásah změnil pravděpodobnostní rozdělení variant tohoto znaku. Jde tedy o\n",[1540,5461,1701],{}," (stejné prvky měřené opakovaně), ne o dva nezávisle naměřené znaky.",[1110,5464,5465],{},"Kontingenční tabulka před\u002Fpo má tvar:",[1194,5467,5468,5503],{},[1197,5469,5470],{},[1200,5471,5472,5475,5478,5480],{},[1203,5473,5474],{},"před \\ po",[1203,5476,5477],{},"+",[1203,5479,3064],{},[1203,5481,5482],{},[1115,5483,5485],{"className":5484},[1138],[1140,5486,5487],{"xmlns":1142},[1144,5488,5489,5501],{},[1147,5490,5491],{},[1150,5492,5493,5495],{},[1153,5494,1372],{},[1147,5496,5497,5499],{},[1153,5498,1878],{},[1242,5500,1979],{},[1159,5502,2213],{"encoding":1161},[1210,5504,5505,5570,5635],{},[1200,5506,5507,5509,5528,5547],{},[1215,5508,5477],{},[1215,5510,5511],{},[1115,5512,5514],{"className":5513},[1138],[1140,5515,5516],{"xmlns":1142},[1144,5517,5518,5526],{},[1147,5519,5520],{},[1150,5521,5522,5524],{},[1153,5523,1372],{},[1565,5525,2255],{},[1159,5527,2258],{"encoding":1161},[1215,5529,5530],{},[1115,5531,5533],{"className":5532},[1138],[1140,5534,5535],{"xmlns":1142},[1144,5536,5537,5545],{},[1147,5538,5539],{},[1150,5540,5541,5543],{},[1153,5542,1372],{},[1565,5544,2276],{},[1159,5546,2279],{"encoding":1161},[1215,5548,5549],{},[1115,5550,5552],{"className":5551},[1138],[1140,5553,5554],{"xmlns":1142},[1144,5555,5556,5568],{},[1147,5557,5558],{},[1150,5559,5560,5562],{},[1153,5561,1372],{},[1147,5563,5564,5566],{},[1565,5565,1794],{},[1242,5567,1979],{},[1159,5569,2329],{"encoding":1161},[1200,5571,5572,5574,5593,5612],{},[1215,5573,3064],{},[1215,5575,5576],{},[1115,5577,5579],{"className":5578},[1138],[1140,5580,5581],{"xmlns":1142},[1144,5582,5583,5591],{},[1147,5584,5585],{},[1150,5586,5587,5589],{},[1153,5588,1372],{},[1565,5590,2369],{},[1159,5592,2372],{"encoding":1161},[1215,5594,5595],{},[1115,5596,5598],{"className":5597},[1138],[1140,5599,5600],{"xmlns":1142},[1144,5601,5602,5610],{},[1147,5603,5604],{},[1150,5605,5606,5608],{},[1153,5607,1372],{},[1565,5609,2390],{},[1159,5611,2393],{"encoding":1161},[1215,5613,5614],{},[1115,5615,5617],{"className":5616},[1138],[1140,5618,5619],{"xmlns":1142},[1144,5620,5621,5633],{},[1147,5622,5623],{},[1150,5624,5625,5627],{},[1153,5626,1372],{},[1147,5628,5629,5631],{},[1565,5630,1589],{},[1242,5632,1979],{},[1159,5634,2443],{"encoding":1161},[1200,5636,5637,5660,5683,5706],{},[1215,5638,5639],{},[1115,5640,5642],{"className":5641},[1138],[1140,5643,5644],{"xmlns":1142},[1144,5645,5646,5658],{},[1147,5647,5648],{},[1150,5649,5650,5652],{},[1153,5651,1372],{},[1147,5653,5654,5656],{},[1242,5655,1979],{},[1153,5657,1883],{},[1159,5659,2605],{"encoding":1161},[1215,5661,5662],{},[1115,5663,5665],{"className":5664},[1138],[1140,5666,5667],{"xmlns":1142},[1144,5668,5669,5681],{},[1147,5670,5671],{},[1150,5672,5673,5675],{},[1153,5674,1372],{},[1147,5676,5677,5679],{},[1242,5678,1979],{},[1565,5680,1794],{},[1159,5682,2629],{"encoding":1161},[1215,5684,5685],{},[1115,5686,5688],{"className":5687},[1138],[1140,5689,5690],{"xmlns":1142},[1144,5691,5692,5704],{},[1147,5693,5694],{},[1150,5695,5696,5698],{},[1153,5697,1372],{},[1147,5699,5700,5702],{},[1242,5701,1979],{},[1565,5703,1589],{},[1159,5705,2653],{"encoding":1161},[1215,5707,5708],{},[1115,5709,5711],{"className":5710},[1138],[1140,5712,5713],{"xmlns":1142},[1144,5714,5715,5719],{},[1147,5716,5717],{},[1153,5718,1372],{},[1159,5720,1372],{"encoding":1161},[1110,5722,5723,5724,1163,5741,5758,5759,5762,5763,1163,5780,5797,5798,5801],{},"Pole ",[1115,5725,5727],{"className":5726},[1138],[1140,5728,5729],{"xmlns":1142},[1144,5730,5731,5739],{},[1147,5732,5733],{},[1150,5734,5735,5737],{},[1153,5736,1372],{},[1565,5738,2255],{},[1159,5740,2258],{"encoding":1161},[1115,5742,5744],{"className":5743},[1138],[1140,5745,5746],{"xmlns":1142},[1144,5747,5748,5756],{},[1147,5749,5750],{},[1150,5751,5752,5754],{},[1153,5753,1372],{},[1565,5755,2390],{},[1159,5757,2393],{"encoding":1161}," jsou ",[1540,5760,5761],{},"shodná"," (prvek zůstal ve stejné variantě), pole ",[1115,5764,5766],{"className":5765},[1138],[1140,5767,5768],{"xmlns":1142},[1144,5769,5770,5778],{},[1147,5771,5772],{},[1150,5773,5774,5776],{},[1153,5775,1372],{},[1565,5777,2276],{},[1159,5779,2279],{"encoding":1161},[1115,5781,5783],{"className":5782},[1138],[1140,5784,5785],{"xmlns":1142},[1144,5786,5787,5795],{},[1147,5788,5789],{},[1150,5790,5791,5793],{},[1153,5792,1372],{},[1565,5794,2369],{},[1159,5796,2372],{"encoding":1161}," jsou\n",[1540,5799,5800],{},"diskordantní"," (prvek mezi měřeními variantu změnil) — jen ta rozhodují o výsledku testu:",[1110,5803,5804],{},[4383,5805],{"alt":5806,"className":5807,"src":5808},"mask-kt-mcnemar-tabulka",[1130,4387],"\u002Fwiki-assets\u002Fmask-kt-mcnemar-tabulka.png",[1110,5810,5811],{},[1540,5812,2863],{},[2865,5814,5815,5852,5933,5991],{},[1439,5816,5817,5851],{},[1115,5818,5820],{"className":5819},[1138],[1140,5821,5822],{"xmlns":1142},[1144,5823,5824,5848],{},[1147,5825,5826,5832,5834,5840,5842],{},[1150,5827,5828,5830],{},[1153,5829,1563],{},[1565,5831,1567],{},[1242,5833,1958],{},[1150,5835,5836,5838],{},[1153,5837,1110],{},[1565,5839,2276],{},[1242,5841,1982],{},[1150,5843,5844,5846],{},[1153,5845,1110],{},[1565,5847,2369],{},[1159,5849,5850],{"encoding":1161},"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.",[1439,5853,3000,5854,5916,5918,5919,5932],{},[1115,5855,5857],{"className":5856},[1138],[1140,5858,5859],{"xmlns":1142,"display":1964},[1144,5860,5861,5913],{},[1147,5862,5863,5869,5871],{},[1582,5864,5865,5867],{},[1153,5866,1586],{},[1565,5868,1589],{},[1242,5870,1982],{},[2739,5872,5873,5897],{},[1147,5874,5875,5877,5883,5885,5891],{},[1242,5876,1875],{"stretchy":1874},[1150,5878,5879,5881],{},[1153,5880,1372],{},[1565,5882,2276],{},[1242,5884,3064],{},[1150,5886,5887,5889],{},[1153,5888,1372],{},[1565,5890,2369],{},[1582,5892,5893,5895],{},[1242,5894,1886],{"stretchy":1874},[1565,5896,1589],{},[1147,5898,5899,5905,5907],{},[1150,5900,5901,5903],{},[1153,5902,1372],{},[1565,5904,2276],{},[1242,5906,5477],{},[1150,5908,5909,5911],{},[1153,5910,1372],{},[1565,5912,2369],{},[1159,5914,5915],{"encoding":1161},"\\chi^2 = \\frac{(n_{12} - n_{21})^2}{n_{12} + n_{21}}",[3159,5917],{},"má asymptoticky Pearsonovo rozdělení o ",[1115,5920,5922],{"className":5921},[1138],[1140,5923,5924],{"xmlns":1142},[1144,5925,5926,5930],{},[1147,5927,5928],{},[1565,5929,1794],{},[1159,5931,1794],{"encoding":1161}," stupni volnosti.",[1439,5934,3318,5935,1669],{},[1115,5936,5938],{"className":5937},[1138],[1140,5939,5940],{"xmlns":1142},[1144,5941,5942,5988],{},[1147,5943,5944,5946,5948,5950,5956,5958,5964,5966,5980,5982,5984,5986],{},[1153,5945,1605],{},[1242,5947,1982],{},[1242,5949,3334],{"stretchy":1874},[1582,5951,5952,5954],{},[1153,5953,1586],{},[1565,5955,1589],{},[1242,5957,1958],{},[1582,5959,5960,5962],{},[1153,5961,1586],{},[1565,5963,1589],{},[1242,5965,3351],{},[3353,5967,5968,5970,5978],{},[1153,5969,1586],{},[1147,5971,5972,5974,5976],{},[1565,5973,1794],{},[1242,5975,3064],{},[1153,5977,3365],{},[1565,5979,1589],{},[1242,5981,1875],{"stretchy":1874},[1565,5983,1794],{},[1242,5985,1886],{"stretchy":1874},[1242,5987,3394],{"stretchy":1874},[1159,5989,5990],{"encoding":1161},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}(1)\\}",[1439,5992,3400,5993,6006,6007,6024,6025,6042],{},[1115,5994,5996],{"className":5995},[1138],[1140,5997,5998],{"xmlns":1142},[1144,5999,6000,6004],{},[1147,6001,6002],{},[1153,6003,1605],{},[1159,6005,1605],{"encoding":1161},", zamítáme ",[1115,6008,6010],{"className":6009},[1138],[1140,6011,6012],{"xmlns":1142},[1144,6013,6014,6022],{},[1147,6015,6016],{},[1150,6017,6018,6020],{},[1153,6019,1563],{},[1565,6021,1567],{},[1159,6023,1570],{"encoding":1161}," a přijímáme ",[1115,6026,6028],{"className":6027},[1138],[1140,6029,6030],{"xmlns":1142},[1144,6031,6032,6040],{},[1147,6033,6034],{},[1150,6035,6036,6038],{},[1153,6037,1563],{},[1565,6039,1794],{},[1159,6041,2996],{"encoding":1161},": zásah rozdělení variant změnil.",[1110,6044,6045,6046,6049,6050,6053,6054,6056],{},"V R počítá tento test funkce ",[3470,6047,6048],{},"mcnemar.test()",". Vzorec výše ",[1540,6051,6052],{},"neobsahuje korekci na kontinuitu"," — aby R vrátilo\npřesně tuto hodnotu, musí se volat s ",[3470,6055,5437],{}," (viz Časté chyby níže).",[1103,6058,6060,6067,6070,6073,6170],{"className":6059,"dataCallout":3477},[1106,3476],[1110,6061,6063,6066],{"className":6062},[1113],[1115,6064],{"className":6065,"ariaHidden":1121},[1118,3484,1120],"Příklad: informační kampaň a zveřejňování na Facebooku",[1110,6068,6069],{},"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.",[1110,6071,6072],{},"Základní soubor: všichni studenti; výběrový soubor: vybraní studenti; měřený znak: zveřejňování (ano \u002F ne).",[1194,6074,6075,6110],{},[1197,6076,6077],{},[1200,6078,6079,6081,6084,6087],{},[1203,6080,5474],{},[1203,6082,6083],{},"nezveřejňuje",[1203,6085,6086],{},"zveřejňuje",[1203,6088,6089],{},[1115,6090,6092],{"className":6091},[1138],[1140,6093,6094],{"xmlns":1142},[1144,6095,6096,6108],{},[1147,6097,6098],{},[1150,6099,6100,6102],{},[1153,6101,1372],{},[1147,6103,6104,6106],{},[1153,6105,1878],{},[1242,6107,1979],{},[1159,6109,2213],{"encoding":1161},[1210,6111,6112,6124,6136],{},[1200,6113,6114,6116,6118,6121],{},[1215,6115,6083],{},[1215,6117,3600],{},[1215,6119,6120],{},"68",[1215,6122,6123],{},"92",[1200,6125,6126,6128,6130,6133],{},[1215,6127,6086],{},[1215,6129,4061],{},[1215,6131,6132],{},"50",[1215,6134,6135],{},"78",[1200,6137,6138,6161,6164,6167],{},[1215,6139,6140],{},[1115,6141,6143],{"className":6142},[1138],[1140,6144,6145],{"xmlns":1142},[1144,6146,6147,6159],{},[1147,6148,6149],{},[1150,6150,6151,6153],{},[1153,6152,1372],{},[1147,6154,6155,6157],{},[1242,6156,1979],{},[1153,6158,1883],{},[1159,6160,2605],{"encoding":1161},[1215,6162,6163],{},"52",[1215,6165,6166],{},"118",[1215,6168,6169],{},"170",[1110,6171,6172,6205],{},[1115,6173,6175],{"className":6174},[1138],[1140,6176,6177],{"xmlns":1142},[1144,6178,6179,6203],{},[1147,6180,6181,6187,6189,6195,6197],{},[1150,6182,6183,6185],{},[1153,6184,1563],{},[1565,6186,1567],{},[1242,6188,1958],{},[1150,6190,6191,6193],{},[1153,6192,1110],{},[1565,6194,2276],{},[1242,6196,1982],{},[1150,6198,6199,6201],{},[1153,6200,1110],{},[1565,6202,2369],{},[1159,6204,5850],{"encoding":1161}," — informační kampaň nemá na chování vliv.",[3694,6207,6209],{"className":3696,"code":6208,"language":71,"meta":1490,"style":1490},"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",[3470,6210,6211,6235,6249,6267,6277,6300,6319],{"__ignoreMap":1490},[1115,6212,6213,6216,6218,6220,6222,6224,6226,6228,6230,6233],{"class":3702,"line":10},[1115,6214,6215],{"class":3705},"tab3",[1115,6217,3710],{"class":3709},[1115,6219,3714],{"class":3713},[1115,6221,1875],{"class":3717},[1115,6223,1343],{"class":3713},[1115,6225,1875],{"class":3717},[1115,6227,3600],{"class":3724},[1115,6229,1797],{"class":3709},[1115,6231,6232],{"class":3724}," 68",[1115,6234,3737],{"class":3709},[1115,6236,6237,6240,6242,6245,6247],{"class":3702,"line":27},[1115,6238,6239],{"class":3724},"                 28",[1115,6241,1797],{"class":3709},[1115,6243,6244],{"class":3724}," 50",[1115,6246,1886],{"class":3717},[1115,6248,3737],{"class":3709},[1115,6250,6251,6253,6255,6257,6259,6261,6263,6265],{"class":3702,"line":148},[1115,6252,3794],{"class":3705},[1115,6254,3797],{"class":3709},[1115,6256,4180],{"class":3724},[1115,6258,1797],{"class":3709},[1115,6260,3805],{"class":3705},[1115,6262,3797],{"class":3709},[1115,6264,3810],{"class":3724},[1115,6266,3737],{"class":3709},[1115,6268,6269,6271,6273,6275],{"class":3702,"line":111},[1115,6270,3817],{"class":3705},[1115,6272,3797],{"class":3709},[1115,6274,3822],{"class":3713},[1115,6276,3825],{"class":3717},[1115,6278,6279,6282,6284,6286,6288,6291,6293,6296,6298],{"class":3702,"line":96},[1115,6280,6281],{"class":3705},"                 pred",[1115,6283,3797],{"class":3709},[1115,6285,3835],{"class":3713},[1115,6287,1875],{"class":3717},[1115,6289,6290],{"class":3840},"\"nezverejnuje\"",[1115,6292,1797],{"class":3709},[1115,6294,6295],{"class":3840}," \"zverejnuje\"",[1115,6297,1886],{"class":3717},[1115,6299,3737],{"class":3709},[1115,6301,6302,6305,6307,6309,6311,6313,6315,6317],{"class":3702,"line":89},[1115,6303,6304],{"class":3705},"                 po",[1115,6306,4230],{"class":3709},[1115,6308,3835],{"class":3713},[1115,6310,1875],{"class":3717},[1115,6312,6290],{"class":3840},[1115,6314,1797],{"class":3709},[1115,6316,6295],{"class":3840},[1115,6318,3888],{"class":3717},[1115,6320,6321,6324,6326,6328,6330,6333,6335,6338],{"class":3702,"line":82},[1115,6322,6323],{"class":3713},"mcnemar.test",[1115,6325,1875],{"class":3717},[1115,6327,6215],{"class":3705},[1115,6329,1797],{"class":3709},[1115,6331,6332],{"class":3705}," correct",[1115,6334,3797],{"class":3709},[1115,6336,6337],{"class":3724}," FALSE",[1115,6339,3901],{"class":3717},[3694,6341,6344],{"className":6342,"code":6343,"language":3923,"meta":1490},[3921],"    McNemar's Chi-squared test\n\ndata:  tab3\nMcNemar's chi-squared = 16.667, df = 1, p-value = 4.456e-05\n",[3470,6345,6343],{"__ignoreMap":1490},[1110,6347,6348,6349,3988,6368,6385,6386,6403],{},"P-hodnota ",[1115,6350,6352],{"className":6351},[1138],[1140,6353,6354],{"xmlns":1142},[1144,6355,6356,6365],{},[1147,6357,6358,6361,6363],{},[1565,6359,6360],{},"0,00004456",[1242,6362,4332],{},[1565,6364,3984],{},[1159,6366,6367],{"encoding":1161},"0{,}00004456 \u003C 0{,}05",[1115,6369,6371],{"className":6370},[1138],[1140,6372,6373],{"xmlns":1142},[1144,6374,6375,6383],{},[1147,6376,6377],{},[1150,6378,6379,6381],{},[1153,6380,1563],{},[1565,6382,1567],{},[1159,6384,1570],{"encoding":1161}," zamítáme, přijímáme ",[1115,6387,6389],{"className":6388},[1138],[1140,6390,6391],{"xmlns":1142},[1144,6392,6393,6401],{},[1147,6394,6395],{},[1150,6396,6397,6399],{},[1153,6398,1563],{},[1565,6400,1794],{},[1159,6402,2996],{"encoding":1161}," — informační kampaň měla vliv na změnu\nchování studentů ve zveřejňování údajů na Facebooku.",[1189,6405,6407],{"id":6406},"časté-chyby","Časté chyby",[1103,6409,6413,6421],{"className":6410,"dataCallout":6412},[1106,6411],"callout-warning","warning",[1110,6414,6416,6420],{"className":6415},[1113],[1115,6417],{"className":6418,"ariaHidden":1121},[1118,6419,1120],"i-lucide:triangle-alert","Test nezávislosti na párovaných datech",[1110,6422,6423,6424,6426],{},"Tabulka před\u002Fpo vypadá jako obyčejná kontingenční tabulka, ale ",[3470,6425,3472],{}," 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.",[3694,6428,6430],{"className":3696,"code":6429,"language":71,"meta":1490,"style":1490},"chisq.test(tab3)\n",[3470,6431,6432],{"__ignoreMap":1490},[1115,6433,6434,6436,6438,6440],{"class":3702,"line":10},[1115,6435,3894],{"class":3713},[1115,6437,1875],{"class":3717},[1115,6439,6215],{"class":3705},[1115,6441,3901],{"class":3717},[3694,6443,6446],{"className":6444,"code":6445,"language":3923,"meta":1490},[3921],"    Pearson's Chi-squared test with Yates' continuity correction\n\ndata:  tab3\nX-squared = 1.4793, df = 1, p-value = 0.2239\n",[3470,6447,6445],{"__ignoreMap":1490},[1110,6449,6348,6450,6469,6470,6487,6488,6490,6491,1669],{},[1115,6451,6453],{"className":6452},[1138],[1140,6454,6455],{"xmlns":1142},[1144,6456,6457,6466],{},[1147,6458,6459,6462,6464],{},[1565,6460,6461],{},"0,224",[1242,6463,1689],{},[1565,6465,3984],{},[1159,6467,6468],{"encoding":1161},"0{,}224 > 0{,}05"," by vedla k nezamítnutí ",[1115,6471,6473],{"className":6472},[1138],[1140,6474,6475],{"xmlns":1142},[1144,6476,6477,6485],{},[1147,6478,6479],{},[1150,6480,6481,6483],{},[1153,6482,1563],{},[1565,6484,1567],{},[1159,6486,1570],{"encoding":1161}," — opačný závěr než správný McNemarův test. Na\npárovaná data (stejné prvky měřené dvakrát) vždy patří ",[3470,6489,6048],{},", nikdy ",[3470,6492,3472],{},[1103,6494,6496,6505],{"className":6495,"dataCallout":6412},[1106,6411],[1110,6497,6499,6502,6503],{"className":6498},[1113],[1115,6500],{"className":6501,"ariaHidden":1121},[1118,6419,1120],"Výchozí korekce na kontinuitu v ",[3470,6504,6048],{},[1110,6506,6507,6508,6511],{},"Bez argumentu ",[3470,6509,6510],{},"correct"," R ve výchozím nastavení použije Yatesovu korekci na kontinuitu, která dá jinou\np-hodnotu než nekorigovaný vzorec uvedený výše.",[3694,6513,6515],{"className":3696,"code":6514,"language":71,"meta":1490,"style":1490},"mcnemar.test(tab3)\n",[3470,6516,6517],{"__ignoreMap":1490},[1115,6518,6519,6521,6523,6525],{"class":3702,"line":10},[1115,6520,6323],{"class":3713},[1115,6522,1875],{"class":3717},[1115,6524,6215],{"class":3705},[1115,6526,3901],{"class":3717},[3694,6528,6531],{"className":6529,"code":6530,"language":3923,"meta":1490},[3921],"    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",[3470,6532,6530],{"__ignoreMap":1490},[1110,6534,6535,6536,6554,6555,6574,6575,6588,6589,1669],{},"Oproti nekorigované hodnotě ",[1115,6537,6539],{"className":6538},[1138],[1140,6540,6541],{"xmlns":1142},[1144,6542,6543,6551],{},[1147,6544,6545,6547,6549],{},[1153,6546,1110],{},[1242,6548,1982],{},[1565,6550,6360],{},[1159,6552,6553],{"encoding":1161},"p = 0{,}00004456"," vyjde ",[1115,6556,6558],{"className":6557},[1138],[1140,6559,6560],{"xmlns":1142},[1144,6561,6562,6571],{},[1147,6563,6564,6566,6568],{},[1153,6565,1110],{},[1242,6567,1982],{},[1565,6569,6570],{},"0,00006879",[1159,6572,6573],{"encoding":1161},"p = 0{,}00006879"," — v tomto příkladu obě vedou ke\nstejnému rozhodnutí, ale u hodnot blíž hranici ",[1115,6576,6578],{"className":6577},[1138],[1140,6579,6580],{"xmlns":1142},[1144,6581,6582,6586],{},[1147,6583,6584],{},[1153,6585,3365],{},[1159,6587,3428],{"encoding":1161}," by korekce mohla rozhodnutí změnit. Aby R reprodukovalo\nnekorigovaný vzorec, je třeba vždy volat ",[3470,6590,6591],{},"mcnemar.test(x, correct = FALSE)",[1189,6593,1434],{"id":1433},[1436,6595,6596,6601,6607,6615,6623,6631,6636],{},[1439,6597,6598],{},[1127,6599,1133],{"className":6600,"dataFsResolvedFilePath":1131,"href":1132},[1130],[1439,6602,6603],{},[1127,6604,6606],{"className":6605,"dataFsResolvedFilePath":1721,"href":1722},[1130],"Testování statistických hypotéz",[1439,6608,6609],{},[1127,6610,6614],{"className":6611,"dataFsResolvedFilePath":6612,"href":6613},[1130],"topics\u002Fpopisna-statistika.md","\u002Fwiki\u002Fpopisna-statistika","Popisná statistika a datové soubory",[1439,6616,6617],{},[1127,6618,6622],{"className":6619,"dataFsResolvedFilePath":6620,"href":6621},[1130],"topics\u002Fnahodne-veliciny-a-rozdeleni.md","\u002Fwiki\u002Fnahodne-veliciny-a-rozdeleni","Náhodné veličiny a rozdělení pravděpodobnosti",[1439,6624,6625],{},[1127,6626,6630],{"className":6627,"dataFsResolvedFilePath":6628,"href":6629},[1130],"topics\u002Fregresni-a-korelacni-analyza.md","\u002Fwiki\u002Fregresni-a-korelacni-analyza","Regresní a korelační analýza",[1439,6632,6633],{},[1127,6634,1222],{"className":6635,"dataFsResolvedFilePath":1220,"href":1221},[1130],[1439,6637,6638],{},[1127,6639,6641],{"className":6640,"dataFsResolvedFilePath":1454,"href":1455},[1130],"Tahák pro R",[1189,6643,1459],{"id":934},[1110,6645,1462,6646,1467],{},[1464,6647,1466],{},[6649,6650,6651],"style",{},"html pre.shiki code .sP4rz, html code.shiki .sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html 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var(--shiki-dark-text-decoration);}",{"title":1490,"searchDepth":27,"depth":27,"links":6653},[6654,6655,6656,6657,6658,6659,6660,6661],{"id":1709,"depth":27,"text":1710},{"id":2826,"depth":27,"text":2827},{"id":4432,"depth":27,"text":1653},{"id":4810,"depth":27,"text":1674},{"id":5441,"depth":27,"text":1705},{"id":6406,"depth":27,"text":6407},{"id":1433,"depth":27,"text":1434},{"id":934,"depth":27,"text":1459},{},"\u002Ftopics\u002Fkontingencni-tabulky",{"title":1515,"description":1490},[6666,6667],"raw\u002Fmask\u002F05 kontingenční tabulky.pdf","raw\u002Fmask\u002Fpříklady 04 a 05.docx","topics\u002Fkontingencni-tabulky",[23,67,714,486,768,71],"topic","E-gDO0c3LOdVy6YB6I-h8KKMQKlrqjomMSQWFmOANZE",{"id":6673,"title":6622,"body":6674,"course":23,"courses":1495,"created":1496,"description":1490,"extension":1497,"meta":11127,"navigation":1499,"path":11128,"seo":11129,"sources":11130,"stem":11134,"tags":11135,"type":6670,"updated":1496,"__hash__":11136},"topics\u002Ftopics\u002Fnahodne-veliciny-a-rozdeleni.md",{"type":1096,"value":6675,"toc":11115},[6676,6679,6965,6969,7202,7205,7272,7276,7283,7290,7449,7488,7491,7725,7728,7806,7860,7958,7962,8064,8067,8071,8077,8133,8136,8144,8295,8302,8355,8385,8504,8507,8555,8717,8772,8779,8886,8948,8952,9055,9058,9095,9101,9160,9209,9216,9252,9258,9261,9309,9316,9378,9384,9387,9451,9458,9497,9503,9506,9510,9536,9867,9905,9960,10090,10096,10100,10107,10126,10231,10275,10294,10389,10406,10448,10623,10630,10633,10636,10790,10793,10869,10875,10877,11063,11065,11106,11108,11112],[1099,6677,6622],{"id":6678},"náhodné-veličiny-a-rozdělení-pravděpodobnosti",[1103,6680,6682,6688],{"className":6681,"dataCallout":1525},[1106,1524],[1110,6683,6685,1533],{"className":6684},[1113],[1115,6686],{"className":6687,"ariaHidden":1121},[1118,1532,1120],[1436,6689,6690,6701,6805,6872,6953],{},[1439,6691,6692,6693,6696,6697,6700],{},"Náhodná veličina je funkce, která výsledkům pokusu přiřazuje reálná čísla; rozlišujeme ",[1540,6694,6695],{},"diskrétní"," (izolované hodnoty s nenulovou pravděpodobností) a ",[1540,6698,6699],{},"spojité"," (hodnoty z intervalu, každý bod má nulovou pravděpodobnost).",[1439,6702,6703,6704,1654,6707,6745,6746,6783,6784,6804],{},"Každou náhodnou veličinu popisuje ",[1540,6705,6706],{},"distribuční funkce",[1115,6708,6710],{"className":6709},[1138],[1140,6711,6712],{"xmlns":1142},[1144,6713,6714,6742],{},[1147,6715,6716,6719,6721,6723,6725,6727,6730,6732,6735,6738,6740],{},[1153,6717,6718],{},"F",[1242,6720,1875],{"stretchy":1874},[1153,6722,1240],{},[1242,6724,1886],{"stretchy":1874},[1242,6726,1982],{},[1153,6728,6729],{},"P",[1242,6731,1875],{"stretchy":1874},[1153,6733,6734],{},"X",[1242,6736,6737],{},"≤",[1153,6739,1240],{},[1242,6741,1886],{"stretchy":1874},[1159,6743,6744],{"encoding":1161},"F(x) = P(X \\le x)","; u spojité veličiny platí ",[1115,6747,6749],{"className":6748},[1138],[1140,6750,6751],{"xmlns":1142},[1144,6752,6753,6780],{},[1147,6754,6755,6763,6765,6767,6769,6771,6774,6776,6778],{},[1582,6756,6757,6759],{},[1153,6758,6718],{},[1242,6760,6762],{"mathvariant":2121,"lspace":6761,"rspace":6761},"0em","′",[1242,6764,1875],{"stretchy":1874},[1153,6766,1240],{},[1242,6768,1886],{"stretchy":1874},[1242,6770,1982],{},[1153,6772,6773],{},"f",[1242,6775,1875],{"stretchy":1874},[1153,6777,1240],{},[1242,6779,1886],{"stretchy":1874},[1159,6781,6782],{"encoding":1161},"F'(x) = f(x)",", kde ",[1115,6785,6787],{"className":6786},[1138],[1140,6788,6789],{"xmlns":1142},[1144,6790,6791,6801],{},[1147,6792,6793,6795,6797,6799],{},[1153,6794,6773],{},[1242,6796,1875],{"stretchy":1874},[1153,6798,1240],{},[1242,6800,1886],{"stretchy":1874},[1159,6802,6803],{"encoding":1161},"f(x)"," je hustota pravděpodobnosti.",[1439,6806,6807,6808,1669],{},"Pravděpodobnost na intervalu se počítá jako ",[1115,6809,6811],{"className":6810},[1138],[1140,6812,6813],{"xmlns":1142},[1144,6814,6815,6869],{},[1147,6816,6817,6819,6821,6827,6829,6831,6833,6839,6841,6843,6845,6847,6853,6855,6857,6859,6861,6867],{},[1153,6818,6729],{},[1242,6820,1875],{"stretchy":1874},[1150,6822,6823,6825],{},[1153,6824,1240],{},[1565,6826,1794],{},[1242,6828,4332],{},[1153,6830,6734],{},[1242,6832,4332],{},[1150,6834,6835,6837],{},[1153,6836,1240],{},[1565,6838,1589],{},[1242,6840,1886],{"stretchy":1874},[1242,6842,1982],{},[1153,6844,6718],{},[1242,6846,1875],{"stretchy":1874},[1150,6848,6849,6851],{},[1153,6850,1240],{},[1565,6852,1589],{},[1242,6854,1886],{"stretchy":1874},[1242,6856,3064],{},[1153,6858,6718],{},[1242,6860,1875],{"stretchy":1874},[1150,6862,6863,6865],{},[1153,6864,1240],{},[1565,6866,1794],{},[1242,6868,1886],{"stretchy":1874},[1159,6870,6871],{"encoding":1161},"P(x_1 \u003C X \u003C x_2) = F(x_2) - F(x_1)",[1439,6873,6874,1654,6877,6909,6910,1346,6913,1346,6916,6919,6920,6934,6935,1669],{},[1540,6875,6876],{},"Normální rozdělení",[1115,6878,6880],{"className":6879},[1138],[1140,6881,6882],{"xmlns":1142},[1144,6883,6884,6906],{},[1147,6885,6886,6889,6891,6894,6897,6904],{},[1153,6887,6888],{},"N",[1242,6890,1875],{"stretchy":1874},[1153,6892,6893],{},"μ",[1242,6895,6896],{"separator":1121},";",[1582,6898,6899,6902],{},[1153,6900,6901],{},"σ",[1565,6903,1589],{},[1242,6905,1886],{"stretchy":1874},[1159,6907,6908],{"encoding":1161},"N(\\mu; \\sigma^2)"," je nejdůležitější spojité rozdělení; v R ho počítáme funkcemi ",[3470,6911,6912],{},"dnorm",[3470,6914,6915],{},"pnorm",[3470,6917,6918],{},"qnorm"," — R jako parametr očekává směrodatnou odchylku ",[1115,6921,6923],{"className":6922},[1138],[1140,6924,6925],{"xmlns":1142},[1144,6926,6927,6931],{},[1147,6928,6929],{},[1153,6930,6901],{},[1159,6932,6933],{"encoding":1161},"\\sigma",", ne rozptyl ",[1115,6936,6938],{"className":6937},[1138],[1140,6939,6940],{"xmlns":1142},[1144,6941,6942,6950],{},[1147,6943,6944],{},[1582,6945,6946,6948],{},[1153,6947,6901],{},[1565,6949,1589],{},[1159,6951,6952],{"encoding":1161},"\\sigma^2",[1439,6954,6955,1346,6958,1163,6961,6964],{},[1540,6956,6957],{},"Studentovo",[1540,6959,6960],{},"Pearsonovo (χ²)",[1540,6962,6963],{},"Fisherovo-Snedecorovo"," rozdělení slouží jako nástroj pro pozdější konstrukci intervalů spolehlivosti a testování hypotéz.",[1189,6966,6968],{"id":6967},"náhodná-veličina","Náhodná veličina",[1110,6970,6971,6974,6975,6990,6991,1654,6993,7006,7007,7027,7028,6783,7041,7065,7066,1346,7079,1346,7093,7107,7108,1346,7121,1346,7135,7149,7150,7163,7164,7177,7178,1669],{},[1127,6972,1133],{"className":6973,"dataFsResolvedFilePath":1131,"href":1132},[1130]," pracuje s veličinami, jejichž hodnota závisí na náhodě. Formálně: uvažujeme základní prostor ",[1115,6976,6978],{"className":6977},[1138],[1140,6979,6980],{"xmlns":1142},[1144,6981,6982,6987],{},[1147,6983,6984],{},[1153,6985,6986],{"mathvariant":2121},"Ω",[1159,6988,6989],{"encoding":1161},"\\Omega"," přiřazený výsledkům pokusu. ",[1540,6992,6968],{},[1115,6994,6996],{"className":6995},[1138],[1140,6997,6998],{"xmlns":1142},[1144,6999,7000,7004],{},[1147,7001,7002],{},[1153,7003,6734],{},[1159,7005,6734],{"encoding":1161}," je funkce, která prvkům ",[1115,7008,7010],{"className":7009},[1138],[1140,7011,7012],{"xmlns":1142},[1144,7013,7014,7024],{},[1147,7015,7016,7019,7022],{},[1153,7017,7018],{},"ω",[1242,7020,7021],{},"∈",[1153,7023,6986],{"mathvariant":2121},[1159,7025,7026],{"encoding":1161},"\\omega \\in \\Omega"," přiřazuje reálná čísla ",[1115,7029,7031],{"className":7030},[1138],[1140,7032,7033],{"xmlns":1142},[1144,7034,7035,7039],{},[1147,7036,7037],{},[1153,7038,1240],{},[1159,7040,1240],{"encoding":1161},[1115,7042,7044],{"className":7043},[1138],[1140,7045,7046],{"xmlns":1142},[1144,7047,7048,7062],{},[1147,7049,7050,7052,7054,7056,7058,7060],{},[1153,7051,1240],{},[1242,7053,1982],{},[1153,7055,6734],{},[1242,7057,1875],{"stretchy":1874},[1153,7059,7018],{},[1242,7061,1886],{"stretchy":1874},[1159,7063,7064],{"encoding":1161},"x = X(\\omega)",". Náhodné veličiny značíme velkými písmeny (",[1115,7067,7069],{"className":7068},[1138],[1140,7070,7071],{"xmlns":1142},[1144,7072,7073,7077],{},[1147,7074,7075],{},[1153,7076,6734],{},[1159,7078,6734],{"encoding":1161},[1115,7080,7082],{"className":7081},[1138],[1140,7083,7084],{"xmlns":1142},[1144,7085,7086,7091],{},[1147,7087,7088],{},[1153,7089,7090],{},"Y",[1159,7092,7090],{"encoding":1161},[1115,7094,7096],{"className":7095},[1138],[1140,7097,7098],{"xmlns":1142},[1144,7099,7100,7105],{},[1147,7101,7102],{},[1153,7103,7104],{},"T",[1159,7106,7104],{"encoding":1161},"), jejich konkrétní hodnoty odpovídajícími malými písmeny (",[1115,7109,7111],{"className":7110},[1138],[1140,7112,7113],{"xmlns":1142},[1144,7114,7115,7119],{},[1147,7116,7117],{},[1153,7118,1240],{},[1159,7120,1240],{"encoding":1161},[1115,7122,7124],{"className":7123},[1138],[1140,7125,7126],{"xmlns":1142},[1144,7127,7128,7133],{},[1147,7129,7130],{},[1153,7131,7132],{},"y",[1159,7134,7132],{"encoding":1161},[1115,7136,7138],{"className":7137},[1138],[1140,7139,7140],{"xmlns":1142},[1144,7141,7142,7147],{},[1147,7143,7144],{},[1153,7145,7146],{},"t",[1159,7148,7146],{"encoding":1161},"); pravděpodobnost, že ",[1115,7151,7153],{"className":7152},[1138],[1140,7154,7155],{"xmlns":1142},[1144,7156,7157,7161],{},[1147,7158,7159],{},[1153,7160,6734],{},[1159,7162,6734],{"encoding":1161}," nabyla hodnoty ",[1115,7165,7167],{"className":7166},[1138],[1140,7168,7169],{"xmlns":1142},[1144,7170,7171,7175],{},[1147,7172,7173],{},[1153,7174,1240],{},[1159,7176,1240],{"encoding":1161},", zapisujeme ",[1115,7179,7181],{"className":7180},[1138],[1140,7182,7183],{"xmlns":1142},[1144,7184,7185,7199],{},[1147,7186,7187,7189,7191,7193,7195,7197],{},[1153,7188,6729],{},[1242,7190,1875],{"stretchy":1874},[1153,7192,6734],{},[1242,7194,1982],{},[1153,7196,1240],{},[1242,7198,1886],{"stretchy":1874},[1159,7200,7201],{"encoding":1161},"P(X = x)",[1110,7203,7204],{},"Podle typu hodnot, kterých náhodná veličina nabývá, rozlišujeme dva typy:",[1436,7206,7207,7266],{},[1439,7208,7209,7212,7213,7226,7227,7265],{},[1540,7210,7211],{},"Diskrétní náhodná veličina"," — prvky ",[1115,7214,7216],{"className":7215},[1138],[1140,7217,7218],{"xmlns":1142},[1144,7219,7220,7224],{},[1147,7221,7222],{},[1153,7223,6986],{"mathvariant":2121},[1159,7225,6989],{"encoding":1161}," se zobrazí na osu reálných čísel jako izolované body ",[1115,7228,7230],{"className":7229},[1138],[1140,7231,7232],{"xmlns":1142},[1144,7233,7234,7262],{},[1147,7235,7236,7242,7244,7250,7252,7254,7256],{},[1150,7237,7238,7240],{},[1153,7239,1240],{},[1565,7241,1794],{},[1242,7243,1797],{"separator":1121},[1150,7245,7246,7248],{},[1153,7247,1240],{},[1565,7249,1589],{},[1242,7251,1797],{"separator":1121},[1242,7253,1800],{},[1242,7255,1797],{"separator":1121},[1150,7257,7258,7260],{},[1153,7259,1240],{},[1153,7261,1183],{},[1159,7263,7264],{"encoding":1161},"x_1, x_2, \\dots, x_k",", přičemž každý z nich má nenulovou pravděpodobnost. Příklad: počet bodů při hodu kostkou, počet studentů na cvičení.",[1439,7267,7268,7271],{},[1540,7269,7270],{},"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.",[1189,7273,7275],{"id":7274},"distribuční-funkce","Distribuční funkce",[1110,7277,7278,7279,7282],{},"Náhodná veličina nabývá při pokusu určité hodnoty, aniž bychom předem věděli, které. Při opakování pokusu se ale projevují zákonitosti, které popisují ",[1540,7280,7281],{},"zákony rozdělení",". Nejobecnějším z nich je distribuční funkce.",[1110,7284,7285],{},[4383,7286],{"alt":7287,"className":7288,"src":7289},"mask-nv-distribucni-funkce",[1130,4387],"\u002Fwiki-assets\u002Fmask-nv-distribucni-funkce.png",[1103,7291,7294,7301],{"className":7292,"dataCallout":654},[1106,7293],"callout-info",[1110,7295,7297,7300],{"className":7296},[1113],[1115,7298],{"className":7299,"ariaHidden":1121},[1118,1532,1120],"Definice",[1110,7302,7303,7304,7317,7318,7338,7339,7352,7353,7389,7408,7409,7422,7423,1669],{},"Distribuční funkcí náhodné veličiny ",[1115,7305,7307],{"className":7306},[1138],[1140,7308,7309],{"xmlns":1142},[1144,7310,7311,7315],{},[1147,7312,7313],{},[1153,7314,6734],{},[1159,7316,6734],{"encoding":1161}," nazýváme reálnou funkci ",[1115,7319,7321],{"className":7320},[1138],[1140,7322,7323],{"xmlns":1142},[1144,7324,7325,7335],{},[1147,7326,7327,7329,7331,7333],{},[1153,7328,6718],{},[1242,7330,1875],{"stretchy":1874},[1153,7332,1240],{},[1242,7334,1886],{"stretchy":1874},[1159,7336,7337],{"encoding":1161},"F(x)"," definovanou pro každé reálné číslo ",[1115,7340,7342],{"className":7341},[1138],[1140,7343,7344],{"xmlns":1142},[1144,7345,7346,7350],{},[1147,7347,7348],{},[1153,7349,1240],{},[1159,7351,1240],{"encoding":1161}," jako\n",[1115,7354,7356],{"className":7355},[1138],[1140,7357,7358],{"xmlns":1142},[1144,7359,7360,7386],{},[1147,7361,7362,7364,7366,7368,7370,7372,7374,7376,7378,7380,7382,7384],{},[1153,7363,6718],{},[1242,7365,1875],{"stretchy":1874},[1153,7367,1240],{},[1242,7369,1886],{"stretchy":1874},[1242,7371,1982],{},[1153,7373,6729],{},[1242,7375,1875],{"stretchy":1874},[1153,7377,6734],{},[1242,7379,6737],{},[1153,7381,1240],{},[1242,7383,1886],{"stretchy":1874},[1153,7385,1669],{"mathvariant":2121},[1159,7387,7388],{"encoding":1161},"F(x) = P(X \\le x).",[1115,7390,7392],{"className":7391},[1138],[1140,7393,7394],{"xmlns":1142},[1144,7395,7396,7406],{},[1147,7397,7398,7400,7402,7404],{},[1153,7399,6718],{},[1242,7401,1875],{"stretchy":1874},[1153,7403,1240],{},[1242,7405,1886],{"stretchy":1874},[1159,7407,7337],{"encoding":1161}," tedy vyjadřuje pravděpodobnost, s jakou ",[1115,7410,7412],{"className":7411},[1138],[1140,7413,7414],{"xmlns":1142},[1144,7415,7416,7420],{},[1147,7417,7418],{},[1153,7419,6734],{},[1159,7421,6734],{"encoding":1161}," nabude hodnoty z intervalu ",[1115,7424,7426],{"className":7425},[1138],[1140,7427,7428],{"xmlns":1142},[1144,7429,7430,7446],{},[1147,7431,7432,7434,7436,7439,7441,7443],{},[1242,7433,1875],{"stretchy":1874},[1242,7435,3064],{},[1153,7437,7438],{"mathvariant":2121},"∞",[1242,7440,1797],{"separator":1121},[1153,7442,1240],{},[1242,7444,7445],{"stretchy":1874},"⟩",[1159,7447,7448],{"encoding":1161},"(-\\infty, x\\rangle",[1110,7450,7451,7452,7465,7466,7487],{},"Značí-li například ",[1115,7453,7455],{"className":7454},[1138],[1140,7456,7457],{"xmlns":1142},[1144,7458,7459,7463],{},[1147,7460,7461],{},[1153,7462,6734],{},[1159,7464,6734],{"encoding":1161}," výšku mužů v populaci, pak ",[1115,7467,7469],{"className":7468},[1138],[1140,7470,7471],{"xmlns":1142},[1144,7472,7473,7484],{},[1147,7474,7475,7477,7479,7482],{},[1153,7476,6718],{},[1242,7478,1875],{"stretchy":1874},[1565,7480,7481],{},"175",[1242,7483,1886],{"stretchy":1874},[1159,7485,7486],{"encoding":1161},"F(175)"," je pravděpodobnost, že muž měří nejvýše 175 cm.",[1110,7489,7490],{},"Pro distribuční funkci vždy platí:",[1436,7492,7493,7523,7581,7641],{},[1439,7494,7495,1797],{},[1115,7496,7498],{"className":7497},[1138],[1140,7499,7500],{"xmlns":1142},[1144,7501,7502,7520],{},[1147,7503,7504,7506,7508,7510,7512,7514,7516,7518],{},[1565,7505,1567],{},[1242,7507,6737],{},[1153,7509,6718],{},[1242,7511,1875],{"stretchy":1874},[1153,7513,1240],{},[1242,7515,1886],{"stretchy":1874},[1242,7517,6737],{},[1565,7519,1794],{},[1159,7521,7522],{"encoding":1161},"0 \\le F(x) \\le 1",[1439,7524,7525,7526,1797],{},"je neklesající: ",[1115,7527,7529],{"className":7528},[1138],[1140,7530,7531],{"xmlns":1142},[1144,7532,7533,7578],{},[1147,7534,7535,7541,7543,7549,7552,7554,7556,7562,7564,7566,7568,7570,7576],{},[1150,7536,7537,7539],{},[1153,7538,1240],{},[1565,7540,1794],{},[1242,7542,6737],{},[1150,7544,7545,7547],{},[1153,7546,1240],{},[1565,7548,1589],{},[1242,7550,7551],{},"⇒",[1153,7553,6718],{},[1242,7555,1875],{"stretchy":1874},[1150,7557,7558,7560],{},[1153,7559,1240],{},[1565,7561,1794],{},[1242,7563,1886],{"stretchy":1874},[1242,7565,6737],{},[1153,7567,6718],{},[1242,7569,1875],{"stretchy":1874},[1150,7571,7572,7574],{},[1153,7573,1240],{},[1565,7575,1589],{},[1242,7577,1886],{"stretchy":1874},[1159,7579,7580],{"encoding":1161},"x_1 \\le x_2 \\Rightarrow F(x_1) \\le F(x_2)",[1439,7582,7583,7584,1797],{},"je spojitá zprava: ",[1115,7585,7587],{"className":7586},[1138],[1140,7588,7589],{"xmlns":1142},[1144,7590,7591,7638],{},[1147,7592,7593,7616,7618,7620,7622,7624,7626,7628,7630,7632,7634,7636],{},[1150,7594,7595,7602],{},[1147,7596,7597,7600],{},[1153,7598,7599],{},"lim",[1242,7601,4491],{},[1147,7603,7604,7607,7610],{},[1153,7605,7606],{},"h",[1242,7608,7609],{},"→",[1582,7611,7612,7614],{},[1565,7613,1567],{},[1242,7615,5477],{},[1153,7617,6718],{},[1242,7619,1875],{"stretchy":1874},[1153,7621,1240],{},[1242,7623,5477],{},[1153,7625,7606],{},[1242,7627,1886],{"stretchy":1874},[1242,7629,1982],{},[1153,7631,6718],{},[1242,7633,1875],{"stretchy":1874},[1153,7635,1240],{},[1242,7637,1886],{"stretchy":1874},[1159,7639,7640],{"encoding":1161},"\\lim_{h \\to 0^+} F(x+h) = F(x)",[1439,7642,7643,1346,7685,1669],{},[1115,7644,7646],{"className":7645},[1138],[1140,7647,7648],{"xmlns":1142},[1144,7649,7650,7682],{},[1147,7651,7652,7670,7672,7674,7676,7678,7680],{},[1150,7653,7654,7660],{},[1147,7655,7656,7658],{},[1153,7657,7599],{},[1242,7659,4491],{},[1147,7661,7662,7664,7666,7668],{},[1153,7663,1240],{},[1242,7665,7609],{},[1242,7667,3064],{},[1153,7669,7438],{"mathvariant":2121},[1153,7671,6718],{},[1242,7673,1875],{"stretchy":1874},[1153,7675,1240],{},[1242,7677,1886],{"stretchy":1874},[1242,7679,1982],{},[1565,7681,1567],{},[1159,7683,7684],{"encoding":1161},"\\lim_{x \\to -\\infty} F(x) = 0",[1115,7686,7688],{"className":7687},[1138],[1140,7689,7690],{"xmlns":1142},[1144,7691,7692,7722],{},[1147,7693,7694,7710,7712,7714,7716,7718,7720],{},[1150,7695,7696,7702],{},[1147,7697,7698,7700],{},[1153,7699,7599],{},[1242,7701,4491],{},[1147,7703,7704,7706,7708],{},[1153,7705,1240],{},[1242,7707,7609],{},[1153,7709,7438],{"mathvariant":2121},[1153,7711,6718],{},[1242,7713,1875],{"stretchy":1874},[1153,7715,1240],{},[1242,7717,1886],{"stretchy":1874},[1242,7719,1982],{},[1565,7721,1794],{},[1159,7723,7724],{"encoding":1161},"\\lim_{x \\to \\infty} F(x) = 1",[1110,7726,7727],{},"U spojité náhodné veličiny je distribuční funkce svázaná s hustotou pravděpodobnosti vztahem",[1115,7729,7731],{"className":7730},[1138],[1140,7732,7733],{"xmlns":1142,"display":1964},[1144,7734,7735,7803],{},[1147,7736,7737,7743,7745,7747,7749,7751,7753,7755,7757,7759,7761,7763,7765,7767,7769,7771,7773,7786,7788,7790,7792,7794,7796,7799,7801],{},[1582,7738,7739,7741],{},[1153,7740,6718],{},[1242,7742,6762],{"mathvariant":2121,"lspace":6761,"rspace":6761},[1242,7744,1875],{"stretchy":1874},[1153,7746,1240],{},[1242,7748,1886],{"stretchy":1874},[1242,7750,1982],{},[1153,7752,6773],{},[1242,7754,1875],{"stretchy":1874},[1153,7756,1240],{},[1242,7758,1886],{"stretchy":1874},[1242,7760,1797],{"separator":1121},[2012,7762],{"width":2014},[1153,7764,6718],{},[1242,7766,1875],{"stretchy":1874},[1153,7768,1240],{},[1242,7770,1886],{"stretchy":1874},[1242,7772,1982],{},[3353,7774,7775,7778,7784],{},[1242,7776,7777],{},"∫",[1147,7779,7780,7782],{},[1242,7781,3064],{},[1153,7783,7438],{"mathvariant":2121},[1153,7785,1240],{},[1153,7787,6773],{},[1242,7789,1875],{"stretchy":1874},[1153,7791,7146],{},[1242,7793,1886],{"stretchy":1874},[2909,7795,2911],{},[1153,7797,7798],{},"d",[1153,7800,7146],{},[1153,7802,1669],{"mathvariant":2121},[1159,7804,7805],{"encoding":1161},"F'(x) = f(x), \\qquad F(x) = \\int_{-\\infty}^{x} f(t)\\,dt.",[1110,7807,7808,7809,7822,7823,1163,7841,7859],{},"Pravděpodobnost, že ",[1115,7810,7812],{"className":7811},[1138],[1140,7813,7814],{"xmlns":1142},[1144,7815,7816,7820],{},[1147,7817,7818],{},[1153,7819,6734],{},[1159,7821,6734],{"encoding":1161}," padne mezi body ",[1115,7824,7826],{"className":7825},[1138],[1140,7827,7828],{"xmlns":1142},[1144,7829,7830,7838],{},[1147,7831,7832],{},[1150,7833,7834,7836],{},[1153,7835,1240],{},[1565,7837,1794],{},[1159,7839,7840],{"encoding":1161},"x_1",[1115,7842,7844],{"className":7843},[1138],[1140,7845,7846],{"xmlns":1142},[1144,7847,7848,7856],{},[1147,7849,7850],{},[1150,7851,7852,7854],{},[1153,7853,1240],{},[1565,7855,1589],{},[1159,7857,7858],{"encoding":1161},"x_2",", se pak počítá jako",[1115,7861,7863],{"className":7862},[1138],[1140,7864,7865],{"xmlns":1142,"display":1964},[1144,7866,7867,7955],{},[1147,7868,7869,7871,7873,7879,7881,7883,7885,7891,7893,7895,7911,7913,7915,7917,7919,7921,7923,7925,7927,7929,7931,7937,7939,7941,7943,7945,7951,7953],{},[1153,7870,6729],{},[1242,7872,1875],{"stretchy":1874},[1150,7874,7875,7877],{},[1153,7876,1240],{},[1565,7878,1794],{},[1242,7880,4332],{},[1153,7882,6734],{},[1242,7884,4332],{},[1150,7886,7887,7889],{},[1153,7888,1240],{},[1565,7890,1589],{},[1242,7892,1886],{"stretchy":1874},[1242,7894,1982],{},[3353,7896,7897,7899,7905],{},[1242,7898,7777],{},[1150,7900,7901,7903],{},[1153,7902,1240],{},[1565,7904,1794],{},[1150,7906,7907,7909],{},[1153,7908,1240],{},[1565,7910,1589],{},[1153,7912,6773],{},[1242,7914,1875],{"stretchy":1874},[1153,7916,7146],{},[1242,7918,1886],{"stretchy":1874},[2909,7920,2911],{},[1153,7922,7798],{},[1153,7924,7146],{},[1242,7926,1982],{},[1153,7928,6718],{},[1242,7930,1875],{"stretchy":1874},[1150,7932,7933,7935],{},[1153,7934,1240],{},[1565,7936,1589],{},[1242,7938,1886],{"stretchy":1874},[1242,7940,3064],{},[1153,7942,6718],{},[1242,7944,1875],{"stretchy":1874},[1150,7946,7947,7949],{},[1153,7948,1240],{},[1565,7950,1794],{},[1242,7952,1886],{"stretchy":1874},[1153,7954,1669],{"mathvariant":2121},[1159,7956,7957],{"encoding":1161},"P(x_1 \u003C X \u003C x_2) = \\int_{x_1}^{x_2} f(t)\\,dt = F(x_2) - F(x_1).",[1189,7959,7961],{"id":7960},"hustota-pravděpodobnosti","Hustota pravděpodobnosti",[1103,7963,7965,7971],{"className":7964,"dataCallout":654},[1106,7293],[1110,7966,7968,7300],{"className":7967},[1113],[1115,7969],{"className":7970,"ariaHidden":1121},[1118,1532,1120],[1110,7972,7973,7974,7993,7994,8007,8008,8021,8022,1669],{},"Hustota pravděpodobnosti ",[1115,7975,7977],{"className":7976},[1138],[1140,7978,7979],{"xmlns":1142},[1144,7980,7981,7991],{},[1147,7982,7983,7985,7987,7989],{},[1153,7984,6773],{},[1242,7986,1875],{"stretchy":1874},[1153,7988,1240],{},[1242,7990,1886],{"stretchy":1874},[1159,7992,6803],{"encoding":1161}," určuje, jak jsou hodnoty spojité náhodné veličiny ",[1115,7995,7997],{"className":7996},[1138],[1140,7998,7999],{"xmlns":1142},[1144,8000,8001,8005],{},[1147,8002,8003],{},[1153,8004,6734],{},[1159,8006,6734],{"encoding":1161}," nahuštěny v okolí bodu ",[1115,8009,8011],{"className":8010},[1138],[1140,8012,8013],{"xmlns":1142},[1144,8014,8015,8019],{},[1147,8016,8017],{},[1153,8018,1240],{},[1159,8020,1240],{"encoding":1161},". Je vždy nezáporná a platí pro ni ",[1115,8023,8025],{"className":8024},[1138],[1140,8026,8027],{"xmlns":1142},[1144,8028,8029,8061],{},[1147,8030,8031,8043,8045,8047,8049,8051,8053,8055,8057,8059],{},[3353,8032,8033,8035,8041],{},[1242,8034,7777],{},[1147,8036,8037,8039],{},[1242,8038,3064],{},[1153,8040,7438],{"mathvariant":2121},[1153,8042,7438],{"mathvariant":2121},[1153,8044,6773],{},[1242,8046,1875],{"stretchy":1874},[1153,8048,1240],{},[1242,8050,1886],{"stretchy":1874},[2909,8052,2911],{},[1153,8054,7798],{},[1153,8056,1240],{},[1242,8058,1982],{},[1565,8060,1794],{},[1159,8062,8063],{"encoding":1161},"\\int_{-\\infty}^{\\infty} f(x)\\,dx = 1",[1110,8065,8066],{},"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.",[1189,8068,8070],{"id":8069},"charakteristiky-spojité-náhodné-veličiny","Charakteristiky spojité náhodné veličiny",[1110,8072,8073,8076],{},[1540,8074,8075],{},"Střední hodnota"," je nejdůležitější charakteristika náhodné veličiny:",[1115,8078,8080],{"className":8079},[1138],[1140,8081,8082],{"xmlns":1142,"display":1964},[1144,8083,8084,8130],{},[1147,8085,8086,8089,8091,8093,8095,8097,8109,8111,8114,8116,8118,8120,8122,8124,8126,8128],{},[1153,8087,8088],{},"E",[1242,8090,1875],{"stretchy":1874},[1153,8092,6734],{},[1242,8094,1886],{"stretchy":1874},[1242,8096,1982],{},[3353,8098,8099,8101,8107],{},[1242,8100,7777],{},[1147,8102,8103,8105],{},[1242,8104,3064],{},[1153,8106,7438],{"mathvariant":2121},[1153,8108,7438],{"mathvariant":2121},[1153,8110,1240],{},[1242,8112,8113],{},"⋅",[1153,8115,6773],{},[1242,8117,1875],{"stretchy":1874},[1153,8119,1240],{},[1242,8121,1886],{"stretchy":1874},[2909,8123,2911],{},[1153,8125,7798],{},[1153,8127,1240],{},[1153,8129,1669],{"mathvariant":2121},[1159,8131,8132],{"encoding":1161},"E(X) = \\int_{-\\infty}^{\\infty} x \\cdot f(x)\\,dx.",[1110,8134,8135],{},"Je to číslo, kolem něhož kolísají výběrové průměry vypočtené ze sérií pozorovaných hodnot náhodné veličiny.",[1110,8137,8138,1163,8141,1958],{},[1540,8139,8140],{},"Rozptyl",[1540,8142,8143],{},"směrodatná odchylka",[1115,8145,8147],{"className":8146},[1138],[1140,8148,8149],{"xmlns":1142,"display":1964},[1144,8150,8151,8292],{},[1147,8152,8153,8156,8158,8160,8162,8164,8176,8179,8181,8183,8185,8187,8189,8191,8198,8200,8202,8204,8206,8208,8210,8212,8214,8226,8232,8234,8236,8238,8240,8242,8244,8246,8248,8250,8252,8254,8256,8258,8264,8266,8268,8270,8272,8274,8276,8278,8290],{},[1153,8154,8155],{},"D",[1242,8157,1875],{"stretchy":1874},[1153,8159,6734],{},[1242,8161,1886],{"stretchy":1874},[1242,8163,1982],{},[3353,8165,8166,8168,8174],{},[1242,8167,7777],{},[1147,8169,8170,8172],{},[1242,8171,3064],{},[1153,8173,7438],{"mathvariant":2121},[1153,8175,7438],{"mathvariant":2121},[1242,8177,8178],{"stretchy":1874},"[",[1153,8180,1240],{},[1242,8182,3064],{},[1153,8184,8088],{},[1242,8186,1875],{"stretchy":1874},[1153,8188,6734],{},[1242,8190,1886],{"stretchy":1874},[1582,8192,8193,8196],{},[1242,8194,8195],{"stretchy":1874},"]",[1565,8197,1589],{},[1153,8199,6773],{},[1242,8201,1875],{"stretchy":1874},[1153,8203,1240],{},[1242,8205,1886],{"stretchy":1874},[2909,8207,2911],{},[1153,8209,7798],{},[1153,8211,1240],{},[1242,8213,1982],{},[3353,8215,8216,8218,8224],{},[1242,8217,7777],{},[1147,8219,8220,8222],{},[1242,8221,3064],{},[1153,8223,7438],{"mathvariant":2121},[1153,8225,7438],{"mathvariant":2121},[1582,8227,8228,8230],{},[1153,8229,1240],{},[1565,8231,1589],{},[1153,8233,6773],{},[1242,8235,1875],{"stretchy":1874},[1153,8237,1240],{},[1242,8239,1886],{"stretchy":1874},[2909,8241,2911],{},[1153,8243,7798],{},[1153,8245,1240],{},[1242,8247,3064],{},[1242,8249,8178],{"stretchy":1874},[1153,8251,8088],{},[1242,8253,1875],{"stretchy":1874},[1153,8255,6734],{},[1242,8257,1886],{"stretchy":1874},[1582,8259,8260,8262],{},[1242,8261,8195],{"stretchy":1874},[1565,8263,1589],{},[1242,8265,1797],{"separator":1121},[2012,8267],{"width":2014},[1153,8269,6901],{},[1242,8271,1875],{"stretchy":1874},[1153,8273,6734],{},[1242,8275,1886],{"stretchy":1874},[1242,8277,1982],{},[4453,8279,8280],{},[1147,8281,8282,8284,8286,8288],{},[1153,8283,8155],{},[1242,8285,1875],{"stretchy":1874},[1153,8287,6734],{},[1242,8289,1886],{"stretchy":1874},[1153,8291,1669],{"mathvariant":2121},[1159,8293,8294],{"encoding":1161},"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)}.",[1110,8296,8297,8298,8301],{},"Směrodatná odchylka udává, jak moc jsou hodnoty náhodné veličiny rozptýlené kolem střední hodnoty. (Pro odhad těchto charakteristik z naměřených dat viz empirické protějšky v ",[1127,8299,886],{"className":8300,"dataFsResolvedFilePath":6612,"href":6613},[1130],".)",[1110,8303,8304,8307,8308,8321,8322,8340,8341,8354],{},[1540,8305,8306],{},"Kvantily"," udávají, jak jsou hodnoty náhodné veličiny ",[1115,8309,8311],{"className":8310},[1138],[1140,8312,8313],{"xmlns":1142},[1144,8314,8315,8319],{},[1147,8316,8317],{},[1153,8318,6734],{},[1159,8320,6734],{"encoding":1161}," rozděleny na ose reálných čísel v určitém pravděpodobnostním poměru. 100p%-ní kvantil ",[1115,8323,8325],{"className":8324},[1138],[1140,8326,8327],{"xmlns":1142},[1144,8328,8329,8337],{},[1147,8330,8331],{},[1150,8332,8333,8335],{},[1153,8334,1240],{},[1153,8336,1110],{},[1159,8338,8339],{"encoding":1161},"x_p"," je číslo, pro které při zvolené pravděpodobnosti ",[1115,8342,8344],{"className":8343},[1138],[1140,8345,8346],{"xmlns":1142},[1144,8347,8348,8352],{},[1147,8349,8350],{},[1153,8351,1110],{},[1159,8353,1110],{"encoding":1161}," platí",[1115,8356,8358],{"className":8357},[1138],[1140,8359,8360],{"xmlns":1142,"display":1964},[1144,8361,8362,8382],{},[1147,8363,8364,8366,8368,8374,8376,8378,8380],{},[1153,8365,6718],{},[1242,8367,1875],{"stretchy":1874},[1150,8369,8370,8372],{},[1153,8371,1240],{},[1153,8373,1110],{},[1242,8375,1886],{"stretchy":1874},[1242,8377,1982],{},[1153,8379,1110],{},[1153,8381,1669],{"mathvariant":2121},[1159,8383,8384],{"encoding":1161},"F(x_p) = p.",[1110,8386,8387,8388,8416,8417,8444,8445,8464,8465,8484,8485,1669],{},"V intervalu ",[1115,8389,8391],{"className":8390},[1138],[1140,8392,8393],{"xmlns":1142},[1144,8394,8395,8413],{},[1147,8396,8397,8399,8401,8403,8405,8411],{},[1242,8398,1875],{"stretchy":1874},[1242,8400,3064],{},[1153,8402,7438],{"mathvariant":2121},[1242,8404,6896],{"separator":1121},[1150,8406,8407,8409],{},[1153,8408,1240],{},[1153,8410,1110],{},[1242,8412,1886],{"stretchy":1874},[1159,8414,8415],{"encoding":1161},"(-\\infty; x_p)"," leží 100p % hodnot, v intervalu ",[1115,8418,8420],{"className":8419},[1138],[1140,8421,8422],{"xmlns":1142},[1144,8423,8424,8441],{},[1147,8425,8426,8429,8435,8437,8439],{},[1242,8427,8428],{"stretchy":1874},"⟨",[1150,8430,8431,8433],{},[1153,8432,1240],{},[1153,8434,1110],{},[1242,8436,6896],{"separator":1121},[1153,8438,7438],{"mathvariant":2121},[1242,8440,1886],{"stretchy":1874},[1159,8442,8443],{"encoding":1161},"\\langle x_p; \\infty)"," leží 100(1-p) % hodnot. Nejdůležitější kvantily jsou medián ",[1115,8446,8448],{"className":8447},[1138],[1140,8449,8450],{"xmlns":1142},[1144,8451,8452,8461],{},[1147,8453,8454],{},[1150,8455,8456,8458],{},[1153,8457,1240],{},[1565,8459,8460],{},"0,5",[1159,8462,8463],{"encoding":1161},"x_{0{,}5}",", dolní kvartil ",[1115,8466,8468],{"className":8467},[1138],[1140,8469,8470],{"xmlns":1142},[1144,8471,8472,8481],{},[1147,8473,8474],{},[1150,8475,8476,8478],{},[1153,8477,1240],{},[1565,8479,8480],{},"0,25",[1159,8482,8483],{"encoding":1161},"x_{0{,}25}"," a horní kvartil ",[1115,8486,8488],{"className":8487},[1138],[1140,8489,8490],{"xmlns":1142},[1144,8491,8492,8501],{},[1147,8493,8494],{},[1150,8495,8496,8498],{},[1153,8497,1240],{},[1565,8499,8500],{},"0,75",[1159,8502,8503],{"encoding":1161},"x_{0{,}75}",[1189,8505,6876],{"id":8506},"normální-rozdělení",[1110,8508,8509,8510,8523,8524,1654,8527,8554],{},"Spojitá náhodná veličina ",[1115,8511,8513],{"className":8512},[1138],[1140,8514,8515],{"xmlns":1142},[1144,8516,8517,8521],{},[1147,8518,8519],{},[1153,8520,6734],{},[1159,8522,6734],{"encoding":1161}," má ",[1540,8525,8526],{},"normální rozdělení",[1115,8528,8530],{"className":8529},[1138],[1140,8531,8532],{"xmlns":1142},[1144,8533,8534,8552],{},[1147,8535,8536,8538,8540,8542,8544,8550],{},[1153,8537,6888],{},[1242,8539,1875],{"stretchy":1874},[1153,8541,6893],{},[1242,8543,6896],{"separator":1121},[1582,8545,8546,8548],{},[1153,8547,6901],{},[1565,8549,1589],{},[1242,8551,1886],{"stretchy":1874},[1159,8553,6908],{"encoding":1161},", jestliže její hustota pravděpodobnosti a distribuční funkce jsou dány předpisy",[1115,8556,8558],{"className":8557},[1138],[1140,8559,8560],{"xmlns":1142,"display":1964},[1144,8561,8562,8714],{},[1147,8563,8564,8566,8568,8570,8572,8574,8591,8628,8630,8632,8634,8636,8638,8640,8642,8658,8670,8706,8708,8710,8712],{},[1153,8565,6773],{},[1242,8567,1875],{"stretchy":1874},[1153,8569,1240],{},[1242,8571,1886],{"stretchy":1874},[1242,8573,1982],{},[2739,8575,8576,8578],{},[1565,8577,1794],{},[1147,8579,8580,8582],{},[1153,8581,6901],{},[4453,8583,8584],{},[1147,8585,8586,8588],{},[1565,8587,1589],{},[1153,8589,8590],{},"π",[1582,8592,8593,8596],{},[1153,8594,8595],{},"e",[1147,8597,8598,8600],{},[1242,8599,3064],{},[2739,8601,8602,8618],{},[1147,8603,8604,8606,8608,8610,8612],{},[1242,8605,1875],{"stretchy":1874},[1153,8607,1240],{},[1242,8609,3064],{},[1153,8611,6893],{},[1582,8613,8614,8616],{},[1242,8615,1886],{"stretchy":1874},[1565,8617,1589],{},[1147,8619,8620,8622],{},[1565,8621,1589],{},[1582,8623,8624,8626],{},[1153,8625,6901],{},[1565,8627,1589],{},[1242,8629,1797],{"separator":1121},[2012,8631],{"width":2014},[1153,8633,6718],{},[1242,8635,1875],{"stretchy":1874},[1153,8637,1240],{},[1242,8639,1886],{"stretchy":1874},[1242,8641,1982],{},[2739,8643,8644,8646],{},[1565,8645,1794],{},[1147,8647,8648,8650],{},[1153,8649,6901],{},[4453,8651,8652],{},[1147,8653,8654,8656],{},[1565,8655,1589],{},[1153,8657,8590],{},[3353,8659,8660,8662,8668],{},[1242,8661,7777],{},[1147,8663,8664,8666],{},[1242,8665,3064],{},[1153,8667,7438],{"mathvariant":2121},[1153,8669,1240],{},[1582,8671,8672,8674],{},[1153,8673,8595],{},[1147,8675,8676,8678],{},[1242,8677,3064],{},[2739,8679,8680,8696],{},[1147,8681,8682,8684,8686,8688,8690],{},[1242,8683,1875],{"stretchy":1874},[1153,8685,7146],{},[1242,8687,3064],{},[1153,8689,6893],{},[1582,8691,8692,8694],{},[1242,8693,1886],{"stretchy":1874},[1565,8695,1589],{},[1147,8697,8698,8700],{},[1565,8699,1589],{},[1582,8701,8702,8704],{},[1153,8703,6901],{},[1565,8705,1589],{},[2909,8707,2911],{},[1153,8709,7798],{},[1153,8711,7146],{},[1242,8713,1797],{"separator":1121},[1159,8715,8716],{"encoding":1161},"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,",[1110,8718,8719,8720,1346,8744,1669],{},"přičemž ",[1115,8721,8723],{"className":8722},[1138],[1140,8724,8725],{"xmlns":1142},[1144,8726,8727,8741],{},[1147,8728,8729,8731,8733,8735,8737,8739],{},[1153,8730,8088],{},[1242,8732,1875],{"stretchy":1874},[1153,8734,6734],{},[1242,8736,1886],{"stretchy":1874},[1242,8738,1982],{},[1153,8740,6893],{},[1159,8742,8743],{"encoding":1161},"E(X) = \\mu",[1115,8745,8747],{"className":8746},[1138],[1140,8748,8749],{"xmlns":1142},[1144,8750,8751,8769],{},[1147,8752,8753,8755,8757,8759,8761,8763],{},[1153,8754,8155],{},[1242,8756,1875],{"stretchy":1874},[1153,8758,6734],{},[1242,8760,1886],{"stretchy":1874},[1242,8762,1982],{},[1582,8764,8765,8767],{},[1153,8766,6901],{},[1565,8768,1589],{},[1159,8770,8771],{"encoding":1161},"D(X) = \\sigma^2",[1110,8773,8774],{},[4383,8775],{"alt":8776,"className":8777,"src":8778},"mask-nv-normalni",[1130,4387],"\u002Fwiki-assets\u002Fmask-nv-normalni.png",[1110,8780,8781,8782,8785,8786,8800,8801,8820,8821,8837,8838,8851,8852,1669],{},"Křivka hustoty se nazývá ",[1540,8783,8784],{},"Gaussova křivka",": je symetrická kolem svislé přímky procházející ",[1115,8787,8789],{"className":8788},[1138],[1140,8790,8791],{"xmlns":1142},[1144,8792,8793,8797],{},[1147,8794,8795],{},[1153,8796,6893],{},[1159,8798,8799],{"encoding":1161},"\\mu",", kde má ",[1115,8802,8804],{"className":8803},[1138],[1140,8805,8806],{"xmlns":1142},[1144,8807,8808,8818],{},[1147,8809,8810,8812,8814,8816],{},[1153,8811,6773],{},[1242,8813,1875],{"stretchy":1874},[1153,8815,1240],{},[1242,8817,1886],{"stretchy":1874},[1159,8819,6803],{"encoding":1161}," globální maximum, a ve vzdálenosti ",[1115,8822,8824],{"className":8823},[1138],[1140,8825,8826],{"xmlns":1142},[1144,8827,8828,8834],{},[1147,8829,8830,8832],{},[1565,8831,3592],{},[1153,8833,6901],{},[1159,8835,8836],{"encoding":1161},"3\\sigma"," od ",[1115,8839,8841],{"className":8840},[1138],[1140,8842,8843],{"xmlns":1142},[1144,8844,8845,8849],{},[1147,8846,8847],{},[1153,8848,6893],{},[1159,8850,8799],{"encoding":1161}," se téměř dotýká osy x — zhruba 99,73 % hodnot leží v intervalu ",[1115,8853,8855],{"className":8854},[1138],[1140,8856,8857],{"xmlns":1142},[1144,8858,8859,8883],{},[1147,8860,8861,8863,8865,8867,8869,8871,8873,8875,8877,8879,8881],{},[1242,8862,1875],{"stretchy":1874},[1153,8864,6893],{},[1242,8866,3064],{},[1565,8868,3592],{},[1153,8870,6901],{},[1242,8872,6896],{"separator":1121},[1153,8874,6893],{},[1242,8876,5477],{},[1565,8878,3592],{},[1153,8880,6901],{},[1242,8882,1886],{"stretchy":1874},[1159,8884,8885],{"encoding":1161},"(\\mu - 3\\sigma; \\mu + 3\\sigma)",[1110,8887,8888,8889,1654,8892,8916,8917,1669],{},"Zvláštní postavení má ",[1540,8890,8891],{},"normované normální rozdělení",[1115,8893,8895],{"className":8894},[1138],[1140,8896,8897],{"xmlns":1142},[1144,8898,8899,8913],{},[1147,8900,8901,8903,8905,8907,8909,8911],{},[1153,8902,6888],{},[1242,8904,1875],{"stretchy":1874},[1565,8906,1567],{},[1242,8908,6896],{"separator":1121},[1565,8910,1794],{},[1242,8912,1886],{"stretchy":1874},[1159,8914,8915],{"encoding":1161},"N(0; 1)",", na které se dá libovolné normální rozdělení převést standardizací ",[1115,8918,8920],{"className":8919},[1138],[1140,8921,8922],{"xmlns":1142},[1144,8923,8924,8945],{},[1147,8925,8926,8929,8931,8933,8935,8937,8939,8941,8943],{},[1153,8927,8928],{},"Z",[1242,8930,1982],{},[1242,8932,1875],{"stretchy":1874},[1153,8934,6734],{},[1242,8936,3064],{},[1153,8938,6893],{},[1242,8940,1886],{"stretchy":1874},[1153,8942,4604],{"mathvariant":2121},[1153,8944,6901],{},[1159,8946,8947],{"encoding":1161},"Z = (X-\\mu)\u002F\\sigma",[8949,8950],"graph-mount",{"spec":8951},"{\"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\"}]}",[1103,8953,8955,8962],{"className":8954,"dataCallout":6412},[1106,6411],[1110,8956,8958,8961],{"className":8957},[1113],[1115,8959],{"className":8960,"ariaHidden":1121},[1118,6419,1120],"R očekává směrodatnou odchylku, ne rozptyl",[1110,8963,8964,8965,8992,8993,8996,8997,1346,8999,1163,9001,9003,9004,1654,9007,9020,9021,9047,9048,9051,9052,1669],{},"Zápis ",[1115,8966,8968],{"className":8967},[1138],[1140,8969,8970],{"xmlns":1142},[1144,8971,8972,8990],{},[1147,8973,8974,8976,8978,8980,8982,8988],{},[1153,8975,6888],{},[1242,8977,1875],{"stretchy":1874},[1153,8979,6893],{},[1242,8981,6896],{"separator":1121},[1582,8983,8984,8986],{},[1153,8985,6901],{},[1565,8987,1589],{},[1242,8989,1886],{"stretchy":1874},[1159,8991,6908],{"encoding":1161}," v definici používá ",[1540,8994,8995],{},"rozptyl",". Funkce ",[3470,8998,6912],{},[3470,9000,6915],{},[3470,9002,6918],{}," v R ale jako třetí argument berou ",[1540,9005,9006],{},"směrodatnou odchylku",[1115,9008,9010],{"className":9009},[1138],[1140,9011,9012],{"xmlns":1142},[1144,9013,9014,9018],{},[1147,9015,9016],{},[1153,9017,6901],{},[1159,9019,6933],{"encoding":1161},". Má-li náhodná veličina rozdělení ",[1115,9022,9024],{"className":9023},[1138],[1140,9025,9026],{"xmlns":1142},[1144,9027,9028,9044],{},[1147,9029,9030,9032,9034,9037,9039,9042],{},[1153,9031,6888],{},[1242,9033,1875],{"stretchy":1874},[1565,9035,9036],{},"10",[1242,9038,6896],{"separator":1121},[1565,9040,9041],{},"0,12",[1242,9043,1886],{"stretchy":1874},[1159,9045,9046],{"encoding":1161},"N(10; 0{,}12)",", je ",[3470,9049,9050],{},"sd = sqrt(0.12)",", ne ",[3470,9053,9054],{},"sd = 0.12",[1110,9056,9057],{},"V R:",[3694,9059,9061],{"className":3696,"code":9060,"language":71,"meta":1490,"style":1490},"dnorm(0)\npnorm(1.96)\nqnorm(0.975)\n",[3470,9062,9063,9073,9084],{"__ignoreMap":1490},[1115,9064,9065,9067,9069,9071],{"class":3702,"line":10},[1115,9066,6912],{"class":3713},[1115,9068,1875],{"class":3717},[1115,9070,1567],{"class":3724},[1115,9072,3901],{"class":3717},[1115,9074,9075,9077,9079,9082],{"class":3702,"line":27},[1115,9076,6915],{"class":3713},[1115,9078,1875],{"class":3717},[1115,9080,9081],{"class":3724},"1.96",[1115,9083,3901],{"class":3717},[1115,9085,9086,9088,9090,9093],{"class":3702,"line":148},[1115,9087,6918],{"class":3713},[1115,9089,1875],{"class":3717},[1115,9091,9092],{"class":3724},"0.975",[1115,9094,3901],{"class":3717},[3694,9096,9099],{"className":9097,"code":9098,"language":3923,"meta":1490},[3921],"[1] 0.3989423\n[1] 0.9750021\n[1] 1.959964\n",[3470,9100,9098],{"__ignoreMap":1490},[1110,9102,9103,9106,9107,9131,9132,1890,9135,1163,9156,9159],{},[3470,9104,9105],{},"dnorm(0)"," je hodnota hustoty ",[1115,9108,9110],{"className":9109},[1138],[1140,9111,9112],{"xmlns":1142},[1144,9113,9114,9128],{},[1147,9115,9116,9118,9120,9122,9124,9126],{},[1153,9117,6888],{},[1242,9119,1875],{"stretchy":1874},[1565,9121,1567],{},[1242,9123,6896],{"separator":1121},[1565,9125,1794],{},[1242,9127,1886],{"stretchy":1874},[1159,9129,9130],{"encoding":1161},"N(0;1)"," v bodě 0, ",[3470,9133,9134],{},"pnorm(1.96)",[1115,9136,9138],{"className":9137},[1138],[1140,9139,9140],{"xmlns":1142},[1144,9141,9142,9153],{},[1147,9143,9144,9146,9148,9151],{},[1153,9145,6718],{},[1242,9147,1875],{"stretchy":1874},[1565,9149,9150],{},"1,96",[1242,9152,1886],{"stretchy":1874},[1159,9154,9155],{"encoding":1161},"F(1{,}96)",[3470,9157,9158],{},"qnorm(0.975)"," je 97,5%-ní kvantil — hodnota, pod kterou leží 97,5 % pravděpodobnosti.",[1103,9161,9163,9170],{"className":9162,"dataCallout":3477},[1106,3476],[1110,9164,9166,9169],{"className":9165},[1113],[1115,9167],{"className":9168,"ariaHidden":1121},[1118,3484,1120],"Příklad: Návštěvnost zábavního parku",[1110,9171,9172,9173,9208],{},"Denní návštěvnost zábavního parku je náhodná veličina s normálním rozdělením, průměrnou hodnotou 230 a směrodatnou odchylkou 27,5 návštěvníků: ",[1115,9174,9176],{"className":9175},[1138],[1140,9177,9178],{"xmlns":1142},[1144,9179,9180,9205],{},[1147,9181,9182,9184,9187,9189,9191,9194,9196,9203],{},[1153,9183,6734],{},[1242,9185,9186],{},"∼",[1153,9188,6888],{},[1242,9190,1875],{"stretchy":1874},[1565,9192,9193],{},"230",[1242,9195,6896],{"separator":1121},[1582,9197,9198,9201],{},[1565,9199,9200],{},"27,5",[1565,9202,1589],{},[1242,9204,1886],{"stretchy":1874},[1159,9206,9207],{"encoding":1161},"X \\sim N(230; 27{,}5^2)",". Přijde-li za den méně než 180 návštěvníků, je park ztrátový. Kolik procent dní je ztrátových?",[1110,9210,9211],{},[4383,9212],{"alt":9213,"className":9214,"src":9215},"mask-nv-priklad-park",[1130,4387],"\u002Fwiki-assets\u002Fmask-nv-priklad-park.png",[3694,9217,9219],{"className":3696,"code":9218,"language":71,"meta":1490,"style":1490},"pnorm(180, mean = 230, sd = 27.5)\n",[3470,9220,9221],{"__ignoreMap":1490},[1115,9222,9223,9225,9227,9230,9232,9235,9237,9240,9242,9245,9247,9250],{"class":3702,"line":10},[1115,9224,6915],{"class":3713},[1115,9226,1875],{"class":3717},[1115,9228,9229],{"class":3724},"180",[1115,9231,1797],{"class":3709},[1115,9233,9234],{"class":3705}," mean",[1115,9236,3797],{"class":3709},[1115,9238,9239],{"class":3724}," 230",[1115,9241,1797],{"class":3709},[1115,9243,9244],{"class":3705}," sd",[1115,9246,3797],{"class":3709},[1115,9248,9249],{"class":3724}," 27.5",[1115,9251,3901],{"class":3717},[3694,9253,9256],{"className":9254,"code":9255,"language":3923,"meta":1490},[3921],"[1] 0.03451817\n",[3470,9257,9255],{"__ignoreMap":1490},[1110,9259,9260],{},"Park je ztrátový přibližně v 3,45 % dní.",[1103,9262,9264,9271],{"className":9263,"dataCallout":3477},[1106,3476],[1110,9265,9267,9270],{"className":9266},[1113],[1115,9268],{"className":9269,"ariaHidden":1121},[1118,3484,1120],"Příklad: Délka výrobku",[1110,9272,9273,9274,9308],{},"Automat je seřízen tak, aby střední hodnota délky výrobku byla 42 mm, s přesností charakterizovanou směrodatnou odchylkou 1,2 mm: ",[1115,9275,9277],{"className":9276},[1138],[1140,9278,9279],{"xmlns":1142},[1144,9280,9281,9305],{},[1147,9282,9283,9285,9287,9289,9291,9294,9296,9303],{},[1153,9284,6734],{},[1242,9286,9186],{},[1153,9288,6888],{},[1242,9290,1875],{"stretchy":1874},[1565,9292,9293],{},"42",[1242,9295,6896],{"separator":1121},[1582,9297,9298,9301],{},[1565,9299,9300],{},"1,2",[1565,9302,1589],{},[1242,9304,1886],{"stretchy":1874},[1159,9306,9307],{"encoding":1161},"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?",[1110,9310,9311],{},[4383,9312],{"alt":9313,"className":9314,"src":9315},"mask-nv-priklad-delka",[1130,4387],"\u002Fwiki-assets\u002Fmask-nv-priklad-delka.png",[3694,9317,9319],{"className":3696,"code":9318,"language":71,"meta":1490,"style":1490},"pnorm(43, mean = 42, sd = 1.2) - pnorm(41, mean = 42, sd = 1.2)\n",[3470,9320,9321],{"__ignoreMap":1490},[1115,9322,9323,9325,9327,9330,9332,9334,9336,9339,9341,9343,9345,9348,9350,9352,9355,9357,9360,9362,9364,9366,9368,9370,9372,9374,9376],{"class":3702,"line":10},[1115,9324,6915],{"class":3713},[1115,9326,1875],{"class":3717},[1115,9328,9329],{"class":3724},"43",[1115,9331,1797],{"class":3709},[1115,9333,9234],{"class":3705},[1115,9335,3797],{"class":3709},[1115,9337,9338],{"class":3724}," 42",[1115,9340,1797],{"class":3709},[1115,9342,9244],{"class":3705},[1115,9344,3797],{"class":3709},[1115,9346,9347],{"class":3724}," 1.2",[1115,9349,4601],{"class":3717},[1115,9351,4638],{"class":3709},[1115,9353,9354],{"class":3713}," pnorm",[1115,9356,1875],{"class":3717},[1115,9358,9359],{"class":3724},"41",[1115,9361,1797],{"class":3709},[1115,9363,9234],{"class":3705},[1115,9365,3797],{"class":3709},[1115,9367,9338],{"class":3724},[1115,9369,1797],{"class":3709},[1115,9371,9244],{"class":3705},[1115,9373,3797],{"class":3709},[1115,9375,9347],{"class":3724},[1115,9377,3901],{"class":3717},[3694,9379,9382],{"className":9380,"code":9381,"language":3923,"meta":1490},[3921],"[1] 0.5953432\n",[3470,9383,9381],{"__ignoreMap":1490},[1110,9385,9386],{},"Do 1. jakostní třídy spadá přibližně 59,53 % výrobků.",[1103,9388,9390,9397],{"className":9389,"dataCallout":3477},[1106,3476],[1110,9391,9393,9396],{"className":9392},[1113],[1115,9394],{"className":9395,"ariaHidden":1121},[1118,3484,1120],"Příklad: Obsah ampulky",[1110,9398,9399,9400,9423,9424,9450],{},"Obsah ampulky s lékem (v cm³) má rozdělení ",[1115,9401,9403],{"className":9402},[1138],[1140,9404,9405],{"xmlns":1142},[1144,9406,9407,9421],{},[1147,9408,9409,9411,9413,9415,9417,9419],{},[1153,9410,6888],{},[1242,9412,1875],{"stretchy":1874},[1565,9414,9036],{},[1242,9416,6896],{"separator":1121},[1565,9418,9041],{},[1242,9420,1886],{"stretchy":1874},[1159,9422,9046],{"encoding":1161},", tedy střední hodnota 10 a rozptyl 0,12 (",[1115,9425,9427],{"className":9426},[1138],[1140,9428,9429],{"xmlns":1142},[1144,9430,9431,9447],{},[1147,9432,9433,9435,9437,9441,9444],{},[1153,9434,6901],{},[1242,9436,1982],{},[4453,9438,9439],{},[1565,9440,9041],{},[1242,9442,9443],{},"≈",[1565,9445,9446],{},"0,346",[1159,9448,9449],{"encoding":1161},"\\sigma = \\sqrt{0{,}12} \\approx 0{,}346","). Kolik procent ampulek má obsah menší než 9,8 cm³?",[1110,9452,9453],{},[4383,9454],{"alt":9455,"className":9456,"src":9457},"mask-nv-priklad-ampulka",[1130,4387],"\u002Fwiki-assets\u002Fmask-nv-priklad-ampulka.png",[3694,9459,9461],{"className":3696,"code":9460,"language":71,"meta":1490,"style":1490},"pnorm(9.8, mean = 10, sd = sqrt(0.12))\n",[3470,9462,9463],{"__ignoreMap":1490},[1115,9464,9465,9467,9469,9472,9474,9476,9478,9481,9483,9485,9487,9489,9491,9494],{"class":3702,"line":10},[1115,9466,6915],{"class":3713},[1115,9468,1875],{"class":3717},[1115,9470,9471],{"class":3724},"9.8",[1115,9473,1797],{"class":3709},[1115,9475,9234],{"class":3705},[1115,9477,3797],{"class":3709},[1115,9479,9480],{"class":3724}," 10",[1115,9482,1797],{"class":3709},[1115,9484,9244],{"class":3705},[1115,9486,3797],{"class":3709},[1115,9488,4578],{"class":3713},[1115,9490,1875],{"class":3717},[1115,9492,9493],{"class":3724},"0.12",[1115,9495,9496],{"class":3717},"))\n",[3694,9498,9501],{"className":9499,"code":9500,"language":3923,"meta":1490},[3921],"[1] 0.2818514\n",[3470,9502,9500],{"__ignoreMap":1490},[1110,9504,9505],{},"Obsah menší než 9,8 cm³ má přibližně 28,19 % ampulek.",[1189,9507,9509],{"id":9508},"další-rozdělení-dostupná-v-r","Další rozdělení dostupná v R",[1110,9511,9512,9513,9516,9517,9520,9521,9524,9525,4604,9528,9531,9532,9535],{},"Vedle normálního rozdělení R přímo nabízí hustotu, distribuční funkci a kvantilovou funkci i pro další běžná rozdělení. Pojmenování funkcí je jednotné: ",[3470,9514,9515],{},"d*"," je hustota\u002Fpravděpodobnostní funkce, ",[3470,9518,9519],{},"p*"," distribuční funkce (s ",[3470,9522,9523],{},"lower.tail = FALSE",", případně čtvrtým argumentem ",[3470,9526,9527],{},"TRUE",[3470,9529,9530],{},"FALSE",", pro horní chvost) a ",[3470,9533,9534],{},"q*"," kvantilová funkce.",[1194,9537,9538,9644],{},[1197,9539,9540],{},[1200,9541,9542,9545,9591,9617],{},[1203,9543,9544],{},"Rozdělení",[1203,9546,9547,9571,9572],{},[1115,9548,9550],{"className":9549},[1138],[1140,9551,9552],{"xmlns":1142},[1144,9553,9554,9568],{},[1147,9555,9556,9558,9560,9562,9564,9566],{},[1153,9557,6729],{},[1242,9559,1875],{"stretchy":1874},[1153,9561,6734],{},[1242,9563,1982],{},[1153,9565,1183],{},[1242,9567,1886],{"stretchy":1874},[1159,9569,9570],{"encoding":1161},"P(X=k)"," \u002F ",[1115,9573,9575],{"className":9574},[1138],[1140,9576,9577],{"xmlns":1142},[1144,9578,9579,9589],{},[1147,9580,9581,9583,9585,9587],{},[1153,9582,6773],{},[1242,9584,1875],{"stretchy":1874},[1153,9586,1240],{},[1242,9588,1886],{"stretchy":1874},[1159,9590,6803],{"encoding":1161},[1203,9592,9593],{},[1115,9594,9596],{"className":9595},[1138],[1140,9597,9598],{"xmlns":1142},[1144,9599,9600,9614],{},[1147,9601,9602,9604,9606,9608,9610,9612],{},[1153,9603,6729],{},[1242,9605,1875],{"stretchy":1874},[1153,9607,6734],{},[1242,9609,6737],{},[1153,9611,1183],{},[1242,9613,1886],{"stretchy":1874},[1159,9615,9616],{"encoding":1161},"P(X \\le k)",[1203,9618,9619,9620],{},"horní chvost ",[1115,9621,9623],{"className":9622},[1138],[1140,9624,9625],{"xmlns":1142},[1144,9626,9627,9641],{},[1147,9628,9629,9631,9633,9635,9637,9639],{},[1153,9630,6729],{},[1242,9632,1875],{"stretchy":1874},[1153,9634,6734],{},[1242,9636,1689],{},[1153,9638,1183],{},[1242,9640,1886],{"stretchy":1874},[1159,9642,9643],{"encoding":1161},"P(X>k)",[1210,9645,9646,9692,9736,9777,9826],{},[1200,9647,9648,9677,9682,9687],{},[1215,9649,9650,9651],{},"Binomické ",[1115,9652,9654],{"className":9653},[1138],[1140,9655,9656],{"xmlns":1142},[1144,9657,9658,9674],{},[1147,9659,9660,9662,9664,9666,9668,9670,9672],{},[1153,9661,1824],{},[1153,9663,1878],{},[1242,9665,1875],{"stretchy":1874},[1153,9667,1372],{},[1242,9669,1797],{"separator":1121},[1153,9671,1110],{},[1242,9673,1886],{"stretchy":1874},[1159,9675,9676],{"encoding":1161},"Bi(n,p)",[1215,9678,9679],{},[3470,9680,9681],{},"dbinom(k, n, p)",[1215,9683,9684],{},[3470,9685,9686],{},"pbinom(k, n, p)",[1215,9688,9689],{},[3470,9690,9691],{},"pbinom(k, n, p, FALSE)",[1200,9693,9694,9721,9726,9731],{},[1215,9695,9696,9697],{},"Poissonovo ",[1115,9698,9700],{"className":9699},[1138],[1140,9701,9702],{"xmlns":1142},[1144,9703,9704,9718],{},[1147,9705,9706,9708,9711,9713,9716],{},[1153,9707,6729],{},[1153,9709,9710],{},"o",[1242,9712,1875],{"stretchy":1874},[1153,9714,9715],{},"λ",[1242,9717,1886],{"stretchy":1874},[1159,9719,9720],{"encoding":1161},"Po(\\lambda)",[1215,9722,9723],{},[3470,9724,9725],{},"dpois(k, lambda)",[1215,9727,9728],{},[3470,9729,9730],{},"ppois(k, lambda)",[1215,9732,9733],{},[3470,9734,9735],{},"ppois(k, lambda, FALSE)",[1200,9737,9738,9762,9767,9772],{},[1215,9739,9740,9741],{},"Geometrické ",[1115,9742,9744],{"className":9743},[1138],[1140,9745,9746],{"xmlns":1142},[1144,9747,9748,9759],{},[1147,9749,9750,9753,9755,9757],{},[1153,9751,9752],{},"G",[1242,9754,1875],{"stretchy":1874},[1153,9756,1110],{},[1242,9758,1886],{"stretchy":1874},[1159,9760,9761],{"encoding":1161},"G(p)",[1215,9763,9764],{},[3470,9765,9766],{},"dgeom(k, p)",[1215,9768,9769],{},[3470,9770,9771],{},"pgeom(k, p)",[1215,9773,9774],{},[3470,9775,9776],{},"pgeom(k, p, FALSE)",[1200,9778,9779,9811,9816,9821],{},[1215,9780,9781,9782],{},"Hypergeometrické ",[1115,9783,9785],{"className":9784},[1138],[1140,9786,9787],{"xmlns":1142},[1144,9788,9789,9808],{},[1147,9790,9791,9793,9795,9797,9799,9802,9804,9806],{},[1153,9792,1563],{},[1242,9794,1875],{"stretchy":1874},[1153,9796,6888],{},[1242,9798,1797],{"separator":1121},[1153,9800,9801],{},"M",[1242,9803,1797],{"separator":1121},[1153,9805,1372],{},[1242,9807,1886],{"stretchy":1874},[1159,9809,9810],{"encoding":1161},"H(N,M,n)",[1215,9812,9813],{},[3470,9814,9815],{},"dhyper(k, M, N-M, n)",[1215,9817,9818],{},[3470,9819,9820],{},"phyper(k, M, N-M, n)",[1215,9822,9823],{},[3470,9824,9825],{},"phyper(k, M, N-M, n, FALSE)",[1200,9827,9828,9852,9857,9862],{},[1215,9829,9830,9831],{},"Exponenciální ",[1115,9832,9834],{"className":9833},[1138],[1140,9835,9836],{"xmlns":1142},[1144,9837,9838,9849],{},[1147,9839,9840,9842,9844,9847],{},[1153,9841,8088],{},[1242,9843,1875],{"stretchy":1874},[1153,9845,9846],{},"δ",[1242,9848,1886],{"stretchy":1874},[1159,9850,9851],{"encoding":1161},"E(\\delta)",[1215,9853,9854],{},[3470,9855,9856],{},"dexp(k, 1\u002Fdelta)",[1215,9858,9859],{},[3470,9860,9861],{},"pexp(k, 1\u002Fdelta)",[1215,9863,9864],{},[3470,9865,9866],{},"pexp(k, 1\u002Fdelta, FALSE)",[1103,9868,9870,9877],{"className":9869,"dataCallout":6412},[1106,6411],[1110,9871,9873,9876],{"className":9872},[1113],[1115,9874],{"className":9875,"ariaHidden":1121},[1118,6419,1120],"Exponenciální rozdělení: R bere intenzitu, ne střední hodnotu",[1110,9878,9879,9880,9883,9884,9898,9899,9051,9902,1669],{},"R parametrizuje exponenciální rozdělení intenzitou (",[3470,9881,9882],{},"rate","). Je-li ",[1115,9885,9887],{"className":9886},[1138],[1140,9888,9889],{"xmlns":1142},[1144,9890,9891,9895],{},[1147,9892,9893],{},[1153,9894,9846],{},[1159,9896,9897],{"encoding":1161},"\\delta"," střední doba do události, do R se dosazuje ",[3470,9900,9901],{},"1\u002Fdelta",[3470,9903,9904],{},"delta",[1110,9906,9907,9908,9940,9941,9959],{},"V R (pravděpodobnostní a distribuční funkce diskrétní náhodné veličiny ",[1115,9909,9911],{"className":9910},[1138],[1140,9912,9913],{"xmlns":1142},[1144,9914,9915,9937],{},[1147,9916,9917,9919,9921,9923,9925,9927,9930,9932,9935],{},[1153,9918,6734],{},[1242,9920,9186],{},[1153,9922,1824],{},[1153,9924,1878],{},[1242,9926,1875],{"stretchy":1874},[1565,9928,9929],{},"5",[1242,9931,6896],{"separator":1121},[1565,9933,9934],{},"0,95",[1242,9936,1886],{"stretchy":1874},[1159,9938,9939],{"encoding":1161},"X \\sim Bi(5; 0{,}95)",", a pravděpodobnost, že u exponenciálního rozdělení se střední hodnotou ",[1115,9942,9944],{"className":9943},[1138],[1140,9945,9946],{"xmlns":1142},[1144,9947,9948,9956],{},[1147,9949,9950,9952,9954],{},[1153,9951,9846],{},[1242,9953,1982],{},[1565,9955,9929],{},[1159,9957,9958],{"encoding":1161},"\\delta = 5"," nastane událost do 3 jednotek času):",[3694,9961,9963],{"className":3696,"code":9962,"language":71,"meta":1490,"style":1490},"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",[3470,9964,9965,9979,10011,10040,10045,10054],{"__ignoreMap":1490},[1115,9966,9967,9969,9971,9974,9976],{"class":3702,"line":10},[1115,9968,1240],{"class":3705},[1115,9970,3710],{"class":3709},[1115,9972,9973],{"class":3724}," 0",[1115,9975,1958],{"class":3709},[1115,9977,9978],{"class":3724},"5\n",[1115,9980,9981,9984,9986,9989,9991,9993,9995,9998,10000,10003,10005,10007,10009],{"class":3702,"line":27},[1115,9982,9983],{"class":3713},"round",[1115,9985,1875],{"class":3717},[1115,9987,9988],{"class":3713},"dbinom",[1115,9990,1875],{"class":3717},[1115,9992,1240],{"class":3705},[1115,9994,1797],{"class":3709},[1115,9996,9997],{"class":3724}," 5",[1115,9999,1797],{"class":3709},[1115,10001,10002],{"class":3724}," 0.95",[1115,10004,1886],{"class":3717},[1115,10006,1797],{"class":3709},[1115,10008,3800],{"class":3724},[1115,10010,3901],{"class":3717},[1115,10012,10013,10015,10017,10020,10022,10024,10026,10028,10030,10032,10034,10036,10038],{"class":3702,"line":148},[1115,10014,9983],{"class":3713},[1115,10016,1875],{"class":3717},[1115,10018,10019],{"class":3713},"pbinom",[1115,10021,1875],{"class":3717},[1115,10023,1240],{"class":3705},[1115,10025,1797],{"class":3709},[1115,10027,9997],{"class":3724},[1115,10029,1797],{"class":3709},[1115,10031,10002],{"class":3724},[1115,10033,1886],{"class":3717},[1115,10035,1797],{"class":3709},[1115,10037,3800],{"class":3724},[1115,10039,3901],{"class":3717},[1115,10041,10042],{"class":3702,"line":111},[1115,10043,10044],{"emptyLinePlaceholder":1499},"\n",[1115,10046,10047,10049,10051],{"class":3702,"line":96},[1115,10048,9904],{"class":3705},[1115,10050,3710],{"class":3709},[1115,10052,10053],{"class":3724}," 5\n",[1115,10055,10056,10058,10060,10063,10065,10067,10069,10072,10074,10076,10079,10082,10084,10086,10088],{"class":3702,"line":89},[1115,10057,9983],{"class":3713},[1115,10059,1875],{"class":3717},[1115,10061,10062],{"class":3713},"pexp",[1115,10064,1875],{"class":3717},[1115,10066,3592],{"class":3724},[1115,10068,1797],{"class":3709},[1115,10070,10071],{"class":3705}," rate",[1115,10073,3797],{"class":3709},[1115,10075,4641],{"class":3724},[1115,10077,10078],{"class":3709}," \u002F",[1115,10080,10081],{"class":3705}," delta",[1115,10083,1886],{"class":3717},[1115,10085,1797],{"class":3709},[1115,10087,3800],{"class":3724},[1115,10089,3901],{"class":3717},[3694,10091,10094],{"className":10092,"code":10093,"language":3923,"meta":1490},[3921],"[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",[3470,10095,10093],{"__ignoreMap":1490},[1189,10097,10099],{"id":10098},"studentovo-pearsonovo-a-fisherovo-snedecorovo-rozdělení","Studentovo, Pearsonovo a Fisherovo-Snedecorovo rozdělení",[1110,10101,10102,10103,10106],{},"Tato tři rozdělení mají statistiky, které se dále používají při konstrukci intervalů spolehlivosti a testování hypotéz (viz ",[1127,10104,141],{"className":10105,"dataFsResolvedFilePath":1721,"href":1722},[1130],") — na rozdíl od normálního rozdělení se v příkladech této kapitoly samostatně nepočítají, jsou to nástroje pro další kapitoly.",[1110,10108,10109,3952,10112,10125],{},[1540,10110,10111],{},"Studentovo rozdělení",[1115,10113,10115],{"className":10114},[1138],[1140,10116,10117],{"xmlns":1142},[1144,10118,10119,10123],{},[1147,10120,10121],{},[1153,10122,1183],{},[1159,10124,1183],{"encoding":1161}," stupni volnosti má hustotu pravděpodobnosti",[1115,10127,10129],{"className":10128},[1138],[1140,10130,10131],{"xmlns":1142,"display":1964},[1144,10132,10133,10228],{},[1147,10134,10135,10137,10139,10141,10143,10145,10177,10215,10217,10219,10221,10223,10226],{},[1153,10136,6773],{},[1242,10138,1875],{"stretchy":1874},[1153,10140,1240],{},[1242,10142,1886],{"stretchy":1874},[1242,10144,1982],{},[2739,10146,10147,10149],{},[1565,10148,1794],{},[1147,10150,10151,10153,10173],{},[1153,10152,1824],{},[1147,10154,10155,10157,10163,10165,10171],{},[1242,10156,1875],{"fence":1121},[2739,10158,10159,10161],{},[1565,10160,1794],{},[1565,10162,1589],{},[1242,10164,1797],{"separator":1121},[2739,10166,10167,10169],{},[1153,10168,1183],{},[1565,10170,1589],{},[1242,10172,1886],{"fence":1121},[4453,10174,10175],{},[1153,10176,1183],{},[1582,10178,10179,10199],{},[1147,10180,10181,10183,10185,10187,10197],{},[1242,10182,1875],{"fence":1121},[1565,10184,1794],{},[1242,10186,5477],{},[2739,10188,10189,10195],{},[1582,10190,10191,10193],{},[1153,10192,1240],{},[1565,10194,1589],{},[1153,10196,1183],{},[1242,10198,1886],{"fence":1121},[1147,10200,10201,10203],{},[1242,10202,3064],{},[2739,10204,10205,10213],{},[1147,10206,10207,10209,10211],{},[1153,10208,1183],{},[1242,10210,5477],{},[1565,10212,1794],{},[1565,10214,1589],{},[1242,10216,1797],{"separator":1121},[2012,10218],{"width":2014},[1153,10220,1240],{},[1242,10222,7021],{},[1153,10224,1260],{"mathvariant":10225},"double-struck",[1242,10227,1797],{"separator":1121},[1159,10229,10230],{"encoding":1161},"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},",[1110,10232,4507,10233,10246,10247,10260,10261,10274],{},[1115,10234,10236],{"className":10235},[1138],[1140,10237,10238],{"xmlns":1142},[1144,10239,10240,10244],{},[1147,10241,10242],{},[1153,10243,1824],{},[1159,10245,1824],{"encoding":1161}," je funkce beta. Je symetrické kolem nuly; číslo ",[1115,10248,10250],{"className":10249},[1138],[1140,10251,10252],{"xmlns":1142},[1144,10253,10254,10258],{},[1147,10255,10256],{},[1153,10257,1183],{},[1159,10259,1183],{"encoding":1161}," určuje tvar křivky — s rostoucím ",[1115,10262,10264],{"className":10263},[1138],[1140,10265,10266],{"xmlns":1142},[1144,10267,10268,10272],{},[1147,10269,10270],{},[1153,10271,1183],{},[1159,10273,1183],{"encoding":1161}," se rozdělení blíží normálnímu.",[1110,10276,10277,3952,10280,10293],{},[1540,10278,10279],{},"Pearsonovo (chí-kvadrát) rozdělení",[1115,10281,10283],{"className":10282},[1138],[1140,10284,10285],{"xmlns":1142},[1144,10286,10287,10291],{},[1147,10288,10289],{},[1153,10290,1183],{},[1159,10292,1183],{"encoding":1161}," stupni volnosti:",[1115,10295,10297],{"className":10296},[1138],[1140,10298,10299],{"xmlns":1142,"display":1964},[1144,10300,10301,10386],{},[1147,10302,10303,10305,10307,10309,10311,10313,10344,10360,10374,10376,10378,10380,10382,10384],{},[1153,10304,6773],{},[1242,10306,1875],{"stretchy":1874},[1153,10308,1240],{},[1242,10310,1886],{"stretchy":1874},[1242,10312,1982],{},[2739,10314,10315,10317],{},[1565,10316,1794],{},[1147,10318,10319,10331,10334,10336,10338,10340,10342],{},[1582,10320,10321,10323],{},[1565,10322,1589],{},[1147,10324,10325,10327,10329],{},[1153,10326,1183],{},[1153,10328,4604],{"mathvariant":2121},[1565,10330,1589],{},[1153,10332,10333],{"mathvariant":2121},"Γ",[1242,10335,1875],{"stretchy":1874},[1153,10337,1183],{},[1153,10339,4604],{"mathvariant":2121},[1565,10341,1589],{},[1242,10343,1886],{"stretchy":1874},[1582,10345,10346,10348],{},[1153,10347,1240],{},[1147,10349,10350,10352,10354,10356,10358],{},[1153,10351,1183],{},[1153,10353,4604],{"mathvariant":2121},[1565,10355,1589],{},[1242,10357,3064],{},[1565,10359,1794],{},[1582,10361,10362,10364],{},[1153,10363,8595],{},[1147,10365,10366,10368,10370,10372],{},[1242,10367,3064],{},[1153,10369,1240],{},[1153,10371,4604],{"mathvariant":2121},[1565,10373,1589],{},[1242,10375,1797],{"separator":1121},[2012,10377],{"width":2014},[1153,10379,1240],{},[1242,10381,1689],{},[1565,10383,1567],{},[1242,10385,1797],{"separator":1121},[1159,10387,10388],{"encoding":1161},"f(x) = \\frac{1}{2^{k\u002F2}\\Gamma(k\u002F2)} x^{k\u002F2-1} e^{-x\u002F2}, \\qquad x > 0,",[1110,10390,4507,10391,10405],{},[1115,10392,10394],{"className":10393},[1138],[1140,10395,10396],{"xmlns":1142},[1144,10397,10398,10402],{},[1147,10399,10400],{},[1153,10401,10333],{"mathvariant":2121},[1159,10403,10404],{"encoding":1161},"\\Gamma"," je funkce gama.",[1110,10407,10408,10411,10412,1163,10430,1958],{},[1540,10409,10410],{},"Fisherovo-Snedecorovo rozdělení"," se stupni volnosti ",[1115,10413,10415],{"className":10414},[1138],[1140,10416,10417],{"xmlns":1142},[1144,10418,10419,10427],{},[1147,10420,10421],{},[1150,10422,10423,10425],{},[1153,10424,1183],{},[1565,10426,1794],{},[1159,10428,10429],{"encoding":1161},"k_1",[1115,10431,10433],{"className":10432},[1138],[1140,10434,10435],{"xmlns":1142},[1144,10436,10437,10445],{},[1147,10438,10439],{},[1150,10440,10441,10443],{},[1153,10442,1183],{},[1565,10444,1589],{},[1159,10446,10447],{"encoding":1161},"k_2",[1115,10449,10451],{"className":10450},[1138],[1140,10452,10453],{"xmlns":1142,"display":1964},[1144,10454,10455,10620],{},[1147,10456,10457,10459,10461,10463,10465,10467,10503,10537,10557,10609,10611,10613,10615,10617],{},[1153,10458,6773],{},[1242,10460,1875],{"stretchy":1874},[1153,10462,1240],{},[1242,10464,1886],{"stretchy":1874},[1242,10466,1982],{},[2739,10468,10469,10471],{},[1565,10470,1794],{},[1147,10472,10473,10475],{},[1153,10474,1824],{},[1147,10476,10477,10479,10489,10491,10501],{},[1242,10478,1875],{"fence":1121},[2739,10480,10481,10487],{},[1150,10482,10483,10485],{},[1153,10484,1183],{},[1565,10486,1794],{},[1565,10488,1589],{},[1242,10490,1797],{"separator":1121},[2739,10492,10493,10499],{},[1150,10494,10495,10497],{},[1153,10496,1183],{},[1565,10498,1589],{},[1565,10500,1589],{},[1242,10502,1886],{"fence":1121},[1582,10504,10505,10525],{},[1147,10506,10507,10509,10523],{},[1242,10508,1875],{"fence":1121},[2739,10510,10511,10517],{},[1150,10512,10513,10515],{},[1153,10514,1183],{},[1565,10516,1794],{},[1150,10518,10519,10521],{},[1153,10520,1183],{},[1565,10522,1589],{},[1242,10524,1886],{"fence":1121},[1147,10526,10527,10533,10535],{},[1150,10528,10529,10531],{},[1153,10530,1183],{},[1565,10532,1794],{},[1153,10534,4604],{"mathvariant":2121},[1565,10536,1589],{},[1582,10538,10539,10541],{},[1153,10540,1240],{},[1147,10542,10543,10549,10551,10553,10555],{},[1150,10544,10545,10547],{},[1153,10546,1183],{},[1565,10548,1794],{},[1153,10550,4604],{"mathvariant":2121},[1565,10552,1589],{},[1242,10554,3064],{},[1565,10556,1794],{},[1582,10558,10559,10585],{},[1147,10560,10561,10563,10565,10567,10581,10583],{},[1242,10562,1875],{"fence":1121},[1565,10564,1794],{},[1242,10566,5477],{},[2739,10568,10569,10575],{},[1150,10570,10571,10573],{},[1153,10572,1183],{},[1565,10574,1794],{},[1150,10576,10577,10579],{},[1153,10578,1183],{},[1565,10580,1589],{},[1153,10582,1240],{},[1242,10584,1886],{"fence":1121},[1147,10586,10587,10589],{},[1242,10588,3064],{},[2739,10590,10591,10607],{},[1147,10592,10593,10599,10601],{},[1150,10594,10595,10597],{},[1153,10596,1183],{},[1565,10598,1794],{},[1242,10600,5477],{},[1150,10602,10603,10605],{},[1153,10604,1183],{},[1565,10606,1589],{},[1565,10608,1589],{},[1242,10610,1797],{"separator":1121},[2012,10612],{"width":2014},[1153,10614,1240],{},[1242,10616,1689],{},[1565,10618,10619],{},"0.",[1159,10621,10622],{"encoding":1161},"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.",[1110,10624,10625],{},[4383,10626],{"alt":10627,"className":10628,"src":10629},"mask-nv-specialni-rozdeleni",[1130,4387],"\u002Fwiki-assets\u002Fmask-nv-specialni-rozdeleni.png",[8949,10631],{"spec":10632},"{\"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\":[]}",[1110,10634,10635],{},"R funkce pro tato tři rozdělení:",[1194,10637,10638,10652],{},[1197,10639,10640],{},[1200,10641,10642,10644,10647,10649],{},[1203,10643,9544],{},[1203,10645,10646],{},"hustota",[1203,10648,6706],{},[1203,10650,10651],{},"kvantil",[1210,10653,10654,10694,10738],{},[1200,10655,10656,10679,10684,10689],{},[1215,10657,10658,10659],{},"Studentovo ",[1115,10660,10662],{"className":10661},[1138],[1140,10663,10664],{"xmlns":1142},[1144,10665,10666,10676],{},[1147,10667,10668,10670,10672,10674],{},[1153,10669,7146],{},[1242,10671,1875],{"stretchy":1874},[1153,10673,1183],{},[1242,10675,1886],{"stretchy":1874},[1159,10677,10678],{"encoding":1161},"t(k)",[1215,10680,10681],{},[3470,10682,10683],{},"dt(x, df = k)",[1215,10685,10686],{},[3470,10687,10688],{},"pt(x, df = k)",[1215,10690,10691],{},[3470,10692,10693],{},"qt(p, df = k)",[1200,10695,10696,10723,10728,10733],{},[1215,10697,10698,10699],{},"Pearsonovo ",[1115,10700,10702],{"className":10701},[1138],[1140,10703,10704],{"xmlns":1142},[1144,10705,10706,10720],{},[1147,10707,10708,10714,10716,10718],{},[1582,10709,10710,10712],{},[1153,10711,1586],{},[1565,10713,1589],{},[1242,10715,1875],{"stretchy":1874},[1153,10717,1183],{},[1242,10719,1886],{"stretchy":1874},[1159,10721,10722],{"encoding":1161},"\\chi^2(k)",[1215,10724,10725],{},[3470,10726,10727],{},"dchisq(x, df = k)",[1215,10729,10730],{},[3470,10731,10732],{},"pchisq(x, df = k)",[1215,10734,10735],{},[3470,10736,10737],{},"qchisq(p, df = k)",[1200,10739,10740,10775,10780,10785],{},[1215,10741,10742,10743],{},"Fisherovo-Snedecorovo ",[1115,10744,10746],{"className":10745},[1138],[1140,10747,10748],{"xmlns":1142},[1144,10749,10750,10772],{},[1147,10751,10752,10754,10756,10762,10764,10770],{},[1153,10753,6718],{},[1242,10755,1875],{"stretchy":1874},[1150,10757,10758,10760],{},[1153,10759,1183],{},[1565,10761,1794],{},[1242,10763,1797],{"separator":1121},[1150,10765,10766,10768],{},[1153,10767,1183],{},[1565,10769,1589],{},[1242,10771,1886],{"stretchy":1874},[1159,10773,10774],{"encoding":1161},"F(k_1, k_2)",[1215,10776,10777],{},[3470,10778,10779],{},"df(x, df1 = k1, df2 = k2)",[1215,10781,10782],{},[3470,10783,10784],{},"pf(x, df1 = k1, df2 = k2)",[1215,10786,10787],{},[3470,10788,10789],{},"qf(p, df1 = k1, df2 = k2)",[1110,10791,10792],{},"V R (97,5%-ní kvantil Studentova rozdělení s 9 stupni volnosti, 95%-ní kvantily Pearsonova a Fisherova-Snedecorova rozdělení):",[3694,10794,10796],{"className":3696,"code":10795,"language":71,"meta":1490,"style":1490},"qt(0.975, df = 9)\nqchisq(0.95, df = 9)\nqf(0.95, df1 = 3, df2 = 10)\n",[3470,10797,10798,10819,10839],{"__ignoreMap":1490},[1115,10799,10800,10803,10805,10807,10809,10812,10814,10817],{"class":3702,"line":10},[1115,10801,10802],{"class":3713},"qt",[1115,10804,1875],{"class":3717},[1115,10806,9092],{"class":3724},[1115,10808,1797],{"class":3709},[1115,10810,10811],{"class":3705}," df",[1115,10813,3797],{"class":3709},[1115,10815,10816],{"class":3724}," 9",[1115,10818,3901],{"class":3717},[1115,10820,10821,10824,10826,10829,10831,10833,10835,10837],{"class":3702,"line":27},[1115,10822,10823],{"class":3713},"qchisq",[1115,10825,1875],{"class":3717},[1115,10827,10828],{"class":3724},"0.95",[1115,10830,1797],{"class":3709},[1115,10832,10811],{"class":3705},[1115,10834,3797],{"class":3709},[1115,10836,10816],{"class":3724},[1115,10838,3901],{"class":3717},[1115,10840,10841,10844,10846,10848,10850,10853,10855,10858,10860,10863,10865,10867],{"class":3702,"line":148},[1115,10842,10843],{"class":3713},"qf",[1115,10845,1875],{"class":3717},[1115,10847,10828],{"class":3724},[1115,10849,1797],{"class":3709},[1115,10851,10852],{"class":3705}," df1",[1115,10854,3797],{"class":3709},[1115,10856,10857],{"class":3724}," 3",[1115,10859,1797],{"class":3709},[1115,10861,10862],{"class":3705}," df2",[1115,10864,3797],{"class":3709},[1115,10866,9480],{"class":3724},[1115,10868,3901],{"class":3717},[3694,10870,10873],{"className":10871,"code":10872,"language":3923,"meta":1490},[3921],"[1] 2.262157\n[1] 16.91898\n[1] 3.708265\n",[3470,10874,10872],{"__ignoreMap":1490},[1189,10876,6407],{"id":6406},[1436,10878,10879,10965,11015],{},[1439,10880,10881,10884,10885,10912,10913,4604,10915,4604,10917,10919,10920,10940,10941,10964],{},[1540,10882,10883],{},"Rozptyl vs. směrodatná odchylka v R."," Zápis ",[1115,10886,10888],{"className":10887},[1138],[1140,10889,10890],{"xmlns":1142},[1144,10891,10892,10910],{},[1147,10893,10894,10896,10898,10900,10902,10908],{},[1153,10895,6888],{},[1242,10897,1875],{"stretchy":1874},[1153,10899,6893],{},[1242,10901,6896],{"separator":1121},[1582,10903,10904,10906],{},[1153,10905,6901],{},[1565,10907,1589],{},[1242,10909,1886],{"stretchy":1874},[1159,10911,6908],{"encoding":1161}," používá rozptyl, ale ",[3470,10914,6912],{},[3470,10916,6915],{},[3470,10918,6918],{}," očekávají směrodatnou odchylku. Dosazení rozptylu místo ",[1115,10921,10923],{"className":10922},[1138],[1140,10924,10925],{"xmlns":1142},[1144,10926,10927,10937],{},[1147,10928,10929],{},[4453,10930,10931],{},[1582,10932,10933,10935],{},[1153,10934,6901],{},[1565,10936,1589],{},[1159,10938,10939],{"encoding":1161},"\\sqrt{\\sigma^2}"," dává jiný — a pro ",[1115,10942,10944],{"className":10943},[1138],[1140,10945,10946],{"xmlns":1142},[1144,10947,10948,10961],{},[1147,10949,10950,10956,10959],{},[1582,10951,10952,10954],{},[1153,10953,6901],{},[1565,10955,1589],{},[1242,10957,10958],{"mathvariant":2121},"≠",[1565,10960,1794],{},[1159,10962,10963],{"encoding":1161},"\\sigma^2 \\ne 1"," výrazně odlišný — výsledek (viz příklad s ampulkou).",[1439,10966,10967,10994,10995,11014],{},[1540,10968,10969,10993],{},[1115,10970,10972],{"className":10971},[1138],[1140,10973,10974],{"xmlns":1142},[1144,10975,10976,10990],{},[1147,10977,10978,10980,10982,10984,10986,10988],{},[1153,10979,6729],{},[1242,10981,1875],{"stretchy":1874},[1153,10983,6734],{},[1242,10985,1982],{},[1153,10987,1240],{},[1242,10989,1886],{"stretchy":1874},[1159,10991,10992],{"encoding":1161},"P(X=x)"," u spojité veličiny je vždy 0."," Hustota ",[1115,10996,10998],{"className":10997},[1138],[1140,10999,11000],{"xmlns":1142},[1144,11001,11002,11012],{},[1147,11003,11004,11006,11008,11010],{},[1153,11005,6773],{},[1242,11007,1875],{"stretchy":1874},[1153,11009,1240],{},[1242,11011,1886],{"stretchy":1874},[1159,11013,6803],{"encoding":1161}," sama o sobě pravděpodobnost neudává — pravděpodobnost dává až plocha pod křivkou na intervalu.",[1439,11016,11017,1654,11020,11037,11038,11055,11056,11059,11060,1669],{},[1540,11018,11019],{},"Záměna stupňů volnosti u Fisherova-Snedecorova rozdělení.",[1115,11021,11023],{"className":11022},[1138],[1140,11024,11025],{"xmlns":1142},[1144,11026,11027,11035],{},[1147,11028,11029],{},[1150,11030,11031,11033],{},[1153,11032,1183],{},[1565,11034,1794],{},[1159,11036,10429],{"encoding":1161}," (čitatel) a ",[1115,11039,11041],{"className":11040},[1138],[1140,11042,11043],{"xmlns":1142},[1144,11044,11045,11053],{},[1147,11046,11047],{},[1150,11048,11049,11051],{},[1153,11050,1183],{},[1565,11052,1589],{},[1159,11054,10447],{"encoding":1161}," (jmenovatel) nejsou zaměnitelné — ",[3470,11057,11058],{},"qf(p, df1, df2)"," dá jiný výsledek než ",[3470,11061,11062],{},"qf(p, df2, df1)",[1189,11064,1434],{"id":1433},[1436,11066,11067,11072,11077,11082,11088,11095,11101],{},[1439,11068,11069],{},[1127,11070,1133],{"className":11071,"dataFsResolvedFilePath":1131,"href":1132},[1130],[1439,11073,11074],{},[1127,11075,886],{"className":11076,"dataFsResolvedFilePath":6612,"href":6613},[1130],[1439,11078,11079],{},[1127,11080,141],{"className":11081,"dataFsResolvedFilePath":1721,"href":1722},[1130],[1439,11083,11084],{},[1127,11085,11087],{"className":11086,"dataFsResolvedFilePath":6628,"href":6629},[1130],"regresni-a-korelacni-analyza",[1439,11089,11090],{},[1127,11091,716],{"className":11092,"dataFsResolvedFilePath":11093,"href":11094},[1130],"topics\u002Fkontingencni-tabulky.md","\u002Fwiki\u002Fkontingencni-tabulky",[1439,11096,11097],{},[1127,11098,11100],{"className":11099,"dataFsResolvedFilePath":1220,"href":1221},[1130],"regulacni-diagramy-a-indexy-zpusobilosti",[1439,11102,11103],{},[1127,11104,6641],{"className":11105,"dataFsResolvedFilePath":1454,"href":1455},[1130],[1189,11107,1459],{"id":934},[1110,11109,1462,11110,1467],{},[1464,11111,1466],{},[6649,11113,11114],{},"html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: 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.sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}",{"title":1490,"searchDepth":27,"depth":27,"links":11116},[11117,11118,11119,11120,11121,11122,11123,11124,11125,11126],{"id":6967,"depth":27,"text":6968},{"id":7274,"depth":27,"text":7275},{"id":7960,"depth":27,"text":7961},{"id":8069,"depth":27,"text":8070},{"id":8506,"depth":27,"text":6876},{"id":9508,"depth":27,"text":9509},{"id":10098,"depth":27,"text":10099},{"id":6406,"depth":27,"text":6407},{"id":1433,"depth":27,"text":1434},{"id":934,"depth":27,"text":1459},{},"\u002Ftopics\u002Fnahodne-veliciny-a-rozdeleni",{"title":6622,"description":1490},[11131,11132,11133],"raw\u002Fmask\u002F01 náhodné veličiny.pdf","raw\u002Fmask\u002F01 náhodné veličiny - návod R.pdf","raw\u002Fmask\u002Fpříklady 01 a 02.docx","topics\u002Fnahodne-veliciny-a-rozdeleni",[23,67,812,332,532,71],"y7MCWBwmskoGgsMoqVPhRRaL6YYTo3Cf-R4Yf-89eMs",{"id":11138,"title":6614,"body":11139,"course":23,"courses":1495,"created":1496,"description":1490,"extension":1497,"meta":15888,"navigation":1499,"path":15889,"seo":15890,"sources":15891,"stem":15898,"tags":15899,"type":6670,"updated":1496,"__hash__":15900},"topics\u002Ftopics\u002Fpopisna-statistika.md",{"type":1096,"value":11140,"toc":15879},[11141,11144,11238,11242,11252,11378,11385,11396,11400,11443,11448,11548,11558,11563,11702,11778,11782,11883,11964,11971,12042,12061,12063,12279,12285,12295,12302,12305,12359,12365,12375,12388,12534,12537,12550,12869,12875,12878,12882,12961,12995,13024,13026,13104,13110,13171,13178,13191,13268,13384,13434,13447,13602,13608,13635,13639,13664,13667,13880,13948,14049,14056,14069,14572,14578,14610,14870,15023,15134,15163,15169,15176,15182,15195,15625,15631,15634,15636,15831,15833,15870,15872,15876],[1099,11142,6614],{"id":11143},"popisná-statistika-a-datové-soubory",[1103,11145,11147,11153],{"className":11146,"dataCallout":1525},[1106,1524],[1110,11148,11150,1533],{"className":11149},[1113],[1115,11151],{"className":11152,"ariaHidden":1121},[1118,1532,1120],[1436,11154,11155,11158,11161,11188,11235],{},[1439,11156,11157],{},"Rozlišit základní a výběrový soubor, typ statistického znaku (kvantitativní\u002Fkvalitativní, diskrétní\u002Fspojitý) a požadavek reprezentativity a nezávislého výběru.",[1439,11159,11160],{},"Spočítat výběrový průměr, rozptyl, směrodatnou odchylku a variační rozpětí; interpretovat je jako bodové odhady charakteristik náhodné veličiny.",[1439,11162,11163,11164,1669],{},"Určit medián a kvartily a číst empirickou distribuční funkci ",[1115,11165,11167],{"className":11166},[1138],[1140,11168,11169],{"xmlns":1142},[1144,11170,11171,11185],{},[1147,11172,11173,11179,11181,11183],{},[1150,11174,11175,11177],{},[1153,11176,6718],{},[1153,11178,1372],{},[1242,11180,1875],{"stretchy":1874},[1153,11182,1240],{},[1242,11184,1886],{"stretchy":1874},[1159,11186,11187],{"encoding":1161},"F_n(x)",[1439,11189,11190,11191,11234],{},"Roztřídit velký datový soubor do tříd (intervalové rozdělení četností), sestavit tabulku ",[1115,11192,11194],{"className":11193},[1138],[1140,11195,11196],{"xmlns":1142},[1144,11197,11198,11231],{},[1147,11199,11200,11207,11209,11215,11217,11223,11225],{},[1150,11201,11202,11205],{},[1153,11203,11204],{},"I",[1153,11206,1883],{},[1242,11208,1797],{"separator":1121},[1150,11210,11211,11213],{},[1153,11212,8928],{},[1153,11214,1883],{},[1242,11216,1797],{"separator":1121},[1150,11218,11219,11221],{},[1153,11220,6773],{},[1153,11222,1883],{},[1242,11224,1797],{"separator":1121},[1150,11226,11227,11229],{},[1153,11228,1110],{},[1153,11230,1883],{},[1159,11232,11233],{"encoding":1161},"I_j, Z_j, f_j, p_j"," a nakreslit histogram.",[1439,11236,11237],{},"Z histogramu odhadnout zákon rozdělení dat; formální test shody patří do testování hypotéz.",[1189,11239,11241],{"id":11240},"základní-pojmy","Základní pojmy",[1110,11243,11244,11247,11248,11251],{},[1127,11245,1133],{"className":11246,"dataFsResolvedFilePath":1131,"href":1132},[1130]," pracuje s ",[1540,11249,11250],{},"datovými soubory"," — konkrétními hodnotami, které popisují vlastnost zkoumaných prvků.",[1436,11253,11254,11260,11284,11290,11365],{},[1439,11255,11256,11259],{},[1540,11257,11258],{},"Základní soubor"," — množina prvků, na nichž provádíme šetření (např. všichni výdělečně činní obyvatelé ČR).",[1439,11261,11262,11265,11266],{},[1540,11263,11264],{},"Statistický znak"," — funkce, která vyjadřuje určitou vlastnost prvku (např. velikost platu). Znaky dělíme na:\n",[1436,11267,11268,11279],{},[1439,11269,11270,11272,11273,11275,11276,11278],{},[1540,11271,1734],{}," (vyjádřitelné číslem) — dále ",[1540,11274,6695],{}," (spočetně mnoho hodnot) nebo ",[1540,11277,6699],{}," (libovolná hodnota v intervalu);",[1439,11280,11281,11283],{},[1540,11282,1727],{}," (vyjádřitelné slovně).",[1439,11285,11286,11289],{},[1540,11287,11288],{},"Výběrový soubor"," — podmnožina prvků základního souboru, na níž znak skutečně zjišťujeme (např. 5 náhodně vybraných obyvatel).",[1439,11291,11292,11295,11296,1669],{},[1540,11293,11294],{},"Datový soubor"," — n-tice naměřených hodnot zkoumaného znaku, např. ",[1115,11297,11299],{"className":11298},[1138],[1140,11300,11301],{"xmlns":1142},[1144,11302,11303,11362],{},[1147,11304,11305,11307,11309,11311,11314,11316,11319,11322,11324,11327,11329,11331,11334,11336,11339,11341,11343,11345,11347,11349,11351,11353,11355,11357,11360],{},[1242,11306,1875],{"stretchy":1874},[1565,11308,3550],{},[2909,11310,2911],{},[1565,11312,11313],{},"500",[1242,11315,1797],{"separator":1121},[2909,11317,11318],{}," ",[1565,11320,11321],{},"38",[2909,11323,2911],{},[1565,11325,11326],{},"000",[1242,11328,1797],{"separator":1121},[2909,11330,11318],{},[1565,11332,11333],{},"37",[2909,11335,2911],{},[1565,11337,11338],{},"800",[1242,11340,1797],{"separator":1121},[2909,11342,11318],{},[1565,11344,9359],{},[2909,11346,2911],{},[1565,11348,11326],{},[1242,11350,1797],{"separator":1121},[2909,11352,11318],{},[1565,11354,3558],{},[2909,11356,2911],{},[1565,11358,11359],{},"200",[1242,11361,1886],{"stretchy":1874},[1159,11363,11364],{"encoding":1161},"(29\\,500,\\ 38\\,000,\\ 37\\,800,\\ 41\\,000,\\ 31\\,200)",[1439,11366,11367,11368,1346,11371,1163,11374,11377],{},"Podle počtu sledovaných znaků rozlišujeme ",[1540,11369,11370],{},"jednorozměrné",[1540,11372,11373],{},"dvourozměrné",[1540,11375,11376],{},"vícerozměrné"," datové soubory.",[1110,11379,11380],{},[4383,11381],{"alt":11382,"className":11383,"src":11384},"mask-ilu-zakladni-soubor-vyber",[1130,4387],"\u002Fwiki-assets\u002Fmask-ilu-zakladni-soubor-vyber.png",[1110,11386,11387,11388,11391,11392,11395],{},"Aby výběrový soubor dobře vypovídal o základním souboru, měl by být ",[1540,11389,11390],{},"reprezentativní"," (podobný základnímu souboru svým složením). Není-li to možné zajistit přímo, volí se prvky do výběru náhodně — ",[1540,11393,11394],{},"nezávislý výběr",". Bez náhodnosti výběru nelze vlastnosti základního souboru správně vystihnout.",[1189,11397,11399],{"id":11398},"empirické-charakteristiky","Empirické charakteristiky",[1110,11401,11402,11403,11406,11407,11410,11411,11424,11425,11428,11429,11442],{},"Zpracováním datového souboru získáme ",[1540,11404,11405],{},"empirické charakteristiky"," a odhad ",[1540,11408,11409],{},"zákona rozdělení"," zkoumané náhodné veličiny ",[1115,11412,11414],{"className":11413},[1138],[1140,11415,11416],{"xmlns":1142},[1144,11417,11418,11422],{},[1147,11419,11420],{},[1153,11421,6734],{},[1159,11423,6734],{"encoding":1161},". Jde o ",[1540,11426,11427],{},"bodové odhady"," charakteristik ",[1115,11430,11432],{"className":11431},[1138],[1140,11433,11434],{"xmlns":1142},[1144,11435,11436,11440],{},[1147,11437,11438],{},[1153,11439,6734],{},[1159,11441,6734],{"encoding":1161},"; ruční výpočet podle vzorců níže je potřeba jen bez dostupného softwaru.",[1110,11444,11445],{},[1540,11446,11447],{},"Míry polohy",[1115,11449,11451],{"className":11450},[1138],[1140,11452,11453],{"xmlns":1142,"display":1964},[1144,11454,11455,11545],{},[1147,11456,11457,11463,11465,11471,11485,11491,11493],{},[1236,11458,11459,11461],{"accent":1121},[1153,11460,1240],{},[1242,11462,1244],{},[1242,11464,1982],{},[2739,11466,11467,11469],{},[1565,11468,1794],{},[1153,11470,1372],{},[1984,11472,11473,11475,11483],{},[1242,11474,1988],{},[1147,11476,11477,11479,11481],{},[1153,11478,1878],{},[1242,11480,1982],{},[1565,11482,1794],{},[1153,11484,1372],{},[1150,11486,11487,11489],{},[1153,11488,1240],{},[1153,11490,1878],{},[2012,11492],{"width":2014},[1147,11494,11495,11498,11505,11508,11515,11518,11524,11527,11534,11536,11542],{},[2909,11496,11497],{},"(v",[1236,11499,11500,11502],{"accent":1121},[2909,11501,7132],{},[1242,11503,11504],{},"ˊ",[2909,11506,11507],{},"b",[1236,11509,11510,11512],{"accent":1121},[2909,11511,8595],{},[1242,11513,11514],{},"ˇ",[2909,11516,11517],{},"rov",[1236,11519,11520,11522],{"accent":1121},[2909,11521,7132],{},[1242,11523,11504],{},[2909,11525,11526],{}," pr",[1236,11528,11529,11531],{"accent":1121},[2909,11530,1358],{},[1242,11532,11533],{},"˚",[2909,11535,4471],{},[1236,11537,11538,11540],{"accent":1121},[2909,11539,8595],{},[1242,11541,11514],{},[2909,11543,11544],{},"r)",[1159,11546,11547],{"encoding":1161},"\\bar{x} = \\frac{1}{n}\\sum_{i=1}^{n} x_i \\qquad \\text{(výběrový průměr)}",[1110,11549,11550,11551,1163,11554,11557],{},"Dalšími mírami polohy jsou ",[1540,11552,11553],{},"medián",[1540,11555,11556],{},"modus"," (nejčetnější hodnota výběru).",[1110,11559,11560],{},[1540,11561,11562],{},"Míry variability",[1115,11564,11566],{"className":11565},[1138],[1140,11567,11568],{"xmlns":1142,"display":1964},[1144,11569,11570,11699],{},[1147,11571,11572,11578,11580,11592,11634,11636,11638,11640,11642,11650,11652],{},[1582,11573,11574,11576],{},[1153,11575,1291],{},[1565,11577,1589],{},[1242,11579,1982],{},[2739,11581,11582,11584],{},[1565,11583,1794],{},[1147,11585,11586,11588,11590],{},[1153,11587,1372],{},[1242,11589,3064],{},[1565,11591,1794],{},[1147,11593,11594,11596,11610,11618,11620,11622,11632],{},[1242,11595,1875],{"fence":1121},[1984,11597,11598,11600,11608],{},[1242,11599,1988],{},[1147,11601,11602,11604,11606],{},[1153,11603,1878],{},[1242,11605,1982],{},[1565,11607,1794],{},[1153,11609,1372],{},[3353,11611,11612,11614,11616],{},[1153,11613,1240],{},[1153,11615,1878],{},[1565,11617,1589],{},[1242,11619,3064],{},[1153,11621,1372],{},[1582,11623,11624,11630],{},[1236,11625,11626,11628],{"accent":1121},[1153,11627,1240],{},[1242,11629,1244],{},[1565,11631,1589],{},[1242,11633,1886],{"fence":1121},[1242,11635,1797],{"separator":1121},[2012,11637],{"width":2014},[1153,11639,1291],{},[1242,11641,1982],{},[4453,11643,11644],{},[1582,11645,11646,11648],{},[1153,11647,1291],{},[1565,11649,1589],{},[2012,11651],{"width":2014},[1147,11653,11654,11656,11662,11664,11670,11672,11678,11681,11687,11690,11696],{},[2909,11655,11497],{},[1236,11657,11658,11660],{"accent":1121},[2909,11659,7132],{},[1242,11661,11504],{},[2909,11663,11507],{},[1236,11665,11666,11668],{"accent":1121},[2909,11667,8595],{},[1242,11669,11514],{},[2909,11671,11517],{},[1236,11673,11674,11676],{"accent":1121},[2909,11675,7132],{},[1242,11677,11504],{},[2909,11679,11680],{}," rozptyl, sm",[1236,11682,11683,11685],{"accent":1121},[2909,11684,8595],{},[1242,11686,11514],{},[2909,11688,11689],{},"rodatn",[1236,11691,11692,11694],{"accent":1121},[2909,11693,1127],{},[1242,11695,11504],{},[2909,11697,11698],{}," odchylka)",[1159,11700,11701],{"encoding":1161},"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)}",[1115,11703,11705],{"className":11704},[1138],[1140,11706,11707],{"xmlns":1142,"display":1964},[1144,11708,11709,11775],{},[1147,11710,11711,11713,11715,11724,11726,11734,11736],{},[1153,11712,1260],{},[1242,11714,1982],{},[1150,11716,11717,11719,11722],{},[1153,11718,1240],{},[1153,11720,11721],{},"max",[1242,11723,4491],{},[1242,11725,3064],{},[1150,11727,11728,11730,11732],{},[1153,11729,1240],{},[1153,11731,4488],{},[1242,11733,4491],{},[2012,11735],{"width":2014},[1147,11737,11738,11741,11747,11749,11756,11759,11765,11767,11773],{},[2909,11739,11740],{},"(varia",[1236,11742,11743,11745],{"accent":1121},[2909,11744,1343],{},[1242,11746,11514],{},[2909,11748,1372],{},[1236,11750,11751,11754],{"accent":1121},[2909,11752,11753],{},"ı",[1242,11755,11504],{},[2909,11757,11758],{}," rozp",[1236,11760,11761,11763],{"accent":1121},[2909,11762,8595],{},[1242,11764,11514],{},[2909,11766,7146],{},[1236,11768,11769,11771],{"accent":1121},[2909,11770,11753],{},[1242,11772,11504],{},[2909,11774,1886],{},[1159,11776,11777],{"encoding":1161},"R = x_{\\max} - x_{\\min} \\qquad \\text{(variační rozpětí)}",[1110,11779,11780],{},[1540,11781,8306],{},[1110,11783,11784,11785,11808,11809,11831,11832,11853,11854,11882],{},"Kvantil ",[1115,11786,11788],{"className":11787},[1138],[1140,11789,11790],{"xmlns":1142},[1144,11791,11792,11805],{},[1147,11793,11794],{},[1150,11795,11796,11803],{},[1236,11797,11798,11800],{"accent":1121},[1153,11799,1240],{},[1242,11801,11802],{},"~",[1153,11804,1110],{},[1159,11806,11807],{"encoding":1161},"\\tilde{x}_p"," dělí hodnoty datového souboru na dvě části: ",[1115,11810,11812],{"className":11811},[1138],[1140,11813,11814],{"xmlns":1142},[1144,11815,11816,11828],{},[1147,11817,11818,11821,11823,11825],{},[1565,11819,11820],{},"100",[1153,11822,1110],{},[2909,11824,2911],{},[1153,11826,11827],{"mathvariant":2121},"%",[1159,11829,11830],{"encoding":1161},"100p\\,\\%"," hodnot je menších nebo rovných ",[1115,11833,11835],{"className":11834},[1138],[1140,11836,11837],{"xmlns":1142},[1144,11838,11839,11851],{},[1147,11840,11841],{},[1150,11842,11843,11849],{},[1236,11844,11845,11847],{"accent":1121},[1153,11846,1240],{},[1242,11848,11802],{},[1153,11850,1110],{},[1159,11852,11807],{"encoding":1161},", zbylých ",[1115,11855,11857],{"className":11856},[1138],[1140,11858,11859],{"xmlns":1142},[1144,11860,11861,11879],{},[1147,11862,11863,11865,11867,11869,11871,11873,11875,11877],{},[1565,11864,11820],{},[1242,11866,1875],{"stretchy":1874},[1565,11868,1794],{},[1242,11870,3064],{},[1153,11872,1110],{},[1242,11874,1886],{"stretchy":1874},[2909,11876,2911],{},[1153,11878,11827],{"mathvariant":2121},[1159,11880,11881],{"encoding":1161},"100(1-p)\\,\\%"," je větších. Nejdůležitější kvantily:",[1436,11884,11885,11912],{},[1439,11886,11887,1654,11889,11911],{},[1540,11888,11553],{},[1115,11890,11892],{"className":11891},[1138],[1140,11893,11894],{"xmlns":1142},[1144,11895,11896,11908],{},[1147,11897,11898],{},[1150,11899,11900,11906],{},[1236,11901,11902,11904],{"accent":1121},[1153,11903,1240],{},[1242,11905,11802],{},[1565,11907,8460],{},[1159,11909,11910],{"encoding":1161},"\\tilde{x}_{0{,}5}"," — pro lichý počet prvků uspořádaného souboru prostřední prvek, pro sudý počet průměr dvou prostředních prvků;",[1439,11913,11914,1654,11917,1163,11939,1654,11942,1669],{},[1540,11915,11916],{},"dolní kvartil",[1115,11918,11920],{"className":11919},[1138],[1140,11921,11922],{"xmlns":1142},[1144,11923,11924,11936],{},[1147,11925,11926],{},[1150,11927,11928,11934],{},[1236,11929,11930,11932],{"accent":1121},[1153,11931,1240],{},[1242,11933,11802],{},[1565,11935,8480],{},[1159,11937,11938],{"encoding":1161},"\\tilde{x}_{0{,}25}",[1540,11940,11941],{},"horní kvartil",[1115,11943,11945],{"className":11944},[1138],[1140,11946,11947],{"xmlns":1142},[1144,11948,11949,11961],{},[1147,11950,11951],{},[1150,11952,11953,11959],{},[1236,11954,11955,11957],{"accent":1121},[1153,11956,1240],{},[1242,11958,11802],{},[1565,11960,8500],{},[1159,11962,11963],{"encoding":1161},"\\tilde{x}_{0{,}75}",[1110,11965,11966,11967,11970],{},"Datový soubor se do R zadává buď přímo (",[3470,11968,11969],{},"x \u003C- c(...)","), nebo načtením ze souboru:",[3694,11972,11974],{"className":3696,"code":11973,"language":71,"meta":1490,"style":1490},"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",[3470,11975,11976,12037],{"__ignoreMap":1490},[1115,11977,11978,11980,11982,11984,11986,11989,11991,11994,11996,11999,12001,12004,12006,12008,12010,12012,12014,12017,12019,12022,12024,12026,12028,12030,12033],{"class":3702,"line":10},[1115,11979,1240],{"class":3705},[1115,11981,3710],{"class":3709},[1115,11983,3835],{"class":3713},[1115,11985,1875],{"class":3717},[1115,11987,11988],{"class":3724},"4.1",[1115,11990,1797],{"class":3709},[1115,11992,11993],{"class":3724}," 4.0",[1115,11995,1797],{"class":3709},[1115,11997,11998],{"class":3724}," 3.8",[1115,12000,1797],{"class":3709},[1115,12002,12003],{"class":3724}," 3.9",[1115,12005,1797],{"class":3709},[1115,12007,11998],{"class":3724},[1115,12009,1797],{"class":3709},[1115,12011,11998],{"class":3724},[1115,12013,1797],{"class":3709},[1115,12015,12016],{"class":3724}," 3.5",[1115,12018,1797],{"class":3709},[1115,12020,12021],{"class":3724}," 3.7",[1115,12023,1797],{"class":3709},[1115,12025,11993],{"class":3724},[1115,12027,1797],{"class":3709},[1115,12029,11993],{"class":3724},[1115,12031,12032],{"class":3717},")   ",[1115,12034,12036],{"class":12035},"sCsY4","# přímé zadání hodnot\n",[1115,12038,12039],{"class":3702,"line":27},[1115,12040,12041],{"class":12035},"# x \u003C- read.table(\"data.txt\")[, 1]                       # načtení prvního sloupce ze souboru\n",[1110,12043,12044,12045,12048,12049,12052,12053,12056,12057,12060],{},"Řádek s načtením ze souboru je zakomentovaný znakem ",[3470,12046,12047],{},"#",": soubor musí ležet v pracovním adresáři R. ",[3470,12050,12051],{},"read.table()"," vrací datovou tabulku (",[3470,12054,12055],{},"data.frame","), proto ",[3470,12058,12059],{},"[, 1]"," vybere její první sloupec jako vektor.",[1110,12062,9057],{},[3694,12064,12066],{"className":3696,"code":12065,"language":71,"meta":1490,"style":1490},"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",[3470,12067,12068,12125,12136,12147,12158,12169,12207,12233,12256],{"__ignoreMap":1490},[1115,12069,12070,12072,12074,12076,12078,12081,12083,12086,12088,12091,12093,12096,12098,12100,12102,12105,12107,12109,12111,12114,12116,12119,12121,12123],{"class":3702,"line":10},[1115,12071,1240],{"class":3705},[1115,12073,3710],{"class":3709},[1115,12075,3835],{"class":3713},[1115,12077,1875],{"class":3717},[1115,12079,12080],{"class":3724},"11.1",[1115,12082,1797],{"class":3709},[1115,12084,12085],{"class":3724}," 12.7",[1115,12087,1797],{"class":3709},[1115,12089,12090],{"class":3724}," 10.8",[1115,12092,1797],{"class":3709},[1115,12094,12095],{"class":3724}," 13.2",[1115,12097,1797],{"class":3709},[1115,12099,12085],{"class":3724},[1115,12101,1797],{"class":3709},[1115,12103,12104],{"class":3724}," 13.4",[1115,12106,1797],{"class":3709},[1115,12108,12085],{"class":3724},[1115,12110,1797],{"class":3709},[1115,12112,12113],{"class":3724}," 14.4",[1115,12115,1797],{"class":3709},[1115,12117,12118],{"class":3724}," 14.7",[1115,12120,1797],{"class":3709},[1115,12122,12113],{"class":3724},[1115,12124,3901],{"class":3717},[1115,12126,12127,12130,12132,12134],{"class":3702,"line":27},[1115,12128,12129],{"class":3713},"length",[1115,12131,1875],{"class":3717},[1115,12133,1240],{"class":3705},[1115,12135,3901],{"class":3717},[1115,12137,12138,12141,12143,12145],{"class":3702,"line":148},[1115,12139,12140],{"class":3713},"mean",[1115,12142,1875],{"class":3717},[1115,12144,1240],{"class":3705},[1115,12146,3901],{"class":3717},[1115,12148,12149,12152,12154,12156],{"class":3702,"line":111},[1115,12150,12151],{"class":3713},"var",[1115,12153,1875],{"class":3717},[1115,12155,1240],{"class":3705},[1115,12157,3901],{"class":3717},[1115,12159,12160,12163,12165,12167],{"class":3702,"line":96},[1115,12161,12162],{"class":3713},"sd",[1115,12164,1875],{"class":3717},[1115,12166,1240],{"class":3705},[1115,12168,3901],{"class":3717},[1115,12170,12171,12173,12175,12177,12180,12182,12184,12186,12188,12190,12192,12194,12196,12198,12201,12203,12205],{"class":3702,"line":89},[1115,12172,4488],{"class":3713},[1115,12174,1875],{"class":3717},[1115,12176,1240],{"class":3705},[1115,12178,12179],{"class":3717},"); ",[1115,12181,11721],{"class":3713},[1115,12183,1875],{"class":3717},[1115,12185,1240],{"class":3705},[1115,12187,12179],{"class":3717},[1115,12189,11721],{"class":3713},[1115,12191,1875],{"class":3717},[1115,12193,1240],{"class":3705},[1115,12195,4601],{"class":3717},[1115,12197,4638],{"class":3709},[1115,12199,12200],{"class":3713}," min",[1115,12202,1875],{"class":3717},[1115,12204,1240],{"class":3705},[1115,12206,3901],{"class":3717},[1115,12208,12209,12212,12214,12216,12218,12221,12223,12226,12228,12231],{"class":3702,"line":82},[1115,12210,12211],{"class":3713},"quantile",[1115,12213,1875],{"class":3717},[1115,12215,1240],{"class":3705},[1115,12217,1797],{"class":3709},[1115,12219,12220],{"class":3724}," 0.5",[1115,12222,1797],{"class":3709},[1115,12224,12225],{"class":3705}," type",[1115,12227,3797],{"class":3709},[1115,12229,12230],{"class":3724}," 6",[1115,12232,3901],{"class":3717},[1115,12234,12235,12237,12239,12241,12243,12246,12248,12250,12252,12254],{"class":3702,"line":75},[1115,12236,12211],{"class":3713},[1115,12238,1875],{"class":3717},[1115,12240,1240],{"class":3705},[1115,12242,1797],{"class":3709},[1115,12244,12245],{"class":3724}," 0.25",[1115,12247,1797],{"class":3709},[1115,12249,12225],{"class":3705},[1115,12251,3797],{"class":3709},[1115,12253,12230],{"class":3724},[1115,12255,3901],{"class":3717},[1115,12257,12258,12260,12262,12264,12266,12269,12271,12273,12275,12277],{"class":3702,"line":3891},[1115,12259,12211],{"class":3713},[1115,12261,1875],{"class":3717},[1115,12263,1240],{"class":3705},[1115,12265,1797],{"class":3709},[1115,12267,12268],{"class":3724}," 0.75",[1115,12270,1797],{"class":3709},[1115,12272,12225],{"class":3705},[1115,12274,3797],{"class":3709},[1115,12276,12230],{"class":3724},[1115,12278,3901],{"class":3717},[3694,12280,12283],{"className":12281,"code":12282,"language":3923,"meta":1490},[3921],"[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",[3470,12284,12282],{"__ignoreMap":1490},[1110,12286,12287,12290,12291,12294],{},[3470,12288,12289],{},"quantile(x, p, type = 6)"," je potřeba zadat explicitně — výchozí typ v R (",[3470,12292,12293],{},"type = 7",") by u některých souborů dal mírně odlišné hodnoty kvantilů než ruční výpočet použitý v této kapitole.",[1110,12296,12297],{},[4383,12298],{"alt":12299,"className":12300,"src":12301},"mask-ps-kvantily",[1130,4387],"\u002Fwiki-assets\u002Fmask-ps-kvantily.png",[1110,12303,12304],{},"Seřazení souboru a krabicový graf:",[3694,12306,12308],{"className":3696,"code":12307,"language":71,"meta":1490,"style":1490},"sort(x)                     # vzestupně\nsort(x, decreasing = TRUE)  # sestupně\nboxplot(x)\n",[3470,12309,12310,12325,12348],{"__ignoreMap":1490},[1115,12311,12312,12315,12317,12319,12322],{"class":3702,"line":10},[1115,12313,12314],{"class":3713},"sort",[1115,12316,1875],{"class":3717},[1115,12318,1240],{"class":3705},[1115,12320,12321],{"class":3717},")                     ",[1115,12323,12324],{"class":12035},"# vzestupně\n",[1115,12326,12327,12329,12331,12333,12335,12338,12340,12342,12345],{"class":3702,"line":27},[1115,12328,12314],{"class":3713},[1115,12330,1875],{"class":3717},[1115,12332,1240],{"class":3705},[1115,12334,1797],{"class":3709},[1115,12336,12337],{"class":3705}," decreasing",[1115,12339,3797],{"class":3709},[1115,12341,3810],{"class":3724},[1115,12343,12344],{"class":3717},")  ",[1115,12346,12347],{"class":12035},"# sestupně\n",[1115,12349,12350,12353,12355,12357],{"class":3702,"line":148},[1115,12351,12352],{"class":3713},"boxplot",[1115,12354,1875],{"class":3717},[1115,12356,1240],{"class":3705},[1115,12358,3901],{"class":3717},[3694,12360,12363],{"className":12361,"code":12362,"language":3923,"meta":1490},[3921]," [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",[3470,12364,12362],{"__ignoreMap":1490},[1110,12366,12367,12370,12371,12374],{},[3470,12368,12369],{},"boxplot()"," kreslí krabici mezi hodnotami ",[3470,12372,12373],{},"fivenum(x)"," (zde 12,7 a 14,4), které se od kvartilů typu 6 mohou mírně lišit.",[1103,12376,12378,12385],{"className":12377,"dataCallout":3477},[1106,3476],[1110,12379,12381,12384],{"className":12380},[1113],[1115,12382],{"className":12383,"ariaHidden":1121},[1118,3484,1120],"Příklad: Empirické charakteristiky",[1110,12386,12387],{},"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.",[1110,12389,12390,12391,1346,12414,1346,12437,1346,12456,12475,12476,8464,12503,12518,12519,1669],{},"Výstup R kódu výše dává ",[1115,12392,12394],{"className":12393},[1138],[1140,12395,12396],{"xmlns":1142},[1144,12397,12398,12411],{},[1147,12399,12400,12406,12408],{},[1236,12401,12402,12404],{"accent":1121},[1153,12403,1240],{},[1242,12405,1244],{},[1242,12407,1982],{},[1565,12409,12410],{},"13,01",[1159,12412,12413],{"encoding":1161},"\\bar{x}=13{,}01",[1115,12415,12417],{"className":12416},[1138],[1140,12418,12419],{"xmlns":1142},[1144,12420,12421,12434],{},[1147,12422,12423,12429,12431],{},[1582,12424,12425,12427],{},[1153,12426,1291],{},[1565,12428,1589],{},[1242,12430,1982],{},[1565,12432,12433],{},"1,75",[1159,12435,12436],{"encoding":1161},"s^2=1{,}75",[1115,12438,12440],{"className":12439},[1138],[1140,12441,12442],{"xmlns":1142},[1144,12443,12444,12453],{},[1147,12445,12446,12448,12450],{},[1153,12447,1291],{},[1242,12449,1982],{},[1565,12451,12452],{},"1,32",[1159,12454,12455],{"encoding":1161},"s=1{,}32",[1115,12457,12459],{"className":12458},[1138],[1140,12460,12461],{"xmlns":1142},[1144,12462,12463,12472],{},[1147,12464,12465,12467,12469],{},[1153,12466,1260],{},[1242,12468,1982],{},[1565,12470,12471],{},"3,9",[1159,12473,12474],{"encoding":1161},"R=3{,}9",", medián ",[1115,12477,12479],{"className":12478},[1138],[1140,12480,12481],{"xmlns":1142},[1144,12482,12483,12500],{},[1147,12484,12485,12495,12497],{},[1150,12486,12487,12493],{},[1236,12488,12489,12491],{"accent":1121},[1153,12490,1240],{},[1242,12492,11802],{},[1565,12494,8460],{},[1242,12496,1982],{},[1565,12498,12499],{},"12,95",[1159,12501,12502],{"encoding":1161},"\\tilde{x}_{0{,}5}=12{,}95",[1115,12504,12506],{"className":12505},[1138],[1140,12507,12508],{"xmlns":1142},[1144,12509,12510,12515],{},[1147,12511,12512],{},[1565,12513,12514],{},"12,3",[1159,12516,12517],{"encoding":1161},"12{,}3",", horní kvartil ",[1115,12520,12522],{"className":12521},[1138],[1140,12523,12524],{"xmlns":1142},[1144,12525,12526,12531],{},[1147,12527,12528],{},[1565,12529,12530],{},"14,4",[1159,12532,12533],{"encoding":1161},"14{,}4",[1110,12535,12536],{},"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.",[1103,12538,12540,12547],{"className":12539,"dataCallout":3477},[1106,3476],[1110,12541,12543,12546],{"className":12542},[1113],[1115,12544],{"className":12545,"ariaHidden":1121},[1118,3484,1120],"Příklad: Doba oprav televizorů",[1110,12548,12549],{},"Při 50 opravách určité závady televizoru byly naměřeny časy (v minutách). Určete empirické charakteristiky.",[3694,12551,12553],{"className":3696,"code":12552,"language":71,"meta":1490,"style":1490},"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",[3470,12554,12555,12615,12666,12713,12760,12808,12818,12828,12838,12858],{"__ignoreMap":1490},[1115,12556,12557,12560,12562,12564,12566,12568,12570,12573,12575,12578,12580,12583,12585,12588,12590,12593,12595,12598,12600,12603,12605,12608,12610,12613],{"class":3702,"line":10},[1115,12558,12559],{"class":3705},"x6",[1115,12561,3710],{"class":3709},[1115,12563,3835],{"class":3713},[1115,12565,1875],{"class":3717},[1115,12567,3575],{"class":3724},[1115,12569,1797],{"class":3709},[1115,12571,12572],{"class":3724}," 40.2",[1115,12574,1797],{"class":3709},[1115,12576,12577],{"class":3724}," 41.9",[1115,12579,1797],{"class":3709},[1115,12581,12582],{"class":3724}," 43.4",[1115,12584,1797],{"class":3709},[1115,12586,12587],{"class":3724}," 42.8",[1115,12589,1797],{"class":3709},[1115,12591,12592],{"class":3724}," 42.3",[1115,12594,1797],{"class":3709},[1115,12596,12597],{"class":3724}," 43.2",[1115,12599,1797],{"class":3709},[1115,12601,12602],{"class":3724}," 45",[1115,12604,1797],{"class":3709},[1115,12606,12607],{"class":3724}," 41.5",[1115,12609,1797],{"class":3709},[1115,12611,12612],{"class":3724}," 42.7",[1115,12614,3737],{"class":3709},[1115,12616,12617,12620,12622,12625,12627,12630,12632,12635,12637,12640,12642,12645,12647,12650,12652,12655,12657,12659,12661,12664],{"class":3702,"line":27},[1115,12618,12619],{"class":3724},"        43.9",[1115,12621,1797],{"class":3709},[1115,12623,12624],{"class":3724}," 40.1",[1115,12626,1797],{"class":3709},[1115,12628,12629],{"class":3724}," 43.3",[1115,12631,1797],{"class":3709},[1115,12633,12634],{"class":3724}," 41.1",[1115,12636,1797],{"class":3709},[1115,12638,12639],{"class":3724}," 42.5",[1115,12641,1797],{"class":3709},[1115,12643,12644],{"class":3724}," 42.4",[1115,12646,1797],{"class":3709},[1115,12648,12649],{"class":3724}," 41.4",[1115,12651,1797],{"class":3709},[1115,12653,12654],{"class":3724}," 40.8",[1115,12656,1797],{"class":3709},[1115,12658,9338],{"class":3724},[1115,12660,1797],{"class":3709},[1115,12662,12663],{"class":3724}," 44.7",[1115,12665,3737],{"class":3709},[1115,12667,12668,12671,12673,12675,12677,12679,12681,12684,12686,12689,12691,12694,12696,12698,12700,12703,12705,12707,12709,12711],{"class":3702,"line":148},[1115,12669,12670],{"class":3724},"        41.2",[1115,12672,1797],{"class":3709},[1115,12674,12577],{"class":3724},[1115,12676,1797],{"class":3709},[1115,12678,12644],{"class":3724},[1115,12680,1797],{"class":3709},[1115,12682,12683],{"class":3724}," 44.4",[1115,12685,1797],{"class":3709},[1115,12687,12688],{"class":3724}," 40.5",[1115,12690,1797],{"class":3709},[1115,12692,12693],{"class":3724}," 39.7",[1115,12695,1797],{"class":3709},[1115,12697,12634],{"class":3724},[1115,12699,1797],{"class":3709},[1115,12701,12702],{"class":3724}," 41",[1115,12704,1797],{"class":3709},[1115,12706,12577],{"class":3724},[1115,12708,1797],{"class":3709},[1115,12710,12654],{"class":3724},[1115,12712,3737],{"class":3709},[1115,12714,12715,12718,12720,12722,12724,12727,12729,12731,12733,12735,12737,12740,12742,12745,12747,12749,12751,12754,12756,12758],{"class":3702,"line":111},[1115,12716,12717],{"class":3724},"        43",[1115,12719,1797],{"class":3709},[1115,12721,12587],{"class":3724},[1115,12723,1797],{"class":3709},[1115,12725,12726],{"class":3724}," 42.9",[1115,12728,1797],{"class":3709},[1115,12730,12612],{"class":3724},[1115,12732,1797],{"class":3709},[1115,12734,12629],{"class":3724},[1115,12736,1797],{"class":3709},[1115,12738,12739],{"class":3724}," 42.2",[1115,12741,1797],{"class":3709},[1115,12743,12744],{"class":3724}," 39.2",[1115,12746,1797],{"class":3709},[1115,12748,12607],{"class":3724},[1115,12750,1797],{"class":3709},[1115,12752,12753],{"class":3724}," 41.6",[1115,12755,1797],{"class":3709},[1115,12757,12612],{"class":3724},[1115,12759,3737],{"class":3709},[1115,12761,12762,12765,12767,12769,12771,12774,12776,12778,12780,12783,12785,12788,12790,12793,12795,12797,12799,12802,12804,12806],{"class":3702,"line":96},[1115,12763,12764],{"class":3724},"        45",[1115,12766,1797],{"class":3709},[1115,12768,12592],{"class":3724},[1115,12770,1797],{"class":3709},[1115,12772,12773],{"class":3724}," 43.6",[1115,12775,1797],{"class":3709},[1115,12777,12597],{"class":3724},[1115,12779,1797],{"class":3709},[1115,12781,12782],{"class":3724}," 38.8",[1115,12784,1797],{"class":3709},[1115,12786,12787],{"class":3724}," 43",[1115,12789,1797],{"class":3709},[1115,12791,12792],{"class":3724}," 44.2",[1115,12794,1797],{"class":3709},[1115,12796,12787],{"class":3724},[1115,12798,1797],{"class":3709},[1115,12800,12801],{"class":3724}," 40",[1115,12803,1797],{"class":3709},[1115,12805,12683],{"class":3724},[1115,12807,3901],{"class":3717},[1115,12809,12810,12812,12814,12816],{"class":3702,"line":89},[1115,12811,12129],{"class":3713},[1115,12813,1875],{"class":3717},[1115,12815,12559],{"class":3705},[1115,12817,3901],{"class":3717},[1115,12819,12820,12822,12824,12826],{"class":3702,"line":82},[1115,12821,12140],{"class":3713},[1115,12823,1875],{"class":3717},[1115,12825,12559],{"class":3705},[1115,12827,3901],{"class":3717},[1115,12829,12830,12832,12834,12836],{"class":3702,"line":75},[1115,12831,12162],{"class":3713},[1115,12833,1875],{"class":3717},[1115,12835,12559],{"class":3705},[1115,12837,3901],{"class":3717},[1115,12839,12840,12842,12844,12846,12848,12850,12852,12854,12856],{"class":3702,"line":3891},[1115,12841,11721],{"class":3713},[1115,12843,1875],{"class":3717},[1115,12845,12559],{"class":3705},[1115,12847,4601],{"class":3717},[1115,12849,4638],{"class":3709},[1115,12851,12200],{"class":3713},[1115,12853,1875],{"class":3717},[1115,12855,12559],{"class":3705},[1115,12857,3901],{"class":3717},[1115,12859,12860,12863,12865,12867],{"class":3702,"line":72},[1115,12861,12862],{"class":3713},"median",[1115,12864,1875],{"class":3717},[1115,12866,12559],{"class":3705},[1115,12868,3901],{"class":3717},[3694,12870,12873],{"className":12871,"code":12872,"language":3923,"meta":1490},[3921],"[1] 50\n[1] 42.27\n[1] 1.48052\n[1] 6.2\n[1] 42.4\n",[3470,12874,12872],{"__ignoreMap":1490},[1110,12876,12877],{},"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.",[1189,12879,12881],{"id":12880},"empirická-distribuční-funkce","Empirická distribuční funkce",[1110,12883,12884,12885,12898,12899,1654,12902,12925,12926,12960],{},"Pro libovolný rozsah datového souboru, diskrétní i spojitou náhodnou veličinu ",[1115,12886,12888],{"className":12887},[1138],[1140,12889,12890],{"xmlns":1142},[1144,12891,12892,12896],{},[1147,12893,12894],{},[1153,12895,6734],{},[1159,12897,6734],{"encoding":1161},", lze sestrojit ",[1540,12900,12901],{},"empirickou distribuční funkci",[1115,12903,12905],{"className":12904},[1138],[1140,12906,12907],{"xmlns":1142},[1144,12908,12909,12923],{},[1147,12910,12911,12917,12919,12921],{},[1150,12912,12913,12915],{},[1153,12914,6718],{},[1153,12916,1372],{},[1242,12918,1875],{"stretchy":1874},[1153,12920,1240],{},[1242,12922,1886],{"stretchy":1874},[1159,12924,11187],{"encoding":1161},". Pro datový soubor ",[1115,12927,12929],{"className":12928},[1138],[1140,12930,12931],{"xmlns":1142},[1144,12932,12933,12957],{},[1147,12934,12935,12937,12943,12945,12947,12949,12955],{},[1242,12936,1875],{"stretchy":1874},[1150,12938,12939,12941],{},[1153,12940,1240],{},[1565,12942,1794],{},[1242,12944,1797],{"separator":1121},[1242,12946,1800],{},[1242,12948,1797],{"separator":1121},[1150,12950,12951,12953],{},[1153,12952,1240],{},[1153,12954,1372],{},[1242,12956,1886],{"stretchy":1874},[1159,12958,12959],{"encoding":1161},"(x_1,\\dots,x_n)"," je",[1115,12962,12964],{"className":12963},[1138],[1140,12965,12966],{"xmlns":1142,"display":1964},[1144,12967,12968,12992],{},[1147,12969,12970,12976,12978,12980,12982,12984,12990],{},[1150,12971,12972,12974],{},[1153,12973,6718],{},[1153,12975,1372],{},[1242,12977,1875],{"stretchy":1874},[1153,12979,1240],{},[1242,12981,1886],{"stretchy":1874},[1242,12983,1982],{},[2739,12985,12986,12988],{},[1153,12987,1183],{},[1153,12989,1372],{},[1242,12991,1797],{"separator":1121},[1159,12993,12994],{"encoding":1161},"F_n(x) = \\frac{k}{n},",[1110,12996,4507,12997,13010,13011,1669],{},[1115,12998,13000],{"className":12999},[1138],[1140,13001,13002],{"xmlns":1142},[1144,13003,13004,13008],{},[1147,13005,13006],{},[1153,13007,1183],{},[1159,13009,1183],{"encoding":1161}," je počet prvků datového souboru menších nebo rovných číslu ",[1115,13012,13014],{"className":13013},[1138],[1140,13015,13016],{"xmlns":1142},[1144,13017,13018,13022],{},[1147,13019,13020],{},[1153,13021,1240],{},[1159,13023,1240],{"encoding":1161},[1110,13025,9057],{},[3694,13027,13029],{"className":3696,"code":13028,"language":71,"meta":1490,"style":1490},"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",[3470,13030,13031,13046,13061,13079,13093],{"__ignoreMap":1490},[1115,13032,13033,13035,13037,13040,13042,13044],{"class":3702,"line":10},[1115,13034,6773],{"class":3705},[1115,13036,3710],{"class":3709},[1115,13038,13039],{"class":3713}," ecdf",[1115,13041,1875],{"class":3717},[1115,13043,1240],{"class":3705},[1115,13045,3901],{"class":3717},[1115,13047,13048,13051,13053,13055,13058],{"class":3702,"line":27},[1115,13049,13050],{"class":3713},"knots",[1115,13052,1875],{"class":3717},[1115,13054,6773],{"class":3705},[1115,13056,13057],{"class":3717},")        ",[1115,13059,13060],{"class":12035},"# vzestupně seřazené různé hodnoty datového souboru\n",[1115,13062,13063,13065,13067,13069,13071,13073,13076],{"class":3702,"line":148},[1115,13064,6773],{"class":3713},[1115,13066,1875],{"class":3717},[1115,13068,13050],{"class":3713},[1115,13070,1875],{"class":3717},[1115,13072,6773],{"class":3705},[1115,13074,13075],{"class":3717},"))      ",[1115,13077,13078],{"class":12035},"# hodnoty Fn(x) v těchto bodech\n",[1115,13080,13081,13083,13085,13087,13090],{"class":3702,"line":111},[1115,13082,6773],{"class":3713},[1115,13084,1875],{"class":3717},[1115,13086,3545],{"class":3724},[1115,13088,13089],{"class":3717},")            ",[1115,13091,13092],{"class":12035},"# Fn v libovolném bodě\n",[1115,13094,13095,13098,13100,13102],{"class":3702,"line":96},[1115,13096,13097],{"class":3713},"plot",[1115,13099,1875],{"class":3717},[1115,13101,6773],{"class":3705},[1115,13103,3901],{"class":3717},[3694,13105,13108],{"className":13106,"code":13107,"language":3923,"meta":1490},[3921],"[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",[3470,13109,13107],{"__ignoreMap":1490},[1110,13111,13112,13115,13116,13134,13135,13138,13139,13152,13153,1669],{},[3470,13113,13114],{},"knots()"," vrací jen různé hodnoty (opakující se hodnota 12,7 je ve výpočtu ",[1115,13117,13119],{"className":13118},[1138],[1140,13120,13121],{"xmlns":1142},[1144,13122,13123,13131],{},[1147,13124,13125],{},[1150,13126,13127,13129],{},[1153,13128,6718],{},[1153,13130,1372],{},[1159,13132,13133],{"encoding":1161},"F_n"," započtena třikrát, v seznamu uzlů je ale jen jednou); ",[3470,13136,13137],{},"plot(f)"," nakreslí schodovitý graf, který v každém uzlu skáče o ",[1115,13140,13142],{"className":13141},[1138],[1140,13143,13144],{"xmlns":1142},[1144,13145,13146,13150],{},[1147,13147,13148],{},[1153,13149,1183],{},[1159,13151,1183],{"encoding":1161},"-násobek ",[1115,13154,13156],{"className":13155},[1138],[1140,13157,13158],{"xmlns":1142},[1144,13159,13160,13168],{},[1147,13161,13162,13164,13166],{},[1565,13163,1794],{},[1153,13165,4604],{"mathvariant":2121},[1153,13167,1372],{},[1159,13169,13170],{"encoding":1161},"1\u002Fn",[1110,13172,13173],{},[4383,13174],{"alt":13175,"className":13176,"src":13177},"mask-ps-ecdf",[1130,4387],"\u002Fwiki-assets\u002Fmask-ps-ecdf.png",[1103,13179,13181,13188],{"className":13180,"dataCallout":3477},[1106,3476],[1110,13182,13184,13187],{"className":13183},[1113],[1115,13185],{"className":13186,"ariaHidden":1121},[1118,3484,1120],"Příklad: Empirická distribuční funkce",[1110,13189,13190],{},"Pro předchozí datový soubor (doba opravy součástky) určete empirickou distribuční funkci.",[1110,13192,13193,13194,1669],{},"Uspořádaný soubor je ",[1115,13195,13197],{"className":13196},[1138],[1140,13198,13199],{"xmlns":1142},[1144,13200,13201,13265],{},[1147,13202,13203,13206,13208,13210,13213,13215,13217,13220,13222,13224,13226,13228,13230,13232,13234,13236,13239,13241,13243,13246,13248,13250,13252,13254,13256,13258,13260,13262],{},[1565,13204,13205],{},"10,8",[1242,13207,6896],{"separator":1121},[2909,13209,11318],{},[1565,13211,13212],{},"11,1",[1242,13214,6896],{"separator":1121},[2909,13216,11318],{},[1565,13218,13219],{},"12,7",[1242,13221,6896],{"separator":1121},[2909,13223,11318],{},[1565,13225,13219],{},[1242,13227,6896],{"separator":1121},[2909,13229,11318],{},[1565,13231,13219],{},[1242,13233,6896],{"separator":1121},[2909,13235,11318],{},[1565,13237,13238],{},"13,2",[1242,13240,6896],{"separator":1121},[2909,13242,11318],{},[1565,13244,13245],{},"13,4",[1242,13247,6896],{"separator":1121},[2909,13249,11318],{},[1565,13251,12530],{},[1242,13253,6896],{"separator":1121},[2909,13255,11318],{},[1565,13257,12530],{},[1242,13259,6896],{"separator":1121},[2909,13261,11318],{},[1565,13263,13264],{},"14,7",[1159,13266,13267],{"encoding":1161},"10{,}8;\\ 11{,}1;\\ 12{,}7;\\ 12{,}7;\\ 12{,}7;\\ 13{,}2;\\ 13{,}4;\\ 14{,}4;\\ 14{,}4;\\ 14{,}7",[1194,13269,13270,13303],{},[1197,13271,13272],{},[1200,13273,13274,13289,13291,13293,13295,13297,13299,13301],{},[1203,13275,13276],{},[1115,13277,13279],{"className":13278},[1138],[1140,13280,13281],{"xmlns":1142},[1144,13282,13283,13287],{},[1147,13284,13285],{},[1153,13286,1240],{},[1159,13288,1240],{"encoding":1161},[1203,13290,13205],{},[1203,13292,13212],{},[1203,13294,13219],{},[1203,13296,13238],{},[1203,13298,13245],{},[1203,13300,12530],{},[1203,13302,13264],{},[1210,13304,13305,13337],{},[1200,13306,13307,13322,13324,13326,13328,13330,13333,13335],{},[1215,13308,13309],{},[1115,13310,13312],{"className":13311},[1138],[1140,13313,13314],{"xmlns":1142},[1144,13315,13316,13320],{},[1147,13317,13318],{},[1153,13319,1183],{},[1159,13321,1183],{"encoding":1161},[1215,13323,1794],{},[1215,13325,1589],{},[1215,13327,9929],{},[1215,13329,3964],{},[1215,13331,13332],{},"7",[1215,13334,3595],{},[1215,13336,9036],{},[1200,13338,13339,13364,13367,13370,13372,13375,13378,13381],{},[1215,13340,13341],{},[1115,13342,13344],{"className":13343},[1138],[1140,13345,13346],{"xmlns":1142},[1144,13347,13348,13362],{},[1147,13349,13350,13356,13358,13360],{},[1150,13351,13352,13354],{},[1153,13353,6718],{},[1153,13355,1372],{},[1242,13357,1875],{"stretchy":1874},[1153,13359,1240],{},[1242,13361,1886],{"stretchy":1874},[1159,13363,11187],{"encoding":1161},[1215,13365,13366],{},"0,1",[1215,13368,13369],{},"0,2",[1215,13371,8460],{},[1215,13373,13374],{},"0,6",[1215,13376,13377],{},"0,7",[1215,13379,13380],{},"0,9",[1215,13382,13383],{},"1,0",[1110,13385,13386,13387,13409,13410,13433],{},"Graf (levý panel výše) odpovídá tabulce: funkce je nulová pod 10,8, skáče o ",[1115,13388,13390],{"className":13389},[1138],[1140,13391,13392],{"xmlns":1142},[1144,13393,13394,13406],{},[1147,13395,13396,13398,13400,13402,13404],{},[1565,13397,1794],{},[1153,13399,4604],{"mathvariant":2121},[1153,13401,1372],{},[1242,13403,1982],{},[1565,13405,13366],{},[1159,13407,13408],{"encoding":1161},"1\u002Fn = 0{,}1"," v každé jednoduché hodnotě a o ",[1115,13411,13413],{"className":13412},[1138],[1140,13414,13415],{"xmlns":1142},[1144,13416,13417,13430],{},[1147,13418,13419,13421,13423,13425,13427],{},[1565,13420,3592],{},[1153,13422,4604],{"mathvariant":2121},[1153,13424,1372],{},[1242,13426,1982],{},[1565,13428,13429],{},"0,3",[1159,13431,13432],{"encoding":1161},"3\u002Fn = 0{,}3"," v bodě 12,7, kde se hodnota opakuje třikrát.",[1103,13435,13437,13444],{"className":13436,"dataCallout":3477},[1106,3476],[1110,13438,13440,13443],{"className":13439},[1113],[1115,13441],{"className":13442,"ariaHidden":1121},[1118,3484,1120],"Příklad: Odpad materiálu",[1110,13445,13446],{},"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.",[3694,13448,13450],{"className":3696,"code":13449,"language":71,"meta":1490,"style":1490},"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",[3470,13451,13452,13503,13513,13523,13533,13553,13563,13578,13588],{"__ignoreMap":1490},[1115,13453,13454,13457,13459,13461,13463,13465,13467,13469,13471,13473,13475,13477,13479,13481,13483,13485,13487,13489,13491,13493,13495,13497,13499,13501],{"class":3702,"line":10},[1115,13455,13456],{"class":3705},"x4",[1115,13458,3710],{"class":3709},[1115,13460,3835],{"class":3713},[1115,13462,1875],{"class":3717},[1115,13464,11988],{"class":3724},[1115,13466,1797],{"class":3709},[1115,13468,11993],{"class":3724},[1115,13470,1797],{"class":3709},[1115,13472,11998],{"class":3724},[1115,13474,1797],{"class":3709},[1115,13476,12003],{"class":3724},[1115,13478,1797],{"class":3709},[1115,13480,11998],{"class":3724},[1115,13482,1797],{"class":3709},[1115,13484,11998],{"class":3724},[1115,13486,1797],{"class":3709},[1115,13488,12016],{"class":3724},[1115,13490,1797],{"class":3709},[1115,13492,12021],{"class":3724},[1115,13494,1797],{"class":3709},[1115,13496,11993],{"class":3724},[1115,13498,1797],{"class":3709},[1115,13500,11993],{"class":3724},[1115,13502,3901],{"class":3717},[1115,13504,13505,13507,13509,13511],{"class":3702,"line":27},[1115,13506,12129],{"class":3713},[1115,13508,1875],{"class":3717},[1115,13510,13456],{"class":3705},[1115,13512,3901],{"class":3717},[1115,13514,13515,13517,13519,13521],{"class":3702,"line":148},[1115,13516,12140],{"class":3713},[1115,13518,1875],{"class":3717},[1115,13520,13456],{"class":3705},[1115,13522,3901],{"class":3717},[1115,13524,13525,13527,13529,13531],{"class":3702,"line":111},[1115,13526,12162],{"class":3713},[1115,13528,1875],{"class":3717},[1115,13530,13456],{"class":3705},[1115,13532,3901],{"class":3717},[1115,13534,13535,13537,13539,13541,13543,13545,13547,13549,13551],{"class":3702,"line":96},[1115,13536,11721],{"class":3713},[1115,13538,1875],{"class":3717},[1115,13540,13456],{"class":3705},[1115,13542,4601],{"class":3717},[1115,13544,4638],{"class":3709},[1115,13546,12200],{"class":3713},[1115,13548,1875],{"class":3717},[1115,13550,13456],{"class":3705},[1115,13552,3901],{"class":3717},[1115,13554,13555,13557,13559,13561],{"class":3702,"line":89},[1115,13556,12862],{"class":3713},[1115,13558,1875],{"class":3717},[1115,13560,13456],{"class":3705},[1115,13562,3901],{"class":3717},[1115,13564,13565,13568,13570,13572,13574,13576],{"class":3702,"line":82},[1115,13566,13567],{"class":3705},"f4",[1115,13569,3710],{"class":3709},[1115,13571,13039],{"class":3713},[1115,13573,1875],{"class":3717},[1115,13575,13456],{"class":3705},[1115,13577,3901],{"class":3717},[1115,13579,13580,13582,13584,13586],{"class":3702,"line":75},[1115,13581,13050],{"class":3713},[1115,13583,1875],{"class":3717},[1115,13585,13567],{"class":3705},[1115,13587,3901],{"class":3717},[1115,13589,13590,13592,13594,13596,13598,13600],{"class":3702,"line":3891},[1115,13591,13567],{"class":3713},[1115,13593,1875],{"class":3717},[1115,13595,13050],{"class":3713},[1115,13597,1875],{"class":3717},[1115,13599,13567],{"class":3705},[1115,13601,9496],{"class":3717},[3694,13603,13606],{"className":13604,"code":13605,"language":3923,"meta":1490},[3921],"[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",[3470,13607,13605],{"__ignoreMap":1490},[1110,13609,13610,13611,13634],{},"Průměrný odpad je 3,86 % se směrodatnou odchylkou 0,18 % a mediánem 3,85 %. Pravý panel obrázku výše ukazuje tvar ",[1115,13612,13614],{"className":13613},[1138],[1140,13615,13616],{"xmlns":1142},[1144,13617,13618,13632],{},[1147,13619,13620,13626,13628,13630],{},[1150,13621,13622,13624],{},[1153,13623,6718],{},[1153,13625,1372],{},[1242,13627,1875],{"stretchy":1874},[1153,13629,1240],{},[1242,13631,1886],{"stretchy":1874},[1159,13633,11187],{"encoding":1161},": hodnota 3,8 se v souboru opakuje třikrát, proto zde funkce skáče o 0,3 najednou, stejně jako hodnota 4,0.",[1189,13636,13638],{"id":13637},"třídění-datového-souboru-do-tříd","Třídění datového souboru do tříd",[1110,13640,13641,13642,13645,13646,13659,13660,13663],{},"Je-li rozsah datového souboru velký (řádově přes 30 až 50 pozorování), hodnoty se před dalším zpracováním ",[1540,13643,13644],{},"roztřídí",": variační rozpětí ",[1115,13647,13649],{"className":13648},[1138],[1140,13650,13651],{"xmlns":1142},[1144,13652,13653,13657],{},[1147,13654,13655],{},[1153,13656,1260],{},[1159,13658,1260],{"encoding":1161}," se rozdělí na určitý počet ",[1540,13661,13662],{},"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.",[1110,13665,13666],{},"Výsledkem je tabulka četností se sloupci:",[1436,13668,13669,13749,13770,13791],{},[1439,13670,13671,13689,13690,13703,13704,13748],{},[1115,13672,13674],{"className":13673},[1138],[1140,13675,13676],{"xmlns":1142},[1144,13677,13678,13686],{},[1147,13679,13680],{},[1150,13681,13682,13684],{},[1153,13683,11204],{},[1153,13685,1883],{},[1159,13687,13688],{"encoding":1161},"I_j"," — ",[1115,13691,13693],{"className":13692},[1138],[1140,13694,13695],{"xmlns":1142},[1144,13696,13697,13701],{},[1147,13698,13699],{},[1153,13700,1883],{},[1159,13702,1883],{"encoding":1161},"-tý interval (v této kapitole vždy zleva uzavřený a zprava otevřený, ",[1115,13705,13707],{"className":13706},[1138],[1140,13708,13709],{"xmlns":1142},[1144,13710,13711,13745],{},[1147,13712,13713,13719,13721,13723,13729,13731,13743],{},[1150,13714,13715,13717],{},[1153,13716,11204],{},[1153,13718,1883],{},[1242,13720,1982],{},[1242,13722,8428],{"stretchy":1874},[1150,13724,13725,13727],{},[1153,13726,1343],{},[1153,13728,1883],{},[1242,13730,6896],{"separator":1121},[1150,13732,13733,13735],{},[1153,13734,1343],{},[1147,13736,13737,13739,13741],{},[1153,13738,1883],{},[1242,13740,5477],{},[1565,13742,1794],{},[1242,13744,1886],{"stretchy":1874},[1159,13746,13747],{"encoding":1161},"I_j = \\langle c_j; c_{j+1})","),",[1439,13750,13751,13769],{},[1115,13752,13754],{"className":13753},[1138],[1140,13755,13756],{"xmlns":1142},[1144,13757,13758,13766],{},[1147,13759,13760],{},[1150,13761,13762,13764],{},[1153,13763,8928],{},[1153,13765,1883],{},[1159,13767,13768],{"encoding":1161},"Z_j"," — střed (reprezentant) intervalu,",[1439,13771,13772,13790],{},[1115,13773,13775],{"className":13774},[1138],[1140,13776,13777],{"xmlns":1142},[1144,13778,13779,13787],{},[1147,13780,13781],{},[1150,13782,13783,13785],{},[1153,13784,6773],{},[1153,13786,1883],{},[1159,13788,13789],{"encoding":1161},"f_j"," — četnost, počet hodnot v intervalu,",[1439,13792,13793,13823,13824,1163,13852,1669],{},[1115,13794,13796],{"className":13795},[1138],[1140,13797,13798],{"xmlns":1142},[1144,13799,13800,13820],{},[1147,13801,13802,13808,13810,13816,13818],{},[1150,13803,13804,13806],{},[1153,13805,1110],{},[1153,13807,1883],{},[1242,13809,1982],{},[1150,13811,13812,13814],{},[1153,13813,6773],{},[1153,13815,1883],{},[1153,13817,4604],{"mathvariant":2121},[1153,13819,1372],{},[1159,13821,13822],{"encoding":1161},"p_j = f_j\u002Fn"," — relativní četnost, přičemž ",[1115,13825,13827],{"className":13826},[1138],[1140,13828,13829],{"xmlns":1142},[1144,13830,13831,13849],{},[1147,13832,13833,13839,13845,13847],{},[1150,13834,13835,13837],{},[1242,13836,1988],{},[1153,13838,1883],{},[1150,13840,13841,13843],{},[1153,13842,6773],{},[1153,13844,1883],{},[1242,13846,1982],{},[1153,13848,1372],{},[1159,13850,13851],{"encoding":1161},"\\sum_j f_j = n",[1115,13853,13855],{"className":13854},[1138],[1140,13856,13857],{"xmlns":1142},[1144,13858,13859,13877],{},[1147,13860,13861,13867,13873,13875],{},[1150,13862,13863,13865],{},[1242,13864,1988],{},[1153,13866,1883],{},[1150,13868,13869,13871],{},[1153,13870,1110],{},[1153,13872,1883],{},[1242,13874,1982],{},[1565,13876,1794],{},[1159,13878,13879],{"encoding":1161},"\\sum_j p_j = 1",[1110,13881,13882,13883,13886,13887,13890,13891,13894,13895,13898,13899,4607,13902,13919,13920,13923,13924,4607,13927,1812,13944,13947],{},"V R se třídění provádí příkazem ",[3470,13884,13885],{},"hist()"," — buď necháme R zvolit třídy samo (",[3470,13888,13889],{},"hist(x)","), nebo zadáme hranice přímo (",[3470,13892,13893],{},"hist(x, br = seq(0, 550, by = 50))","). Uložením výsledku do proměnné (",[3470,13896,13897],{},"y \u003C- hist(...)",") získáme jednotlivé sloupce tabulky: ",[3470,13900,13901],{},"y$counts",[1115,13903,13905],{"className":13904},[1138],[1140,13906,13907],{"xmlns":1142},[1144,13908,13909,13917],{},[1147,13910,13911],{},[1150,13912,13913,13915],{},[1153,13914,6773],{},[1153,13916,1883],{},[1159,13918,13789],{"encoding":1161},"), ",[3470,13921,13922],{},"y$breaks"," (hranice tříd), ",[3470,13925,13926],{},"y$mids",[1115,13928,13930],{"className":13929},[1138],[1140,13931,13932],{"xmlns":1142},[1144,13933,13934,13942],{},[1147,13935,13936],{},[1150,13937,13938,13940],{},[1153,13939,8928],{},[1153,13941,1883],{},[1159,13943,13768],{"encoding":1161},[3470,13945,13946],{},"y$density"," (relativní četnosti na škále hustoty).",[1110,13949,13950,13951,13968,13969,13971,13972,14008,14009,14012,14013,1669],{},"Interval ",[1115,13952,13954],{"className":13953},[1138],[1140,13955,13956],{"xmlns":1142},[1144,13957,13958,13966],{},[1147,13959,13960],{},[1150,13961,13962,13964],{},[1153,13963,11204],{},[1153,13965,1883],{},[1159,13967,13688],{"encoding":1161}," je ve výchozím nastavení ",[3470,13970,13885],{}," zleva otevřený a zprava uzavřený, ",[1115,13973,13975],{"className":13974},[1138],[1140,13976,13977],{"xmlns":1142},[1144,13978,13979,14005],{},[1147,13980,13981,13983,13989,13991,14003],{},[1242,13982,1875],{"stretchy":1874},[1150,13984,13985,13987],{},[1153,13986,1343],{},[1153,13988,1883],{},[1242,13990,6896],{"separator":1121},[1150,13992,13993,13995],{},[1153,13994,1343],{},[1147,13996,13997,13999,14001],{},[1153,13998,1883],{},[1242,14000,5477],{},[1565,14002,1794],{},[1242,14004,7445],{"stretchy":1874},[1159,14006,14007],{"encoding":1161},"(c_j; c_{j+1}\\rangle"," — opačně, než jak třídy zapisujeme v této kapitole. Parametr ",[3470,14010,14011],{},"right = FALSE"," třídy obrátí na ",[1115,14014,14016],{"className":14015},[1138],[1140,14017,14018],{"xmlns":1142},[1144,14019,14020,14046],{},[1147,14021,14022,14024,14030,14032,14044],{},[1242,14023,8428],{"stretchy":1874},[1150,14025,14026,14028],{},[1153,14027,1343],{},[1153,14029,1883],{},[1242,14031,6896],{"separator":1121},[1150,14033,14034,14036],{},[1153,14035,1343],{},[1147,14037,14038,14040,14042],{},[1153,14039,1883],{},[1242,14041,5477],{},[1565,14043,1794],{},[1242,14045,1886],{"stretchy":1874},[1159,14047,14048],{"encoding":1161},"\\langle c_j; c_{j+1})",[1110,14050,14051],{},[4383,14052],{"alt":14053,"className":14054,"src":14055},"mask-ps-histogram-trideni",[1130,4387],"\u002Fwiki-assets\u002Fmask-ps-histogram-trideni.png",[1103,14057,14059,14066],{"className":14058,"dataCallout":3477},[1106,3476],[1110,14060,14062,14065],{"className":14061},[1113],[1115,14063],{"className":14064,"ariaHidden":1121},[1118,3484,1120],"Příklad: Třídění datového souboru",[1110,14067,14068],{},"Byly provedeny zkoušky životnosti nového výrobku. Datový soubor obsahuje 68 hodnot doby do poruchy (v minutách). Určete odhady charakteristik a zákona rozdělení.",[3694,14070,14072],{"className":3696,"code":14071,"language":71,"meta":1490,"style":1490},"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",[3470,14073,14074,14131,14182,14232,14283,14333,14381,14421,14431,14451,14515,14524,14554],{"__ignoreMap":1490},[1115,14075,14076,14079,14081,14083,14085,14088,14090,14093,14095,14098,14100,14103,14105,14107,14109,14111,14113,14115,14117,14120,14122,14124,14126,14129],{"class":3702,"line":10},[1115,14077,14078],{"class":3705},"x9",[1115,14080,3710],{"class":3709},[1115,14082,3835],{"class":3713},[1115,14084,1875],{"class":3717},[1115,14086,14087],{"class":3724},"101",[1115,14089,1797],{"class":3709},[1115,14091,14092],{"class":3724}," 338",[1115,14094,1797],{"class":3709},[1115,14096,14097],{"class":3724}," 150",[1115,14099,1797],{"class":3709},[1115,14101,14102],{"class":3724}," 47",[1115,14104,1797],{"class":3709},[1115,14106,9480],{"class":3724},[1115,14108,1797],{"class":3709},[1115,14110,4180],{"class":3724},[1115,14112,1797],{"class":3709},[1115,14114,3734],{"class":3724},[1115,14116,1797],{"class":3709},[1115,14118,14119],{"class":3724}," 392",[1115,14121,1797],{"class":3709},[1115,14123,9997],{"class":3724},[1115,14125,1797],{"class":3709},[1115,14127,14128],{"class":3724}," 73",[1115,14130,3737],{"class":3709},[1115,14132,14133,14136,14138,14141,14143,14146,14148,14151,14153,14155,14157,14160,14162,14165,14167,14170,14172,14175,14177,14180],{"class":3702,"line":27},[1115,14134,14135],{"class":3724},"        367",[1115,14137,1797],{"class":3709},[1115,14139,14140],{"class":3724}," 54",[1115,14142,1797],{"class":3709},[1115,14144,14145],{"class":3724}," 114",[1115,14147,1797],{"class":3709},[1115,14149,14150],{"class":3724}," 213",[1115,14152,1797],{"class":3709},[1115,14154,3752],{"class":3724},[1115,14156,1797],{"class":3709},[1115,14158,14159],{"class":3724}," 341",[1115,14161,1797],{"class":3709},[1115,14163,14164],{"class":3724}," 313",[1115,14166,1797],{"class":3709},[1115,14168,14169],{"class":3724}," 112",[1115,14171,1797],{"class":3709},[1115,14173,14174],{"class":3724}," 343",[1115,14176,1797],{"class":3709},[1115,14178,14179],{"class":3724}," 151",[1115,14181,3737],{"class":3709},[1115,14183,14184,14187,14189,14192,14194,14197,14199,14202,14204,14207,14209,14211,14213,14216,14218,14220,14222,14225,14227,14230],{"class":3702,"line":148},[1115,14185,14186],{"class":3724},"        9",[1115,14188,1797],{"class":3709},[1115,14190,14191],{"class":3724}," 160",[1115,14193,1797],{"class":3709},[1115,14195,14196],{"class":3724}," 18",[1115,14198,1797],{"class":3709},[1115,14200,14201],{"class":3724}," 113",[1115,14203,1797],{"class":3709},[1115,14205,14206],{"class":3724}," 77",[1115,14208,1797],{"class":3709},[1115,14210,3752],{"class":3724},[1115,14212,1797],{"class":3709},[1115,14214,14215],{"class":3724}," 159",[1115,14217,1797],{"class":3709},[1115,14219,3734],{"class":3724},[1115,14221,1797],{"class":3709},[1115,14223,14224],{"class":3724}," 119",[1115,14226,1797],{"class":3709},[1115,14228,14229],{"class":3724}," 130",[1115,14231,3737],{"class":3709},[1115,14233,14234,14237,14239,14242,14244,14247,14249,14251,14253,14256,14258,14261,14263,14266,14268,14271,14273,14276,14278,14281],{"class":3702,"line":111},[1115,14235,14236],{"class":3724},"        140",[1115,14238,1797],{"class":3709},[1115,14240,14241],{"class":3724}," 161",[1115,14243,1797],{"class":3709},[1115,14245,14246],{"class":3724}," 379",[1115,14248,1797],{"class":3709},[1115,14250,14140],{"class":3724},[1115,14252,1797],{"class":3709},[1115,14254,14255],{"class":3724}," 373",[1115,14257,1797],{"class":3709},[1115,14259,14260],{"class":3724}," 168",[1115,14262,1797],{"class":3709},[1115,14264,14265],{"class":3724}," 365",[1115,14267,1797],{"class":3709},[1115,14269,14270],{"class":3724}," 110",[1115,14272,1797],{"class":3709},[1115,14274,14275],{"class":3724}," 145",[1115,14277,1797],{"class":3709},[1115,14279,14280],{"class":3724}," 88",[1115,14282,3737],{"class":3709},[1115,14284,14285,14288,14290,14293,14295,14298,14300,14303,14305,14308,14310,14312,14314,14317,14319,14321,14323,14326,14328,14331],{"class":3702,"line":96},[1115,14286,14287],{"class":3724},"        74",[1115,14289,1797],{"class":3709},[1115,14291,14292],{"class":3724}," 46",[1115,14294,1797],{"class":3709},[1115,14296,14297],{"class":3724}," 246",[1115,14299,1797],{"class":3709},[1115,14301,14302],{"class":3724}," 259",[1115,14304,1797],{"class":3709},[1115,14306,14307],{"class":3724}," 19",[1115,14309,1797],{"class":3709},[1115,14311,14224],{"class":3724},[1115,14313,1797],{"class":3709},[1115,14315,14316],{"class":3724}," 48",[1115,14318,1797],{"class":3709},[1115,14320,10857],{"class":3724},[1115,14322,1797],{"class":3709},[1115,14324,14325],{"class":3724}," 163",[1115,14327,1797],{"class":3709},[1115,14329,14330],{"class":3724}," 179",[1115,14332,3737],{"class":3709},[1115,14334,14335,14338,14340,14342,14344,14347,14349,14352,14354,14357,14359,14361,14363,14365,14367,14369,14371,14374,14376,14379],{"class":3702,"line":89},[1115,14336,14337],{"class":3724},"        194",[1115,14339,1797],{"class":3709},[1115,14341,4145],{"class":3724},[1115,14343,1797],{"class":3709},[1115,14345,14346],{"class":3724}," 49",[1115,14348,1797],{"class":3709},[1115,14350,14351],{"class":3724}," 501",[1115,14353,1797],{"class":3709},[1115,14355,14356],{"class":3724}," 193",[1115,14358,1797],{"class":3709},[1115,14360,14307],{"class":3724},[1115,14362,1797],{"class":3709},[1115,14364,9997],{"class":3724},[1115,14366,1797],{"class":3709},[1115,14368,4180],{"class":3724},[1115,14370,1797],{"class":3709},[1115,14372,14373],{"class":3724}," 221",[1115,14375,1797],{"class":3709},[1115,14377,14378],{"class":3724}," 300",[1115,14380,3737],{"class":3709},[1115,14382,14383,14386,14388,14390,14392,14395,14397,14400,14402,14405,14407,14410,14412,14414,14416,14419],{"class":3702,"line":82},[1115,14384,14385],{"class":3724},"        88",[1115,14387,1797],{"class":3709},[1115,14389,3729],{"class":3724},[1115,14391,1797],{"class":3709},[1115,14393,14394],{"class":3724}," 428",[1115,14396,1797],{"class":3709},[1115,14398,14399],{"class":3724}," 249",[1115,14401,1797],{"class":3709},[1115,14403,14404],{"class":3724}," 25",[1115,14406,1797],{"class":3709},[1115,14408,14409],{"class":3724}," 209",[1115,14411,1797],{"class":3709},[1115,14413,14140],{"class":3724},[1115,14415,1797],{"class":3709},[1115,14417,14418],{"class":3724}," 91",[1115,14420,3901],{"class":3717},[1115,14422,14423,14425,14427,14429],{"class":3702,"line":75},[1115,14424,12129],{"class":3713},[1115,14426,1875],{"class":3717},[1115,14428,14078],{"class":3705},[1115,14430,3901],{"class":3717},[1115,14432,14433,14435,14437,14439,14441,14443,14445,14447,14449],{"class":3702,"line":3891},[1115,14434,11721],{"class":3713},[1115,14436,1875],{"class":3717},[1115,14438,14078],{"class":3705},[1115,14440,4601],{"class":3717},[1115,14442,4638],{"class":3709},[1115,14444,12200],{"class":3713},[1115,14446,1875],{"class":3717},[1115,14448,14078],{"class":3705},[1115,14450,3901],{"class":3717},[1115,14452,14453,14456,14458,14461,14463,14465,14467,14470,14472,14475,14477,14479,14481,14484,14486,14489,14491,14493,14495,14497,14500,14502,14504,14506,14509,14511,14513],{"class":3702,"line":72},[1115,14454,14455],{"class":3705},"y9",[1115,14457,3710],{"class":3709},[1115,14459,14460],{"class":3713}," hist",[1115,14462,1875],{"class":3717},[1115,14464,14078],{"class":3705},[1115,14466,1797],{"class":3709},[1115,14468,14469],{"class":3705}," br",[1115,14471,3797],{"class":3709},[1115,14473,14474],{"class":3713}," seq",[1115,14476,1875],{"class":3717},[1115,14478,1567],{"class":3724},[1115,14480,1797],{"class":3709},[1115,14482,14483],{"class":3724}," 550",[1115,14485,1797],{"class":3709},[1115,14487,14488],{"class":3705}," by",[1115,14490,3797],{"class":3709},[1115,14492,6244],{"class":3724},[1115,14494,1886],{"class":3717},[1115,14496,1797],{"class":3709},[1115,14498,14499],{"class":3705}," right",[1115,14501,3797],{"class":3709},[1115,14503,6337],{"class":3724},[1115,14505,1797],{"class":3709},[1115,14507,14508],{"class":3705}," plot",[1115,14510,3797],{"class":3709},[1115,14512,6337],{"class":3724},[1115,14514,3901],{"class":3717},[1115,14516,14517,14519,14521],{"class":3702,"line":25},[1115,14518,14455],{"class":3705},[1115,14520,3914],{"class":3709},[1115,14522,14523],{"class":3705},"counts\n",[1115,14525,14526,14528,14530,14532,14534,14537,14539,14542,14544,14546,14548,14550,14552],{"class":3702,"line":65},[1115,14527,9983],{"class":3713},[1115,14529,1875],{"class":3717},[1115,14531,14455],{"class":3705},[1115,14533,3914],{"class":3709},[1115,14535,14536],{"class":3705},"counts",[1115,14538,10078],{"class":3709},[1115,14540,14541],{"class":3713}," length",[1115,14543,1875],{"class":3717},[1115,14545,14078],{"class":3705},[1115,14547,1886],{"class":3717},[1115,14549,1797],{"class":3709},[1115,14551,10857],{"class":3724},[1115,14553,3901],{"class":3717},[1115,14555,14556,14558,14560,14562,14564,14566,14568,14570],{"class":3702,"line":63},[1115,14557,12140],{"class":3713},[1115,14559,1875],{"class":3717},[1115,14561,14078],{"class":3705},[1115,14563,12179],{"class":3717},[1115,14565,12162],{"class":3713},[1115,14567,1875],{"class":3717},[1115,14569,14078],{"class":3705},[1115,14571,3901],{"class":3717},[3694,14573,14576],{"className":14574,"code":14575,"language":3923,"meta":1490},[3921],"[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",[3470,14577,14575],{"__ignoreMap":1490},[1110,14579,14580,14581,14609],{},"Variační rozpětí je ",[1115,14582,14584],{"className":14583},[1138],[1140,14585,14586],{"xmlns":1142},[1144,14587,14588,14606],{},[1147,14589,14590,14592,14594,14597,14599,14601,14603],{},[1153,14591,1260],{},[1242,14593,1982],{},[1565,14595,14596],{},"501",[1242,14598,3064],{},[1565,14600,1589],{},[1242,14602,1982],{},[1565,14604,14605],{},"499",[1159,14607,14608],{"encoding":1161},"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:",[1194,14611,14612,14708],{},[1197,14613,14614],{},[1200,14615,14616,14631,14650,14669,14688],{},[1203,14617,14618],{},[1115,14619,14621],{"className":14620},[1138],[1140,14622,14623],{"xmlns":1142},[1144,14624,14625,14629],{},[1147,14626,14627],{},[1153,14628,1883],{},[1159,14630,1883],{"encoding":1161},[1203,14632,14633],{},[1115,14634,14636],{"className":14635},[1138],[1140,14637,14638],{"xmlns":1142},[1144,14639,14640,14648],{},[1147,14641,14642],{},[1150,14643,14644,14646],{},[1153,14645,11204],{},[1153,14647,1883],{},[1159,14649,13688],{"encoding":1161},[1203,14651,14652],{},[1115,14653,14655],{"className":14654},[1138],[1140,14656,14657],{"xmlns":1142},[1144,14658,14659,14667],{},[1147,14660,14661],{},[1150,14662,14663,14665],{},[1153,14664,8928],{},[1153,14666,1883],{},[1159,14668,13768],{"encoding":1161},[1203,14670,14671],{},[1115,14672,14674],{"className":14673},[1138],[1140,14675,14676],{"xmlns":1142},[1144,14677,14678,14686],{},[1147,14679,14680],{},[1150,14681,14682,14684],{},[1153,14683,6773],{},[1153,14685,1883],{},[1159,14687,13789],{"encoding":1161},[1203,14689,14690],{},[1115,14691,14693],{"className":14692},[1138],[1140,14694,14695],{"xmlns":1142},[1144,14696,14697,14705],{},[1147,14698,14699],{},[1150,14700,14701,14703],{},[1153,14702,1110],{},[1153,14704,1883],{},[1159,14706,14707],{"encoding":1161},"p_j",[1210,14709,14710,14725,14740,14755,14768,14783,14798,14812,14827,14841,14856],{},[1200,14711,14712,14714,14717,14719,14722],{},[1215,14713,1794],{},[1215,14715,14716],{},"⟨0; 50)",[1215,14718,4058],{},[1215,14720,14721],{},"19",[1215,14723,14724],{},"0,279",[1200,14726,14727,14729,14732,14735,14737],{},[1215,14728,1589],{},[1215,14730,14731],{},"⟨50; 100)",[1215,14733,14734],{},"75",[1215,14736,2255],{},[1215,14738,14739],{},"0,162",[1200,14741,14742,14744,14747,14750,14752],{},[1215,14743,3592],{},[1215,14745,14746],{},"⟨100; 150)",[1215,14748,14749],{},"125",[1215,14751,9036],{},[1215,14753,14754],{},"0,147",[1200,14756,14757,14759,14762,14764,14766],{},[1215,14758,3542],{},[1215,14760,14761],{},"⟨150; 200)",[1215,14763,7481],{},[1215,14765,9036],{},[1215,14767,14754],{},[1200,14769,14770,14772,14775,14778,14780],{},[1215,14771,9929],{},[1215,14773,14774],{},"⟨200; 250)",[1215,14776,14777],{},"225",[1215,14779,9929],{},[1215,14781,14782],{},"0,074",[1200,14784,14785,14787,14790,14793,14795],{},[1215,14786,3964],{},[1215,14788,14789],{},"⟨250; 300)",[1215,14791,14792],{},"275",[1215,14794,1794],{},[1215,14796,14797],{},"0,015",[1200,14799,14800,14802,14805,14808,14810],{},[1215,14801,13332],{},[1215,14803,14804],{},"⟨300; 350)",[1215,14806,14807],{},"325",[1215,14809,9929],{},[1215,14811,14782],{},[1200,14813,14814,14817,14820,14823,14825],{},[1215,14815,14816],{},"8",[1215,14818,14819],{},"⟨350; 400)",[1215,14821,14822],{},"375",[1215,14824,9929],{},[1215,14826,14782],{},[1200,14828,14829,14831,14834,14837,14839],{},[1215,14830,3595],{},[1215,14832,14833],{},"⟨400; 450)",[1215,14835,14836],{},"425",[1215,14838,1794],{},[1215,14840,14797],{},[1200,14842,14843,14845,14848,14851,14853],{},[1215,14844,9036],{},[1215,14846,14847],{},"⟨450; 500)",[1215,14849,14850],{},"475",[1215,14852,1567],{},[1215,14854,14855],{},"0,000",[1200,14857,14858,14860,14863,14866,14868],{},[1215,14859,2255],{},[1215,14861,14862],{},"⟨500; ∞)",[1215,14864,14865],{},"525",[1215,14867,1794],{},[1215,14869,14797],{},[1110,14871,14872,14873,14890,14891,14908,14909,1346,14932,1346,14960,14979,14980,1346,15003,15022],{},"Asi 27,9 % výrobků vydrželo méně než 50 minut, jen asi 1,5 % mezi 250 a 300 minutami. Charakteristiky spočtené ze středů tříd ",[1115,14874,14876],{"className":14875},[1138],[1140,14877,14878],{"xmlns":1142},[1144,14879,14880,14888],{},[1147,14881,14882],{},[1150,14883,14884,14886],{},[1153,14885,8928],{},[1153,14887,1883],{},[1159,14889,13768],{"encoding":1161}," (vážený průměr a rozptyl se střední hodnotou nahrazenou ",[1115,14892,14894],{"className":14893},[1138],[1140,14895,14896],{"xmlns":1142},[1144,14897,14898,14906],{},[1147,14899,14900],{},[1150,14901,14902,14904],{},[1153,14903,8928],{},[1153,14905,1883],{},[1159,14907,13768],{"encoding":1161},") vycházejí ",[1115,14910,14912],{"className":14911},[1138],[1140,14913,14914],{"xmlns":1142},[1144,14915,14916,14929],{},[1147,14917,14918,14924,14926],{},[1236,14919,14920,14922],{"accent":1121},[1153,14921,1240],{},[1242,14923,1244],{},[1242,14925,9443],{},[1565,14927,14928],{},"149,26",[1159,14930,14931],{"encoding":1161},"\\bar{x} \\approx 149{,}26",[1115,14933,14935],{"className":14934},[1138],[1140,14936,14937],{"xmlns":1142},[1144,14938,14939,14957],{},[1147,14940,14941,14947,14949,14952,14954],{},[1582,14942,14943,14945],{},[1153,14944,1291],{},[1565,14946,1589],{},[1242,14948,9443],{},[1565,14950,14951],{},"15",[2909,14953,2911],{},[1565,14955,14956],{},"484,5",[1159,14958,14959],{"encoding":1161},"s^2 \\approx 15\\,484{,}5",[1115,14961,14963],{"className":14962},[1138],[1140,14964,14965],{"xmlns":1142},[1144,14966,14967,14976],{},[1147,14968,14969,14971,14973],{},[1153,14970,1291],{},[1242,14972,9443],{},[1565,14974,14975],{},"124,44",[1159,14977,14978],{"encoding":1161},"s \\approx 124{,}44"," — blízko hodnotám ",[1115,14981,14983],{"className":14982},[1138],[1140,14984,14985],{"xmlns":1142},[1144,14986,14987,15000],{},[1147,14988,14989,14995,14997],{},[1236,14990,14991,14993],{"accent":1121},[1153,14992,1240],{},[1242,14994,1244],{},[1242,14996,1982],{},[1565,14998,14999],{},"145,44",[1159,15001,15002],{"encoding":1161},"\\bar{x}=145{,}44",[1115,15004,15006],{"className":15005},[1138],[1140,15007,15008],{"xmlns":1142},[1144,15009,15010,15019],{},[1147,15011,15012,15014,15016],{},[1153,15013,1291],{},[1242,15015,1982],{},[1565,15017,15018],{},"126,13",[1159,15020,15021],{"encoding":1161},"s=126{,}13"," spočteným přímo z nerozdělených dat; malý rozdíl vzniká tím, že třídění nahrazuje skutečné hodnoty středy tříd.",[1110,15024,15025,15026,15029,15030,15066,15067,15085,15086,15100,15101,15127,15128,15130,15131,4866],{},"Tvar histogramu — vysoká četnost u krátkých dob, rychlý pokles — odpovídá ",[1540,15027,15028],{},"exponenciálnímu rozdělení",", které se pro dobu do poruchy používá nejčastěji. Jeho hustota je ",[1115,15031,15033],{"className":15032},[1138],[1140,15034,15035],{"xmlns":1142},[1144,15036,15037,15063],{},[1147,15038,15039,15041,15043,15045,15047,15049,15051],{},[1153,15040,6773],{},[1242,15042,1875],{"stretchy":1874},[1153,15044,1240],{},[1242,15046,1886],{"stretchy":1874},[1242,15048,1982],{},[1153,15050,9715],{},[1582,15052,15053,15055],{},[1153,15054,8595],{},[1147,15056,15057,15059,15061],{},[1242,15058,3064],{},[1153,15060,9715],{},[1153,15062,1240],{},[1159,15064,15065],{"encoding":1161},"f(x) = \\lambda e^{-\\lambda x}"," pro ",[1115,15068,15070],{"className":15069},[1138],[1140,15071,15072],{"xmlns":1142},[1144,15073,15074,15082],{},[1147,15075,15076,15078,15080],{},[1153,15077,1240],{},[1242,15079,3351],{},[1565,15081,1567],{},[1159,15083,15084],{"encoding":1161},"x \\ge 0",", s parametrem ",[1115,15087,15089],{"className":15088},[1138],[1140,15090,15091],{"xmlns":1142},[1144,15092,15093,15097],{},[1147,15094,15095],{},[1153,15096,9715],{},[1159,15098,15099],{"encoding":1161},"\\lambda"," odhadnutým jako ",[1115,15102,15104],{"className":15103},[1138],[1140,15105,15106],{"xmlns":1142},[1144,15107,15108,15124],{},[1147,15109,15110,15112,15114,15116,15118],{},[1153,15111,9715],{},[1242,15113,1982],{},[1565,15115,1794],{},[1153,15117,4604],{"mathvariant":2121},[1236,15119,15120,15122],{"accent":1121},[1153,15121,1240],{},[1242,15123,1244],{},[1159,15125,15126],{"encoding":1161},"\\lambda = 1\u002F\\bar{x}"," (v R je ",[3470,15129,9882],{}," parametrem ",[3470,15132,15133],{},"dexp()",[3694,15135,15137],{"className":3696,"code":15136,"language":71,"meta":1490,"style":1490},"rate9 \u003C- 1 \u002F mean(x9)\nrate9\n",[3470,15138,15139,15158],{"__ignoreMap":1490},[1115,15140,15141,15144,15146,15148,15150,15152,15154,15156],{"class":3702,"line":10},[1115,15142,15143],{"class":3705},"rate9",[1115,15145,3710],{"class":3709},[1115,15147,4641],{"class":3724},[1115,15149,10078],{"class":3709},[1115,15151,9234],{"class":3713},[1115,15153,1875],{"class":3717},[1115,15155,14078],{"class":3705},[1115,15157,3901],{"class":3717},[1115,15159,15160],{"class":3702,"line":27},[1115,15161,15162],{"class":3705},"rate9\n",[3694,15164,15167],{"className":15165,"code":15166,"language":3923,"meta":1490},[3921],"[1] 0.006875632\n",[3470,15168,15166],{"__ignoreMap":1490},[1110,15170,15171],{},[4383,15172],{"alt":15173,"className":15174,"src":15175},"mask-ps-hustota-fit",[1130,4387],"\u002Fwiki-assets\u002Fmask-ps-hustota-fit.png",[1110,15177,15178,15179,1669],{},"Proložená křivka dobře sleduje tvar sloupců. Zda data odpovídají exponenciálnímu rozdělení formálně, posuzuje test dobré shody popsaný v ",[1127,15180,6606],{"className":15181,"dataFsResolvedFilePath":1721,"href":1722},[1130],[1103,15183,15185,15192],{"className":15184,"dataCallout":3477},[1106,3476],[1110,15186,15188,15191],{"className":15187},[1113],[1115,15189],{"className":15190,"ariaHidden":1121},[1118,3484,1120],"Příklad: Doba života výrobku",[1110,15193,15194],{},"Sledováním doby života výrobku bylo naměřeno 50 hodnot (v minutách). Určete empirické charakteristiky, roztřiďte datový soubor a nakreslete histogram četností.",[3694,15196,15198],{"className":3696,"code":15197,"language":71,"meta":1490,"style":1490},"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",[3470,15199,15200,15261,15312,15363,15414,15466,15476,15502,15522,15580,15589,15597],{"__ignoreMap":1490},[1115,15201,15202,15205,15207,15209,15211,15214,15216,15219,15221,15224,15226,15229,15231,15234,15236,15239,15241,15244,15246,15249,15251,15254,15256,15259],{"class":3702,"line":10},[1115,15203,15204],{"class":3705},"x5",[1115,15206,3710],{"class":3709},[1115,15208,3835],{"class":3713},[1115,15210,1875],{"class":3717},[1115,15212,15213],{"class":3724},"63",[1115,15215,1797],{"class":3709},[1115,15217,15218],{"class":3724}," 156",[1115,15220,1797],{"class":3709},[1115,15222,15223],{"class":3724}," 184",[1115,15225,1797],{"class":3709},[1115,15227,15228],{"class":3724}," 786",[1115,15230,1797],{"class":3709},[1115,15232,15233],{"class":3724}," 822",[1115,15235,1797],{"class":3709},[1115,15237,15238],{"class":3724}," 278",[1115,15240,1797],{"class":3709},[1115,15242,15243],{"class":3724}," 15",[1115,15245,1797],{"class":3709},[1115,15247,15248],{"class":3724}," 561",[1115,15250,1797],{"class":3709},[1115,15252,15253],{"class":3724}," 229",[1115,15255,1797],{"class":3709},[1115,15257,15258],{"class":3724}," 8",[1115,15260,3737],{"class":3709},[1115,15262,15263,15266,15268,15271,15273,15275,15277,15280,15282,15285,15287,15290,15292,15295,15297,15300,15302,15305,15307,15310],{"class":3702,"line":27},[1115,15264,15265],{"class":3724},"        4",[1115,15267,1797],{"class":3709},[1115,15269,15270],{"class":3724}," 35",[1115,15272,1797],{"class":3709},[1115,15274,14128],{"class":3724},[1115,15276,1797],{"class":3709},[1115,15278,15279],{"class":3724}," 203",[1115,15281,1797],{"class":3709},[1115,15283,15284],{"class":3724}," 178",[1115,15286,1797],{"class":3709},[1115,15288,15289],{"class":3724}," 323",[1115,15291,1797],{"class":3709},[1115,15293,15294],{"class":3724}," 275",[1115,15296,1797],{"class":3709},[1115,15298,15299],{"class":3724}," 176",[1115,15301,1797],{"class":3709},[1115,15303,15304],{"class":3724}," 427",[1115,15306,1797],{"class":3709},[1115,15308,15309],{"class":3724}," 196",[1115,15311,3737],{"class":3709},[1115,15313,15314,15317,15319,15322,15324,15327,15329,15332,15334,15337,15339,15342,15344,15347,15349,15351,15353,15356,15358,15361],{"class":3702,"line":148},[1115,15315,15316],{"class":3724},"        415",[1115,15318,1797],{"class":3709},[1115,15320,15321],{"class":3724}," 140",[1115,15323,1797],{"class":3709},[1115,15325,15326],{"class":3724}," 17",[1115,15328,1797],{"class":3709},[1115,15330,15331],{"class":3724}," 293",[1115,15333,1797],{"class":3709},[1115,15335,15336],{"class":3724}," 991",[1115,15338,1797],{"class":3709},[1115,15340,15341],{"class":3724}," 100",[1115,15343,1797],{"class":3709},[1115,15345,15346],{"class":3724}," 189",[1115,15348,1797],{"class":3709},[1115,15350,15299],{"class":3724},[1115,15352,1797],{"class":3709},[1115,15354,15355],{"class":3724}," 672",[1115,15357,1797],{"class":3709},[1115,15359,15360],{"class":3724}," 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1050",[1115,15553,1797],{"class":3709},[1115,15555,14488],{"class":3705},[1115,15557,3797],{"class":3709},[1115,15559,14097],{"class":3724},[1115,15561,1886],{"class":3717},[1115,15563,1797],{"class":3709},[1115,15565,14499],{"class":3705},[1115,15567,3797],{"class":3709},[1115,15569,6337],{"class":3724},[1115,15571,1797],{"class":3709},[1115,15573,14508],{"class":3705},[1115,15575,3797],{"class":3709},[1115,15577,6337],{"class":3724},[1115,15579,3901],{"class":3717},[1115,15581,15582,15584,15586],{"class":3702,"line":72},[1115,15583,15526],{"class":3705},[1115,15585,3914],{"class":3709},[1115,15587,15588],{"class":3705},"mids\n",[1115,15590,15591,15593,15595],{"class":3702,"line":25},[1115,15592,15526],{"class":3705},[1115,15594,3914],{"class":3709},[1115,15596,14523],{"class":3705},[1115,15598,15599,15601,15603,15605,15607,15609,15611,15613,15615,15617,15619,15621,15623],{"class":3702,"line":65},[1115,15600,9983],{"class":3713},[1115,15602,1875],{"class":3717},[1115,15604,15526],{"class":3705},[1115,15606,3914],{"class":3709},[1115,15608,14536],{"class":3705},[1115,15610,10078],{"class":3709},[1115,15612,14541],{"class":3713},[1115,15614,1875],{"class":3717},[1115,15616,15204],{"class":3705},[1115,15618,1886],{"class":3717},[1115,15620,1797],{"class":3709},[1115,15622,10857],{"class":3724},[1115,15624,3901],{"class":3717},[3694,15626,15629],{"className":15627,"code":15628,"language":3923,"meta":1490},[3921],"[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",[3470,15630,15628],{"__ignoreMap":1490},[1110,15632,15633],{},"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.",[1189,15635,6407],{"id":6406},[1436,15637,15638,15656,15757,15825],{},[1439,15639,15640,1654,15643,15646,15647,15650,15651,15653,15654,1669],{},[1540,15641,15642],{},"Výchozí typ kvantilu v R.",[3470,15644,15645],{},"quantile()"," bez argumentu ",[3470,15648,15649],{},"type"," používá jiný výpočetní vzorec (",[3470,15652,12293],{},") než ruční postup v této kapitole — u některých souborů se hodnoty liší. Pro shodu s ručním výpočtem zadávejte ",[3470,15655,12289],{},[1439,15657,15658,15663,15664,15666,15667,15702,15703,15738,15739,15756],{},[1540,15659,15660,15661,1669],{},"Výchozí ohraničení tříd v ",[3470,15662,13885],{}," Bez ",[3470,15665,14011],{}," jsou třídy zprava uzavřené, ",[1115,15668,15670],{"className":15669},[1138],[1140,15671,15672],{"xmlns":1142},[1144,15673,15674,15700],{},[1147,15675,15676,15678,15684,15686,15698],{},[1242,15677,1875],{"stretchy":1874},[1150,15679,15680,15682],{},[1153,15681,1343],{},[1153,15683,1883],{},[1242,15685,6896],{"separator":1121},[1150,15687,15688,15690],{},[1153,15689,1343],{},[1147,15691,15692,15694,15696],{},[1153,15693,1883],{},[1242,15695,5477],{},[1565,15697,1794],{},[1242,15699,7445],{"stretchy":1874},[1159,15701,14007],{"encoding":1161}," — opačně než konvence ",[1115,15704,15706],{"className":15705},[1138],[1140,15707,15708],{"xmlns":1142},[1144,15709,15710,15736],{},[1147,15711,15712,15714,15720,15722,15734],{},[1242,15713,8428],{"stretchy":1874},[1150,15715,15716,15718],{},[1153,15717,1343],{},[1153,15719,1883],{},[1242,15721,6896],{"separator":1121},[1150,15723,15724,15726],{},[1153,15725,1343],{},[1147,15727,15728,15730,15732],{},[1153,15729,1883],{},[1242,15731,5477],{},[1565,15733,1794],{},[1242,15735,1886],{"stretchy":1874},[1159,15737,14048],{"encoding":1161}," použitá v tabulkách výše. Hodnota ležící přesně na hranici pak spadne do jiné třídy a četnosti ",[1115,15740,15742],{"className":15741},[1138],[1140,15743,15744],{"xmlns":1142},[1144,15745,15746,15754],{},[1147,15747,15748],{},[1150,15749,15750,15752],{},[1153,15751,6773],{},[1153,15753,1883],{},[1159,15755,13789],{"encoding":1161}," vyjdou jinak.",[1439,15758,15759,1654,15762,15780,15781,15794,15795,9051,15808,1669],{},[1540,15760,15761],{},"Rozptyl vs. směrodatná odchylka.",[1115,15763,15765],{"className":15764},[1138],[1140,15766,15767],{"xmlns":1142},[1144,15768,15769,15777],{},[1147,15770,15771],{},[1582,15772,15773,15775],{},[1153,15774,1291],{},[1565,15776,1589],{},[1159,15778,15779],{"encoding":1161},"s^2"," se udává v jednotkách znaku na druhou, ",[1115,15782,15784],{"className":15783},[1138],[1140,15785,15786],{"xmlns":1142},[1144,15787,15788,15792],{},[1147,15789,15790],{},[1153,15791,1291],{},[1159,15793,1291],{"encoding":1161}," ve stejných jednotkách jako data — pro interpretaci (např. „kolísání kolem průměru\") patří vždy ",[1115,15796,15798],{"className":15797},[1138],[1140,15799,15800],{"xmlns":1142},[1144,15801,15802,15806],{},[1147,15803,15804],{},[1153,15805,1291],{},[1159,15807,1291],{"encoding":1161},[1115,15809,15811],{"className":15810},[1138],[1140,15812,15813],{"xmlns":1142},[1144,15814,15815,15823],{},[1147,15816,15817],{},[1582,15818,15819,15821],{},[1153,15820,1291],{},[1565,15822,1589],{},[1159,15824,15779],{"encoding":1161},[1439,15826,15827,15830],{},[1540,15828,15829],{},"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.",[1189,15832,1434],{"id":1433},[1436,15834,15835,15840,15845,15850,15855,15860,15865],{},[1439,15836,15837],{},[1127,15838,1133],{"className":15839,"dataFsResolvedFilePath":1131,"href":1132},[1130],[1439,15841,15842],{},[1127,15843,6622],{"className":15844,"dataFsResolvedFilePath":6620,"href":6621},[1130],[1439,15846,15847],{},[1127,15848,6606],{"className":15849,"dataFsResolvedFilePath":1721,"href":1722},[1130],[1439,15851,15852],{},[1127,15853,6630],{"className":15854,"dataFsResolvedFilePath":6628,"href":6629},[1130],[1439,15856,15857],{},[1127,15858,1515],{"className":15859,"dataFsResolvedFilePath":11093,"href":11094},[1130],[1439,15861,15862],{},[1127,15863,1222],{"className":15864,"dataFsResolvedFilePath":1220,"href":1221},[1130],[1439,15866,15867],{},[1127,15868,6641],{"className":15869,"dataFsResolvedFilePath":1454,"href":1455},[1130],[1189,15871,1459],{"id":934},[1110,15873,1462,15874,1467],{},[1464,15875,1466],{},[6649,15877,15878],{},"html pre.shiki code .sP4rz, 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příkladům\u002F9.txt","topics\u002Fpopisna-statistika",[23,67,886,624,732,71],"S7Mr0W_asypsa_HGrO-Qlzv4HzQm_pC2nyjSomTKbnk",{"id":15902,"title":6630,"body":15903,"course":23,"courses":1495,"created":1496,"description":1490,"extension":1497,"meta":20594,"navigation":1499,"path":20595,"seo":20596,"sources":20597,"stem":20600,"tags":20601,"type":6670,"updated":1496,"__hash__":20602},"topics\u002Ftopics\u002Fregresni-a-korelacni-analyza.md",{"type":1096,"value":15904,"toc":20567},[15905,15908,16136,16138,16206,16212,16215,16293,16304,16308,16527,16534,16594,16597,16604,16626,16630,16636,16698,16748,16753,16764,16876,16882,17012,17015,17053,17059,17178,17195,17322,17328,17372,17376,17389,17417,17423,17480,17507,17513,17569,17589,17595,17616,17623,17626,17865,17869,17981,18301,18358,18400,18407,18411,18417,18541,18547,18596,18600,18606,18667,18673,18712,18756,18762,18855,18859,18865,18907,18913,18973,19084,19190,19194,19199,19277,19312,19343,19403,19440,19447,19510,19513,19534,19540,19570,19613,19617,19634,19754,19758,19780,19784,19795,19896,19900,19972,19979,19982,19985,19996,20063,20066,20070,20094,20097,20100,20304,20313,20343,20345,20480,20493,20506,20519,20521,20558,20560,20564],[1099,15906,6630],{"id":15907},"regresní-a-korelační-analýza",[1103,15909,15911,15917],{"className":15910,"dataCallout":1525},[1106,1524],[1110,15912,15914,1533],{"className":15913},[1113],[1115,15915],{"className":15916,"ariaHidden":1121},[1118,1532,1120],[1436,15918,15919,15957,16004,16082,16097,16103],{},[1439,15920,15921,15924,15925,15938,15939,15952,15953,15956],{},[1540,15922,15923],{},"Regresní analýza"," zkoumá jednostrannou závislost vysvětlované proměnné ",[1115,15926,15928],{"className":15927},[1138],[1140,15929,15930],{"xmlns":1142},[1144,15931,15932,15936],{},[1147,15933,15934],{},[1153,15935,7132],{},[1159,15937,7132],{"encoding":1161}," na vysvětlujících proměnných ",[1115,15940,15942],{"className":15941},[1138],[1140,15943,15944],{"xmlns":1142},[1144,15945,15946,15950],{},[1147,15947,15948],{},[1153,15949,1240],{},[1159,15951,1240],{"encoding":1161}," (příčina → následek); ",[1540,15954,15955],{},"korelační analýza"," měří intenzitu (těsnost) vzájemné závislosti.",[1439,15958,15959,15960,15963,15964,1669],{},"Parametry regresní funkce se odhadují ",[1540,15961,15962],{},"metodou nejmenších čtverců"," — minimalizací součtu čtverců reziduí ",[1115,15965,15967],{"className":15966},[1138],[1140,15968,15969],{"xmlns":1142},[1144,15970,15971,16001],{},[1147,15972,15973,15975,15977,15983,15985,15995],{},[1242,15974,1988],{},[1242,15976,1875],{"stretchy":1874},[1150,15978,15979,15981],{},[1153,15980,7132],{},[1153,15982,1878],{},[1242,15984,3064],{},[1150,15986,15987,15993],{},[1236,15988,15989,15991],{"accent":1121},[1153,15990,7132],{},[1242,15992,2729],{},[1153,15994,1878],{},[1582,15996,15997,15999],{},[1242,15998,1886],{"stretchy":1874},[1565,16000,1589],{},[1159,16002,16003],{"encoding":1161},"\\sum(y_i-\\hat y_i)^2",[1439,16005,16006,16007,1654,16010,16028,16029,1654,16032,16056,16057,1654,16060,1669],{},"Kvalitu fitu měří ",[1540,16008,16009],{},"index determinace",[1115,16011,16013],{"className":16012},[1138],[1140,16014,16015],{"xmlns":1142},[1144,16016,16017,16025],{},[1147,16018,16019],{},[1582,16020,16021,16023],{},[1153,16022,1260],{},[1565,16024,1589],{},[1159,16026,16027],{"encoding":1161},"R^2","; obecnou těsnost závislosti ",[1540,16030,16031],{},"index korelace",[1115,16033,16035],{"className":16034},[1138],[1140,16036,16037],{"xmlns":1142},[1144,16038,16039,16053],{},[1147,16040,16041,16043,16045],{},[1153,16042,11204],{},[1242,16044,1982],{},[4453,16046,16047],{},[1582,16048,16049,16051],{},[1153,16050,1260],{},[1565,16052,1589],{},[1159,16054,16055],{"encoding":1161},"I=\\sqrt{R^2}",", který je pro regresní přímku roven ",[1540,16058,16059],{},"koeficientu korelace",[1115,16061,16063],{"className":16062},[1138],[1140,16064,16065],{"xmlns":1142},[1144,16066,16067,16079],{},[1147,16068,16069],{},[1150,16070,16071,16073],{},[1153,16072,71],{},[1147,16074,16075,16077],{},[1153,16076,1240],{},[1153,16078,7132],{},[1159,16080,16081],{"encoding":1161},"r_{xy}",[1439,16083,16084,16085,16088,16089,16092,16093,16096],{},"Když přímka nestačí, volí se ",[1540,16086,16087],{},"parabolická, polynomická, hyperbolická nebo logaritmická"," regrese (stále lineární v parametrech, odhad metodou nejmenších čtverců) nebo ",[1540,16090,16091],{},"exponenciální"," regrese (nelineární v parametrech, odhad přes ",[3470,16094,16095],{},"nls2",").",[1439,16098,16099,16102],{},[1540,16100,16101],{},"Vícenásobná regrese"," rozšiřuje model o více regresorů; vyžaduje výběr proměnných (ENTER\u002Fstepwise), ověření šesti předpokladů modelu a kontrolu multikolinearity přes VIF.",[1439,16104,16105,16106,1346,16109,1346,16112,1346,16115,1346,16118,1346,16121,1346,16124,1346,16127,1346,16130,1346,16133,1669],{},"V R: ",[3470,16107,16108],{},"lm()",[3470,16110,16111],{},"nls2()",[3470,16113,16114],{},"summary()",[3470,16116,16117],{},"confint()",[3470,16119,16120],{},"predict()",[3470,16122,16123],{},"step()",[3470,16125,16126],{},"car::vif()",[3470,16128,16129],{},"lmtest::dwtest()",[3470,16131,16132],{},"whitestrap::white_test()",[3470,16134,16135],{},"shapiro.test()",[1189,16137,11241],{"id":11240},[1110,16139,16140,16143,16144,1163,16157,16170,16171,16173,16174,16187,16188,16201,16202,16205],{},[1127,16141,1133],{"className":16142,"dataFsResolvedFilePath":1131,"href":1132},[1130]," pracuje se dvěma znaky ",[1115,16145,16147],{"className":16146},[1138],[1140,16148,16149],{"xmlns":1142},[1144,16150,16151,16155],{},[1147,16152,16153],{},[1153,16154,1240],{},[1159,16156,1240],{"encoding":1161},[1115,16158,16160],{"className":16159},[1138],[1140,16161,16162],{"xmlns":1142},[1144,16163,16164,16168],{},[1147,16165,16166],{},[1153,16167,7132],{},[1159,16169,7132],{"encoding":1161}," zjištěnými na stejných jednotkách. ",[1540,16172,15923],{}," se zabývá jednostrannými závislostmi, kdy proti sobě stojí vysvětlující (nezávisle) proměnná ",[1115,16175,16177],{"className":16176},[1138],[1140,16178,16179],{"xmlns":1142},[1144,16180,16181,16185],{},[1147,16182,16183],{},[1153,16184,1240],{},[1159,16186,1240],{"encoding":1161}," v úloze příčiny a vysvětlovaná (závisle) proměnná ",[1115,16189,16191],{"className":16190},[1138],[1140,16192,16193],{"xmlns":1142},[1144,16194,16195,16199],{},[1147,16196,16197],{},[1153,16198,7132],{},[1159,16200,7132],{"encoding":1161}," v úloze následku. ",[1540,16203,16204],{},"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.",[1110,16207,16208,16209,16096],{},"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 (",[1540,16210,16211],{},"regresní funkce",[1110,16213,16214],{},"Druh regresní analýzy určuje struktura datového souboru:",[1436,16216,16217,16254],{},[1439,16218,16219,16222,16223,16236,16237,16250,16251,1797],{},[1540,16220,16221],{},"dvourozměrný datový soubor"," (jedna ",[1115,16224,16226],{"className":16225},[1138],[1140,16227,16228],{"xmlns":1142},[1144,16229,16230,16234],{},[1147,16231,16232],{},[1153,16233,1240],{},[1159,16235,1240],{"encoding":1161},", jedna ",[1115,16238,16240],{"className":16239},[1138],[1140,16241,16242],{"xmlns":1142},[1144,16243,16244,16248],{},[1147,16245,16246],{},[1153,16247,7132],{},[1159,16249,7132],{"encoding":1161},") → ",[1540,16252,16253],{},"regresní analýza dvou proměnných",[1439,16255,16256,16259,16260,16250,16290,1669],{},[1540,16257,16258],{},"vícerozměrný datový soubor"," (více ",[1115,16261,16263],{"className":16262},[1138],[1140,16264,16265],{"xmlns":1142},[1144,16266,16267,16287],{},[1147,16268,16269,16275,16277,16279,16281],{},[1150,16270,16271,16273],{},[1153,16272,1240],{},[1565,16274,1794],{},[1242,16276,1797],{"separator":1121},[1242,16278,1800],{},[1242,16280,1797],{"separator":1121},[1150,16282,16283,16285],{},[1153,16284,1240],{},[1153,16286,1110],{},[1159,16288,16289],{"encoding":1161},"x_1,\\dots,x_p",[1540,16291,16292],{},"vícenásobná regresní analýza",[1110,16294,16295,16296,16299,16300,16303],{},"Volba konkrétní regresní funkce by měla vycházet jak z ",[1540,16297,16298],{},"ekonomické teorie"," (ta napovídá, zda závislost roste, nebo klesá, zda je přímková, nebo zakřivená), tak z ",[1540,16301,16302],{},"grafické a matematicko-statistické analýzy"," dat — oba přístupy je vhodné kombinovat.",[1189,16305,16307],{"id":16306},"metoda-nejmenších-čtverců","Metoda nejmenších čtverců",[1110,16309,16310,16311,1654,16314,16368,16369,16387,16388,1654,16391,16447,16448,16466,16467,16484,16485,16523,16524,1669],{},"Rozlišují se ",[1540,16312,16313],{},"teoretická regresní funkce",[1115,16315,16317],{"className":16316},[1138],[1140,16318,16319],{"xmlns":1142},[1144,16320,16321,16365],{},[1147,16322,16323,16326,16328,16330,16332,16334,16336,16343,16345,16351,16353,16355,16357,16363],{},[1153,16324,16325],{},"η",[1242,16327,1982],{},[1153,16329,6773],{},[1242,16331,1875],{"stretchy":1874},[1153,16333,1240],{},[1242,16335,6896],{"separator":1121},[1150,16337,16338,16341],{},[1153,16339,16340],{},"β",[1565,16342,1567],{},[1242,16344,1797],{"separator":1121},[1150,16346,16347,16349],{},[1153,16348,16340],{},[1565,16350,1794],{},[1242,16352,1797],{"separator":1121},[1242,16354,1800],{},[1242,16356,1797],{"separator":1121},[1150,16358,16359,16361],{},[1153,16360,16340],{},[1153,16362,1110],{},[1242,16364,1886],{"stretchy":1874},[1159,16366,16367],{"encoding":1161},"\\eta = f(x;\\beta_0,\\beta_1,\\dots,\\beta_p)"," — neznámá, populační, daná neznámými parametry ",[1115,16370,16372],{"className":16371},[1138],[1140,16373,16374],{"xmlns":1142},[1144,16375,16376,16384],{},[1147,16377,16378],{},[1150,16379,16380,16382],{},[1153,16381,16340],{},[1153,16383,1878],{},[1159,16385,16386],{"encoding":1161},"\\beta_i"," — a ",[1540,16389,16390],{},"empirická regresní funkce",[1115,16392,16394],{"className":16393},[1138],[1140,16395,16396],{"xmlns":1142},[1144,16397,16398,16444],{},[1147,16399,16400,16406,16408,16410,16412,16414,16416,16422,16424,16430,16432,16434,16436,16442],{},[1236,16401,16402,16404],{"accent":1121},[1153,16403,7132],{},[1242,16405,2729],{},[1242,16407,1982],{},[1153,16409,6773],{},[1242,16411,1875],{"stretchy":1874},[1153,16413,1240],{},[1242,16415,6896],{"separator":1121},[1150,16417,16418,16420],{},[1153,16419,11507],{},[1565,16421,1567],{},[1242,16423,1797],{"separator":1121},[1150,16425,16426,16428],{},[1153,16427,11507],{},[1565,16429,1794],{},[1242,16431,1797],{"separator":1121},[1242,16433,1800],{},[1242,16435,1797],{"separator":1121},[1150,16437,16438,16440],{},[1153,16439,11507],{},[1153,16441,1110],{},[1242,16443,1886],{"stretchy":1874},[1159,16445,16446],{"encoding":1161},"\\hat y = f(x; b_0,b_1,\\dots,b_p)",", jejíž odhadnuté parametry ",[1115,16449,16451],{"className":16450},[1138],[1140,16452,16453],{"xmlns":1142},[1144,16454,16455,16463],{},[1147,16456,16457],{},[1150,16458,16459,16461],{},[1153,16460,11507],{},[1153,16462,1878],{},[1159,16464,16465],{"encoding":1161},"b_i"," jsou odhadem ",[1115,16468,16470],{"className":16469},[1138],[1140,16471,16472],{"xmlns":1142},[1144,16473,16474,16482],{},[1147,16475,16476],{},[1150,16477,16478,16480],{},[1153,16479,16340],{},[1153,16481,1878],{},[1159,16483,16386],{"encoding":1161}," vypočteným z konkrétních dat. Odchylky skutečných hodnot od empirické funkce, ",[1115,16486,16488],{"className":16487},[1138],[1140,16489,16490],{"xmlns":1142},[1144,16491,16492,16520],{},[1147,16493,16494,16500,16502,16508,16510],{},[1150,16495,16496,16498],{},[1153,16497,8595],{},[1153,16499,1878],{},[1242,16501,1982],{},[1150,16503,16504,16506],{},[1153,16505,7132],{},[1153,16507,1878],{},[1242,16509,3064],{},[1150,16511,16512,16518],{},[1236,16513,16514,16516],{"accent":1121},[1153,16515,7132],{},[1242,16517,2729],{},[1153,16519,1878],{},[1159,16521,16522],{"encoding":1161},"e_i=y_i-\\hat y_i",", se nazývají ",[1540,16525,16526],{},"rezidua",[1110,16528,16529,16530,16533],{},"Nejpoužívanější metodou odhadu parametrů je ",[1540,16531,16532],{},"metoda nejmenších čtverců (OLS)",": hledají se takové parametry, pro které je součet čtverců reziduí minimální,",[1115,16535,16537],{"className":16536},[1138],[1140,16538,16539],{"xmlns":1142,"display":1964},[1144,16540,16541,16591],{},[1147,16542,16543,16557,16559,16565,16567,16577,16583,16585,16587,16589],{},[1984,16544,16545,16547,16555],{},[1242,16546,1988],{},[1147,16548,16549,16551,16553],{},[1153,16550,1878],{},[1242,16552,1982],{},[1565,16554,1794],{},[1153,16556,1372],{},[1242,16558,1875],{"stretchy":1874},[1150,16560,16561,16563],{},[1153,16562,7132],{},[1153,16564,1878],{},[1242,16566,3064],{},[1150,16568,16569,16575],{},[1236,16570,16571,16573],{"accent":1121},[1153,16572,7132],{},[1242,16574,2729],{},[1153,16576,1878],{},[1582,16578,16579,16581],{},[1242,16580,1886],{"stretchy":1874},[1565,16582,1589],{},[1242,16584,7609],{},[1153,16586,4488],{},[1242,16588,4491],{},[1153,16590,1669],{"mathvariant":2121},[1159,16592,16593],{"encoding":1161},"\\sum_{i=1}^n (y_i - \\hat y_i)^2 \\to \\min.",[1110,16595,16596],{},"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.",[1110,16598,16599],{},[4383,16600],{"alt":16601,"className":16602,"src":16603},"mask-ra-primka-rezidua",[1130,4387],"\u002Fwiki-assets\u002Fmask-ra-primka-rezidua.png",[1110,16605,16606,16607,16625],{},"Obrázek ukazuje přesně to, co metoda minimalizuje: délky červených úseček jsou rezidua ",[1115,16608,16610],{"className":16609},[1138],[1140,16611,16612],{"xmlns":1142},[1144,16613,16614,16622],{},[1147,16615,16616],{},[1150,16617,16618,16620],{},[1153,16619,8595],{},[1153,16621,1878],{},[1159,16623,16624],{"encoding":1161},"e_i",", metoda nejmenších čtverců volí přímku tak, aby součet jejich čtverců byl nejmenší možný.",[1189,16627,16629],{"id":16628},"regresní-přímka","Regresní přímka",[1110,16631,16632,16633,1958],{},"Nejjednodušší regresní funkcí je ",[1540,16634,16635],{},"regresní přímka",[1115,16637,16639],{"className":16638},[1138],[1140,16640,16641],{"xmlns":1142,"display":1964},[1144,16642,16643,16695],{},[1147,16644,16645,16647,16649,16655,16657,16663,16665,16667,16669,16675,16677,16683,16685,16691,16693],{},[1153,16646,16325],{},[1242,16648,1982],{},[1150,16650,16651,16653],{},[1153,16652,16340],{},[1565,16654,1567],{},[1242,16656,5477],{},[1150,16658,16659,16661],{},[1153,16660,16340],{},[1565,16662,1794],{},[1153,16664,1240],{},[1242,16666,1797],{"separator":1121},[2012,16668],{"width":2014},[1236,16670,16671,16673],{"accent":1121},[1153,16672,7132],{},[1242,16674,2729],{},[1242,16676,1982],{},[1150,16678,16679,16681],{},[1153,16680,11507],{},[1565,16682,1567],{},[1242,16684,5477],{},[1150,16686,16687,16689],{},[1153,16688,11507],{},[1565,16690,1794],{},[1153,16692,1240],{},[1153,16694,1669],{"mathvariant":2121},[1159,16696,16697],{"encoding":1161},"\\eta = \\beta_0 + \\beta_1 x, \\qquad \\hat y = b_0 + b_1 x.",[1110,16699,16700,16701,16719,16720,16733,16734,16747],{},"Koeficient ",[1115,16702,16704],{"className":16703},[1138],[1140,16705,16706],{"xmlns":1142},[1144,16707,16708,16716],{},[1147,16709,16710],{},[1150,16711,16712,16714],{},[1153,16713,11507],{},[1565,16715,1794],{},[1159,16717,16718],{"encoding":1161},"b_1"," udává změnu průměru ",[1115,16721,16723],{"className":16722},[1138],[1140,16724,16725],{"xmlns":1142},[1144,16726,16727,16731],{},[1147,16728,16729],{},[1153,16730,7132],{},[1159,16732,7132],{"encoding":1161}," při jednotkové změně ",[1115,16735,16737],{"className":16736},[1138],[1140,16738,16739],{"xmlns":1142},[1144,16740,16741,16745],{},[1147,16742,16743],{},[1153,16744,1240],{},[1159,16746,1240],{"encoding":1161},"; jeho znaménko určuje, zda je závislost přímá, nebo nepřímá.",[16749,16750,16752],"h3",{"id":16751},"v-r","V R",[1110,16754,16755,16756,16759,16760,16763],{},"Vstupní data se nahrají buď ze souboru (",[3470,16757,16758],{},"d \u003C- read.table(\"data.txt\")",", případně ",[3470,16761,16762],{},"d \u003C- read.table(file.choose())","), nebo zapíší přímo jako vektory. Na šesti domácnostech sledujeme počet členů domácnosti a jejich týdenní výdaje:",[3694,16765,16767],{"className":3696,"code":16766,"language":71,"meta":1490,"style":1490},"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",[3470,16768,16769,16804,16845,16866],{"__ignoreMap":1490},[1115,16770,16771,16774,16776,16778,16780,16782,16784,16786,16788,16790,16792,16794,16796,16798,16800,16802],{"class":3702,"line":10},[1115,16772,16773],{"class":3705},"pocet_clenu",[1115,16775,3710],{"class":3709},[1115,16777,3835],{"class":3713},[1115,16779,1875],{"class":3717},[1115,16781,1794],{"class":3724},[1115,16783,1797],{"class":3709},[1115,16785,4180],{"class":3724},[1115,16787,1797],{"class":3709},[1115,16789,10857],{"class":3724},[1115,16791,1797],{"class":3709},[1115,16793,3800],{"class":3724},[1115,16795,1797],{"class":3709},[1115,16797,9997],{"class":3724},[1115,16799,1797],{"class":3709},[1115,16801,12230],{"class":3724},[1115,16803,3901],{"class":3717},[1115,16805,16806,16809,16811,16813,16815,16818,16820,16823,16825,16828,16830,16833,16835,16838,16840,16843],{"class":3702,"line":27},[1115,16807,16808],{"class":3705},"tydenni_vydaje",[1115,16810,3710],{"class":3709},[1115,16812,3835],{"class":3713},[1115,16814,1875],{"class":3717},[1115,16816,16817],{"class":3724},"490",[1115,16819,1797],{"class":3709},[1115,16821,16822],{"class":3724}," 820",[1115,16824,1797],{"class":3709},[1115,16826,16827],{"class":3724}," 1230",[1115,16829,1797],{"class":3709},[1115,16831,16832],{"class":3724}," 1570",[1115,16834,1797],{"class":3709},[1115,16836,16837],{"class":3724}," 1950",[1115,16839,1797],{"class":3709},[1115,16841,16842],{"class":3724}," 2320",[1115,16844,3901],{"class":3717},[1115,16846,16847,16849,16851,16854,16856,16858,16861,16864],{"class":3702,"line":148},[1115,16848,786],{"class":3705},[1115,16850,3710],{"class":3709},[1115,16852,16853],{"class":3713}," lm",[1115,16855,1875],{"class":3717},[1115,16857,16808],{"class":3705},[1115,16859,16860],{"class":3709}," ~",[1115,16862,16863],{"class":3705}," pocet_clenu",[1115,16865,3901],{"class":3717},[1115,16867,16868,16870,16872,16874],{"class":3702,"line":111},[1115,16869,1509],{"class":3713},[1115,16871,1875],{"class":3717},[1115,16873,786],{"class":3705},[1115,16875,3901],{"class":3717},[3694,16877,16880],{"className":16878,"code":16879,"language":3923,"meta":1490},[3921],"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",[3470,16881,16879],{"__ignoreMap":1490},[1110,16883,16884,16885,16917,16918,16921,16922,16952,16953,16983,16984,16987,16988,17011],{},"Odhadnutý model je ",[1115,16886,16888],{"className":16887},[1138],[1140,16889,16890],{"xmlns":1142},[1144,16891,16892,16914],{},[1147,16893,16894,16900,16902,16905,16907,16910,16912],{},[1236,16895,16896,16898],{"accent":1121},[1153,16897,7132],{},[1242,16899,2729],{},[1242,16901,1982],{},[1565,16903,16904],{},"108,7",[1242,16906,5477],{},[1565,16908,16909],{},"368,0",[2909,16911,2911],{},[1153,16913,1240],{},[1159,16915,16916],{"encoding":1161},"\\hat y = 108{,}7 + 368{,}0\\,x",". Sloupec ",[3470,16919,16920],{},"Pr(>|t|)"," je p-hodnota t-testu ",[1115,16923,16925],{"className":16924},[1138],[1140,16926,16927],{"xmlns":1142},[1144,16928,16929,16949],{},[1147,16930,16931,16937,16939,16945,16947],{},[1150,16932,16933,16935],{},[1153,16934,1563],{},[1565,16936,1567],{},[1242,16938,1958],{},[1150,16940,16941,16943],{},[1153,16942,16340],{},[1153,16944,1878],{},[1242,16946,1982],{},[1565,16948,1567],{},[1159,16950,16951],{"encoding":1161},"H_0:\\beta_i=0"," proti ",[1115,16954,16956],{"className":16955},[1138],[1140,16957,16958],{"xmlns":1142},[1144,16959,16960,16980],{},[1147,16961,16962,16968,16970,16976,16978],{},[1150,16963,16964,16966],{},[1153,16965,1563],{},[1565,16967,1794],{},[1242,16969,1958],{},[1150,16971,16972,16974],{},[1153,16973,16340],{},[1153,16975,1878],{},[1242,16977,10958],{"mathvariant":2121},[1565,16979,1567],{},[1159,16981,16982],{"encoding":1161},"H_1:\\beta_i\\neq0"," pro každý parametr — obě p-hodnoty jsou hluboko pod 0,05, oba parametry jsou tedy statisticky významné. ",[3470,16985,16986],{},"Multiple R-squared"," je index determinace ",[1115,16989,16991],{"className":16990},[1138],[1140,16992,16993],{"xmlns":1142},[1144,16994,16995,17008],{},[1147,16996,16997,17003,17005],{},[1582,16998,16999,17001],{},[1153,17000,1260],{},[1565,17002,1589],{},[1242,17004,1982],{},[1565,17006,17007],{},"0,9995",[1159,17009,17010],{"encoding":1161},"R^2=0{,}9995",": model vysvětluje 99,95 % rozptylu výdajů.",[1110,17013,17014],{},"Pro doplňkový přehled slouží přímé přístupové funkce:",[3694,17016,17018],{"className":3696,"code":17017,"language":71,"meta":1490,"style":1490},"coef(model)\nfitted(model)\nresiduals(model)\n",[3470,17019,17020,17031,17042],{"__ignoreMap":1490},[1115,17021,17022,17025,17027,17029],{"class":3702,"line":10},[1115,17023,17024],{"class":3713},"coef",[1115,17026,1875],{"class":3717},[1115,17028,786],{"class":3705},[1115,17030,3901],{"class":3717},[1115,17032,17033,17036,17038,17040],{"class":3702,"line":27},[1115,17034,17035],{"class":3713},"fitted",[1115,17037,1875],{"class":3717},[1115,17039,786],{"class":3705},[1115,17041,3901],{"class":3717},[1115,17043,17044,17047,17049,17051],{"class":3702,"line":148},[1115,17045,17046],{"class":3713},"residuals",[1115,17048,1875],{"class":3717},[1115,17050,786],{"class":3705},[1115,17052,3901],{"class":3717},[3694,17054,17057],{"className":17055,"code":17056,"language":3923,"meta":1490},[3921],"(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",[3470,17058,17056],{"__ignoreMap":1490},[1110,17060,17061,17064,17065,1346,17091,17094,17095,17117,17118,1346,17136,17139,17140,17177],{},[3470,17062,17063],{},"coef()"," vrací odhadnuté parametry ",[1115,17066,17068],{"className":17067},[1138],[1140,17069,17070],{"xmlns":1142},[1144,17071,17072,17088],{},[1147,17073,17074,17080,17082],{},[1150,17075,17076,17078],{},[1153,17077,11507],{},[1565,17079,1567],{},[1242,17081,1797],{"separator":1121},[1150,17083,17084,17086],{},[1153,17085,11507],{},[1565,17087,1794],{},[1159,17089,17090],{"encoding":1161},"b_0,b_1",[3470,17092,17093],{},"fitted()"," predikce ",[1115,17096,17098],{"className":17097},[1138],[1140,17099,17100],{"xmlns":1142},[1144,17101,17102,17114],{},[1147,17103,17104],{},[1150,17105,17106,17112],{},[1236,17107,17108,17110],{"accent":1121},[1153,17109,7132],{},[1242,17111,2729],{},[1153,17113,1878],{},[1159,17115,17116],{"encoding":1161},"\\hat y_i"," pro pozorované ",[1115,17119,17121],{"className":17120},[1138],[1140,17122,17123],{"xmlns":1142},[1144,17124,17125,17133],{},[1147,17126,17127],{},[1150,17128,17129,17131],{},[1153,17130,1240],{},[1153,17132,1878],{},[1159,17134,17135],{"encoding":1161},"x_i",[3470,17137,17138],{},"residuals()"," rezidua ",[1115,17141,17143],{"className":17142},[1138],[1140,17144,17145],{"xmlns":1142},[1144,17146,17147,17175],{},[1147,17148,17149,17155,17157,17163,17165],{},[1150,17150,17151,17153],{},[1153,17152,8595],{},[1153,17154,1878],{},[1242,17156,1982],{},[1150,17158,17159,17161],{},[1153,17160,7132],{},[1153,17162,1878],{},[1242,17164,3064],{},[1150,17166,17167,17173],{},[1236,17168,17169,17171],{"accent":1121},[1153,17170,7132],{},[1242,17172,2729],{},[1153,17174,1878],{},[1159,17176,16522],{"encoding":1161}," — stejná čísla, která na obrázku výše tvoří délky červených úseček.",[1110,17179,17180,17181,17194],{},"Intervaly spolehlivosti pro parametry a pro predikci v nových bodech ",[1115,17182,17184],{"className":17183},[1138],[1140,17185,17186],{"xmlns":1142},[1144,17187,17188,17192],{},[1147,17189,17190],{},[1153,17191,1240],{},[1159,17193,1240],{"encoding":1161}," (zde 7 a 8 členů domácnosti):",[3694,17196,17198],{"className":3696,"code":17197,"language":71,"meta":1490,"style":1490},"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",[3470,17199,17200,17220,17248,17287],{"__ignoreMap":1490},[1115,17201,17202,17205,17207,17209,17211,17214,17216,17218],{"class":3702,"line":10},[1115,17203,17204],{"class":3713},"confint",[1115,17206,1875],{"class":3717},[1115,17208,786],{"class":3705},[1115,17210,1797],{"class":3709},[1115,17212,17213],{"class":3705}," level",[1115,17215,3797],{"class":3709},[1115,17217,10002],{"class":3724},[1115,17219,3901],{"class":3717},[1115,17221,17222,17225,17227,17230,17232,17234,17236,17238,17240,17242,17244,17246],{"class":3702,"line":27},[1115,17223,17224],{"class":3705},"nove",[1115,17226,3710],{"class":3709},[1115,17228,17229],{"class":3713}," data.frame",[1115,17231,1875],{"class":3717},[1115,17233,16773],{"class":3705},[1115,17235,3797],{"class":3709},[1115,17237,3835],{"class":3713},[1115,17239,1875],{"class":3717},[1115,17241,13332],{"class":3724},[1115,17243,1797],{"class":3709},[1115,17245,15258],{"class":3724},[1115,17247,9496],{"class":3717},[1115,17249,17250,17253,17255,17257,17259,17262,17264,17267,17269,17272,17274,17277,17279,17281,17283,17285],{"class":3702,"line":148},[1115,17251,17252],{"class":3713},"predict",[1115,17254,1875],{"class":3717},[1115,17256,786],{"class":3705},[1115,17258,1797],{"class":3709},[1115,17260,17261],{"class":3705}," newdata",[1115,17263,3797],{"class":3709},[1115,17265,17266],{"class":3705}," nove",[1115,17268,1797],{"class":3709},[1115,17270,17271],{"class":3705}," interval",[1115,17273,3797],{"class":3709},[1115,17275,17276],{"class":3840}," \"confidence\"",[1115,17278,1797],{"class":3709},[1115,17280,17213],{"class":3705},[1115,17282,3797],{"class":3709},[1115,17284,10002],{"class":3724},[1115,17286,3901],{"class":3717},[1115,17288,17289,17291,17293,17295,17297,17299,17301,17303,17305,17307,17309,17312,17314,17316,17318,17320],{"class":3702,"line":111},[1115,17290,17252],{"class":3713},[1115,17292,1875],{"class":3717},[1115,17294,786],{"class":3705},[1115,17296,1797],{"class":3709},[1115,17298,17261],{"class":3705},[1115,17300,3797],{"class":3709},[1115,17302,17266],{"class":3705},[1115,17304,1797],{"class":3709},[1115,17306,17271],{"class":3705},[1115,17308,3797],{"class":3709},[1115,17310,17311],{"class":3840}," \"prediction\"",[1115,17313,1797],{"class":3709},[1115,17315,17213],{"class":3705},[1115,17317,3797],{"class":3709},[1115,17319,10002],{"class":3724},[1115,17321,3901],{"class":3717},[3694,17323,17326],{"className":17324,"code":17325,"language":3923,"meta":1490},[3921],"                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",[3470,17327,17325],{"__ignoreMap":1490},[1110,17329,17330,17333,17334,1654,17337,17350,17351,1346,17364,17367,17368,17371],{},[3470,17331,17332],{},"interval = \"confidence\""," dává interval spolehlivosti pro ",[1540,17335,17336],{},"střední hodnotu",[1115,17338,17340],{"className":17339},[1138],[1140,17341,17342],{"xmlns":1142},[1144,17343,17344,17348],{},[1147,17345,17346],{},[1153,17347,7132],{},[1159,17349,7132],{"encoding":1161}," při daném ",[1115,17352,17354],{"className":17353},[1138],[1140,17355,17356],{"xmlns":1142},[1144,17357,17358,17362],{},[1147,17359,17360],{},[1153,17361,1240],{},[1159,17363,1240],{"encoding":1161},[3470,17365,17366],{},"interval = \"prediction\""," širší interval pro ",[1540,17369,17370],{},"jednotlivé budoucí pozorování"," — ten musí zahrnout i rozptyl kolem regresní přímky, proto je vždy širší.",[16749,17373,17375],{"id":17374},"diagnostika-modelu","Diagnostika modelu",[1110,17377,17378,17379,1346,17382,1163,17385,17388],{},"Platnost závěrů z regresní přímky stojí na předpokladech o reziduích: ",[1540,17380,17381],{},"absenci autokorelace",[1540,17383,17384],{},"stálosti rozptylu (homoskedasticitě)",[1540,17386,17387],{},"normalitě",". V R se ověřují takto:",[3694,17390,17392],{"className":3696,"code":17391,"language":71,"meta":1490,"style":1490},"library(lmtest)\ndwtest(model)\n",[3470,17393,17394,17406],{"__ignoreMap":1490},[1115,17395,17396,17399,17401,17404],{"class":3702,"line":10},[1115,17397,17398],{"class":3709},"library",[1115,17400,1875],{"class":3717},[1115,17402,17403],{"class":3705},"lmtest",[1115,17405,3901],{"class":3717},[1115,17407,17408,17411,17413,17415],{"class":3702,"line":27},[1115,17409,17410],{"class":3713},"dwtest",[1115,17412,1875],{"class":3717},[1115,17414,786],{"class":3705},[1115,17416,3901],{"class":3717},[3694,17418,17421],{"className":17419,"code":17420,"language":3923,"meta":1490},[3921],"    Durbin-Watson test\n\ndata:  model\nDW = 3.4121, p-value = 0.9555\nalternative hypothesis: true autocorrelation is greater than 0\n",[3470,17422,17420],{"__ignoreMap":1490},[1110,17424,17425,17426,17443,17444,17461,17462,17479],{},"Durbinův–Watsonův test má ",[1115,17427,17429],{"className":17428},[1138],[1140,17430,17431],{"xmlns":1142},[1144,17432,17433,17441],{},[1147,17434,17435],{},[1150,17436,17437,17439],{},[1153,17438,1563],{},[1565,17440,1567],{},[1159,17442,1570],{"encoding":1161},": v modelu není problém s autokorelací, proti ",[1115,17445,17447],{"className":17446},[1138],[1140,17448,17449],{"xmlns":1142},[1144,17450,17451,17459],{},[1147,17452,17453],{},[1150,17454,17455,17457],{},[1153,17456,1563],{},[1565,17458,1794],{},[1159,17460,2996],{"encoding":1161},": 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, ",[1115,17463,17465],{"className":17464},[1138],[1140,17466,17467],{"xmlns":1142},[1144,17468,17469,17477],{},[1147,17470,17471],{},[1150,17472,17473,17475],{},[1153,17474,1563],{},[1565,17476,1567],{},[1159,17478,1570],{"encoding":1161}," se nezamítá.",[3694,17481,17483],{"className":3696,"code":17482,"language":71,"meta":1490,"style":1490},"library(whitestrap)\nwhite_test(model)\n",[3470,17484,17485,17496],{"__ignoreMap":1490},[1115,17486,17487,17489,17491,17494],{"class":3702,"line":10},[1115,17488,17398],{"class":3709},[1115,17490,1875],{"class":3717},[1115,17492,17493],{"class":3705},"whitestrap",[1115,17495,3901],{"class":3717},[1115,17497,17498,17501,17503,17505],{"class":3702,"line":27},[1115,17499,17500],{"class":3713},"white_test",[1115,17502,1875],{"class":3717},[1115,17504,786],{"class":3705},[1115,17506,3901],{"class":3717},[3694,17508,17511],{"className":17509,"code":17510,"language":3923,"meta":1490},[3921],"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",[3470,17512,17510],{"__ignoreMap":1490},[1110,17514,17515,17516,17533,17534,17551,17552,17479],{},"Whiteův test má ",[1115,17517,17519],{"className":17518},[1138],[1140,17520,17521],{"xmlns":1142},[1144,17522,17523,17531],{},[1147,17524,17525],{},[1150,17526,17527,17529],{},[1153,17528,1563],{},[1565,17530,1567],{},[1159,17532,1570],{"encoding":1161},": rozptyl reziduí je stálý (homoskedasticita), proti ",[1115,17535,17537],{"className":17536},[1138],[1140,17538,17539],{"xmlns":1142},[1144,17540,17541,17549],{},[1147,17542,17543],{},[1150,17544,17545,17547],{},[1153,17546,1563],{},[1565,17548,1794],{},[1159,17550,2996],{"encoding":1161},": rozptyl není stálý (heteroskedasticita). P-hodnota 0,21 je nad 0,05, ",[1115,17553,17555],{"className":17554},[1138],[1140,17556,17557],{"xmlns":1142},[1144,17558,17559,17567],{},[1147,17560,17561],{},[1150,17562,17563,17565],{},[1153,17564,1563],{},[1565,17566,1567],{},[1159,17568,1570],{"encoding":1161},[3694,17570,17572],{"className":3696,"code":17571,"language":71,"meta":1490,"style":1490},"shapiro.test(residuals(model))\n",[3470,17573,17574],{"__ignoreMap":1490},[1115,17575,17576,17579,17581,17583,17585,17587],{"class":3702,"line":10},[1115,17577,17578],{"class":3713},"shapiro.test",[1115,17580,1875],{"class":3717},[1115,17582,17046],{"class":3713},[1115,17584,1875],{"class":3717},[1115,17586,786],{"class":3705},[1115,17588,9496],{"class":3717},[3694,17590,17593],{"className":17591,"code":17592,"language":3923,"meta":1490},[3921],"    Shapiro-Wilk normality test\n\ndata:  residuals(model)\nW = 0.94818, p-value = 0.7255\n",[3470,17594,17592],{"__ignoreMap":1490},[1110,17596,17597,17598,17615],{},"Shapiro–Wilkův test má ",[1115,17599,17601],{"className":17600},[1138],[1140,17602,17603],{"xmlns":1142},[1144,17604,17605,17613],{},[1147,17606,17607],{},[1150,17608,17609,17611],{},[1153,17610,1563],{},[1565,17612,1567],{},[1159,17614,1570],{"encoding":1161},": rezidua pocházejí z normálního rozdělení. P-hodnota 0,73 opět nevede k zamítnutí — všechny tři předpoklady model splňuje.",[1110,17617,17618],{},[4383,17619],{"alt":17620,"className":17621,"src":17622},"mask-ra-diagnostika-rezidui",[1130,4387],"\u002Fwiki-assets\u002Fmask-ra-diagnostika-rezidui.png",[1110,17624,17625],{},"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.",[1103,17627,17629,17636,17667,17702,17767],{"className":17628,"dataCallout":3477},[1106,3476],[1110,17630,17632,17635],{"className":17631},[1113],[1115,17633],{"className":17634,"ariaHidden":1121},[1118,3484,1120],"Příklad: Regresní přímka",[1110,17637,17638,17639,17652,17653,17666],{},"V souboru s údaji o hodnotě produkce (v milionech Kč, proměnná ",[1115,17640,17642],{"className":17641},[1138],[1140,17643,17644],{"xmlns":1142},[1144,17645,17646,17650],{},[1147,17647,17648],{},[1153,17649,7132],{},[1159,17651,7132],{"encoding":1161},") a výši investic (ve stovkách tisíc Kč, proměnná ",[1115,17654,17656],{"className":17655},[1138],[1140,17657,17658],{"xmlns":1142},[1144,17659,17660,17664],{},[1147,17661,17662],{},[1153,17663,1240],{},[1159,17665,1240],{"encoding":1161},") 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.",[1110,17668,17669,17670,1669],{},"Výsledek: ",[1115,17671,17673],{"className":17672},[1138],[1140,17674,17675],{"xmlns":1142},[1144,17676,17677,17699],{},[1147,17678,17679,17685,17687,17690,17692,17695,17697],{},[1236,17680,17681,17683],{"accent":1121},[1153,17682,7132],{},[1242,17684,2729],{},[1242,17686,1982],{},[1565,17688,17689],{},"32,74",[1242,17691,5477],{},[1565,17693,17694],{},"2,15",[2909,17696,2911],{},[1153,17698,1240],{},[1159,17700,17701],{"encoding":1161},"\\hat y = 32{,}74 + 2{,}15\\,x",[1110,17703,16700,17704,17726,17727,17766],{},[1115,17705,17707],{"className":17706},[1138],[1140,17708,17709],{"xmlns":1142},[1144,17710,17711,17723],{},[1147,17712,17713,17719,17721],{},[1150,17714,17715,17717],{},[1153,17716,11507],{},[1565,17718,1794],{},[1242,17720,1982],{},[1565,17722,17694],{},[1159,17724,17725],{"encoding":1161},"b_1=2{,}15"," říká, že se zvýšením investic o 100 000 Kč vzroste produkce v průměru o ",[1115,17728,17730],{"className":17729},[1138],[1140,17731,17732],{"xmlns":1142},[1144,17733,17734,17763],{},[1147,17735,17736,17738,17740,17742,17744,17746,17748,17750,17752,17754,17756,17759,17761],{},[1565,17737,17694],{},[1242,17739,8113],{},[1565,17741,1794],{},[2909,17743,2911],{},[1565,17745,11326],{},[2909,17747,2911],{},[1565,17749,11326],{},[1242,17751,1982],{},[1565,17753,1589],{},[2909,17755,2911],{},[1565,17757,17758],{},"150",[2909,17760,2911],{},[1565,17762,11326],{},[1159,17764,17765],{"encoding":1161},"2{,}15\\cdot 1\\,000\\,000=2\\,150\\,000"," Kč.",[1110,17768,17769,17770,3988,17789,17837,17838,16096],{},"Dosazením libovolné hodnoty investic do empirické regresní funkce dostaneme predikci produkce, například pro třináctou firmu s investicemi ",[1115,17771,17773],{"className":17772},[1138],[1140,17774,17775],{"xmlns":1142},[1144,17776,17777,17786],{},[1147,17778,17779,17781,17783],{},[1153,17780,1240],{},[1242,17782,1982],{},[1565,17784,17785],{},"34",[1159,17787,17788],{"encoding":1161},"x=34",[1115,17790,17792],{"className":17791},[1138],[1140,17793,17794],{"xmlns":1142},[1144,17795,17796,17834],{},[1147,17797,17798,17808,17810,17816,17818,17824,17826,17828,17831],{},[1150,17799,17800,17806],{},[1236,17801,17802,17804],{"accent":1121},[1153,17803,7132],{},[1242,17805,2729],{},[1565,17807,3545],{},[1242,17809,1982],{},[1150,17811,17812,17814],{},[1153,17813,11507],{},[1565,17815,1567],{},[1242,17817,5477],{},[1150,17819,17820,17822],{},[1153,17821,11507],{},[1565,17823,1794],{},[1242,17825,8113],{},[1565,17827,17785],{},[1242,17829,17830],{},"≐",[1565,17832,17833],{},"105,81",[1159,17835,17836],{"encoding":1161},"\\hat y_{13} = b_0 + b_1\\cdot 34 \\doteq 105{,}81"," milionu Kč (se zaokrouhlenými koeficienty ",[1115,17839,17841],{"className":17840},[1138],[1140,17842,17843],{"xmlns":1142},[1144,17844,17845,17862],{},[1147,17846,17847,17849,17851,17853,17855,17857,17859],{},[1565,17848,17689],{},[1242,17850,5477],{},[1565,17852,17694],{},[1242,17854,8113],{},[1565,17856,17785],{},[1242,17858,17830],{},[1565,17860,17861],{},"105,8",[1159,17863,17864],{"encoding":1161},"32{,}74 + 2{,}15\\cdot 34 \\doteq 105{,}8",[1189,17866,17868],{"id":17867},"nelineární-a-vyšší-řády-regresních-funkcí","Nelineární a vyšší řády regresních funkcí",[1110,17870,17871,17872,17875,17876,17943,17944,17962,17963,17980],{},"Když přímka závislost nevystihuje, nabízí se další ",[1540,17873,17874],{},"lineární funkce"," — tedy funkce lineární ve svých parametrech, zapsatelné ve tvaru ",[1115,17877,17879],{"className":17878},[1138],[1140,17880,17881],{"xmlns":1142},[1144,17882,17883,17940],{},[1147,17884,17885,17887,17889,17895,17897,17903,17909,17911,17913,17915,17917,17920,17922,17928,17934,17936,17938],{},[1153,17886,16325],{},[1242,17888,1982],{},[1150,17890,17891,17893],{},[1153,17892,16340],{},[1565,17894,1567],{},[1242,17896,5477],{},[1150,17898,17899,17901],{},[1153,17900,16340],{},[1565,17902,1794],{},[1150,17904,17905,17907],{},[1153,17906,6773],{},[1565,17908,1794],{},[1242,17910,1875],{"stretchy":1874},[1153,17912,1240],{},[1242,17914,1886],{"stretchy":1874},[1242,17916,5477],{},[1242,17918,17919],{},"⋯",[1242,17921,5477],{},[1150,17923,17924,17926],{},[1153,17925,16340],{},[1153,17927,1110],{},[1150,17929,17930,17932],{},[1153,17931,6773],{},[1153,17933,1110],{},[1242,17935,1875],{"stretchy":1874},[1153,17937,1240],{},[1242,17939,1886],{"stretchy":1874},[1159,17941,17942],{"encoding":1161},"\\eta=\\beta_0+\\beta_1 f_1(x)+\\dots+\\beta_p f_p(x)"," se známými funkcemi ",[1115,17945,17947],{"className":17946},[1138],[1140,17948,17949],{"xmlns":1142},[1144,17950,17951,17959],{},[1147,17952,17953],{},[1150,17954,17955,17957],{},[1153,17956,6773],{},[1153,17958,1878],{},[1159,17960,17961],{"encoding":1161},"f_i"," a neznámými parametry ",[1115,17964,17966],{"className":17965},[1138],[1140,17967,17968],{"xmlns":1142},[1144,17969,17970,17978],{},[1147,17971,17972],{},[1150,17973,17974,17976],{},[1153,17975,16340],{},[1153,17977,1878],{},[1159,17979,16386],{"encoding":1161},". I tyto parametry se odhadují metodou nejmenších čtverců, stejně jako u přímky:",[1115,17982,17984],{"className":17983},[1138],[1140,17985,17986],{"xmlns":1142,"display":1964},[1144,17987,17988,18298],{},[17989,17990,17993,18066,18179,18238],"mtable",{"rowspacing":17991,"columnalign":17992,"columnspacing":6761},"0.25em","right left",[17994,17995,17996,18020],"mtr",{},[17997,17998,17999],"mtd",{},[3241,18000,18001],{"scriptlevel":1567,"displaystyle":1121},[1147,18002,18003,18017],{},[1147,18004,18005,18008,18014],{},[2909,18006,18007],{},"parabolick",[1236,18009,18010,18012],{"accent":1121},[2909,18011,1127],{},[1242,18013,11504],{},[2909,18015,18016],{}," regrese: ",[2012,18018],{"width":18019},"1em",[17997,18021,18022],{},[3241,18023,18024],{"scriptlevel":1567,"displaystyle":1121},[1147,18025,18026,18028,18034,18036,18042,18044,18050,18052,18054,18060],{},[1147,18027],{},[1236,18029,18030,18032],{"accent":1121},[1153,18031,7132],{},[1242,18033,2729],{},[1242,18035,1982],{},[1150,18037,18038,18040],{},[1153,18039,11507],{},[1565,18041,1567],{},[1242,18043,5477],{},[1150,18045,18046,18048],{},[1153,18047,11507],{},[1565,18049,1794],{},[1153,18051,1240],{},[1242,18053,5477],{},[1150,18055,18056,18058],{},[1153,18057,11507],{},[1565,18059,1589],{},[1582,18061,18062,18064],{},[1153,18063,1240],{},[1565,18065,1589],{},[17994,18067,18068,18115],{},[17997,18069,18070],{},[3241,18071,18072],{"scriptlevel":1567,"displaystyle":1121},[1147,18073,18074,18113],{},[1147,18075,18076,18079,18085,18088,18092,18095,18101,18104,18110],{},[2909,18077,18078],{},"polynomick",[1236,18080,18081,18083],{"accent":1121},[2909,18082,1127],{},[1242,18084,11504],{},[2909,18086,18087],{}," regrese ",[3241,18089,18090],{"scriptlevel":1567,"displaystyle":1874},[1153,18091,1110],{},[2909,18093,18094],{},"-t",[1236,18096,18097,18099],{"accent":1121},[2909,18098,8595],{},[1242,18100,11504],{},[2909,18102,18103],{},"ho stupn",[1236,18105,18106,18108],{"accent":1121},[2909,18107,8595],{},[1242,18109,11514],{},[2909,18111,18112],{},": ",[2012,18114],{"width":18019},[17997,18116,18117],{},[3241,18118,18119],{"scriptlevel":1567,"displaystyle":1121},[1147,18120,18121,18123,18129,18131,18137,18139,18145,18147,18149,18155,18161,18163,18165,18167,18173],{},[1147,18122],{},[1236,18124,18125,18127],{"accent":1121},[1153,18126,7132],{},[1242,18128,2729],{},[1242,18130,1982],{},[1150,18132,18133,18135],{},[1153,18134,11507],{},[1565,18136,1567],{},[1242,18138,5477],{},[1150,18140,18141,18143],{},[1153,18142,11507],{},[1565,18144,1794],{},[1153,18146,1240],{},[1242,18148,5477],{},[1150,18150,18151,18153],{},[1153,18152,11507],{},[1565,18154,1589],{},[1582,18156,18157,18159],{},[1153,18158,1240],{},[1565,18160,1589],{},[1242,18162,5477],{},[1242,18164,17919],{},[1242,18166,5477],{},[1150,18168,18169,18171],{},[1153,18170,11507],{},[1153,18172,1110],{},[1582,18174,18175,18177],{},[1153,18176,1240],{},[1153,18178,1110],{},[17994,18180,18181,18202],{},[17997,18182,18183],{},[3241,18184,18185],{"scriptlevel":1567,"displaystyle":1121},[1147,18186,18187,18200],{},[1147,18188,18189,18192,18198],{},[2909,18190,18191],{},"hyperbolick",[1236,18193,18194,18196],{"accent":1121},[2909,18195,1127],{},[1242,18197,11504],{},[2909,18199,18016],{},[2012,18201],{"width":18019},[17997,18203,18204],{},[3241,18205,18206],{"scriptlevel":1567,"displaystyle":1121},[1147,18207,18208,18210,18216,18218,18224,18226,18232],{},[1147,18209],{},[1236,18211,18212,18214],{"accent":1121},[1153,18213,7132],{},[1242,18215,2729],{},[1242,18217,1982],{},[1150,18219,18220,18222],{},[1153,18221,11507],{},[1565,18223,1567],{},[1242,18225,5477],{},[1150,18227,18228,18230],{},[1153,18229,11507],{},[1565,18231,1794],{},[2739,18233,18234,18236],{},[1565,18235,1794],{},[1153,18237,1240],{},[17994,18239,18240,18261],{},[17997,18241,18242],{},[3241,18243,18244],{"scriptlevel":1567,"displaystyle":1121},[1147,18245,18246,18259],{},[1147,18247,18248,18251,18257],{},[2909,18249,18250],{},"logaritmick",[1236,18252,18253,18255],{"accent":1121},[2909,18254,1127],{},[1242,18256,11504],{},[2909,18258,18016],{},[2012,18260],{"width":18019},[17997,18262,18263],{},[3241,18264,18265],{"scriptlevel":1567,"displaystyle":1121},[1147,18266,18267,18269,18275,18277,18283,18285,18291,18294,18296],{},[1147,18268],{},[1236,18270,18271,18273],{"accent":1121},[1153,18272,7132],{},[1242,18274,2729],{},[1242,18276,1982],{},[1150,18278,18279,18281],{},[1153,18280,11507],{},[1565,18282,1567],{},[1242,18284,5477],{},[1150,18286,18287,18289],{},[1153,18288,11507],{},[1565,18290,1794],{},[1153,18292,18293],{},"ln",[1242,18295,4491],{},[1153,18297,1240],{},[1159,18299,18300],{"encoding":1161},"\\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}",[1110,18302,18303,18304,18307,18308,18354,18355,1958],{},"Naproti tomu ",[1540,18305,18306],{},"nelineární funkce"," nelze do tvaru ",[1115,18309,18311],{"className":18310},[1138],[1140,18312,18313],{"xmlns":1142},[1144,18314,18315,18351],{},[1147,18316,18317,18319,18321,18327,18329,18335,18341,18343,18345,18347,18349],{},[1153,18318,16325],{},[1242,18320,1982],{},[1150,18322,18323,18325],{},[1153,18324,16340],{},[1565,18326,1567],{},[1242,18328,5477],{},[1150,18330,18331,18333],{},[1153,18332,16340],{},[1565,18334,1794],{},[1150,18336,18337,18339],{},[1153,18338,6773],{},[1565,18340,1794],{},[1242,18342,1875],{"stretchy":1874},[1153,18344,1240],{},[1242,18346,1886],{"stretchy":1874},[1242,18348,5477],{},[1242,18350,1800],{},[1159,18352,18353],{"encoding":1161},"\\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 ",[1540,18356,18357],{},"exponenciální regrese",[1115,18359,18361],{"className":18360},[1138],[1140,18362,18363],{"xmlns":1142,"display":1964},[1144,18364,18365,18397],{},[1147,18366,18367,18373,18375,18381,18383,18395],{},[1236,18368,18369,18371],{"accent":1121},[1153,18370,7132],{},[1242,18372,2729],{},[1242,18374,1982],{},[1150,18376,18377,18379],{},[1153,18378,11507],{},[1565,18380,1567],{},[1242,18382,8113],{},[3353,18384,18385,18387,18389],{},[1153,18386,11507],{},[1565,18388,1794],{},[1147,18390,18391,18393],{},[2909,18392,2911],{},[1153,18394,1240],{},[1153,18396,1669],{"mathvariant":2121},[1159,18398,18399],{"encoding":1161},"\\hat y = b_0 \\cdot b_1^{\\,x}.",[1110,18401,18402],{},[4383,18403],{"alt":18404,"className":18405,"src":18406},"mask-ra-nelinearni-krivky",[1130,4387],"\u002Fwiki-assets\u002Fmask-ra-nelinearni-krivky.png",[16749,18408,18410],{"id":18409},"v-r-parabolická-regrese","V R — parabolická regrese",[1110,18412,18413,18414,1958],{},"Na ročních ziscích firmy (šest let) se parabolická regrese odhadne přidáním kvadratického členu ",[3470,18415,18416],{},"I(x^2)",[3694,18418,18420],{"className":3696,"code":18419,"language":71,"meta":1490,"style":1490},"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",[3470,18421,18422,18457,18497,18531],{"__ignoreMap":1490},[1115,18423,18424,18427,18429,18431,18433,18435,18437,18439,18441,18443,18445,18447,18449,18451,18453,18455],{"class":3702,"line":10},[1115,18425,18426],{"class":3705},"rok",[1115,18428,3710],{"class":3709},[1115,18430,3835],{"class":3713},[1115,18432,1875],{"class":3717},[1115,18434,1794],{"class":3724},[1115,18436,1797],{"class":3709},[1115,18438,4180],{"class":3724},[1115,18440,1797],{"class":3709},[1115,18442,10857],{"class":3724},[1115,18444,1797],{"class":3709},[1115,18446,3800],{"class":3724},[1115,18448,1797],{"class":3709},[1115,18450,9997],{"class":3724},[1115,18452,1797],{"class":3709},[1115,18454,12230],{"class":3724},[1115,18456,3901],{"class":3717},[1115,18458,18459,18461,18463,18465,18467,18470,18472,18475,18477,18480,18482,18485,18487,18490,18492,18495],{"class":3702,"line":27},[1115,18460,1088],{"class":3705},[1115,18462,3710],{"class":3709},[1115,18464,3835],{"class":3713},[1115,18466,1875],{"class":3717},[1115,18468,18469],{"class":3724},"112",[1115,18471,1797],{"class":3709},[1115,18473,18474],{"class":3724}," 149",[1115,18476,1797],{"class":3709},[1115,18478,18479],{"class":3724}," 238",[1115,18481,1797],{"class":3709},[1115,18483,18484],{"class":3724}," 354",[1115,18486,1797],{"class":3709},[1115,18488,18489],{"class":3724}," 580",[1115,18491,1797],{"class":3709},[1115,18493,18494],{"class":3724}," 867",[1115,18496,3901],{"class":3717},[1115,18498,18499,18502,18504,18506,18508,18510,18512,18515,18518,18521,18523,18525,18527,18529],{"class":3702,"line":148},[1115,18500,18501],{"class":3705},"model_parabola",[1115,18503,3710],{"class":3709},[1115,18505,16853],{"class":3713},[1115,18507,1875],{"class":3717},[1115,18509,1088],{"class":3705},[1115,18511,16860],{"class":3709},[1115,18513,18514],{"class":3705}," rok",[1115,18516,18517],{"class":3709}," +",[1115,18519,18520],{"class":3713}," I",[1115,18522,1875],{"class":3717},[1115,18524,18426],{"class":3705},[1115,18526,2729],{"class":3709},[1115,18528,1589],{"class":3724},[1115,18530,9496],{"class":3717},[1115,18532,18533,18535,18537,18539],{"class":3702,"line":111},[1115,18534,1509],{"class":3713},[1115,18536,1875],{"class":3717},[1115,18538,18501],{"class":3705},[1115,18540,3901],{"class":3717},[3694,18542,18545],{"className":18543,"code":18544,"language":3923,"meta":1490},[3921],"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",[3470,18546,18544],{"__ignoreMap":1490},[1110,18548,18549,18550,18595],{},"Odhadnutá parabola ",[1115,18551,18553],{"className":18552},[1138],[1140,18554,18555],{"xmlns":1142},[1144,18556,18557,18592],{},[1147,18558,18559,18565,18567,18570,18572,18575,18577,18579,18581,18584,18586],{},[1236,18560,18561,18563],{"accent":1121},[1153,18562,7132],{},[1242,18564,2729],{},[1242,18566,1982],{},[1565,18568,18569],{},"164,6",[1242,18571,3064],{},[1565,18573,18574],{},"76,6",[2909,18576,2911],{},[1153,18578,1240],{},[1242,18580,5477],{},[1565,18582,18583],{},"32,1",[2909,18585,2911],{},[1582,18587,18588,18590],{},[1153,18589,1240],{},[1565,18591,1589],{},[1159,18593,18594],{"encoding":1161},"\\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.",[16749,18597,18599],{"id":18598},"v-r-exponenciální-regrese","V R — exponenciální regrese",[1110,18601,18602,18603,18605],{},"Nelineární funkce se v R odhadují funkcí ",[3470,18604,16111],{}," ze stejnojmenného balíčku. Bez zadaných počátečních hodnot R upozorní, že parametry nastavil na 1, a odhad dopočítá iteračně:",[3694,18607,18609],{"className":3696,"code":18608,"language":71,"meta":1490,"style":1490},"library(nls2)\nmodel_exp \u003C- nls2(zisk ~ b1 * exp(b2 * rok))\nsummary(model_exp)\n",[3470,18610,18611,18621,18657],{"__ignoreMap":1490},[1115,18612,18613,18615,18617,18619],{"class":3702,"line":10},[1115,18614,17398],{"class":3709},[1115,18616,1875],{"class":3717},[1115,18618,16095],{"class":3705},[1115,18620,3901],{"class":3717},[1115,18622,18623,18626,18628,18631,18633,18635,18637,18640,18643,18646,18648,18651,18653,18655],{"class":3702,"line":27},[1115,18624,18625],{"class":3705},"model_exp",[1115,18627,3710],{"class":3709},[1115,18629,18630],{"class":3713}," nls2",[1115,18632,1875],{"class":3717},[1115,18634,1088],{"class":3705},[1115,18636,16860],{"class":3709},[1115,18638,18639],{"class":3705}," b1",[1115,18641,18642],{"class":3709}," *",[1115,18644,18645],{"class":3713}," exp",[1115,18647,1875],{"class":3717},[1115,18649,18650],{"class":3705},"b2",[1115,18652,18642],{"class":3709},[1115,18654,18514],{"class":3705},[1115,18656,9496],{"class":3717},[1115,18658,18659,18661,18663,18665],{"class":3702,"line":148},[1115,18660,1509],{"class":3713},[1115,18662,1875],{"class":3717},[1115,18664,18625],{"class":3705},[1115,18666,3901],{"class":3717},[3694,18668,18671],{"className":18669,"code":18670,"language":3923,"meta":1490},[3921],"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",[3470,18672,18670],{"__ignoreMap":1490},[1110,18674,18675,18676,1958],{},"Stejnou křivku lze zapsat i v mocninném tvaru ",[1115,18677,18679],{"className":18678},[1138],[1140,18680,18681],{"xmlns":1142},[1144,18682,18683,18709],{},[1147,18684,18685,18691,18693,18699,18701],{},[1236,18686,18687,18689],{"accent":1121},[1153,18688,7132],{},[1242,18690,2729],{},[1242,18692,1982],{},[1150,18694,18695,18697],{},[1153,18696,11507],{},[1565,18698,1794],{},[1242,18700,8113],{},[3353,18702,18703,18705,18707],{},[1153,18704,11507],{},[1565,18706,1589],{},[1153,18708,1240],{},[1159,18710,18711],{"encoding":1161},"\\hat y=b_1\\cdot b_2^{x}",[3694,18713,18715],{"className":3696,"code":18714,"language":71,"meta":1490,"style":1490},"model_pow \u003C- nls2(zisk ~ b1 * (b2^rok))\nsummary(model_pow)\n",[3470,18716,18717,18746],{"__ignoreMap":1490},[1115,18718,18719,18722,18724,18726,18728,18730,18732,18734,18736,18738,18740,18742,18744],{"class":3702,"line":10},[1115,18720,18721],{"class":3705},"model_pow",[1115,18723,3710],{"class":3709},[1115,18725,18630],{"class":3713},[1115,18727,1875],{"class":3717},[1115,18729,1088],{"class":3705},[1115,18731,16860],{"class":3709},[1115,18733,18639],{"class":3705},[1115,18735,18642],{"class":3709},[1115,18737,4607],{"class":3717},[1115,18739,18650],{"class":3705},[1115,18741,2729],{"class":3709},[1115,18743,18426],{"class":3705},[1115,18745,9496],{"class":3717},[1115,18747,18748,18750,18752,18754],{"class":3702,"line":27},[1115,18749,1509],{"class":3713},[1115,18751,1875],{"class":3717},[1115,18753,18721],{"class":3705},[1115,18755,3901],{"class":3717},[3694,18757,18760],{"className":18758,"code":18759,"language":3923,"meta":1490},[3921],"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",[3470,18761,18759],{"__ignoreMap":1490},[1110,18763,18764,18765,18829,18830,18854],{},"Obě varianty popisují stejnou křivku (",[1115,18766,18768],{"className":18767},[1138],[1140,18769,18770],{"xmlns":1142},[1144,18771,18772,18826],{},[1147,18773,18774,18791,18793],{},[3353,18775,18776,18778,18780],{},[1153,18777,11507],{},[1565,18779,1589],{},[1147,18781,18782,18785],{},[2909,18783,18784],{},"mocninn",[1236,18786,18787,18789],{"accent":1121},[2909,18788,7132],{},[1242,18790,11504],{},[1242,18792,1982],{},[1582,18794,18795,18797],{},[1153,18796,8595],{},[1147,18798,18799,18801],{},[2909,18800,2911],{},[3353,18802,18803,18805,18807],{},[1153,18804,11507],{},[1565,18806,1589],{},[1147,18808,18809,18812,18818,18820],{},[2909,18810,18811],{},"exponenci",[1236,18813,18814,18816],{"accent":1121},[2909,18815,1127],{},[1242,18817,11504],{},[2909,18819,18293],{},[1236,18821,18822,18824],{"accent":1121},[2909,18823,11753],{},[1242,18825,11504],{},[1159,18827,18828],{"encoding":1161},"b_2^{\\text{mocninný}} = e^{\\,b_2^{\\text{exponenciální}}}",", zde ",[1115,18831,18833],{"className":18832},[1138],[1140,18834,18835],{"xmlns":1142},[1144,18836,18837,18851],{},[1147,18838,18839,18846,18848],{},[1582,18840,18841,18843],{},[1153,18842,8595],{},[1565,18844,18845],{},"0,4316",[1242,18847,9443],{},[1565,18849,18850],{},"1,540",[1159,18852,18853],{"encoding":1161},"e^{0{,}4316}\\approx 1{,}540",") a mají totožnou reziduální chybu — je to jen otázka parametrizace.",[16749,18856,18858],{"id":18857},"v-r-hyperbolická-regrese","V R — hyperbolická regrese",[1110,18860,18861,18862,1958],{},"Hyperbolická regrese se odhadne jako obyčejná lineární regrese na transformované proměnné ",[3470,18863,18864],{},"I(1\u002Fx)",[3694,18866,18868],{"className":3696,"code":18867,"language":71,"meta":1490,"style":1490},"model_hyperbola \u003C- lm(tydenni_vydaje ~ I(1 \u002F pocet_clenu))\nsummary(model_hyperbola)\n",[3470,18869,18870,18897],{"__ignoreMap":1490},[1115,18871,18872,18875,18877,18879,18881,18883,18885,18887,18889,18891,18893,18895],{"class":3702,"line":10},[1115,18873,18874],{"class":3705},"model_hyperbola",[1115,18876,3710],{"class":3709},[1115,18878,16853],{"class":3713},[1115,18880,1875],{"class":3717},[1115,18882,16808],{"class":3705},[1115,18884,16860],{"class":3709},[1115,18886,18520],{"class":3713},[1115,18888,1875],{"class":3717},[1115,18890,1794],{"class":3724},[1115,18892,10078],{"class":3709},[1115,18894,16863],{"class":3705},[1115,18896,9496],{"class":3717},[1115,18898,18899,18901,18903,18905],{"class":3702,"line":27},[1115,18900,1509],{"class":3713},[1115,18902,1875],{"class":3717},[1115,18904,18874],{"class":3705},[1115,18906,3901],{"class":3717},[3694,18908,18911],{"className":18909,"code":18910,"language":3923,"meta":1490},[3921],"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",[3470,18912,18910],{"__ignoreMap":1490},[1110,18914,18915,18916,18950,18951,18972],{},"Model ",[1115,18917,18919],{"className":18918},[1138],[1140,18920,18921],{"xmlns":1142},[1144,18922,18923,18947],{},[1147,18924,18925,18931,18933,18936,18938],{},[1236,18926,18927,18929],{"accent":1121},[1153,18928,7132],{},[1242,18930,2729],{},[1242,18932,1982],{},[1565,18934,18935],{},"2180,7",[1242,18937,3064],{},[3241,18939,18940],{"scriptlevel":1567,"displaystyle":1121},[2739,18941,18942,18945],{},[1565,18943,18944],{},"1920,0",[1153,18946,1240],{},[1159,18948,18949],{"encoding":1161},"\\hat y = 2180{,}7 - \\dfrac{1920{,}0}{x}"," vysvětluje jen 76,3 % rozptylu — u těchto dat je hyperbola podstatně horší volbou než přímka (",[1115,18952,18954],{"className":18953},[1138],[1140,18955,18956],{"xmlns":1142},[1144,18957,18958,18970],{},[1147,18959,18960,18966,18968],{},[1582,18961,18962,18964],{},[1153,18963,1260],{},[1565,18965,1589],{},[1242,18967,1982],{},[1565,18969,17007],{},[1159,18971,17010],{"encoding":1161},"). Právě k takovému porovnání slouží index determinace: nízká hodnota signalizuje, že zvolený typ funkce k datům nesedí.",[1103,18974,18976,18983,19014,19062],{"className":18975,"dataCallout":3477},[1106,3476],[1110,18977,18979,18982],{"className":18978},[1113],[1115,18980],{"className":18981,"ariaHidden":1121},[1118,3484,1120],"Příklad: Parabolická regrese",[1110,18984,18985,18986,18999,19000,19013],{},"Prodejna počítačových her nechala prodavače absolvovat kurz prodejních dovedností. Při dvaceti měřeních sledovala, kolik zákazníků navštíví prodejnu během prodejní doby (proměnná ",[1115,18987,18989],{"className":18988},[1138],[1140,18990,18991],{"xmlns":1142},[1144,18992,18993,18997],{},[1147,18994,18995],{},[1153,18996,1240],{},[1159,18998,1240],{"encoding":1161},") a jaká je toho dne tržba v tisících Kč (proměnná ",[1115,19001,19003],{"className":19002},[1138],[1140,19004,19005],{"xmlns":1142},[1144,19006,19007,19011],{},[1147,19008,19009],{},[1153,19010,7132],{},[1159,19012,7132],{"encoding":1161},"). Zároveň chtěla zjistit, zda při rostoucím počtu zákazníků stačí stávající počet prodavačů.",[1110,19015,17669,19016,1669],{},[1115,19017,19019],{"className":19018},[1138],[1140,19020,19021],{"xmlns":1142},[1144,19022,19023,19059],{},[1147,19024,19025,19031,19033,19035,19038,19040,19043,19045,19047,19049,19051,19053],{},[1236,19026,19027,19029],{"accent":1121},[1153,19028,7132],{},[1242,19030,2729],{},[1242,19032,1982],{},[1242,19034,3064],{},[1565,19036,19037],{},"60,3",[1242,19039,5477],{},[1565,19041,19042],{},"4,55",[2909,19044,2911],{},[1153,19046,1240],{},[1242,19048,3064],{},[1565,19050,3984],{},[2909,19052,2911],{},[1582,19054,19055,19057],{},[1153,19056,1240],{},[1565,19058,1589],{},[1159,19060,19061],{"encoding":1161},"\\hat y = -60{,}3 + 4{,}55\\,x - 0{,}05\\,x^2",[1110,19063,19064,19065,19083],{},"Záporný koeficient ",[1115,19066,19068],{"className":19067},[1138],[1140,19069,19070],{"xmlns":1142},[1144,19071,19072,19080],{},[1147,19073,19074],{},[1150,19075,19076,19078],{},[1153,19077,11507],{},[1565,19079,1589],{},[1159,19081,19082],{"encoding":1161},"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.",[1103,19085,19087,19094,19124,19169],{"className":19086,"dataCallout":3477},[1106,3476],[1110,19088,19090,19093],{"className":19089},[1113],[1115,19091],{"className":19092,"ariaHidden":1121},[1118,3484,1120],"Příklad: Hyperbolická regrese",[1110,19095,19096,19097,19110,19111,16096],{},"V podniku se podle interního účetnictví sledovala závislost vlastních nákladů na jednotku produkce v Kč (proměnná ",[1115,19098,19100],{"className":19099},[1138],[1140,19101,19102],{"xmlns":1142},[1144,19103,19104,19108],{},[1147,19105,19106],{},[1153,19107,7132],{},[1159,19109,7132],{"encoding":1161},") na objemu produkce v tisících kusů (proměnná ",[1115,19112,19114],{"className":19113},[1138],[1140,19115,19116],{"xmlns":1142},[1144,19117,19118,19122],{},[1147,19119,19120],{},[1153,19121,1240],{},[1159,19123,1240],{"encoding":1161},[1110,19125,17669,19126,1669],{},[1115,19127,19129],{"className":19128},[1138],[1140,19130,19131],{"xmlns":1142},[1144,19132,19133,19166],{},[1147,19134,19135,19141,19143,19145,19148,19150],{},[1236,19136,19137,19139],{"accent":1121},[1153,19138,7132],{},[1242,19140,2729],{},[1242,19142,1982],{},[1242,19144,3064],{},[1565,19146,19147],{},"96,78",[1242,19149,5477],{},[3241,19151,19152],{"scriptlevel":1567,"displaystyle":1121},[2739,19153,19154,19164],{},[1147,19155,19156,19159,19161],{},[1565,19157,19158],{},"250",[2909,19160,2911],{},[1565,19162,19163],{},"528,88",[1153,19165,1240],{},[1159,19167,19168],{"encoding":1161},"\\hat y = -96{,}78 + \\dfrac{250\\,528{,}88}{x}",[1110,19170,19171,19172,19189],{},"Záporná hodnota ",[1115,19173,19175],{"className":19174},[1138],[1140,19176,19177],{"xmlns":1142},[1144,19178,19179,19187],{},[1147,19180,19181],{},[1150,19182,19183,19185],{},[1153,19184,11507],{},[1565,19186,1794],{},[1159,19188,16718],{"encoding":1161}," v čitateli ukazuje klesající náklady na jednotku s rostoucím objemem produkce — typický projev úspor z rozsahu, který hyperbola dobře zachycuje.",[1189,19191,19193],{"id":19192},"kvalita-regresní-funkce-a-korelační-analýza","Kvalita regresní funkce a korelační analýza",[1110,19195,19196,19197,1958],{},"Kvalitu odhadnuté regresní funkce vyjadřuje ",[1540,19198,16009],{},[1115,19200,19202],{"className":19201},[1138],[1140,19203,19204],{"xmlns":1142,"display":1964},[1144,19205,19206,19274],{},[1147,19207,19208,19214,19216,19238,19240,19242,19244,19272],{},[1582,19209,19210,19212],{},[1153,19211,1260],{},[1565,19213,1589],{},[1242,19215,1982],{},[2739,19217,19218,19230],{},[3353,19219,19220,19222,19228],{},[1153,19221,1291],{},[1236,19223,19224,19226],{"accent":1121},[1153,19225,7132],{},[1242,19227,2729],{},[1565,19229,1589],{},[3353,19231,19232,19234,19236],{},[1153,19233,1291],{},[1153,19235,7132],{},[1565,19237,1589],{},[1242,19239,1982],{},[1565,19241,1794],{},[1242,19243,3064],{},[2739,19245,19246,19264],{},[3353,19247,19248,19250,19262],{},[1153,19249,1291],{},[1147,19251,19252,19254,19256],{},[1153,19253,7132],{},[1242,19255,3064],{},[1236,19257,19258,19260],{"accent":1121},[1153,19259,7132],{},[1242,19261,2729],{},[1565,19263,1589],{},[3353,19265,19266,19268,19270],{},[1153,19267,1291],{},[1153,19269,7132],{},[1565,19271,1589],{},[1153,19273,1669],{"mathvariant":2121},[1159,19275,19276],{"encoding":1161},"R^2 = \\frac{s^2_{\\hat y}}{s^2_y} = 1 - \\frac{s^2_{y-\\hat y}}{s^2_y}.",[1110,19278,19279,19280,19297,19298,19311],{},"Čím blíž je ",[1115,19281,19283],{"className":19282},[1138],[1140,19284,19285],{"xmlns":1142},[1144,19286,19287,19295],{},[1147,19288,19289],{},[1582,19290,19291,19293],{},[1153,19292,1260],{},[1565,19294,1589],{},[1159,19296,16027],{"encoding":1161}," k 1, tím silnější je závislost; v procentech udává, jakou část rozptylu závisle proměnné ",[1115,19299,19301],{"className":19300},[1138],[1140,19302,19303],{"xmlns":1142},[1144,19304,19305,19309],{},[1147,19306,19307],{},[1153,19308,7132],{},[1159,19310,7132],{"encoding":1161}," se podařilo vysvětlit zvolenou regresní funkcí. Nízký index determinace může signalizovat špatně zvolený typ regresní funkce, ne nutně absenci závislosti.",[1110,19313,19314,19315,1654,19317,19340,19341,1958],{},"Obecnou mírou těsnosti závislosti — platnou pro libovolný typ regresní funkce — je ",[1540,19316,16031],{},[1115,19318,19320],{"className":19319},[1138],[1140,19321,19322],{"xmlns":1142},[1144,19323,19324,19338],{},[1147,19325,19326,19328,19330],{},[1153,19327,11204],{},[1242,19329,1982],{},[4453,19331,19332],{},[1582,19333,19334,19336],{},[1153,19335,1260],{},[1565,19337,1589],{},[1159,19339,16055],{"encoding":1161},". Je-li zvolenou funkcí regresní přímka, index korelace je roven (až na znaménko) ",[1540,19342,16059],{},[1115,19344,19346],{"className":19345},[1138],[1140,19347,19348],{"xmlns":1142,"display":1964},[1144,19349,19350,19400],{},[1147,19351,19352,19362,19364,19398],{},[1150,19353,19354,19356],{},[1153,19355,71],{},[1147,19357,19358,19360],{},[1153,19359,1240],{},[1153,19361,7132],{},[1242,19363,1982],{},[2739,19365,19366,19376],{},[1150,19367,19368,19370],{},[1153,19369,1291],{},[1147,19371,19372,19374],{},[1153,19373,1240],{},[1153,19375,7132],{},[4453,19377,19378],{},[1147,19379,19380,19388,19390],{},[3353,19381,19382,19384,19386],{},[1153,19383,1291],{},[1153,19385,1240],{},[1565,19387,1589],{},[1242,19389,8113],{},[3353,19391,19392,19394,19396],{},[1153,19393,1291],{},[1153,19395,7132],{},[1565,19397,1589],{},[1153,19399,1669],{"mathvariant":2121},[1159,19401,19402],{"encoding":1161},"r_{xy} = \\frac{s_{xy}}{\\sqrt{s^2_x\\cdot s^2_y}}.",[1110,19404,19405,19406,19422,19423,19439],{},"Koeficient korelace nabývá hodnot od ",[1115,19407,19409],{"className":19408},[1138],[1140,19410,19411],{"xmlns":1142},[1144,19412,19413,19419],{},[1147,19414,19415,19417],{},[1242,19416,3064],{},[1565,19418,1794],{},[1159,19420,19421],{"encoding":1161},"-1"," do ",[1115,19424,19426],{"className":19425},[1138],[1140,19427,19428],{"xmlns":1142},[1144,19429,19430,19436],{},[1147,19431,19432,19434],{},[1242,19433,5477],{},[1565,19435,1794],{},[1159,19437,19438],{"encoding":1161},"+1",": znaménko určuje typ závislosti (pozitivní, nebo negativní), absolutní hodnota její sílu — čím blíž k 0, tím je závislost slabší.",[1110,19441,19442],{},[4383,19443],{"alt":19444,"className":19445,"src":19446},"mask-ra-korelace-sila",[1130,4387],"\u002Fwiki-assets\u002Fmask-ra-korelace-sila.png",[1110,19448,19449,19450,19463,19464,19482,19483,1163,19496,19509],{},"S rostoucí absolutní hodnotou ",[1115,19451,19453],{"className":19452},[1138],[1140,19454,19455],{"xmlns":1142},[1144,19456,19457,19461],{},[1147,19458,19459],{},[1153,19460,71],{},[1159,19462,71],{"encoding":1161}," se body v rozptylovém grafu víc blíží přímce; kolem ",[1115,19465,19467],{"className":19466},[1138],[1140,19468,19469],{"xmlns":1142},[1144,19470,19471,19479],{},[1147,19472,19473,19475,19477],{},[1153,19474,71],{},[1242,19476,9443],{},[1565,19478,1567],{},[1159,19480,19481],{"encoding":1161},"r\\approx 0"," je mezi ",[1115,19484,19486],{"className":19485},[1138],[1140,19487,19488],{"xmlns":1142},[1144,19489,19490,19494],{},[1147,19491,19492],{},[1153,19493,1240],{},[1159,19495,1240],{"encoding":1161},[1115,19497,19499],{"className":19498},[1138],[1140,19500,19501],{"xmlns":1142},[1144,19502,19503,19507],{},[1147,19504,19505],{},[1153,19506,7132],{},[1159,19508,7132],{"encoding":1161}," patrná jen náhodná rozptýlenost bez lineárního trendu.",[16749,19511,16752],{"id":19512},"v-r-1",[3694,19514,19516],{"className":3696,"code":19515,"language":71,"meta":1490,"style":1490},"cor(pocet_clenu, tydenni_vydaje)\n",[3470,19517,19518],{"__ignoreMap":1490},[1115,19519,19520,19523,19525,19527,19529,19532],{"class":3702,"line":10},[1115,19521,19522],{"class":3713},"cor",[1115,19524,1875],{"class":3717},[1115,19526,16773],{"class":3705},[1115,19528,1797],{"class":3709},[1115,19530,19531],{"class":3705}," tydenni_vydaje",[1115,19533,3901],{"class":3717},[3694,19535,19538],{"className":19536,"code":19537,"language":3923,"meta":1490},[3921],"[1] 0.9997441\n",[3470,19539,19537],{"__ignoreMap":1490},[1110,19541,19542,19543,19569],{},"Hodnota 0,9997 odpovídá ",[1115,19544,19546],{"className":19545},[1138],[1140,19547,19548],{"xmlns":1142},[1144,19549,19550,19566],{},[1147,19551,19552,19560,19562],{},[4453,19553,19554],{},[1582,19555,19556,19558],{},[1153,19557,1260],{},[1565,19559,1589],{},[1242,19561,1982],{},[4453,19563,19564],{},[1565,19565,17007],{},[1159,19567,19568],{"encoding":1161},"\\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.",[1103,19571,19573,19580,19583],{"className":19572,"dataCallout":3477},[1106,3476],[1110,19574,19576,19579],{"className":19575},[1113],[1115,19577],{"className":19578,"ariaHidden":1121},[1118,3484,1120],"Příklad: Koeficient korelace",[1110,19581,19582],{},"Pro stejná data o hodnotě produkce a výši investic dvanácti firem jako u regresní přímky byl spočten koeficient korelace mezi oběma proměnnými.",[1110,19584,17669,19585,19612],{},[1115,19586,19588],{"className":19587},[1138],[1140,19589,19590],{"xmlns":1142},[1144,19591,19592,19609],{},[1147,19593,19594,19604,19606],{},[1150,19595,19596,19598],{},[1153,19597,71],{},[1147,19599,19600,19602],{},[1153,19601,1240],{},[1153,19603,7132],{},[1242,19605,1982],{},[1565,19607,19608],{},"0,739",[1159,19610,19611],{"encoding":1161},"r_{xy} = 0{,}739"," — silná kladná závislost hodnoty produkce na výši investic.",[1189,19614,19616],{"id":19615},"vícenásobná-regrese-a-korelace","Vícenásobná regrese a korelace",[1110,19618,19619,19620,19633],{},"Pokud na závisle proměnnou ",[1115,19621,19623],{"className":19622},[1138],[1140,19624,19625],{"xmlns":1142},[1144,19626,19627,19631],{},[1147,19628,19629],{},[1153,19630,7132],{},[1159,19632,7132],{"encoding":1161}," působí víc vysvětlujících proměnných současně, analyzuje se zvlášť vliv každé z nich a výsledná regresní funkce se konstruuje jako součet jednoduchých regresních funkcí:",[1115,19635,19637],{"className":19636},[1138],[1140,19638,19639],{"xmlns":1142,"display":1964},[1144,19640,19641,19751],{},[1147,19642,19643,19645,19647,19653,19655,19661,19667,19669,19675,19681,19683,19685,19687,19693,19699,19701,19703,19709,19711,19717,19719,19725,19731,19733,19735,19737,19743,19749],{},[1153,19644,16325],{},[1242,19646,1982],{},[1150,19648,19649,19651],{},[1153,19650,16340],{},[1565,19652,1567],{},[1242,19654,5477],{},[1150,19656,19657,19659],{},[1153,19658,16340],{},[1565,19660,1794],{},[1150,19662,19663,19665],{},[1153,19664,1240],{},[1565,19666,1794],{},[1242,19668,5477],{},[1150,19670,19671,19673],{},[1153,19672,16340],{},[1565,19674,1589],{},[1150,19676,19677,19679],{},[1153,19678,1240],{},[1565,19680,1589],{},[1242,19682,5477],{},[1242,19684,17919],{},[1242,19686,5477],{},[1150,19688,19689,19691],{},[1153,19690,16340],{},[1153,19692,1110],{},[1150,19694,19695,19697],{},[1153,19696,1240],{},[1153,19698,1110],{},[1242,19700,1797],{"separator":1121},[2012,19702],{"width":2014},[1236,19704,19705,19707],{"accent":1121},[1153,19706,7132],{},[1242,19708,2729],{},[1242,19710,1982],{},[1150,19712,19713,19715],{},[1153,19714,11507],{},[1565,19716,1567],{},[1242,19718,5477],{},[1150,19720,19721,19723],{},[1153,19722,11507],{},[1565,19724,1794],{},[1150,19726,19727,19729],{},[1153,19728,1240],{},[1565,19730,1794],{},[1242,19732,5477],{},[1242,19734,17919],{},[1242,19736,5477],{},[1150,19738,19739,19741],{},[1153,19740,11507],{},[1153,19742,1110],{},[1150,19744,19745,19747],{},[1153,19746,1240],{},[1153,19748,1110],{},[1153,19750,1669],{"mathvariant":2121},[1159,19752,19753],{"encoding":1161},"\\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.",[16749,19755,19757],{"id":19756},"výběr-proměnných","Výběr proměnných",[1436,19759,19760,19766],{},[1439,19761,19762,19765],{},[1540,19763,19764],{},"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.",[1439,19767,19768,19771,19772,19775,19776,19779],{},[1540,19769,19770],{},"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 ",[1540,19773,19774],{},"forward"," proměnné postupně přidává, varianta ",[1540,19777,19778],{},"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.",[16749,19781,19783],{"id":19782},"postup-odhadu","Postup odhadu",[2865,19785,19786,19789,19792],{},[1439,19787,19788],{},"ověření předpokladů regresního modelu,",[1439,19790,19791],{},"samotný odhad parametrů,",[1439,19793,19794],{},"reziduální analýza výsledného modelu.",[1110,19796,19797,19798,19815,19816,3988,19818,19847,19848,19877,19878,19895],{},"Důležitost každého parametru ",[1115,19799,19801],{"className":19800},[1138],[1140,19802,19803],{"xmlns":1142},[1144,19804,19805,19813],{},[1147,19806,19807],{},[1150,19808,19809,19811],{},[1153,19810,11507],{},[1153,19812,1878],{},[1159,19814,16465],{"encoding":1161}," v modelu ověřuje ",[1540,19817,992],{},[1115,19819,19821],{"className":19820},[1138],[1140,19822,19823],{"xmlns":1142},[1144,19824,19825,19845],{},[1147,19826,19827,19833,19835,19841,19843],{},[1150,19828,19829,19831],{},[1153,19830,1563],{},[1565,19832,1567],{},[1242,19834,1958],{},[1150,19836,19837,19839],{},[1153,19838,16340],{},[1153,19840,1878],{},[1242,19842,1982],{},[1565,19844,1567],{},[1159,19846,16951],{"encoding":1161}," (proměnná je v modelu nevýznamná) proti ",[1115,19849,19851],{"className":19850},[1138],[1140,19852,19853],{"xmlns":1142},[1144,19854,19855,19875],{},[1147,19856,19857,19863,19865,19871,19873],{},[1150,19858,19859,19861],{},[1153,19860,1563],{},[1565,19862,1794],{},[1242,19864,1958],{},[1150,19866,19867,19869],{},[1153,19868,16340],{},[1153,19870,1878],{},[1242,19872,10958],{"mathvariant":2121},[1565,19874,1567],{},[1159,19876,16982],{"encoding":1161}," (proměnná je významná). Při nezamítnutí ",[1115,19879,19881],{"className":19880},[1138],[1140,19882,19883],{"xmlns":1142},[1144,19884,19885,19893],{},[1147,19886,19887],{},[1150,19888,19889,19891],{},[1153,19890,1563],{},[1565,19892,1567],{},[1159,19894,1570],{"encoding":1161}," by proměnná — a s ní spojený regresor — v modelu neměla zůstat.",[16749,19897,19899],{"id":19898},"předpoklady-modelu","Předpoklady modelu",[2865,19901,19902,19919,19952,19958,19961,19964],{},[1439,19903,19904,19905,19918],{},"Závisle proměnná ",[1115,19906,19908],{"className":19907},[1138],[1140,19909,19910],{"xmlns":1142},[1144,19911,19912,19916],{},[1147,19913,19914],{},[1153,19915,7132],{},[1159,19917,7132],{"encoding":1161}," musí být aspoň intervalového typu (ne binární, diskrétní s málo hodnotami apod.) — jinak je na místě logistická regrese.",[1439,19920,19921,19922,19951],{},"Nezávislé proměnné ",[1115,19923,19925],{"className":19924},[1138],[1140,19926,19927],{"xmlns":1142},[1144,19928,19929,19949],{},[1147,19930,19931,19937,19939,19941,19943],{},[1150,19932,19933,19935],{},[1153,19934,1240],{},[1565,19936,1794],{},[1242,19938,1797],{"separator":1121},[1242,19940,1800],{},[1242,19942,1797],{"separator":1121},[1150,19944,19945,19947],{},[1153,19946,1240],{},[1153,19948,1110],{},[1159,19950,16289],{"encoding":1161}," jsou rovněž aspoň intervalového typu, mohou být i alternativní.",[1439,19953,19954,19955,1669],{},"Nezávislé proměnné by mezi sebou neměly být příliš vysoce korelované — ",[1540,19956,19957],{},"multikolinearita",[1439,19959,19960],{},"V datech nesmí být odlehlé či extrémní hodnoty; regresní analýza je na ně citlivá a mohou vážně narušit kvalitu odhadů.",[1439,19962,19963],{},"Proměnné musí být ve vzájemně lineárním vztahu — vícenásobná lineární regrese je založená na Pearsonově koeficientu korelace, takže nelineární vztahy mezi proměnnými zůstanou neodhalené.",[1439,19965,19966,19967,19971],{},"Proměnné mají mít ",[1127,19968,19970],{"className":19969,"dataFsResolvedFilePath":6620,"href":6621},[1130],"normální rozložení","; význam tohoto předpokladu ustupuje do pozadí u dostatečně velkého datového souboru díky centrální limitní větě.",[1110,19973,19974,19975,19978],{},"Normalita se u menšího počtu pozorování ověřuje stejnými testy jako u jiných znaků (viz ",[1127,19976,1723],{"className":19977,"dataFsResolvedFilePath":1721,"href":1722},[1130],") — Shapiro–Wilkovým nebo Kolmogorovovým–Smirnovovým testem — nebo graficky grafem reziduí proti predikovaným hodnotám, kde by body měly být rovnoměrně rozptýlené po obou stranách vodorovné osy.",[16749,19980,19981],{"id":19957},"Multikolinearita",[1110,19983,19984],{},"Multikolinearita vzniká, když vysvětlující proměnné silně závisejí jedna na druhé. Je nežádoucí, protože:",[1436,19986,19987,19990,19993],{},[1439,19988,19989],{},"výsledky regrese jsou pak nespolehlivé,",[1439,19991,19992],{},"zvyšuje pravděpodobnost, že se důležitá proměnná jeví jako statisticky nevýznamná a bude z modelu vyřazena,",[1439,19994,19995],{},"směrodatné odchylky odhadnutých parametrů jsou vysoké, testová kritéria t-testů nízká, p-hodnoty vysoké.",[1110,19997,19998,19999,20002,20003,20026,20027,20045,20046,20062],{},"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 ",[1540,20000,20001],{},"VIF (Variance Inflation Factor)",": hodnoty ",[1115,20004,20006],{"className":20005},[1138],[1140,20007,20008],{"xmlns":1142},[1144,20009,20010,20023],{},[1147,20011,20012,20014,20016,20019,20021],{},[1565,20013,1794],{},[1242,20015,4332],{},[2909,20017,20018],{},"VIF",[1242,20020,4332],{},[1565,20022,9929],{},[1159,20024,20025],{"encoding":1161},"1\u003C\\text{VIF}\u003C5"," jsou varující, ",[1115,20028,20030],{"className":20029},[1138],[1140,20031,20032],{"xmlns":1142},[1144,20033,20034,20042],{},[1147,20035,20036,20038,20040],{},[2909,20037,20018],{},[1242,20039,1689],{},[1565,20041,9929],{},[1159,20043,20044],{"encoding":1161},"\\text{VIF}>5"," (přísněji ",[1115,20047,20049],{"className":20048},[1138],[1140,20050,20051],{"xmlns":1142},[1144,20052,20053,20059],{},[1147,20054,20055,20057],{},[1242,20056,1689],{},[1565,20058,9036],{},[1159,20060,20061],{"encoding":1161},">10",") značí vysokou multikolinearitu.",[1110,20064,20065],{},"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.",[16749,20067,20069],{"id":20068},"další-ukazatele-kvality-modelu","Další ukazatele kvality modelu",[1436,20071,20072,20078,20084],{},[1439,20073,20074,20077],{},[1540,20075,20076],{},"F-test"," — testuje hypotézu, že všechny regresní koeficienty jsou rovny nule, proti alternativě, že aspoň jeden v modelu být má (celková významnost modelu).",[1439,20079,20080,20083],{},[1540,20081,20082],{},"RMSE"," (odmocnina z reziduálního rozptylu) — absolutní měřítko vhodnosti funkce (na rozdíl od indexu determinace, který je relativní); nižší hodnota znamená lepší fit.",[1439,20085,20086,20089,20090,20093],{},[1540,20087,20088],{},"AIC"," (Akaikeho informační kritérium) a ",[1540,20091,20092],{},"BIC"," (Bayesovo informační kritérium) — čím nižší hodnoty obou kritérií, tím lepší model; používají se hlavně při stepwise výběru proměnných.",[16749,20095,16752],{"id":20096},"v-r-2",[1110,20098,20099],{},"Pro vícenásobnou regresi je postup v R rozšířením postupu pro regresní přímku — přibývá výběr proměnných a kontrola multikolinearity:",[3694,20101,20103],{"className":3696,"code":20102,"language":71,"meta":1490,"style":1490},"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",[3470,20104,20105,20131,20175,20201,20211,20215,20226,20237,20241,20251,20261,20265,20275,20285,20290],{"__ignoreMap":1490},[1115,20106,20107,20110,20112,20115,20117,20120,20122,20125,20127,20129],{"class":3702,"line":10},[1115,20108,20109],{"class":3705},"data",[1115,20111,3710],{"class":3709},[1115,20113,20114],{"class":3713}," read.table",[1115,20116,1875],{"class":3717},[1115,20118,20119],{"class":3840},"\"4_4.txt\"",[1115,20121,1797],{"class":3709},[1115,20123,20124],{"class":3705}," header",[1115,20126,3797],{"class":3709},[1115,20128,3810],{"class":3724},[1115,20130,3901],{"class":3717},[1115,20132,20133,20136,20138,20140,20142,20144,20146,20149,20151,20154,20156,20159,20161,20164,20166,20169,20171,20173],{"class":3702,"line":27},[1115,20134,20135],{"class":3705},"model_plny",[1115,20137,3710],{"class":3709},[1115,20139,16853],{"class":3713},[1115,20141,1875],{"class":3717},[1115,20143,7132],{"class":3705},[1115,20145,16860],{"class":3709},[1115,20147,20148],{"class":3705}," x1",[1115,20150,18517],{"class":3709},[1115,20152,20153],{"class":3705}," x2",[1115,20155,18517],{"class":3709},[1115,20157,20158],{"class":3705}," x3",[1115,20160,18517],{"class":3709},[1115,20162,20163],{"class":3705}," x4",[1115,20165,1797],{"class":3709},[1115,20167,20168],{"class":3705}," data",[1115,20170,3797],{"class":3709},[1115,20172,20168],{"class":3705},[1115,20174,3901],{"class":3717},[1115,20176,20177,20180,20182,20185,20187,20189,20191,20194,20196,20199],{"class":3702,"line":148},[1115,20178,20179],{"class":3705},"model_krok",[1115,20181,3710],{"class":3709},[1115,20183,20184],{"class":3713}," step",[1115,20186,1875],{"class":3717},[1115,20188,20135],{"class":3705},[1115,20190,1797],{"class":3709},[1115,20192,20193],{"class":3705}," direction",[1115,20195,3797],{"class":3709},[1115,20197,20198],{"class":3840}," \"both\"",[1115,20200,3901],{"class":3717},[1115,20202,20203,20205,20207,20209],{"class":3702,"line":111},[1115,20204,1509],{"class":3713},[1115,20206,1875],{"class":3717},[1115,20208,20179],{"class":3705},[1115,20210,3901],{"class":3717},[1115,20212,20213],{"class":3702,"line":96},[1115,20214,10044],{"emptyLinePlaceholder":1499},[1115,20216,20217,20219,20221,20224],{"class":3702,"line":89},[1115,20218,17398],{"class":3709},[1115,20220,1875],{"class":3717},[1115,20222,20223],{"class":3705},"car",[1115,20225,3901],{"class":3717},[1115,20227,20228,20231,20233,20235],{"class":3702,"line":82},[1115,20229,20230],{"class":3713},"vif",[1115,20232,1875],{"class":3717},[1115,20234,20179],{"class":3705},[1115,20236,3901],{"class":3717},[1115,20238,20239],{"class":3702,"line":75},[1115,20240,10044],{"emptyLinePlaceholder":1499},[1115,20242,20243,20245,20247,20249],{"class":3702,"line":3891},[1115,20244,17398],{"class":3709},[1115,20246,1875],{"class":3717},[1115,20248,17403],{"class":3705},[1115,20250,3901],{"class":3717},[1115,20252,20253,20255,20257,20259],{"class":3702,"line":72},[1115,20254,17410],{"class":3713},[1115,20256,1875],{"class":3717},[1115,20258,20179],{"class":3705},[1115,20260,3901],{"class":3717},[1115,20262,20263],{"class":3702,"line":25},[1115,20264,10044],{"emptyLinePlaceholder":1499},[1115,20266,20267,20269,20271,20273],{"class":3702,"line":65},[1115,20268,17398],{"class":3709},[1115,20270,1875],{"class":3717},[1115,20272,17493],{"class":3705},[1115,20274,3901],{"class":3717},[1115,20276,20277,20279,20281,20283],{"class":3702,"line":63},[1115,20278,17500],{"class":3713},[1115,20280,1875],{"class":3717},[1115,20282,20179],{"class":3705},[1115,20284,3901],{"class":3717},[1115,20286,20288],{"class":3702,"line":20287},14,[1115,20289,10044],{"emptyLinePlaceholder":1499},[1115,20291,20292,20294,20296,20298,20300,20302],{"class":3702,"line":60},[1115,20293,17578],{"class":3713},[1115,20295,1875],{"class":3717},[1115,20297,17046],{"class":3713},[1115,20299,1875],{"class":3717},[1115,20301,20179],{"class":3705},[1115,20303,9496],{"class":3717},[1110,20305,20306,20308,20309,20312],{},[3470,20307,16123],{}," provádí stepwise výběr podle AIC, ",[3470,20310,20311],{},"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.",[1103,20314,20316,20323,20326,20329],{"className":20315,"dataCallout":3477},[1106,3476],[1110,20317,20319,20322],{"className":20318},[1113],[1115,20320],{"className":20321,"ariaHidden":1121},[1118,3484,1120],"Příklad: Vícenásobná regrese",[1110,20324,20325],{},"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.",[1110,20327,20328],{},"Postup: odhad plného modelu → stepwise analýza podle AIC → ověření předpokladů.",[1110,20330,20331,20332,20335,20336,20338,20339,20342],{},"Diagnostika odhaleného modelu ukázala tři problémy: (1) ",[1540,20333,20334],{},"nelinearita"," — mezi některými vysvětlujícími proměnnými a cenou je zjevně jiný než lineární vztah, řešením je zkusit u nich druhou mocninu; (2) ",[1540,20337,19957],{}," mezi dvojicí proměnných popisujících vzdálenost (k silnici a ke spalovně) — doporučeno jednu z nich vynechat; (3) ",[1540,20340,20341],{},"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.",[1189,20344,6407],{"id":6406},[1103,20346,20348,20355],{"className":20347,"dataCallout":6412},[1106,6411],[1110,20349,20351,20354],{"className":20350},[1113],[1115,20352],{"className":20353,"ariaHidden":1121},[1118,6419,1120],"Koeficient korelace jen pro přímku",[1110,20356,20357,20358,20414,20415,20432,20433,20453,20454,1163,20467,1669],{},"Vzorec ",[1115,20359,20361],{"className":20360},[1138],[1140,20362,20363],{"xmlns":1142},[1144,20364,20365,20411],{},[1147,20366,20367,20377,20379,20389,20391],{},[1150,20368,20369,20371],{},[1153,20370,71],{},[1147,20372,20373,20375],{},[1153,20374,1240],{},[1153,20376,7132],{},[1242,20378,1982],{},[1150,20380,20381,20383],{},[1153,20382,1291],{},[1147,20384,20385,20387],{},[1153,20386,1240],{},[1153,20388,7132],{},[1153,20390,4604],{"mathvariant":2121},[4453,20392,20393],{},[1147,20394,20395,20403],{},[3353,20396,20397,20399,20401],{},[1153,20398,1291],{},[1153,20400,1240],{},[1565,20402,1589],{},[3353,20404,20405,20407,20409],{},[1153,20406,1291],{},[1153,20408,7132],{},[1565,20410,1589],{},[1159,20412,20413],{"encoding":1161},"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 ",[1115,20416,20418],{"className":20417},[1138],[1140,20419,20420],{"xmlns":1142},[1144,20421,20422,20430],{},[1147,20423,20424],{},[1582,20425,20426,20428],{},[1153,20427,1260],{},[1565,20429,1589],{},[1159,20431,16027],{"encoding":1161},", případně obecným indexem korelace ",[1115,20434,20436],{"className":20435},[1138],[1140,20437,20438],{"xmlns":1142},[1144,20439,20440,20450],{},[1147,20441,20442],{},[4453,20443,20444],{},[1582,20445,20446,20448],{},[1153,20447,1260],{},[1565,20449,1589],{},[1159,20451,20452],{"encoding":1161},"\\sqrt{R^2}"," — ne koeficientem korelace mezi ",[1115,20455,20457],{"className":20456},[1138],[1140,20458,20459],{"xmlns":1142},[1144,20460,20461,20465],{},[1147,20462,20463],{},[1153,20464,1240],{},[1159,20466,1240],{"encoding":1161},[1115,20468,20470],{"className":20469},[1138],[1140,20471,20472],{"xmlns":1142},[1144,20473,20474,20478],{},[1147,20475,20476],{},[1153,20477,7132],{},[1159,20479,7132],{"encoding":1161},[1103,20481,20483,20490],{"className":20482,"dataCallout":6412},[1106,6411],[1110,20484,20486,20489],{"className":20485},[1113],[1115,20487],{"className":20488,"ariaHidden":1121},[1118,6419,1120],"Významný F-test, nevýznamné t-testy",[1110,20491,20492],{},"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.",[1103,20494,20496,20503],{"className":20495,"dataCallout":6412},[1106,6411],[1110,20497,20499,20502],{"className":20498},[1113],[1115,20500],{"className":20501,"ariaHidden":1121},[1118,6419,1120],"Durbin-Watsonova statistika mimo okolí 2",[1110,20504,20505],{},"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.",[1103,20507,20509,20516],{"className":20508,"dataCallout":6412},[1106,6411],[1110,20510,20512,20515],{"className":20511},[1113],[1115,20513],{"className":20514,"ariaHidden":1121},[1118,6419,1120],"Nízký počet pozorování při stepwise výběru",[1110,20517,20518],{},"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 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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.",[1439,20625,20626,20627,1346,20653,1163,20679,1669],{},"Regulace měřením (spojitá veličina s normálním rozdělením): diagramy ",[1115,20628,20630],{"className":20629},[1138],[1140,20631,20632],{"xmlns":1142},[1144,20633,20634,20650],{},[1147,20635,20636,20638,20644,20646,20648],{},[1242,20637,1875],{"stretchy":1874},[1236,20639,20640,20642],{"accent":1121},[1153,20641,1240],{},[1242,20643,1244],{},[1242,20645,1797],{"separator":1121},[1153,20647,1260],{},[1242,20649,1886],{"stretchy":1874},[1159,20651,20652],{"encoding":1161},"(\\bar{x}, R)",[1115,20654,20656],{"className":20655},[1138],[1140,20657,20658],{"xmlns":1142},[1144,20659,20660,20676],{},[1147,20661,20662,20664,20670,20672,20674],{},[1242,20663,1875],{"stretchy":1874},[1236,20665,20666,20668],{"accent":1121},[1153,20667,1240],{},[1242,20669,1244],{},[1242,20671,1797],{"separator":1121},[1153,20673,1291],{},[1242,20675,1886],{"stretchy":1874},[1159,20677,20678],{"encoding":1161},"(\\bar{x}, s)",[1115,20680,20682],{"className":20681},[1138],[1140,20683,20684],{"xmlns":1142},[1144,20685,20686,20714],{},[1147,20687,20688,20690,20696,20698,20712],{},[1242,20689,1875],{"stretchy":1874},[1150,20691,20692,20694],{},[1153,20693,1240],{},[1153,20695,1878],{},[1242,20697,1797],{"separator":1121},[1150,20699,20700,20702],{},[1153,20701,1260],{},[1147,20703,20704,20706,20708,20710],{},[1153,20705,1183],{},[1153,20707,1327],{},[1242,20709,1797],{"separator":1121},[1153,20711,1878],{},[1242,20713,1886],{"stretchy":1874},[1159,20715,20716],{"encoding":1161},"(x_i, R_{kl,i})",[1439,20718,20719,20720,20733,20734,20747,20748,20763,20764,20777],{},"Regulace srovnáváním (diskrétní veličina): počet neshod ",[1115,20721,20723],{"className":20722},[1138],[1140,20724,20725],{"xmlns":1142},[1144,20726,20727,20731],{},[1147,20728,20729],{},[1153,20730,1343],{},[1159,20732,1343],{"encoding":1161}," (konstantní rozsah) a ",[1115,20735,20737],{"className":20736},[1138],[1140,20738,20739],{"xmlns":1142},[1144,20740,20741,20745],{},[1147,20742,20743],{},[1153,20744,1358],{},[1159,20746,1358],{"encoding":1161}," (nekonstantní rozsah), počet neshodných produktů ",[1115,20749,20751],{"className":20750},[1138],[1140,20752,20753],{"xmlns":1142},[1144,20754,20755,20761],{},[1147,20756,20757,20759],{},[1153,20758,1372],{},[1153,20760,1110],{},[1159,20762,1377],{"encoding":1161}," (konstantní rozsah) a jejich podíl ",[1115,20765,20767],{"className":20766},[1138],[1140,20768,20769],{"xmlns":1142},[1144,20770,20771,20775],{},[1147,20772,20773],{},[1153,20774,1110],{},[1159,20776,1110],{"encoding":1161}," (nekonstantní rozsah).",[1439,20779,20780],{},"Podskupiny s vymezitelnou příčinou se po jejím odstranění z výpočtu vyřadí a meze se přepočítají, dokud jsou všechny body uvnitř mezí.",[1439,20782,20783,20784,1346,20801,1346,20822,1346,20844,20868,20869,20890],{},"Indexy způsobilosti ",[1115,20785,20787],{"className":20786},[1138],[1140,20788,20789],{"xmlns":1142},[1144,20790,20791,20799],{},[1147,20792,20793],{},[1150,20794,20795,20797],{},[1153,20796,1155],{},[1153,20798,1110],{},[1159,20800,1162],{"encoding":1161},[1115,20802,20804],{"className":20803},[1138],[1140,20805,20806],{"xmlns":1142},[1144,20807,20808,20820],{},[1147,20809,20810],{},[1150,20811,20812,20814],{},[1153,20813,1155],{},[1147,20815,20816,20818],{},[1153,20817,1110],{},[1153,20819,1183],{},[1159,20821,1186],{"encoding":1161},[1115,20823,20825],{"className":20824},[1138],[1140,20826,20827],{"xmlns":1142},[1144,20828,20829,20841],{},[1147,20830,20831],{},[1150,20832,20833,20835],{},[1153,20834,1155],{},[1147,20836,20837,20839],{},[1153,20838,1110],{},[1153,20840,4471],{},[1159,20842,20843],{"encoding":1161},"C_{pm}",[1115,20845,20847],{"className":20846},[1138],[1140,20848,20849],{"xmlns":1142},[1144,20850,20851,20865],{},[1147,20852,20853],{},[1150,20854,20855,20857],{},[1153,20856,1155],{},[1147,20858,20859,20861,20863],{},[1153,20860,1110],{},[1153,20862,4471],{},[1153,20864,1183],{},[1159,20866,20867],{"encoding":1161},"C_{pmk}"," posuzují, zda statisticky zvládnutý proces vyhovuje tolerančním mezím; ",[1115,20870,20872],{"className":20871},[1138],[1140,20873,20874],{"xmlns":1142},[1144,20875,20876,20888],{},[1147,20877,20878],{},[1150,20879,20880,20882],{},[1153,20881,1155],{},[1147,20883,20884,20886],{},[1153,20885,1110],{},[1153,20887,1183],{},[1159,20889,1186],{"encoding":1161}," navíc zohledňuje vychýlení střední hodnoty.",[1439,20892,20893,20894,1669],{},"V R diagramy i indexy počítá balíček ",[3470,20895,360],{},[1189,20897,20899],{"id":20898},"statistická-regulace-procesu","Statistická regulace procesu",[1110,20901,20902,20903,20905,20906,1669],{},"Tradiční zabezpečování jakosti kontroluje výrobky až po jejich vyrobení, což je neekonomické. ",[1540,20904,20899],{}," 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 ",[1540,20907,20908],{},"statisticky zvládnutém stavu",[1110,20910,20911,20912,20915],{},"Teorie regulace vychází z ",[1540,20913,20914],{},"variability"," procesu, kterou způsobují dva druhy příčin:",[1194,20917,20918,20930],{},[1197,20919,20920],{},[1200,20921,20922,20924,20927],{},[1203,20923],{},[1203,20925,20926],{},"Náhodné příčiny",[1203,20928,20929],{},"Vymezitelné příčiny",[1210,20931,20932,20943,20954],{},[1200,20933,20934,20937,20940],{},[1215,20935,20936],{},"Povaha",[1215,20938,20939],{},"široká skupina neidentifikovatelných vlivů, každý přispívá k variabilitě malou měrou",[1215,20941,20942],{},"vlivy, které za běžných podmínek na proces nepůsobí; vyvolají nepřirozené kolísání údajů",[1200,20944,20945,20948,20951],{},[1215,20946,20947],{},"Stav procesu",[1215,20949,20950],{},"ustálený, jakost výstupů je předvídatelná, není nutné zasahovat — statisticky zvládnutý",[1215,20952,20953],{},"jakost výstupů není předvídatelná, je nutné zasáhnout — proces není statisticky zvládnutý",[1200,20955,20956,20959,20962],{},[1215,20957,20958],{},"Příklady",[1215,20960,20961],{},"psychický stav pracovníka, chvění stroje, teplota ovzduší",[1215,20963,20964],{},"změna materiálu, nezaškolená obsluha",[1110,20966,20967,20968,20971,20972,20975],{},"Vymezitelné příčiny jsou ",[1540,20969,20970],{},"sporadické"," (vznikají náhle, změny trvají krátce) nebo ",[1540,20973,20974],{},"přetrvávající"," (trvají stále nebo se mění).",[1110,20977,20978],{},[4383,20979],{"alt":20980,"className":20981,"src":20982},"mask-ilu-pricin-variability",[1130,4387],"\u002Fwiki-assets\u002Fmask-ilu-pricin-variability.png",[1110,20984,20985],{},"Regulace probíhá ve třech fázích:",[2865,20987,20988,20998,21004],{},[1439,20989,20990,20993,20994,20997],{},[1540,20991,20992],{},"Fáze přípravná"," — stanoví se sledované znaky jakosti (rozměr, hmotnost, počet vad…), délka časového intervalu mezi měřeními, ",[1540,20995,20996],{},"logická podskupina"," (skupina měření, v níž se předpokládá působení pouze náhodných příčin), typ regulačního diagramu a místa kontroly v procesu.",[1439,20999,21000,21003],{},[1540,21001,21002],{},"Fáze zabezpečování statistické zvládnutosti"," — pomocí regulačních diagramů se identifikují vymezitelné příčiny a odstraní se jejich působení.",[1439,21005,21006,21009],{},[1540,21007,21008],{},"Fáze analýzy a zabezpečení způsobilosti"," — zkoumá se, zda statisticky zvládnutý proces vyhovuje požadavkům zákazníka; k tomu slouží indexy způsobilosti (níže).",[1189,21011,21013],{"id":21012},"princip-regulačního-diagramu","Princip regulačního diagramu",[1110,21015,21016,21019],{},[1540,21017,21018],{},"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.",[1436,21021,21022,21028,21034],{},[1439,21023,21024,21027],{},[1540,21025,21026],{},"CL"," — střední přímka, odpovídá požadované (referenční) hodnotě použité charakteristiky,",[1439,21029,21030,21033],{},[1540,21031,21032],{},"UCL"," — horní akční regulační mez,",[1439,21035,21036,21039],{},[1540,21037,21038],{},"LCL"," — dolní akční regulační mez.",[1110,21041,21042],{},"Akční meze vymezují pásmo působení pouze náhodných příčin variability.",[1110,21044,21045],{},[4383,21046],{"alt":21047,"className":21048,"src":21049},"mask-rd-schema",[1130,4387],"\u002Fwiki-assets\u002Fmask-rd-schema.png",[1110,21051,21052,21055],{},[1540,21053,21054],{},"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.",[1110,21057,21058,21059,21062,21063,21066],{},"Podle charakteru regulované veličiny se diagramy dělí na diagramy pro ",[1540,21060,21061],{},"regulaci měřením"," (regulovaná veličina je spojitá náhodná veličina) a pro ",[1540,21064,21065],{},"regulaci srovnáváním"," (diskrétní náhodná veličina).",[1110,21068,21069],{},"Postup při konstrukci regulačního diagramu:",[2865,21071,21072,21075,21078,21081,21084,21087,21090,21093,21096],{},[1439,21073,21074],{},"volba regulované veličiny,",[1439,21076,21077],{},"sběr a záznam dat,",[1439,21079,21080],{},"ověření požadovaných předpokladů o datech,",[1439,21082,21083],{},"volba rozsahu logických podskupin,",[1439,21085,21086],{},"volba vhodného regulačního diagramu,",[1439,21088,21089],{},"výpočet hodnot zvoleného testového kritéria pro jednotlivé výběry,",[1439,21091,21092],{},"ověření a zajištění statistické zvládnutosti procesu,",[1439,21094,21095],{},"ověření způsobilosti procesu,",[1439,21097,21098],{},"vlastní regulace procesu.",[1189,21100,21102],{"id":21101},"regulace-měřením","Regulace měřením",[1110,21104,21105],{},"Diagramy pro regulaci měřením se používají, když je regulovaná veličina měřitelná. Požaduje se, aby:",[1436,21107,21108,21111],{},[1439,21109,21110],{},"jednotlivá měření byla vzájemně nezávislá,",[1439,21112,21113,21114,21127,21128,21141,21142,21155,21156,21169],{},"regulovaná veličina byla spojitá náhodná veličina s normálním rozdělením se střední hodnotou ",[1115,21115,21117],{"className":21116},[1138],[1140,21118,21119],{"xmlns":1142},[1144,21120,21121,21125],{},[1147,21122,21123],{},[1153,21124,6893],{},[1159,21126,8799],{"encoding":1161}," a směrodatnou odchylkou ",[1115,21129,21131],{"className":21130},[1138],[1140,21132,21133],{"xmlns":1142},[1144,21134,21135,21139],{},[1147,21136,21137],{},[1153,21138,6901],{},[1159,21140,6933],{"encoding":1161}," — tyto dva parametry charakterizují statistickou stabilitu procesu; ",[1115,21143,21145],{"className":21144},[1138],[1140,21146,21147],{"xmlns":1142},[1144,21148,21149,21153],{},[1147,21150,21151],{},[1153,21152,6893],{},[1159,21154,8799],{"encoding":1161}," je hodnota, na niž je proces nastaven, ",[1115,21157,21159],{"className":21158},[1138],[1140,21160,21161],{"xmlns":1142},[1144,21162,21163,21167],{},[1147,21164,21165],{},[1153,21166,6901],{},[1159,21168,6933],{"encoding":1161}," charakterizuje jeho přesnost.",[1110,21171,21172,21173,1346,21198,1163,21223,21260],{},"Jsou-li předpoklady splněny, volí se diagramy, které současně sledují stabilitu polohy i stabilitu rozptylu: ",[1115,21174,21176],{"className":21175},[1138],[1140,21177,21178],{"xmlns":1142},[1144,21179,21180,21196],{},[1147,21181,21182,21184,21190,21192,21194],{},[1242,21183,1875],{"stretchy":1874},[1236,21185,21186,21188],{"accent":1121},[1153,21187,1240],{},[1242,21189,1244],{},[1242,21191,1797],{"separator":1121},[1153,21193,1260],{},[1242,21195,1886],{"stretchy":1874},[1159,21197,20652],{"encoding":1161},[1115,21199,21201],{"className":21200},[1138],[1140,21202,21203],{"xmlns":1142},[1144,21204,21205,21221],{},[1147,21206,21207,21209,21215,21217,21219],{},[1242,21208,1875],{"stretchy":1874},[1236,21210,21211,21213],{"accent":1121},[1153,21212,1240],{},[1242,21214,1244],{},[1242,21216,1797],{"separator":1121},[1153,21218,1291],{},[1242,21220,1886],{"stretchy":1874},[1159,21222,20678],{"encoding":1161},[1115,21224,21226],{"className":21225},[1138],[1140,21227,21228],{"xmlns":1142},[1144,21229,21230,21258],{},[1147,21231,21232,21234,21240,21242,21256],{},[1242,21233,1875],{"stretchy":1874},[1150,21235,21236,21238],{},[1153,21237,1240],{},[1153,21239,1878],{},[1242,21241,1797],{"separator":1121},[1150,21243,21244,21246],{},[1153,21245,1260],{},[1147,21247,21248,21250,21252,21254],{},[1153,21249,1183],{},[1153,21251,1327],{},[1242,21253,1797],{"separator":1121},[1153,21255,1878],{},[1242,21257,1886],{"stretchy":1874},[1159,21259,20716],{"encoding":1161},". Výsledkem jsou vždy dva diagramy.",[16749,21262,21264,21265],{"id":21263},"diagram-xˉrbarx-r","Diagram ",[1115,21266,21268],{"className":21267},[1138],[1140,21269,21270],{"xmlns":1142},[1144,21271,21272,21288],{},[1147,21273,21274,21276,21282,21284,21286],{},[1242,21275,1875],{"stretchy":1874},[1236,21277,21278,21280],{"accent":1121},[1153,21279,1240],{},[1242,21281,1244],{},[1242,21283,1797],{"separator":1121},[1153,21285,1260],{},[1242,21287,1886],{"stretchy":1874},[1159,21289,20652],{"encoding":1161},[1110,21291,21292,21293,21315,21316,21334],{},"Regulované veličiny jsou výběrové průměry ",[1115,21294,21296],{"className":21295},[1138],[1140,21297,21298],{"xmlns":1142},[1144,21299,21300,21312],{},[1147,21301,21302],{},[1150,21303,21304,21310],{},[1236,21305,21306,21308],{"accent":1121},[1153,21307,1240],{},[1242,21309,1244],{},[1153,21311,1878],{},[1159,21313,21314],{"encoding":1161},"\\bar{x}_i"," a výběrová rozpětí ",[1115,21317,21319],{"className":21318},[1138],[1140,21320,21321],{"xmlns":1142},[1144,21322,21323,21331],{},[1147,21324,21325],{},[1150,21326,21327,21329],{},[1153,21328,1260],{},[1153,21330,1878],{},[1159,21332,21333],{"encoding":1161},"R_i"," v logických podskupinách:",[1115,21336,21338],{"className":21337},[1138],[1140,21339,21340],{"xmlns":1142,"display":1964},[1144,21341,21342,21443],{},[1147,21343,21344,21354,21356,21362,21376,21386,21388,21390,21396,21398,21409,21419,21421,21431,21441],{},[1150,21345,21346,21352],{},[1236,21347,21348,21350],{"accent":1121},[1153,21349,1240],{},[1242,21351,1244],{},[1153,21353,1878],{},[1242,21355,1982],{},[2739,21357,21358,21360],{},[1565,21359,1794],{},[1153,21361,1372],{},[1984,21363,21364,21366,21374],{},[1242,21365,1988],{},[1147,21367,21368,21370,21372],{},[1153,21369,1883],{},[1242,21371,1982],{},[1565,21373,1794],{},[1153,21375,1372],{},[1150,21377,21378,21380],{},[1153,21379,1240],{},[1147,21381,21382,21384],{},[1153,21383,1878],{},[1153,21385,1883],{},[1242,21387,1797],{"separator":1121},[2012,21389],{"width":2014},[1150,21391,21392,21394],{},[1153,21393,1260],{},[1153,21395,1878],{},[1242,21397,1982],{},[21399,21400,21401,21407],"munder",{},[1147,21402,21403,21405],{},[1153,21404,11721],{},[1242,21406,4491],{},[1153,21408,1883],{},[1150,21410,21411,21413],{},[1153,21412,1240],{},[1147,21414,21415,21417],{},[1153,21416,1878],{},[1153,21418,1883],{},[1242,21420,3064],{},[21399,21422,21423,21429],{},[1147,21424,21425,21427],{},[1153,21426,4488],{},[1242,21428,4491],{},[1153,21430,1883],{},[1150,21432,21433,21435],{},[1153,21434,1240],{},[1147,21436,21437,21439],{},[1153,21438,1878],{},[1153,21440,1883],{},[1153,21442,1669],{"mathvariant":2121},[1159,21444,21445],{"encoding":1161},"\\bar{x}_i = \\frac{1}{n}\\sum_{j=1}^n x_{ij}, \\qquad R_i = \\max_j x_{ij} - \\min_j x_{ij}.",[1110,21447,21448],{},"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.",[1110,21450,21451,21452,21478,21479,21492,21493,1163,21514,21531,21532,21545,21546,21564,21565,1669],{},"Data se zapisují do tabulky: řádek ",[1115,21453,21455],{"className":21454},[1138],[1140,21456,21457],{"xmlns":1142},[1144,21458,21459,21475],{},[1147,21460,21461,21463,21465,21467,21469,21471,21473],{},[1153,21462,1878],{},[1242,21464,1982],{},[1565,21466,1794],{},[1242,21468,1797],{"separator":1121},[1242,21470,1800],{},[1242,21472,1797],{"separator":1121},[1153,21474,1183],{},[1159,21476,21477],{"encoding":1161},"i = 1, \\dots, k"," je logická podskupina v pořadí, v jakém byla získána, sloupce obsahují ",[1115,21480,21482],{"className":21481},[1138],[1140,21483,21484],{"xmlns":1142},[1144,21485,21486,21490],{},[1147,21487,21488],{},[1153,21489,1372],{},[1159,21491,1372],{"encoding":1161}," naměřených hodnot a poslední dva sloupce ",[1115,21494,21496],{"className":21495},[1138],[1140,21497,21498],{"xmlns":1142},[1144,21499,21500,21512],{},[1147,21501,21502],{},[1150,21503,21504,21510],{},[1236,21505,21506,21508],{"accent":1121},[1153,21507,1240],{},[1242,21509,1244],{},[1153,21511,1878],{},[1159,21513,21314],{"encoding":1161},[1115,21515,21517],{"className":21516},[1138],[1140,21518,21519],{"xmlns":1142},[1144,21520,21521,21529],{},[1147,21522,21523],{},[1150,21524,21525,21527],{},[1153,21526,1260],{},[1153,21528,1878],{},[1159,21530,21333],{"encoding":1161},". Pro sestrojení diagramu je potřeba aspoň 20 podskupin. Nejprve se určí diagram ",[1115,21533,21535],{"className":21534},[1138],[1140,21536,21537],{"xmlns":1142},[1144,21538,21539,21543],{},[1147,21540,21541],{},[1153,21542,1260],{},[1159,21544,1260],{"encoding":1161},", potom diagram ",[1115,21547,21549],{"className":21548},[1138],[1140,21550,21551],{"xmlns":1142},[1144,21552,21553,21561],{},[1147,21554,21555],{},[1236,21556,21557,21559],{"accent":1121},[1153,21558,1240],{},[1242,21560,1244],{},[1159,21562,21563],{"encoding":1161},"\\bar{x}"," — u obou střední přímka a akční meze. V R se diagramy konstruují funkcí ",[3470,21566,21567],{},"qcc()",[1103,21569,21571,21578],{"className":21570,"dataCallout":3477},[1106,3476],[1110,21572,21574,21577],{"className":21573},[1113],[1115,21575],{"className":21576,"ariaHidden":1121},[1118,3484,1120],"Příklad: kontrola rozměru dílu ve 20 logických podskupinách",[1110,21579,21580,21581,21594,21595,1346,21613,21631,21632,1669],{},"Naměřená data znaku jakosti ",[1115,21582,21584],{"className":21583},[1138],[1140,21585,21586],{"xmlns":1142},[1144,21587,21588,21592],{},[1147,21589,21590],{},[1153,21591,6734],{},[1159,21593,6734],{"encoding":1161}," byla získána ve 20 logických podskupinách po 4 měřeních (",[1115,21596,21598],{"className":21597},[1138],[1140,21599,21600],{"xmlns":1142},[1144,21601,21602,21610],{},[1147,21603,21604,21606,21608],{},[1153,21605,1183],{},[1242,21607,1982],{},[1565,21609,4045],{},[1159,21611,21612],{"encoding":1161},"k=20",[1115,21614,21616],{"className":21615},[1138],[1140,21617,21618],{"xmlns":1142},[1144,21619,21620,21628],{},[1147,21621,21622,21624,21626],{},[1153,21623,1372],{},[1242,21625,1982],{},[1565,21627,3542],{},[1159,21629,21630],{"encoding":1161},"n=4","); znak je měřitelný a má normální rozdělení. Sestrojte regulační diagram ",[1115,21633,21635],{"className":21634},[1138],[1140,21636,21637],{"xmlns":1142},[1144,21638,21639,21655],{},[1147,21640,21641,21643,21649,21651,21653],{},[1242,21642,1875],{"stretchy":1874},[1236,21644,21645,21647],{"accent":1121},[1153,21646,1240],{},[1242,21648,1244],{},[1242,21650,1797],{"separator":1121},[1153,21652,1260],{},[1242,21654,1886],{"stretchy":1874},[1159,21656,20652],{"encoding":1161},[1194,21658,21659,21774],{},[1197,21660,21661],{},[1200,21662,21663,21678,21702,21726,21750],{},[1203,21664,21665],{},[1115,21666,21668],{"className":21667},[1138],[1140,21669,21670],{"xmlns":1142},[1144,21671,21672,21676],{},[1147,21673,21674],{},[1153,21675,1878],{},[1159,21677,1878],{"encoding":1161},[1203,21679,21680],{},[1115,21681,21683],{"className":21682},[1138],[1140,21684,21685],{"xmlns":1142},[1144,21686,21687,21699],{},[1147,21688,21689],{},[1150,21690,21691,21693],{},[1153,21692,1240],{},[1147,21694,21695,21697],{},[1153,21696,1878],{},[1565,21698,1794],{},[1159,21700,21701],{"encoding":1161},"x_{i1}",[1203,21703,21704],{},[1115,21705,21707],{"className":21706},[1138],[1140,21708,21709],{"xmlns":1142},[1144,21710,21711,21723],{},[1147,21712,21713],{},[1150,21714,21715,21717],{},[1153,21716,1240],{},[1147,21718,21719,21721],{},[1153,21720,1878],{},[1565,21722,1589],{},[1159,21724,21725],{"encoding":1161},"x_{i2}",[1203,21727,21728],{},[1115,21729,21731],{"className":21730},[1138],[1140,21732,21733],{"xmlns":1142},[1144,21734,21735,21747],{},[1147,21736,21737],{},[1150,21738,21739,21741],{},[1153,21740,1240],{},[1147,21742,21743,21745],{},[1153,21744,1878],{},[1565,21746,3592],{},[1159,21748,21749],{"encoding":1161},"x_{i3}",[1203,21751,21752],{},[1115,21753,21755],{"className":21754},[1138],[1140,21756,21757],{"xmlns":1142},[1144,21758,21759,21771],{},[1147,21760,21761],{},[1150,21762,21763,21765],{},[1153,21764,1240],{},[1147,21766,21767,21769],{},[1153,21768,1878],{},[1565,21770,3542],{},[1159,21772,21773],{"encoding":1161},"x_{i4}",[1210,21775,21776,21790,21805,21821,21836,21848,21862,21874,21887],{},[1200,21777,21778,21780,21783,21786,21788],{},[1215,21779,1794],{},[1215,21781,21782],{},"106",[1215,21784,21785],{},"98",[1215,21787,14087],{},[1215,21789,14087],{},[1200,21791,21792,21794,21797,21800,21803],{},[1215,21793,1589],{},[1215,21795,21796],{},"95",[1215,21798,21799],{},"94",[1215,21801,21802],{},"108",[1215,21804,6123],{},[1200,21806,21807,21809,21812,21815,21818],{},[1215,21808,3592],{},[1215,21810,21811],{},"122",[1215,21813,21814],{},"105",[1215,21816,21817],{},"103",[1215,21819,21820],{},"133",[1200,21822,21823,21825,21828,21830,21833],{},[1215,21824,3542],{},[1215,21826,21827],{},"113",[1215,21829,3564],{},[1215,21831,21832],{},"128",[1215,21834,21835],{},"135",[1200,21837,21838,21840,21842,21844,21846],{},[1215,21839,9929],{},[1215,21841,14087],{},[1215,21843,6123],{},[1215,21845,21817],{},[1215,21847,6123],{},[1200,21849,21850,21852,21854,21856,21859],{},[1215,21851,3964],{},[1215,21853,21785],{},[1215,21855,21817],{},[1215,21857,21858],{},"97",[1215,21860,21861],{},"99",[1200,21863,21864,21866,21868,21870,21872],{},[1215,21865,1800],{},[1215,21867,1800],{},[1215,21869,1800],{},[1215,21871,1800],{},[1215,21873,1800],{},[1200,21875,21876,21878,21880,21882,21885],{},[1215,21877,14721],{},[1215,21879,21832],{},[1215,21881,21820],{},[1215,21883,21884],{},"120",[1215,21886,14749],{},[1200,21888,21889,21891,21893,21895,21897],{},[1215,21890,4045],{},[1215,21892,21785],{},[1215,21894,21817],{},[1215,21896,21858],{},[1215,21898,21861],{},[1110,21900,21901,21902,21923,21924,1958],{},"Pro každou podskupinu se dopočítá výběrový průměr ",[1115,21903,21905],{"className":21904},[1138],[1140,21906,21907],{"xmlns":1142},[1144,21908,21909,21921],{},[1147,21910,21911],{},[1150,21912,21913,21919],{},[1236,21914,21915,21917],{"accent":1121},[1153,21916,1240],{},[1242,21918,1244],{},[1153,21920,1878],{},[1159,21922,21314],{"encoding":1161}," a rozpětí ",[1115,21925,21927],{"className":21926},[1138],[1140,21928,21929],{"xmlns":1142},[1144,21930,21931,21939],{},[1147,21932,21933],{},[1150,21934,21935,21937],{},[1153,21936,1260],{},[1153,21938,1878],{},[1159,21940,21333],{"encoding":1161},[1194,21942,21943,22004],{},[1197,21944,21945],{},[1200,21946,21947,21962,21985],{},[1203,21948,21949],{},[1115,21950,21952],{"className":21951},[1138],[1140,21953,21954],{"xmlns":1142},[1144,21955,21956,21960],{},[1147,21957,21958],{},[1153,21959,1878],{},[1159,21961,1878],{"encoding":1161},[1203,21963,21964],{},[1115,21965,21967],{"className":21966},[1138],[1140,21968,21969],{"xmlns":1142},[1144,21970,21971,21983],{},[1147,21972,21973],{},[1150,21974,21975,21981],{},[1236,21976,21977,21979],{"accent":1121},[1153,21978,1240],{},[1242,21980,1244],{},[1153,21982,1878],{},[1159,21984,21314],{"encoding":1161},[1203,21986,21987],{},[1115,21988,21990],{"className":21989},[1138],[1140,21991,21992],{"xmlns":1142},[1144,21993,21994,22002],{},[1147,21995,21996],{},[1150,21997,21998,22000],{},[1153,21999,1260],{},[1153,22001,1878],{},[1159,22003,21333],{"encoding":1161},[1210,22005,22006,22015,22025,22035,22045,22054,22063,22071,22080],{},[1200,22007,22008,22010,22013],{},[1215,22009,1794],{},[1215,22011,22012],{},"101,50",[1215,22014,14816],{},[1200,22016,22017,22019,22022],{},[1215,22018,1589],{},[1215,22020,22021],{},"97,25",[1215,22023,22024],{},"16",[1200,22026,22027,22029,22032],{},[1215,22028,3592],{},[1215,22030,22031],{},"115,75",[1215,22033,22034],{},"30",[1200,22036,22037,22039,22042],{},[1215,22038,3542],{},[1215,22040,22041],{},"111,75",[1215,22043,22044],{},"64",[1200,22046,22047,22049,22052],{},[1215,22048,9929],{},[1215,22050,22051],{},"97,00",[1215,22053,2255],{},[1200,22055,22056,22058,22061],{},[1215,22057,3964],{},[1215,22059,22060],{},"99,25",[1215,22062,3964],{},[1200,22064,22065,22067,22069],{},[1215,22066,1800],{},[1215,22068,1800],{},[1215,22070,1800],{},[1200,22072,22073,22075,22078],{},[1215,22074,14721],{},[1215,22076,22077],{},"126,50",[1215,22079,3545],{},[1200,22081,22082,22084,22086],{},[1215,22083,4045],{},[1215,22085,22060],{},[1215,22087,3964],{},[1110,22089,22090,22091,22104,22105,1346,22133,1346,22163,22191,22192,22214,22215,1346,22242,1346,22271,22298,22299,1669],{},"Nejprve se posoudí diagram ",[1115,22092,22094],{"className":22093},[1138],[1140,22095,22096],{"xmlns":1142},[1144,22097,22098,22102],{},[1147,22099,22100],{},[1153,22101,1260],{},[1159,22103,1260],{"encoding":1161}," na všech 20 podskupinách: ",[1115,22106,22108],{"className":22107},[1138],[1140,22109,22110],{"xmlns":1142},[1144,22111,22112,22130],{},[1147,22113,22114,22116,22119,22121,22123,22125,22127],{},[1153,22115,1155],{},[1153,22117,22118],{},"L",[1242,22120,1875],{"stretchy":1874},[1153,22122,1260],{},[1242,22124,1886],{"stretchy":1874},[1242,22126,1982],{},[1565,22128,22129],{},"15,8",[1159,22131,22132],{"encoding":1161},"CL(R)=15{,}8",[1115,22134,22136],{"className":22135},[1138],[1140,22137,22138],{"xmlns":1142},[1144,22139,22140,22160],{},[1147,22141,22142,22145,22147,22149,22151,22153,22155,22157],{},[1153,22143,22144],{},"U",[1153,22146,1155],{},[1153,22148,22118],{},[1242,22150,1875],{"stretchy":1874},[1153,22152,1260],{},[1242,22154,1886],{"stretchy":1874},[1242,22156,1982],{},[1565,22158,22159],{},"36,06",[1159,22161,22162],{"encoding":1161},"UCL(R)=36{,}06",[1115,22164,22166],{"className":22165},[1138],[1140,22167,22168],{"xmlns":1142},[1144,22169,22170,22188],{},[1147,22171,22172,22174,22176,22178,22180,22182,22184,22186],{},[1153,22173,22118],{},[1153,22175,1155],{},[1153,22177,22118],{},[1242,22179,1875],{"stretchy":1874},[1153,22181,1260],{},[1242,22183,1886],{"stretchy":1874},[1242,22185,1982],{},[1565,22187,1567],{},[1159,22189,22190],{"encoding":1161},"LCL(R)=0",". Rozpětí čtvrté podskupiny (",[1115,22193,22195],{"className":22194},[1138],[1140,22196,22197],{"xmlns":1142},[1144,22198,22199,22211],{},[1147,22200,22201,22207,22209],{},[1150,22202,22203,22205],{},[1153,22204,1260],{},[1565,22206,3542],{},[1242,22208,1982],{},[1565,22210,22044],{},[1159,22212,22213],{"encoding":1161},"R_4=64",") mez překračuje; po potvrzení vymezitelné příčiny se podskupina 4 z výpočtu vyřadí a meze se přepočítají — ",[1115,22216,22218],{"className":22217},[1138],[1140,22219,22220],{"xmlns":1142},[1144,22221,22222,22239],{},[1147,22223,22224,22226,22228,22230,22232,22234,22236],{},[1153,22225,1155],{},[1153,22227,22118],{},[1242,22229,1875],{"stretchy":1874},[1153,22231,1260],{},[1242,22233,1886],{"stretchy":1874},[1242,22235,1982],{},[1565,22237,22238],{},"13,26",[1159,22240,22241],{"encoding":1161},"CL(R)=13{,}26",[1115,22243,22245],{"className":22244},[1138],[1140,22246,22247],{"xmlns":1142},[1144,22248,22249,22268],{},[1147,22250,22251,22253,22255,22257,22259,22261,22263,22265],{},[1153,22252,22144],{},[1153,22254,1155],{},[1153,22256,22118],{},[1242,22258,1875],{"stretchy":1874},[1153,22260,1260],{},[1242,22262,1886],{"stretchy":1874},[1242,22264,1982],{},[1565,22266,22267],{},"30,27",[1159,22269,22270],{"encoding":1161},"UCL(R)=30{,}27",[1115,22272,22274],{"className":22273},[1138],[1140,22275,22276],{"xmlns":1142},[1144,22277,22278,22296],{},[1147,22279,22280,22282,22284,22286,22288,22290,22292,22294],{},[1153,22281,22118],{},[1153,22283,1155],{},[1153,22285,22118],{},[1242,22287,1875],{"stretchy":1874},[1153,22289,1260],{},[1242,22291,1886],{"stretchy":1874},[1242,22293,1982],{},[1565,22295,1567],{},[1159,22297,22190],{"encoding":1161},". Diagram rozpětí je teď zvládnutý, lze tedy posoudit diagram ",[1115,22300,22302],{"className":22301},[1138],[1140,22303,22304],{"xmlns":1142},[1144,22305,22306,22314],{},[1147,22307,22308],{},[1236,22309,22310,22312],{"accent":1121},[1153,22311,1240],{},[1242,22313,1244],{},[1159,22315,21563],{"encoding":1161},[1110,22317,21264,22318,22335,22336,1346,22367,1346,22400,22433,22434,22447,22448,1346,22475,1346,22504,22531],{},[1115,22319,22321],{"className":22320},[1138],[1140,22322,22323],{"xmlns":1142},[1144,22324,22325,22333],{},[1147,22326,22327],{},[1236,22328,22329,22331],{"accent":1121},[1153,22330,1240],{},[1242,22332,1244],{},[1159,22334,21563],{"encoding":1161}," bez čtvrté podskupiny dává ",[1115,22337,22339],{"className":22338},[1138],[1140,22340,22341],{"xmlns":1142},[1144,22342,22343,22364],{},[1147,22344,22345,22347,22349,22351,22357,22359,22361],{},[1153,22346,1155],{},[1153,22348,22118],{},[1242,22350,1875],{"stretchy":1874},[1236,22352,22353,22355],{"accent":1121},[1153,22354,1240],{},[1242,22356,1244],{},[1242,22358,1886],{"stretchy":1874},[1242,22360,1982],{},[1565,22362,22363],{},"102,01",[1159,22365,22366],{"encoding":1161},"CL(\\bar{x})=102{,}01",[1115,22368,22370],{"className":22369},[1138],[1140,22371,22372],{"xmlns":1142},[1144,22373,22374,22397],{},[1147,22375,22376,22378,22380,22382,22384,22390,22392,22394],{},[1153,22377,22144],{},[1153,22379,1155],{},[1153,22381,22118],{},[1242,22383,1875],{"stretchy":1874},[1236,22385,22386,22388],{"accent":1121},[1153,22387,1240],{},[1242,22389,1244],{},[1242,22391,1886],{"stretchy":1874},[1242,22393,1982],{},[1565,22395,22396],{},"111,68",[1159,22398,22399],{"encoding":1161},"UCL(\\bar{x})=111{,}68",[1115,22401,22403],{"className":22402},[1138],[1140,22404,22405],{"xmlns":1142},[1144,22406,22407,22430],{},[1147,22408,22409,22411,22413,22415,22417,22423,22425,22427],{},[1153,22410,22118],{},[1153,22412,1155],{},[1153,22414,22118],{},[1242,22416,1875],{"stretchy":1874},[1236,22418,22419,22421],{"accent":1121},[1153,22420,1240],{},[1242,22422,1244],{},[1242,22424,1886],{"stretchy":1874},[1242,22426,1982],{},[1565,22428,22429],{},"92,34",[1159,22431,22432],{"encoding":1161},"LCL(\\bar{x})=92{,}34",". Mez teď překračují průměry podskupin 3 a 19. Po potvrzení vymezitelné příčiny se vyřadí obě najednou a meze diagramu ",[1115,22435,22437],{"className":22436},[1138],[1140,22438,22439],{"xmlns":1142},[1144,22440,22441,22445],{},[1147,22442,22443],{},[1153,22444,1260],{},[1159,22446,1260],{"encoding":1161}," se přepočítají bez podskupin 3, 4 a 19: ",[1115,22449,22451],{"className":22450},[1138],[1140,22452,22453],{"xmlns":1142},[1144,22454,22455,22472],{},[1147,22456,22457,22459,22461,22463,22465,22467,22469],{},[1153,22458,1155],{},[1153,22460,22118],{},[1242,22462,1875],{"stretchy":1874},[1153,22464,1260],{},[1242,22466,1886],{"stretchy":1874},[1242,22468,1982],{},[1565,22470,22471],{},"12,29",[1159,22473,22474],{"encoding":1161},"CL(R)=12{,}29",[1115,22476,22478],{"className":22477},[1138],[1140,22479,22480],{"xmlns":1142},[1144,22481,22482,22501],{},[1147,22483,22484,22486,22488,22490,22492,22494,22496,22498],{},[1153,22485,22144],{},[1153,22487,1155],{},[1153,22489,22118],{},[1242,22491,1875],{"stretchy":1874},[1153,22493,1260],{},[1242,22495,1886],{"stretchy":1874},[1242,22497,1982],{},[1565,22499,22500],{},"28,06",[1159,22502,22503],{"encoding":1161},"UCL(R)=28{,}06",[1115,22505,22507],{"className":22506},[1138],[1140,22508,22509],{"xmlns":1142},[1144,22510,22511,22529],{},[1147,22512,22513,22515,22517,22519,22521,22523,22525,22527],{},[1153,22514,22118],{},[1153,22516,1155],{},[1153,22518,22118],{},[1242,22520,1875],{"stretchy":1874},[1153,22522,1260],{},[1242,22524,1886],{"stretchy":1874},[1242,22526,1982],{},[1565,22528,1567],{},[1159,22530,22190],{"encoding":1161}," — žádná z 17 zbývajících podskupin mez nepřekračuje.",[1110,22533,22534,22535,22552,22553,1346,22584,1346,22617,22650],{},"Konečný diagram ",[1115,22536,22538],{"className":22537},[1138],[1140,22539,22540],{"xmlns":1142},[1144,22541,22542,22550],{},[1147,22543,22544],{},[1236,22545,22546,22548],{"accent":1121},[1153,22547,1240],{},[1242,22549,1244],{},[1159,22551,21563],{"encoding":1161}," na stejných 17 podskupinách má ",[1115,22554,22556],{"className":22555},[1138],[1140,22557,22558],{"xmlns":1142},[1144,22559,22560,22581],{},[1147,22561,22562,22564,22566,22568,22574,22576,22578],{},[1153,22563,1155],{},[1153,22565,22118],{},[1242,22567,1875],{"stretchy":1874},[1236,22569,22570,22572],{"accent":1121},[1153,22571,1240],{},[1242,22573,1244],{},[1242,22575,1886],{"stretchy":1874},[1242,22577,1982],{},[1565,22579,22580],{},"99,76",[1159,22582,22583],{"encoding":1161},"CL(\\bar{x})=99{,}76",[1115,22585,22587],{"className":22586},[1138],[1140,22588,22589],{"xmlns":1142},[1144,22590,22591,22614],{},[1147,22592,22593,22595,22597,22599,22601,22607,22609,22611],{},[1153,22594,22144],{},[1153,22596,1155],{},[1153,22598,22118],{},[1242,22600,1875],{"stretchy":1874},[1236,22602,22603,22605],{"accent":1121},[1153,22604,1240],{},[1242,22606,1244],{},[1242,22608,1886],{"stretchy":1874},[1242,22610,1982],{},[1565,22612,22613],{},"108,73",[1159,22615,22616],{"encoding":1161},"UCL(\\bar{x})=108{,}73",[1115,22618,22620],{"className":22619},[1138],[1140,22621,22622],{"xmlns":1142},[1144,22623,22624,22647],{},[1147,22625,22626,22628,22630,22632,22634,22640,22642,22644],{},[1153,22627,22118],{},[1153,22629,1155],{},[1153,22631,22118],{},[1242,22633,1875],{"stretchy":1874},[1236,22635,22636,22638],{"accent":1121},[1153,22637,1240],{},[1242,22639,1244],{},[1242,22641,1886],{"stretchy":1874},[1242,22643,1982],{},[1565,22645,22646],{},"90,80",[1159,22648,22649],{"encoding":1161},"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.",[1110,22652,22653],{},[4383,22654],{"alt":22655,"className":22656,"src":22657},"mask-rd-priklad1-meze",[1130,4387],"\u002Fwiki-assets\u002Fmask-rd-priklad1-meze.png",[1110,22659,22660,22661,22663,22664,22666],{},"V R se diagramy sestrojí funkcí ",[3470,22662,21567],{}," z balíčku ",[3470,22665,360],{},". Data jsou tabulka, v níž řádek odpovídá logické podskupině a sloupce jednotlivým měřením:",[3694,22668,22670],{"className":3696,"code":22669,"language":71,"meta":1490,"style":1490},"library(qcc)\ndata \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"R\")      # diagram R\nqcc(data, type = \"xbar\")   # diagram x̄\n",[3470,22671,22672,22682,22705,22728],{"__ignoreMap":1490},[1115,22673,22674,22676,22678,22680],{"class":3702,"line":10},[1115,22675,17398],{"class":3709},[1115,22677,1875],{"class":3717},[1115,22679,360],{"class":3705},[1115,22681,3901],{"class":3717},[1115,22683,22684,22686,22688,22690,22692,22695,22697,22699,22701,22703],{"class":3702,"line":27},[1115,22685,20109],{"class":3705},[1115,22687,3710],{"class":3709},[1115,22689,20114],{"class":3713},[1115,22691,1875],{"class":3717},[1115,22693,22694],{"class":3840},"\"3_2.txt\"",[1115,22696,1797],{"class":3709},[1115,22698,20124],{"class":3705},[1115,22700,3797],{"class":3709},[1115,22702,3810],{"class":3724},[1115,22704,3901],{"class":3717},[1115,22706,22707,22709,22711,22713,22715,22717,22719,22722,22725],{"class":3702,"line":148},[1115,22708,360],{"class":3713},[1115,22710,1875],{"class":3717},[1115,22712,20109],{"class":3705},[1115,22714,1797],{"class":3709},[1115,22716,12225],{"class":3705},[1115,22718,3797],{"class":3709},[1115,22720,22721],{"class":3840}," \"R\"",[1115,22723,22724],{"class":3717},")      ",[1115,22726,22727],{"class":12035},"# diagram R\n",[1115,22729,22730,22732,22734,22736,22738,22740,22742,22745,22747],{"class":3702,"line":111},[1115,22731,360],{"class":3713},[1115,22733,1875],{"class":3717},[1115,22735,20109],{"class":3705},[1115,22737,1797],{"class":3709},[1115,22739,12225],{"class":3705},[1115,22741,3797],{"class":3709},[1115,22743,22744],{"class":3840}," \"xbar\"",[1115,22746,12032],{"class":3717},[1115,22748,22749],{"class":12035},"# diagram x̄\n",[1110,22751,22752,22753,22756],{},"Funkce vykreslí diagram se střední přímkou a akčními mezemi a body mimo meze zvýrazní. Podskupina s potvrzenou vymezitelnou příčinou se vyřadí z dat (například ",[3470,22754,22755],{},"data[-4, ]",") a diagram se sestrojí znovu.",[16749,22758,21264,22760],{"id":22759},"diagram-xˉsbarx-s",[1115,22761,22763],{"className":22762},[1138],[1140,22764,22765],{"xmlns":1142},[1144,22766,22767,22783],{},[1147,22768,22769,22771,22777,22779,22781],{},[1242,22770,1875],{"stretchy":1874},[1236,22772,22773,22775],{"accent":1121},[1153,22774,1240],{},[1242,22776,1244],{},[1242,22778,1797],{"separator":1121},[1153,22780,1291],{},[1242,22782,1886],{"stretchy":1874},[1159,22784,20678],{"encoding":1161},[1110,22786,21292,22787,22808,22809,22827,22828,22853],{},[1115,22788,22790],{"className":22789},[1138],[1140,22791,22792],{"xmlns":1142},[1144,22793,22794,22806],{},[1147,22795,22796],{},[1150,22797,22798,22804],{},[1236,22799,22800,22802],{"accent":1121},[1153,22801,1240],{},[1242,22803,1244],{},[1153,22805,1878],{},[1159,22807,21314],{"encoding":1161}," a výběrové směrodatné odchylky ",[1115,22810,22812],{"className":22811},[1138],[1140,22813,22814],{"xmlns":1142},[1144,22815,22816,22824],{},[1147,22817,22818],{},[1150,22819,22820,22822],{},[1153,22821,1291],{},[1153,22823,1878],{},[1159,22825,22826],{"encoding":1161},"s_i"," v logických podskupinách. Podmínky použití jsou stejné jako u ",[1115,22829,22831],{"className":22830},[1138],[1140,22832,22833],{"xmlns":1142},[1144,22834,22835,22851],{},[1147,22836,22837,22839,22845,22847,22849],{},[1242,22838,1875],{"stretchy":1874},[1236,22840,22841,22843],{"accent":1121},[1153,22842,1240],{},[1242,22844,1244],{},[1242,22846,1797],{"separator":1121},[1153,22848,1260],{},[1242,22850,1886],{"stretchy":1874},[1159,22852,20652],{"encoding":1161},", logické podskupiny ale sestávají z většího počtu měření. Data se zapisují do obdobné tabulky.",[3694,22855,22857],{"className":3696,"code":22856,"language":71,"meta":1490,"style":1490},"data \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"S\")      # diagram s\nqcc(data, type = \"xbar\")   # diagram x̄\n",[3470,22858,22859,22881,22903],{"__ignoreMap":1490},[1115,22860,22861,22863,22865,22867,22869,22871,22873,22875,22877,22879],{"class":3702,"line":10},[1115,22862,20109],{"class":3705},[1115,22864,3710],{"class":3709},[1115,22866,20114],{"class":3713},[1115,22868,1875],{"class":3717},[1115,22870,22694],{"class":3840},[1115,22872,1797],{"class":3709},[1115,22874,20124],{"class":3705},[1115,22876,3797],{"class":3709},[1115,22878,3810],{"class":3724},[1115,22880,3901],{"class":3717},[1115,22882,22883,22885,22887,22889,22891,22893,22895,22898,22900],{"class":3702,"line":27},[1115,22884,360],{"class":3713},[1115,22886,1875],{"class":3717},[1115,22888,20109],{"class":3705},[1115,22890,1797],{"class":3709},[1115,22892,12225],{"class":3705},[1115,22894,3797],{"class":3709},[1115,22896,22897],{"class":3840}," \"S\"",[1115,22899,22724],{"class":3717},[1115,22901,22902],{"class":12035},"# diagram s\n",[1115,22904,22905,22907,22909,22911,22913,22915,22917,22919,22921],{"class":3702,"line":148},[1115,22906,360],{"class":3713},[1115,22908,1875],{"class":3717},[1115,22910,20109],{"class":3705},[1115,22912,1797],{"class":3709},[1115,22914,12225],{"class":3705},[1115,22916,3797],{"class":3709},[1115,22918,22744],{"class":3840},[1115,22920,12032],{"class":3717},[1115,22922,22749],{"class":12035},[16749,22924,21264,22926],{"id":22925},"diagram-xirklix_i-r_kli",[1115,22927,22929],{"className":22928},[1138],[1140,22930,22931],{"xmlns":1142},[1144,22932,22933,22961],{},[1147,22934,22935,22937,22943,22945,22959],{},[1242,22936,1875],{"stretchy":1874},[1150,22938,22939,22941],{},[1153,22940,1240],{},[1153,22942,1878],{},[1242,22944,1797],{"separator":1121},[1150,22946,22947,22949],{},[1153,22948,1260],{},[1147,22950,22951,22953,22955,22957],{},[1153,22952,1183],{},[1153,22954,1327],{},[1242,22956,1797],{"separator":1121},[1153,22958,1878],{},[1242,22960,1886],{"stretchy":1874},[1159,22962,20716],{"encoding":1161},[1110,22964,22965,22966,22991,22992,1958],{},"Používá se za stejných podmínek jako ",[1115,22967,22969],{"className":22968},[1138],[1140,22970,22971],{"xmlns":1142},[1144,22972,22973,22989],{},[1147,22974,22975,22977,22983,22985,22987],{},[1242,22976,1875],{"stretchy":1874},[1236,22978,22979,22981],{"accent":1121},[1153,22980,1240],{},[1242,22982,1244],{},[1242,22984,1797],{"separator":1121},[1153,22986,1260],{},[1242,22988,1886],{"stretchy":1874},[1159,22990,20652],{"encoding":1161},", 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 ",[1540,22993,22994],{},"klouzavé rozpětí",[1115,22996,22998],{"className":22997},[1138],[1140,22999,23000],{"xmlns":1142,"display":1964},[1144,23001,23002,23129],{},[1147,23003,23004,23018,23020,23023,23029,23031,23043,23045,23047,23049,23051,23053,23055,23057,23059,23061,23063,23065,23067,23069,23071,23085,23087,23099,23113,23127],{},[1150,23005,23006,23008],{},[1153,23007,1260],{},[1147,23009,23010,23012,23014,23016],{},[1153,23011,1183],{},[1153,23013,1327],{},[1242,23015,1797],{"separator":1121},[1153,23017,1878],{},[1242,23019,1982],{},[1153,23021,23022],{"mathvariant":2121},"∣",[1150,23024,23025,23027],{},[1153,23026,1240],{},[1153,23028,1878],{},[1242,23030,3064],{},[1150,23032,23033,23035],{},[1153,23034,1240],{},[1147,23036,23037,23039,23041],{},[1153,23038,1878],{},[1242,23040,3064],{},[1565,23042,1794],{},[1153,23044,23022],{"mathvariant":2121},[1242,23046,1797],{"separator":1121},[2012,23048],{"width":18019},[1153,23050,1878],{},[1242,23052,1982],{},[1565,23054,1589],{},[1242,23056,1797],{"separator":1121},[1565,23058,3592],{},[1242,23060,1797],{"separator":1121},[1242,23062,1800],{},[1242,23064,1797],{"separator":1121},[1153,23066,1183],{},[1242,23068,1797],{"separator":1121},[2012,23070],{"width":2014},[1150,23072,23073,23079],{},[1236,23074,23075,23077],{"accent":1121},[1153,23076,1260],{},[1242,23078,1244],{},[1147,23080,23081,23083],{},[1153,23082,1183],{},[1153,23084,1327],{},[1242,23086,1982],{},[2739,23088,23089,23091],{},[1565,23090,1794],{},[1147,23092,23093,23095,23097],{},[1153,23094,1183],{},[1242,23096,3064],{},[1565,23098,1794],{},[1984,23100,23101,23103,23111],{},[1242,23102,1988],{},[1147,23104,23105,23107,23109],{},[1153,23106,1878],{},[1242,23108,1982],{},[1565,23110,1589],{},[1153,23112,1183],{},[1150,23114,23115,23117],{},[1153,23116,1260],{},[1147,23118,23119,23121,23123,23125],{},[1153,23120,1183],{},[1153,23122,1327],{},[1242,23124,1797],{"separator":1121},[1153,23126,1878],{},[1153,23128,1669],{"mathvariant":2121},[1159,23130,23131],{"encoding":1161},"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}.",[1110,23133,23134,23135,1163,23152,23178,23179,23204,23205,23222],{},"Regulované veličiny jsou hodnoty ",[1115,23136,23138],{"className":23137},[1138],[1140,23139,23140],{"xmlns":1142},[1144,23141,23142,23150],{},[1147,23143,23144],{},[1150,23145,23146,23148],{},[1153,23147,1240],{},[1153,23149,1878],{},[1159,23151,17135],{"encoding":1161},[1115,23153,23155],{"className":23154},[1138],[1140,23156,23157],{"xmlns":1142},[1144,23158,23159,23175],{},[1147,23160,23161],{},[1150,23162,23163,23165],{},[1153,23164,1260],{},[1147,23166,23167,23169,23171,23173],{},[1153,23168,1183],{},[1153,23170,1327],{},[1242,23172,1797],{"separator":1121},[1153,23174,1878],{},[1159,23176,23177],{"encoding":1161},"R_{kl,i}","; nejdříve se určí střední přímka a meze diagramu ",[1115,23180,23182],{"className":23181},[1138],[1140,23183,23184],{"xmlns":1142},[1144,23185,23186,23202],{},[1147,23187,23188],{},[1150,23189,23190,23192],{},[1153,23191,1260],{},[1147,23193,23194,23196,23198,23200],{},[1153,23195,1183],{},[1153,23197,1327],{},[1242,23199,1797],{"separator":1121},[1153,23201,1878],{},[1159,23203,23177],{"encoding":1161},", potom diagramu ",[1115,23206,23208],{"className":23207},[1138],[1140,23209,23210],{"xmlns":1142},[1144,23211,23212,23220],{},[1147,23213,23214],{},[1150,23215,23216,23218],{},[1153,23217,1240],{},[1153,23219,1878],{},[1159,23221,17135],{"encoding":1161},". Data jsou jeden vektor naměřených hodnot:",[3694,23224,23226],{"className":3696,"code":23225,"language":71,"meta":1490,"style":1490},"data \u003C- read.table(\"3_3.txt\", header = TRUE)\nqcc(data[, 1], type = \"xbar.one\")\n",[3470,23227,23228,23251],{"__ignoreMap":1490},[1115,23229,23230,23232,23234,23236,23238,23241,23243,23245,23247,23249],{"class":3702,"line":10},[1115,23231,20109],{"class":3705},[1115,23233,3710],{"class":3709},[1115,23235,20114],{"class":3713},[1115,23237,1875],{"class":3717},[1115,23239,23240],{"class":3840},"\"3_3.txt\"",[1115,23242,1797],{"class":3709},[1115,23244,20124],{"class":3705},[1115,23246,3797],{"class":3709},[1115,23248,3810],{"class":3724},[1115,23250,3901],{"class":3717},[1115,23252,23253,23255,23257,23259,23261,23263,23265,23267,23269,23271,23273,23276],{"class":3702,"line":27},[1115,23254,360],{"class":3713},[1115,23256,1875],{"class":3717},[1115,23258,20109],{"class":3705},[1115,23260,8178],{"class":3717},[1115,23262,1797],{"class":3709},[1115,23264,4641],{"class":3724},[1115,23266,8195],{"class":3717},[1115,23268,1797],{"class":3709},[1115,23270,12225],{"class":3705},[1115,23272,3797],{"class":3709},[1115,23274,23275],{"class":3840}," \"xbar.one\"",[1115,23277,3901],{"class":3717},[1189,23279,23281],{"id":23280},"regulace-srovnáváním","Regulace srovnáváním",[1110,23283,23284],{},"Diagramy pro regulaci srovnáváním se používají, sledují-li se počty neshodných produktů nebo počty neshod na produktech — regulovaná veličina je diskrétní náhodná veličina.",[1194,23286,23287,23300],{},[1197,23288,23289],{},[1200,23290,23291,23294,23297],{},[1203,23292,23293],{},"Sleduje se",[1203,23295,23296],{},"Konstantní rozsah podskupin",[1203,23298,23299],{},"Nekonstantní rozsah podskupin",[1210,23301,23302,23337],{},[1200,23303,23304,23307,23322],{},[1215,23305,23306],{},"počet neshod na produktech (např. vady na stejných tabulích skla)",[1215,23308,23309],{},[1115,23310,23312],{"className":23311},[1138],[1140,23313,23314],{"xmlns":1142},[1144,23315,23316,23320],{},[1147,23317,23318],{},[1153,23319,1343],{},[1159,23321,1343],{"encoding":1161},[1215,23323,23324],{},[1115,23325,23327],{"className":23326},[1138],[1140,23328,23329],{"xmlns":1142},[1144,23330,23331,23335],{},[1147,23332,23333],{},[1153,23334,1358],{},[1159,23336,1358],{"encoding":1161},[1200,23338,23339,23342,23359],{},[1215,23340,23341],{},"počet neshodných produktů ve výběru (např. neshodné kusy ze série na výrobní lince)",[1215,23343,23344],{},[1115,23345,23347],{"className":23346},[1138],[1140,23348,23349],{"xmlns":1142},[1144,23350,23351,23357],{},[1147,23352,23353,23355],{},[1153,23354,1372],{},[1153,23356,1110],{},[1159,23358,1377],{"encoding":1161},[1215,23360,23361],{},[1115,23362,23364],{"className":23363},[1138],[1140,23365,23366],{"xmlns":1142},[1144,23367,23368,23372],{},[1147,23369,23370],{},[1153,23371,1110],{},[1159,23373,1110],{"encoding":1161},[16749,23375,21264,23377],{"id":23376},"diagram-cc",[1115,23378,23380],{"className":23379},[1138],[1140,23381,23382],{"xmlns":1142},[1144,23383,23384,23388],{},[1147,23385,23386],{},[1153,23387,1343],{},[1159,23389,1343],{"encoding":1161},[1110,23391,23392,23393,23411,23412,23425,23426,23451,23452,23465],{},"Regulovanou veličinou ",[1115,23394,23396],{"className":23395},[1138],[1140,23397,23398],{"xmlns":1142},[1144,23399,23400,23408],{},[1147,23401,23402],{},[1150,23403,23404,23406],{},[1153,23405,1343],{},[1153,23407,1878],{},[1159,23409,23410],{"encoding":1161},"c_i"," je počet neshod na produktech v ",[1115,23413,23415],{"className":23414},[1138],[1140,23416,23417],{"xmlns":1142},[1144,23418,23419,23423],{},[1147,23420,23421],{},[1153,23422,1878],{},[1159,23424,1878],{"encoding":1161},"-té logické podskupině, ",[1115,23427,23429],{"className":23428},[1138],[1140,23430,23431],{"xmlns":1142},[1144,23432,23433,23449],{},[1147,23434,23435,23437,23439,23441,23443,23445,23447],{},[1153,23436,1878],{},[1242,23438,1982],{},[1565,23440,1794],{},[1242,23442,1797],{"separator":1121},[1242,23444,1800],{},[1242,23446,1797],{"separator":1121},[1153,23448,1183],{},[1159,23450,21477],{"encoding":1161},"; v každé podskupině je stejný počet ",[1115,23453,23455],{"className":23454},[1138],[1140,23456,23457],{"xmlns":1142},[1144,23458,23459,23463],{},[1147,23460,23461],{},[1153,23462,1372],{},[1159,23464,1372],{"encoding":1161}," 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.",[1103,23467,23469,23476],{"className":23468,"dataCallout":3477},[1106,3476],[1110,23470,23472,23475],{"className":23471},[1113],[1115,23473],{"className":23474,"ariaHidden":1121},[1118,3484,1120],"Příklad: bodové vady na pásech látky",[1110,23477,23478,23479,23496,23497,1669],{},"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 ",[1115,23480,23482],{"className":23481},[1138],[1140,23483,23484],{"xmlns":1142},[1144,23485,23486,23494],{},[1147,23487,23488],{},[1150,23489,23490,23492],{},[1153,23491,1343],{},[1153,23493,1878],{},[1159,23495,23410],{"encoding":1161},". Sestrojte regulační diagram ",[1115,23498,23500],{"className":23499},[1138],[1140,23501,23502],{"xmlns":1142},[1144,23503,23504,23508],{},[1147,23505,23506],{},[1153,23507,1343],{},[1159,23509,1343],{"encoding":1161},[3694,23511,23513],{"className":3696,"code":23512,"language":71,"meta":1490,"style":1490},"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",[3470,23514,23515,23605,23609,23634],{"__ignoreMap":1490},[1115,23516,23517,23519,23521,23523,23525,23527,23529,23531,23533,23535,23537,23539,23541,23543,23545,23547,23549,23551,23553,23555,23557,23559,23561,23563,23565,23567,23569,23571,23573,23575,23577,23579,23581,23583,23585,23587,23589,23591,23593,23595,23597,23599,23601,23603],{"class":3702,"line":10},[1115,23518,23410],{"class":3705},[1115,23520,3710],{"class":3709},[1115,23522,3835],{"class":3713},[1115,23524,1875],{"class":3717},[1115,23526,13332],{"class":3724},[1115,23528,1797],{"class":3709},[1115,23530,4641],{"class":3724},[1115,23532,1797],{"class":3709},[1115,23534,4180],{"class":3724},[1115,23536,1797],{"class":3709},[1115,23538,9997],{"class":3724},[1115,23540,1797],{"class":3709},[1115,23542,9973],{"class":3724},[1115,23544,1797],{"class":3709},[1115,23546,12230],{"class":3724},[1115,23548,1797],{"class":3709},[1115,23550,4180],{"class":3724},[1115,23552,1797],{"class":3709},[1115,23554,9973],{"class":3724},[1115,23556,1797],{"class":3709},[1115,23558,3800],{"class":3724},[1115,23560,1797],{"class":3709},[1115,23562,3800],{"class":3724},[1115,23564,1797],{"class":3709},[1115,23566,12230],{"class":3724},[1115,23568,1797],{"class":3709},[1115,23570,10857],{"class":3724},[1115,23572,1797],{"class":3709},[1115,23574,10857],{"class":3724},[1115,23576,1797],{"class":3709},[1115,23578,10857],{"class":3724},[1115,23580,1797],{"class":3709},[1115,23582,4641],{"class":3724},[1115,23584,1797],{"class":3709},[1115,23586,12230],{"class":3724},[1115,23588,1797],{"class":3709},[1115,23590,10857],{"class":3724},[1115,23592,1797],{"class":3709},[1115,23594,4641],{"class":3724},[1115,23596,1797],{"class":3709},[1115,23598,9997],{"class":3724},[1115,23600,1797],{"class":3709},[1115,23602,12230],{"class":3724},[1115,23604,3901],{"class":3717},[1115,23606,23607],{"class":3702,"line":27},[1115,23608,10044],{"emptyLinePlaceholder":1499},[1115,23610,23611,23614,23616,23619,23621,23623,23625,23627,23629,23632],{"class":3702,"line":148},[1115,23612,23613],{"class":3705},"q_c",[1115,23615,3710],{"class":3709},[1115,23617,23618],{"class":3713}," qcc",[1115,23620,1875],{"class":3717},[1115,23622,23410],{"class":3705},[1115,23624,1797],{"class":3709},[1115,23626,12225],{"class":3705},[1115,23628,3797],{"class":3709},[1115,23630,23631],{"class":3840}," \"c\"",[1115,23633,3901],{"class":3717},[1115,23635,23636,23638,23640,23642],{"class":3702,"line":111},[1115,23637,1509],{"class":3713},[1115,23639,1875],{"class":3717},[1115,23641,23613],{"class":3705},[1115,23643,3901],{"class":3717},[3694,23645,23648],{"className":23646,"code":23647,"language":3923,"meta":1490},[3921],"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",[3470,23649,23647],{"__ignoreMap":1490},[1110,23651,23652,23653,23682,23683,23706,23707,23729],{},"Průměrný počet vad na pás je ",[1115,23654,23656],{"className":23655},[1138],[1140,23657,23658],{"xmlns":1142},[1144,23659,23660,23679],{},[1147,23661,23662,23664,23666,23668,23674,23676],{},[1153,23663,1155],{},[1153,23665,22118],{},[1242,23667,1982],{},[1236,23669,23670,23672],{"accent":1121},[1153,23671,1343],{},[1242,23673,1244],{},[1242,23675,1982],{},[1565,23677,23678],{},"3,4",[1159,23680,23681],{"encoding":1161},"CL = \\bar{c} = 3{,}4",", horní mez ",[1115,23684,23686],{"className":23685},[1138],[1140,23687,23688],{"xmlns":1142},[1144,23689,23690,23703],{},[1147,23691,23692,23694,23696,23698,23700],{},[1153,23693,22144],{},[1153,23695,1155],{},[1153,23697,22118],{},[1242,23699,1982],{},[1565,23701,23702],{},"8,93",[1159,23704,23705],{"encoding":1161},"UCL = 8{,}93"," a dolní mez ",[1115,23708,23710],{"className":23709},[1138],[1140,23711,23712],{"xmlns":1142},[1144,23713,23714,23726],{},[1147,23715,23716,23718,23720,23722,23724],{},[1153,23717,22118],{},[1153,23719,1155],{},[1153,23721,22118],{},[1242,23723,1982],{},[1565,23725,1567],{},[1159,23727,23728],{"encoding":1161},"LCL = 0",". Žádný pás meze nepřekračuje — proces je zvládnutý.",[1110,23731,23732],{},[4383,23733],{"alt":23734,"className":23735,"src":23736},"mask-rd-priklad2-c",[1130,4387],"\u002Fwiki-assets\u002Fmask-rd-priklad2-c.png",[16749,23738,21264,23740],{"id":23739},"diagram-uu",[1115,23741,23743],{"className":23742},[1138],[1140,23744,23745],{"xmlns":1142},[1144,23746,23747,23751],{},[1147,23748,23749],{},[1153,23750,1358],{},[1159,23752,1358],{"encoding":1161},[1110,23754,23392,23755,23789,23790,23808],{},[1115,23756,23758],{"className":23757},[1138],[1140,23759,23760],{"xmlns":1142},[1144,23761,23762,23786],{},[1147,23763,23764,23770,23772,23778,23780],{},[1150,23765,23766,23768],{},[1153,23767,1358],{},[1153,23769,1878],{},[1242,23771,1982],{},[1150,23773,23774,23776],{},[1153,23775,1343],{},[1153,23777,1878],{},[1153,23779,4604],{"mathvariant":2121},[1150,23781,23782,23784],{},[1153,23783,1372],{},[1153,23785,1878],{},[1159,23787,23788],{"encoding":1161},"u_i = c_i\u002Fn_i"," je průměrný počet neshod přepočítaný na jeden produkt z logické podskupiny; rozsah podskupin ",[1115,23791,23793],{"className":23792},[1138],[1140,23794,23795],{"xmlns":1142},[1144,23796,23797,23805],{},[1147,23798,23799],{},[1150,23800,23801,23803],{},[1153,23802,1372],{},[1153,23804,1878],{},[1159,23806,23807],{"encoding":1161},"n_i"," není konstantní, a proto se bod od bodu mění i meze.",[1110,23810,23811,23812,23815],{},"Za ",[3470,23813,23814],{},"sizes"," se dosadí vektor rozsahů jednotlivých logických podskupin, resp. rozměr jejich jednotek:",[3694,23817,23819],{"className":3696,"code":23818,"language":71,"meta":1490,"style":1490},"data \u003C- read.table(\"3_4.txt\", header = TRUE)   # počty suků a rozměry prken\nqcc(data[, 1], type = \"u\", sizes = data[, 2])\n",[3470,23820,23821,23847],{"__ignoreMap":1490},[1115,23822,23823,23825,23827,23829,23831,23834,23836,23838,23840,23842,23844],{"class":3702,"line":10},[1115,23824,20109],{"class":3705},[1115,23826,3710],{"class":3709},[1115,23828,20114],{"class":3713},[1115,23830,1875],{"class":3717},[1115,23832,23833],{"class":3840},"\"3_4.txt\"",[1115,23835,1797],{"class":3709},[1115,23837,20124],{"class":3705},[1115,23839,3797],{"class":3709},[1115,23841,3810],{"class":3724},[1115,23843,12032],{"class":3717},[1115,23845,23846],{"class":12035},"# počty suků a rozměry prken\n",[1115,23848,23849,23851,23853,23855,23857,23859,23861,23863,23865,23867,23869,23872,23874,23877,23879,23881,23883,23885,23887],{"class":3702,"line":27},[1115,23850,360],{"class":3713},[1115,23852,1875],{"class":3717},[1115,23854,20109],{"class":3705},[1115,23856,8178],{"class":3717},[1115,23858,1797],{"class":3709},[1115,23860,4641],{"class":3724},[1115,23862,8195],{"class":3717},[1115,23864,1797],{"class":3709},[1115,23866,12225],{"class":3705},[1115,23868,3797],{"class":3709},[1115,23870,23871],{"class":3840}," \"u\"",[1115,23873,1797],{"class":3709},[1115,23875,23876],{"class":3705}," sizes",[1115,23878,3797],{"class":3709},[1115,23880,20168],{"class":3705},[1115,23882,8178],{"class":3717},[1115,23884,1797],{"class":3709},[1115,23886,4180],{"class":3724},[1115,23888,23889],{"class":3717},"])\n",[16749,23891,21264,23893],{"id":23892},"diagram-npnp",[1115,23894,23896],{"className":23895},[1138],[1140,23897,23898],{"xmlns":1142},[1144,23899,23900,23906],{},[1147,23901,23902,23904],{},[1153,23903,1372],{},[1153,23905,1110],{},[1159,23907,1377],{"encoding":1161},[1110,23909,23910,23911,6783,23926,23939],{},"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 ",[1115,23912,23914],{"className":23913},[1138],[1140,23915,23916],{"xmlns":1142},[1144,23917,23918,23924],{},[1147,23919,23920,23922],{},[1153,23921,1372],{},[1153,23923,1110],{},[1159,23925,1377],{"encoding":1161},[1115,23927,23929],{"className":23928},[1138],[1140,23930,23931],{"xmlns":1142},[1144,23932,23933,23937],{},[1147,23934,23935],{},[1153,23936,1110],{},[1159,23938,1110],{"encoding":1161}," je pravděpodobnost, že vyrobený produkt je neshodný.",[1110,23941,23942,23943,1958],{},"Pro konstantní rozsah ",[1115,23944,23946],{"className":23945},[1138],[1140,23947,23948],{"xmlns":1142},[1144,23949,23950,23954],{},[1147,23951,23952],{},[1153,23953,1372],{},[1159,23955,1372],{"encoding":1161},[3694,23957,23959],{"className":3696,"code":23958,"language":71,"meta":1490,"style":1490},"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",[3470,23960,23961,23987],{"__ignoreMap":1490},[1115,23962,23963,23965,23967,23969,23971,23974,23976,23978,23980,23982,23984],{"class":3702,"line":10},[1115,23964,20109],{"class":3705},[1115,23966,3710],{"class":3709},[1115,23968,20114],{"class":3713},[1115,23970,1875],{"class":3717},[1115,23972,23973],{"class":3840},"\"3_7.txt\"",[1115,23975,1797],{"class":3709},[1115,23977,20124],{"class":3705},[1115,23979,3797],{"class":3709},[1115,23981,3810],{"class":3724},[1115,23983,12032],{"class":3717},[1115,23985,23986],{"class":12035},"# počty vadných tabletů v sériích po 100 kusech\n",[1115,23988,23989,23991,23993,23995,23997,23999,24001,24003,24005,24007,24009,24012,24014,24016,24018,24020],{"class":3702,"line":27},[1115,23990,360],{"class":3713},[1115,23992,1875],{"class":3717},[1115,23994,20109],{"class":3705},[1115,23996,8178],{"class":3717},[1115,23998,1797],{"class":3709},[1115,24000,4641],{"class":3724},[1115,24002,8195],{"class":3717},[1115,24004,1797],{"class":3709},[1115,24006,12225],{"class":3705},[1115,24008,3797],{"class":3709},[1115,24010,24011],{"class":3840}," \"np\"",[1115,24013,1797],{"class":3709},[1115,24015,23876],{"class":3705},[1115,24017,3797],{"class":3709},[1115,24019,15341],{"class":3724},[1115,24021,3901],{"class":3717},[16749,24023,21264,24025],{"id":24024},"diagram-pp",[1115,24026,24028],{"className":24027},[1138],[1140,24029,24030],{"xmlns":1142},[1144,24031,24032,24036],{},[1147,24033,24034],{},[1153,24035,1110],{},[1159,24037,1110],{"encoding":1161},[1110,24039,24040,24041,24077],{},"Regulovanou veličinou je počet neshodných produktů v logické podskupině přepočtený na jednotku, ",[1115,24042,24044],{"className":24043},[1138],[1140,24045,24046],{"xmlns":1142},[1144,24047,24048,24074],{},[1147,24049,24050,24056,24058,24060,24066,24068],{},[1150,24051,24052,24054],{},[1153,24053,1110],{},[1153,24055,1878],{},[1242,24057,1982],{},[1153,24059,1372],{},[1150,24061,24062,24064],{},[1153,24063,1110],{},[1153,24065,1878],{},[1153,24067,4604],{"mathvariant":2121},[1150,24069,24070,24072],{},[1153,24071,1372],{},[1153,24073,1878],{},[1159,24075,24076],{"encoding":1161},"p_i = np_i\u002Fn_i","; rozsahy podskupin nemusí být konstantní.",[1110,24079,23811,24080,24082],{},[3470,24081,23814],{}," se dosadí vektor rozsahů logických podskupin:",[3694,24084,24086],{"className":3696,"code":24085,"language":71,"meta":1490,"style":1490},"data \u003C- read.table(\"3_6.txt\", header = TRUE)   # počty vadných tabletů a rozsahy sérií\nqcc(data[, 1], type = \"p\", sizes = data[, 2])\n",[3470,24087,24088,24114],{"__ignoreMap":1490},[1115,24089,24090,24092,24094,24096,24098,24101,24103,24105,24107,24109,24111],{"class":3702,"line":10},[1115,24091,20109],{"class":3705},[1115,24093,3710],{"class":3709},[1115,24095,20114],{"class":3713},[1115,24097,1875],{"class":3717},[1115,24099,24100],{"class":3840},"\"3_6.txt\"",[1115,24102,1797],{"class":3709},[1115,24104,20124],{"class":3705},[1115,24106,3797],{"class":3709},[1115,24108,3810],{"class":3724},[1115,24110,12032],{"class":3717},[1115,24112,24113],{"class":12035},"# počty vadných tabletů a rozsahy sérií\n",[1115,24115,24116,24118,24120,24122,24124,24126,24128,24130,24132,24134,24136,24139,24141,24143,24145,24147,24149,24151,24153],{"class":3702,"line":27},[1115,24117,360],{"class":3713},[1115,24119,1875],{"class":3717},[1115,24121,20109],{"class":3705},[1115,24123,8178],{"class":3717},[1115,24125,1797],{"class":3709},[1115,24127,4641],{"class":3724},[1115,24129,8195],{"class":3717},[1115,24131,1797],{"class":3709},[1115,24133,12225],{"class":3705},[1115,24135,3797],{"class":3709},[1115,24137,24138],{"class":3840}," \"p\"",[1115,24140,1797],{"class":3709},[1115,24142,23876],{"class":3705},[1115,24144,3797],{"class":3709},[1115,24146,20168],{"class":3705},[1115,24148,8178],{"class":3717},[1115,24150,1797],{"class":3709},[1115,24152,4180],{"class":3724},[1115,24154,23889],{"class":3717},[1189,24156,24158],{"id":24157},"indexy-způsobilosti","Indexy způsobilosti",[1110,24160,24161,24162,24181,24182,24200],{},"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 ",[1115,24163,24165],{"className":24164},[1138],[1140,24166,24167],{"xmlns":1142},[1144,24168,24169,24178],{},[1147,24170,24171,24173,24176],{},[1153,24172,22118],{},[1153,24174,24175],{},"S",[1153,24177,22118],{},[1159,24179,24180],{"encoding":1161},"LSL"," a horní meze ",[1115,24183,24185],{"className":24184},[1138],[1140,24186,24187],{"xmlns":1142},[1144,24188,24189,24197],{},[1147,24190,24191,24193,24195],{},[1153,24192,22144],{},[1153,24194,24175],{},[1153,24196,22118],{},[1159,24198,24199],{"encoding":1161},"USL",". Způsobilost se zkoumá až pro proces, který je podle regulačních diagramů statisticky zvládnutý (třetí fáze regulace).",[16749,24202,24204,24221],{"id":24203},"cpc_p-index-způsobilosti",[1115,24205,24207],{"className":24206},[1138],[1140,24208,24209],{"xmlns":1142},[1144,24210,24211,24219],{},[1147,24212,24213],{},[1150,24214,24215,24217],{},[1153,24216,1155],{},[1153,24218,1110],{},[1159,24220,1162],{"encoding":1161}," — index způsobilosti",[1110,24223,24224,24225,1958],{},"Podíl mezi délkou tolerančního intervalu a délkou intervalu, ve kterém by za normálního rozdělení mělo ležet skoro všech 99,73 % hodnot znaku, tedy ",[1115,24226,24228],{"className":24227},[1138],[1140,24229,24230],{"xmlns":1142},[1144,24231,24232,24238],{},[1147,24233,24234,24236],{},[1565,24235,3964],{},[1153,24237,6901],{},[1159,24239,24240],{"encoding":1161},"6\\sigma",[1115,24242,24244],{"className":24243},[1138],[1140,24245,24246],{"xmlns":1142,"display":1964},[1144,24247,24248,24284],{},[1147,24249,24250,24256,24258,24282],{},[1150,24251,24252,24254],{},[1153,24253,1155],{},[1153,24255,1110],{},[1242,24257,1982],{},[2739,24259,24260,24276],{},[1147,24261,24262,24264,24266,24268,24270,24272,24274],{},[1153,24263,22144],{},[1153,24265,24175],{},[1153,24267,22118],{},[1242,24269,3064],{},[1153,24271,22118],{},[1153,24273,24175],{},[1153,24275,22118],{},[1147,24277,24278,24280],{},[1565,24279,3964],{},[1153,24281,6901],{},[1153,24283,1669],{"mathvariant":2121},[1159,24285,24286],{"encoding":1161},"C_p = \\frac{USL - LSL}{6\\sigma}.",[1110,24288,24289,24306,24307,24320,24321,1669],{},[1115,24290,24292],{"className":24291},[1138],[1140,24293,24294],{"xmlns":1142},[1144,24295,24296,24304],{},[1147,24297,24298],{},[1150,24299,24300,24302],{},[1153,24301,1155],{},[1153,24303,1110],{},[1159,24305,1162],{"encoding":1161}," srovnává jen délky, nevšímá si, kde uprostřed tolerance proces leží — centrovaný i silně vychýlený proces se stejným ",[1115,24308,24310],{"className":24309},[1138],[1140,24311,24312],{"xmlns":1142},[1144,24313,24314,24318],{},[1147,24315,24316],{},[1153,24317,6901],{},[1159,24319,6933],{"encoding":1161}," mají stejné ",[1115,24322,24324],{"className":24323},[1138],[1140,24325,24326],{"xmlns":1142},[1144,24327,24328,24336],{},[1147,24329,24330],{},[1150,24331,24332,24334],{},[1153,24333,1155],{},[1153,24335,1110],{},[1159,24337,1162],{"encoding":1161},[1110,24339,24340],{},"Doplňkové charakteristiky využití tolerančního intervalu:",[1436,24342,24343,24377,24465],{},[1439,24344,24345,3988,24348,24376],{},[1540,24346,24347],{},"míra využití tolerančního intervalu",[1115,24349,24351],{"className":24350},[1138],[1140,24352,24353],{"xmlns":1142},[1144,24354,24355,24373],{},[1147,24356,24357,24369,24371],{},[3241,24358,24359],{"scriptlevel":1567,"displaystyle":1121},[2739,24360,24361,24363],{},[1565,24362,11820],{},[1150,24364,24365,24367],{},[1153,24366,1155],{},[1153,24368,1110],{},[2909,24370,2911],{},[1153,24372,11827],{"mathvariant":2121},[1159,24374,24375],{"encoding":1161},"\\dfrac{100}{C_p}\\,\\%"," — na kolik procent je toleranční interval využíván sledovaným znakem,",[1439,24378,24379,24382,24383,24400,24401,1163,24433,1797],{},[1540,24380,24381],{},"robustnost procesu",": rezerva, kterou máme v tolerančních mezích, než index ",[1115,24384,24386],{"className":24385},[1138],[1140,24387,24388],{"xmlns":1142},[1144,24389,24390,24398],{},[1147,24391,24392],{},[1150,24393,24394,24396],{},[1153,24395,1155],{},[1153,24397,1110],{},[1159,24399,1162],{"encoding":1161}," nabyde hodnotu 1 — rovná se menší hodnotě z výrazů ",[1115,24402,24404],{"className":24403},[1138],[1140,24405,24406],{"xmlns":1142},[1144,24407,24408,24430],{},[1147,24409,24410,24412,24414,24416,24418,24420,24422,24424,24426,24428],{},[1153,24411,22144],{},[1153,24413,24175],{},[1153,24415,22118],{},[1242,24417,3064],{},[1242,24419,1875],{"stretchy":1874},[1153,24421,6893],{},[1242,24423,5477],{},[1565,24425,3592],{},[1153,24427,6901],{},[1242,24429,1886],{"stretchy":1874},[1159,24431,24432],{"encoding":1161},"USL-(\\mu+3\\sigma)",[1115,24434,24436],{"className":24435},[1138],[1140,24437,24438],{"xmlns":1142},[1144,24439,24440,24462],{},[1147,24441,24442,24444,24446,24448,24450,24452,24454,24456,24458,24460],{},[1242,24443,1875],{"stretchy":1874},[1153,24445,6893],{},[1242,24447,3064],{},[1565,24449,3592],{},[1153,24451,6901],{},[1242,24453,1886],{"stretchy":1874},[1242,24455,3064],{},[1153,24457,22118],{},[1153,24459,24175],{},[1153,24461,22118],{},[1159,24463,24464],{"encoding":1161},"(\\mu-3\\sigma)-LSL",[1439,24466,24467,3988,24470,6783,24510,24524],{},[1540,24468,24469],{},"podíl zmetků",[1115,24471,24473],{"className":24472},[1138],[1140,24474,24475],{"xmlns":1142},[1144,24476,24477,24507],{},[1147,24478,24479,24486,24488,24490,24493,24495,24497,24499,24505],{},[1150,24480,24481,24483],{},[1153,24482,6729],{},[1153,24484,24485],{},"z",[1242,24487,1982],{},[1565,24489,1589],{},[1153,24491,24492],{"mathvariant":2121},"Φ",[1242,24494,1875],{"stretchy":1874},[1242,24496,3064],{},[1565,24498,3592],{},[1150,24500,24501,24503],{},[1153,24502,1155],{},[1153,24504,1110],{},[1242,24506,1886],{"stretchy":1874},[1159,24508,24509],{"encoding":1161},"P_z = 2\\Phi(-3C_p)",[1115,24511,24513],{"className":24512},[1138],[1140,24514,24515],{"xmlns":1142},[1144,24516,24517,24521],{},[1147,24518,24519],{},[1153,24520,24492],{"mathvariant":2121},[1159,24522,24523],{"encoding":1161},"\\Phi"," je distribuční funkce normovaného normálního rozdělení.",[16749,24526,24528,24549],{"id":24527},"cpkc_pk-index-způsobilosti-s-ohledem-na-vychýlení",[1115,24529,24531],{"className":24530},[1138],[1140,24532,24533],{"xmlns":1142},[1144,24534,24535,24547],{},[1147,24536,24537],{},[1150,24538,24539,24541],{},[1153,24540,1155],{},[1147,24542,24543,24545],{},[1153,24544,1110],{},[1153,24546,1183],{},[1159,24548,1186],{"encoding":1161}," — index způsobilosti s ohledem na vychýlení",[1110,24551,24552],{},"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:",[1115,24554,24556],{"className":24555},[1138],[1140,24557,24558],{"xmlns":1142,"display":1964},[1144,24559,24560,24630],{},[1147,24561,24562,24572,24574,24576,24578,24628],{},[1150,24563,24564,24566],{},[1153,24565,1155],{},[1147,24567,24568,24570],{},[1153,24569,1110],{},[1153,24571,1183],{},[1242,24573,1982],{},[1153,24575,4488],{},[1242,24577,4491],{},[1147,24579,24580,24582,24602,24604,24606,24626],{},[1242,24581,1875],{"fence":1121},[2739,24583,24584,24596],{},[1147,24585,24586,24588,24590,24592,24594],{},[1153,24587,22144],{},[1153,24589,24175],{},[1153,24591,22118],{},[1242,24593,3064],{},[1153,24595,6893],{},[1147,24597,24598,24600],{},[1565,24599,3592],{},[1153,24601,6901],{},[1242,24603,1797],{"separator":1121},[2909,24605,11318],{},[2739,24607,24608,24620],{},[1147,24609,24610,24612,24614,24616,24618],{},[1153,24611,6893],{},[1242,24613,3064],{},[1153,24615,22118],{},[1153,24617,24175],{},[1153,24619,22118],{},[1147,24621,24622,24624],{},[1565,24623,3592],{},[1153,24625,6901],{},[1242,24627,1886],{"fence":1121},[1153,24629,1669],{"mathvariant":2121},[1159,24631,24632],{"encoding":1161},"C_{pk} = \\min\\left(\\frac{USL-\\mu}{3\\sigma},\\ \\frac{\\mu-LSL}{3\\sigma}\\right).",[1110,24634,24635,24636,24649,24650,24680,24681,24702,24703,1669],{},"Vyjde-li některý z obou podílů záporný, položí se roven nule; to nastane, když střední hodnota ",[1115,24637,24639],{"className":24638},[1138],[1140,24640,24641],{"xmlns":1142},[1144,24642,24643,24647],{},[1147,24644,24645],{},[1153,24646,6893],{},[1159,24648,8799],{"encoding":1161}," leží mimo toleranční interval, a proces pak není pod statistickou kontrolou. U centrovaného procesu jsou oba podíly stejné a ",[1115,24651,24653],{"className":24652},[1138],[1140,24654,24655],{"xmlns":1142},[1144,24656,24657,24677],{},[1147,24658,24659,24669,24671],{},[1150,24660,24661,24663],{},[1153,24662,1155],{},[1147,24664,24665,24667],{},[1153,24666,1110],{},[1153,24668,1183],{},[1242,24670,1982],{},[1150,24672,24673,24675],{},[1153,24674,1155],{},[1153,24676,1110],{},[1159,24678,24679],{"encoding":1161},"C_{pk} = C_p","; čím víc je proces vychýlený, tím víc je ",[1115,24682,24684],{"className":24683},[1138],[1140,24685,24686],{"xmlns":1142},[1144,24687,24688,24700],{},[1147,24689,24690],{},[1150,24691,24692,24694],{},[1153,24693,1155],{},[1147,24695,24696,24698],{},[1153,24697,1110],{},[1153,24699,1183],{},[1159,24701,1186],{"encoding":1161}," menší než ",[1115,24704,24706],{"className":24705},[1138],[1140,24707,24708],{"xmlns":1142},[1144,24709,24710,24718],{},[1147,24711,24712],{},[1150,24713,24714,24716],{},[1153,24715,1155],{},[1153,24717,1110],{},[1159,24719,1162],{"encoding":1161},[16749,24721,24723,1163,24744,24767],{"id":24722},"cpmc_pm-a-cpmkc_pmk-indexy-vztažené-k-cíli",[1115,24724,24726],{"className":24725},[1138],[1140,24727,24728],{"xmlns":1142},[1144,24729,24730,24742],{},[1147,24731,24732],{},[1150,24733,24734,24736],{},[1153,24735,1155],{},[1147,24737,24738,24740],{},[1153,24739,1110],{},[1153,24741,4471],{},[1159,24743,20843],{"encoding":1161},[1115,24745,24747],{"className":24746},[1138],[1140,24748,24749],{"xmlns":1142},[1144,24750,24751,24765],{},[1147,24752,24753],{},[1150,24754,24755,24757],{},[1153,24756,1155],{},[1147,24758,24759,24761,24763],{},[1153,24760,1110],{},[1153,24762,4471],{},[1153,24764,1183],{},[1159,24766,20867],{"encoding":1161}," — indexy vztažené k cíli",[1110,24769,24770,24771,24784,24785,24798,24799,24842,24843,1958],{},"Pokud má proces zadaný cílový střed ",[1115,24772,24774],{"className":24773},[1138],[1140,24775,24776],{"xmlns":1142},[1144,24777,24778,24782],{},[1147,24779,24780],{},[1153,24781,7104],{},[1159,24783,7104],{"encoding":1161}," (ne nutně střed tolerance), nahradí se ",[1115,24786,24788],{"className":24787},[1138],[1140,24789,24790],{"xmlns":1142},[1144,24791,24792,24796],{},[1147,24793,24794],{},[1153,24795,6901],{},[1159,24797,6933],{"encoding":1161}," odmocninou ze střední čtvercové odchylky od cíle ",[1115,24800,24802],{"className":24801},[1138],[1140,24803,24804],{"xmlns":1142},[1144,24805,24806,24839],{},[1147,24807,24808,24811,24813],{},[1153,24809,24810],{},"τ",[1242,24812,1982],{},[4453,24814,24815],{},[1147,24816,24817,24823,24825,24827,24829,24831,24833],{},[1582,24818,24819,24821],{},[1153,24820,6901],{},[1565,24822,1589],{},[1242,24824,5477],{},[1242,24826,1875],{"stretchy":1874},[1153,24828,6893],{},[1242,24830,3064],{},[1153,24832,7104],{},[1582,24834,24835,24837],{},[1242,24836,1886],{"stretchy":1874},[1565,24838,1589],{},[1159,24840,24841],{"encoding":1161},"\\tau = \\sqrt{\\sigma^2+(\\mu-T)^2}",", která trestá i vychýlení od ",[1115,24844,24846],{"className":24845},[1138],[1140,24847,24848],{"xmlns":1142},[1144,24849,24850,24854],{},[1147,24851,24852],{},[1153,24853,7104],{},[1159,24855,7104],{"encoding":1161},[1115,24857,24859],{"className":24858},[1138],[1140,24860,24861],{"xmlns":1142,"display":1964},[1144,24862,24863,24975],{},[1147,24864,24865,24875,24877,24901,24903,24905,24917,24919,24921,24923,24973],{},[1150,24866,24867,24869],{},[1153,24868,1155],{},[1147,24870,24871,24873],{},[1153,24872,1110],{},[1153,24874,4471],{},[1242,24876,1982],{},[2739,24878,24879,24895],{},[1147,24880,24881,24883,24885,24887,24889,24891,24893],{},[1153,24882,22144],{},[1153,24884,24175],{},[1153,24886,22118],{},[1242,24888,3064],{},[1153,24890,22118],{},[1153,24892,24175],{},[1153,24894,22118],{},[1147,24896,24897,24899],{},[1565,24898,3964],{},[1153,24900,24810],{},[1242,24902,1797],{"separator":1121},[2012,24904],{"width":2014},[1150,24906,24907,24909],{},[1153,24908,1155],{},[1147,24910,24911,24913,24915],{},[1153,24912,1110],{},[1153,24914,4471],{},[1153,24916,1183],{},[1242,24918,1982],{},[1153,24920,4488],{},[1242,24922,4491],{},[1147,24924,24925,24927,24947,24949,24951,24971],{},[1242,24926,1875],{"fence":1121},[2739,24928,24929,24941],{},[1147,24930,24931,24933,24935,24937,24939],{},[1153,24932,22144],{},[1153,24934,24175],{},[1153,24936,22118],{},[1242,24938,3064],{},[1153,24940,6893],{},[1147,24942,24943,24945],{},[1565,24944,3592],{},[1153,24946,24810],{},[1242,24948,1797],{"separator":1121},[2909,24950,11318],{},[2739,24952,24953,24965],{},[1147,24954,24955,24957,24959,24961,24963],{},[1153,24956,6893],{},[1242,24958,3064],{},[1153,24960,22118],{},[1153,24962,24175],{},[1153,24964,22118],{},[1147,24966,24967,24969],{},[1565,24968,3592],{},[1153,24970,24810],{},[1242,24972,1886],{"fence":1121},[1153,24974,1669],{"mathvariant":2121},[1159,24976,24977],{"encoding":1161},"C_{pm} = \\frac{USL-LSL}{6\\tau}, \\qquad C_{pmk} = \\min\\left(\\frac{USL-\\mu}{3\\tau},\\ \\frac{\\mu-LSL}{3\\tau}\\right).",[16749,24979,24981],{"id":24980},"interpretace","Interpretace",[1194,24983,24984,25011],{},[1197,24985,24986],{},[1200,24987,24988,25008],{},[1203,24989,24990,24991],{},"Hodnota ",[1115,24992,24994],{"className":24993},[1138],[1140,24995,24996],{"xmlns":1142},[1144,24997,24998,25006],{},[1147,24999,25000],{},[1150,25001,25002,25004],{},[1153,25003,1155],{},[1153,25005,1110],{},[1159,25007,1162],{"encoding":1161},[1203,25009,25010],{},"Způsobilost procesu",[1210,25012,25013,25042,25085],{},[1200,25014,25015,25039],{},[1215,25016,25017],{},[1115,25018,25020],{"className":25019},[1138],[1140,25021,25022],{"xmlns":1142},[1144,25023,25024,25036],{},[1147,25025,25026,25032,25034],{},[1150,25027,25028,25030],{},[1153,25029,1155],{},[1153,25031,1110],{},[1242,25033,4332],{},[1565,25035,1794],{},[1159,25037,25038],{"encoding":1161},"C_p \u003C 1",[1215,25040,25041],{},"dosahovaná přesnost je menší než předepsaná — proces je nezpůsobilý",[1200,25043,25044,25068],{},[1215,25045,25046],{},[1115,25047,25049],{"className":25048},[1138],[1140,25050,25051],{"xmlns":1142},[1144,25052,25053,25065],{},[1147,25054,25055,25061,25063],{},[1150,25056,25057,25059],{},[1153,25058,1155],{},[1153,25060,1110],{},[1242,25062,1982],{},[1565,25064,1794],{},[1159,25066,25067],{"encoding":1161},"C_p = 1",[1215,25069,25070,25071,25084],{},"dosahovaná přesnost je rovna předepsané — proces je způsobilý, ale sebemenší zvětšení ",[1115,25072,25074],{"className":25073},[1138],[1140,25075,25076],{"xmlns":1142},[1144,25077,25078,25082],{},[1147,25079,25080],{},[1153,25081,6901],{},[1159,25083,6933],{"encoding":1161}," jej posune na nezpůsobilý",[1200,25086,25087,25111],{},[1215,25088,25089],{},[1115,25090,25092],{"className":25091},[1138],[1140,25093,25094],{"xmlns":1142},[1144,25095,25096,25108],{},[1147,25097,25098,25104,25106],{},[1150,25099,25100,25102],{},[1153,25101,1155],{},[1153,25103,1110],{},[1242,25105,1689],{},[1565,25107,1794],{},[1159,25109,25110],{"encoding":1161},"C_p > 1",[1215,25112,25113],{},"dosahovaná přesnost je větší než předepsaná — proces je způsobilý",[1110,25115,25116,25117,25138,25139,1669],{},"U indexu ",[1115,25118,25120],{"className":25119},[1138],[1140,25121,25122],{"xmlns":1142},[1144,25123,25124,25136],{},[1147,25125,25126],{},[1150,25127,25128,25130],{},[1153,25129,1155],{},[1147,25131,25132,25134],{},[1153,25133,1110],{},[1153,25135,1183],{},[1159,25137,1186],{"encoding":1161}," se v praxi požaduje víc než jen hodnota nad 1: s rozvojem technologií roste nárok na rezervu, a běžně se dnes vyžaduje hodnota alespoň ",[1115,25140,25142],{"className":25141},[1138],[1140,25143,25144],{"xmlns":1142},[1144,25145,25146,25151],{},[1147,25147,25148],{},[1565,25149,25150],{},"1,5",[1159,25152,25153],{"encoding":1161},"1{,}5",[1110,25155,25156],{},[4383,25157],{"alt":25158,"className":25159,"src":25160},"mask-rd-cp-panely",[1130,4387],"\u002Fwiki-assets\u002Fmask-rd-cp-panely.png",[1110,25162,25163],{},[4383,25164],{"alt":25165,"className":25166,"src":25167},"mask-rd-cpk-off-centre",[1130,4387],"\u002Fwiki-assets\u002Fmask-rd-cpk-off-centre.png",[16749,25169,25171],{"id":25170},"výpočet-v-r","Výpočet v R",[1110,25173,25174,25175,25178,25179,25182,25183,25186,25187,1163,25204,1346,25221,25224,25225,25238],{},"Indexy způsobilosti počítá ",[3470,25176,25177],{},"process.capability()"," z výstupu regulačního diagramu ",[3470,25180,25181],{},"q","; ",[3470,25184,25185],{},"spec.limits"," jsou toleranční meze ",[1115,25188,25190],{"className":25189},[1138],[1140,25191,25192],{"xmlns":1142},[1144,25193,25194,25202],{},[1147,25195,25196,25198,25200],{},[1153,25197,22118],{},[1153,25199,24175],{},[1153,25201,22118],{},[1159,25203,24180],{"encoding":1161},[1115,25205,25207],{"className":25206},[1138],[1140,25208,25209],{"xmlns":1142},[1144,25210,25211,25219],{},[1147,25212,25213,25215,25217],{},[1153,25214,22144],{},[1153,25216,24175],{},[1153,25218,22118],{},[1159,25220,24199],{"encoding":1161},[3470,25222,25223],{},"target"," cílová hodnota ",[1115,25226,25228],{"className":25227},[1138],[1140,25229,25230],{"xmlns":1142},[1144,25231,25232,25236],{},[1147,25233,25234],{},[1153,25235,7104],{},[1159,25237,7104],{"encoding":1161},". Pro velikost výrobku v mm s tolerančními mezemi 100 a 110 mm a cílovou hodnotou 105 mm:",[3694,25240,25242],{"className":3696,"code":25241,"language":71,"meta":1490,"style":1490},"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",[3470,25243,25244,25254,25277,25292,25314],{"__ignoreMap":1490},[1115,25245,25246,25248,25250,25252],{"class":3702,"line":10},[1115,25247,17398],{"class":3709},[1115,25249,1875],{"class":3717},[1115,25251,360],{"class":3705},[1115,25253,3901],{"class":3717},[1115,25255,25256,25258,25260,25262,25264,25267,25269,25271,25273,25275],{"class":3702,"line":27},[1115,25257,20109],{"class":3705},[1115,25259,3710],{"class":3709},[1115,25261,20114],{"class":3713},[1115,25263,1875],{"class":3717},[1115,25265,25266],{"class":3840},"\"3_8.txt\"",[1115,25268,1797],{"class":3709},[1115,25270,20124],{"class":3705},[1115,25272,3797],{"class":3709},[1115,25274,3810],{"class":3724},[1115,25276,3901],{"class":3717},[1115,25278,25279,25281,25283,25286,25288,25290],{"class":3702,"line":148},[1115,25280,1240],{"class":3705},[1115,25282,3710],{"class":3709},[1115,25284,25285],{"class":3713}," as.matrix",[1115,25287,1875],{"class":3717},[1115,25289,20109],{"class":3705},[1115,25291,3901],{"class":3717},[1115,25293,25294,25296,25298,25300,25302,25304,25306,25308,25310,25312],{"class":3702,"line":111},[1115,25295,25181],{"class":3705},[1115,25297,3710],{"class":3709},[1115,25299,23618],{"class":3713},[1115,25301,1875],{"class":3717},[1115,25303,1240],{"class":3705},[1115,25305,1797],{"class":3709},[1115,25307,12225],{"class":3705},[1115,25309,3797],{"class":3709},[1115,25311,22744],{"class":3840},[1115,25313,3901],{"class":3717},[1115,25315,25316,25319,25321,25323,25325,25328,25330,25332,25334,25336,25338,25340,25342,25344,25347,25349,25352,25354,25357,25359,25361,25363,25365],{"class":3702,"line":96},[1115,25317,25318],{"class":3713},"process.capability",[1115,25320,1875],{"class":3717},[1115,25322,25181],{"class":3705},[1115,25324,1797],{"class":3709},[1115,25326,25327],{"class":3705}," spec.limits",[1115,25329,3797],{"class":3709},[1115,25331,3835],{"class":3713},[1115,25333,1875],{"class":3717},[1115,25335,11820],{"class":3724},[1115,25337,1797],{"class":3709},[1115,25339,14270],{"class":3724},[1115,25341,1886],{"class":3717},[1115,25343,1797],{"class":3709},[1115,25345,25346],{"class":3705}," target",[1115,25348,3797],{"class":3709},[1115,25350,25351],{"class":3724}," 105",[1115,25353,1797],{"class":3709},[1115,25355,25356],{"class":3705}," std.dev",[1115,25358,3797],{"class":3709},[1115,25360,9244],{"class":3713},[1115,25362,1875],{"class":3717},[1115,25364,1240],{"class":3705},[1115,25366,9496],{"class":3717},[1110,25368,25369,25370,1346,25373,1346,25376,1346,25379,1163,25382,25385,25386,1163,25388,25390,25391,25412,25413,25436],{},"Výpis obsahuje řádky ",[3470,25371,25372],{},"Cp",[3470,25374,25375],{},"Cp_l",[3470,25377,25378],{},"Cp_u",[3470,25380,25381],{},"Cp_k",[3470,25383,25384],{},"Cpm"," s hodnotou indexu a 95% intervalem spolehlivosti. ",[3470,25387,25375],{},[3470,25389,25378],{}," jsou dílčí poměry k dolní a horní mezi, jejich minimum je ",[1115,25392,25394],{"className":25393},[1138],[1140,25395,25396],{"xmlns":1142},[1144,25397,25398,25410],{},[1147,25399,25400],{},[1150,25401,25402,25404],{},[1153,25403,1155],{},[1147,25405,25406,25408],{},[1153,25407,1110],{},[1153,25409,1183],{},[1159,25411,1186],{"encoding":1161},". Index ",[1115,25414,25416],{"className":25415},[1138],[1140,25417,25418],{"xmlns":1142},[1144,25419,25420,25434],{},[1147,25421,25422],{},[1150,25423,25424,25426],{},[1153,25425,1155],{},[1147,25427,25428,25430,25432],{},[1153,25429,1110],{},[1153,25431,4471],{},[1153,25433,1183],{},[1159,25435,20867],{"encoding":1161}," a doplňkové charakteristiky se dopočítají ze vzorců výše:",[3694,25438,25440],{"className":3696,"code":25439,"language":71,"meta":1490,"style":1490},"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",[3470,25441,25442,25469,25494,25531,25561,25619,25633,25684],{"__ignoreMap":1490},[1115,25443,25444,25447,25449,25451,25453,25455,25457,25459,25461,25463,25465,25467],{"class":3702,"line":10},[1115,25445,25446],{"class":3705},"mu",[1115,25448,3710],{"class":3709},[1115,25450,9234],{"class":3713},[1115,25452,1875],{"class":3717},[1115,25454,1240],{"class":3705},[1115,25456,12179],{"class":3717},[1115,25458,380],{"class":3705},[1115,25460,3710],{"class":3709},[1115,25462,9244],{"class":3713},[1115,25464,1875],{"class":3717},[1115,25466,1240],{"class":3705},[1115,25468,3901],{"class":3717},[1115,25470,25471,25473,25475,25477,25479,25481,25483,25485,25487,25489,25491],{"class":3702,"line":27},[1115,25472,24180],{"class":3705},[1115,25474,3710],{"class":3709},[1115,25476,15341],{"class":3724},[1115,25478,25182],{"class":3717},[1115,25480,24199],{"class":3705},[1115,25482,3710],{"class":3709},[1115,25484,14270],{"class":3724},[1115,25486,25182],{"class":3717},[1115,25488,7104],{"class":3705},[1115,25490,3710],{"class":3709},[1115,25492,25493],{"class":3724}," 105\n",[1115,25495,25496,25499,25501,25503,25505,25507,25509,25511,25513,25515,25517,25520,25523,25525,25527,25529],{"class":3702,"line":148},[1115,25497,25498],{"class":3705},"tau",[1115,25500,3710],{"class":3709},[1115,25502,4578],{"class":3713},[1115,25504,1875],{"class":3717},[1115,25506,380],{"class":3705},[1115,25508,2729],{"class":3709},[1115,25510,1589],{"class":3724},[1115,25512,18517],{"class":3709},[1115,25514,4607],{"class":3717},[1115,25516,25446],{"class":3705},[1115,25518,25519],{"class":3709}," -",[1115,25521,25522],{"class":3705}," T",[1115,25524,1886],{"class":3717},[1115,25526,2729],{"class":3709},[1115,25528,1589],{"class":3724},[1115,25530,3901],{"class":3717},[1115,25532,25533,25535,25537,25539,25541,25543,25546,25548,25550,25552,25554,25556,25559],{"class":3702,"line":111},[1115,25534,25372],{"class":3705},[1115,25536,3710],{"class":3709},[1115,25538,4607],{"class":3717},[1115,25540,24199],{"class":3705},[1115,25542,25519],{"class":3709},[1115,25544,25545],{"class":3705}," LSL",[1115,25547,4601],{"class":3717},[1115,25549,4604],{"class":3709},[1115,25551,4607],{"class":3717},[1115,25553,3964],{"class":3724},[1115,25555,18642],{"class":3709},[1115,25557,25558],{"class":3705}," sigma",[1115,25560,3901],{"class":3717},[1115,25562,25563,25566,25568,25570,25573,25575,25577,25580,25582,25584,25586,25588,25590,25593,25595,25597,25599,25601,25603,25605,25607,25609,25611,25613,25615,25617],{"class":3702,"line":96},[1115,25564,25565],{"class":3705},"Cpmk",[1115,25567,3710],{"class":3709},[1115,25569,12200],{"class":3713},[1115,25571,25572],{"class":3717},"((",[1115,25574,24199],{"class":3705},[1115,25576,25519],{"class":3709},[1115,25578,25579],{"class":3705}," mu",[1115,25581,4601],{"class":3717},[1115,25583,4604],{"class":3709},[1115,25585,4607],{"class":3717},[1115,25587,3592],{"class":3724},[1115,25589,18642],{"class":3709},[1115,25591,25592],{"class":3705}," tau",[1115,25594,1886],{"class":3717},[1115,25596,1797],{"class":3709},[1115,25598,4607],{"class":3717},[1115,25600,25446],{"class":3705},[1115,25602,25519],{"class":3709},[1115,25604,25545],{"class":3705},[1115,25606,4601],{"class":3717},[1115,25608,4604],{"class":3709},[1115,25610,4607],{"class":3717},[1115,25612,3592],{"class":3724},[1115,25614,18642],{"class":3709},[1115,25616,25592],{"class":3705},[1115,25618,9496],{"class":3717},[1115,25620,25621,25624,25626,25628,25630],{"class":3702,"line":89},[1115,25622,25623],{"class":3705},"miravyuziti",[1115,25625,3710],{"class":3709},[1115,25627,15341],{"class":3724},[1115,25629,10078],{"class":3709},[1115,25631,25632],{"class":3705}," Cp\n",[1115,25634,25635,25638,25640,25642,25644,25646,25648,25650,25652,25654,25656,25658,25660,25662,25664,25666,25668,25670,25672,25674,25676,25678,25680,25682],{"class":3702,"line":82},[1115,25636,25637],{"class":3705},"robustnost",[1115,25639,3710],{"class":3709},[1115,25641,12200],{"class":3713},[1115,25643,1875],{"class":3717},[1115,25645,24199],{"class":3705},[1115,25647,25519],{"class":3709},[1115,25649,4607],{"class":3717},[1115,25651,25446],{"class":3705},[1115,25653,18517],{"class":3709},[1115,25655,10857],{"class":3724},[1115,25657,18642],{"class":3709},[1115,25659,25558],{"class":3705},[1115,25661,1886],{"class":3717},[1115,25663,1797],{"class":3709},[1115,25665,4607],{"class":3717},[1115,25667,25446],{"class":3705},[1115,25669,25519],{"class":3709},[1115,25671,10857],{"class":3724},[1115,25673,18642],{"class":3709},[1115,25675,25558],{"class":3705},[1115,25677,4601],{"class":3717},[1115,25679,4638],{"class":3709},[1115,25681,25545],{"class":3705},[1115,25683,3901],{"class":3717},[1115,25685,25686,25689,25691,25693,25695,25697,25699,25701,25703,25705,25708],{"class":3702,"line":75},[1115,25687,25688],{"class":3705},"Pz",[1115,25690,3710],{"class":3709},[1115,25692,4180],{"class":3724},[1115,25694,18642],{"class":3709},[1115,25696,9354],{"class":3713},[1115,25698,1875],{"class":3717},[1115,25700,4638],{"class":3709},[1115,25702,3592],{"class":3724},[1115,25704,18642],{"class":3709},[1115,25706,25707],{"class":3705}," Cp",[1115,25709,3901],{"class":3717},[1189,25711,6407],{"id":6406},[1436,25713,25714,25717,25777,25868,25934],{},[1439,25715,25716],{},"Počítat indexy způsobilosti pro proces, který není statisticky zvládnutý — způsobilost se zkoumá až ve třetí fázi regulace.",[1439,25718,25719,25720,25737,25738,25755,25756,1669],{},"Posuzovat jen ",[1115,25721,25723],{"className":25722},[1138],[1140,25724,25725],{"xmlns":1142},[1144,25726,25727,25735],{},[1147,25728,25729],{},[1150,25730,25731,25733],{},[1153,25732,1155],{},[1153,25734,1110],{},[1159,25736,1162],{"encoding":1161}," u vychýleného procesu — ",[1115,25739,25741],{"className":25740},[1138],[1140,25742,25743],{"xmlns":1142},[1144,25744,25745,25753],{},[1147,25746,25747],{},[1150,25748,25749,25751],{},[1153,25750,1155],{},[1153,25752,1110],{},[1159,25754,1162],{"encoding":1161}," polohu střední hodnoty nezohledňuje, vychýlení zachytí až ",[1115,25757,25759],{"className":25758},[1138],[1140,25760,25761],{"xmlns":1142},[1144,25762,25763,25775],{},[1147,25764,25765],{},[1150,25766,25767,25769],{},[1153,25768,1155],{},[1147,25770,25771,25773],{},[1153,25772,1110],{},[1153,25774,1183],{},[1159,25776,1186],{"encoding":1161},[1439,25778,25779,25780,25793,25794,25807,25808,25793,25823,25836,25837,25850,25851,25864,25865,25867],{},"Zaměnit diagram ",[1115,25781,25783],{"className":25782},[1138],[1140,25784,25785],{"xmlns":1142},[1144,25786,25787,25791],{},[1147,25788,25789],{},[1153,25790,1343],{},[1159,25792,1343],{"encoding":1161}," s diagramem ",[1115,25795,25797],{"className":25796},[1138],[1140,25798,25799],{"xmlns":1142},[1144,25800,25801,25805],{},[1147,25802,25803],{},[1153,25804,1358],{},[1159,25806,1358],{"encoding":1161}," nebo diagram ",[1115,25809,25811],{"className":25810},[1138],[1140,25812,25813],{"xmlns":1142},[1144,25814,25815,25821],{},[1147,25816,25817,25819],{},[1153,25818,1372],{},[1153,25820,1110],{},[1159,25822,1377],{"encoding":1161},[1115,25824,25826],{"className":25825},[1138],[1140,25827,25828],{"xmlns":1142},[1144,25829,25830,25834],{},[1147,25831,25832],{},[1153,25833,1110],{},[1159,25835,1110],{"encoding":1161}," — při nekonstantním rozsahu podskupin se volí ",[1115,25838,25840],{"className":25839},[1138],[1140,25841,25842],{"xmlns":1142},[1144,25843,25844,25848],{},[1147,25845,25846],{},[1153,25847,1358],{},[1159,25849,1358],{"encoding":1161},", resp. ",[1115,25852,25854],{"className":25853},[1138],[1140,25855,25856],{"xmlns":1142},[1144,25857,25858,25862],{},[1147,25859,25860],{},[1153,25861,1110],{},[1159,25863,1110],{"encoding":1161},", a do ",[3470,25866,23814],{}," se zadává vektor rozsahů.",[1439,25869,25870,25871,25888,25889,25902,25903,25916,25917,1669],{},"Posuzovat diagram ",[1115,25872,25874],{"className":25873},[1138],[1140,25875,25876],{"xmlns":1142},[1144,25877,25878,25886],{},[1147,25879,25880],{},[1236,25881,25882,25884],{"accent":1121},[1153,25883,1240],{},[1242,25885,1244],{},[1159,25887,21563],{"encoding":1161}," dřív než diagram rozpětí — nejprve se určí a stabilizuje diagram ",[1115,25890,25892],{"className":25891},[1138],[1140,25893,25894],{"xmlns":1142},[1144,25895,25896,25900],{},[1147,25897,25898],{},[1153,25899,1260],{},[1159,25901,1260],{"encoding":1161}," (resp. ",[1115,25904,25906],{"className":25905},[1138],[1140,25907,25908],{"xmlns":1142},[1144,25909,25910,25914],{},[1147,25911,25912],{},[1153,25913,1291],{},[1159,25915,1291],{"encoding":1161},"), potom diagram ",[1115,25918,25920],{"className":25919},[1138],[1140,25921,25922],{"xmlns":1142},[1144,25923,25924,25932],{},[1147,25925,25926],{},[1236,25927,25928,25930],{"accent":1121},[1153,25929,1240],{},[1242,25931,1244],{},[1159,25933,21563],{"encoding":1161},[1439,25935,25936],{},"Vyřadit podskupinu jen podle polohy bodu — vyřazuje se až po zjištění a odstranění vymezitelné příčiny.",[1189,25938,1434],{"id":1433},[1436,25940,25941,25946,25951,25957,25962,25967,25972],{},[1439,25942,25943],{},[1127,25944,1133],{"className":25945,"dataFsResolvedFilePath":1131,"href":1132},[1130],[1439,25947,25948],{},[1127,25949,886],{"className":25950,"dataFsResolvedFilePath":6612,"href":6613},[1130],[1439,25952,25953],{},[1127,25954,25956],{"className":25955,"dataFsResolvedFilePath":6620,"href":6621},[1130],"nahodne-veliciny-a-rozdeleni",[1439,25958,25959],{},[1127,25960,141],{"className":25961,"dataFsResolvedFilePath":1721,"href":1722},[1130],[1439,25963,25964],{},[1127,25965,11087],{"className":25966,"dataFsResolvedFilePath":6628,"href":6629},[1130],[1439,25968,25969],{},[1127,25970,716],{"className":25971,"dataFsResolvedFilePath":11093,"href":11094},[1130],[1439,25973,25974],{},[1127,25975,6641],{"className":25976,"dataFsResolvedFilePath":1454,"href":1455},[1130],[1189,25978,1459],{"id":934},[1110,25980,1462,25981,1467],{},[1464,25982,1466],{},[1110,25984,1470,25985,1474],{},[1464,25986,1473],{},[1110,25988,1477,25989,1481],{},[1464,25990,1480],{},[1110,25992,1484,25993,1488],{},[1464,25994,1487],{},[6649,25996,25997],{},"html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sP4rz, html code.shiki .sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sCsY4, html code.shiki .sCsY4{--shiki-light:#6A737D;--shiki-default:#6A737D;--shiki-dark:#6A737D}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: 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.shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":1490,"searchDepth":27,"depth":27,"links":25999},[26000,26001,26002,26010,26020,26030,26031,26032],{"id":20898,"depth":27,"text":20899},{"id":21012,"depth":27,"text":21013},{"id":21101,"depth":27,"text":21102,"children":26003},[26004,26006,26008],{"id":21263,"depth":148,"text":26005},"Diagram (xˉ,R)(\\bar{x}, R)",{"id":22759,"depth":148,"text":26007},"Diagram (xˉ,s)(\\bar{x}, s)",{"id":22925,"depth":148,"text":26009},"Diagram (xi,Rkl,i)(x_i, R_{kl,i})",{"id":23280,"depth":27,"text":23281,"children":26011},[26012,26014,26016,26018],{"id":23376,"depth":148,"text":26013},"Diagram cc",{"id":23739,"depth":148,"text":26015},"Diagram uu",{"id":23892,"depth":148,"text":26017},"Diagram npnp",{"id":24024,"depth":148,"text":26019},"Diagram pp",{"id":24157,"depth":27,"text":24158,"children":26021},[26022,26024,26026,26028,26029],{"id":24203,"depth":148,"text":26023},"CpC_p — index způsobilosti",{"id":24527,"depth":148,"text":26025},"CpkC_{pk} — index způsobilosti s ohledem na vychýlení",{"id":24722,"depth":148,"text":26027},"CpmC_{pm} a CpmkC_{pmk} — indexy vztažené k cíli",{"id":24980,"depth":148,"text":24981},{"id":25170,"depth":148,"text":25171},{"id":6406,"depth":27,"text":6407},{"id":1433,"depth":27,"text":1434},{"id":934,"depth":27,"text":1459},{},"\u002Ftopics\u002Fregulacni-diagramy-a-indexy-zpusobilosti",{"title":1222,"description":1490},[1503,1504,1505,1506],"topics\u002Fregulacni-diagramy-a-indexy-zpusobilosti",[23,137,274,360,67,71],"bwtPTtx6g53SO_ovQdrK_C3d6vq9rKG9Vb8jM13_yag",{"id":26041,"title":6606,"body":26042,"course":23,"courses":1495,"created":1496,"description":1490,"extension":1497,"meta":35853,"navigation":1499,"path":35854,"seo":35855,"sources":35856,"stem":35862,"tags":35863,"type":6670,"updated":1496,"__hash__":35864},"topics\u002Ftopics\u002Ftestovani-hypotez.md",{"type":1096,"value":26043,"toc":35826},[26044,26047,26246,26290,26294,26304,26307,26373,26423,26576,26580,26583,26677,26827,26846,26853,26942,26946,26981,27018,27056,27091,27095,27102,27320,27439,27443,27575,27629,27651,27993,28000,28088,28094,28135,28420,28429,28544,28550,28557,28562,28568,28662,28668,28694,28700,28792,28798,28848,28852,29048,29108,29470,29809,29908,29914,30142,30146,30412,30416,30419,30485,30532,30988,30992,30995,31182,31215,31437,31756,31795,31802,32459,32598,32604,32760,32766,32773,32826,32832,33005,33011,33075,33080,33265,33271,33316,33320,33323,33327,33374,33602,33618,33707,33713,33739,33743,33746,33818,33911,33980,33986,34009,34456,34463,34467,34497,34501,34751,34770,34831,34840,34996,35002,35028,35203,35207,35228,35259,35263,35287,35317,35321,35381,35439,35443,35450,35623,35625,35778,35780,35817,35819,35823],[1099,26045,6606],{"id":26046},"testování-statistických-hypotéz",[1103,26048,26050,26056],{"className":26049,"dataCallout":1525},[1106,1524],[1110,26051,26053,1533],{"className":26052},[1113],[1115,26054],{"className":26055,"ariaHidden":1121},[1118,1532,1120],[1436,26057,26058,26128,26210,26213,26216],{},[1439,26059,26060,26061,26078,26079,26096,26097,1346,26110,26127],{},"Test porovnává tvrzení ",[1115,26062,26064],{"className":26063},[1138],[1140,26065,26066],{"xmlns":1142},[1144,26067,26068,26076],{},[1147,26069,26070],{},[1150,26071,26072,26074],{},[1153,26073,1563],{},[1565,26075,1567],{},[1159,26077,1570],{"encoding":1161}," s alternativou ",[1115,26080,26082],{"className":26081},[1138],[1140,26083,26084],{"xmlns":1142},[1144,26085,26086,26094],{},[1147,26087,26088],{},[1150,26089,26090,26092],{},[1153,26091,1563],{},[1565,26093,1794],{},[1159,26095,2996],{"encoding":1161}," pomocí testového kritéria spočteného z výběru; padne-li kritérium do kritického oboru ",[1115,26098,26100],{"className":26099},[1138],[1140,26101,26102],{"xmlns":1142},[1144,26103,26104,26108],{},[1147,26105,26106],{},[1153,26107,1605],{},[1159,26109,1605],{"encoding":1161},[1115,26111,26113],{"className":26112},[1138],[1140,26114,26115],{"xmlns":1142},[1144,26116,26117,26125],{},[1147,26118,26119],{},[1150,26120,26121,26123],{},[1153,26122,1563],{},[1565,26124,1567],{},[1159,26126,1570],{"encoding":1161}," zamítáme.",[1439,26129,26130,26131,26144,26145,26162,26163,26177,26178,26195,26196,26209],{},"Rozhodnutí nese dva typy chyb: chybu I. druhu (",[1115,26132,26134],{"className":26133},[1138],[1140,26135,26136],{"xmlns":1142},[1144,26137,26138,26142],{},[1147,26139,26140],{},[1153,26141,3365],{},[1159,26143,3428],{"encoding":1161},", zamítnutí platné ",[1115,26146,26148],{"className":26147},[1138],[1140,26149,26150],{"xmlns":1142},[1144,26151,26152,26160],{},[1147,26153,26154],{},[1150,26155,26156,26158],{},[1153,26157,1563],{},[1565,26159,1567],{},[1159,26161,1570],{"encoding":1161},") a chybu II. druhu (",[1115,26164,26166],{"className":26165},[1138],[1140,26167,26168],{"xmlns":1142},[1144,26169,26170,26174],{},[1147,26171,26172],{},[1153,26173,16340],{},[1159,26175,26176],{"encoding":1161},"\\beta",", přijetí neplatné ",[1115,26179,26181],{"className":26180},[1138],[1140,26182,26183],{"xmlns":1142},[1144,26184,26185,26193],{},[1147,26186,26187],{},[1150,26188,26189,26191],{},[1153,26190,1563],{},[1565,26192,1567],{},[1159,26194,1570],{"encoding":1161},"). Hladina významnosti ",[1115,26197,26199],{"className":26198},[1138],[1140,26200,26201],{"xmlns":1142},[1144,26202,26203,26207],{},[1147,26204,26205],{},[1153,26206,3365],{},[1159,26208,3428],{"encoding":1161}," se volí předem, obvykle 0,05.",[1439,26211,26212],{},"Pro střední hodnotu normálního rozdělení slouží jednovýběrový a párový t-test; pro srovnání dvou souborů F-test (rozptyly) a dvouvýběrový t-test (střední hodnoty).",[1439,26214,26215],{},"Normalitu ověřuje Shapiro-Wilkův test, shodu s libovolným rozdělením Kolmogorov-Smirnovův test; při porušené normalitě nastupují neparametrické testy (Wilcoxonovy, Kruskalův-Wallisův, mediánový, Friedmanův).",[1439,26217,26218,26219,26232,26233,1669],{},"Rozhodnutí lze číst dvěma rovnocennými způsoby — podle polohy kritéria vůči ",[1115,26220,26222],{"className":26221},[1138],[1140,26223,26224],{"xmlns":1142},[1144,26225,26226,26230],{},[1147,26227,26228],{},[1153,26229,1605],{},[1159,26231,1605],{"encoding":1161},", nebo podle p-hodnoty vůči ",[1115,26234,26236],{"className":26235},[1138],[1140,26237,26238],{"xmlns":1142},[1144,26239,26240,26244],{},[1147,26241,26242],{},[1153,26243,3365],{},[1159,26245,3428],{"encoding":1161},[1110,26247,26248,26249,26253,26254,26258,26259,26263,26264,1346,26277,16096],{},"Testy statistických hypotéz jsou nástroj ",[1127,26250,26252],{"className":26251,"dataFsResolvedFilePath":1131,"href":1132},[1130],"Metod aplikované statistiky"," pro rozhodování o parametrech nebo tvaru rozdělení na základě náhodného výběru, nikoli vyčerpávajícího šetření celého základního souboru. Vycházejí z charakteristik, které lze předem spočítat jako ",[1127,26255,26257],{"className":26256,"dataFsResolvedFilePath":6612,"href":6613},[1130],"popisnou statistiku"," výběru, a z rozdělení uvedených u ",[1127,26260,26262],{"className":26261,"dataFsResolvedFilePath":6620,"href":6621},[1130],"náhodných veličin"," (normální, ",[1115,26265,26267],{"className":26266},[1138],[1140,26268,26269],{"xmlns":1142},[1144,26270,26271,26275],{},[1147,26272,26273],{},[1153,26274,7146],{},[1159,26276,7146],{"encoding":1161},[1115,26278,26280],{"className":26279},[1138],[1140,26281,26282],{"xmlns":1142},[1144,26283,26284,26288],{},[1147,26285,26286],{},[1153,26287,6718],{},[1159,26289,6718],{"encoding":1161},[1189,26291,26293],{"id":26292},"statistická-hypotéza-a-její-test","Statistická hypotéza a její test",[1110,26295,26296,26299,26300,26303],{},[1540,26297,26298],{},"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. ",[1540,26301,26302],{},"Testování hypotéz"," je proces ověření správnosti nebo nesprávnosti hypotézy pomocí výsledků získaných náhodným výběrem.",[1110,26305,26306],{},"Proti sobě stojí dvě hypotézy:",[1436,26308,26309,26332],{},[1439,26310,26311,26331],{},[1540,26312,26313,26314],{},"Nulová hypotéza ",[1115,26315,26317],{"className":26316},[1138],[1140,26318,26319],{"xmlns":1142},[1144,26320,26321,26329],{},[1147,26322,26323],{},[1150,26324,26325,26327],{},[1153,26326,1563],{},[1565,26328,1567],{},[1159,26330,1570],{"encoding":1161}," — tvrzení o parametru nebo rozdělení, které chceme ověřit.",[1439,26333,26334,26354,26355,26372],{},[1540,26335,26336,26337],{},"Alternativní hypotéza ",[1115,26338,26340],{"className":26339},[1138],[1140,26341,26342],{"xmlns":1142},[1144,26343,26344,26352],{},[1147,26345,26346],{},[1150,26347,26348,26350],{},[1153,26349,1563],{},[1565,26351,1794],{},[1159,26353,2996],{"encoding":1161}," — staví se proti ",[1115,26356,26358],{"className":26357},[1138],[1140,26359,26360],{"xmlns":1142},[1144,26361,26362,26370],{},[1147,26363,26364],{},[1150,26365,26366,26368],{},[1153,26367,1563],{},[1565,26369,1567],{},[1159,26371,1570],{"encoding":1161}," a určitým způsobem popírá její tvrzení.",[1110,26374,1698,26375,26405,26406,1958],{},[1115,26376,26378],{"className":26377},[1138],[1140,26379,26380],{"xmlns":1142},[1144,26381,26382,26402],{},[1147,26383,26384,26390,26392,26394,26396],{},[1150,26385,26386,26388],{},[1153,26387,1563],{},[1565,26389,1567],{},[1242,26391,1958],{},[1153,26393,6893],{},[1242,26395,1982],{},[1150,26397,26398,26400],{},[1153,26399,6893],{},[1565,26401,1567],{},[1159,26403,26404],{"encoding":1161},"H_0: \\mu = \\mu_0"," existují tři varianty ",[1115,26407,26409],{"className":26408},[1138],[1140,26410,26411],{"xmlns":1142},[1144,26412,26413,26421],{},[1147,26414,26415],{},[1150,26416,26417,26419],{},[1153,26418,1563],{},[1565,26420,1794],{},[1159,26422,2996],{"encoding":1161},[1194,26424,26425,26455],{},[1197,26426,26427],{},[1200,26428,26429,26449,26452],{},[1203,26430,26431,26432],{},"Tvar ",[1115,26433,26435],{"className":26434},[1138],[1140,26436,26437],{"xmlns":1142},[1144,26438,26439,26447],{},[1147,26440,26441],{},[1150,26442,26443,26445],{},[1153,26444,1563],{},[1565,26446,1794],{},[1159,26448,2996],{"encoding":1161},[1203,26450,26451],{},"Zápis",[1203,26453,26454],{},"Typ",[1210,26456,26457,26497,26537],{},[1200,26458,26459,26462,26494],{},[1215,26460,26461],{},"nerovnost",[1215,26463,26464],{},[1115,26465,26467],{"className":26466},[1138],[1140,26468,26469],{"xmlns":1142},[1144,26470,26471,26491],{},[1147,26472,26473,26479,26481,26483,26485],{},[1150,26474,26475,26477],{},[1153,26476,1563],{},[1565,26478,1794],{},[1242,26480,1958],{},[1153,26482,6893],{},[1242,26484,10958],{"mathvariant":2121},[1150,26486,26487,26489],{},[1153,26488,6893],{},[1565,26490,1567],{},[1159,26492,26493],{"encoding":1161},"H_1: \\mu \\neq \\mu_0",[1215,26495,26496],{},"dvoustranná",[1200,26498,26499,26502,26534],{},[1215,26500,26501],{},"větší",[1215,26503,26504],{},[1115,26505,26507],{"className":26506},[1138],[1140,26508,26509],{"xmlns":1142},[1144,26510,26511,26531],{},[1147,26512,26513,26519,26521,26523,26525],{},[1150,26514,26515,26517],{},[1153,26516,1563],{},[1565,26518,1794],{},[1242,26520,1958],{},[1153,26522,6893],{},[1242,26524,1689],{},[1150,26526,26527,26529],{},[1153,26528,6893],{},[1565,26530,1567],{},[1159,26532,26533],{"encoding":1161},"H_1: \\mu > \\mu_0",[1215,26535,26536],{},"jednostranná",[1200,26538,26539,26542,26574],{},[1215,26540,26541],{},"menší",[1215,26543,26544],{},[1115,26545,26547],{"className":26546},[1138],[1140,26548,26549],{"xmlns":1142},[1144,26550,26551,26571],{},[1147,26552,26553,26559,26561,26563,26565],{},[1150,26554,26555,26557],{},[1153,26556,1563],{},[1565,26558,1794],{},[1242,26560,1958],{},[1153,26562,6893],{},[1242,26564,4332],{},[1150,26566,26567,26569],{},[1153,26568,6893],{},[1565,26570,1567],{},[1159,26572,26573],{"encoding":1161},"H_1: \\mu \u003C \\mu_0",[1215,26575,26536],{},[16749,26577,26579],{"id":26578},"chyba-i-a-ii-druhu","Chyba I. a II. druhu",[1110,26581,26582],{},"Protože je úsudek odvozen z náhodného výběru, může vést ke dvěma typům chybného rozhodnutí:",[1436,26584,26585,26622],{},[1439,26586,26587,26590,26591,26608,26609,1669],{},[1540,26588,26589],{},"Chyba I. druhu"," — zamítnutí ",[1115,26592,26594],{"className":26593},[1138],[1140,26595,26596],{"xmlns":1142},[1144,26597,26598,26606],{},[1147,26599,26600],{},[1150,26601,26602,26604],{},[1153,26603,1563],{},[1565,26605,1567],{},[1159,26607,1570],{"encoding":1161},", ačkoliv ve skutečnosti platí. Pravděpodobnost ",[1115,26610,26612],{"className":26611},[1138],[1140,26613,26614],{"xmlns":1142},[1144,26615,26616,26620],{},[1147,26617,26618],{},[1153,26619,3365],{},[1159,26621,3428],{"encoding":1161},[1439,26623,26624,26627,26628,26645,26646,26663,26664,1669],{},[1540,26625,26626],{},"Chyba II. druhu"," — přijetí ",[1115,26629,26631],{"className":26630},[1138],[1140,26632,26633],{"xmlns":1142},[1144,26634,26635,26643],{},[1147,26636,26637],{},[1150,26638,26639,26641],{},[1153,26640,1563],{},[1565,26642,1567],{},[1159,26644,1570],{"encoding":1161},", ačkoliv platí ",[1115,26647,26649],{"className":26648},[1138],[1140,26650,26651],{"xmlns":1142},[1144,26652,26653,26661],{},[1147,26654,26655],{},[1150,26656,26657,26659],{},[1153,26658,1563],{},[1565,26660,1794],{},[1159,26662,2996],{"encoding":1161},". Pravděpodobnost ",[1115,26665,26667],{"className":26666},[1138],[1140,26668,26669],{"xmlns":1142},[1144,26670,26671,26675],{},[1147,26672,26673],{},[1153,26674,16340],{},[1159,26676,26176],{"encoding":1161},[1194,26678,26679,26742],{},[1197,26680,26681],{},[1200,26682,26683,26703,26722],{},[1203,26684,26685,26686],{},"Úsudek o ",[1115,26687,26689],{"className":26688},[1138],[1140,26690,26691],{"xmlns":1142},[1144,26692,26693,26701],{},[1147,26694,26695],{},[1150,26696,26697,26699],{},[1153,26698,1563],{},[1565,26700,1567],{},[1159,26702,1570],{"encoding":1161},[1203,26704,26705,8354],{},[1115,26706,26708],{"className":26707},[1138],[1140,26709,26710],{"xmlns":1142},[1144,26711,26712,26720],{},[1147,26713,26714],{},[1150,26715,26716,26718],{},[1153,26717,1563],{},[1565,26719,1567],{},[1159,26721,1570],{"encoding":1161},[1203,26723,26724,26741],{},[1115,26725,26727],{"className":26726},[1138],[1140,26728,26729],{"xmlns":1142},[1144,26730,26731,26739],{},[1147,26732,26733],{},[1150,26734,26735,26737],{},[1153,26736,1563],{},[1565,26738,1567],{},[1159,26740,1570],{"encoding":1161}," neplatí",[1210,26743,26744,26786],{},[1200,26745,26746,26749,26770],{},[1215,26747,26748],{},"Nezamítá se",[1215,26750,26751,26752],{},"správné rozhodnutí, ",[1115,26753,26755],{"className":26754},[1138],[1140,26756,26757],{"xmlns":1142},[1144,26758,26759,26767],{},[1147,26760,26761,26763,26765],{},[1565,26762,1794],{},[1242,26764,3064],{},[1153,26766,3365],{},[1159,26768,26769],{"encoding":1161},"1-\\alpha",[1215,26771,26772,26773],{},"chyba II. druhu, ",[1115,26774,26776],{"className":26775},[1138],[1140,26777,26778],{"xmlns":1142},[1144,26779,26780,26784],{},[1147,26781,26782],{},[1153,26783,16340],{},[1159,26785,26176],{"encoding":1161},[1200,26787,26788,26791,26807],{},[1215,26789,26790],{},"Zamítá se",[1215,26792,26793,26794],{},"chyba I. druhu, ",[1115,26795,26797],{"className":26796},[1138],[1140,26798,26799],{"xmlns":1142},[1144,26800,26801,26805],{},[1147,26802,26803],{},[1153,26804,3365],{},[1159,26806,3428],{"encoding":1161},[1215,26808,26751,26809],{},[1115,26810,26812],{"className":26811},[1138],[1140,26813,26814],{"xmlns":1142},[1144,26815,26816,26824],{},[1147,26817,26818,26820,26822],{},[1565,26819,1794],{},[1242,26821,3064],{},[1153,26823,16340],{},[1159,26825,26826],{"encoding":1161},"1-\\beta",[1110,26828,26829,1654,26832,26845],{},[1540,26830,26831],{},"Hladina významnosti",[1115,26833,26835],{"className":26834},[1138],[1140,26836,26837],{"xmlns":1142},[1144,26838,26839,26843],{},[1147,26840,26841],{},[1153,26842,3365],{},[1159,26844,3428],{"encoding":1161}," 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.",[1110,26847,26848],{},[4383,26849],{"alt":26850,"className":26851,"src":26852},"mask-th-chyba-i-ii",[1130,4387],"\u002Fwiki-assets\u002Fmask-th-chyba-i-ii.png",[1110,26854,26855,26856,26869,26870,26883,26884,26897,26898,1890,26911,26924,26925,1669],{},"Obrázek ukazuje, proč jde o kompromis: posunutí kritické hodnoty ",[1115,26857,26859],{"className":26858},[1138],[1140,26860,26861],{"xmlns":1142},[1144,26862,26863,26867],{},[1147,26864,26865],{},[1153,26866,1343],{},[1159,26868,1343],{"encoding":1161}," doleva zmenší ",[1115,26871,26873],{"className":26872},[1138],[1140,26874,26875],{"xmlns":1142},[1144,26876,26877,26881],{},[1147,26878,26879],{},[1153,26880,16340],{},[1159,26882,26176],{"encoding":1161},", ale zvětší ",[1115,26885,26887],{"className":26886},[1138],[1140,26888,26889],{"xmlns":1142},[1144,26890,26891,26895],{},[1147,26892,26893],{},[1153,26894,3365],{},[1159,26896,3428],{"encoding":1161},", a naopak. Pro danou hladinu ",[1115,26899,26901],{"className":26900},[1138],[1140,26902,26903],{"xmlns":1142},[1144,26904,26905,26909],{},[1147,26906,26907],{},[1153,26908,3365],{},[1159,26910,3428],{"encoding":1161},[1115,26912,26914],{"className":26913},[1138],[1140,26915,26916],{"xmlns":1142},[1144,26917,26918,26922],{},[1147,26919,26920],{},[1153,26921,1343],{},[1159,26923,1343],{"encoding":1161}," jednoznačně určena rozdělením kritéria za platnosti ",[1115,26926,26928],{"className":26927},[1138],[1140,26929,26930],{"xmlns":1142},[1144,26931,26932,26940],{},[1147,26933,26934],{},[1150,26935,26936,26938],{},[1153,26937,1563],{},[1565,26939,1567],{},[1159,26941,1570],{"encoding":1161},[16749,26943,26945],{"id":26944},"testové-kritérium-a-kritický-obor","Testové kritérium a kritický obor",[1110,26947,26948,1654,26950,26963,26964,1669],{},[1540,26949,3000],{},[1115,26951,26953],{"className":26952},[1138],[1140,26954,26955],{"xmlns":1142},[1144,26956,26957,26961],{},[1147,26958,26959],{},[1153,26960,7104],{},[1159,26962,7104],{"encoding":1161}," je statistika spočtená z výběru; aby bylo možné test provést, musí být známo jeho rozdělení za platnosti ",[1115,26965,26967],{"className":26966},[1138],[1140,26968,26969],{"xmlns":1142},[1144,26970,26971,26979],{},[1147,26972,26973],{},[1150,26974,26975,26977],{},[1153,26976,1563],{},[1565,26978,1567],{},[1159,26980,1570],{"encoding":1161},[1110,26982,26983,1654,26986,26999,27000,27017],{},[1540,26984,26985],{},"Kritický obor",[1115,26987,26989],{"className":26988},[1138],[1140,26990,26991],{"xmlns":1142},[1144,26992,26993,26997],{},[1147,26994,26995],{},[1153,26996,1605],{},[1159,26998,1605],{"encoding":1161}," je množina hodnot svědčících pro ",[1115,27001,27003],{"className":27002},[1138],[1140,27004,27005],{"xmlns":1142},[1144,27006,27007,27015],{},[1147,27008,27009],{},[1150,27010,27011,27013],{},[1153,27012,1563],{},[1565,27014,1794],{},[1159,27016,2996],{"encoding":1161},". Je zkonstruován tak, aby",[1115,27019,27021],{"className":27020},[1138],[1140,27022,27023],{"xmlns":1142,"display":1964},[1144,27024,27025,27053],{},[1147,27026,27027,27029,27031,27033,27035,27037,27039,27045,27047,27049,27051],{},[1153,27028,6729],{},[1242,27030,1875],{"stretchy":1874},[1153,27032,7104],{},[1242,27034,7021],{},[1153,27036,1605],{},[1242,27038,23022],{},[1150,27040,27041,27043],{},[1153,27042,1563],{},[1565,27044,1567],{},[1242,27046,1886],{"stretchy":1874},[1242,27048,1982],{},[1153,27050,3365],{},[1242,27052,1797],{"separator":1121},[1159,27054,27055],{"encoding":1161},"P(T \\in W \\mid H_0) = \\alpha,",[1110,27057,27058,27059,27072,27073,27090],{},"tedy aby pravděpodobnost, že výběr dá hodnotu kritéria v ",[1115,27060,27062],{"className":27061},[1138],[1140,27063,27064],{"xmlns":1142},[1144,27065,27066,27070],{},[1147,27067,27068],{},[1153,27069,1605],{},[1159,27071,1605],{"encoding":1161}," i při platné ",[1115,27074,27076],{"className":27075},[1138],[1140,27077,27078],{"xmlns":1142},[1144,27079,27080,27088],{},[1147,27081,27082],{},[1150,27083,27084,27086],{},[1153,27085,1563],{},[1565,27087,1567],{},[1159,27089,1570],{"encoding":1161},", byla rovna zvolené hladině významnosti.",[16749,27092,27094],{"id":27093},"postup-testování-hypotézy","Postup testování hypotézy",[1110,27096,27097],{},[4383,27098],{"alt":27099,"className":27100,"src":27101},"mask-ilu-postup-testovani",[1130,4387],"\u002Fwiki-assets\u002Fmask-ilu-postup-testovani.png",[2865,27103,27104,27141,27144,27160],{},[1439,27105,27106,27107,1163,27124,1669],{},"Formulace hypotéz ",[1115,27108,27110],{"className":27109},[1138],[1140,27111,27112],{"xmlns":1142},[1144,27113,27114,27122],{},[1147,27115,27116],{},[1150,27117,27118,27120],{},[1153,27119,1563],{},[1565,27121,1567],{},[1159,27123,1570],{"encoding":1161},[1115,27125,27127],{"className":27126},[1138],[1140,27128,27129],{"xmlns":1142},[1144,27130,27131,27139],{},[1147,27132,27133],{},[1150,27134,27135,27137],{},[1153,27136,1563],{},[1565,27138,1794],{},[1159,27140,2996],{"encoding":1161},[1439,27142,27143],{},"Volba testového kritéria a výpočet jeho hodnoty.",[1439,27145,27146,27147,1669],{},"Volba hladiny významnosti a sestrojení příslušného kritického oboru ",[1115,27148,27150],{"className":27149},[1138],[1140,27151,27152],{"xmlns":1142},[1144,27153,27154,27158],{},[1147,27155,27156],{},[1153,27157,1605],{},[1159,27159,1605],{"encoding":1161},[1439,27161,27162,27163],{},"Formulace závěru:\n",[1436,27164,27165,27243],{},[1439,27166,27167,27168,3988,27186,27203,27204,27224,27225,27242],{},"pokud ",[1115,27169,27171],{"className":27170},[1138],[1140,27172,27173],{"xmlns":1142},[1144,27174,27175,27183],{},[1147,27176,27177,27179,27181],{},[1153,27178,7104],{},[1242,27180,7021],{},[1153,27182,1605],{},[1159,27184,27185],{"encoding":1161},"T \\in W",[1115,27187,27189],{"className":27188},[1138],[1140,27190,27191],{"xmlns":1142},[1144,27192,27193,27201],{},[1147,27194,27195],{},[1150,27196,27197,27199],{},[1153,27198,1563],{},[1565,27200,1794],{},[1159,27202,2996],{"encoding":1161}," je testem prokázána na hladině významnosti ",[1115,27205,27207],{"className":27206},[1138],[1140,27208,27209],{"xmlns":1142},[1144,27210,27211,27221],{},[1147,27212,27213,27215,27217,27219],{},[1565,27214,11820],{},[1153,27216,3365],{},[2909,27218,2911],{},[1153,27220,11827],{"mathvariant":2121},[1159,27222,27223],{"encoding":1161},"100\\alpha\\,\\%"," (zamítáme ",[1115,27226,27228],{"className":27227},[1138],[1140,27229,27230],{"xmlns":1142},[1144,27231,27232,27240],{},[1147,27233,27234],{},[1150,27235,27236,27238],{},[1153,27237,1563],{},[1565,27239,1567],{},[1159,27241,1570],{"encoding":1161},");",[1439,27244,27167,27245,3988,27264,27281,27282,27301,27302,27319],{},[1115,27246,27248],{"className":27247},[1138],[1140,27249,27250],{"xmlns":1142},[1144,27251,27252,27261],{},[1147,27253,27254,27256,27259],{},[1153,27255,7104],{},[1242,27257,27258],{"mathvariant":2121},"∉",[1153,27260,1605],{},[1159,27262,27263],{"encoding":1161},"T \\notin W",[1115,27265,27267],{"className":27266},[1138],[1140,27268,27269],{"xmlns":1142},[1144,27270,27271,27279],{},[1147,27272,27273],{},[1150,27274,27275,27277],{},[1153,27276,1563],{},[1565,27278,1794],{},[1159,27280,2996],{"encoding":1161}," není testem prokázána na hladině významnosti ",[1115,27283,27285],{"className":27284},[1138],[1140,27286,27287],{"xmlns":1142},[1144,27288,27289,27299],{},[1147,27290,27291,27293,27295,27297],{},[1565,27292,11820],{},[1153,27294,3365],{},[2909,27296,2911],{},[1153,27298,11827],{"mathvariant":2121},[1159,27300,27223],{"encoding":1161}," ; ",[1115,27303,27305],{"className":27304},[1138],[1140,27306,27307],{"xmlns":1142},[1144,27308,27309,27317],{},[1147,27310,27311],{},[1150,27312,27313,27315],{},[1153,27314,1563],{},[1565,27316,1567],{},[1159,27318,1570],{"encoding":1161}," nezamítáme.",[1110,27321,27322,27323,27326,27327,27344,27345,27362,27363,27383,27384,25182,27401,1654,27421,27438],{},"Rovnocennou alternativou je ",[1540,27324,27325],{},"p-hodnota",": udává, nakolik jsou data slučitelná s ",[1115,27328,27330],{"className":27329},[1138],[1140,27331,27332],{"xmlns":1142},[1144,27333,27334,27342],{},[1147,27335,27336],{},[1150,27337,27338,27340],{},[1153,27339,1563],{},[1565,27341,1567],{},[1159,27343,1570],{"encoding":1161},". Čím menší p-hodnota, tím více data svědčí proti ",[1115,27346,27348],{"className":27347},[1138],[1140,27349,27350],{"xmlns":1142},[1144,27351,27352,27360],{},[1147,27353,27354],{},[1150,27355,27356,27358],{},[1153,27357,1563],{},[1565,27359,1567],{},[1159,27361,1570],{"encoding":1161},". Rozhodovací pravidlo: ",[1115,27364,27366],{"className":27365},[1138],[1140,27367,27368],{"xmlns":1142},[1144,27369,27370,27380],{},[1147,27371,27372,27374,27376,27378],{},[1153,27373,1110],{},[1242,27375,6737],{},[1153,27377,3365],{},[1242,27379,7551],{},[1159,27381,27382],{"encoding":1161},"p \\le \\alpha \\Rightarrow"," zamítáme ",[1115,27385,27387],{"className":27386},[1138],[1140,27388,27389],{"xmlns":1142},[1144,27390,27391,27399],{},[1147,27392,27393],{},[1150,27394,27395,27397],{},[1153,27396,1563],{},[1565,27398,1567],{},[1159,27400,1570],{"encoding":1161},[1115,27402,27404],{"className":27403},[1138],[1140,27405,27406],{"xmlns":1142},[1144,27407,27408,27418],{},[1147,27409,27410,27412,27414,27416],{},[1153,27411,1110],{},[1242,27413,1689],{},[1153,27415,3365],{},[1242,27417,7551],{},[1159,27419,27420],{"encoding":1161},"p > \\alpha \\Rightarrow",[1115,27422,27424],{"className":27423},[1138],[1140,27425,27426],{"xmlns":1142},[1144,27427,27428,27436],{},[1147,27429,27430],{},[1150,27431,27432,27434],{},[1153,27433,1563],{},[1565,27435,1567],{},[1159,27437,1570],{"encoding":1161}," nezamítáme. Obě cesty — kritický obor i p-hodnota — vedou vždy ke stejnému závěru; R u všech testů vrací p-hodnotu přímo.",[1189,27440,27442],{"id":27441},"jednovýběrový-t-test","Jednovýběrový t-test",[1110,27444,27445,27446,27459,27460,27492,27493,27506,27507,1163,27524,27541,27542,27560,27561,27574],{},"Test o střední hodnotě ",[1115,27447,27449],{"className":27448},[1138],[1140,27450,27451],{"xmlns":1142},[1144,27452,27453,27457],{},[1147,27454,27455],{},[1153,27456,6893],{},[1159,27458,8799],{"encoding":1161}," rozdělení ",[1115,27461,27463],{"className":27462},[1138],[1140,27464,27465],{"xmlns":1142},[1144,27466,27467,27489],{},[1147,27468,27469,27471,27473,27475,27477,27479,27481,27487],{},[1153,27470,6734],{},[1242,27472,9186],{},[1153,27474,6888],{},[1242,27476,1875],{"stretchy":1874},[1153,27478,6893],{},[1242,27480,1797],{"separator":1121},[1582,27482,27483,27485],{},[1153,27484,6901],{},[1565,27486,1589],{},[1242,27488,1886],{"stretchy":1874},[1159,27490,27491],{"encoding":1161},"X \\sim N(\\mu, \\sigma^2)",". Z výběru o rozsahu ",[1115,27494,27496],{"className":27495},[1138],[1140,27497,27498],{"xmlns":1142},[1144,27499,27500,27504],{},[1147,27501,27502],{},[1153,27503,1372],{},[1159,27505,1372],{"encoding":1161}," se určí charakteristiky ",[1115,27508,27510],{"className":27509},[1138],[1140,27511,27512],{"xmlns":1142},[1144,27513,27514,27522],{},[1147,27515,27516],{},[1236,27517,27518,27520],{"accent":1121},[1153,27519,1240],{},[1242,27521,1244],{},[1159,27523,21563],{"encoding":1161},[1115,27525,27527],{"className":27526},[1138],[1140,27528,27529],{"xmlns":1142},[1144,27530,27531,27539],{},[1147,27532,27533],{},[1582,27534,27535,27537],{},[1153,27536,1291],{},[1565,27538,1589],{},[1159,27540,15779],{"encoding":1161},"; testem se posuzuje vztah mezi zvoleným číslem ",[1115,27543,27545],{"className":27544},[1138],[1140,27546,27547],{"xmlns":1142},[1144,27548,27549,27557],{},[1147,27550,27551],{},[1150,27552,27553,27555],{},[1153,27554,6893],{},[1565,27556,1567],{},[1159,27558,27559],{"encoding":1161},"\\mu_0"," a neznámou hodnotou ",[1115,27562,27564],{"className":27563},[1138],[1140,27565,27566],{"xmlns":1142},[1144,27567,27568,27572],{},[1147,27569,27570],{},[1153,27571,6893],{},[1159,27573,8799],{"encoding":1161},". Testové kritérium",[1115,27576,27578],{"className":27577},[1138],[1140,27579,27580],{"xmlns":1142,"display":1964},[1144,27581,27582,27626],{},[1147,27583,27584,27586,27588,27608,27612,27614],{},[1153,27585,7104],{},[1242,27587,1982],{},[2739,27589,27590,27606],{},[1147,27591,27592,27598,27600],{},[1236,27593,27594,27596],{"accent":1121},[1153,27595,1240],{},[1242,27597,1244],{},[1242,27599,3064],{},[1150,27601,27602,27604],{},[1153,27603,6893],{},[1565,27605,1567],{},[1153,27607,1291],{},[4453,27609,27610],{},[1153,27611,1372],{},[1242,27613,9186],{},[1150,27615,27616,27618],{},[1153,27617,7146],{},[1147,27619,27620,27622,27624],{},[1153,27621,1372],{},[1242,27623,3064],{},[1565,27625,1794],{},[1159,27627,27628],{"encoding":1161},"T = \\frac{\\bar{x} - \\mu_0}{s}\\sqrt{n} \\sim t_{n-1}",[1110,27630,27631,27632,27650],{},"má Studentovo rozdělení o ",[1115,27633,27635],{"className":27634},[1138],[1140,27636,27637],{"xmlns":1142},[1144,27638,27639,27647],{},[1147,27640,27641,27643,27645],{},[1153,27642,1372],{},[1242,27644,3064],{},[1565,27646,1794],{},[1159,27648,27649],{"encoding":1161},"n-1"," stupních volnosti.",[1194,27652,27653,27711],{},[1197,27654,27655],{},[1200,27656,27657,27676,27695],{},[1203,27658,27659],{},[1115,27660,27662],{"className":27661},[1138],[1140,27663,27664],{"xmlns":1142},[1144,27665,27666,27674],{},[1147,27667,27668],{},[1150,27669,27670,27672],{},[1153,27671,1563],{},[1565,27673,1567],{},[1159,27675,1570],{"encoding":1161},[1203,27677,27678],{},[1115,27679,27681],{"className":27680},[1138],[1140,27682,27683],{"xmlns":1142},[1144,27684,27685,27693],{},[1147,27686,27687],{},[1150,27688,27689,27691],{},[1153,27690,1563],{},[1565,27692,1794],{},[1159,27694,2996],{"encoding":1161},[1203,27696,27697,27698],{},"Kritický obor ",[1115,27699,27701],{"className":27700},[1138],[1140,27702,27703],{"xmlns":1142},[1144,27704,27705,27709],{},[1147,27706,27707],{},[1153,27708,1605],{},[1159,27710,1605],{"encoding":1161},[1210,27712,27713,27803,27901],{},[1200,27714,27715,27739,27763],{},[1215,27716,27717],{},[1115,27718,27720],{"className":27719},[1138],[1140,27721,27722],{"xmlns":1142},[1144,27723,27724,27736],{},[1147,27725,27726,27728,27730],{},[1153,27727,6893],{},[1242,27729,6737],{},[1150,27731,27732,27734],{},[1153,27733,6893],{},[1565,27735,1567],{},[1159,27737,27738],{"encoding":1161},"\\mu \\le \\mu_0",[1215,27740,27741],{},[1115,27742,27744],{"className":27743},[1138],[1140,27745,27746],{"xmlns":1142},[1144,27747,27748,27760],{},[1147,27749,27750,27752,27754],{},[1153,27751,6893],{},[1242,27753,1689],{},[1150,27755,27756,27758],{},[1153,27757,6893],{},[1565,27759,1567],{},[1159,27761,27762],{"encoding":1161},"\\mu > \\mu_0",[1215,27764,27765],{},[1115,27766,27768],{"className":27767},[1138],[1140,27769,27770],{"xmlns":1142},[1144,27771,27772,27800],{},[1147,27773,27774,27776,27778,27790,27792,27794,27796,27798],{},[1153,27775,7146],{},[1242,27777,3351],{},[1150,27779,27780,27782],{},[1153,27781,7146],{},[1147,27783,27784,27786,27788],{},[1565,27785,1794],{},[1242,27787,3064],{},[1153,27789,3365],{},[1242,27791,1875],{"stretchy":1874},[1153,27793,1372],{},[1242,27795,3064],{},[1565,27797,1794],{},[1242,27799,1886],{"stretchy":1874},[1159,27801,27802],{"encoding":1161},"t \\ge t_{1-\\alpha}(n-1)",[1200,27804,27805,27829,27853],{},[1215,27806,27807],{},[1115,27808,27810],{"className":27809},[1138],[1140,27811,27812],{"xmlns":1142},[1144,27813,27814,27826],{},[1147,27815,27816,27818,27820],{},[1153,27817,6893],{},[1242,27819,1982],{},[1150,27821,27822,27824],{},[1153,27823,6893],{},[1565,27825,1567],{},[1159,27827,27828],{"encoding":1161},"\\mu = \\mu_0",[1215,27830,27831],{},[1115,27832,27834],{"className":27833},[1138],[1140,27835,27836],{"xmlns":1142},[1144,27837,27838,27850],{},[1147,27839,27840,27842,27844],{},[1153,27841,6893],{},[1242,27843,10958],{"mathvariant":2121},[1150,27845,27846,27848],{},[1153,27847,6893],{},[1565,27849,1567],{},[1159,27851,27852],{"encoding":1161},"\\mu \\neq \\mu_0",[1215,27854,27855],{},[1115,27856,27858],{"className":27857},[1138],[1140,27859,27860],{"xmlns":1142},[1144,27861,27862,27898],{},[1147,27863,27864,27866,27868,27870,27872,27888,27890,27892,27894,27896],{},[1242,27865,23022],{"stretchy":1874},[1153,27867,7146],{},[1242,27869,23022],{"stretchy":1874},[1242,27871,3351],{},[1150,27873,27874,27876],{},[1153,27875,7146],{},[1147,27877,27878,27880,27882,27884,27886],{},[1565,27879,1794],{},[1242,27881,3064],{},[1153,27883,3365],{},[1153,27885,4604],{"mathvariant":2121},[1565,27887,1589],{},[1242,27889,1875],{"stretchy":1874},[1153,27891,1372],{},[1242,27893,3064],{},[1565,27895,1794],{},[1242,27897,1886],{"stretchy":1874},[1159,27899,27900],{"encoding":1161},"\\lvert t \\rvert \\ge t_{1-\\alpha\u002F2}(n-1)",[1200,27902,27903,27927,27951],{},[1215,27904,27905],{},[1115,27906,27908],{"className":27907},[1138],[1140,27909,27910],{"xmlns":1142},[1144,27911,27912,27924],{},[1147,27913,27914,27916,27918],{},[1153,27915,6893],{},[1242,27917,3351],{},[1150,27919,27920,27922],{},[1153,27921,6893],{},[1565,27923,1567],{},[1159,27925,27926],{"encoding":1161},"\\mu \\ge \\mu_0",[1215,27928,27929],{},[1115,27930,27932],{"className":27931},[1138],[1140,27933,27934],{"xmlns":1142},[1144,27935,27936,27948],{},[1147,27937,27938,27940,27942],{},[1153,27939,6893],{},[1242,27941,4332],{},[1150,27943,27944,27946],{},[1153,27945,6893],{},[1565,27947,1567],{},[1159,27949,27950],{"encoding":1161},"\\mu \u003C \\mu_0",[1215,27952,27953],{},[1115,27954,27956],{"className":27955},[1138],[1140,27957,27958],{"xmlns":1142},[1144,27959,27960,27990],{},[1147,27961,27962,27964,27966,27968,27980,27982,27984,27986,27988],{},[1153,27963,7146],{},[1242,27965,6737],{},[1242,27967,3064],{},[1150,27969,27970,27972],{},[1153,27971,7146],{},[1147,27973,27974,27976,27978],{},[1565,27975,1794],{},[1242,27977,3064],{},[1153,27979,3365],{},[1242,27981,1875],{"stretchy":1874},[1153,27983,1372],{},[1242,27985,3064],{},[1565,27987,1794],{},[1242,27989,1886],{"stretchy":1874},[1159,27991,27992],{"encoding":1161},"t \\le -t_{1-\\alpha}(n-1)",[1110,27994,27995,27996,27999],{},"V R test provádí ",[3470,27997,27998],{},"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?",[3694,28001,28003],{"className":3696,"code":28002,"language":71,"meta":1490,"style":1490},"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",[3470,28004,28005,28059],{"__ignoreMap":1490},[1115,28006,28007,28009,28011,28013,28015,28018,28020,28023,28025,28028,28030,28033,28035,28038,28040,28043,28045,28047,28049,28052,28054,28057],{"class":3702,"line":10},[1115,28008,1240],{"class":3705},[1115,28010,3710],{"class":3709},[1115,28012,3835],{"class":3713},[1115,28014,1875],{"class":3717},[1115,28016,28017],{"class":3724},"12.5",[1115,28019,1797],{"class":3709},[1115,28021,28022],{"class":3724}," 13.5",[1115,28024,1797],{"class":3709},[1115,28026,28027],{"class":3724}," 11.9",[1115,28029,1797],{"class":3709},[1115,28031,28032],{"class":3724}," 12.2",[1115,28034,1797],{"class":3709},[1115,28036,28037],{"class":3724}," 13.0",[1115,28039,1797],{"class":3709},[1115,28041,28042],{"class":3724}," 14.3",[1115,28044,1797],{"class":3709},[1115,28046,28032],{"class":3724},[1115,28048,1797],{"class":3709},[1115,28050,28051],{"class":3724}," 11.8",[1115,28053,1797],{"class":3709},[1115,28055,28056],{"class":3724}," 14.0",[1115,28058,3901],{"class":3717},[1115,28060,28061,28064,28066,28068,28070,28072,28074,28076,28078,28081,28083,28086],{"class":3702,"line":27},[1115,28062,28063],{"class":3713},"t.test",[1115,28065,1875],{"class":3717},[1115,28067,1240],{"class":3705},[1115,28069,1797],{"class":3709},[1115,28071,25579],{"class":3705},[1115,28073,3797],{"class":3709},[1115,28075,3734],{"class":3724},[1115,28077,1797],{"class":3709},[1115,28079,28080],{"class":3705}," alternative",[1115,28082,3797],{"class":3709},[1115,28084,28085],{"class":3840}," \"two.sided\"",[1115,28087,3901],{"class":3717},[3694,28089,28092],{"className":28090,"code":28091,"language":3923,"meta":1490},[3921],"    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",[3470,28093,28091],{"__ignoreMap":1490},[1110,28095,28096,28098,28099,28102,28103,28106,28107,28110,28111,28134],{},[3470,28097,7146],{}," je testové kritérium, ",[3470,28100,28101],{},"df"," stupně volnosti, ",[3470,28104,28105],{},"p-value"," p-hodnota pro zvolenou alternativu a ",[3470,28108,28109],{},"mean of x"," výběrový průměr. Zde ",[1115,28112,28114],{"className":28113},[1138],[1140,28115,28116],{"xmlns":1142},[1144,28117,28118,28131],{},[1147,28119,28120,28122,28124,28127,28129],{},[1153,28121,1110],{},[1242,28123,1982],{},[1565,28125,28126],{},"0,02843",[1242,28128,4332],{},[1565,28130,3984],{},[1159,28132,28133],{"encoding":1161},"p = 0{,}02843 \u003C 0{,}05",": úprava trasy průměrnou dobu jízdy (původně 12 minut) statisticky významně změnila.",[1103,28136,28138,28145,28233,28289,28381],{"className":28137,"dataCallout":3477},[1106,3476],[1110,28139,28141,28144],{"className":28140},[1113],[1115,28142],{"className":28143,"ariaHidden":1121},[1118,3484,1120],"Příklad: Kontrola objemu lahví",[1110,28146,28147,28148,28170,28171,28189,28190,28213,28214,28232],{},"Pivovar plní lahve, deklarovaný objem je ",[1115,28149,28151],{"className":28150},[1138],[1140,28152,28153],{"xmlns":1142},[1144,28154,28155,28167],{},[1147,28156,28157,28163,28165],{},[1150,28158,28159,28161],{},[1153,28160,6893],{},[1565,28162,1567],{},[1242,28164,1982],{},[1565,28166,8460],{},[1159,28168,28169],{"encoding":1161},"\\mu_0 = 0{,}5"," l. Náhodný výběr ",[1115,28172,28174],{"className":28173},[1138],[1140,28175,28176],{"xmlns":1142},[1144,28177,28178,28186],{},[1147,28179,28180,28182,28184],{},[1153,28181,1372],{},[1242,28183,1982],{},[1565,28185,4045],{},[1159,28187,28188],{"encoding":1161},"n = 20"," lahví dal ",[1115,28191,28193],{"className":28192},[1138],[1140,28194,28195],{"xmlns":1142},[1144,28196,28197,28210],{},[1147,28198,28199,28205,28207],{},[1236,28200,28201,28203],{"accent":1121},[1153,28202,1240],{},[1242,28204,1244],{},[1242,28206,1982],{},[1565,28208,28209],{},"0,492",[1159,28211,28212],{"encoding":1161},"\\bar{x} = 0{,}492"," l, ",[1115,28215,28217],{"className":28216},[1138],[1140,28218,28219],{"xmlns":1142},[1144,28220,28221,28229],{},[1147,28222,28223,28225,28227],{},[1153,28224,1291],{},[1242,28226,1982],{},[1565,28228,14797],{},[1159,28230,28231],{"encoding":1161},"s = 0{,}015"," l. Na hladině významnosti 5 % ověřte podezření, že pivovar lahve nedoplňuje.",[1110,28234,28235,28261,28262,28288],{},[1115,28236,28238],{"className":28237},[1138],[1140,28239,28240],{"xmlns":1142},[1144,28241,28242,28258],{},[1147,28243,28244,28250,28252,28254,28256],{},[1150,28245,28246,28248],{},[1153,28247,1563],{},[1565,28249,1567],{},[1242,28251,1958],{},[1153,28253,6893],{},[1242,28255,3351],{},[1565,28257,8460],{},[1159,28259,28260],{"encoding":1161},"H_0: \\mu \\ge 0{,}5"," l (objem je v pořádku nebo větší), ",[1115,28263,28265],{"className":28264},[1138],[1140,28266,28267],{"xmlns":1142},[1144,28268,28269,28285],{},[1147,28270,28271,28277,28279,28281,28283],{},[1150,28272,28273,28275],{},[1153,28274,1563],{},[1565,28276,1794],{},[1242,28278,1958],{},[1153,28280,6893],{},[1242,28282,4332],{},[1565,28284,8460],{},[1159,28286,28287],{"encoding":1161},"H_1: \\mu \u003C 0{,}5"," l (lahve jsou nedoplněné).",[1110,28290,28291],{},[1115,28292,28294],{"className":28293},[1138],[1140,28295,28296],{"xmlns":1142},[1144,28297,28298,28378],{},[1147,28299,28300,28302,28304,28316,28320,28322,28324,28327,28329,28331,28333,28335,28337,28339,28341,28343,28355,28357,28359,28361,28363,28365,28367,28369,28371,28373,28376],{},[1153,28301,7146],{},[1242,28303,1982],{},[2739,28305,28306,28314],{},[1147,28307,28308,28310,28312],{},[1565,28309,28209],{},[1242,28311,3064],{},[1565,28313,8460],{},[1565,28315,14797],{},[4453,28317,28318],{},[1565,28319,4045],{},[1242,28321,1982],{},[1242,28323,3064],{},[1565,28325,28326],{},"2,385",[1242,28328,1797],{"separator":1121},[2012,28330],{"width":2014},[1153,28332,1605],{},[1242,28334,1982],{},[1242,28336,3334],{"stretchy":1874},[1153,28338,7146],{},[1242,28340,6737],{},[1242,28342,3064],{},[1150,28344,28345,28347],{},[1153,28346,7146],{},[1147,28348,28349,28351,28353],{},[1565,28350,1567],{},[1242,28352,1797],{"separator":1121},[1565,28354,21796],{},[1242,28356,1875],{"stretchy":1874},[1565,28358,14721],{},[1242,28360,1886],{"stretchy":1874},[1242,28362,3394],{"stretchy":1874},[1242,28364,1982],{},[1242,28366,3334],{"stretchy":1874},[1153,28368,7146],{},[1242,28370,6737],{},[1242,28372,3064],{},[1565,28374,28375],{},"1,729",[1242,28377,3394],{"stretchy":1874},[1159,28379,28380],{"encoding":1161},"t = \\frac{0{,}492 - 0{,}5}{0{,}015}\\sqrt{20} = -2{,}385, \\qquad W = \\{t \\le -t_{0,95}(19)\\} = \\{t \\le -1{,}729\\}",[1110,28382,28383,28384,6006,28402,28419],{},"Protože ",[1115,28385,28387],{"className":28386},[1138],[1140,28388,28389],{"xmlns":1142},[1144,28390,28391,28399],{},[1147,28392,28393,28395,28397],{},[1153,28394,7146],{},[1242,28396,7021],{},[1153,28398,1605],{},[1159,28400,28401],{"encoding":1161},"t \\in W",[1115,28403,28405],{"className":28404},[1138],[1140,28406,28407],{"xmlns":1142},[1144,28408,28409,28417],{},[1147,28410,28411],{},[1150,28412,28413,28415],{},[1153,28414,1563],{},[1565,28416,1567],{},[1159,28418,1570],{"encoding":1161},": na hladině významnosti 5 % se potvrdilo, že pivovar plní lahve pod deklarovaný objem.",[1110,28421,28422,28423,28425,28426,1958],{},"Ze souhrnných charakteristik bez surových dat ",[3470,28424,27998],{}," spustit nelze — kritérium a kritická hodnota se dopočítají přímo z definice pomocí ",[3470,28427,28428],{},"qt()",[3694,28430,28432],{"className":3696,"code":28431,"language":71,"meta":1490,"style":1490},"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",[3470,28433,28434,28472,28504,28534,28539],{"__ignoreMap":1490},[1115,28435,28436,28439,28441,28444,28446,28448,28450,28453,28455,28457,28459,28462,28464,28467,28469],{"class":3702,"line":10},[1115,28437,28438],{"class":3705},"xbar",[1115,28440,3710],{"class":3709},[1115,28442,28443],{"class":3724}," 0.492",[1115,28445,25182],{"class":3717},[1115,28447,1291],{"class":3705},[1115,28449,3710],{"class":3709},[1115,28451,28452],{"class":3724}," 0.015",[1115,28454,25182],{"class":3717},[1115,28456,1372],{"class":3705},[1115,28458,3710],{"class":3709},[1115,28460,28461],{"class":3724}," 20",[1115,28463,25182],{"class":3717},[1115,28465,28466],{"class":3705},"mu0",[1115,28468,3710],{"class":3709},[1115,28470,28471],{"class":3724}," 0.5\n",[1115,28473,28474,28476,28478,28480,28482,28484,28487,28489,28491,28494,28496,28498,28500,28502],{"class":3702,"line":27},[1115,28475,7146],{"class":3705},[1115,28477,3710],{"class":3709},[1115,28479,4607],{"class":3717},[1115,28481,28438],{"class":3705},[1115,28483,25519],{"class":3709},[1115,28485,28486],{"class":3705}," mu0",[1115,28488,4601],{"class":3717},[1115,28490,4604],{"class":3709},[1115,28492,28493],{"class":3705}," s",[1115,28495,18642],{"class":3709},[1115,28497,4578],{"class":3713},[1115,28499,1875],{"class":3717},[1115,28501,1372],{"class":3705},[1115,28503,3901],{"class":3717},[1115,28505,28506,28509,28511,28514,28516,28519,28521,28523,28525,28528,28530,28532],{"class":3702,"line":148},[1115,28507,28508],{"class":3705},"t_krit",[1115,28510,3710],{"class":3709},[1115,28512,28513],{"class":3713}," qt",[1115,28515,1875],{"class":3717},[1115,28517,28518],{"class":3724},"0.05",[1115,28520,1797],{"class":3709},[1115,28522,10811],{"class":3705},[1115,28524,3797],{"class":3709},[1115,28526,28527],{"class":3705}," n",[1115,28529,25519],{"class":3709},[1115,28531,4641],{"class":3724},[1115,28533,3901],{"class":3717},[1115,28535,28536],{"class":3702,"line":111},[1115,28537,28538],{"class":3705},"t\n",[1115,28540,28541],{"class":3702,"line":96},[1115,28542,28543],{"class":3705},"t_krit\n",[3694,28545,28548],{"className":28546,"code":28547,"language":3923,"meta":1490},[3921],"[1] -2.385139\n[1] -1.729133\n",[3470,28549,28547],{"__ignoreMap":1490},[1110,28551,28552],{},[4383,28553],{"alt":28554,"className":28555,"src":28556},"mask-th-t-jednostranny",[1130,4387],"\u002Fwiki-assets\u002Fmask-th-t-jednostranny.png",[1110,28558,28559,28560,1958],{},"Další dva příklady mají k dispozici surová data, takže je lze otestovat přímo ",[3470,28561,27998],{},[1110,28563,28564,28567],{},[1540,28565,28566],{},"Životnost baterií."," Výrobce udává průměrnou životnost 10 hodin, na 11 bateriích byly naměřeny hodnoty v hodinách.",[3694,28569,28571],{"className":3696,"code":28570,"language":71,"meta":1490,"style":1490},"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",[3470,28572,28573,28636],{"__ignoreMap":1490},[1115,28574,28575,28578,28580,28582,28584,28587,28589,28592,28594,28597,28599,28602,28604,28607,28609,28612,28614,28616,28618,28621,28623,28625,28627,28630,28632,28634],{"class":3702,"line":10},[1115,28576,28577],{"class":3705},"x2",[1115,28579,3710],{"class":3709},[1115,28581,3835],{"class":3713},[1115,28583,1875],{"class":3717},[1115,28585,28586],{"class":3724},"9.5",[1115,28588,1797],{"class":3709},[1115,28590,28591],{"class":3724}," 10.5",[1115,28593,1797],{"class":3709},[1115,28595,28596],{"class":3724}," 8.9",[1115,28598,1797],{"class":3709},[1115,28600,28601],{"class":3724}," 9.2",[1115,28603,1797],{"class":3709},[1115,28605,28606],{"class":3724}," 10.0",[1115,28608,1797],{"class":3709},[1115,28610,28611],{"class":3724}," 8.5",[1115,28613,1797],{"class":3709},[1115,28615,28601],{"class":3724},[1115,28617,1797],{"class":3709},[1115,28619,28620],{"class":3724}," 8.8",[1115,28622,1797],{"class":3709},[1115,28624,28606],{"class":3724},[1115,28626,1797],{"class":3709},[1115,28628,28629],{"class":3724}," 9.5",[1115,28631,1797],{"class":3709},[1115,28633,28601],{"class":3724},[1115,28635,3901],{"class":3717},[1115,28637,28638,28640,28642,28644,28646,28648,28650,28652,28654,28656,28658,28660],{"class":3702,"line":27},[1115,28639,28063],{"class":3713},[1115,28641,1875],{"class":3717},[1115,28643,28577],{"class":3705},[1115,28645,1797],{"class":3709},[1115,28647,25579],{"class":3705},[1115,28649,3797],{"class":3709},[1115,28651,9480],{"class":3724},[1115,28653,1797],{"class":3709},[1115,28655,28080],{"class":3705},[1115,28657,3797],{"class":3709},[1115,28659,28085],{"class":3840},[1115,28661,3901],{"class":3717},[3694,28663,28666],{"className":28664,"code":28665,"language":3923,"meta":1490},[3921],"    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",[3470,28667,28665],{"__ignoreMap":1490},[1110,28669,28670,28693],{},[1115,28671,28673],{"className":28672},[1138],[1140,28674,28675],{"xmlns":1142},[1144,28676,28677,28690],{},[1147,28678,28679,28681,28683,28686,28688],{},[1153,28680,1110],{},[1242,28682,1982],{},[1565,28684,28685],{},"0,006548",[1242,28687,4332],{},[1565,28689,3984],{},[1159,28691,28692],{"encoding":1161},"p = 0{,}006548 \u003C 0{,}05",": skutečná životnost se od deklarovaných 10 hodin statisticky významně liší (baterie vydrží méně).",[1110,28695,28696,28699],{},[1540,28697,28698],{},"Odpad materiálu."," Na deseti obráběných kusech byl naměřen odpad materiálu v procentech; testuje se rozdíl proti 4 % a zároveň normalita dat.",[3694,28701,28703],{"className":3696,"code":28702,"language":71,"meta":1490,"style":1490},"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",[3470,28704,28705,28756,28782],{"__ignoreMap":1490},[1115,28706,28707,28710,28712,28714,28716,28718,28720,28722,28724,28726,28728,28730,28732,28734,28736,28738,28740,28742,28744,28746,28748,28750,28752,28754],{"class":3702,"line":10},[1115,28708,28709],{"class":3705},"x3",[1115,28711,3710],{"class":3709},[1115,28713,3835],{"class":3713},[1115,28715,1875],{"class":3717},[1115,28717,11988],{"class":3724},[1115,28719,1797],{"class":3709},[1115,28721,11993],{"class":3724},[1115,28723,1797],{"class":3709},[1115,28725,11998],{"class":3724},[1115,28727,1797],{"class":3709},[1115,28729,12003],{"class":3724},[1115,28731,1797],{"class":3709},[1115,28733,11998],{"class":3724},[1115,28735,1797],{"class":3709},[1115,28737,11998],{"class":3724},[1115,28739,1797],{"class":3709},[1115,28741,12016],{"class":3724},[1115,28743,1797],{"class":3709},[1115,28745,12021],{"class":3724},[1115,28747,1797],{"class":3709},[1115,28749,11993],{"class":3724},[1115,28751,1797],{"class":3709},[1115,28753,11993],{"class":3724},[1115,28755,3901],{"class":3717},[1115,28757,28758,28760,28762,28764,28766,28768,28770,28772,28774,28776,28778,28780],{"class":3702,"line":27},[1115,28759,28063],{"class":3713},[1115,28761,1875],{"class":3717},[1115,28763,28709],{"class":3705},[1115,28765,1797],{"class":3709},[1115,28767,25579],{"class":3705},[1115,28769,3797],{"class":3709},[1115,28771,3800],{"class":3724},[1115,28773,1797],{"class":3709},[1115,28775,28080],{"class":3705},[1115,28777,3797],{"class":3709},[1115,28779,28085],{"class":3840},[1115,28781,3901],{"class":3717},[1115,28783,28784,28786,28788,28790],{"class":3702,"line":148},[1115,28785,17578],{"class":3713},[1115,28787,1875],{"class":3717},[1115,28789,28709],{"class":3705},[1115,28791,3901],{"class":3717},[3694,28793,28796],{"className":28794,"code":28795,"language":3923,"meta":1490},[3921],"    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",[3470,28797,28795],{"__ignoreMap":1490},[1110,28799,28800,28823,28824,28847],{},[1115,28801,28803],{"className":28802},[1138],[1140,28804,28805],{"xmlns":1142},[1144,28806,28807,28820],{},[1147,28808,28809,28811,28813,28816,28818],{},[1153,28810,1110],{},[1242,28812,1982],{},[1565,28814,28815],{},"0,0343",[1242,28817,4332],{},[1565,28819,3984],{},[1159,28821,28822],{"encoding":1161},"p = 0{,}0343 \u003C 0{,}05",": průměrný odpad se od 4 % statisticky významně liší (výběrový průměr 3,86 %). Shapiro-Wilkův test dává ",[1115,28825,28827],{"className":28826},[1138],[1140,28828,28829],{"xmlns":1142},[1144,28830,28831,28844],{},[1147,28832,28833,28835,28837,28840,28842],{},[1153,28834,1110],{},[1242,28836,1982],{},[1565,28838,28839],{},"0,4634",[1242,28841,1689],{},[1565,28843,3984],{},[1159,28845,28846],{"encoding":1161},"p = 0{,}4634 > 0{,}05",", předpoklad normality pro t-test je v pořádku.",[1189,28849,28851],{"id":28850},"párový-t-test","Párový t-test",[1110,28853,28854,28855,28885,28886,6783,28920,28958,28959,28972,28973,1163,28991,29011,29012,29029,29030,27574],{},"Používá se, když jsou měření závislá — na stejných objektech se měří dvě hodnoty ",[1115,28856,28858],{"className":28857},[1138],[1140,28859,28860],{"xmlns":1142},[1144,28861,28862,28882],{},[1147,28863,28864,28866,28872,28874,28880],{},[1242,28865,1875],{"stretchy":1874},[1150,28867,28868,28870],{},[1153,28869,6734],{},[1153,28871,1878],{},[1242,28873,1797],{"separator":1121},[1150,28875,28876,28878],{},[1153,28877,7090],{},[1153,28879,1878],{},[1242,28881,1886],{"stretchy":1874},[1159,28883,28884],{"encoding":1161},"(X_i, Y_i)"," a vyhodnocují se jejich diference ",[1115,28887,28889],{"className":28888},[1138],[1140,28890,28891],{"xmlns":1142},[1144,28892,28893,28917],{},[1147,28894,28895,28901,28903,28909,28911],{},[1150,28896,28897,28899],{},[1153,28898,8155],{},[1153,28900,1878],{},[1242,28902,1982],{},[1150,28904,28905,28907],{},[1153,28906,6734],{},[1153,28908,1878],{},[1242,28910,3064],{},[1150,28912,28913,28915],{},[1153,28914,7090],{},[1153,28916,1878],{},[1159,28918,28919],{"encoding":1161},"D_i = X_i - Y_i",[1115,28921,28923],{"className":28922},[1138],[1140,28924,28925],{"xmlns":1142},[1144,28926,28927,28955],{},[1147,28928,28929,28931,28933,28935,28937,28943,28945,28953],{},[1153,28930,8155],{},[1242,28932,9186],{},[1153,28934,6888],{},[1242,28936,1875],{"stretchy":1874},[1150,28938,28939,28941],{},[1153,28940,6893],{},[1153,28942,8155],{},[1242,28944,1797],{"separator":1121},[3353,28946,28947,28949,28951],{},[1153,28948,6901],{},[1153,28950,8155],{},[1565,28952,1589],{},[1242,28954,1886],{"stretchy":1874},[1159,28956,28957],{"encoding":1161},"D \\sim N(\\mu_D, \\sigma_D^2)",". Z ",[1115,28960,28962],{"className":28961},[1138],[1140,28963,28964],{"xmlns":1142},[1144,28965,28966,28970],{},[1147,28967,28968],{},[1153,28969,1372],{},[1159,28971,1372],{"encoding":1161}," dvojic se určí ",[1115,28974,28976],{"className":28975},[1138],[1140,28977,28978],{"xmlns":1142},[1144,28979,28980,28988],{},[1147,28981,28982],{},[1236,28983,28984,28986],{"accent":1121},[1153,28985,7798],{},[1242,28987,1244],{},[1159,28989,28990],{"encoding":1161},"\\bar{d}",[1115,28992,28994],{"className":28993},[1138],[1140,28995,28996],{"xmlns":1142},[1144,28997,28998,29008],{},[1147,28999,29000],{},[3353,29001,29002,29004,29006],{},[1153,29003,1291],{},[1153,29005,7798],{},[1565,29007,1589],{},[1159,29009,29010],{"encoding":1161},"s_d^2","; testuje se vztah mezi zvoleným číslem ",[1115,29013,29015],{"className":29014},[1138],[1140,29016,29017],{"xmlns":1142},[1144,29018,29019,29027],{},[1147,29020,29021],{},[1150,29022,29023,29025],{},[1153,29024,6893],{},[1565,29026,1567],{},[1159,29028,27559],{"encoding":1161}," (obvykle 0) a ",[1115,29031,29033],{"className":29032},[1138],[1140,29034,29035],{"xmlns":1142},[1144,29036,29037,29045],{},[1147,29038,29039],{},[1150,29040,29041,29043],{},[1153,29042,6893],{},[1153,29044,8155],{},[1159,29046,29047],{"encoding":1161},"\\mu_D",[1115,29049,29051],{"className":29050},[1138],[1140,29052,29053],{"xmlns":1142,"display":1964},[1144,29054,29055,29105],{},[1147,29056,29057,29059,29061,29085,29089,29091,29103],{},[1153,29058,7104],{},[1242,29060,1982],{},[2739,29062,29063,29079],{},[1147,29064,29065,29071,29073],{},[1236,29066,29067,29069],{"accent":1121},[1153,29068,7798],{},[1242,29070,1244],{},[1242,29072,3064],{},[1150,29074,29075,29077],{},[1153,29076,6893],{},[1565,29078,1567],{},[1150,29080,29081,29083],{},[1153,29082,1291],{},[1153,29084,7798],{},[4453,29086,29087],{},[1153,29088,1372],{},[1242,29090,9186],{},[1150,29092,29093,29095],{},[1153,29094,7146],{},[1147,29096,29097,29099,29101],{},[1153,29098,1372],{},[1242,29100,3064],{},[1565,29102,1794],{},[1153,29104,1669],{"mathvariant":2121},[1159,29106,29107],{"encoding":1161},"T = \\frac{\\bar{d} - \\mu_0}{s_d}\\sqrt{n} \\sim t_{n-1}.",[1194,29109,29110,29167],{},[1197,29111,29112],{},[1200,29113,29114,29133,29152],{},[1203,29115,29116],{},[1115,29117,29119],{"className":29118},[1138],[1140,29120,29121],{"xmlns":1142},[1144,29122,29123,29131],{},[1147,29124,29125],{},[1150,29126,29127,29129],{},[1153,29128,1563],{},[1565,29130,1567],{},[1159,29132,1570],{"encoding":1161},[1203,29134,29135],{},[1115,29136,29138],{"className":29137},[1138],[1140,29139,29140],{"xmlns":1142},[1144,29141,29142,29150],{},[1147,29143,29144],{},[1150,29145,29146,29148],{},[1153,29147,1563],{},[1565,29149,1794],{},[1159,29151,2996],{"encoding":1161},[1203,29153,27697,29154],{},[1115,29155,29157],{"className":29156},[1138],[1140,29158,29159],{"xmlns":1142},[1144,29160,29161,29165],{},[1147,29162,29163],{},[1153,29164,1605],{},[1159,29166,1605],{"encoding":1161},[1210,29168,29169,29266,29371],{},[1200,29170,29171,29199,29227],{},[1215,29172,29173],{},[1115,29174,29176],{"className":29175},[1138],[1140,29177,29178],{"xmlns":1142},[1144,29179,29180,29196],{},[1147,29181,29182,29188,29190],{},[1150,29183,29184,29186],{},[1153,29185,6893],{},[1153,29187,8155],{},[1242,29189,6737],{},[1150,29191,29192,29194],{},[1153,29193,6893],{},[1565,29195,1567],{},[1159,29197,29198],{"encoding":1161},"\\mu_D \\le \\mu_0",[1215,29200,29201],{},[1115,29202,29204],{"className":29203},[1138],[1140,29205,29206],{"xmlns":1142},[1144,29207,29208,29224],{},[1147,29209,29210,29216,29218],{},[1150,29211,29212,29214],{},[1153,29213,6893],{},[1153,29215,8155],{},[1242,29217,1689],{},[1150,29219,29220,29222],{},[1153,29221,6893],{},[1565,29223,1567],{},[1159,29225,29226],{"encoding":1161},"\\mu_D > \\mu_0",[1215,29228,29229],{},[1115,29230,29232],{"className":29231},[1138],[1140,29233,29234],{"xmlns":1142},[1144,29235,29236,29264],{},[1147,29237,29238,29240,29242,29254,29256,29258,29260,29262],{},[1153,29239,7146],{},[1242,29241,3351],{},[1150,29243,29244,29246],{},[1153,29245,7146],{},[1147,29247,29248,29250,29252],{},[1565,29249,1794],{},[1242,29251,3064],{},[1153,29253,3365],{},[1242,29255,1875],{"stretchy":1874},[1153,29257,1372],{},[1242,29259,3064],{},[1565,29261,1794],{},[1242,29263,1886],{"stretchy":1874},[1159,29265,27802],{"encoding":1161},[1200,29267,29268,29296,29324],{},[1215,29269,29270],{},[1115,29271,29273],{"className":29272},[1138],[1140,29274,29275],{"xmlns":1142},[1144,29276,29277,29293],{},[1147,29278,29279,29285,29287],{},[1150,29280,29281,29283],{},[1153,29282,6893],{},[1153,29284,8155],{},[1242,29286,1982],{},[1150,29288,29289,29291],{},[1153,29290,6893],{},[1565,29292,1567],{},[1159,29294,29295],{"encoding":1161},"\\mu_D = \\mu_0",[1215,29297,29298],{},[1115,29299,29301],{"className":29300},[1138],[1140,29302,29303],{"xmlns":1142},[1144,29304,29305,29321],{},[1147,29306,29307,29313,29315],{},[1150,29308,29309,29311],{},[1153,29310,6893],{},[1153,29312,8155],{},[1242,29314,10958],{"mathvariant":2121},[1150,29316,29317,29319],{},[1153,29318,6893],{},[1565,29320,1567],{},[1159,29322,29323],{"encoding":1161},"\\mu_D \\neq \\mu_0",[1215,29325,29326],{},[1115,29327,29329],{"className":29328},[1138],[1140,29330,29331],{"xmlns":1142},[1144,29332,29333,29369],{},[1147,29334,29335,29337,29339,29341,29343,29359,29361,29363,29365,29367],{},[1242,29336,23022],{"stretchy":1874},[1153,29338,7146],{},[1242,29340,23022],{"stretchy":1874},[1242,29342,3351],{},[1150,29344,29345,29347],{},[1153,29346,7146],{},[1147,29348,29349,29351,29353,29355,29357],{},[1565,29350,1794],{},[1242,29352,3064],{},[1153,29354,3365],{},[1153,29356,4604],{"mathvariant":2121},[1565,29358,1589],{},[1242,29360,1875],{"stretchy":1874},[1153,29362,1372],{},[1242,29364,3064],{},[1565,29366,1794],{},[1242,29368,1886],{"stretchy":1874},[1159,29370,27900],{"encoding":1161},[1200,29372,29373,29401,29429],{},[1215,29374,29375],{},[1115,29376,29378],{"className":29377},[1138],[1140,29379,29380],{"xmlns":1142},[1144,29381,29382,29398],{},[1147,29383,29384,29390,29392],{},[1150,29385,29386,29388],{},[1153,29387,6893],{},[1153,29389,8155],{},[1242,29391,3351],{},[1150,29393,29394,29396],{},[1153,29395,6893],{},[1565,29397,1567],{},[1159,29399,29400],{"encoding":1161},"\\mu_D \\ge \\mu_0",[1215,29402,29403],{},[1115,29404,29406],{"className":29405},[1138],[1140,29407,29408],{"xmlns":1142},[1144,29409,29410,29426],{},[1147,29411,29412,29418,29420],{},[1150,29413,29414,29416],{},[1153,29415,6893],{},[1153,29417,8155],{},[1242,29419,4332],{},[1150,29421,29422,29424],{},[1153,29423,6893],{},[1565,29425,1567],{},[1159,29427,29428],{"encoding":1161},"\\mu_D \u003C \\mu_0",[1215,29430,29431],{},[1115,29432,29434],{"className":29433},[1138],[1140,29435,29436],{"xmlns":1142},[1144,29437,29438,29468],{},[1147,29439,29440,29442,29444,29446,29458,29460,29462,29464,29466],{},[1153,29441,7146],{},[1242,29443,6737],{},[1242,29445,3064],{},[1150,29447,29448,29450],{},[1153,29449,7146],{},[1147,29451,29452,29454,29456],{},[1565,29453,1794],{},[1242,29455,3064],{},[1153,29457,3365],{},[1242,29459,1875],{"stretchy":1874},[1153,29461,1372],{},[1242,29463,3064],{},[1565,29465,1794],{},[1242,29467,1886],{"stretchy":1874},[1159,29469,27992],{"encoding":1161},[1103,29471,29473,29480,29622,29686,29772],{"className":29472,"dataCallout":3477},[1106,3476],[1110,29474,29476,29479],{"className":29475},[1113],[1115,29477],{"className":29478,"ariaHidden":1121},[1118,3484,1120],"Příklad: Snížení spotřeby paliva aditivem",[1110,29481,29482,29483,29501,29502,29520,29521,29539,29540,29573,29574,29597,29598,29621],{},"U ",[1115,29484,29486],{"className":29485},[1138],[1140,29487,29488],{"xmlns":1142},[1144,29489,29490,29498],{},[1147,29491,29492,29494,29496],{},[1153,29493,1372],{},[1242,29495,1982],{},[1565,29497,9036],{},[1159,29499,29500],{"encoding":1161},"n = 10"," vozů se změřila spotřeba před přidáním aditiva (",[1115,29503,29505],{"className":29504},[1138],[1140,29506,29507],{"xmlns":1142},[1144,29508,29509,29517],{},[1147,29510,29511],{},[1150,29512,29513,29515],{},[1153,29514,6734],{},[1153,29516,1878],{},[1159,29518,29519],{"encoding":1161},"X_i",") a po něm (",[1115,29522,29524],{"className":29523},[1138],[1140,29525,29526],{"xmlns":1142},[1144,29527,29528,29536],{},[1147,29529,29530],{},[1150,29531,29532,29534],{},[1153,29533,7090],{},[1153,29535,1878],{},[1159,29537,29538],{"encoding":1161},"Y_i","), diference ",[1115,29541,29543],{"className":29542},[1138],[1140,29544,29545],{"xmlns":1142},[1144,29546,29547,29571],{},[1147,29548,29549,29555,29557,29563,29565],{},[1150,29550,29551,29553],{},[1153,29552,8155],{},[1153,29554,1878],{},[1242,29556,1982],{},[1150,29558,29559,29561],{},[1153,29560,6734],{},[1153,29562,1878],{},[1242,29564,3064],{},[1150,29566,29567,29569],{},[1153,29568,7090],{},[1153,29570,1878],{},[1159,29572,28919],{"encoding":1161}," představují úsporu paliva. Z dat vyšla průměrná úspora ",[1115,29575,29577],{"className":29576},[1138],[1140,29578,29579],{"xmlns":1142},[1144,29580,29581,29594],{},[1147,29582,29583,29589,29591],{},[1236,29584,29585,29587],{"accent":1121},[1153,29586,7798],{},[1242,29588,1244],{},[1242,29590,1982],{},[1565,29592,29593],{},"0,4",[1159,29595,29596],{"encoding":1161},"\\bar{d} = 0{,}4"," l\u002F100 km, ",[1115,29599,29601],{"className":29600},[1138],[1140,29602,29603],{"xmlns":1142},[1144,29604,29605,29618],{},[1147,29606,29607,29613,29615],{},[1150,29608,29609,29611],{},[1153,29610,1291],{},[1153,29612,7798],{},[1242,29614,1982],{},[1565,29616,29617],{},"0,35",[1159,29619,29620],{"encoding":1161},"s_d = 0{,}35"," l\u002F100 km. Ověřte, že aditivum spotřebu statisticky významně snižuje.",[1110,29623,29624,29654,29655,29685],{},[1115,29625,29627],{"className":29626},[1138],[1140,29628,29629],{"xmlns":1142},[1144,29630,29631,29651],{},[1147,29632,29633,29639,29641,29647,29649],{},[1150,29634,29635,29637],{},[1153,29636,1563],{},[1565,29638,1567],{},[1242,29640,1958],{},[1150,29642,29643,29645],{},[1153,29644,6893],{},[1153,29646,8155],{},[1242,29648,6737],{},[1565,29650,1567],{},[1159,29652,29653],{"encoding":1161},"H_0: \\mu_D \\le 0"," (aditivum nemá vliv nebo spotřebu zvyšuje), ",[1115,29656,29658],{"className":29657},[1138],[1140,29659,29660],{"xmlns":1142},[1144,29661,29662,29682],{},[1147,29663,29664,29670,29672,29678,29680],{},[1150,29665,29666,29668],{},[1153,29667,1563],{},[1565,29669,1794],{},[1242,29671,1958],{},[1150,29673,29674,29676],{},[1153,29675,6893],{},[1153,29677,8155],{},[1242,29679,1689],{},[1565,29681,1567],{},[1159,29683,29684],{"encoding":1161},"H_1: \\mu_D > 0"," (aditivum spotřebu snižuje).",[1110,29687,29688],{},[1115,29689,29691],{"className":29690},[1138],[1140,29692,29693],{"xmlns":1142},[1144,29694,29695,29769],{},[1147,29696,29697,29699,29701,29713,29717,29719,29722,29724,29726,29728,29730,29732,29734,29736,29748,29750,29752,29754,29756,29758,29760,29762,29764,29767],{},[1153,29698,7146],{},[1242,29700,1982],{},[2739,29702,29703,29711],{},[1147,29704,29705,29707,29709],{},[1565,29706,29593],{},[1242,29708,3064],{},[1565,29710,1567],{},[1565,29712,29617],{},[4453,29714,29715],{},[1565,29716,9036],{},[1242,29718,1982],{},[1565,29720,29721],{},"3,614",[1242,29723,1797],{"separator":1121},[2012,29725],{"width":2014},[1153,29727,1605],{},[1242,29729,1982],{},[1242,29731,3334],{"stretchy":1874},[1153,29733,7146],{},[1242,29735,3351],{},[1150,29737,29738,29740],{},[1153,29739,7146],{},[1147,29741,29742,29744,29746],{},[1565,29743,1567],{},[1242,29745,1797],{"separator":1121},[1565,29747,21796],{},[1242,29749,1875],{"stretchy":1874},[1565,29751,3595],{},[1242,29753,1886],{"stretchy":1874},[1242,29755,3394],{"stretchy":1874},[1242,29757,1982],{},[1242,29759,3334],{"stretchy":1874},[1153,29761,7146],{},[1242,29763,3351],{},[1565,29765,29766],{},"1,833",[1242,29768,3394],{"stretchy":1874},[1159,29770,29771],{"encoding":1161},"t = \\frac{0{,}4 - 0}{0{,}35}\\sqrt{10} = 3{,}614, \\qquad W = \\{t \\ge t_{0,95}(9)\\} = \\{t \\ge 1{,}833\\}",[1110,29773,28383,29774,6006,29791,29808],{},[1115,29775,29777],{"className":29776},[1138],[1140,29778,29779],{"xmlns":1142},[1144,29780,29781,29789],{},[1147,29782,29783,29785,29787],{},[1153,29784,7146],{},[1242,29786,7021],{},[1153,29788,1605],{},[1159,29790,28401],{"encoding":1161},[1115,29792,29794],{"className":29793},[1138],[1140,29795,29796],{"xmlns":1142},[1144,29797,29798,29806],{},[1147,29799,29800],{},[1150,29801,29802,29804],{},[1153,29803,1563],{},[1565,29805,1567],{},[1159,29807,1570],{"encoding":1161},": aditivum prokazatelně snižuje průměrnou spotřebu paliva.",[3694,29810,29812],{"className":3696,"code":29811,"language":71,"meta":1490,"style":1490},"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",[3470,29813,29814,29843,29874,29900,29904],{"__ignoreMap":1490},[1115,29815,29816,29819,29821,29824,29826,29829,29831,29834,29836,29838,29840],{"class":3702,"line":10},[1115,29817,29818],{"class":3705},"dbar",[1115,29820,3710],{"class":3709},[1115,29822,29823],{"class":3724}," 0.4",[1115,29825,25182],{"class":3717},[1115,29827,29828],{"class":3705},"sd_d",[1115,29830,3710],{"class":3709},[1115,29832,29833],{"class":3724}," 0.35",[1115,29835,25182],{"class":3717},[1115,29837,1372],{"class":3705},[1115,29839,3710],{"class":3709},[1115,29841,29842],{"class":3724}," 10\n",[1115,29844,29845,29847,29849,29851,29853,29855,29857,29859,29861,29864,29866,29868,29870,29872],{"class":3702,"line":27},[1115,29846,7146],{"class":3705},[1115,29848,3710],{"class":3709},[1115,29850,4607],{"class":3717},[1115,29852,29818],{"class":3705},[1115,29854,25519],{"class":3709},[1115,29856,9973],{"class":3724},[1115,29858,4601],{"class":3717},[1115,29860,4604],{"class":3709},[1115,29862,29863],{"class":3705}," sd_d",[1115,29865,18642],{"class":3709},[1115,29867,4578],{"class":3713},[1115,29869,1875],{"class":3717},[1115,29871,1372],{"class":3705},[1115,29873,3901],{"class":3717},[1115,29875,29876,29878,29880,29882,29884,29886,29888,29890,29892,29894,29896,29898],{"class":3702,"line":148},[1115,29877,28508],{"class":3705},[1115,29879,3710],{"class":3709},[1115,29881,28513],{"class":3713},[1115,29883,1875],{"class":3717},[1115,29885,10828],{"class":3724},[1115,29887,1797],{"class":3709},[1115,29889,10811],{"class":3705},[1115,29891,3797],{"class":3709},[1115,29893,28527],{"class":3705},[1115,29895,25519],{"class":3709},[1115,29897,4641],{"class":3724},[1115,29899,3901],{"class":3717},[1115,29901,29902],{"class":3702,"line":111},[1115,29903,28538],{"class":3705},[1115,29905,29906],{"class":3702,"line":96},[1115,29907,28543],{"class":3705},[3694,29909,29912],{"className":29910,"code":29911,"language":3923,"meta":1490},[3921],"[1] 3.614032\n[1] 1.833113\n",[3470,29913,29911],{"__ignoreMap":1490},[1103,29915,29917,29924,29927,30072,30078],{"className":29916,"dataCallout":6412},[1106,6411],[1110,29918,29920,29923],{"className":29919},[1113],[1115,29921],{"className":29922,"ariaHidden":1121},[1118,6419,1120],"Ověřte normalitu diferencí, ne jen výsledek testu",[1110,29925,29926],{},"Realitní kancelář nechala dva odhadce ocenit osm nemovitostí (tisíce Kč):",[3694,29928,29930],{"className":3696,"code":29929,"language":71,"meta":1490,"style":1490},"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",[3470,29931,29932,29983,30034,30058],{"__ignoreMap":1490},[1115,29933,29934,29937,29939,29941,29943,29946,29948,29951,29953,29956,29958,29961,29963,29966,29968,29971,29973,29976,29978,29981],{"class":3702,"line":10},[1115,29935,29936],{"class":3705},"estA",[1115,29938,3710],{"class":3709},[1115,29940,3835],{"class":3713},[1115,29942,1875],{"class":3717},[1115,29944,29945],{"class":3724},"3282",[1115,29947,1797],{"class":3709},[1115,29949,29950],{"class":3724}," 2506",[1115,29952,1797],{"class":3709},[1115,29954,29955],{"class":3724}," 2812",[1115,29957,1797],{"class":3709},[1115,29959,29960],{"class":3724}," 5453",[1115,29962,1797],{"class":3709},[1115,29964,29965],{"class":3724}," 3263",[1115,29967,1797],{"class":3709},[1115,29969,29970],{"class":3724}," 4571",[1115,29972,1797],{"class":3709},[1115,29974,29975],{"class":3724}," 3121",[1115,29977,1797],{"class":3709},[1115,29979,29980],{"class":3724}," 2963",[1115,29982,3901],{"class":3717},[1115,29984,29985,29988,29990,29992,29994,29997,29999,30002,30004,30007,30009,30012,30014,30017,30019,30022,30024,30027,30029,30032],{"class":3702,"line":27},[1115,29986,29987],{"class":3705},"estB",[1115,29989,3710],{"class":3709},[1115,29991,3835],{"class":3713},[1115,29993,1875],{"class":3717},[1115,29995,29996],{"class":3724},"3271",[1115,29998,1797],{"class":3709},[1115,30000,30001],{"class":3724}," 2531",[1115,30003,1797],{"class":3709},[1115,30005,30006],{"class":3724}," 2799",[1115,30008,1797],{"class":3709},[1115,30010,30011],{"class":3724}," 5471",[1115,30013,1797],{"class":3709},[1115,30015,30016],{"class":3724}," 3285",[1115,30018,1797],{"class":3709},[1115,30020,30021],{"class":3724}," 4557",[1115,30023,1797],{"class":3709},[1115,30025,30026],{"class":3724}," 3139",[1115,30028,1797],{"class":3709},[1115,30030,30031],{"class":3724}," 2976",[1115,30033,3901],{"class":3717},[1115,30035,30036,30038,30040,30042,30044,30047,30049,30052,30054,30056],{"class":3702,"line":148},[1115,30037,28063],{"class":3713},[1115,30039,1875],{"class":3717},[1115,30041,29936],{"class":3705},[1115,30043,1797],{"class":3709},[1115,30045,30046],{"class":3705}," estB",[1115,30048,1797],{"class":3709},[1115,30050,30051],{"class":3705}," paired",[1115,30053,3797],{"class":3709},[1115,30055,3810],{"class":3724},[1115,30057,3901],{"class":3717},[1115,30059,30060,30062,30064,30066,30068,30070],{"class":3702,"line":111},[1115,30061,17578],{"class":3713},[1115,30063,1875],{"class":3717},[1115,30065,29936],{"class":3705},[1115,30067,25519],{"class":3709},[1115,30069,30046],{"class":3705},[1115,30071,3901],{"class":3717},[3694,30073,30076],{"className":30074,"code":30075,"language":3923,"meta":1490},[3921],"    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",[3470,30077,30075],{"__ignoreMap":1490},[1110,30079,30080,30081,4607,30098,30117,30118,30141],{},"Párový t-test sám nezamítá ",[1115,30082,30084],{"className":30083},[1138],[1140,30085,30086],{"xmlns":1142},[1144,30087,30088,30096],{},[1147,30089,30090],{},[1150,30091,30092,30094],{},[1153,30093,1563],{},[1565,30095,1567],{},[1159,30097,1570],{"encoding":1161},[1115,30099,30101],{"className":30100},[1138],[1140,30102,30103],{"xmlns":1142},[1144,30104,30105,30114],{},[1147,30106,30107,30109,30111],{},[1153,30108,1110],{},[1242,30110,1982],{},[1565,30112,30113],{},"0,2635",[1159,30115,30116],{"encoding":1161},"p = 0{,}2635","): odhadci se podle něj neliší. Shapiro-Wilkův test na diferencích ale dává ",[1115,30119,30121],{"className":30120},[1138],[1140,30122,30123],{"xmlns":1142},[1144,30124,30125,30138],{},[1147,30126,30127,30129,30131,30134,30136],{},[1153,30128,1110],{},[1242,30130,1982],{},[1565,30132,30133],{},"0,03203",[1242,30135,4332],{},[1565,30137,3984],{},[1159,30139,30140],{"encoding":1161},"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).",[1189,30143,30145],{"id":30144},"testy-o-dvou-základních-souborech","Testy o dvou základních souborech",[1110,30147,30148,30149,30175,30176,30214,30215,1163,30233,30214,30271,30289,30290,1163,30322,30354,30355,30381,30382,1669],{},"Uvažují se dva nezávislé základní soubory ",[1115,30150,30152],{"className":30151},[1138],[1140,30153,30154],{"xmlns":1142},[1144,30155,30156,30172],{},[1147,30157,30158,30164,30166],{},[1150,30159,30160,30162],{},[1153,30161,8928],{},[1565,30163,1794],{},[1242,30165,1797],{"separator":1121},[1150,30167,30168,30170],{},[1153,30169,8928],{},[1565,30171,1589],{},[1159,30173,30174],{"encoding":1161},"Z_1, Z_2"," se znakem ",[1115,30177,30179],{"className":30178},[1138],[1140,30180,30181],{"xmlns":1142},[1144,30182,30183,30211],{},[1147,30184,30185,30187,30189,30191,30193,30199,30201,30209],{},[1153,30186,6734],{},[1242,30188,9186],{},[1153,30190,6888],{},[1242,30192,1875],{"stretchy":1874},[1150,30194,30195,30197],{},[1153,30196,6893],{},[1565,30198,1794],{},[1242,30200,1797],{"separator":1121},[3353,30202,30203,30205,30207],{},[1153,30204,6901],{},[1565,30206,1794],{},[1565,30208,1589],{},[1242,30210,1886],{"stretchy":1874},[1159,30212,30213],{"encoding":1161},"X \\sim N(\\mu_1, \\sigma_1^2)"," v ",[1115,30216,30218],{"className":30217},[1138],[1140,30219,30220],{"xmlns":1142},[1144,30221,30222,30230],{},[1147,30223,30224],{},[1150,30225,30226,30228],{},[1153,30227,8928],{},[1565,30229,1794],{},[1159,30231,30232],{"encoding":1161},"Z_1",[1115,30234,30236],{"className":30235},[1138],[1140,30237,30238],{"xmlns":1142},[1144,30239,30240,30268],{},[1147,30241,30242,30244,30246,30248,30250,30256,30258,30266],{},[1153,30243,6734],{},[1242,30245,9186],{},[1153,30247,6888],{},[1242,30249,1875],{"stretchy":1874},[1150,30251,30252,30254],{},[1153,30253,6893],{},[1565,30255,1589],{},[1242,30257,1797],{"separator":1121},[3353,30259,30260,30262,30264],{},[1153,30261,6901],{},[1565,30263,1589],{},[1565,30265,1589],{},[1242,30267,1886],{"stretchy":1874},[1159,30269,30270],{"encoding":1161},"X \\sim N(\\mu_2, \\sigma_2^2)",[1115,30272,30274],{"className":30273},[1138],[1140,30275,30276],{"xmlns":1142},[1144,30277,30278,30286],{},[1147,30279,30280],{},[1150,30281,30282,30284],{},[1153,30283,8928],{},[1565,30285,1589],{},[1159,30287,30288],{"encoding":1161},"Z_2",". Z výběrů se určí ",[1115,30291,30293],{"className":30292},[1138],[1140,30294,30295],{"xmlns":1142},[1144,30296,30297,30319],{},[1147,30298,30299,30309,30311],{},[1150,30300,30301,30307],{},[1236,30302,30303,30305],{"accent":1121},[1153,30304,1240],{},[1242,30306,1244],{},[1565,30308,1794],{},[1242,30310,1797],{"separator":1121},[3353,30312,30313,30315,30317],{},[1153,30314,1291],{},[1565,30316,1794],{},[1565,30318,1589],{},[1159,30320,30321],{"encoding":1161},"\\bar{x}_1, s_1^2",[1115,30323,30325],{"className":30324},[1138],[1140,30326,30327],{"xmlns":1142},[1144,30328,30329,30351],{},[1147,30330,30331,30341,30343],{},[1150,30332,30333,30339],{},[1236,30334,30335,30337],{"accent":1121},[1153,30336,1240],{},[1242,30338,1244],{},[1565,30340,1589],{},[1242,30342,1797],{"separator":1121},[3353,30344,30345,30347,30349],{},[1153,30346,1291],{},[1565,30348,1589],{},[1565,30350,1589],{},[1159,30352,30353],{"encoding":1161},"\\bar{x}_2, s_2^2",". Testují se varianty vztahů mezi ",[1115,30356,30358],{"className":30357},[1138],[1140,30359,30360],{"xmlns":1142},[1144,30361,30362,30378],{},[1147,30363,30364,30370,30372],{},[1150,30365,30366,30368],{},[1153,30367,6893],{},[1565,30369,1794],{},[1242,30371,1797],{"separator":1121},[1150,30373,30374,30376],{},[1153,30375,6893],{},[1565,30377,1589],{},[1159,30379,30380],{"encoding":1161},"\\mu_1, \\mu_2",", resp. mezi ",[1115,30383,30385],{"className":30384},[1138],[1140,30386,30387],{"xmlns":1142},[1144,30388,30389,30409],{},[1147,30390,30391,30399,30401],{},[3353,30392,30393,30395,30397],{},[1153,30394,6901],{},[1565,30396,1794],{},[1565,30398,1589],{},[1242,30400,1797],{"separator":1121},[3353,30402,30403,30405,30407],{},[1153,30404,6901],{},[1565,30406,1589],{},[1565,30408,1589],{},[1159,30410,30411],{"encoding":1161},"\\sigma_1^2, \\sigma_2^2",[16749,30413,30415],{"id":30414},"f-test-o-rozptylech","F-test o rozptylech",[1110,30417,30418],{},"Statistika",[1115,30420,30422],{"className":30421},[1138],[1140,30423,30424],{"xmlns":1142,"display":1964},[1144,30425,30426,30482],{},[1147,30427,30428,30430,30432,30450,30452],{},[1153,30429,6718],{},[1242,30431,1982],{},[2739,30433,30434,30442],{},[3353,30435,30436,30438,30440],{},[1153,30437,1291],{},[1565,30439,1794],{},[1565,30441,1589],{},[3353,30443,30444,30446,30448],{},[1153,30445,1291],{},[1565,30447,1589],{},[1565,30449,1589],{},[1242,30451,9186],{},[1150,30453,30454,30456],{},[1153,30455,6718],{},[1147,30457,30458,30464,30466,30468,30470,30472,30478,30480],{},[1150,30459,30460,30462],{},[1153,30461,1372],{},[1565,30463,1794],{},[1242,30465,3064],{},[1565,30467,1794],{},[1242,30469,1797],{"separator":1121},[2909,30471,2911],{},[1150,30473,30474,30476],{},[1153,30475,1372],{},[1565,30477,1589],{},[1242,30479,3064],{},[1565,30481,1794],{},[1159,30483,30484],{"encoding":1161},"F = \\frac{s_1^2}{s_2^2} \\sim F_{n_1-1,\\,n_2-1}",[1110,30486,30487,30488,1163,30510,27650],{},"má Fisherovo-Snedecorovo rozdělení o ",[1115,30489,30491],{"className":30490},[1138],[1140,30492,30493],{"xmlns":1142},[1144,30494,30495,30507],{},[1147,30496,30497,30503,30505],{},[1150,30498,30499,30501],{},[1153,30500,1372],{},[1565,30502,1794],{},[1242,30504,3064],{},[1565,30506,1794],{},[1159,30508,30509],{"encoding":1161},"n_1-1",[1115,30511,30513],{"className":30512},[1138],[1140,30514,30515],{"xmlns":1142},[1144,30516,30517,30529],{},[1147,30518,30519,30525,30527],{},[1150,30520,30521,30523],{},[1153,30522,1372],{},[1565,30524,1589],{},[1242,30526,3064],{},[1565,30528,1794],{},[1159,30530,30531],{"encoding":1161},"n_2-1",[1194,30533,30534,30591],{},[1197,30535,30536],{},[1200,30537,30538,30557,30576],{},[1203,30539,30540],{},[1115,30541,30543],{"className":30542},[1138],[1140,30544,30545],{"xmlns":1142},[1144,30546,30547,30555],{},[1147,30548,30549],{},[1150,30550,30551,30553],{},[1153,30552,1563],{},[1565,30554,1567],{},[1159,30556,1570],{"encoding":1161},[1203,30558,30559],{},[1115,30560,30562],{"className":30561},[1138],[1140,30563,30564],{"xmlns":1142},[1144,30565,30566,30574],{},[1147,30567,30568],{},[1150,30569,30570,30572],{},[1153,30571,1563],{},[1565,30573,1794],{},[1159,30575,2996],{"encoding":1161},[1203,30577,27697,30578],{},[1115,30579,30581],{"className":30580},[1138],[1140,30582,30583],{"xmlns":1142},[1144,30584,30585,30589],{},[1147,30586,30587],{},[1153,30588,1605],{},[1159,30590,1605],{"encoding":1161},[1210,30592,30593,30707,30880],{},[1200,30594,30595,30623,30651],{},[1215,30596,30597],{},[1115,30598,30600],{"className":30599},[1138],[1140,30601,30602],{"xmlns":1142},[1144,30603,30604,30620],{},[1147,30605,30606,30612,30614],{},[1150,30607,30608,30610],{},[1153,30609,6901],{},[1565,30611,1794],{},[1242,30613,6737],{},[1150,30615,30616,30618],{},[1153,30617,6901],{},[1565,30619,1589],{},[1159,30621,30622],{"encoding":1161},"\\sigma_1 \\le \\sigma_2",[1215,30624,30625],{},[1115,30626,30628],{"className":30627},[1138],[1140,30629,30630],{"xmlns":1142},[1144,30631,30632,30648],{},[1147,30633,30634,30640,30642],{},[1150,30635,30636,30638],{},[1153,30637,6901],{},[1565,30639,1794],{},[1242,30641,1689],{},[1150,30643,30644,30646],{},[1153,30645,6901],{},[1565,30647,1589],{},[1159,30649,30650],{"encoding":1161},"\\sigma_1 > \\sigma_2",[1215,30652,30653],{},[1115,30654,30656],{"className":30655},[1138],[1140,30657,30658],{"xmlns":1142},[1144,30659,30660,30704],{},[1147,30661,30662,30664,30666,30678,30680,30686,30688,30690,30692,30698,30700,30702],{},[1153,30663,6718],{},[1242,30665,3351],{},[1150,30667,30668,30670],{},[1153,30669,6718],{},[1147,30671,30672,30674,30676],{},[1565,30673,1794],{},[1242,30675,3064],{},[1153,30677,3365],{},[1242,30679,1875],{"stretchy":1874},[1150,30681,30682,30684],{},[1153,30683,1372],{},[1565,30685,1794],{},[1242,30687,3064],{},[1565,30689,1794],{},[1242,30691,1797],{"separator":1121},[1150,30693,30694,30696],{},[1153,30695,1372],{},[1565,30697,1589],{},[1242,30699,3064],{},[1565,30701,1794],{},[1242,30703,1886],{"stretchy":1874},[1159,30705,30706],{"encoding":1161},"F \\ge F_{1-\\alpha}(n_1-1, n_2-1)",[1200,30708,30709,30737,30765],{},[1215,30710,30711],{},[1115,30712,30714],{"className":30713},[1138],[1140,30715,30716],{"xmlns":1142},[1144,30717,30718,30734],{},[1147,30719,30720,30726,30728],{},[1150,30721,30722,30724],{},[1153,30723,6901],{},[1565,30725,1794],{},[1242,30727,1982],{},[1150,30729,30730,30732],{},[1153,30731,6901],{},[1565,30733,1589],{},[1159,30735,30736],{"encoding":1161},"\\sigma_1 = \\sigma_2",[1215,30738,30739],{},[1115,30740,30742],{"className":30741},[1138],[1140,30743,30744],{"xmlns":1142},[1144,30745,30746,30762],{},[1147,30747,30748,30754,30756],{},[1150,30749,30750,30752],{},[1153,30751,6901],{},[1565,30753,1794],{},[1242,30755,10958],{"mathvariant":2121},[1150,30757,30758,30760],{},[1153,30759,6901],{},[1565,30761,1589],{},[1159,30763,30764],{"encoding":1161},"\\sigma_1 \\neq \\sigma_2",[1215,30766,30767,30821,30822],{},[1115,30768,30770],{"className":30769},[1138],[1140,30771,30772],{"xmlns":1142},[1144,30773,30774,30818],{},[1147,30775,30776,30778,30780,30792,30794,30800,30802,30804,30806,30812,30814,30816],{},[1153,30777,6718],{},[1242,30779,6737],{},[1150,30781,30782,30784],{},[1153,30783,6718],{},[1147,30785,30786,30788,30790],{},[1153,30787,3365],{},[1153,30789,4604],{"mathvariant":2121},[1565,30791,1589],{},[1242,30793,1875],{"stretchy":1874},[1150,30795,30796,30798],{},[1153,30797,1372],{},[1565,30799,1794],{},[1242,30801,3064],{},[1565,30803,1794],{},[1242,30805,1797],{"separator":1121},[1150,30807,30808,30810],{},[1153,30809,1372],{},[1565,30811,1589],{},[1242,30813,3064],{},[1565,30815,1794],{},[1242,30817,1886],{"stretchy":1874},[1159,30819,30820],{"encoding":1161},"F \\le F_{\\alpha\u002F2}(n_1-1, n_2-1)"," nebo ",[1115,30823,30825],{"className":30824},[1138],[1140,30826,30827],{"xmlns":1142},[1144,30828,30829,30877],{},[1147,30830,30831,30833,30835,30851,30853,30859,30861,30863,30865,30871,30873,30875],{},[1153,30832,6718],{},[1242,30834,3351],{},[1150,30836,30837,30839],{},[1153,30838,6718],{},[1147,30840,30841,30843,30845,30847,30849],{},[1565,30842,1794],{},[1242,30844,3064],{},[1153,30846,3365],{},[1153,30848,4604],{"mathvariant":2121},[1565,30850,1589],{},[1242,30852,1875],{"stretchy":1874},[1150,30854,30855,30857],{},[1153,30856,1372],{},[1565,30858,1794],{},[1242,30860,3064],{},[1565,30862,1794],{},[1242,30864,1797],{"separator":1121},[1150,30866,30867,30869],{},[1153,30868,1372],{},[1565,30870,1589],{},[1242,30872,3064],{},[1565,30874,1794],{},[1242,30876,1886],{"stretchy":1874},[1159,30878,30879],{"encoding":1161},"F \\ge F_{1-\\alpha\u002F2}(n_1-1, n_2-1)",[1200,30881,30882,30910,30938],{},[1215,30883,30884],{},[1115,30885,30887],{"className":30886},[1138],[1140,30888,30889],{"xmlns":1142},[1144,30890,30891,30907],{},[1147,30892,30893,30899,30901],{},[1150,30894,30895,30897],{},[1153,30896,6901],{},[1565,30898,1794],{},[1242,30900,3351],{},[1150,30902,30903,30905],{},[1153,30904,6901],{},[1565,30906,1589],{},[1159,30908,30909],{"encoding":1161},"\\sigma_1 \\ge \\sigma_2",[1215,30911,30912],{},[1115,30913,30915],{"className":30914},[1138],[1140,30916,30917],{"xmlns":1142},[1144,30918,30919,30935],{},[1147,30920,30921,30927,30929],{},[1150,30922,30923,30925],{},[1153,30924,6901],{},[1565,30926,1794],{},[1242,30928,4332],{},[1150,30930,30931,30933],{},[1153,30932,6901],{},[1565,30934,1589],{},[1159,30936,30937],{"encoding":1161},"\\sigma_1 \u003C \\sigma_2",[1215,30939,30940],{},[1115,30941,30943],{"className":30942},[1138],[1140,30944,30945],{"xmlns":1142},[1144,30946,30947,30985],{},[1147,30948,30949,30951,30953,30959,30961,30967,30969,30971,30973,30979,30981,30983],{},[1153,30950,6718],{},[1242,30952,6737],{},[1150,30954,30955,30957],{},[1153,30956,6718],{},[1153,30958,3365],{},[1242,30960,1875],{"stretchy":1874},[1150,30962,30963,30965],{},[1153,30964,1372],{},[1565,30966,1794],{},[1242,30968,3064],{},[1565,30970,1794],{},[1242,30972,1797],{"separator":1121},[1150,30974,30975,30977],{},[1153,30976,1372],{},[1565,30978,1589],{},[1242,30980,3064],{},[1565,30982,1794],{},[1242,30984,1886],{"stretchy":1874},[1159,30986,30987],{"encoding":1161},"F \\le F_{\\alpha}(n_1-1, n_2-1)",[16749,30989,30991],{"id":30990},"dvouvýběrový-t-test-o-středních-hodnotách","Dvouvýběrový t-test o středních hodnotách",[1110,30993,30994],{},"Volba statistiky závisí na tom, zda jsou rozptyly považovány za shodné:",[1115,30996,30998],{"className":30997},[1138],[1140,30999,31000],{"xmlns":1142,"display":1964},[1144,31001,31002,31179],{},[1147,31003,31004,31010,31012,31088,31136,31138,31140,31149,31151,31157,31159,31165,31167,31173,31175,31177],{},[1150,31005,31006,31008],{},[1153,31007,7104],{},[1565,31009,1794],{},[1242,31011,1982],{},[2739,31013,31014,31038],{},[1147,31015,31016,31026,31028],{},[1150,31017,31018,31024],{},[1236,31019,31020,31022],{"accent":1121},[1153,31021,1240],{},[1242,31023,1244],{},[1565,31025,1794],{},[1242,31027,3064],{},[1150,31029,31030,31036],{},[1236,31031,31032,31034],{"accent":1121},[1153,31033,1240],{},[1242,31035,1244],{},[1565,31037,1589],{},[4453,31039,31040],{},[1147,31041,31042,31044,31050,31052,31054,31056,31064,31066,31068,31074,31076,31078,31080],{},[1242,31043,1875],{"stretchy":1874},[1150,31045,31046,31048],{},[1153,31047,1372],{},[1565,31049,1794],{},[1242,31051,3064],{},[1565,31053,1794],{},[1242,31055,1886],{"stretchy":1874},[3353,31057,31058,31060,31062],{},[1153,31059,1291],{},[1565,31061,1794],{},[1565,31063,1589],{},[1242,31065,5477],{},[1242,31067,1875],{"stretchy":1874},[1150,31069,31070,31072],{},[1153,31071,1372],{},[1565,31073,1589],{},[1242,31075,3064],{},[1565,31077,1794],{},[1242,31079,1886],{"stretchy":1874},[3353,31081,31082,31084,31086],{},[1153,31083,1291],{},[1565,31085,1589],{},[1565,31087,1589],{},[4453,31089,31090],{},[2739,31091,31092,31112],{},[1147,31093,31094,31100,31102,31108,31110],{},[1150,31095,31096,31098],{},[1153,31097,1372],{},[1565,31099,1794],{},[1242,31101,5477],{},[1150,31103,31104,31106],{},[1153,31105,1372],{},[1565,31107,1589],{},[1242,31109,3064],{},[1565,31111,1589],{},[1147,31113,31114,31124,31126],{},[2739,31115,31116,31118],{},[1565,31117,1794],{},[1150,31119,31120,31122],{},[1153,31121,1372],{},[1565,31123,1794],{},[1242,31125,5477],{},[2739,31127,31128,31130],{},[1565,31129,1794],{},[1150,31131,31132,31134],{},[1153,31133,1372],{},[1565,31135,1589],{},[1242,31137,1797],{"separator":1121},[2012,31139],{"width":2014},[3353,31141,31142,31144,31146],{},[1153,31143,7146],{},[1153,31145,1110],{},[1242,31147,31148],{},"∗",[1242,31150,1982],{},[1150,31152,31153,31155],{},[1153,31154,7146],{},[1153,31156,1110],{},[1242,31158,1875],{"stretchy":1874},[1150,31160,31161,31163],{},[1153,31162,1372],{},[1565,31164,1794],{},[1242,31166,5477],{},[1150,31168,31169,31171],{},[1153,31170,1372],{},[1565,31172,1589],{},[1242,31174,3064],{},[1565,31176,1589],{},[1242,31178,1886],{"stretchy":1874},[1159,31180,31181],{"encoding":1161},"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)",[1110,31183,31184,31185,31214],{},"se použije, pokud jsou rozptyly ",[1115,31186,31188],{"className":31187},[1138],[1140,31189,31190],{"xmlns":1142},[1144,31191,31192,31212],{},[1147,31193,31194,31202,31204],{},[3353,31195,31196,31198,31200],{},[1153,31197,6901],{},[1565,31199,1794],{},[1565,31201,1589],{},[1242,31203,1797],{"separator":1121},[3353,31205,31206,31208,31210],{},[1153,31207,6901],{},[1565,31209,1589],{},[1565,31211,1589],{},[1159,31213,30411],{"encoding":1161}," alespoň přibližně shodné; při rozdílných rozptylech",[1115,31216,31218],{"className":31217},[1138],[1140,31219,31220],{"xmlns":1142,"display":1964},[1144,31221,31222,31434],{},[1147,31223,31224,31230,31232,31296,31298,31300,31308,31310,31432],{},[1150,31225,31226,31228],{},[1153,31227,7104],{},[1565,31229,1589],{},[1242,31231,1982],{},[2739,31233,31234,31258],{},[1147,31235,31236,31246,31248],{},[1150,31237,31238,31244],{},[1236,31239,31240,31242],{"accent":1121},[1153,31241,1240],{},[1242,31243,1244],{},[1565,31245,1794],{},[1242,31247,3064],{},[1150,31249,31250,31256],{},[1236,31251,31252,31254],{"accent":1121},[1153,31253,1240],{},[1242,31255,1244],{},[1565,31257,1589],{},[4453,31259,31260],{},[1147,31261,31262,31270,31272,31278,31280,31288,31290],{},[3353,31263,31264,31266,31268],{},[1153,31265,1291],{},[1565,31267,1794],{},[1565,31269,1589],{},[1153,31271,4604],{"mathvariant":2121},[1150,31273,31274,31276],{},[1153,31275,1372],{},[1565,31277,1794],{},[1242,31279,5477],{},[3353,31281,31282,31284,31286],{},[1153,31283,1291],{},[1565,31285,1589],{},[1565,31287,1589],{},[1153,31289,4604],{"mathvariant":2121},[1150,31291,31292,31294],{},[1153,31293,1372],{},[1565,31295,1589],{},[1242,31297,1797],{"separator":1121},[2012,31299],{"width":2014},[3353,31301,31302,31304,31306],{},[1153,31303,7146],{},[1153,31305,1110],{},[1242,31307,31148],{},[1242,31309,1982],{},[2739,31311,31312,31392],{},[1147,31313,31314,31332,31338,31340,31346,31348,31350,31352,31354,31372,31378,31380,31386,31388,31390],{},[3241,31315,31316],{"scriptlevel":1567,"displaystyle":1121},[2739,31317,31318,31326],{},[3353,31319,31320,31322,31324],{},[1153,31321,1291],{},[1565,31323,1794],{},[1565,31325,1589],{},[1150,31327,31328,31330],{},[1153,31329,1372],{},[1565,31331,1794],{},[1150,31333,31334,31336],{},[1153,31335,7146],{},[1153,31337,1110],{},[1242,31339,1875],{"stretchy":1874},[1150,31341,31342,31344],{},[1153,31343,1372],{},[1565,31345,1794],{},[1242,31347,3064],{},[1565,31349,1794],{},[1242,31351,1886],{"stretchy":1874},[1242,31353,5477],{},[3241,31355,31356],{"scriptlevel":1567,"displaystyle":1121},[2739,31357,31358,31366],{},[3353,31359,31360,31362,31364],{},[1153,31361,1291],{},[1565,31363,1589],{},[1565,31365,1589],{},[1150,31367,31368,31370],{},[1153,31369,1372],{},[1565,31371,1589],{},[1150,31373,31374,31376],{},[1153,31375,7146],{},[1153,31377,1110],{},[1242,31379,1875],{"stretchy":1874},[1150,31381,31382,31384],{},[1153,31383,1372],{},[1565,31385,1589],{},[1242,31387,3064],{},[1565,31389,1794],{},[1242,31391,1886],{"stretchy":1874},[1147,31393,31394,31412,31414],{},[3241,31395,31396],{"scriptlevel":1567,"displaystyle":1121},[2739,31397,31398,31406],{},[3353,31399,31400,31402,31404],{},[1153,31401,1291],{},[1565,31403,1794],{},[1565,31405,1589],{},[1150,31407,31408,31410],{},[1153,31409,1372],{},[1565,31411,1794],{},[1242,31413,5477],{},[3241,31415,31416],{"scriptlevel":1567,"displaystyle":1121},[2739,31417,31418,31426],{},[3353,31419,31420,31422,31424],{},[1153,31421,1291],{},[1565,31423,1589],{},[1565,31425,1589],{},[1150,31427,31428,31430],{},[1153,31429,1372],{},[1565,31431,1589],{},[1153,31433,1669],{"mathvariant":2121},[1159,31435,31436],{"encoding":1161},"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}}.",[1194,31438,31439,31496],{},[1197,31440,31441],{},[1200,31442,31443,31462,31481],{},[1203,31444,31445],{},[1115,31446,31448],{"className":31447},[1138],[1140,31449,31450],{"xmlns":1142},[1144,31451,31452,31460],{},[1147,31453,31454],{},[1150,31455,31456,31458],{},[1153,31457,1563],{},[1565,31459,1567],{},[1159,31461,1570],{"encoding":1161},[1203,31463,31464],{},[1115,31465,31467],{"className":31466},[1138],[1140,31468,31469],{"xmlns":1142},[1144,31470,31471,31479],{},[1147,31472,31473],{},[1150,31474,31475,31477],{},[1153,31476,1563],{},[1565,31478,1794],{},[1159,31480,2996],{"encoding":1161},[1203,31482,27697,31483],{},[1115,31484,31486],{"className":31485},[1138],[1140,31487,31488],{"xmlns":1142},[1144,31489,31490,31494],{},[1147,31491,31492],{},[1153,31493,1605],{},[1159,31495,1605],{"encoding":1161},[1210,31497,31498,31582,31670],{},[1200,31499,31500,31528,31556],{},[1215,31501,31502],{},[1115,31503,31505],{"className":31504},[1138],[1140,31506,31507],{"xmlns":1142},[1144,31508,31509,31525],{},[1147,31510,31511,31517,31519],{},[1150,31512,31513,31515],{},[1153,31514,6893],{},[1565,31516,1794],{},[1242,31518,6737],{},[1150,31520,31521,31523],{},[1153,31522,6893],{},[1565,31524,1589],{},[1159,31526,31527],{"encoding":1161},"\\mu_1 \\le \\mu_2",[1215,31529,31530],{},[1115,31531,31533],{"className":31532},[1138],[1140,31534,31535],{"xmlns":1142},[1144,31536,31537,31553],{},[1147,31538,31539,31545,31547],{},[1150,31540,31541,31543],{},[1153,31542,6893],{},[1565,31544,1794],{},[1242,31546,1689],{},[1150,31548,31549,31551],{},[1153,31550,6893],{},[1565,31552,1589],{},[1159,31554,31555],{"encoding":1161},"\\mu_1 > \\mu_2",[1215,31557,31558],{},[1115,31559,31561],{"className":31560},[1138],[1140,31562,31563],{"xmlns":1142},[1144,31564,31565,31579],{},[1147,31566,31567,31569,31571],{},[1153,31568,7146],{},[1242,31570,3351],{},[3353,31572,31573,31575,31577],{},[1153,31574,7146],{},[1153,31576,1110],{},[1242,31578,31148],{},[1159,31580,31581],{"encoding":1161},"t \\ge t_p^*",[1200,31583,31584,31612,31640],{},[1215,31585,31586],{},[1115,31587,31589],{"className":31588},[1138],[1140,31590,31591],{"xmlns":1142},[1144,31592,31593,31609],{},[1147,31594,31595,31601,31603],{},[1150,31596,31597,31599],{},[1153,31598,6893],{},[1565,31600,1794],{},[1242,31602,1982],{},[1150,31604,31605,31607],{},[1153,31606,6893],{},[1565,31608,1589],{},[1159,31610,31611],{"encoding":1161},"\\mu_1 = \\mu_2",[1215,31613,31614],{},[1115,31615,31617],{"className":31616},[1138],[1140,31618,31619],{"xmlns":1142},[1144,31620,31621,31637],{},[1147,31622,31623,31629,31631],{},[1150,31624,31625,31627],{},[1153,31626,6893],{},[1565,31628,1794],{},[1242,31630,10958],{"mathvariant":2121},[1150,31632,31633,31635],{},[1153,31634,6893],{},[1565,31636,1589],{},[1159,31638,31639],{"encoding":1161},"\\mu_1 \\neq \\mu_2",[1215,31641,31642],{},[1115,31643,31645],{"className":31644},[1138],[1140,31646,31647],{"xmlns":1142},[1144,31648,31649,31667],{},[1147,31650,31651,31653,31655,31657,31659],{},[1242,31652,23022],{"stretchy":1874},[1153,31654,7146],{},[1242,31656,23022],{"stretchy":1874},[1242,31658,3351],{},[3353,31660,31661,31663,31665],{},[1153,31662,7146],{},[1153,31664,1110],{},[1242,31666,31148],{},[1159,31668,31669],{"encoding":1161},"\\lvert t \\rvert \\ge t_p^*",[1200,31671,31672,31700,31728],{},[1215,31673,31674],{},[1115,31675,31677],{"className":31676},[1138],[1140,31678,31679],{"xmlns":1142},[1144,31680,31681,31697],{},[1147,31682,31683,31689,31691],{},[1150,31684,31685,31687],{},[1153,31686,6893],{},[1565,31688,1794],{},[1242,31690,3351],{},[1150,31692,31693,31695],{},[1153,31694,6893],{},[1565,31696,1589],{},[1159,31698,31699],{"encoding":1161},"\\mu_1 \\ge \\mu_2",[1215,31701,31702],{},[1115,31703,31705],{"className":31704},[1138],[1140,31706,31707],{"xmlns":1142},[1144,31708,31709,31725],{},[1147,31710,31711,31717,31719],{},[1150,31712,31713,31715],{},[1153,31714,6893],{},[1565,31716,1794],{},[1242,31718,4332],{},[1150,31720,31721,31723],{},[1153,31722,6893],{},[1565,31724,1589],{},[1159,31726,31727],{"encoding":1161},"\\mu_1 \u003C \\mu_2",[1215,31729,31730],{},[1115,31731,31733],{"className":31732},[1138],[1140,31734,31735],{"xmlns":1142},[1144,31736,31737,31753],{},[1147,31738,31739,31741,31743,31745],{},[1153,31740,7146],{},[1242,31742,6737],{},[1242,31744,3064],{},[3353,31746,31747,31749,31751],{},[1153,31748,7146],{},[1153,31750,1110],{},[1242,31752,31148],{},[1159,31754,31755],{"encoding":1161},"t \\le -t_p^*",[1110,31757,31758,31759,30821,31777,1669],{},"Postup je dvoukrokový: nejprve F-test rozhodne o shodě rozptylů, pak se podle výsledku zvolí ",[1115,31760,31762],{"className":31761},[1138],[1140,31763,31764],{"xmlns":1142},[1144,31765,31766,31774],{},[1147,31767,31768],{},[1150,31769,31770,31772],{},[1153,31771,7104],{},[1565,31773,1794],{},[1159,31775,31776],{"encoding":1161},"T_1",[1115,31778,31780],{"className":31779},[1138],[1140,31781,31782],{"xmlns":1142},[1144,31783,31784,31792],{},[1147,31785,31786],{},[1150,31787,31788,31790],{},[1153,31789,7104],{},[1565,31791,1589],{},[1159,31793,31794],{"encoding":1161},"T_2",[1110,31796,31797],{},[4383,31798],{"alt":31799,"className":31800,"src":31801},"mask-th-f-kriticky-obor",[1130,4387],"\u002Fwiki-assets\u002Fmask-th-f-kriticky-obor.png",[1103,31803,31805,31812,31962,32043,32172,32210,32283,32422],{"className":31804,"dataCallout":3477},[1106,3476],[1110,31806,31808,31811],{"className":31807},[1113],[1115,31809],{"className":31810,"ariaHidden":1121},[1118,3484,1120],"Příklad: Porovnání dvou dodavatelů součástek",[1110,31813,31814,31815,1346,31837,31863,31864,31888,31889,1346,31911,31863,31937,31961],{},"Pevnost plastových dílů: dodavatel A (",[1115,31816,31818],{"className":31817},[1138],[1140,31819,31820],{"xmlns":1142},[1144,31821,31822,31834],{},[1147,31823,31824,31830,31832],{},[1150,31825,31826,31828],{},[1153,31827,1372],{},[1565,31829,1794],{},[1242,31831,1982],{},[1565,31833,9036],{},[1159,31835,31836],{"encoding":1161},"n_1 = 10",[1115,31838,31840],{"className":31839},[1138],[1140,31841,31842],{"xmlns":1142},[1144,31843,31844,31860],{},[1147,31845,31846,31856,31858],{},[1150,31847,31848,31854],{},[1236,31849,31850,31852],{"accent":1121},[1153,31851,1240],{},[1242,31853,1244],{},[1565,31855,1794],{},[1242,31857,1982],{},[1565,31859,3628],{},[1159,31861,31862],{"encoding":1161},"\\bar{x}_1 = 82"," MPa, ",[1115,31865,31867],{"className":31866},[1138],[1140,31868,31869],{"xmlns":1142},[1144,31870,31871,31885],{},[1147,31872,31873,31881,31883],{},[3353,31874,31875,31877,31879],{},[1153,31876,1291],{},[1565,31878,1794],{},[1565,31880,1589],{},[1242,31882,1982],{},[1565,31884,4058],{},[1159,31886,31887],{"encoding":1161},"s_1^2 = 25","), dodavatel B (",[1115,31890,31892],{"className":31891},[1138],[1140,31893,31894],{"xmlns":1142},[1144,31895,31896,31908],{},[1147,31897,31898,31904,31906],{},[1150,31899,31900,31902],{},[1153,31901,1372],{},[1565,31903,1589],{},[1242,31905,1982],{},[1565,31907,2276],{},[1159,31909,31910],{"encoding":1161},"n_2 = 12",[1115,31912,31914],{"className":31913},[1138],[1140,31915,31916],{"xmlns":1142},[1144,31917,31918,31934],{},[1147,31919,31920,31930,31932],{},[1150,31921,31922,31928],{},[1236,31923,31924,31926],{"accent":1121},[1153,31925,1240],{},[1242,31927,1244],{},[1565,31929,1589],{},[1242,31931,1982],{},[1565,31933,14734],{},[1159,31935,31936],{"encoding":1161},"\\bar{x}_2 = 75",[1115,31938,31940],{"className":31939},[1138],[1140,31941,31942],{"xmlns":1142},[1144,31943,31944,31958],{},[1147,31945,31946,31954,31956],{},[3353,31947,31948,31950,31952],{},[1153,31949,1291],{},[1565,31951,1589],{},[1565,31953,1589],{},[1242,31955,1982],{},[1565,31957,22024],{},[1159,31959,31960],{"encoding":1161},"s_2^2 = 16","). Předpokládá se normalita obou rozdělení.",[1110,31963,31964,1654,31967,1346,32005,1669],{},[1540,31965,31966],{},"Krok 1 — F-test rozptylů.",[1115,31968,31970],{"className":31969},[1138],[1140,31971,31972],{"xmlns":1142},[1144,31973,31974,32002],{},[1147,31975,31976,31982,31984,31992,31994],{},[1150,31977,31978,31980],{},[1153,31979,1563],{},[1565,31981,1567],{},[1242,31983,1958],{},[3353,31985,31986,31988,31990],{},[1153,31987,6901],{},[1565,31989,1794],{},[1565,31991,1589],{},[1242,31993,1982],{},[3353,31995,31996,31998,32000],{},[1153,31997,6901],{},[1565,31999,1589],{},[1565,32001,1589],{},[1159,32003,32004],{"encoding":1161},"H_0: \\sigma_1^2 = \\sigma_2^2",[1115,32006,32008],{"className":32007},[1138],[1140,32009,32010],{"xmlns":1142},[1144,32011,32012,32040],{},[1147,32013,32014,32020,32022,32030,32032],{},[1150,32015,32016,32018],{},[1153,32017,1563],{},[1565,32019,1794],{},[1242,32021,1958],{},[3353,32023,32024,32026,32028],{},[1153,32025,6901],{},[1565,32027,1794],{},[1565,32029,1589],{},[1242,32031,10958],{"mathvariant":2121},[3353,32033,32034,32036,32038],{},[1153,32035,6901],{},[1565,32037,1589],{},[1565,32039,1589],{},[1159,32041,32042],{"encoding":1161},"H_1: \\sigma_1^2 \\neq \\sigma_2^2",[1110,32044,32045],{},[1115,32046,32048],{"className":32047},[1138],[1140,32049,32050],{"xmlns":1142},[1144,32051,32052,32169],{},[1147,32053,32054,32056,32058,32064,32066,32069,32071,32073,32075,32077,32079,32081,32083,32096,32098,32100,32102,32104,32106,32109,32112,32114,32116,32118,32131,32133,32135,32137,32139,32141,32143,32145,32147,32149,32151,32154,32156,32158,32160,32162,32164,32167],{},[1153,32055,6718],{},[1242,32057,1982],{},[2739,32059,32060,32062],{},[1565,32061,4058],{},[1565,32063,22024],{},[1242,32065,1982],{},[1565,32067,32068],{},"1,5625",[1242,32070,1797],{"separator":1121},[2012,32072],{"width":2014},[1153,32074,1605],{},[1242,32076,1982],{},[1242,32078,3334],{"stretchy":1874},[1153,32080,6718],{},[1242,32082,6737],{},[1150,32084,32085,32087],{},[1153,32086,6718],{},[1147,32088,32089,32091,32093],{},[1565,32090,1567],{},[1242,32092,1797],{"separator":1121},[1565,32094,32095],{},"025",[1242,32097,1875],{"stretchy":1874},[1565,32099,3595],{},[1242,32101,1797],{"separator":1121},[1565,32103,2255],{},[1242,32105,1886],{"stretchy":1874},[2909,32107,32108],{},"  ",[2909,32110,32111],{},"nebo",[2909,32113,32108],{},[1153,32115,6718],{},[1242,32117,3351],{},[1150,32119,32120,32122],{},[1153,32121,6718],{},[1147,32123,32124,32126,32128],{},[1565,32125,1567],{},[1242,32127,1797],{"separator":1121},[1565,32129,32130],{},"975",[1242,32132,1875],{"stretchy":1874},[1565,32134,3595],{},[1242,32136,1797],{"separator":1121},[1565,32138,2255],{},[1242,32140,1886],{"stretchy":1874},[1242,32142,3394],{"stretchy":1874},[1242,32144,1982],{},[1242,32146,3334],{"stretchy":1874},[1153,32148,6718],{},[1242,32150,6737],{},[1565,32152,32153],{},"0,256",[2909,32155,32108],{},[2909,32157,32111],{},[2909,32159,32108],{},[1153,32161,6718],{},[1242,32163,3351],{},[1565,32165,32166],{},"3,588",[1242,32168,3394],{"stretchy":1874},[1159,32170,32171],{"encoding":1161},"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\\}",[1110,32173,32174,32192,32193,1669],{},[1115,32175,32177],{"className":32176},[1138],[1140,32178,32179],{"xmlns":1142},[1144,32180,32181,32189],{},[1147,32182,32183,32185,32187],{},[1153,32184,6718],{},[1242,32186,27258],{"mathvariant":2121},[1153,32188,1605],{},[1159,32190,32191],{"encoding":1161},"F \\notin W",", rozptyly nezamítáme jako shodné — pro t-test se použije ",[1115,32194,32196],{"className":32195},[1138],[1140,32197,32198],{"xmlns":1142},[1144,32199,32200,32208],{},[1147,32201,32202],{},[1150,32203,32204,32206],{},[1153,32205,7104],{},[1565,32207,1794],{},[1159,32209,31776],{"encoding":1161},[1110,32211,32212,1654,32215,1346,32249,1669],{},[1540,32213,32214],{},"Krok 2 — dvouvýběrový t-test středních hodnot.",[1115,32216,32218],{"className":32217},[1138],[1140,32219,32220],{"xmlns":1142},[1144,32221,32222,32246],{},[1147,32223,32224,32230,32232,32238,32240],{},[1150,32225,32226,32228],{},[1153,32227,1563],{},[1565,32229,1567],{},[1242,32231,1958],{},[1150,32233,32234,32236],{},[1153,32235,6893],{},[1565,32237,1794],{},[1242,32239,1982],{},[1150,32241,32242,32244],{},[1153,32243,6893],{},[1565,32245,1589],{},[1159,32247,32248],{"encoding":1161},"H_0: \\mu_1 = \\mu_2",[1115,32250,32252],{"className":32251},[1138],[1140,32253,32254],{"xmlns":1142},[1144,32255,32256,32280],{},[1147,32257,32258,32264,32266,32272,32274],{},[1150,32259,32260,32262],{},[1153,32261,1563],{},[1565,32263,1794],{},[1242,32265,1958],{},[1150,32267,32268,32270],{},[1153,32269,6893],{},[1565,32271,1794],{},[1242,32273,10958],{"mathvariant":2121},[1150,32275,32276,32278],{},[1153,32277,6893],{},[1565,32279,1589],{},[1159,32281,32282],{"encoding":1161},"H_1: \\mu_1 \\neq \\mu_2",[1110,32284,32285],{},[1115,32286,32288],{"className":32287},[1138],[1140,32289,32290],{"xmlns":1142},[1144,32291,32292,32419],{},[1147,32293,32294,32302,32304,32324,32326,32329,32331,32333,32335,32337,32351,32359,32361,32364,32366,32368,32370,32372,32374,32376,32378,32380,32382,32394,32396,32398,32400,32402,32404,32406,32408,32410,32412,32414,32417],{},[3353,32295,32296,32298,32300],{},[1153,32297,1291],{},[1153,32299,1110],{},[1565,32301,1589],{},[1242,32303,1982],{},[2739,32305,32306,32322],{},[1147,32307,32308,32310,32312,32314,32316,32318,32320],{},[1565,32309,3595],{},[1242,32311,8113],{},[1565,32313,4058],{},[1242,32315,5477],{},[1565,32317,2255],{},[1242,32319,8113],{},[1565,32321,22024],{},[1565,32323,4045],{},[1242,32325,1982],{},[1565,32327,32328],{},"20,05",[1242,32330,1797],{"separator":1121},[2012,32332],{"width":2014},[1153,32334,7146],{},[1242,32336,1982],{},[2739,32338,32339,32347],{},[1147,32340,32341,32343,32345],{},[1565,32342,3628],{},[1242,32344,3064],{},[1565,32346,14734],{},[4453,32348,32349],{},[1565,32350,32328],{},[4453,32352,32353],{},[2739,32354,32355,32357],{},[1565,32356,21884],{},[1565,32358,2390],{},[1242,32360,9443],{},[1565,32362,32363],{},"3,651",[1242,32365,1797],{"separator":1121},[2012,32367],{"width":2014},[1153,32369,1605],{},[1242,32371,1982],{},[1242,32373,3334],{"stretchy":1874},[1242,32375,23022],{"stretchy":1874},[1153,32377,7146],{},[1242,32379,23022],{"stretchy":1874},[1242,32381,3351],{},[1150,32383,32384,32386],{},[1153,32385,7146],{},[1147,32387,32388,32390,32392],{},[1565,32389,1567],{},[1242,32391,1797],{"separator":1121},[1565,32393,32130],{},[1242,32395,1875],{"stretchy":1874},[1565,32397,4045],{},[1242,32399,1886],{"stretchy":1874},[1242,32401,3394],{"stretchy":1874},[1242,32403,1982],{},[1242,32405,3334],{"stretchy":1874},[1242,32407,23022],{"stretchy":1874},[1153,32409,7146],{},[1242,32411,23022],{"stretchy":1874},[1242,32413,3351],{},[1565,32415,32416],{},"2,086",[1242,32418,3394],{"stretchy":1874},[1159,32420,32421],{"encoding":1161},"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\\}",[1110,32423,32424,6006,32441,32458],{},[1115,32425,32427],{"className":32426},[1138],[1140,32428,32429],{"xmlns":1142},[1144,32430,32431,32439],{},[1147,32432,32433,32435,32437],{},[1153,32434,7146],{},[1242,32436,7021],{},[1153,32438,1605],{},[1159,32440,28401],{"encoding":1161},[1115,32442,32444],{"className":32443},[1138],[1140,32445,32446],{"xmlns":1142},[1144,32447,32448,32456],{},[1147,32449,32450],{},[1150,32451,32452,32454],{},[1153,32453,1563],{},[1565,32455,1567],{},[1159,32457,1570],{"encoding":1161},": pevnost součástek od obou dodavatelů se statisticky významně liší.",[3694,32460,32462],{"className":3696,"code":32461,"language":71,"meta":1490,"style":1490},"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",[3470,32463,32464,32482,32502,32517,32552,32583,32588,32593],{"__ignoreMap":1490},[1115,32465,32466,32469,32471,32473,32475,32478,32480],{"class":3702,"line":10},[1115,32467,32468],{"class":3705},"s1",[1115,32470,3710],{"class":3709},[1115,32472,14404],{"class":3724},[1115,32474,25182],{"class":3717},[1115,32476,32477],{"class":3705},"n1",[1115,32479,3710],{"class":3709},[1115,32481,29842],{"class":3724},[1115,32483,32484,32487,32489,32492,32494,32497,32499],{"class":3702,"line":27},[1115,32485,32486],{"class":3705},"s2",[1115,32488,3710],{"class":3709},[1115,32490,32491],{"class":3724}," 16",[1115,32493,25182],{"class":3717},[1115,32495,32496],{"class":3705},"n2",[1115,32498,3710],{"class":3709},[1115,32500,32501],{"class":3724}," 12\n",[1115,32503,32504,32507,32509,32512,32514],{"class":3702,"line":148},[1115,32505,32506],{"class":3705},"Fstat",[1115,32508,3710],{"class":3709},[1115,32510,32511],{"class":3705}," s1",[1115,32513,10078],{"class":3709},[1115,32515,32516],{"class":3705}," s2\n",[1115,32518,32519,32522,32524,32527,32529,32532,32534,32537,32539,32541,32543,32546,32548,32550],{"class":3702,"line":111},[1115,32520,32521],{"class":3705},"F_dolni",[1115,32523,3710],{"class":3709},[1115,32525,32526],{"class":3713}," qf",[1115,32528,1875],{"class":3717},[1115,32530,32531],{"class":3724},"0.025",[1115,32533,1797],{"class":3709},[1115,32535,32536],{"class":3705}," n1",[1115,32538,25519],{"class":3709},[1115,32540,4641],{"class":3724},[1115,32542,1797],{"class":3709},[1115,32544,32545],{"class":3705}," n2",[1115,32547,25519],{"class":3709},[1115,32549,4641],{"class":3724},[1115,32551,3901],{"class":3717},[1115,32553,32554,32557,32559,32561,32563,32565,32567,32569,32571,32573,32575,32577,32579,32581],{"class":3702,"line":96},[1115,32555,32556],{"class":3705},"F_horni",[1115,32558,3710],{"class":3709},[1115,32560,32526],{"class":3713},[1115,32562,1875],{"class":3717},[1115,32564,9092],{"class":3724},[1115,32566,1797],{"class":3709},[1115,32568,32536],{"class":3705},[1115,32570,25519],{"class":3709},[1115,32572,4641],{"class":3724},[1115,32574,1797],{"class":3709},[1115,32576,32545],{"class":3705},[1115,32578,25519],{"class":3709},[1115,32580,4641],{"class":3724},[1115,32582,3901],{"class":3717},[1115,32584,32585],{"class":3702,"line":89},[1115,32586,32587],{"class":3705},"Fstat\n",[1115,32589,32590],{"class":3702,"line":82},[1115,32591,32592],{"class":3705},"F_dolni\n",[1115,32594,32595],{"class":3702,"line":75},[1115,32596,32597],{"class":3705},"F_horni\n",[3694,32599,32602],{"className":32600,"code":32601,"language":3923,"meta":1490},[3921],"[1] 1.5625\n[1] 0.2556189\n[1] 3.587899\n",[3470,32603,32601],{"__ignoreMap":1490},[3694,32605,32607],{"className":3696,"code":32606,"language":71,"meta":1490,"style":1490},"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",[3470,32608,32609,32666,32717,32747,32752,32756],{"__ignoreMap":1490},[1115,32610,32611,32614,32616,32619,32621,32623,32625,32627,32629,32631,32633,32635,32637,32639,32641,32643,32645,32648,32650,32652,32654,32656,32658,32660,32662,32664],{"class":3702,"line":10},[1115,32612,32613],{"class":3705},"sp2",[1115,32615,3710],{"class":3709},[1115,32617,32618],{"class":3717}," ((",[1115,32620,32477],{"class":3705},[1115,32622,25519],{"class":3709},[1115,32624,4641],{"class":3724},[1115,32626,4601],{"class":3717},[1115,32628,4619],{"class":3709},[1115,32630,32511],{"class":3705},[1115,32632,18517],{"class":3709},[1115,32634,4607],{"class":3717},[1115,32636,32496],{"class":3705},[1115,32638,25519],{"class":3709},[1115,32640,4641],{"class":3724},[1115,32642,4601],{"class":3717},[1115,32644,4619],{"class":3709},[1115,32646,32647],{"class":3705}," s2",[1115,32649,4601],{"class":3717},[1115,32651,4604],{"class":3709},[1115,32653,4607],{"class":3717},[1115,32655,32477],{"class":3705},[1115,32657,18517],{"class":3709},[1115,32659,32545],{"class":3705},[1115,32661,25519],{"class":3709},[1115,32663,4180],{"class":3724},[1115,32665,3901],{"class":3717},[1115,32667,32668,32670,32672,32674,32676,32678,32681,32683,32685,32687,32689,32691,32693,32695,32697,32699,32701,32703,32705,32707,32709,32711,32713,32715],{"class":3702,"line":27},[1115,32669,7146],{"class":3705},[1115,32671,3710],{"class":3709},[1115,32673,4607],{"class":3717},[1115,32675,3628],{"class":3724},[1115,32677,25519],{"class":3709},[1115,32679,32680],{"class":3724}," 75",[1115,32682,4601],{"class":3717},[1115,32684,4604],{"class":3709},[1115,32686,4578],{"class":3713},[1115,32688,1875],{"class":3717},[1115,32690,32613],{"class":3705},[1115,32692,4601],{"class":3717},[1115,32694,4619],{"class":3709},[1115,32696,4578],{"class":3713},[1115,32698,1875],{"class":3717},[1115,32700,32477],{"class":3705},[1115,32702,18642],{"class":3709},[1115,32704,32545],{"class":3705},[1115,32706,10078],{"class":3709},[1115,32708,4607],{"class":3717},[1115,32710,32477],{"class":3705},[1115,32712,18517],{"class":3709},[1115,32714,32545],{"class":3705},[1115,32716,9496],{"class":3717},[1115,32718,32719,32721,32723,32725,32727,32729,32731,32733,32735,32737,32739,32741,32743,32745],{"class":3702,"line":148},[1115,32720,28508],{"class":3705},[1115,32722,3710],{"class":3709},[1115,32724,28513],{"class":3713},[1115,32726,1875],{"class":3717},[1115,32728,9092],{"class":3724},[1115,32730,1797],{"class":3709},[1115,32732,10811],{"class":3705},[1115,32734,3797],{"class":3709},[1115,32736,32536],{"class":3705},[1115,32738,18517],{"class":3709},[1115,32740,32545],{"class":3705},[1115,32742,25519],{"class":3709},[1115,32744,4180],{"class":3724},[1115,32746,3901],{"class":3717},[1115,32748,32749],{"class":3702,"line":111},[1115,32750,32751],{"class":3705},"sp2\n",[1115,32753,32754],{"class":3702,"line":96},[1115,32755,28538],{"class":3705},[1115,32757,32758],{"class":3702,"line":89},[1115,32759,28543],{"class":3705},[3694,32761,32764],{"className":32762,"code":32763,"language":3923,"meta":1490},[3921],"[1] 20.05\n[1] 3.65107\n[1] 2.085963\n",[3470,32765,32763],{"__ignoreMap":1490},[1110,32767,32768],{},[4383,32769],{"alt":32770,"className":32771,"src":32772},"mask-th-t-dvoustranny",[1130,4387],"\u002Fwiki-assets\u002Fmask-th-t-dvoustranny.png",[1110,32774,32775,32776,1163,32779,32781,32782,32785,32786,1163,32803,3988,32820,32822,32823,32825],{},"V R provede obě kroky ",[3470,32777,32778],{},"var.test()",[3470,32780,27998],{},". Parametr ",[3470,32783,32784],{},"var.equal"," nastavuje volbu mezi ",[1115,32787,32789],{"className":32788},[1138],[1140,32790,32791],{"xmlns":1142},[1144,32792,32793,32801],{},[1147,32794,32795],{},[1150,32796,32797,32799],{},[1153,32798,7104],{},[1565,32800,1794],{},[1159,32802,31776],{"encoding":1161},[1115,32804,32806],{"className":32805},[1138],[1140,32807,32808],{"xmlns":1142},[1144,32809,32810,32818],{},[1147,32811,32812],{},[1150,32813,32814,32816],{},[1153,32815,7104],{},[1565,32817,1589],{},[1159,32819,31794],{"encoding":1161},[3470,32821,9527],{}," znamená předpoklad shodných rozptylů (podle výsledku F-testu), ",[3470,32824,9530],{}," předpoklad rozdílných rozptylů.",[1110,32827,32828,32831],{},[1540,32829,32830],{},"Kabely A\u002FB."," Pevnost v tahu dvou výrobců (MPa, 12 kabelů od každého):",[3694,32833,32835],{"className":3696,"code":32834,"language":71,"meta":1490,"style":1490},"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",[3470,32836,32837,32903,32966,32982],{"__ignoreMap":1490},[1115,32838,32839,32841,32843,32845,32847,32850,32852,32855,32857,32860,32862,32865,32867,32869,32871,32874,32876,32879,32881,32883,32885,32888,32890,32892,32894,32897,32899,32901],{"class":3702,"line":10},[1115,32840,1775],{"class":3705},[1115,32842,3710],{"class":3709},[1115,32844,3835],{"class":3713},[1115,32846,1875],{"class":3717},[1115,32848,32849],{"class":3724},"313",[1115,32851,1797],{"class":3709},[1115,32853,32854],{"class":3724}," 299",[1115,32856,1797],{"class":3709},[1115,32858,32859],{"class":3724}," 315",[1115,32861,1797],{"class":3709},[1115,32863,32864],{"class":3724}," 312",[1115,32866,1797],{"class":3709},[1115,32868,15372],{"class":3724},[1115,32870,1797],{"class":3709},[1115,32872,32873],{"class":3724}," 308",[1115,32875,1797],{"class":3709},[1115,32877,32878],{"class":3724}," 314",[1115,32880,1797],{"class":3709},[1115,32882,14164],{"class":3724},[1115,32884,1797],{"class":3709},[1115,32886,32887],{"class":3724}," 305",[1115,32889,1797],{"class":3709},[1115,32891,15372],{"class":3724},[1115,32893,1797],{"class":3709},[1115,32895,32896],{"class":3724}," 309",[1115,32898,1797],{"class":3709},[1115,32900,32878],{"class":3724},[1115,32902,3901],{"class":3717},[1115,32904,32905,32907,32909,32911,32913,32916,32918,32921,32923,32925,32927,32929,32931,32934,32936,32939,32941,32943,32945,32947,32949,32951,32953,32956,32958,32960,32962,32964],{"class":3702,"line":27},[1115,32906,1824],{"class":3705},[1115,32908,3710],{"class":3709},[1115,32910,3835],{"class":3713},[1115,32912,1875],{"class":3717},[1115,32914,32915],{"class":3724},"307",[1115,32917,1797],{"class":3709},[1115,32919,32920],{"class":3724}," 322",[1115,32922,1797],{"class":3709},[1115,32924,14164],{"class":3724},[1115,32926,1797],{"class":3709},[1115,32928,14164],{"class":3724},[1115,32930,1797],{"class":3709},[1115,32932,32933],{"class":3724}," 311",[1115,32935,1797],{"class":3709},[1115,32937,32938],{"class":3724}," 316",[1115,32940,1797],{"class":3709},[1115,32942,32859],{"class":3724},[1115,32944,1797],{"class":3709},[1115,32946,32878],{"class":3724},[1115,32948,1797],{"class":3709},[1115,32950,32873],{"class":3724},[1115,32952,1797],{"class":3709},[1115,32954,32955],{"class":3724}," 319",[1115,32957,1797],{"class":3709},[1115,32959,14164],{"class":3724},[1115,32961,1797],{"class":3709},[1115,32963,32864],{"class":3724},[1115,32965,3901],{"class":3717},[1115,32967,32968,32971,32973,32975,32977,32980],{"class":3702,"line":148},[1115,32969,32970],{"class":3713},"var.test",[1115,32972,1875],{"class":3717},[1115,32974,1775],{"class":3705},[1115,32976,1797],{"class":3709},[1115,32978,32979],{"class":3705}," B",[1115,32981,3901],{"class":3717},[1115,32983,32984,32986,32988,32990,32992,32994,32996,32999,33001,33003],{"class":3702,"line":111},[1115,32985,28063],{"class":3713},[1115,32987,1875],{"class":3717},[1115,32989,1775],{"class":3705},[1115,32991,1797],{"class":3709},[1115,32993,32979],{"class":3705},[1115,32995,1797],{"class":3709},[1115,32997,32998],{"class":3705}," var.equal",[1115,33000,3797],{"class":3709},[1115,33002,3810],{"class":3724},[1115,33004,3901],{"class":3717},[3694,33006,33009],{"className":33007,"code":33008,"language":3923,"meta":1490},[3921],"    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",[3470,33010,33008],{"__ignoreMap":1490},[1110,33012,33013,33014,12056,33033,33036,33037,33056,33057,33074],{},"F-test shodu rozptylů nezamítá (",[1115,33015,33017],{"className":33016},[1138],[1140,33018,33019],{"xmlns":1142},[1144,33020,33021,33030],{},[1147,33022,33023,33025,33027],{},[1153,33024,1110],{},[1242,33026,1982],{},[1565,33028,33029],{},"0,7776",[1159,33031,33032],{"encoding":1161},"p = 0{,}7776",[3470,33034,33035],{},"var.equal = TRUE",". Výsledný t-test dává ",[1115,33038,33040],{"className":33039},[1138],[1140,33041,33042],{"xmlns":1142},[1144,33043,33044,33053],{},[1147,33045,33046,33048,33050],{},[1153,33047,1110],{},[1242,33049,1982],{},[1565,33051,33052],{},"0,06932",[1159,33054,33055],{"encoding":1161},"p = 0{,}06932"," — na hladině 5 % se ",[1115,33058,33060],{"className":33059},[1138],[1140,33061,33062],{"xmlns":1142},[1144,33063,33064,33072],{},[1147,33065,33066],{},[1150,33067,33068,33070],{},[1153,33069,1563],{},[1565,33071,1567],{},[1159,33073,1570],{"encoding":1161}," nezamítá, ale hodnota je těsně nad hranicí.",[1110,33076,33077],{},[1540,33078,33079],{},"Výšky chlapců a dívek v páté třídě:",[3694,33081,33083],{"className":3696,"code":33082,"language":71,"meta":1490,"style":1490},"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",[3470,33084,33085,33165,33228,33243],{"__ignoreMap":1490},[1115,33086,33087,33090,33092,33094,33096,33099,33101,33103,33105,33108,33110,33113,33115,33118,33120,33123,33125,33127,33129,33131,33133,33135,33137,33139,33141,33144,33146,33149,33151,33154,33156,33158,33160,33163],{"class":3702,"line":10},[1115,33088,33089],{"class":3705},"boys",[1115,33091,3710],{"class":3709},[1115,33093,3835],{"class":3713},[1115,33095,1875],{"class":3717},[1115,33097,33098],{"class":3724},"130",[1115,33100,1797],{"class":3709},[1115,33102,15321],{"class":3724},[1115,33104,1797],{"class":3709},[1115,33106,33107],{"class":3724}," 136",[1115,33109,1797],{"class":3709},[1115,33111,33112],{"class":3724}," 141",[1115,33114,1797],{"class":3709},[1115,33116,33117],{"class":3724}," 139",[1115,33119,1797],{"class":3709},[1115,33121,33122],{"class":3724}," 133",[1115,33124,1797],{"class":3709},[1115,33126,18474],{"class":3724},[1115,33128,1797],{"class":3709},[1115,33130,14179],{"class":3724},[1115,33132,1797],{"class":3709},[1115,33134,33117],{"class":3724},[1115,33136,1797],{"class":3709},[1115,33138,33107],{"class":3724},[1115,33140,1797],{"class":3709},[1115,33142,33143],{"class":3724}," 138",[1115,33145,1797],{"class":3709},[1115,33147,33148],{"class":3724}," 142",[1115,33150,1797],{"class":3709},[1115,33152,33153],{"class":3724}," 127",[1115,33155,1797],{"class":3709},[1115,33157,33117],{"class":3724},[1115,33159,1797],{"class":3709},[1115,33161,33162],{"class":3724}," 147",[1115,33164,3901],{"class":3717},[1115,33166,33167,33170,33172,33174,33176,33178,33180,33182,33184,33187,33189,33192,33194,33197,33199,33201,33203,33205,33207,33209,33211,33213,33215,33218,33220,33222,33224,33226],{"class":3702,"line":27},[1115,33168,33169],{"class":3705},"girls",[1115,33171,3710],{"class":3709},[1115,33173,3835],{"class":3713},[1115,33175,1875],{"class":3717},[1115,33177,21835],{"class":3724},[1115,33179,1797],{"class":3709},[1115,33181,33112],{"class":3724},[1115,33183,1797],{"class":3709},[1115,33185,33186],{"class":3724}," 143",[1115,33188,1797],{"class":3709},[1115,33190,33191],{"class":3724}," 132",[1115,33193,1797],{"class":3709},[1115,33195,33196],{"class":3724}," 146",[1115,33198,1797],{"class":3709},[1115,33200,33196],{"class":3724},[1115,33202,1797],{"class":3709},[1115,33204,14179],{"class":3724},[1115,33206,1797],{"class":3709},[1115,33208,33112],{"class":3724},[1115,33210,1797],{"class":3709},[1115,33212,33112],{"class":3724},[1115,33214,1797],{"class":3709},[1115,33216,33217],{"class":3724}," 131",[1115,33219,1797],{"class":3709},[1115,33221,33148],{"class":3724},[1115,33223,1797],{"class":3709},[1115,33225,33112],{"class":3724},[1115,33227,3901],{"class":3717},[1115,33229,33230,33232,33234,33236,33238,33241],{"class":3702,"line":148},[1115,33231,32970],{"class":3713},[1115,33233,1875],{"class":3717},[1115,33235,33089],{"class":3705},[1115,33237,1797],{"class":3709},[1115,33239,33240],{"class":3705}," girls",[1115,33242,3901],{"class":3717},[1115,33244,33245,33247,33249,33251,33253,33255,33257,33259,33261,33263],{"class":3702,"line":111},[1115,33246,28063],{"class":3713},[1115,33248,1875],{"class":3717},[1115,33250,33089],{"class":3705},[1115,33252,1797],{"class":3709},[1115,33254,33240],{"class":3705},[1115,33256,1797],{"class":3709},[1115,33258,32998],{"class":3705},[1115,33260,3797],{"class":3709},[1115,33262,3810],{"class":3724},[1115,33264,3901],{"class":3717},[3694,33266,33269],{"className":33267,"code":33268,"language":3923,"meta":1490},[3921],"    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",[3470,33270,33268],{"__ignoreMap":1490},[1110,33272,33013,33273,33292,33293,33295,33296,33315],{},[1115,33274,33276],{"className":33275},[1138],[1140,33277,33278],{"xmlns":1142},[1144,33279,33280,33289],{},[1147,33281,33282,33284,33286],{},[1153,33283,1110],{},[1242,33285,1982],{},[1565,33287,33288],{},"0,6977",[1159,33290,33291],{"encoding":1161},"p = 0{,}6977","), t-test s ",[3470,33294,33035],{}," dává ",[1115,33297,33299],{"className":33298},[1138],[1140,33300,33301],{"xmlns":1142},[1144,33302,33303,33312],{},[1147,33304,33305,33307,33309],{},[1153,33306,1110],{},[1242,33308,1982],{},[1565,33310,33311],{},"0,4883",[1159,33313,33314],{"encoding":1161},"p = 0{,}4883",": na hladině 5 % se rozdíl průměrných výšek chlapců a dívek neprokázal.",[1189,33317,33319],{"id":33318},"testy-dobré-shody-a-normalita","Testy dobré shody a normalita",[1110,33321,33322],{},"Testy dobré shody ověřují, zda datový soubor pochází ze základního souboru s určitým typem rozdělení (normální, exponenciální apod.).",[16749,33324,33326],{"id":33325},"kolmogorovův-smirnovův-test","Kolmogorovův-Smirnovův test",[1110,33328,33329,33330,33353,33354,33373],{},"Univerzální test pro spojitá rozdělení. Porovnává empirickou distribuční funkci ",[1115,33331,33333],{"className":33332},[1138],[1140,33334,33335],{"xmlns":1142},[1144,33336,33337,33351],{},[1147,33338,33339,33345,33347,33349],{},[1150,33340,33341,33343],{},[1153,33342,6718],{},[1153,33344,1372],{},[1242,33346,1875],{"stretchy":1874},[1153,33348,1240],{},[1242,33350,1886],{"stretchy":1874},[1159,33352,11187],{"encoding":1161}," s teoretickou distribuční funkcí ",[1115,33355,33357],{"className":33356},[1138],[1140,33358,33359],{"xmlns":1142},[1144,33360,33361,33371],{},[1147,33362,33363,33365,33367,33369],{},[1153,33364,6718],{},[1242,33366,1875],{"stretchy":1874},[1153,33368,1240],{},[1242,33370,1886],{"stretchy":1874},[1159,33372,7337],{"encoding":1161}," testovaného rozdělení.",[1436,33375,33376,33439,33459,33515],{},[1439,33377,33378,33395,33396,1163,33419,33438],{},[1115,33379,33381],{"className":33380},[1138],[1140,33382,33383],{"xmlns":1142},[1144,33384,33385,33393],{},[1147,33386,33387],{},[1150,33388,33389,33391],{},[1153,33390,1563],{},[1565,33392,1567],{},[1159,33394,1570],{"encoding":1161},": odchylky mezi ",[1115,33397,33399],{"className":33398},[1138],[1140,33400,33401],{"xmlns":1142},[1144,33402,33403,33417],{},[1147,33404,33405,33411,33413,33415],{},[1150,33406,33407,33409],{},[1153,33408,6718],{},[1153,33410,1372],{},[1242,33412,1875],{"stretchy":1874},[1153,33414,1240],{},[1242,33416,1886],{"stretchy":1874},[1159,33418,11187],{"encoding":1161},[1115,33420,33422],{"className":33421},[1138],[1140,33423,33424],{"xmlns":1142},[1144,33425,33426,33436],{},[1147,33427,33428,33430,33432,33434],{},[1153,33429,6718],{},[1242,33431,1875],{"stretchy":1874},[1153,33433,1240],{},[1242,33435,1886],{"stretchy":1874},[1159,33437,7337],{"encoding":1161}," jsou náhodné (data mají dané rozdělení).",[1439,33440,33441,33458],{},[1115,33442,33444],{"className":33443},[1138],[1140,33445,33446],{"xmlns":1142},[1144,33447,33448,33456],{},[1147,33449,33450],{},[1150,33451,33452,33454],{},[1153,33453,1563],{},[1565,33455,1794],{},[1159,33457,2996],{"encoding":1161},": data nemají dané rozdělení.",[1439,33460,33461,33462,1669],{},"Testové kritérium: ",[1115,33463,33465],{"className":33464},[1138],[1140,33466,33467],{"xmlns":1142},[1144,33468,33469,33512],{},[1147,33470,33471,33473,33475,33486,33488,33494,33496,33498,33500,33502,33504,33506,33508,33510],{},[1153,33472,8155],{},[1242,33474,1982],{},[1150,33476,33477,33484],{},[1147,33478,33479,33482],{},[1153,33480,33481],{},"sup",[1242,33483,4491],{},[1153,33485,1240],{},[1242,33487,23022],{"stretchy":1874},[1150,33489,33490,33492],{},[1153,33491,6718],{},[1153,33493,1372],{},[1242,33495,1875],{"stretchy":1874},[1153,33497,1240],{},[1242,33499,1886],{"stretchy":1874},[1242,33501,3064],{},[1153,33503,6718],{},[1242,33505,1875],{"stretchy":1874},[1153,33507,1240],{},[1242,33509,1886],{"stretchy":1874},[1242,33511,23022],{"stretchy":1874},[1159,33513,33514],{"encoding":1161},"D = \\sup_x \\lvert F_n(x) - F(x) \\rvert",[1439,33516,3318,33517,33561,33562,33580,33581,1669],{},[1115,33518,33520],{"className":33519},[1138],[1140,33521,33522],{"xmlns":1142},[1144,33523,33524,33558],{},[1147,33525,33526,33532,33534,33536,33538,33540,33542,33544,33550,33552,33554,33556],{},[1150,33527,33528,33530],{},[1153,33529,1605],{},[1153,33531,3365],{},[1242,33533,1982],{},[1242,33535,3334],{"stretchy":1874},[1153,33537,7798],{},[1242,33539,1958],{},[1153,33541,7798],{},[1242,33543,1689],{},[1150,33545,33546,33548],{},[1153,33547,8155],{},[1153,33549,3365],{},[1242,33551,1875],{"stretchy":1874},[1153,33553,1372],{},[1242,33555,1886],{"stretchy":1874},[1242,33557,3394],{"stretchy":1874},[1159,33559,33560],{"encoding":1161},"W_\\alpha = \\{d : d > D_\\alpha(n)\\}","; pro ",[1115,33563,33565],{"className":33564},[1138],[1140,33566,33567],{"xmlns":1142},[1144,33568,33569,33577],{},[1147,33570,33571,33573,33575],{},[1153,33572,1372],{},[1242,33574,1689],{},[1565,33576,22034],{},[1159,33578,33579],{"encoding":1161},"n>30"," se kritická hodnota aproximuje zlomkem ",[1115,33582,33584],{"className":33583},[1138],[1140,33585,33586],{"xmlns":1142},[1144,33587,33588,33599],{},[1147,33589,33590,33593,33595],{},[1565,33591,33592],{},"1,36",[1153,33594,4604],{"mathvariant":2121},[4453,33596,33597],{},[1153,33598,1372],{},[1159,33600,33601],{"encoding":1161},"1{,}36\u002F\\sqrt{n}",[1110,33603,27995,33604,33607,33608,33610,33611,1346,33614,33617],{},[3470,33605,33606],{},"ks.test()",", kde se za ",[3470,33609,7337],{}," dosadí příslušná distribuční funkce (",[3470,33612,33613],{},"\"pnorm\"",[3470,33615,33616],{},"\"pexp\"",", …) s jejími parametry:",[3694,33619,33621],{"className":3696,"code":33620,"language":71,"meta":1490,"style":1490},"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",[3470,33622,33623,33673],{"__ignoreMap":1490},[1115,33624,33625,33627,33629,33631,33633,33635,33637,33639,33641,33643,33645,33647,33649,33651,33653,33655,33657,33659,33661,33663,33665,33667,33669,33671],{"class":3702,"line":10},[1115,33626,28709],{"class":3705},[1115,33628,3710],{"class":3709},[1115,33630,3835],{"class":3713},[1115,33632,1875],{"class":3717},[1115,33634,11988],{"class":3724},[1115,33636,1797],{"class":3709},[1115,33638,11993],{"class":3724},[1115,33640,1797],{"class":3709},[1115,33642,11998],{"class":3724},[1115,33644,1797],{"class":3709},[1115,33646,12003],{"class":3724},[1115,33648,1797],{"class":3709},[1115,33650,11998],{"class":3724},[1115,33652,1797],{"class":3709},[1115,33654,11998],{"class":3724},[1115,33656,1797],{"class":3709},[1115,33658,12016],{"class":3724},[1115,33660,1797],{"class":3709},[1115,33662,12021],{"class":3724},[1115,33664,1797],{"class":3709},[1115,33666,11993],{"class":3724},[1115,33668,1797],{"class":3709},[1115,33670,11993],{"class":3724},[1115,33672,3901],{"class":3717},[1115,33674,33675,33678,33680,33682,33684,33687,33689,33691,33693,33695,33697,33699,33701,33703,33705],{"class":3702,"line":27},[1115,33676,33677],{"class":3713},"ks.test",[1115,33679,1875],{"class":3717},[1115,33681,28709],{"class":3705},[1115,33683,1797],{"class":3709},[1115,33685,33686],{"class":3840}," \"pnorm\"",[1115,33688,1797],{"class":3709},[1115,33690,9234],{"class":3713},[1115,33692,1875],{"class":3717},[1115,33694,28709],{"class":3705},[1115,33696,1886],{"class":3717},[1115,33698,1797],{"class":3709},[1115,33700,9244],{"class":3713},[1115,33702,1875],{"class":3717},[1115,33704,28709],{"class":3705},[1115,33706,9496],{"class":3717},[3694,33708,33711],{"className":33709,"code":33710,"language":3923,"meta":1490},[3921],"    Asymptotic one-sample Kolmogorov-Smirnov test\n\ndata:  x3\nD = 0.18469, p-value = 0.8847\nalternative hypothesis: two-sided\n",[3470,33712,33710],{"__ignoreMap":1490},[1110,33714,33715,33738],{},[1115,33716,33718],{"className":33717},[1138],[1140,33719,33720],{"xmlns":1142},[1144,33721,33722,33735],{},[1147,33723,33724,33726,33728,33731,33733],{},[1153,33725,1110],{},[1242,33727,1982],{},[1565,33729,33730],{},"0,8847",[1242,33732,1689],{},[1565,33734,3984],{},[1159,33736,33737],{"encoding":1161},"p = 0{,}8847 > 0{,}05",": odpad materiálu je slučitelný s normálním rozdělením se stejným průměrem a směrodatnou odchylkou.",[16749,33740,33742],{"id":33741},"shapiro-wilkův-test","Shapiro-Wilkův test",[1110,33744,33745],{},"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.",[1436,33747,33748,33768,33788],{},[1439,33749,33750,33767],{},[1115,33751,33753],{"className":33752},[1138],[1140,33754,33755],{"xmlns":1142},[1144,33756,33757,33765],{},[1147,33758,33759],{},[1150,33760,33761,33763],{},[1153,33762,1563],{},[1565,33764,1567],{},[1159,33766,1570],{"encoding":1161},": data mají normální rozdělení.",[1439,33769,33770,33787],{},[1115,33771,33773],{"className":33772},[1138],[1140,33774,33775],{"xmlns":1142},[1144,33776,33777,33785],{},[1147,33778,33779],{},[1150,33780,33781,33783],{},[1153,33782,1563],{},[1565,33784,1794],{},[1159,33786,2996],{"encoding":1161},": data nemají normální rozdělení.",[1439,33789,33790,33791,33817],{},"Testová statistika ",[1115,33792,33794],{"className":33793},[1138],[1140,33795,33796],{"xmlns":1142},[1144,33797,33798,33814],{},[1147,33799,33800,33802,33804,33806,33808,33810,33812],{},[1153,33801,1605],{},[1242,33803,7021],{},[1242,33805,8428],{"stretchy":1874},[1565,33807,1567],{},[1242,33809,1797],{"separator":1121},[1565,33811,1794],{},[1242,33813,7445],{"stretchy":1874},[1159,33815,33816],{"encoding":1161},"W \\in \\langle 0,1 \\rangle","; hodnoty blízké 1 indikují shodu s normalitou.",[1110,33819,33820,33821,33834,33835,1654,33855,33872,33873,1654,33893,33910],{},"Na rozdíl od ostatních testů v této kapitole se Shapiro-Wilkův test v praxi vyhodnocuje pouze přes p-hodnotu (tabulka kritických hodnot pro ",[1115,33822,33824],{"className":33823},[1138],[1140,33825,33826],{"xmlns":1142},[1144,33827,33828,33832],{},[1147,33829,33830],{},[1153,33831,1605],{},[1159,33833,1605],{"encoding":1161}," se běžně neudává): ",[1115,33836,33838],{"className":33837},[1138],[1140,33839,33840],{"xmlns":1142},[1144,33841,33842,33852],{},[1147,33843,33844,33846,33848,33850],{},[1153,33845,1110],{},[1242,33847,3351],{},[1153,33849,3365],{},[1242,33851,7551],{},[1159,33853,33854],{"encoding":1161},"p \\ge \\alpha \\Rightarrow",[1115,33856,33858],{"className":33857},[1138],[1140,33859,33860],{"xmlns":1142},[1144,33861,33862,33870],{},[1147,33863,33864],{},[1150,33865,33866,33868],{},[1153,33867,1563],{},[1565,33869,1567],{},[1159,33871,1570],{"encoding":1161}," nezamítáme (normalitu lze předpokládat); ",[1115,33874,33876],{"className":33875},[1138],[1140,33877,33878],{"xmlns":1142},[1144,33879,33880,33890],{},[1147,33881,33882,33884,33886,33888],{},[1153,33883,1110],{},[1242,33885,4332],{},[1153,33887,3365],{},[1242,33889,7551],{},[1159,33891,33892],{"encoding":1161},"p \u003C \\alpha \\Rightarrow",[1115,33894,33896],{"className":33895},[1138],[1140,33897,33898],{"xmlns":1142},[1144,33899,33900,33908],{},[1147,33901,33902],{},[1150,33903,33904,33906],{},[1153,33905,1563],{},[1565,33907,1567],{},[1159,33909,1570],{"encoding":1161}," zamítáme (předpoklad normality je porušen).",[3694,33912,33914],{"className":3696,"code":33913,"language":71,"meta":1490,"style":1490},"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",[3470,33915,33916,33970],{"__ignoreMap":1490},[1115,33917,33918,33920,33922,33924,33926,33928,33930,33932,33934,33936,33938,33940,33942,33944,33946,33948,33950,33952,33954,33956,33958,33960,33962,33964,33966,33968],{"class":3702,"line":10},[1115,33919,28577],{"class":3705},[1115,33921,3710],{"class":3709},[1115,33923,3835],{"class":3713},[1115,33925,1875],{"class":3717},[1115,33927,28586],{"class":3724},[1115,33929,1797],{"class":3709},[1115,33931,28591],{"class":3724},[1115,33933,1797],{"class":3709},[1115,33935,28596],{"class":3724},[1115,33937,1797],{"class":3709},[1115,33939,28601],{"class":3724},[1115,33941,1797],{"class":3709},[1115,33943,28606],{"class":3724},[1115,33945,1797],{"class":3709},[1115,33947,28611],{"class":3724},[1115,33949,1797],{"class":3709},[1115,33951,28601],{"class":3724},[1115,33953,1797],{"class":3709},[1115,33955,28620],{"class":3724},[1115,33957,1797],{"class":3709},[1115,33959,28606],{"class":3724},[1115,33961,1797],{"class":3709},[1115,33963,28629],{"class":3724},[1115,33965,1797],{"class":3709},[1115,33967,28601],{"class":3724},[1115,33969,3901],{"class":3717},[1115,33971,33972,33974,33976,33978],{"class":3702,"line":27},[1115,33973,17578],{"class":3713},[1115,33975,1875],{"class":3717},[1115,33977,28577],{"class":3705},[1115,33979,3901],{"class":3717},[3694,33981,33984],{"className":33982,"code":33983,"language":3923,"meta":1490},[3921],"    Shapiro-Wilk normality test\n\ndata:  x2\nW = 0.96022, p-value = 0.7744\n",[3470,33985,33983],{"__ignoreMap":1490},[1110,33987,33988,33989,34008],{},"U dat o životnosti baterií se normalita nezamítá (",[1115,33990,33992],{"className":33991},[1138],[1140,33993,33994],{"xmlns":1142},[1144,33995,33996,34005],{},[1147,33997,33998,34000,34002],{},[1153,33999,1110],{},[1242,34001,1982],{},[1565,34003,34004],{},"0,7744",[1159,34006,34007],{"encoding":1161},"p = 0{,}7744","), předpoklad t-testu je tedy splněn.",[1103,34010,34012,34019,34022,34389,34395],{"className":34011,"dataCallout":3477},[1106,3476],[1110,34013,34015,34018],{"className":34014},[1113],[1115,34016],{"className":34017,"ariaHidden":1121},[1118,3484,1120],"Příklad: Doba do poruchy výrobku",[1110,34020,34021],{},"Zkoušky životnosti nového výrobku daly soubor 68 hodnot doby do poruchy (v minutách). Odhadněte charakteristiky a zákon rozdělení.",[3694,34023,34025],{"className":3696,"code":34024,"language":71,"meta":1490,"style":1490},"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",[3470,34026,34027,34118,34196,34284,34318,34328,34338,34348,34358],{"__ignoreMap":1490},[1115,34028,34029,34031,34033,34035,34037,34039,34041,34043,34045,34047,34049,34051,34053,34055,34057,34059,34061,34063,34065,34067,34069,34071,34073,34075,34077,34080,34082,34084,34086,34088,34090,34092,34094,34096,34098,34100,34102,34104,34106,34108,34110,34112,34114,34116],{"class":3702,"line":10},[1115,34030,14078],{"class":3705},[1115,34032,3710],{"class":3709},[1115,34034,3835],{"class":3713},[1115,34036,1875],{"class":3717},[1115,34038,14087],{"class":3724},[1115,34040,1797],{"class":3709},[1115,34042,14092],{"class":3724},[1115,34044,1797],{"class":3709},[1115,34046,14097],{"class":3724},[1115,34048,1797],{"class":3709},[1115,34050,14102],{"class":3724},[1115,34052,1797],{"class":3709},[1115,34054,9480],{"class":3724},[1115,34056,1797],{"class":3709},[1115,34058,4180],{"class":3724},[1115,34060,1797],{"class":3709},[1115,34062,3734],{"class":3724},[1115,34064,1797],{"class":3709},[1115,34066,14119],{"class":3724},[1115,34068,1797],{"class":3709},[1115,34070,9997],{"class":3724},[1115,34072,1797],{"class":3709},[1115,34074,14128],{"class":3724},[1115,34076,1797],{"class":3709},[1115,34078,34079],{"class":3724}," 367",[1115,34081,1797],{"class":3709},[1115,34083,14140],{"class":3724},[1115,34085,1797],{"class":3709},[1115,34087,14145],{"class":3724},[1115,34089,1797],{"class":3709},[1115,34091,14150],{"class":3724},[1115,34093,1797],{"class":3709},[1115,34095,3752],{"class":3724},[1115,34097,1797],{"class":3709},[1115,34099,14159],{"class":3724},[1115,34101,1797],{"class":3709},[1115,34103,14164],{"class":3724},[1115,34105,1797],{"class":3709},[1115,34107,14169],{"class":3724},[1115,34109,1797],{"class":3709},[1115,34111,14174],{"class":3724},[1115,34113,1797],{"class":3709},[1115,34115,14179],{"class":3724},[1115,34117,3737],{"class":3709},[1115,34119,34120,34122,34124,34126,34128,34130,34132,34134,34136,34138,34140,34142,34144,34146,34148,34150,34152,34154,34156,34158,34160,34162,34164,34166,34168,34170,34172,34174,34176,34178,34180,34182,34184,34186,34188,34190,34192,34194],{"class":3702,"line":27},[1115,34121,14186],{"class":3724},[1115,34123,1797],{"class":3709},[1115,34125,14191],{"class":3724},[1115,34127,1797],{"class":3709},[1115,34129,14196],{"class":3724},[1115,34131,1797],{"class":3709},[1115,34133,14201],{"class":3724},[1115,34135,1797],{"class":3709},[1115,34137,14206],{"class":3724},[1115,34139,1797],{"class":3709},[1115,34141,3752],{"class":3724},[1115,34143,1797],{"class":3709},[1115,34145,14215],{"class":3724},[1115,34147,1797],{"class":3709},[1115,34149,3734],{"class":3724},[1115,34151,1797],{"class":3709},[1115,34153,14224],{"class":3724},[1115,34155,1797],{"class":3709},[1115,34157,14229],{"class":3724},[1115,34159,1797],{"class":3709},[1115,34161,15321],{"class":3724},[1115,34163,1797],{"class":3709},[1115,34165,14241],{"class":3724},[1115,34167,1797],{"class":3709},[1115,34169,14246],{"class":3724},[1115,34171,1797],{"class":3709},[1115,34173,14140],{"class":3724},[1115,34175,1797],{"class":3709},[1115,34177,14255],{"class":3724},[1115,34179,1797],{"class":3709},[1115,34181,14260],{"class":3724},[1115,34183,1797],{"class":3709},[1115,34185,14265],{"class":3724},[1115,34187,1797],{"class":3709},[1115,34189,14270],{"class":3724},[1115,34191,1797],{"class":3709},[1115,34193,14275],{"class":3724},[1115,34195,3737],{"class":3709},[1115,34197,34198,34200,34202,34205,34207,34209,34211,34213,34215,34217,34219,34221,34223,34225,34227,34229,34231,34233,34235,34237,34239,34241,34243,34246,34248,34250,34252,34254,34256,34258,34260,34262,34264,34266,34268,34270,34272,34274,34276,34278,34280,34282],{"class":3702,"line":148},[1115,34199,14385],{"class":3724},[1115,34201,1797],{"class":3709},[1115,34203,34204],{"class":3724}," 74",[1115,34206,1797],{"class":3709},[1115,34208,14292],{"class":3724},[1115,34210,1797],{"class":3709},[1115,34212,14297],{"class":3724},[1115,34214,1797],{"class":3709},[1115,34216,14302],{"class":3724},[1115,34218,1797],{"class":3709},[1115,34220,14307],{"class":3724},[1115,34222,1797],{"class":3709},[1115,34224,14224],{"class":3724},[1115,34226,1797],{"class":3709},[1115,34228,14316],{"class":3724},[1115,34230,1797],{"class":3709},[1115,34232,10857],{"class":3724},[1115,34234,1797],{"class":3709},[1115,34236,14325],{"class":3724},[1115,34238,1797],{"class":3709},[1115,34240,14330],{"class":3724},[1115,34242,1797],{"class":3709},[1115,34244,34245],{"class":3724}," 194",[1115,34247,1797],{"class":3709},[1115,34249,4145],{"class":3724},[1115,34251,1797],{"class":3709},[1115,34253,14346],{"class":3724},[1115,34255,1797],{"class":3709},[1115,34257,14351],{"class":3724},[1115,34259,1797],{"class":3709},[1115,34261,14356],{"class":3724},[1115,34263,1797],{"class":3709},[1115,34265,14307],{"class":3724},[1115,34267,1797],{"class":3709},[1115,34269,9997],{"class":3724},[1115,34271,1797],{"class":3709},[1115,34273,4180],{"class":3724},[1115,34275,1797],{"class":3709},[1115,34277,14373],{"class":3724},[1115,34279,1797],{"class":3709},[1115,34281,14378],{"class":3724},[1115,34283,3737],{"class":3709},[1115,34285,34286,34288,34290,34292,34294,34296,34298,34300,34302,34304,34306,34308,34310,34312,34314,34316],{"class":3702,"line":111},[1115,34287,14385],{"class":3724},[1115,34289,1797],{"class":3709},[1115,34291,3729],{"class":3724},[1115,34293,1797],{"class":3709},[1115,34295,14394],{"class":3724},[1115,34297,1797],{"class":3709},[1115,34299,14399],{"class":3724},[1115,34301,1797],{"class":3709},[1115,34303,14404],{"class":3724},[1115,34305,1797],{"class":3709},[1115,34307,14409],{"class":3724},[1115,34309,1797],{"class":3709},[1115,34311,14140],{"class":3724},[1115,34313,1797],{"class":3709},[1115,34315,14418],{"class":3724},[1115,34317,3901],{"class":3717},[1115,34319,34320,34322,34324,34326],{"class":3702,"line":96},[1115,34321,12140],{"class":3713},[1115,34323,1875],{"class":3717},[1115,34325,14078],{"class":3705},[1115,34327,3901],{"class":3717},[1115,34329,34330,34332,34334,34336],{"class":3702,"line":89},[1115,34331,12162],{"class":3713},[1115,34333,1875],{"class":3717},[1115,34335,14078],{"class":3705},[1115,34337,3901],{"class":3717},[1115,34339,34340,34342,34344,34346],{"class":3702,"line":82},[1115,34341,12862],{"class":3713},[1115,34343,1875],{"class":3717},[1115,34345,14078],{"class":3705},[1115,34347,3901],{"class":3717},[1115,34349,34350,34352,34354,34356],{"class":3702,"line":75},[1115,34351,17578],{"class":3713},[1115,34353,1875],{"class":3717},[1115,34355,14078],{"class":3705},[1115,34357,3901],{"class":3717},[1115,34359,34360,34362,34364,34366,34368,34371,34373,34375,34377,34379,34381,34383,34385,34387],{"class":3702,"line":3891},[1115,34361,33677],{"class":3713},[1115,34363,1875],{"class":3717},[1115,34365,14078],{"class":3705},[1115,34367,1797],{"class":3709},[1115,34369,34370],{"class":3840}," \"pexp\"",[1115,34372,1797],{"class":3709},[1115,34374,10071],{"class":3705},[1115,34376,3797],{"class":3709},[1115,34378,4641],{"class":3724},[1115,34380,10078],{"class":3709},[1115,34382,9234],{"class":3713},[1115,34384,1875],{"class":3717},[1115,34386,14078],{"class":3705},[1115,34388,9496],{"class":3717},[3694,34390,34393],{"className":34391,"code":34392,"language":3923,"meta":1490},[3921],"[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",[3470,34394,34392],{"__ignoreMap":1490},[1110,34396,34397,34398,34417,34418,34435,34436,34455],{},"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 (",[1115,34399,34401],{"className":34400},[1138],[1140,34402,34403],{"xmlns":1142},[1144,34404,34405,34414],{},[1147,34406,34407,34409,34411],{},[1153,34408,1110],{},[1242,34410,4332],{},[1565,34412,34413],{},"0,0001",[1159,34415,34416],{"encoding":1161},"p \u003C 0{,}0001","), zatímco Kolmogorov-Smirnovův test proti exponenciálnímu rozdělení se střední hodnotou ",[1115,34419,34421],{"className":34420},[1138],[1140,34422,34423],{"xmlns":1142},[1144,34424,34425,34433],{},[1147,34426,34427],{},[1236,34428,34429,34431],{"accent":1121},[1153,34430,1240],{},[1242,34432,1244],{},[1159,34434,21563],{"encoding":1161}," shodu nezamítá (",[1115,34437,34439],{"className":34438},[1138],[1140,34440,34441],{"xmlns":1142},[1144,34442,34443,34452],{},[1147,34444,34445,34447,34449],{},[1153,34446,1110],{},[1242,34448,1982],{},[1565,34450,34451],{},"0,8421",[1159,34453,34454],{"encoding":1161},"p = 0{,}8421","): data odpovídají spíše exponenciálnímu rozdělení než normálnímu.",[1110,34457,34458],{},[4383,34459],{"alt":34460,"className":34461,"src":34462},"mask-th-exponencialni-shoda",[1130,4387],"\u002Fwiki-assets\u002Fmask-th-exponencialni-shoda.png",[1189,34464,34466],{"id":34465},"neparametrické-testy","Neparametrické testy",[1110,34468,34469,34470,4607,34472,34496],{},"Když předpoklad normality neplatí, nahrazují t-testy jejich neparametrické obdoby — Wilcoxonovy testy posuzují ",[1540,34471,11553],{},[1115,34473,34475],{"className":34474},[1138],[1140,34476,34477],{"xmlns":1142},[1144,34478,34479,34493],{},[1147,34480,34481],{},[1150,34482,34483,34485],{},[1153,34484,1240],{},[1147,34486,34487,34489,34491],{},[1565,34488,1567],{},[1242,34490,1797],{"separator":1121},[1565,34492,9929],{},[1159,34494,34495],{"encoding":1161},"x_{0,5}",") místo střední hodnoty a nevyžadují normalitu dat.",[16749,34498,34500],{"id":34499},"wilcoxonovy-testy","Wilcoxonovy testy",[1194,34502,34503,34548],{},[1197,34504,34505],{},[1200,34506,34507,34526,34545],{},[1203,34508,34509],{},[1115,34510,34512],{"className":34511},[1138],[1140,34513,34514],{"xmlns":1142},[1144,34515,34516,34524],{},[1147,34517,34518],{},[1150,34519,34520,34522],{},[1153,34521,1563],{},[1565,34523,1567],{},[1159,34525,1570],{"encoding":1161},[1203,34527,34528],{},[1115,34529,34531],{"className":34530},[1138],[1140,34532,34533],{"xmlns":1142},[1144,34534,34535,34543],{},[1147,34536,34537],{},[1150,34538,34539,34541],{},[1153,34540,1563],{},[1565,34542,1794],{},[1159,34544,2996],{"encoding":1161},[1203,34546,34547],{},"Příkaz v R",[1210,34549,34550,34617,34684],{},[1200,34551,34552,34582,34612],{},[1215,34553,34554],{},[1115,34555,34557],{"className":34556},[1138],[1140,34558,34559],{"xmlns":1142},[1144,34560,34561,34579],{},[1147,34562,34563,34575,34577],{},[1150,34564,34565,34567],{},[1153,34566,1240],{},[1147,34568,34569,34571,34573],{},[1565,34570,1567],{},[1242,34572,1797],{"separator":1121},[1565,34574,9929],{},[1242,34576,6737],{},[1153,34578,1343],{},[1159,34580,34581],{"encoding":1161},"x_{0,5} \\le c",[1215,34583,34584],{},[1115,34585,34587],{"className":34586},[1138],[1140,34588,34589],{"xmlns":1142},[1144,34590,34591,34609],{},[1147,34592,34593,34605,34607],{},[1150,34594,34595,34597],{},[1153,34596,1240],{},[1147,34598,34599,34601,34603],{},[1565,34600,1567],{},[1242,34602,1797],{"separator":1121},[1565,34604,9929],{},[1242,34606,1689],{},[1153,34608,1343],{},[1159,34610,34611],{"encoding":1161},"x_{0,5} > c",[1215,34613,34614],{},[3470,34615,34616],{},"wilcox.test(x, alternative = \"greater\", mu = c)",[1200,34618,34619,34649,34679],{},[1215,34620,34621],{},[1115,34622,34624],{"className":34623},[1138],[1140,34625,34626],{"xmlns":1142},[1144,34627,34628,34646],{},[1147,34629,34630,34642,34644],{},[1150,34631,34632,34634],{},[1153,34633,1240],{},[1147,34635,34636,34638,34640],{},[1565,34637,1567],{},[1242,34639,1797],{"separator":1121},[1565,34641,9929],{},[1242,34643,1982],{},[1153,34645,1343],{},[1159,34647,34648],{"encoding":1161},"x_{0,5} = c",[1215,34650,34651],{},[1115,34652,34654],{"className":34653},[1138],[1140,34655,34656],{"xmlns":1142},[1144,34657,34658,34676],{},[1147,34659,34660,34672,34674],{},[1150,34661,34662,34664],{},[1153,34663,1240],{},[1147,34665,34666,34668,34670],{},[1565,34667,1567],{},[1242,34669,1797],{"separator":1121},[1565,34671,9929],{},[1242,34673,10958],{"mathvariant":2121},[1153,34675,1343],{},[1159,34677,34678],{"encoding":1161},"x_{0,5} \\neq c",[1215,34680,34681],{},[3470,34682,34683],{},"wilcox.test(x, alternative = \"two.sided\", mu = c)",[1200,34685,34686,34716,34746],{},[1215,34687,34688],{},[1115,34689,34691],{"className":34690},[1138],[1140,34692,34693],{"xmlns":1142},[1144,34694,34695,34713],{},[1147,34696,34697,34709,34711],{},[1150,34698,34699,34701],{},[1153,34700,1240],{},[1147,34702,34703,34705,34707],{},[1565,34704,1567],{},[1242,34706,1797],{"separator":1121},[1565,34708,9929],{},[1242,34710,3351],{},[1153,34712,1343],{},[1159,34714,34715],{"encoding":1161},"x_{0,5} \\ge c",[1215,34717,34718],{},[1115,34719,34721],{"className":34720},[1138],[1140,34722,34723],{"xmlns":1142},[1144,34724,34725,34743],{},[1147,34726,34727,34739,34741],{},[1150,34728,34729,34731],{},[1153,34730,1240],{},[1147,34732,34733,34735,34737],{},[1565,34734,1567],{},[1242,34736,1797],{"separator":1121},[1565,34738,9929],{},[1242,34740,4332],{},[1153,34742,1343],{},[1159,34744,34745],{"encoding":1161},"x_{0,5} \u003C c",[1215,34747,34748],{},[3470,34749,34750],{},"wilcox.test(x, alternative = \"less\", mu = c)",[1110,34752,34753,34756,34757,1669],{},[1464,34754,34755],{},"Jednovýběrový Wilcoxonův test"," (obdoba t-testu) posuzuje odchylku mediánu od konstanty ",[1115,34758,34760],{"className":34759},[1138],[1140,34761,34762],{"xmlns":1142},[1144,34763,34764,34768],{},[1147,34765,34766],{},[1153,34767,1343],{},[1159,34769,1343],{"encoding":1161},[1110,34771,34772,34775,34776,8837,34814,34827,34828,1669],{},[1464,34773,34774],{},"Jednovýběrový Wilcoxonův test na diferencích"," (obdoba párového t-testu) posuzuje odchylku mediánu rozdílu ",[1115,34777,34779],{"className":34778},[1138],[1140,34780,34781],{"xmlns":1142},[1144,34782,34783,34811],{},[1147,34784,34785,34797,34799],{},[1150,34786,34787,34789],{},[1153,34788,1240],{},[1147,34790,34791,34793,34795],{},[1565,34792,1567],{},[1242,34794,1797],{"separator":1121},[1565,34796,9929],{},[1242,34798,3064],{},[1150,34800,34801,34803],{},[1153,34802,7132],{},[1147,34804,34805,34807,34809],{},[1565,34806,1567],{},[1242,34808,1797],{"separator":1121},[1565,34810,9929],{},[1159,34812,34813],{"encoding":1161},"x_{0,5}-y_{0,5}",[1115,34815,34817],{"className":34816},[1138],[1140,34818,34819],{"xmlns":1142},[1144,34820,34821,34825],{},[1147,34822,34823],{},[1153,34824,1343],{},[1159,34826,1343],{"encoding":1161},"; v R se volá se stejnými argumenty jako výše a navíc ",[3470,34829,34830],{},"paired = TRUE",[1110,34832,34833,34836,34837,34839],{},[1464,34834,34835],{},"Dvouvýběrový Wilcoxonův test"," (obdoba dvouvýběrového t-testu) posuzuje odchylku mediánů dvou nezávislých výběrů; argument ",[3470,34838,25446],{}," odpadá. Pro výšky chlapců a dívek z příkladu výše:",[3694,34841,34843],{"className":3696,"code":34842,"language":71,"meta":1490,"style":1490},"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",[3470,34844,34845,34915,34973],{"__ignoreMap":1490},[1115,34846,34847,34849,34851,34853,34855,34857,34859,34861,34863,34865,34867,34869,34871,34873,34875,34877,34879,34881,34883,34885,34887,34889,34891,34893,34895,34897,34899,34901,34903,34905,34907,34909,34911,34913],{"class":3702,"line":10},[1115,34848,33089],{"class":3705},[1115,34850,3710],{"class":3709},[1115,34852,3835],{"class":3713},[1115,34854,1875],{"class":3717},[1115,34856,33098],{"class":3724},[1115,34858,1797],{"class":3709},[1115,34860,15321],{"class":3724},[1115,34862,1797],{"class":3709},[1115,34864,33107],{"class":3724},[1115,34866,1797],{"class":3709},[1115,34868,33112],{"class":3724},[1115,34870,1797],{"class":3709},[1115,34872,33117],{"class":3724},[1115,34874,1797],{"class":3709},[1115,34876,33122],{"class":3724},[1115,34878,1797],{"class":3709},[1115,34880,18474],{"class":3724},[1115,34882,1797],{"class":3709},[1115,34884,14179],{"class":3724},[1115,34886,1797],{"class":3709},[1115,34888,33117],{"class":3724},[1115,34890,1797],{"class":3709},[1115,34892,33107],{"class":3724},[1115,34894,1797],{"class":3709},[1115,34896,33143],{"class":3724},[1115,34898,1797],{"class":3709},[1115,34900,33148],{"class":3724},[1115,34902,1797],{"class":3709},[1115,34904,33153],{"class":3724},[1115,34906,1797],{"class":3709},[1115,34908,33117],{"class":3724},[1115,34910,1797],{"class":3709},[1115,34912,33162],{"class":3724},[1115,34914,3901],{"class":3717},[1115,34916,34917,34919,34921,34923,34925,34927,34929,34931,34933,34935,34937,34939,34941,34943,34945,34947,34949,34951,34953,34955,34957,34959,34961,34963,34965,34967,34969,34971],{"class":3702,"line":27},[1115,34918,33169],{"class":3705},[1115,34920,3710],{"class":3709},[1115,34922,3835],{"class":3713},[1115,34924,1875],{"class":3717},[1115,34926,21835],{"class":3724},[1115,34928,1797],{"class":3709},[1115,34930,33112],{"class":3724},[1115,34932,1797],{"class":3709},[1115,34934,33186],{"class":3724},[1115,34936,1797],{"class":3709},[1115,34938,33191],{"class":3724},[1115,34940,1797],{"class":3709},[1115,34942,33196],{"class":3724},[1115,34944,1797],{"class":3709},[1115,34946,33196],{"class":3724},[1115,34948,1797],{"class":3709},[1115,34950,14179],{"class":3724},[1115,34952,1797],{"class":3709},[1115,34954,33112],{"class":3724},[1115,34956,1797],{"class":3709},[1115,34958,33112],{"class":3724},[1115,34960,1797],{"class":3709},[1115,34962,33217],{"class":3724},[1115,34964,1797],{"class":3709},[1115,34966,33148],{"class":3724},[1115,34968,1797],{"class":3709},[1115,34970,33112],{"class":3724},[1115,34972,3901],{"class":3717},[1115,34974,34975,34978,34980,34982,34984,34986,34988,34990,34992,34994],{"class":3702,"line":148},[1115,34976,34977],{"class":3713},"wilcox.test",[1115,34979,1875],{"class":3717},[1115,34981,33089],{"class":3705},[1115,34983,1797],{"class":3709},[1115,34985,33240],{"class":3705},[1115,34987,1797],{"class":3709},[1115,34989,28080],{"class":3705},[1115,34991,3797],{"class":3709},[1115,34993,28085],{"class":3840},[1115,34995,3901],{"class":3717},[3694,34997,35000],{"className":34998,"code":34999,"language":3923,"meta":1490},[3921],"    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",[3470,35001,34999],{"__ignoreMap":1490},[1110,35003,35004,35027],{},[1115,35005,35007],{"className":35006},[1138],[1140,35008,35009],{"xmlns":1142},[1144,35010,35011,35024],{},[1147,35012,35013,35015,35017,35020,35022],{},[1153,35014,1110],{},[1242,35016,1982],{},[1565,35018,35019],{},"0,315",[1242,35021,1689],{},[1565,35023,3984],{},[1159,35025,35026],{"encoding":1161},"p = 0{,}315 > 0{,}05",": mediány výšek chlapců a dívek se statisticky významně neliší — stejný závěr jako u dvouvýběrového t-testu.",[1103,35029,35031,35038,35060,35171,35177],{"className":35030,"dataCallout":3477},[1106,3476],[1110,35032,35034,35037],{"className":35033},[1113],[1115,35035],{"className":35036,"ariaHidden":1121},[1118,3484,1120],"Příklad: Realitní odhadci — neparametrická alternativa",[1110,35039,35040,35041,35059],{},"U odhadů cen z párového t-testu výše normalita diferencí neplatí (",[1115,35042,35044],{"className":35043},[1138],[1140,35045,35046],{"xmlns":1142},[1144,35047,35048,35056],{},[1147,35049,35050,35052,35054],{},[1153,35051,1110],{},[1242,35053,1982],{},[1565,35055,30133],{},[1159,35057,35058],{"encoding":1161},"p = 0{,}03203","). Správnou volbou je párový Wilcoxonův test:",[3694,35061,35063],{"className":3696,"code":35062,"language":71,"meta":1490,"style":1490},"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",[3470,35064,35065,35107,35149],{"__ignoreMap":1490},[1115,35066,35067,35069,35071,35073,35075,35077,35079,35081,35083,35085,35087,35089,35091,35093,35095,35097,35099,35101,35103,35105],{"class":3702,"line":10},[1115,35068,29936],{"class":3705},[1115,35070,3710],{"class":3709},[1115,35072,3835],{"class":3713},[1115,35074,1875],{"class":3717},[1115,35076,29945],{"class":3724},[1115,35078,1797],{"class":3709},[1115,35080,29950],{"class":3724},[1115,35082,1797],{"class":3709},[1115,35084,29955],{"class":3724},[1115,35086,1797],{"class":3709},[1115,35088,29960],{"class":3724},[1115,35090,1797],{"class":3709},[1115,35092,29965],{"class":3724},[1115,35094,1797],{"class":3709},[1115,35096,29970],{"class":3724},[1115,35098,1797],{"class":3709},[1115,35100,29975],{"class":3724},[1115,35102,1797],{"class":3709},[1115,35104,29980],{"class":3724},[1115,35106,3901],{"class":3717},[1115,35108,35109,35111,35113,35115,35117,35119,35121,35123,35125,35127,35129,35131,35133,35135,35137,35139,35141,35143,35145,35147],{"class":3702,"line":27},[1115,35110,29987],{"class":3705},[1115,35112,3710],{"class":3709},[1115,35114,3835],{"class":3713},[1115,35116,1875],{"class":3717},[1115,35118,29996],{"class":3724},[1115,35120,1797],{"class":3709},[1115,35122,30001],{"class":3724},[1115,35124,1797],{"class":3709},[1115,35126,30006],{"class":3724},[1115,35128,1797],{"class":3709},[1115,35130,30011],{"class":3724},[1115,35132,1797],{"class":3709},[1115,35134,30016],{"class":3724},[1115,35136,1797],{"class":3709},[1115,35138,30021],{"class":3724},[1115,35140,1797],{"class":3709},[1115,35142,30026],{"class":3724},[1115,35144,1797],{"class":3709},[1115,35146,30031],{"class":3724},[1115,35148,3901],{"class":3717},[1115,35150,35151,35153,35155,35157,35159,35161,35163,35165,35167,35169],{"class":3702,"line":148},[1115,35152,34977],{"class":3713},[1115,35154,1875],{"class":3717},[1115,35156,29936],{"class":3705},[1115,35158,1797],{"class":3709},[1115,35160,30046],{"class":3705},[1115,35162,1797],{"class":3709},[1115,35164,30051],{"class":3705},[1115,35166,3797],{"class":3709},[1115,35168,3810],{"class":3724},[1115,35170,3901],{"class":3717},[3694,35172,35175],{"className":35173,"code":35174,"language":3923,"meta":1490},[3921],"    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",[3470,35176,35174],{"__ignoreMap":1490},[1110,35178,35179,35202],{},[1115,35180,35182],{"className":35181},[1138],[1140,35183,35184],{"xmlns":1142},[1144,35185,35186,35199],{},[1147,35187,35188,35190,35192,35195,35197],{},[1153,35189,1110],{},[1242,35191,1982],{},[1565,35193,35194],{},"0,1484",[1242,35196,1689],{},[1565,35198,3984],{},[1159,35200,35201],{"encoding":1161},"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.",[16749,35204,35206],{"id":35205},"kruskalův-wallisův-test","Kruskalův-Wallisův test",[1110,35208,35209,35210,35227],{},"Zobecnění dvouvýběrového Wilcoxonova testu, neparametrická obdoba analýzy rozptylu jednoduchého třídění. ",[1115,35211,35213],{"className":35212},[1138],[1140,35214,35215],{"xmlns":1142},[1144,35216,35217,35225],{},[1147,35218,35219],{},[1150,35220,35221,35223],{},[1153,35222,1563],{},[1565,35224,1567],{},[1159,35226,1570],{"encoding":1161},": všechny výběry pocházejí ze stejného rozdělení.",[3694,35229,35231],{"className":3696,"code":35230,"language":71,"meta":1490,"style":1490},"kruskal.test(kvantitativní_proměnná ~ faktor, data = soubor)\n",[3470,35232,35233],{"__ignoreMap":1490},[1115,35234,35235,35238,35240,35243,35245,35248,35250,35252,35254,35257],{"class":3702,"line":10},[1115,35236,35237],{"class":3713},"kruskal.test",[1115,35239,1875],{"class":3717},[1115,35241,35242],{"class":3705},"kvantitativní_proměnná",[1115,35244,16860],{"class":3709},[1115,35246,35247],{"class":3705}," faktor",[1115,35249,1797],{"class":3709},[1115,35251,20168],{"class":3705},[1115,35253,3797],{"class":3709},[1115,35255,35256],{"class":3705}," soubor",[1115,35258,3901],{"class":3717},[16749,35260,35262],{"id":35261},"mediánový-test","Mediánový test",[1110,35264,35265,35266,35283,35284,1958],{},"Má stejný účel jako Kruskalův-Wallisův test (obdoba analýzy rozptylu jednoduchého třídění, ",[1115,35267,35269],{"className":35268},[1138],[1140,35270,35271],{"xmlns":1142},[1144,35272,35273,35281],{},[1147,35274,35275],{},[1150,35276,35277,35279],{},[1153,35278,1563],{},[1565,35280,1567],{},[1159,35282,1570],{"encoding":1161},": všechny výběry pocházejí ze stejného rozdělení) a je součástí balíčku ",[3470,35285,35286],{},"agricolae",[3694,35288,35290],{"className":3696,"code":35289,"language":71,"meta":1490,"style":1490},"library(agricolae)\nMedian.test(kvantitativní_proměnná, faktor)\n",[3470,35291,35292,35302],{"__ignoreMap":1490},[1115,35293,35294,35296,35298,35300],{"class":3702,"line":10},[1115,35295,17398],{"class":3709},[1115,35297,1875],{"class":3717},[1115,35299,35286],{"class":3705},[1115,35301,3901],{"class":3717},[1115,35303,35304,35307,35309,35311,35313,35315],{"class":3702,"line":27},[1115,35305,35306],{"class":3713},"Median.test",[1115,35308,1875],{"class":3717},[1115,35310,35242],{"class":3705},[1115,35312,1797],{"class":3709},[1115,35314,35247],{"class":3705},[1115,35316,3901],{"class":3717},[16749,35318,35320],{"id":35319},"friedmanův-test","Friedmanův test",[1110,35322,35323,35324,35341,35342,35380],{},"Neparametrická obdoba analýzy rozptylu dvojného třídění s jedním pozorováním v každé podtřídě. ",[1115,35325,35327],{"className":35326},[1138],[1140,35328,35329],{"xmlns":1142},[1144,35330,35331,35339],{},[1147,35332,35333],{},[1150,35334,35335,35337],{},[1153,35336,1563],{},[1565,35338,1567],{},[1159,35340,1570],{"encoding":1161},": distribuční funkce veličin ",[1115,35343,35345],{"className":35344},[1138],[1140,35346,35347],{"xmlns":1142},[1144,35348,35349,35377],{},[1147,35350,35351,35361,35363,35365,35367],{},[1150,35352,35353,35355],{},[1153,35354,6734],{},[1147,35356,35357,35359],{},[1153,35358,1878],{},[1565,35360,1794],{},[1242,35362,1797],{"separator":1121},[1242,35364,1800],{},[1242,35366,1797],{"separator":1121},[1150,35368,35369,35371],{},[1153,35370,6734],{},[1147,35372,35373,35375],{},[1153,35374,1878],{},[1153,35376,1183],{},[1159,35378,35379],{"encoding":1161},"X_{i1}, \\dots, X_{ik}"," jsou totožné.",[3694,35382,35384],{"className":3696,"code":35383,"language":71,"meta":1490,"style":1490},"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",[3470,35385,35386,35416,35421],{"__ignoreMap":1490},[1115,35387,35388,35391,35393,35395,35397,35400,35403,35406,35408,35410,35412,35414],{"class":3702,"line":10},[1115,35389,35390],{"class":3713},"friedman.test",[1115,35392,1875],{"class":3717},[1115,35394,35242],{"class":3705},[1115,35396,16860],{"class":3709},[1115,35398,35399],{"class":3705}," faktor_A",[1115,35401,35402],{"class":3709}," |",[1115,35404,35405],{"class":3705}," faktor_B",[1115,35407,1797],{"class":3709},[1115,35409,20168],{"class":3705},[1115,35411,3797],{"class":3709},[1115,35413,35256],{"class":3705},[1115,35415,3901],{"class":3717},[1115,35417,35418],{"class":3702,"line":27},[1115,35419,35420],{"class":12035},"# jsou-li proměnné samostatné vektory (bez argumentu data):\n",[1115,35422,35423,35425,35427,35429,35431,35433,35435,35437],{"class":3702,"line":148},[1115,35424,35390],{"class":3713},[1115,35426,1875],{"class":3717},[1115,35428,35242],{"class":3705},[1115,35430,1797],{"class":3709},[1115,35432,35399],{"class":3705},[1115,35434,1797],{"class":3709},[1115,35436,35405],{"class":3705},[1115,35438,3901],{"class":3717},[1189,35440,35442],{"id":35441},"přehled-testů","Přehled testů",[1110,35444,35445],{},[4383,35446],{"alt":35447,"className":35448,"src":35449},"mask-ilu-volba-testu",[1130,4387],"\u002Fwiki-assets\u002Fmask-ilu-volba-testu.png",[1194,35451,35452,35465],{},[1197,35453,35454],{},[1200,35455,35456,35459,35462],{},[1203,35457,35458],{},"Situace",[1203,35460,35461],{},"Test",[1203,35463,35464],{},"R funkce",[1210,35466,35467,35480,35493,35505,35518,35533,35545,35558,35571,35584,35596,35611],{},[1200,35468,35469,35472,35475],{},[1215,35470,35471],{},"Jedna střední hodnota vs. zadané číslo, normální data",[1215,35473,35474],{},"jednovýběrový t-test",[1215,35476,35477],{},[3470,35478,35479],{},"t.test(x, mu = ..., alternative = ...)",[1200,35481,35482,35485,35488],{},[1215,35483,35484],{},"Rozdíl dvou závislých měření, diference normální",[1215,35486,35487],{},"párový t-test",[1215,35489,35490],{},[3470,35491,35492],{},"t.test(x, y, paired = TRUE)",[1200,35494,35495,35498,35500],{},[1215,35496,35497],{},"Shoda rozptylů dvou nezávislých normálních výběrů",[1215,35499,20076],{},[1215,35501,35502],{},[3470,35503,35504],{},"var.test(x, y)",[1200,35506,35507,35510,35513],{},[1215,35508,35509],{},"Shoda středních hodnot dvou nezávislých normálních výběrů",[1215,35511,35512],{},"dvouvýběrový t-test",[1215,35514,35515],{},[3470,35516,35517],{},"t.test(x, y, var.equal = TRUE\u002FFALSE)",[1200,35519,35520,35523,35525],{},[1215,35521,35522],{},"Shoda dat se zadaným typem rozdělení (normální, exponenciální, …)",[1215,35524,33326],{},[1215,35526,35527,1346,35530],{},[3470,35528,35529],{},"ks.test(x, \"pnorm\", mu, sigma)",[3470,35531,35532],{},"ks.test(x, \"pexp\", 1\u002Fdelta)",[1200,35534,35535,35538,35540],{},[1215,35536,35537],{},"Normalita dat",[1215,35539,33742],{},[1215,35541,35542],{},[3470,35543,35544],{},"shapiro.test(x)",[1200,35546,35547,35550,35553],{},[1215,35548,35549],{},"Medián jednoho výběru vs. konstanta, data nejsou normální",[1215,35551,35552],{},"jednovýběrový Wilcoxonův test",[1215,35554,35555],{},[3470,35556,35557],{},"wilcox.test(x, mu = c, alternative = ...)",[1200,35559,35560,35563,35566],{},[1215,35561,35562],{},"Medián diferencí dvou závislých měření, data nejsou normální",[1215,35564,35565],{},"párový Wilcoxonův test",[1215,35567,35568],{},[3470,35569,35570],{},"wilcox.test(x, y, paired = TRUE, mu = c)",[1200,35572,35573,35576,35579],{},[1215,35574,35575],{},"Mediány dvou nezávislých výběrů, data nejsou normální",[1215,35577,35578],{},"dvouvýběrový Wilcoxonův test",[1215,35580,35581],{},[3470,35582,35583],{},"wilcox.test(x, y)",[1200,35585,35586,35589,35591],{},[1215,35587,35588],{},"Více než dva nezávislé výběry, data nejsou normální",[1215,35590,35206],{},[1215,35592,35593],{},[3470,35594,35595],{},"kruskal.test(y ~ faktor, data)",[1200,35597,35598,35601,35604],{},[1215,35599,35600],{},"Více než dva nezávislé výběry, data nejsou normální (alternativa)",[1215,35602,35603],{},"mediánový test",[1215,35605,35606,22663,35609],{},[3470,35607,35608],{},"Median.test(y, faktor)",[3470,35610,35286],{},[1200,35612,35613,35616,35618],{},[1215,35614,35615],{},"Více než dva závislé výběry (dvojné třídění, jedno pozorování na podtřídu)",[1215,35617,35320],{},[1215,35619,35620],{},[3470,35621,35622],{},"friedman.test(y ~ A | B, data)",[1189,35624,6407],{"id":6406},[1436,35626,35627,35704,35710,35727,35758],{},[1439,35628,35629,35668,35669,33056,35686,35703],{},[1540,35630,35631,35632,35649,35650,35667],{},"Nezamítnutí ",[1115,35633,35635],{"className":35634},[1138],[1140,35636,35637],{"xmlns":1142},[1144,35638,35639,35647],{},[1147,35640,35641],{},[1150,35642,35643,35645],{},[1153,35644,1563],{},[1565,35646,1567],{},[1159,35648,1570],{"encoding":1161}," není důkaz, že ",[1115,35651,35653],{"className":35652},[1138],[1140,35654,35655],{"xmlns":1142},[1144,35656,35657,35665],{},[1147,35658,35659],{},[1150,35660,35661,35663],{},[1153,35662,1563],{},[1565,35664,1567],{},[1159,35666,1570],{"encoding":1161}," platí."," U kabelů A\u002FB vyšlo ",[1115,35670,35672],{"className":35671},[1138],[1140,35673,35674],{"xmlns":1142},[1144,35675,35676,35684],{},[1147,35677,35678,35680,35682],{},[1153,35679,1110],{},[1242,35681,1982],{},[1565,35683,33052],{},[1159,35685,33055],{"encoding":1161},[1115,35687,35689],{"className":35688},[1138],[1140,35690,35691],{"xmlns":1142},[1144,35692,35693,35701],{},[1147,35694,35695],{},[1150,35696,35697,35699],{},[1153,35698,1563],{},[1565,35700,1567],{},[1159,35702,1570],{"encoding":1161}," nezamítá, ale hodnota je blízko hranice; správná interpretace je „data rovnost průměrů nevyvracejí“, ne „rovnost je prokázána“.",[1439,35705,35706,35709],{},[1540,35707,35708],{},"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.",[1439,35711,35712,35719,35720,35723,35724,35726],{},[1540,35713,35714,30214,35716,35718],{},[3470,35715,32784],{},[3470,35717,27998],{}," se volí podle F-testu, ne podle výchozí hodnoty."," Výchozí nastavení R je ",[3470,35721,35722],{},"var.equal = FALSE"," (Welchova varianta); pokud F-test potvrdí shodné rozptyly, je třeba explicitně napsat ",[3470,35725,33035],{},", jinak se použije jiná statistika a jiné stupně volnosti.",[1439,35728,35729,35732,35733,35736,35737,35754,35755,1669],{},[1540,35730,35731],{},"Jednostranná vs. dvoustranná alternativa mění kritický obor i závěr."," Volba ",[3470,35734,35735],{},"alternative = \"greater\"\u002F\"less\"\u002F\"two.sided\""," musí odpovídat formulaci ",[1115,35738,35740],{"className":35739},[1138],[1140,35741,35742],{"xmlns":1142},[1144,35743,35744,35752],{},[1147,35745,35746],{},[1150,35747,35748,35750],{},[1153,35749,1563],{},[1565,35751,1794],{},[1159,35753,2996],{"encoding":1161}," v zadání, ne být ponechána na výchozí hodnotě ",[3470,35756,35757],{},"\"two.sided\"",[1439,35759,35760,35763,35764,35777],{},[1540,35761,35762],{},"Shapiro-Wilkův test se vyhodnocuje jen přes p-hodnotu",", ne porovnáním ",[1115,35765,35767],{"className":35766},[1138],[1140,35768,35769],{"xmlns":1142},[1144,35770,35771,35775],{},[1147,35772,35773],{},[1153,35774,1605],{},[1159,35776,1605],{"encoding":1161}," s tabulkovou kritickou hodnotou jako u ostatních testů v této kapitole.",[1189,35779,1434],{"id":1433},[1436,35781,35782,35787,35792,35797,35802,35807,35812],{},[1439,35783,35784],{},[1127,35785,1133],{"className":35786,"dataFsResolvedFilePath":1131,"href":1132},[1130],[1439,35788,35789],{},[1127,35790,6622],{"className":35791,"dataFsResolvedFilePath":6620,"href":6621},[1130],[1439,35793,35794],{},[1127,35795,6614],{"className":35796,"dataFsResolvedFilePath":6612,"href":6613},[1130],[1439,35798,35799],{},[1127,35800,6630],{"className":35801,"dataFsResolvedFilePath":6628,"href":6629},[1130],[1439,35803,35804],{},[1127,35805,1515],{"className":35806,"dataFsResolvedFilePath":11093,"href":11094},[1130],[1439,35808,35809],{},[1127,35810,1222],{"className":35811,"dataFsResolvedFilePath":1220,"href":1221},[1130],[1439,35813,35814],{},[1127,35815,6641],{"className":35816,"dataFsResolvedFilePath":1454,"href":1455},[1130],[1189,35818,1459],{"id":934},[1110,35820,1462,35821,1467],{},[1464,35822,1466],{},[6649,35824,35825],{},"html pre.shiki code .sP4rz, 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