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Brno: Fakulta podnikatelská VUT, 2011.",{"title":1229,"searchDepth":27,"depth":27,"links":1230},"",[1231,1232,1233],{"id":1138,"depth":27,"text":1139},{"id":1188,"depth":27,"text":1189},{"id":934,"depth":27,"text":1219},null,"2026-10-02","md",{},true,"\u002Fsummaries\u002Fmask-prednasky-regrese-kontingence",{"title":1094,"description":1229},[1242,1243,1244,1245,1246],"raw\u002Fmask\u002F04 regresní analýza.pdf","raw\u002Fmask\u002F04 regresní analýza - návod R.pdf","raw\u002Fmask\u002F05 kontingenční tabulky.pdf","raw\u002Fmask\u002F05 kontingenční tabulky - návod R.pdf","raw\u002Fmask\u002Fpříklady 04 a 05.docx","summaries\u002Fmask-prednasky-regrese-kontingence",[23,67,135,294,716,71],"summary","r6v3DILwyTY9rf8sYFWNJSWv945Xm2Ws2Jpu5HH4bw8","summaries",[1253,6425,10891,15657,20357,25812],{"id":1254,"title":1182,"body":1255,"course":23,"courses":1234,"created":1235,"description":1229,"extension":1236,"meta":6417,"navigation":1238,"path":6418,"seo":6419,"sources":6420,"stem":6421,"tags":6422,"type":6423,"updated":1235,"__hash__":6424},"topics\u002Ftopics\u002Fkontingencni-tabulky.md",{"type":1096,"value":1256,"toc":6407},[1257,1260,1457,1461,1479,1497,1710,1851,2446,2463,2576,2580,2611,2616,3219,3226,3446,3672,3680,3761,3873,4026,4032,4113,4134,4143,4177,4184,4187,4193,4259,4318,4471,4477,4484,4562,4565,4621,4959,4980,5084,5193,5196,5217,5220,5475,5557,5564,5568,5798,5812,5961,6095,6101,6159,6163,6182,6197,6203,6248,6267,6282,6288,6347,6349,6397,6399,6403],[1099,1258,1182],{"id":1259},"kontingenční-tabulky",[1103,1261,1265,1273],{"className":1262,"dataCallout":1264},[1106,1263],"callout-default","tldr",[1110,1266,1268,1272],{"className":1267},[1113],[1115,1269],{"className":1270,"ariaHidden":1121},[1118,1271,1120],"i-lucide:info","V kostce",[1191,1274,1275,1283,1357,1378,1418,1446],{},[1194,1276,1277,1278,1282],{},"Kontingenční tabulka zaznamenává ",[1279,1280,1281],"strong",{},"simultánní četnosti"," dvou kvalitativních znaků naměřených na stejném souboru.",[1194,1284,1285,1288,1289,1319,1320,1341,1342,1356],{},[1279,1286,1287],{},"Test nezávislosti"," srovnává pozorované četnosti s očekávanými za platnosti ",[1115,1290,1293],{"className":1291},[1292],"katex",[1294,1295,1297],"math",{"xmlns":1296},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1298,1299,1300,1314],"semantics",{},[1301,1302,1303],"mrow",{},[1304,1305,1306,1310],"msub",{},[1307,1308,1309],"mi",{},"H",[1311,1312,1313],"mn",{},"0",[1315,1316,1318],"annotation",{"encoding":1317},"application\u002Fx-tex","H_0"," pomocí statistiky ",[1115,1321,1323],{"className":1322},[1292],[1294,1324,1325],{"xmlns":1296},[1298,1326,1327,1338],{},[1301,1328,1329],{},[1330,1331,1332,1335],"msup",{},[1307,1333,1334],{},"χ",[1311,1336,1337],{},"2",[1315,1339,1340],{"encoding":1317},"\\chi^2","; rozhoduje kritický obor ",[1115,1343,1345],{"className":1344},[1292],[1294,1346,1347],{"xmlns":1296},[1298,1348,1349,1354],{},[1301,1350,1351],{},[1307,1352,1353],{},"W",[1315,1355,1353],{"encoding":1317},", prakticky p-hodnota.",[1194,1358,1359,1360,1377],{},"Aproximace ",[1115,1361,1363],{"className":1362},[1292],[1294,1364,1365],{"xmlns":1296},[1298,1366,1367,1375],{},[1301,1368,1369],{},[1330,1370,1371,1373],{},[1307,1372,1334],{},[1311,1374,1337],{},[1315,1376,1340],{"encoding":1317}," rozdělením platí jen tehdy, když jsou očekávané četnosti dostatečně velké — proto se vždy kontrolují.",[1194,1379,1380,1381,1398,1399,1402,1403,1417],{},"Zamítnutí ",[1115,1382,1384],{"className":1383},[1292],[1294,1385,1386],{"xmlns":1296},[1298,1387,1388,1396],{},[1301,1389,1390],{},[1304,1391,1392,1394],{},[1307,1393,1309],{},[1311,1395,1313],{},[1315,1397,1318],{"encoding":1317}," samo o sobě neříká, jak silná závislost je — na to slouží ",[1279,1400,1401],{},"Cramérův koeficient kontingence"," ",[1115,1404,1406],{"className":1405},[1292],[1294,1407,1408],{"xmlns":1296},[1298,1409,1410,1415],{},[1301,1411,1412],{},[1307,1413,1414],{},"V",[1315,1416,1414],{"encoding":1317},".",[1194,1419,1420,1423,1424,1417],{},[1279,1421,1422],{},"Čtyřpolní tabulka"," (2×2) je speciální případ s vlastním zjednodušeným vzorcem pro ",[1115,1425,1427],{"className":1426},[1292],[1294,1428,1429],{"xmlns":1296},[1298,1430,1431,1443],{},[1301,1432,1433,1436,1440],{},[1307,1434,1435],{},"n",[1437,1438,1439],"mo",{},">",[1311,1441,1442],{},"40",[1315,1444,1445],{"encoding":1317},"n>40",[1194,1447,1448,1449,1452,1453,1456],{},"Pro ",[1279,1450,1451],{},"párová data"," (stejné prvky měřené dvakrát, např. před\u002Fpo zásahu) se používá ",[1279,1454,1455],{},"McNemarův test",", ne obyčejný test nezávislosti.",[1136,1458,1460],{"id":1459},"kontingenční-tabulka","Kontingenční tabulka",[1110,1462,1463,1464,1467,1468,1474,1475,1478],{},"V rámci ",[1127,1465,1133],{"className":1466,"dataFsResolvedFilePath":1131,"href":1132},[1130]," navazují kontingenční tabulky na\n",[1127,1469,1473],{"className":1470,"dataFsResolvedFilePath":1471,"href":1472},[1130],"topics\u002Ftestovani-hypotez.md","\u002Fwiki\u002Ftestovani-hypotez","testování statistických hypotéz",": místo jedné náhodné veličiny teď sledujeme dva\n",[1279,1476,1477],{},"kvalitativní"," (kategoriální) znaky současně a ptáme se, zda spolu souvisí.",[1110,1480,1481,1482,1485,1486,1488,1489,1492,1493,1496],{},"Znak je ",[1279,1483,1484],{},"kvantitativní",", pokud nabývá číselných hodnot (stáří, stav tachometru), a ",[1279,1487,1477],{},"\n(kategoriální), pokud nabývá slovních variant (vzdělání, kuřák\u002Fnekuřák). Kvalitativní znaky dále dělíme na\n",[1279,1490,1491],{},"alternativní"," (dvě varianty, např. vada ano\u002Fne) a ",[1279,1494,1495],{},"množné"," (více než dvě varianty, např. svobodný\u002Frozvedený\u002Fženatý).",[1110,1498,1499,1500,1513,1514,1528,1529,1562,1563,1577,1578,1609,1610,1613,1614,1641,1642,1402,1645,1667,1668,1686,1687,1705,1706,1709],{},"Mějme ",[1115,1501,1503],{"className":1502},[1292],[1294,1504,1505],{"xmlns":1296},[1298,1506,1507,1511],{},[1301,1508,1509],{},[1307,1510,1435],{},[1315,1512,1435],{"encoding":1317}," opakování pokusu, při nichž sledujeme dva kvalitativní znaky ",[1115,1515,1517],{"className":1516},[1292],[1294,1518,1519],{"xmlns":1296},[1298,1520,1521,1526],{},[1301,1522,1523],{},[1307,1524,1525],{},"A",[1315,1527,1525],{"encoding":1317}," (varianty ",[1115,1530,1532],{"className":1531},[1292],[1294,1533,1534],{"xmlns":1296},[1298,1535,1536,1559],{},[1301,1537,1538,1545,1548,1551,1553],{},[1304,1539,1540,1542],{},[1307,1541,1525],{},[1311,1543,1544],{},"1",[1437,1546,1547],{"separator":1121},",",[1437,1549,1550],{},"…",[1437,1552,1547],{"separator":1121},[1304,1554,1555,1557],{},[1307,1556,1525],{},[1307,1558,71],{},[1315,1560,1561],{"encoding":1317},"A_1,\\dots,A_r",") a ",[1115,1564,1566],{"className":1565},[1292],[1294,1567,1568],{"xmlns":1296},[1298,1569,1570,1575],{},[1301,1571,1572],{},[1307,1573,1574],{},"B",[1315,1576,1574],{"encoding":1317},"\n(varianty ",[1115,1579,1581],{"className":1580},[1292],[1294,1582,1583],{"xmlns":1296},[1298,1584,1585,1606],{},[1301,1586,1587,1593,1595,1597,1599],{},[1304,1588,1589,1591],{},[1307,1590,1574],{},[1311,1592,1544],{},[1437,1594,1547],{"separator":1121},[1437,1596,1550],{},[1437,1598,1547],{"separator":1121},[1304,1600,1601,1603],{},[1307,1602,1574],{},[1307,1604,1605],{},"s",[1315,1607,1608],{"encoding":1317},"B_1,\\dots,B_s","). Výsledky zapíšeme do ",[1279,1611,1612],{},"kontingenční tabulky",": v políčku ",[1115,1615,1617],{"className":1616},[1292],[1294,1618,1619],{"xmlns":1296},[1298,1620,1621,1638],{},[1301,1622,1623,1627,1630,1632,1635],{},[1437,1624,1626],{"stretchy":1625},"false","(",[1307,1628,1629],{},"i",[1437,1631,1547],{"separator":1121},[1307,1633,1634],{},"j",[1437,1636,1637],{"stretchy":1625},")",[1315,1639,1640],{"encoding":1317},"(i,j)"," je ",[1279,1643,1644],{},"simultánní\nčetnost",[1115,1646,1648],{"className":1647},[1292],[1294,1649,1650],{"xmlns":1296},[1298,1651,1652,1664],{},[1301,1653,1654],{},[1304,1655,1656,1658],{},[1307,1657,1435],{},[1301,1659,1660,1662],{},[1307,1661,1629],{},[1307,1663,1634],{},[1315,1665,1666],{"encoding":1317},"n_{ij}",", tedy počet pokusů s variantou ",[1115,1669,1671],{"className":1670},[1292],[1294,1672,1673],{"xmlns":1296},[1298,1674,1675,1683],{},[1301,1676,1677],{},[1304,1678,1679,1681],{},[1307,1680,1525],{},[1307,1682,1629],{},[1315,1684,1685],{"encoding":1317},"A_i"," zároveň s variantou ",[1115,1688,1690],{"className":1689},[1292],[1294,1691,1692],{"xmlns":1296},[1298,1693,1694,1702],{},[1301,1695,1696],{},[1304,1697,1698,1700],{},[1307,1699,1574],{},[1307,1701,1634],{},[1315,1703,1704],{"encoding":1317},"B_j",". Řádkové a sloupcové součty\njsou ",[1279,1707,1708],{},"marginální četnosti",":",[1115,1711,1713],{"className":1712},[1292],[1294,1714,1716],{"xmlns":1296,"display":1715},"block",[1298,1717,1718,1848],{},[1301,1719,1720,1731,1734,1750,1760,1762,1766,1776,1778,1792,1802,1804,1806,1808,1810,1824,1838],{},[1304,1721,1722,1724],{},[1307,1723,1435],{},[1301,1725,1726,1728],{},[1307,1727,1629],{},[1437,1729,1730],{},"∙",[1437,1732,1733],{},"=",[1735,1736,1737,1740,1748],"munderover",{},[1437,1738,1739],{},"∑",[1301,1741,1742,1744,1746],{},[1307,1743,1634],{},[1437,1745,1733],{},[1311,1747,1544],{},[1307,1749,1605],{},[1304,1751,1752,1754],{},[1307,1753,1435],{},[1301,1755,1756,1758],{},[1307,1757,1629],{},[1307,1759,1634],{},[1437,1761,1547],{"separator":1121},[1763,1764],"mspace",{"width":1765},"2em",[1304,1767,1768,1770],{},[1307,1769,1435],{},[1301,1771,1772,1774],{},[1437,1773,1730],{},[1307,1775,1634],{},[1437,1777,1733],{},[1735,1779,1780,1782,1790],{},[1437,1781,1739],{},[1301,1783,1784,1786,1788],{},[1307,1785,1629],{},[1437,1787,1733],{},[1311,1789,1544],{},[1307,1791,71],{},[1304,1793,1794,1796],{},[1307,1795,1435],{},[1301,1797,1798,1800],{},[1307,1799,1629],{},[1307,1801,1634],{},[1437,1803,1547],{"separator":1121},[1763,1805],{"width":1765},[1307,1807,1435],{},[1437,1809,1733],{},[1735,1811,1812,1814,1822],{},[1437,1813,1739],{},[1301,1815,1816,1818,1820],{},[1307,1817,1629],{},[1437,1819,1733],{},[1311,1821,1544],{},[1307,1823,71],{},[1735,1825,1826,1828,1836],{},[1437,1827,1739],{},[1301,1829,1830,1832,1834],{},[1307,1831,1634],{},[1437,1833,1733],{},[1311,1835,1544],{},[1307,1837,1605],{},[1304,1839,1840,1842],{},[1307,1841,1435],{},[1301,1843,1844,1846],{},[1307,1845,1629],{},[1307,1847,1634],{},[1315,1849,1850],{"encoding":1317},"n_{i\\bullet} = \\sum_{j=1}^{s} n_{ij}, \\qquad n_{\\bullet j} = \\sum_{i=1}^{r} n_{ij}, \\qquad n = \\sum_{i=1}^r\\sum_{j=1}^s n_{ij}",[1141,1852,1853,1965],{},[1144,1854,1855],{},[1147,1856,1857,1879,1899,1919,1921,1941],{},[1150,1858,1859],{},[1115,1860,1862],{"className":1861},[1292],[1294,1863,1864],{"xmlns":1296},[1298,1865,1866,1876],{},[1301,1867,1868,1870,1874],{},[1307,1869,1525],{},[1307,1871,1873],{"mathvariant":1872},"normal","\\",[1307,1875,1574],{},[1315,1877,1878],{"encoding":1317},"A \\backslash B",[1150,1880,1881],{},[1115,1882,1884],{"className":1883},[1292],[1294,1885,1886],{"xmlns":1296},[1298,1887,1888,1896],{},[1301,1889,1890],{},[1304,1891,1892,1894],{},[1307,1893,1574],{},[1311,1895,1544],{},[1315,1897,1898],{"encoding":1317},"B_1",[1150,1900,1901],{},[1115,1902,1904],{"className":1903},[1292],[1294,1905,1906],{"xmlns":1296},[1298,1907,1908,1916],{},[1301,1909,1910],{},[1304,1911,1912,1914],{},[1307,1913,1574],{},[1311,1915,1337],{},[1315,1917,1918],{"encoding":1317},"B_2",[1150,1920,1550],{},[1150,1922,1923],{},[1115,1924,1926],{"className":1925},[1292],[1294,1927,1928],{"xmlns":1296},[1298,1929,1930,1938],{},[1301,1931,1932],{},[1304,1933,1934,1936],{},[1307,1935,1574],{},[1307,1937,1605],{},[1315,1939,1940],{"encoding":1317},"B_s",[1150,1942,1943],{},[1115,1944,1946],{"className":1945},[1292],[1294,1947,1948],{"xmlns":1296},[1298,1949,1950,1962],{},[1301,1951,1952],{},[1304,1953,1954,1956],{},[1307,1955,1435],{},[1301,1957,1958,1960],{},[1307,1959,1629],{},[1437,1961,1730],{},[1315,1963,1964],{"encoding":1317},"n_{i\\bullet}",[1157,1966,1967,2081,2195,2211,2331],{},[1147,1968,1969,1989,2010,2031,2033,2057],{},[1162,1970,1971],{},[1115,1972,1974],{"className":1973},[1292],[1294,1975,1976],{"xmlns":1296},[1298,1977,1978,1986],{},[1301,1979,1980],{},[1304,1981,1982,1984],{},[1307,1983,1525],{},[1311,1985,1544],{},[1315,1987,1988],{"encoding":1317},"A_1",[1162,1990,1991],{},[1115,1992,1994],{"className":1993},[1292],[1294,1995,1996],{"xmlns":1296},[1298,1997,1998,2007],{},[1301,1999,2000],{},[1304,2001,2002,2004],{},[1307,2003,1435],{},[1311,2005,2006],{},"11",[1315,2008,2009],{"encoding":1317},"n_{11}",[1162,2011,2012],{},[1115,2013,2015],{"className":2014},[1292],[1294,2016,2017],{"xmlns":1296},[1298,2018,2019,2028],{},[1301,2020,2021],{},[1304,2022,2023,2025],{},[1307,2024,1435],{},[1311,2026,2027],{},"12",[1315,2029,2030],{"encoding":1317},"n_{12}",[1162,2032,1550],{},[1162,2034,2035],{},[1115,2036,2038],{"className":2037},[1292],[1294,2039,2040],{"xmlns":1296},[1298,2041,2042,2054],{},[1301,2043,2044],{},[1304,2045,2046,2048],{},[1307,2047,1435],{},[1301,2049,2050,2052],{},[1311,2051,1544],{},[1307,2053,1605],{},[1315,2055,2056],{"encoding":1317},"n_{1s}",[1162,2058,2059],{},[1115,2060,2062],{"className":2061},[1292],[1294,2063,2064],{"xmlns":1296},[1298,2065,2066,2078],{},[1301,2067,2068],{},[1304,2069,2070,2072],{},[1307,2071,1435],{},[1301,2073,2074,2076],{},[1311,2075,1544],{},[1437,2077,1730],{},[1315,2079,2080],{"encoding":1317},"n_{1\\bullet}",[1147,2082,2083,2103,2124,2145,2147,2171],{},[1162,2084,2085],{},[1115,2086,2088],{"className":2087},[1292],[1294,2089,2090],{"xmlns":1296},[1298,2091,2092,2100],{},[1301,2093,2094],{},[1304,2095,2096,2098],{},[1307,2097,1525],{},[1311,2099,1337],{},[1315,2101,2102],{"encoding":1317},"A_2",[1162,2104,2105],{},[1115,2106,2108],{"className":2107},[1292],[1294,2109,2110],{"xmlns":1296},[1298,2111,2112,2121],{},[1301,2113,2114],{},[1304,2115,2116,2118],{},[1307,2117,1435],{},[1311,2119,2120],{},"21",[1315,2122,2123],{"encoding":1317},"n_{21}",[1162,2125,2126],{},[1115,2127,2129],{"className":2128},[1292],[1294,2130,2131],{"xmlns":1296},[1298,2132,2133,2142],{},[1301,2134,2135],{},[1304,2136,2137,2139],{},[1307,2138,1435],{},[1311,2140,2141],{},"22",[1315,2143,2144],{"encoding":1317},"n_{22}",[1162,2146,1550],{},[1162,2148,2149],{},[1115,2150,2152],{"className":2151},[1292],[1294,2153,2154],{"xmlns":1296},[1298,2155,2156,2168],{},[1301,2157,2158],{},[1304,2159,2160,2162],{},[1307,2161,1435],{},[1301,2163,2164,2166],{},[1311,2165,1337],{},[1307,2167,1605],{},[1315,2169,2170],{"encoding":1317},"n_{2s}",[1162,2172,2173],{},[1115,2174,2176],{"className":2175},[1292],[1294,2177,2178],{"xmlns":1296},[1298,2179,2180,2192],{},[1301,2181,2182],{},[1304,2183,2184,2186],{},[1307,2185,1435],{},[1301,2187,2188,2190],{},[1311,2189,1337],{},[1437,2191,1730],{},[1315,2193,2194],{"encoding":1317},"n_{2\\bullet}",[1147,2196,2197,2200,2202,2204,2207,2209],{},[1162,2198,2199],{},"⋮",[1162,2201,2199],{},[1162,2203,2199],{},[1162,2205,2206],{},"⋱",[1162,2208,2199],{},[1162,2210,2199],{},[1147,2212,2213,2233,2257,2281,2283,2307],{},[1162,2214,2215],{},[1115,2216,2218],{"className":2217},[1292],[1294,2219,2220],{"xmlns":1296},[1298,2221,2222,2230],{},[1301,2223,2224],{},[1304,2225,2226,2228],{},[1307,2227,1525],{},[1307,2229,71],{},[1315,2231,2232],{"encoding":1317},"A_r",[1162,2234,2235],{},[1115,2236,2238],{"className":2237},[1292],[1294,2239,2240],{"xmlns":1296},[1298,2241,2242,2254],{},[1301,2243,2244],{},[1304,2245,2246,2248],{},[1307,2247,1435],{},[1301,2249,2250,2252],{},[1307,2251,71],{},[1311,2253,1544],{},[1315,2255,2256],{"encoding":1317},"n_{r1}",[1162,2258,2259],{},[1115,2260,2262],{"className":2261},[1292],[1294,2263,2264],{"xmlns":1296},[1298,2265,2266,2278],{},[1301,2267,2268],{},[1304,2269,2270,2272],{},[1307,2271,1435],{},[1301,2273,2274,2276],{},[1307,2275,71],{},[1311,2277,1337],{},[1315,2279,2280],{"encoding":1317},"n_{r2}",[1162,2282,1550],{},[1162,2284,2285],{},[1115,2286,2288],{"className":2287},[1292],[1294,2289,2290],{"xmlns":1296},[1298,2291,2292,2304],{},[1301,2293,2294],{},[1304,2295,2296,2298],{},[1307,2297,1435],{},[1301,2299,2300,2302],{},[1307,2301,71],{},[1307,2303,1605],{},[1315,2305,2306],{"encoding":1317},"n_{rs}",[1162,2308,2309],{},[1115,2310,2312],{"className":2311},[1292],[1294,2313,2314],{"xmlns":1296},[1298,2315,2316,2328],{},[1301,2317,2318],{},[1304,2319,2320,2322],{},[1307,2321,1435],{},[1301,2323,2324,2326],{},[1307,2325,71],{},[1437,2327,1730],{},[1315,2329,2330],{"encoding":1317},"n_{r\\bullet}",[1147,2332,2333,2357,2381,2405,2407,2431],{},[1162,2334,2335],{},[1115,2336,2338],{"className":2337},[1292],[1294,2339,2340],{"xmlns":1296},[1298,2341,2342,2354],{},[1301,2343,2344],{},[1304,2345,2346,2348],{},[1307,2347,1435],{},[1301,2349,2350,2352],{},[1437,2351,1730],{},[1307,2353,1634],{},[1315,2355,2356],{"encoding":1317},"n_{\\bullet j}",[1162,2358,2359],{},[1115,2360,2362],{"className":2361},[1292],[1294,2363,2364],{"xmlns":1296},[1298,2365,2366,2378],{},[1301,2367,2368],{},[1304,2369,2370,2372],{},[1307,2371,1435],{},[1301,2373,2374,2376],{},[1437,2375,1730],{},[1311,2377,1544],{},[1315,2379,2380],{"encoding":1317},"n_{\\bullet 1}",[1162,2382,2383],{},[1115,2384,2386],{"className":2385},[1292],[1294,2387,2388],{"xmlns":1296},[1298,2389,2390,2402],{},[1301,2391,2392],{},[1304,2393,2394,2396],{},[1307,2395,1435],{},[1301,2397,2398,2400],{},[1437,2399,1730],{},[1311,2401,1337],{},[1315,2403,2404],{"encoding":1317},"n_{\\bullet 2}",[1162,2406,1550],{},[1162,2408,2409],{},[1115,2410,2412],{"className":2411},[1292],[1294,2413,2414],{"xmlns":1296},[1298,2415,2416,2428],{},[1301,2417,2418],{},[1304,2419,2420,2422],{},[1307,2421,1435],{},[1301,2423,2424,2426],{},[1437,2425,1730],{},[1307,2427,1605],{},[1315,2429,2430],{"encoding":1317},"n_{\\bullet s}",[1162,2432,2433],{},[1115,2434,2436],{"className":2435},[1292],[1294,2437,2438],{"xmlns":1296},[1298,2439,2440,2444],{},[1301,2441,2442],{},[1307,2443,1435],{},[1315,2445,1435],{"encoding":1317},[1110,2447,2448,2449,2462],{},"Vydělením četností počtem opakování ",[1115,2450,2452],{"className":2451},[1292],[1294,2453,2454],{"xmlns":1296},[1298,2455,2456,2460],{},[1301,2457,2458],{},[1307,2459,1435],{},[1315,2461,1435],{"encoding":1317}," dostaneme odhady pravděpodobností:",[1115,2464,2466],{"className":2465},[1292],[1294,2467,2468],{"xmlns":1296,"display":1715},[1298,2469,2470,2573],{},[1301,2471,2472,2488,2490,2505,2507,2509,2523,2525,2539,2541,2543,2557,2559],{},[1304,2473,2474,2482],{},[2475,2476,2477,2479],"mover",{"accent":1121},[1307,2478,1110],{},[1437,2480,2481],{},"^",[1301,2483,2484,2486],{},[1307,2485,1629],{},[1307,2487,1634],{},[1437,2489,1733],{},[2491,2492,2493,2503],"mfrac",{},[1304,2494,2495,2497],{},[1307,2496,1435],{},[1301,2498,2499,2501],{},[1307,2500,1629],{},[1307,2502,1634],{},[1307,2504,1435],{},[1437,2506,1547],{"separator":1121},[1763,2508],{"width":1765},[1304,2510,2511,2517],{},[2475,2512,2513,2515],{"accent":1121},[1307,2514,1110],{},[1437,2516,2481],{},[1301,2518,2519,2521],{},[1307,2520,1629],{},[1437,2522,1730],{},[1437,2524,1733],{},[2491,2526,2527,2537],{},[1304,2528,2529,2531],{},[1307,2530,1435],{},[1301,2532,2533,2535],{},[1307,2534,1629],{},[1437,2536,1730],{},[1307,2538,1435],{},[1437,2540,1547],{"separator":1121},[1763,2542],{"width":1765},[1304,2544,2545,2551],{},[2475,2546,2547,2549],{"accent":1121},[1307,2548,1110],{},[1437,2550,2481],{},[1301,2552,2553,2555],{},[1437,2554,1730],{},[1307,2556,1634],{},[1437,2558,1733],{},[2491,2560,2561,2571],{},[1304,2562,2563,2565],{},[1307,2564,1435],{},[1301,2566,2567,2569],{},[1437,2568,1730],{},[1307,2570,1634],{},[1307,2572,1435],{},[1315,2574,2575],{"encoding":1317},"\\hat p_{ij} = \\frac{n_{ij}}{n}, \\qquad \\hat p_{i\\bullet} = \\frac{n_{i\\bullet}}{n}, \\qquad \\hat p_{\\bullet j} = \\frac{n_{\\bullet j}}{n}",[1136,2577,2579],{"id":2578},"test-nezávislosti-dvou-kvalitativních-znaků","Test nezávislosti dvou kvalitativních znaků",[1110,2581,2582,2583,2596,2597,2610],{},"Test ověřuje, zda varianty znaku ",[1115,2584,2586],{"className":2585},[1292],[1294,2587,2588],{"xmlns":1296},[1298,2589,2590,2594],{},[1301,2591,2592],{},[1307,2593,1525],{},[1315,2595,1525],{"encoding":1317}," a varianty znaku ",[1115,2598,2600],{"className":2599},[1292],[1294,2601,2602],{"xmlns":1296},[1298,2603,2604,2608],{},[1301,2605,2606],{},[1307,2607,1574],{},[1315,2609,1574],{"encoding":1317}," jsou na sobě nezávislé, tedy zda simultánní\npravděpodobnost je součinem marginálních pravděpodobností.",[1110,2612,2613],{},[1279,2614,2615],{},"Postup testu:",[2617,2618,2619,2751,3069,3151],"ol",{},[1194,2620,2621,2677,2678,2704,2705,2731,2732,2750],{},[1115,2622,2624],{"className":2623},[1292],[1294,2625,2626],{"xmlns":1296},[1298,2627,2628,2674],{},[1301,2629,2630,2636,2638,2648,2650,2660,2664],{},[1304,2631,2632,2634],{},[1307,2633,1309],{},[1311,2635,1313],{},[1437,2637,1709],{},[1304,2639,2640,2642],{},[1307,2641,1110],{},[1301,2643,2644,2646],{},[1307,2645,1629],{},[1307,2647,1634],{},[1437,2649,1733],{},[1304,2651,2652,2654],{},[1307,2653,1110],{},[1301,2655,2656,2658],{},[1307,2657,1629],{},[1437,2659,1730],{},[2661,2662,2663],"mtext",{}," ",[1304,2665,2666,2668],{},[1307,2667,1110],{},[1301,2669,2670,2672],{},[1437,2671,1730],{},[1307,2673,1634],{},[1315,2675,2676],{"encoding":1317},"H_0: p_{ij} = p_{i\\bullet}\\,p_{\\bullet j}"," pro všechna ",[1115,2679,2681],{"className":2680},[1292],[1294,2682,2683],{"xmlns":1296},[1298,2684,2685,2701],{},[1301,2686,2687,2689,2691,2693,2695,2697,2699],{},[1307,2688,1629],{},[1437,2690,1733],{},[1311,2692,1544],{},[1437,2694,1547],{"separator":1121},[1437,2696,1550],{},[1437,2698,1547],{"separator":1121},[1307,2700,71],{},[1315,2702,2703],{"encoding":1317},"i = 1,\\dots,r",", ",[1115,2706,2708],{"className":2707},[1292],[1294,2709,2710],{"xmlns":1296},[1298,2711,2712,2728],{},[1301,2713,2714,2716,2718,2720,2722,2724,2726],{},[1307,2715,1634],{},[1437,2717,1733],{},[1311,2719,1544],{},[1437,2721,1547],{"separator":1121},[1437,2723,1550],{},[1437,2725,1547],{"separator":1121},[1307,2727,1605],{},[1315,2729,2730],{"encoding":1317},"j = 1,\\dots,s"," (znaky jsou na sobě\nnezávislé) proti ",[1115,2733,2735],{"className":2734},[1292],[1294,2736,2737],{"xmlns":1296},[1298,2738,2739,2747],{},[1301,2740,2741],{},[1304,2742,2743,2745],{},[1307,2744,1309],{},[1311,2746,1544],{},[1315,2748,2749],{"encoding":1317},"H_1",": znaky jsou závislé.",[1194,2752,2753,2754,2911,2914,2915,2932,2933,2965,2966,1641,3025,3028,3029,3050,3051,3068],{},"Testové kritérium",[1115,2755,2757],{"className":2756},[1292],[1294,2758,2759],{"xmlns":1296,"display":1715},[1298,2760,2761,2908],{},[1301,2762,2763,2769,2771,2785,2799,2858,2860,2862,2876,2878,2892,2894],{},[1330,2764,2765,2767],{},[1307,2766,1334],{},[1311,2768,1337],{},[1437,2770,1733],{},[1735,2772,2773,2775,2783],{},[1437,2774,1739],{},[1301,2776,2777,2779,2781],{},[1307,2778,1629],{},[1437,2780,1733],{},[1311,2782,1544],{},[1307,2784,71],{},[1735,2786,2787,2789,2797],{},[1437,2788,1739],{},[1301,2790,2791,2793,2795],{},[1307,2792,1634],{},[1437,2794,1733],{},[1311,2796,1544],{},[1307,2798,1605],{},[2491,2800,2801,2840],{},[1301,2802,2803,2805,2815,2818,2820,2834],{},[1437,2804,1626],{"stretchy":1625},[1304,2806,2807,2809],{},[1307,2808,1435],{},[1301,2810,2811,2813],{},[1307,2812,1629],{},[1307,2814,1634],{},[1437,2816,2817],{},"−",[1307,2819,1435],{},[1304,2821,2822,2828],{},[2475,2823,2824,2826],{"accent":1121},[1307,2825,1110],{},[1437,2827,2481],{},[1301,2829,2830,2832],{},[1307,2831,1629],{},[1307,2833,1634],{},[1330,2835,2836,2838],{},[1437,2837,1637],{"stretchy":1625},[1311,2839,1337],{},[1301,2841,2842,2844],{},[1307,2843,1435],{},[1304,2845,2846,2852],{},[2475,2847,2848,2850],{"accent":1121},[1307,2849,1110],{},[1437,2851,2481],{},[1301,2853,2854,2856],{},[1307,2855,1629],{},[1307,2857,1634],{},[1437,2859,1547],{"separator":1121},[1763,2861],{"width":1765},[1304,2863,2864,2870],{},[2475,2865,2866,2868],{"accent":1121},[1307,2867,1110],{},[1437,2869,2481],{},[1301,2871,2872,2874],{},[1307,2873,1629],{},[1307,2875,1634],{},[1437,2877,1733],{},[1304,2879,2880,2886],{},[2475,2881,2882,2884],{"accent":1121},[1307,2883,1110],{},[1437,2885,2481],{},[1301,2887,2888,2890],{},[1307,2889,1629],{},[1437,2891,1730],{},[2661,2893,2663],{},[1304,2895,2896,2902],{},[2475,2897,2898,2900],{"accent":1121},[1307,2899,1110],{},[1437,2901,2481],{},[1301,2903,2904,2906],{},[1437,2905,1730],{},[1307,2907,1634],{},[1315,2909,2910],{"encoding":1317},"\\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}",[2912,2913],"br",{},"má asymptoticky Pearsonovo (",[1115,2916,2918],{"className":2917},[1292],[1294,2919,2920],{"xmlns":1296},[1298,2921,2922,2930],{},[1301,2923,2924],{},[1330,2925,2926,2928],{},[1307,2927,1334],{},[1311,2929,1337],{},[1315,2931,1340],{"encoding":1317},") rozdělení o ",[1115,2934,2936],{"className":2935},[1292],[1294,2937,2938],{"xmlns":1296},[1298,2939,2940,2962],{},[1301,2941,2942,2944,2946,2948,2950,2952,2954,2956,2958,2960],{},[1437,2943,1626],{"stretchy":1625},[1307,2945,71],{},[1437,2947,2817],{},[1311,2949,1544],{},[1437,2951,1637],{"stretchy":1625},[1437,2953,1626],{"stretchy":1625},[1307,2955,1605],{},[1437,2957,2817],{},[1311,2959,1544],{},[1437,2961,1637],{"stretchy":1625},[1315,2963,2964],{"encoding":1317},"(r-1)(s-1)"," stupních volnosti. Hodnota ",[1115,2967,2969],{"className":2968},[1292],[1294,2970,2971],{"xmlns":1296},[1298,2972,2973,3022],{},[1301,2974,2975,2977,2991,2993],{},[1307,2976,1435],{},[1304,2978,2979,2985],{},[2475,2980,2981,2983],{"accent":1121},[1307,2982,1110],{},[1437,2984,2481],{},[1301,2986,2987,2989],{},[1307,2988,1629],{},[1307,2990,1634],{},[1437,2992,1733],{},[2994,2995,2996],"mstyle",{"scriptlevel":1313,"displaystyle":1121},[2491,2997,2998,3020],{},[1301,2999,3000,3010],{},[1304,3001,3002,3004],{},[1307,3003,1435],{},[1301,3005,3006,3008],{},[1307,3007,1629],{},[1437,3009,1730],{},[1304,3011,3012,3014],{},[1307,3013,1435],{},[1301,3015,3016,3018],{},[1437,3017,1730],{},[1307,3019,1634],{},[1307,3021,1435],{},[1315,3023,3024],{"encoding":1317},"n\\hat p_{ij} = \\dfrac{n_{i\\bullet}n_{\\bullet j}}{n}",[1279,3026,3027],{},"očekávaná četnost"," políčka ",[1115,3030,3032],{"className":3031},[1292],[1294,3033,3034],{"xmlns":1296},[1298,3035,3036,3048],{},[1301,3037,3038,3040,3042,3044,3046],{},[1437,3039,1626],{"stretchy":1625},[1307,3041,1629],{},[1437,3043,1547],{"separator":1121},[1307,3045,1634],{},[1437,3047,1637],{"stretchy":1625},[1315,3049,1640],{"encoding":1317}," — četnost, kterou bychom čekali, kdyby ",[1115,3052,3054],{"className":3053},[1292],[1294,3055,3056],{"xmlns":1296},[1298,3057,3058,3066],{},[1301,3059,3060],{},[1304,3061,3062,3064],{},[1307,3063,1309],{},[1311,3065,1313],{},[1315,3067,1318],{"encoding":1317}," platila.",[1194,3070,3071,3072,1417],{},"Kritický obor: ",[1115,3073,3075],{"className":3074},[1292],[1294,3076,3077],{"xmlns":1296},[1298,3078,3079,3148],{},[1301,3080,3081,3083,3085,3088,3094,3096,3102,3105,3121,3123,3125,3127,3129,3131,3133,3135,3137,3139,3141,3143,3145],{},[1307,3082,1353],{},[1437,3084,1733],{},[1437,3086,3087],{"stretchy":1625},"{",[1330,3089,3090,3092],{},[1307,3091,1334],{},[1311,3093,1337],{},[1437,3095,1709],{},[1330,3097,3098,3100],{},[1307,3099,1334],{},[1311,3101,1337],{},[1437,3103,3104],{},"≥",[3106,3107,3108,3110,3119],"msubsup",{},[1307,3109,1334],{},[1301,3111,3112,3114,3116],{},[1311,3113,1544],{},[1437,3115,2817],{},[1307,3117,3118],{},"α",[1311,3120,1337],{},[1437,3122,1626],{"stretchy":1625},[1437,3124,1626],{"stretchy":1625},[1307,3126,71],{},[1437,3128,2817],{},[1311,3130,1544],{},[1437,3132,1637],{"stretchy":1625},[1437,3134,1626],{"stretchy":1625},[1307,3136,1605],{},[1437,3138,2817],{},[1311,3140,1544],{},[1437,3142,1637],{"stretchy":1625},[1437,3144,1637],{"stretchy":1625},[1437,3146,3147],{"stretchy":1625},"}",[1315,3149,3150],{"encoding":1317},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}((r-1)(s-1))\\}",[1194,3152,3153,3154,3167,3168,3182,3183,3200,3201,3218],{},"Padne-li testové kritérium do ",[1115,3155,3157],{"className":3156},[1292],[1294,3158,3159],{"xmlns":1296},[1298,3160,3161,3165],{},[1301,3162,3163],{},[1307,3164,1353],{},[1315,3166,1353],{"encoding":1317},", zamítáme na hladině ",[1115,3169,3171],{"className":3170},[1292],[1294,3172,3173],{"xmlns":1296},[1298,3174,3175,3179],{},[1301,3176,3177],{},[1307,3178,3118],{},[1315,3180,3181],{"encoding":1317},"\\alpha"," nulovou hypotézu o nezávislosti a přijímáme\n",[1115,3184,3186],{"className":3185},[1292],[1294,3187,3188],{"xmlns":1296},[1298,3189,3190,3198],{},[1301,3191,3192],{},[1304,3193,3194,3196],{},[1307,3195,1309],{},[1311,3197,1544],{},[1315,3199,2749],{"encoding":1317},"; jinak nemáme důvod ",[1115,3202,3204],{"className":3203},[1292],[1294,3205,3206],{"xmlns":1296},[1298,3207,3208,3216],{},[1301,3209,3210],{},[1304,3211,3212,3214],{},[1307,3213,1309],{},[1311,3215,1313],{},[1315,3217,1318],{"encoding":1317}," zamítnout.",[1110,3220,3221,3222,1417],{},"V R počítá test i očekávané četnosti funkce ",[3223,3224,3225],"code",{},"chisq.test()",[1103,3227,3231,3239,3242,3245,3391],{"className":3228,"dataCallout":3230},[1106,3229],"callout-example","example",[1110,3232,3234,3238],{"className":3233},[1113],[1115,3235],{"className":3236,"ariaHidden":1121},[1118,3237,1120],"i-lucide:flask-conical","Příklad: nákup potravin na internetu a vzdělání",[1110,3240,3241],{},"Testujte hypotézu, zda se vzájemně ovlivňuje zkušenost s nákupem potravin na internetu a vzdělání respondenta\n(n = 385 respondentů).",[1110,3243,3244],{},"Základní soubor: respondenti; výběrový soubor: respondenti, kteří odpověděli; měřený znak A: vzdělání, měřený\nznak B: způsob nákupu.",[1141,3246,3247,3286],{},[1144,3248,3249],{},[1147,3250,3251,3254,3257,3260,3263],{},[1150,3252,3253],{},"vzdělání \\ nákup",[1150,3255,3256],{},"ano",[1150,3258,3259],{},"ne, ale plánuji",[1150,3261,3262],{},"ne, neplánuji",[1150,3264,3265],{},[1115,3266,3268],{"className":3267},[1292],[1294,3269,3270],{"xmlns":1296},[1298,3271,3272,3284],{},[1301,3273,3274],{},[1304,3275,3276,3278],{},[1307,3277,1435],{},[1301,3279,3280,3282],{},[1307,3281,1629],{},[1437,3283,1730],{},[1315,3285,1964],{"encoding":1317},[1157,3287,3288,3304,3321,3338,3354],{},[1147,3289,3290,3293,3296,3299,3301],{},[1162,3291,3292],{},"SŠ bez maturity",[1162,3294,3295],{},"4",[1162,3297,3298],{},"13",[1162,3300,2027],{},[1162,3302,3303],{},"29",[1147,3305,3306,3309,3312,3315,3318],{},[1162,3307,3308],{},"SŠ s maturitou, VOŠ",[1162,3310,3311],{},"31",[1162,3313,3314],{},"62",[1162,3316,3317],{},"71",[1162,3319,3320],{},"164",[1147,3322,3323,3326,3329,3332,3335],{},[1162,3324,3325],{},"VŠ",[1162,3327,3328],{},"44",[1162,3330,3331],{},"58",[1162,3333,3334],{},"66",[1162,3336,3337],{},"168",[1147,3339,3340,3343,3346,3349,3351],{},[1162,3341,3342],{},"ZŠ",[1162,3344,3345],{},"3",[1162,3347,3348],{},"9",[1162,3350,2027],{},[1162,3352,3353],{},"24",[1147,3355,3356,3379,3382,3385,3388],{},[1162,3357,3358],{},[1115,3359,3361],{"className":3360},[1292],[1294,3362,3363],{"xmlns":1296},[1298,3364,3365,3377],{},[1301,3366,3367],{},[1304,3368,3369,3371],{},[1307,3370,1435],{},[1301,3372,3373,3375],{},[1437,3374,1730],{},[1307,3376,1634],{},[1315,3378,2356],{"encoding":1317},[1162,3380,3381],{},"82",[1162,3383,3384],{},"142",[1162,3386,3387],{},"161",[1162,3389,3390],{},"385",[1110,3392,3393,3445],{},[1115,3394,3396],{"className":3395},[1292],[1294,3397,3398],{"xmlns":1296},[1298,3399,3400,3442],{},[1301,3401,3402,3408,3410,3420,3422,3432],{},[1304,3403,3404,3406],{},[1307,3405,1309],{},[1311,3407,1313],{},[1437,3409,1709],{},[1304,3411,3412,3414],{},[1307,3413,1110],{},[1301,3415,3416,3418],{},[1307,3417,1629],{},[1307,3419,1634],{},[1437,3421,1733],{},[1304,3423,3424,3426],{},[1307,3425,1110],{},[1301,3427,3428,3430],{},[1307,3429,1629],{},[1437,3431,1730],{},[1304,3433,3434,3436],{},[1307,3435,1110],{},[1301,3437,3438,3440],{},[1437,3439,1730],{},[1307,3441,1634],{},[1315,3443,3444],{"encoding":1317},"H_0: p_{ij} = p_{i\\bullet}p_{\\bullet j}"," — vzdělání a způsob nákupu jsou na sobě nezávislé.",[3447,3448,3451],"pre",{"className":3449,"code":3450,"language":71,"meta":1229,"style":1229},"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",[3223,3452,3453,3492,3509,3526,3544,3567,3580,3615,3643,3656],{"__ignoreMap":1229},[1115,3454,3456,3460,3464,3468,3471,3474,3476,3479,3481,3484,3486,3489],{"class":3455,"line":10},"line",[1115,3457,3459],{"class":3458},"sP4rz","tab1",[1115,3461,3463],{"class":3462},"s8jYJ"," \u003C-",[1115,3465,3467],{"class":3466},"snPdu"," matrix",[1115,3469,1626],{"class":3470},"sxrX7",[1115,3472,3473],{"class":3466},"c",[1115,3475,1626],{"class":3470},[1115,3477,3295],{"class":3478},"sBjJW",[1115,3480,1547],{"class":3462},[1115,3482,3483],{"class":3478}," 13",[1115,3485,1547],{"class":3462},[1115,3487,3488],{"class":3478}," 12",[1115,3490,3491],{"class":3462},",\n",[1115,3493,3494,3497,3499,3502,3504,3507],{"class":3455,"line":27},[1115,3495,3496],{"class":3478},"                 31",[1115,3498,1547],{"class":3462},[1115,3500,3501],{"class":3478}," 62",[1115,3503,1547],{"class":3462},[1115,3505,3506],{"class":3478}," 71",[1115,3508,3491],{"class":3462},[1115,3510,3511,3514,3516,3519,3521,3524],{"class":3455,"line":148},[1115,3512,3513],{"class":3478},"                 44",[1115,3515,1547],{"class":3462},[1115,3517,3518],{"class":3478}," 58",[1115,3520,1547],{"class":3462},[1115,3522,3523],{"class":3478}," 66",[1115,3525,3491],{"class":3462},[1115,3527,3528,3531,3533,3536,3538,3540,3542],{"class":3455,"line":111},[1115,3529,3530],{"class":3478},"                 3",[1115,3532,1547],{"class":3462},[1115,3534,3535],{"class":3478},"  9",[1115,3537,1547],{"class":3462},[1115,3539,3488],{"class":3478},[1115,3541,1637],{"class":3470},[1115,3543,3491],{"class":3462},[1115,3545,3546,3549,3552,3555,3557,3560,3562,3565],{"class":3455,"line":96},[1115,3547,3548],{"class":3458},"               nrow",[1115,3550,3551],{"class":3462}," =",[1115,3553,3554],{"class":3478}," 4",[1115,3556,1547],{"class":3462},[1115,3558,3559],{"class":3458}," byrow",[1115,3561,3551],{"class":3462},[1115,3563,3564],{"class":3478}," TRUE",[1115,3566,3491],{"class":3462},[1115,3568,3569,3572,3574,3577],{"class":3455,"line":89},[1115,3570,3571],{"class":3458},"               dimnames",[1115,3573,3551],{"class":3462},[1115,3575,3576],{"class":3466}," list",[1115,3578,3579],{"class":3470},"(\n",[1115,3581,3582,3585,3587,3590,3592,3596,3598,3601,3603,3606,3608,3611,3613],{"class":3455,"line":82},[1115,3583,3584],{"class":3458},"                 vzdelani",[1115,3586,3551],{"class":3462},[1115,3588,3589],{"class":3466}," c",[1115,3591,1626],{"class":3470},[1115,3593,3595],{"class":3594},"sIIMD","\"SS bez maturity\"",[1115,3597,1547],{"class":3462},[1115,3599,3600],{"class":3594}," \"SS s maturitou nebo VOS\"",[1115,3602,1547],{"class":3462},[1115,3604,3605],{"class":3594}," \"VS\"",[1115,3607,1547],{"class":3462},[1115,3609,3610],{"class":3594}," \"ZS\"",[1115,3612,1637],{"class":3470},[1115,3614,3491],{"class":3462},[1115,3616,3617,3620,3623,3625,3627,3630,3632,3635,3637,3640],{"class":3455,"line":75},[1115,3618,3619],{"class":3458},"                 nakup",[1115,3621,3622],{"class":3462},"    =",[1115,3624,3589],{"class":3466},[1115,3626,1626],{"class":3470},[1115,3628,3629],{"class":3594},"\"ano\"",[1115,3631,1547],{"class":3462},[1115,3633,3634],{"class":3594}," \"ne, ale planuji\"",[1115,3636,1547],{"class":3462},[1115,3638,3639],{"class":3594}," \"ne, neplanuji\"",[1115,3641,3642],{"class":3470},")))\n",[1115,3644,3646,3649,3651,3653],{"class":3455,"line":3645},9,[1115,3647,3648],{"class":3466},"chisq.test",[1115,3650,1626],{"class":3470},[1115,3652,3459],{"class":3458},[1115,3654,3655],{"class":3470},")\n",[1115,3657,3658,3660,3662,3664,3666,3669],{"class":3455,"line":72},[1115,3659,3648],{"class":3466},[1115,3661,1626],{"class":3470},[1115,3663,3459],{"class":3458},[1115,3665,1637],{"class":3470},[1115,3667,3668],{"class":3462},"$",[1115,3670,3671],{"class":3458},"expected\n",[3447,3673,3678],{"className":3674,"code":3676,"language":3677,"meta":1229},[3675],"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",[3223,3679,3676],{"__ignoreMap":1229},[1110,3681,3682,3683,3706,3707,3721,3722,3742,3743,3760],{},"Všechny očekávané četnosti jsou nad 5, aproximace je v pořádku. Testové kritérium ",[1115,3684,3686],{"className":3685},[1292],[1294,3687,3688],{"xmlns":1296},[1298,3689,3690,3703],{},[1301,3691,3692,3698,3700],{},[1330,3693,3694,3696],{},[1307,3695,1334],{},[1311,3697,1337],{},[1437,3699,1733],{},[1311,3701,3702],{},"5,49",[1315,3704,3705],{"encoding":1317},"\\chi^2 = 5{,}49"," s ",[1115,3708,3710],{"className":3709},[1292],[1294,3711,3712],{"xmlns":1296},[1298,3713,3714,3719],{},[1301,3715,3716],{},[1311,3717,3718],{},"6",[1315,3720,3718],{"encoding":1317}," stupni\nvolnosti dává p-hodnotu ",[1115,3723,3725],{"className":3724},[1292],[1294,3726,3727],{"xmlns":1296},[1298,3728,3729,3739],{},[1301,3730,3731,3734,3736],{},[1311,3732,3733],{},"0,483",[1437,3735,1439],{},[1311,3737,3738],{},"0,05",[1315,3740,3741],{"encoding":1317},"0{,}483 > 0{,}05",": ",[1115,3744,3746],{"className":3745},[1292],[1294,3747,3748],{"xmlns":1296},[1298,3749,3750,3758],{},[1301,3751,3752],{},[1304,3753,3754,3756],{},[1307,3755,1309],{},[1311,3757,1313],{},[1315,3759,1318],{"encoding":1317}," nezamítáme, závislost mezi zkušeností s nákupem potravin na\ninternetu a vzděláním respondenta se neprokázala.",[1103,3762,3764,3771,3774,3819],{"className":3763,"dataCallout":3230},[1106,3229],[1110,3765,3767,3770],{"className":3766},[1113],[1115,3768],{"className":3769,"ariaHidden":1121},[1118,3237,1120],"Příklad: vzdělání a zveřejňování citlivých údajů na Facebooku",[1110,3772,3773],{},"Mezi 221 osobami bylo zaznamenáno vzdělání a zda zveřejňují na Facebooku citlivé údaje. Proveďte test\nnezávislosti.",[1141,3775,3776,3790],{},[1144,3777,3778],{},[1147,3779,3780,3783,3786,3788],{},[1150,3781,3782],{},"zveřejňuje \\ vzdělání",[1150,3784,3785],{},"SŠ",[1150,3787,3325],{},[1150,3789,3342],{},[1157,3791,3792,3806],{},[1147,3793,3794,3797,3800,3803],{},[1162,3795,3796],{},"ne",[1162,3798,3799],{},"20",[1162,3801,3802],{},"33",[1162,3804,3805],{},"39",[1147,3807,3808,3810,3813,3816],{},[1162,3809,3256],{},[1162,3811,3812],{},"25",[1162,3814,3815],{},"28",[1162,3817,3818],{},"76",[1110,3820,3821,3872],{},[1115,3822,3824],{"className":3823},[1292],[1294,3825,3826],{"xmlns":1296},[1298,3827,3828,3870],{},[1301,3829,3830,3836,3838,3848,3850,3860],{},[1304,3831,3832,3834],{},[1307,3833,1309],{},[1311,3835,1313],{},[1437,3837,1709],{},[1304,3839,3840,3842],{},[1307,3841,1110],{},[1301,3843,3844,3846],{},[1307,3845,1629],{},[1307,3847,1634],{},[1437,3849,1733],{},[1304,3851,3852,3854],{},[1307,3853,1110],{},[1301,3855,3856,3858],{},[1307,3857,1629],{},[1437,3859,1730],{},[1304,3861,3862,3864],{},[1307,3863,1110],{},[1301,3865,3866,3868],{},[1437,3867,1730],{},[1307,3869,1634],{},[1315,3871,3444],{"encoding":1317}," — vzdělání a zveřejňování citlivých údajů jsou na sobě nezávislé.",[3447,3874,3876],{"className":3449,"code":3875,"language":71,"meta":1229,"style":1229},"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",[3223,3877,3878,3907,3926,3945,3955,3978,4002,4012],{"__ignoreMap":1229},[1115,3879,3880,3883,3885,3887,3889,3891,3893,3895,3897,3900,3902,3905],{"class":3455,"line":10},[1115,3881,3882],{"class":3458},"tab2",[1115,3884,3463],{"class":3462},[1115,3886,3467],{"class":3466},[1115,3888,1626],{"class":3470},[1115,3890,3473],{"class":3466},[1115,3892,1626],{"class":3470},[1115,3894,3799],{"class":3478},[1115,3896,1547],{"class":3462},[1115,3898,3899],{"class":3478}," 33",[1115,3901,1547],{"class":3462},[1115,3903,3904],{"class":3478}," 39",[1115,3906,3491],{"class":3462},[1115,3908,3909,3912,3914,3917,3919,3922,3924],{"class":3455,"line":27},[1115,3910,3911],{"class":3478},"                 25",[1115,3913,1547],{"class":3462},[1115,3915,3916],{"class":3478}," 28",[1115,3918,1547],{"class":3462},[1115,3920,3921],{"class":3478}," 76",[1115,3923,1637],{"class":3470},[1115,3925,3491],{"class":3462},[1115,3927,3928,3930,3932,3935,3937,3939,3941,3943],{"class":3455,"line":148},[1115,3929,3548],{"class":3458},[1115,3931,3551],{"class":3462},[1115,3933,3934],{"class":3478}," 2",[1115,3936,1547],{"class":3462},[1115,3938,3559],{"class":3458},[1115,3940,3551],{"class":3462},[1115,3942,3564],{"class":3478},[1115,3944,3491],{"class":3462},[1115,3946,3947,3949,3951,3953],{"class":3455,"line":111},[1115,3948,3571],{"class":3458},[1115,3950,3551],{"class":3462},[1115,3952,3576],{"class":3466},[1115,3954,3579],{"class":3470},[1115,3956,3957,3960,3962,3964,3966,3969,3971,3974,3976],{"class":3455,"line":96},[1115,3958,3959],{"class":3458},"                 zverejnuje",[1115,3961,3551],{"class":3462},[1115,3963,3589],{"class":3466},[1115,3965,1626],{"class":3470},[1115,3967,3968],{"class":3594},"\"ne\"",[1115,3970,1547],{"class":3462},[1115,3972,3973],{"class":3594}," \"ano\"",[1115,3975,1637],{"class":3470},[1115,3977,3491],{"class":3462},[1115,3979,3980,3982,3985,3987,3989,3992,3994,3996,3998,4000],{"class":3455,"line":89},[1115,3981,3584],{"class":3458},[1115,3983,3984],{"class":3462},"   =",[1115,3986,3589],{"class":3466},[1115,3988,1626],{"class":3470},[1115,3990,3991],{"class":3594},"\"SS\"",[1115,3993,1547],{"class":3462},[1115,3995,3605],{"class":3594},[1115,3997,1547],{"class":3462},[1115,3999,3610],{"class":3594},[1115,4001,3642],{"class":3470},[1115,4003,4004,4006,4008,4010],{"class":3455,"line":82},[1115,4005,3648],{"class":3466},[1115,4007,1626],{"class":3470},[1115,4009,3882],{"class":3458},[1115,4011,3655],{"class":3470},[1115,4013,4014,4016,4018,4020,4022,4024],{"class":3455,"line":75},[1115,4015,3648],{"class":3466},[1115,4017,1626],{"class":3470},[1115,4019,3882],{"class":3458},[1115,4021,1637],{"class":3470},[1115,4023,3668],{"class":3462},[1115,4025,3671],{"class":3458},[3447,4027,4030],{"className":4028,"code":4029,"language":3677,"meta":1229},[3675],"    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",[3223,4031,4029],{"__ignoreMap":1229},[1110,4033,4034,4035,3706,4058,4071,4072,3742,4092,4109,4110,1417],{},"I zde jsou všechny očekávané četnosti nad 5. Testové kritérium ",[1115,4036,4038],{"className":4037},[1292],[1294,4039,4040],{"xmlns":1296},[1298,4041,4042,4055],{},[1301,4043,4044,4050,4052],{},[1330,4045,4046,4048],{},[1307,4047,1334],{},[1311,4049,1337],{},[1437,4051,1733],{},[1311,4053,4054],{},"6,87",[1315,4056,4057],{"encoding":1317},"\\chi^2 = 6{,}87",[1115,4059,4061],{"className":4060},[1292],[1294,4062,4063],{"xmlns":1296},[1298,4064,4065,4069],{},[1301,4066,4067],{},[1311,4068,1337],{},[1315,4070,1337],{"encoding":1317}," stupni volnosti dává\np-hodnotu ",[1115,4073,4075],{"className":4074},[1292],[1294,4076,4077],{"xmlns":1296},[1298,4078,4079,4089],{},[1301,4080,4081,4084,4087],{},[1311,4082,4083],{},"0,032",[1437,4085,4086],{},"\u003C",[1311,4088,3738],{},[1315,4090,4091],{"encoding":1317},"0{,}032 \u003C 0{,}05",[1115,4093,4095],{"className":4094},[1292],[1294,4096,4097],{"xmlns":1296},[1298,4098,4099,4107],{},[1301,4100,4101],{},[1304,4102,4103,4105],{},[1307,4104,1309],{},[1311,4106,1313],{},[1315,4108,1318],{"encoding":1317}," zamítáme — na rozdíl od předchozího příkladu tady vzdělání a zveřejňování\ncitlivých údajů na Facebooku na sobě ",[1279,4111,4112],{},"závisí",[1110,4114,4115,4116,4133],{},"Srovnání pozorovaných a očekávaných četností ukazuje, proč jeden příklad ",[1115,4117,4119],{"className":4118},[1292],[1294,4120,4121],{"xmlns":1296},[1298,4122,4123,4131],{},[1301,4124,4125],{},[1304,4126,4127,4129],{},[1307,4128,1309],{},[1311,4130,1313],{},[1315,4132,1318],{"encoding":1317}," nezamítá a druhý ano — ve druhém\nse pozorované sloupce (zejména u ZŠ) systematicky odchylují od očekávaných, v prvním kolísají jen náhodně kolem nich:",[1110,4135,4136],{},[4137,4138],"img",{"alt":4139,"className":4140,"src":4142},"mask-kt-observed-expected",[1130,4141],"wikilink-broken","\u002Fwiki-assets\u002Fmask-kt-observed-expected.png",[1110,4144,4145,4146,4163,4164,1709],{},"Totéž je vidět na rozdělení testového kritéria: u prvního příkladu leží ",[1115,4147,4149],{"className":4148},[1292],[1294,4150,4151],{"xmlns":1296},[1298,4152,4153,4161],{},[1301,4154,4155],{},[1330,4156,4157,4159],{},[1307,4158,1334],{},[1311,4160,1337],{},[1315,4162,1340],{"encoding":1317}," hluboko pod kritickou hodnotou,\nu druhého uvnitř kritického oboru ",[1115,4165,4167],{"className":4166},[1292],[1294,4168,4169],{"xmlns":1296},[1298,4170,4171,4175],{},[1301,4172,4173],{},[1307,4174,1353],{},[1315,4176,1353],{"encoding":1317},[1110,4178,4179],{},[4137,4180],{"alt":4181,"className":4182,"src":4183},"mask-kt-chi2-kriticky-obor",[1130,4141],"\u002Fwiki-assets\u002Fmask-kt-chi2-kriticky-obor.png",[1136,4185,1401],{"id":4186},"cramérův-koeficient-kontingence",[1110,4188,4189,4190,1709],{},"Test nezávislosti pouze rozhodne, zda jsou znaky závislé, nebo ne. Sílu závislosti měří ",[1279,4191,4192],{},"Cramérův koeficient\nkontingence",[1115,4194,4196],{"className":4195},[1292],[1294,4197,4198],{"xmlns":1296,"display":1715},[1298,4199,4200,4256],{},[1301,4201,4202,4204,4206,4232,4234,4236,4238,4240,4243,4246,4248,4250,4252,4254],{},[1307,4203,1414],{},[1437,4205,1733],{},[4207,4208,4209],"msqrt",{},[2491,4210,4211,4217],{},[1330,4212,4213,4215],{},[1307,4214,1334],{},[1311,4216,1337],{},[1301,4218,4219,4221,4223,4226,4228,4230],{},[1307,4220,1435],{},[1437,4222,1626],{"stretchy":1625},[1307,4224,4225],{},"m",[1437,4227,2817],{},[1311,4229,1544],{},[1437,4231,1637],{"stretchy":1625},[1437,4233,1547],{"separator":1121},[1763,4235],{"width":1765},[1307,4237,4225],{},[1437,4239,1733],{},[1307,4241,4242],{},"min",[1437,4244,4245],{},"⁡",[1437,4247,1626],{"stretchy":1625},[1307,4249,71],{},[1437,4251,1547],{"separator":1121},[1307,4253,1605],{},[1437,4255,1637],{"stretchy":1625},[1315,4257,4258],{"encoding":1317},"V = \\sqrt{\\frac{\\chi^2}{n(m-1)}}, \\qquad m = \\min(r, s)",[1110,4260,4261,4262,4279,4280,4298,4299,4317],{},"kde ",[1115,4263,4265],{"className":4264},[1292],[1294,4266,4267],{"xmlns":1296},[1298,4268,4269,4277],{},[1301,4270,4271],{},[1330,4272,4273,4275],{},[1307,4274,1334],{},[1311,4276,1337],{},[1315,4278,1340],{"encoding":1317}," je hodnota testového kritéria z testu nezávislosti. ",[1115,4281,4283],{"className":4282},[1292],[1294,4284,4285],{"xmlns":1296},[1298,4286,4287,4295],{},[1301,4288,4289,4291,4293],{},[1307,4290,1414],{},[1437,4292,1733],{},[1311,4294,1313],{},[1315,4296,4297],{"encoding":1317},"V = 0"," odpovídá úplné nezávislosti znaků,\n",[1115,4300,4302],{"className":4301},[1292],[1294,4303,4304],{"xmlns":1296},[1298,4305,4306,4314],{},[1301,4307,4308,4310,4312],{},[1307,4309,1414],{},[1437,4311,1733],{},[1311,4313,1544],{},[1315,4315,4316],{"encoding":1317},"V = 1"," jejich úplné závislosti.",[3447,4319,4321],{"className":3449,"code":4320,"language":71,"meta":1229,"style":1229},"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",[3223,4322,4323,4398,4461,4466],{"__ignoreMap":1229},[1115,4324,4325,4328,4330,4333,4335,4338,4340,4342,4344,4346,4348,4350,4353,4356,4359,4362,4365,4367,4369,4371,4374,4376,4378,4380,4383,4385,4387,4390,4393,4396],{"class":3455,"line":10},[1115,4326,4327],{"class":3458},"V1",[1115,4329,3463],{"class":3462},[1115,4331,4332],{"class":3466}," sqrt",[1115,4334,1626],{"class":3470},[1115,4336,4337],{"class":3466},"as.numeric",[1115,4339,1626],{"class":3470},[1115,4341,3648],{"class":3466},[1115,4343,1626],{"class":3470},[1115,4345,3459],{"class":3458},[1115,4347,1637],{"class":3470},[1115,4349,3668],{"class":3462},[1115,4351,4352],{"class":3458},"statistic",[1115,4354,4355],{"class":3470},") ",[1115,4357,4358],{"class":3462},"\u002F",[1115,4360,4361],{"class":3470}," (",[1115,4363,4364],{"class":3466},"sum",[1115,4366,1626],{"class":3470},[1115,4368,3459],{"class":3458},[1115,4370,4355],{"class":3470},[1115,4372,4373],{"class":3462},"*",[1115,4375,4361],{"class":3470},[1115,4377,4242],{"class":3466},[1115,4379,1626],{"class":3470},[1115,4381,4382],{"class":3466},"dim",[1115,4384,1626],{"class":3470},[1115,4386,3459],{"class":3458},[1115,4388,4389],{"class":3470},")) ",[1115,4391,4392],{"class":3462},"-",[1115,4394,4395],{"class":3478}," 1",[1115,4397,3642],{"class":3470},[1115,4399,4400,4403,4405,4407,4409,4411,4413,4415,4417,4419,4421,4423,4425,4427,4429,4431,4433,4435,4437,4439,4441,4443,4445,4447,4449,4451,4453,4455,4457,4459],{"class":3455,"line":27},[1115,4401,4402],{"class":3458},"V2",[1115,4404,3463],{"class":3462},[1115,4406,4332],{"class":3466},[1115,4408,1626],{"class":3470},[1115,4410,4337],{"class":3466},[1115,4412,1626],{"class":3470},[1115,4414,3648],{"class":3466},[1115,4416,1626],{"class":3470},[1115,4418,3882],{"class":3458},[1115,4420,1637],{"class":3470},[1115,4422,3668],{"class":3462},[1115,4424,4352],{"class":3458},[1115,4426,4355],{"class":3470},[1115,4428,4358],{"class":3462},[1115,4430,4361],{"class":3470},[1115,4432,4364],{"class":3466},[1115,4434,1626],{"class":3470},[1115,4436,3882],{"class":3458},[1115,4438,4355],{"class":3470},[1115,4440,4373],{"class":3462},[1115,4442,4361],{"class":3470},[1115,4444,4242],{"class":3466},[1115,4446,1626],{"class":3470},[1115,4448,4382],{"class":3466},[1115,4450,1626],{"class":3470},[1115,4452,3882],{"class":3458},[1115,4454,4389],{"class":3470},[1115,4456,4392],{"class":3462},[1115,4458,4395],{"class":3478},[1115,4460,3642],{"class":3470},[1115,4462,4463],{"class":3455,"line":148},[1115,4464,4465],{"class":3458},"V1\n",[1115,4467,4468],{"class":3455,"line":111},[1115,4469,4470],{"class":3458},"V2\n",[3447,4472,4475],{"className":4473,"code":4474,"language":3677,"meta":1229},[3675],"[1] 0.08441958\n[1] 0.1762822\n",[3223,4476,4474],{"__ignoreMap":1229},[1110,4478,4479],{},[4137,4480],{"alt":4481,"className":4482,"src":4483},"mask-kt-cramerovo-v",[1130,4141],"\u002Fwiki-assets\u002Fmask-kt-cramerovo-v.png",[1110,4485,4486,4487,4506,4507,4524,4525,3742,4544,4561],{},"U nákupu potravin je ",[1115,4488,4490],{"className":4489},[1292],[1294,4491,4492],{"xmlns":1296},[1298,4493,4494,4503],{},[1301,4495,4496,4498,4500],{},[1307,4497,1414],{},[1437,4499,1733],{},[1311,4501,4502],{},"0,084",[1315,4504,4505],{"encoding":1317},"V = 0{,}084"," zanedbatelné — ostatně ",[1115,4508,4510],{"className":4509},[1292],[1294,4511,4512],{"xmlns":1296},[1298,4513,4514,4522],{},[1301,4515,4516],{},[1304,4517,4518,4520],{},[1307,4519,1309],{},[1311,4521,1313],{},[1315,4523,1318],{"encoding":1317}," jsme ani nezamítli. U zveřejňování údajů je ",[1115,4526,4528],{"className":4527},[1292],[1294,4529,4530],{"xmlns":1296},[1298,4531,4532,4541],{},[1301,4533,4534,4536,4538],{},[1307,4535,1414],{},[1437,4537,1733],{},[1311,4539,4540],{},"0,176",[1315,4542,4543],{"encoding":1317},"V = 0{,}176",[1115,4545,4547],{"className":4546},[1292],[1294,4548,4549],{"xmlns":1296},[1298,4550,4551,4559],{},[1301,4552,4553],{},[1304,4554,4555,4557],{},[1307,4556,1309],{},[1311,4558,1313],{},[1315,4560,1318],{"encoding":1317},"\njsme zamítli, ale samotná závislost je stále slabá.",[1136,4563,1422],{"id":4564},"čtyřpolní-tabulka",[1110,4566,4567,4569,4570,4583,4584,4597,4598,4620],{},[1279,4568,1422],{}," je speciální případ kontingenční tabulky, kdy oba znaky ",[1115,4571,4573],{"className":4572},[1292],[1294,4574,4575],{"xmlns":1296},[1298,4576,4577,4581],{},[1301,4578,4579],{},[1307,4580,1525],{},[1315,4582,1525],{"encoding":1317}," i ",[1115,4585,4587],{"className":4586},[1292],[1294,4588,4589],{"xmlns":1296},[1298,4590,4591,4595],{},[1301,4592,4593],{},[1307,4594,1574],{},[1315,4596,1574],{"encoding":1317}," mají jen dvě varianty\n(",[1115,4599,4601],{"className":4600},[1292],[1294,4602,4603],{"xmlns":1296},[1298,4604,4605,4617],{},[1301,4606,4607,4609,4611,4613,4615],{},[1307,4608,71],{},[1437,4610,1733],{},[1307,4612,1605],{},[1437,4614,1733],{},[1311,4616,1337],{},[1315,4618,4619],{"encoding":1317},"r = s = 2","):",[1141,4622,4623,4707],{},[1144,4624,4625],{},[1147,4626,4627,4646,4665,4684],{},[1150,4628,4629],{},[1115,4630,4632],{"className":4631},[1292],[1294,4633,4634],{"xmlns":1296},[1298,4635,4636,4644],{},[1301,4637,4638,4640,4642],{},[1307,4639,1525],{},[1307,4641,1873],{"mathvariant":1872},[1307,4643,1574],{},[1315,4645,1878],{"encoding":1317},[1150,4647,4648],{},[1115,4649,4651],{"className":4650},[1292],[1294,4652,4653],{"xmlns":1296},[1298,4654,4655,4663],{},[1301,4656,4657],{},[1304,4658,4659,4661],{},[1307,4660,1574],{},[1311,4662,1544],{},[1315,4664,1898],{"encoding":1317},[1150,4666,4667],{},[1115,4668,4670],{"className":4669},[1292],[1294,4671,4672],{"xmlns":1296},[1298,4673,4674,4682],{},[1301,4675,4676],{},[1304,4677,4678,4680],{},[1307,4679,1574],{},[1311,4681,1337],{},[1315,4683,1918],{"encoding":1317},[1150,4685,4686],{},[1115,4687,4689],{"className":4688},[1292],[1294,4690,4691],{"xmlns":1296},[1298,4692,4693,4705],{},[1301,4694,4695],{},[1304,4696,4697,4699],{},[1307,4698,1435],{},[1301,4700,4701,4703],{},[1307,4702,1629],{},[1437,4704,1730],{},[1315,4706,1964],{"encoding":1317},[1157,4708,4709,4791,4873],{},[1147,4710,4711,4730,4749,4768],{},[1162,4712,4713],{},[1115,4714,4716],{"className":4715},[1292],[1294,4717,4718],{"xmlns":1296},[1298,4719,4720,4728],{},[1301,4721,4722],{},[1304,4723,4724,4726],{},[1307,4725,1525],{},[1311,4727,1544],{},[1315,4729,1988],{"encoding":1317},[1162,4731,4732],{},[1115,4733,4735],{"className":4734},[1292],[1294,4736,4737],{"xmlns":1296},[1298,4738,4739,4747],{},[1301,4740,4741],{},[1304,4742,4743,4745],{},[1307,4744,1435],{},[1311,4746,2006],{},[1315,4748,2009],{"encoding":1317},[1162,4750,4751],{},[1115,4752,4754],{"className":4753},[1292],[1294,4755,4756],{"xmlns":1296},[1298,4757,4758,4766],{},[1301,4759,4760],{},[1304,4761,4762,4764],{},[1307,4763,1435],{},[1311,4765,2027],{},[1315,4767,2030],{"encoding":1317},[1162,4769,4770],{},[1115,4771,4773],{"className":4772},[1292],[1294,4774,4775],{"xmlns":1296},[1298,4776,4777,4789],{},[1301,4778,4779],{},[1304,4780,4781,4783],{},[1307,4782,1435],{},[1301,4784,4785,4787],{},[1311,4786,1544],{},[1437,4788,1730],{},[1315,4790,2080],{"encoding":1317},[1147,4792,4793,4812,4831,4850],{},[1162,4794,4795],{},[1115,4796,4798],{"className":4797},[1292],[1294,4799,4800],{"xmlns":1296},[1298,4801,4802,4810],{},[1301,4803,4804],{},[1304,4805,4806,4808],{},[1307,4807,1525],{},[1311,4809,1337],{},[1315,4811,2102],{"encoding":1317},[1162,4813,4814],{},[1115,4815,4817],{"className":4816},[1292],[1294,4818,4819],{"xmlns":1296},[1298,4820,4821,4829],{},[1301,4822,4823],{},[1304,4824,4825,4827],{},[1307,4826,1435],{},[1311,4828,2120],{},[1315,4830,2123],{"encoding":1317},[1162,4832,4833],{},[1115,4834,4836],{"className":4835},[1292],[1294,4837,4838],{"xmlns":1296},[1298,4839,4840,4848],{},[1301,4841,4842],{},[1304,4843,4844,4846],{},[1307,4845,1435],{},[1311,4847,2141],{},[1315,4849,2144],{"encoding":1317},[1162,4851,4852],{},[1115,4853,4855],{"className":4854},[1292],[1294,4856,4857],{"xmlns":1296},[1298,4858,4859,4871],{},[1301,4860,4861],{},[1304,4862,4863,4865],{},[1307,4864,1435],{},[1301,4866,4867,4869],{},[1311,4868,1337],{},[1437,4870,1730],{},[1315,4872,2194],{"encoding":1317},[1147,4874,4875,4898,4921,4944],{},[1162,4876,4877],{},[1115,4878,4880],{"className":4879},[1292],[1294,4881,4882],{"xmlns":1296},[1298,4883,4884,4896],{},[1301,4885,4886],{},[1304,4887,4888,4890],{},[1307,4889,1435],{},[1301,4891,4892,4894],{},[1437,4893,1730],{},[1307,4895,1634],{},[1315,4897,2356],{"encoding":1317},[1162,4899,4900],{},[1115,4901,4903],{"className":4902},[1292],[1294,4904,4905],{"xmlns":1296},[1298,4906,4907,4919],{},[1301,4908,4909],{},[1304,4910,4911,4913],{},[1307,4912,1435],{},[1301,4914,4915,4917],{},[1437,4916,1730],{},[1311,4918,1544],{},[1315,4920,2380],{"encoding":1317},[1162,4922,4923],{},[1115,4924,4926],{"className":4925},[1292],[1294,4927,4928],{"xmlns":1296},[1298,4929,4930,4942],{},[1301,4931,4932],{},[1304,4933,4934,4936],{},[1307,4935,1435],{},[1301,4937,4938,4940],{},[1437,4939,1730],{},[1311,4941,1337],{},[1315,4943,2404],{"encoding":1317},[1162,4945,4946],{},[1115,4947,4949],{"className":4948},[1292],[1294,4950,4951],{"xmlns":1296},[1298,4952,4953,4957],{},[1301,4954,4955],{},[1307,4956,1435],{},[1315,4958,1435],{"encoding":1317},[1110,4960,1448,4961,4979],{},[1115,4962,4964],{"className":4963},[1292],[1294,4965,4966],{"xmlns":1296},[1298,4967,4968,4976],{},[1301,4969,4970,4972,4974],{},[1307,4971,1435],{},[1437,4973,1439],{},[1311,4975,1442],{},[1315,4977,4978],{"encoding":1317},"n > 40"," se místo obecného vzorce používá zjednodušená varianta testového kritéria:",[1115,4981,4983],{"className":4982},[1292],[1294,4984,4985],{"xmlns":1296,"display":1715},[1298,4986,4987,5081],{},[1301,4988,4989,4995,4997,4999,5001],{},[1330,4990,4991,4993],{},[1307,4992,1334],{},[1311,4994,1337],{},[1437,4996,1733],{},[1307,4998,1435],{},[2661,5000,2663],{},[2491,5002,5003,5039],{},[1301,5004,5005,5007,5013,5019,5021,5027,5033],{},[1437,5006,1626],{"stretchy":1625},[1304,5008,5009,5011],{},[1307,5010,1435],{},[1311,5012,2006],{},[1304,5014,5015,5017],{},[1307,5016,1435],{},[1311,5018,2141],{},[1437,5020,2817],{},[1304,5022,5023,5025],{},[1307,5024,1435],{},[1311,5026,2027],{},[1304,5028,5029,5031],{},[1307,5030,1435],{},[1311,5032,2120],{},[1330,5034,5035,5037],{},[1437,5036,1637],{"stretchy":1625},[1311,5038,1337],{},[1301,5040,5041,5051,5061,5071],{},[1304,5042,5043,5045],{},[1307,5044,1435],{},[1301,5046,5047,5049],{},[1311,5048,1544],{},[1437,5050,1730],{},[1304,5052,5053,5055],{},[1307,5054,1435],{},[1301,5056,5057,5059],{},[1311,5058,1337],{},[1437,5060,1730],{},[1304,5062,5063,5065],{},[1307,5064,1435],{},[1301,5066,5067,5069],{},[1437,5068,1730],{},[1311,5070,1544],{},[1304,5072,5073,5075],{},[1307,5074,1435],{},[1301,5076,5077,5079],{},[1437,5078,1730],{},[1311,5080,1337],{},[1315,5082,5083],{"encoding":1317},"\\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}}",[1110,5085,5086,5087,5147,5148,5184,5185,5188,5189,5192],{},"s kritickým oborem ",[1115,5088,5090],{"className":5089},[1292],[1294,5091,5092],{"xmlns":1296},[1298,5093,5094,5144],{},[1301,5095,5096,5102,5104,5106,5112,5114,5120,5122,5136,5138,5140,5142],{},[1304,5097,5098,5100],{},[1307,5099,1353],{},[1307,5101,3118],{},[1437,5103,1733],{},[1437,5105,3087],{"stretchy":1625},[1330,5107,5108,5110],{},[1307,5109,1334],{},[1311,5111,1337],{},[1437,5113,1709],{},[1330,5115,5116,5118],{},[1307,5117,1334],{},[1311,5119,1337],{},[1437,5121,3104],{},[3106,5123,5124,5126,5134],{},[1307,5125,1334],{},[1301,5127,5128,5130,5132],{},[1311,5129,1544],{},[1437,5131,2817],{},[1307,5133,3118],{},[1311,5135,1337],{},[1437,5137,1626],{"stretchy":1625},[1311,5139,1544],{},[1437,5141,1637],{"stretchy":1625},[1437,5143,3147],{"stretchy":1625},[1315,5145,5146],{"encoding":1317},"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 ",[1115,5149,5151],{"className":5150},[1292],[1294,5152,5153],{"xmlns":1296},[1298,5154,5155,5181],{},[1301,5156,5157,5159,5161,5163,5165,5167,5169,5171,5173,5175,5177,5179],{},[1437,5158,1626],{"stretchy":1625},[1307,5160,71],{},[1437,5162,2817],{},[1311,5164,1544],{},[1437,5166,1637],{"stretchy":1625},[1437,5168,1626],{"stretchy":1625},[1307,5170,1605],{},[1437,5172,2817],{},[1311,5174,1544],{},[1437,5176,1637],{"stretchy":1625},[1437,5178,1733],{},[1311,5180,1544],{},[1315,5182,5183],{"encoding":1317},"(r-1)(s-1) = 1"," stupeň volnosti. V R dává tuto hodnotu ",[3223,5186,5187],{},"chisq.test(tab, correct = FALSE)",". Bez ",[3223,5190,5191],{},"correct = FALSE"," R u tabulky 2 × 2 použije Yatesovu korekci na kontinuitu a testové kritérium vyjde menší.",[1136,5194,1455],{"id":5195},"mcnemarův-test",[1110,5197,5198,5199,5202,5203,5205,5206,5209,5210,5213,5214,5216],{},"Čtyřpolní tabulka z předchozí sekce porovnává dva ",[1279,5200,5201],{},"různé"," znaky na stejném souboru. ",[1279,5204,1455],{}," řeší\njinou situaci: na prvcích základního souboru se měří ",[1279,5207,5208],{},"jeden"," alternativní znak, a to ",[1279,5211,5212],{},"dvakrát"," — před a po\nnějakém zásahu. Cílem je zjistit, zda zásah změnil pravděpodobnostní rozdělení variant tohoto znaku. Jde tedy o\n",[1279,5215,1451],{}," (stejné prvky měřené opakovaně), ne o dva nezávisle naměřené znaky.",[1110,5218,5219],{},"Kontingenční tabulka před\u002Fpo má tvar:",[1141,5221,5222,5257],{},[1144,5223,5224],{},[1147,5225,5226,5229,5232,5234],{},[1150,5227,5228],{},"před \\ po",[1150,5230,5231],{},"+",[1150,5233,2817],{},[1150,5235,5236],{},[1115,5237,5239],{"className":5238},[1292],[1294,5240,5241],{"xmlns":1296},[1298,5242,5243,5255],{},[1301,5244,5245],{},[1304,5246,5247,5249],{},[1307,5248,1435],{},[1301,5250,5251,5253],{},[1307,5252,1629],{},[1437,5254,1730],{},[1315,5256,1964],{"encoding":1317},[1157,5258,5259,5324,5389],{},[1147,5260,5261,5263,5282,5301],{},[1162,5262,5231],{},[1162,5264,5265],{},[1115,5266,5268],{"className":5267},[1292],[1294,5269,5270],{"xmlns":1296},[1298,5271,5272,5280],{},[1301,5273,5274],{},[1304,5275,5276,5278],{},[1307,5277,1435],{},[1311,5279,2006],{},[1315,5281,2009],{"encoding":1317},[1162,5283,5284],{},[1115,5285,5287],{"className":5286},[1292],[1294,5288,5289],{"xmlns":1296},[1298,5290,5291,5299],{},[1301,5292,5293],{},[1304,5294,5295,5297],{},[1307,5296,1435],{},[1311,5298,2027],{},[1315,5300,2030],{"encoding":1317},[1162,5302,5303],{},[1115,5304,5306],{"className":5305},[1292],[1294,5307,5308],{"xmlns":1296},[1298,5309,5310,5322],{},[1301,5311,5312],{},[1304,5313,5314,5316],{},[1307,5315,1435],{},[1301,5317,5318,5320],{},[1311,5319,1544],{},[1437,5321,1730],{},[1315,5323,2080],{"encoding":1317},[1147,5325,5326,5328,5347,5366],{},[1162,5327,2817],{},[1162,5329,5330],{},[1115,5331,5333],{"className":5332},[1292],[1294,5334,5335],{"xmlns":1296},[1298,5336,5337,5345],{},[1301,5338,5339],{},[1304,5340,5341,5343],{},[1307,5342,1435],{},[1311,5344,2120],{},[1315,5346,2123],{"encoding":1317},[1162,5348,5349],{},[1115,5350,5352],{"className":5351},[1292],[1294,5353,5354],{"xmlns":1296},[1298,5355,5356,5364],{},[1301,5357,5358],{},[1304,5359,5360,5362],{},[1307,5361,1435],{},[1311,5363,2141],{},[1315,5365,2144],{"encoding":1317},[1162,5367,5368],{},[1115,5369,5371],{"className":5370},[1292],[1294,5372,5373],{"xmlns":1296},[1298,5374,5375,5387],{},[1301,5376,5377],{},[1304,5378,5379,5381],{},[1307,5380,1435],{},[1301,5382,5383,5385],{},[1311,5384,1337],{},[1437,5386,1730],{},[1315,5388,2194],{"encoding":1317},[1147,5390,5391,5414,5437,5460],{},[1162,5392,5393],{},[1115,5394,5396],{"className":5395},[1292],[1294,5397,5398],{"xmlns":1296},[1298,5399,5400,5412],{},[1301,5401,5402],{},[1304,5403,5404,5406],{},[1307,5405,1435],{},[1301,5407,5408,5410],{},[1437,5409,1730],{},[1307,5411,1634],{},[1315,5413,2356],{"encoding":1317},[1162,5415,5416],{},[1115,5417,5419],{"className":5418},[1292],[1294,5420,5421],{"xmlns":1296},[1298,5422,5423,5435],{},[1301,5424,5425],{},[1304,5426,5427,5429],{},[1307,5428,1435],{},[1301,5430,5431,5433],{},[1437,5432,1730],{},[1311,5434,1544],{},[1315,5436,2380],{"encoding":1317},[1162,5438,5439],{},[1115,5440,5442],{"className":5441},[1292],[1294,5443,5444],{"xmlns":1296},[1298,5445,5446,5458],{},[1301,5447,5448],{},[1304,5449,5450,5452],{},[1307,5451,1435],{},[1301,5453,5454,5456],{},[1437,5455,1730],{},[1311,5457,1337],{},[1315,5459,2404],{"encoding":1317},[1162,5461,5462],{},[1115,5463,5465],{"className":5464},[1292],[1294,5466,5467],{"xmlns":1296},[1298,5468,5469,5473],{},[1301,5470,5471],{},[1307,5472,1435],{},[1315,5474,1435],{"encoding":1317},[1110,5476,5477,5478,5495,5496,5513,5514,5517,5518,5495,5535,5552,5553,5556],{},"Pole ",[1115,5479,5481],{"className":5480},[1292],[1294,5482,5483],{"xmlns":1296},[1298,5484,5485,5493],{},[1301,5486,5487],{},[1304,5488,5489,5491],{},[1307,5490,1435],{},[1311,5492,2006],{},[1315,5494,2009],{"encoding":1317}," a ",[1115,5497,5499],{"className":5498},[1292],[1294,5500,5501],{"xmlns":1296},[1298,5502,5503,5511],{},[1301,5504,5505],{},[1304,5506,5507,5509],{},[1307,5508,1435],{},[1311,5510,2141],{},[1315,5512,2144],{"encoding":1317}," jsou ",[1279,5515,5516],{},"shodná"," (prvek zůstal ve stejné variantě), pole ",[1115,5519,5521],{"className":5520},[1292],[1294,5522,5523],{"xmlns":1296},[1298,5524,5525,5533],{},[1301,5526,5527],{},[1304,5528,5529,5531],{},[1307,5530,1435],{},[1311,5532,2027],{},[1315,5534,2030],{"encoding":1317},[1115,5536,5538],{"className":5537},[1292],[1294,5539,5540],{"xmlns":1296},[1298,5541,5542,5550],{},[1301,5543,5544],{},[1304,5545,5546,5548],{},[1307,5547,1435],{},[1311,5549,2120],{},[1315,5551,2123],{"encoding":1317}," jsou\n",[1279,5554,5555],{},"diskordantní"," (prvek mezi měřeními variantu změnil) — jen ta rozhodují o výsledku testu:",[1110,5558,5559],{},[4137,5560],{"alt":5561,"className":5562,"src":5563},"mask-kt-mcnemar-tabulka",[1130,4141],"\u002Fwiki-assets\u002Fmask-kt-mcnemar-tabulka.png",[1110,5565,5566],{},[1279,5567,2615],{},[2617,5569,5570,5607,5688,5746],{},[1194,5571,5572,5606],{},[1115,5573,5575],{"className":5574},[1292],[1294,5576,5577],{"xmlns":1296},[1298,5578,5579,5603],{},[1301,5580,5581,5587,5589,5595,5597],{},[1304,5582,5583,5585],{},[1307,5584,1309],{},[1311,5586,1313],{},[1437,5588,1709],{},[1304,5590,5591,5593],{},[1307,5592,1110],{},[1311,5594,2027],{},[1437,5596,1733],{},[1304,5598,5599,5601],{},[1307,5600,1110],{},[1311,5602,2120],{},[1315,5604,5605],{"encoding":1317},"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.",[1194,5608,2753,5609,5671,5673,5674,5687],{},[1115,5610,5612],{"className":5611},[1292],[1294,5613,5614],{"xmlns":1296,"display":1715},[1298,5615,5616,5668],{},[1301,5617,5618,5624,5626],{},[1330,5619,5620,5622],{},[1307,5621,1334],{},[1311,5623,1337],{},[1437,5625,1733],{},[2491,5627,5628,5652],{},[1301,5629,5630,5632,5638,5640,5646],{},[1437,5631,1626],{"stretchy":1625},[1304,5633,5634,5636],{},[1307,5635,1435],{},[1311,5637,2027],{},[1437,5639,2817],{},[1304,5641,5642,5644],{},[1307,5643,1435],{},[1311,5645,2120],{},[1330,5647,5648,5650],{},[1437,5649,1637],{"stretchy":1625},[1311,5651,1337],{},[1301,5653,5654,5660,5662],{},[1304,5655,5656,5658],{},[1307,5657,1435],{},[1311,5659,2027],{},[1437,5661,5231],{},[1304,5663,5664,5666],{},[1307,5665,1435],{},[1311,5667,2120],{},[1315,5669,5670],{"encoding":1317},"\\chi^2 = \\frac{(n_{12} - n_{21})^2}{n_{12} + n_{21}}",[2912,5672],{},"má asymptoticky Pearsonovo rozdělení o ",[1115,5675,5677],{"className":5676},[1292],[1294,5678,5679],{"xmlns":1296},[1298,5680,5681,5685],{},[1301,5682,5683],{},[1311,5684,1544],{},[1315,5686,1544],{"encoding":1317}," stupni volnosti.",[1194,5689,3071,5690,1417],{},[1115,5691,5693],{"className":5692},[1292],[1294,5694,5695],{"xmlns":1296},[1298,5696,5697,5743],{},[1301,5698,5699,5701,5703,5705,5711,5713,5719,5721,5735,5737,5739,5741],{},[1307,5700,1353],{},[1437,5702,1733],{},[1437,5704,3087],{"stretchy":1625},[1330,5706,5707,5709],{},[1307,5708,1334],{},[1311,5710,1337],{},[1437,5712,1709],{},[1330,5714,5715,5717],{},[1307,5716,1334],{},[1311,5718,1337],{},[1437,5720,3104],{},[3106,5722,5723,5725,5733],{},[1307,5724,1334],{},[1301,5726,5727,5729,5731],{},[1311,5728,1544],{},[1437,5730,2817],{},[1307,5732,3118],{},[1311,5734,1337],{},[1437,5736,1626],{"stretchy":1625},[1311,5738,1544],{},[1437,5740,1637],{"stretchy":1625},[1437,5742,3147],{"stretchy":1625},[1315,5744,5745],{"encoding":1317},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}(1)\\}",[1194,5747,3153,5748,5761,5762,5779,5780,5797],{},[1115,5749,5751],{"className":5750},[1292],[1294,5752,5753],{"xmlns":1296},[1298,5754,5755,5759],{},[1301,5756,5757],{},[1307,5758,1353],{},[1315,5760,1353],{"encoding":1317},", zamítáme ",[1115,5763,5765],{"className":5764},[1292],[1294,5766,5767],{"xmlns":1296},[1298,5768,5769,5777],{},[1301,5770,5771],{},[1304,5772,5773,5775],{},[1307,5774,1309],{},[1311,5776,1313],{},[1315,5778,1318],{"encoding":1317}," a přijímáme ",[1115,5781,5783],{"className":5782},[1292],[1294,5784,5785],{"xmlns":1296},[1298,5786,5787,5795],{},[1301,5788,5789],{},[1304,5790,5791,5793],{},[1307,5792,1309],{},[1311,5794,1544],{},[1315,5796,2749],{"encoding":1317},": zásah rozdělení variant změnil.",[1110,5799,5800,5801,5804,5805,5808,5809,5811],{},"V R počítá tento test funkce ",[3223,5802,5803],{},"mcnemar.test()",". Vzorec výše ",[1279,5806,5807],{},"neobsahuje korekci na kontinuitu"," — aby R vrátilo\npřesně tuto hodnotu, musí se volat s ",[3223,5810,5191],{}," (viz Časté chyby níže).",[1103,5813,5815,5822,5825,5828,5925],{"className":5814,"dataCallout":3230},[1106,3229],[1110,5816,5818,5821],{"className":5817},[1113],[1115,5819],{"className":5820,"ariaHidden":1121},[1118,3237,1120],"Příklad: informační kampaň a zveřejňování na Facebooku",[1110,5823,5824],{},"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.",[1110,5826,5827],{},"Základní soubor: všichni studenti; výběrový soubor: vybraní studenti; měřený znak: zveřejňování (ano \u002F ne).",[1141,5829,5830,5865],{},[1144,5831,5832],{},[1147,5833,5834,5836,5839,5842],{},[1150,5835,5228],{},[1150,5837,5838],{},"nezveřejňuje",[1150,5840,5841],{},"zveřejňuje",[1150,5843,5844],{},[1115,5845,5847],{"className":5846},[1292],[1294,5848,5849],{"xmlns":1296},[1298,5850,5851,5863],{},[1301,5852,5853],{},[1304,5854,5855,5857],{},[1307,5856,1435],{},[1301,5858,5859,5861],{},[1307,5860,1629],{},[1437,5862,1730],{},[1315,5864,1964],{"encoding":1317},[1157,5866,5867,5879,5891],{},[1147,5868,5869,5871,5873,5876],{},[1162,5870,5838],{},[1162,5872,3353],{},[1162,5874,5875],{},"68",[1162,5877,5878],{},"92",[1147,5880,5881,5883,5885,5888],{},[1162,5882,5841],{},[1162,5884,3815],{},[1162,5886,5887],{},"50",[1162,5889,5890],{},"78",[1147,5892,5893,5916,5919,5922],{},[1162,5894,5895],{},[1115,5896,5898],{"className":5897},[1292],[1294,5899,5900],{"xmlns":1296},[1298,5901,5902,5914],{},[1301,5903,5904],{},[1304,5905,5906,5908],{},[1307,5907,1435],{},[1301,5909,5910,5912],{},[1437,5911,1730],{},[1307,5913,1634],{},[1315,5915,2356],{"encoding":1317},[1162,5917,5918],{},"52",[1162,5920,5921],{},"118",[1162,5923,5924],{},"170",[1110,5926,5927,5960],{},[1115,5928,5930],{"className":5929},[1292],[1294,5931,5932],{"xmlns":1296},[1298,5933,5934,5958],{},[1301,5935,5936,5942,5944,5950,5952],{},[1304,5937,5938,5940],{},[1307,5939,1309],{},[1311,5941,1313],{},[1437,5943,1709],{},[1304,5945,5946,5948],{},[1307,5947,1110],{},[1311,5949,2027],{},[1437,5951,1733],{},[1304,5953,5954,5956],{},[1307,5955,1110],{},[1311,5957,2120],{},[1315,5959,5605],{"encoding":1317}," — informační kampaň nemá na chování vliv.",[3447,5962,5964],{"className":3449,"code":5963,"language":71,"meta":1229,"style":1229},"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",[3223,5965,5966,5990,6004,6022,6032,6055,6074],{"__ignoreMap":1229},[1115,5967,5968,5971,5973,5975,5977,5979,5981,5983,5985,5988],{"class":3455,"line":10},[1115,5969,5970],{"class":3458},"tab3",[1115,5972,3463],{"class":3462},[1115,5974,3467],{"class":3466},[1115,5976,1626],{"class":3470},[1115,5978,3473],{"class":3466},[1115,5980,1626],{"class":3470},[1115,5982,3353],{"class":3478},[1115,5984,1547],{"class":3462},[1115,5986,5987],{"class":3478}," 68",[1115,5989,3491],{"class":3462},[1115,5991,5992,5995,5997,6000,6002],{"class":3455,"line":27},[1115,5993,5994],{"class":3478},"                 28",[1115,5996,1547],{"class":3462},[1115,5998,5999],{"class":3478}," 50",[1115,6001,1637],{"class":3470},[1115,6003,3491],{"class":3462},[1115,6005,6006,6008,6010,6012,6014,6016,6018,6020],{"class":3455,"line":148},[1115,6007,3548],{"class":3458},[1115,6009,3551],{"class":3462},[1115,6011,3934],{"class":3478},[1115,6013,1547],{"class":3462},[1115,6015,3559],{"class":3458},[1115,6017,3551],{"class":3462},[1115,6019,3564],{"class":3478},[1115,6021,3491],{"class":3462},[1115,6023,6024,6026,6028,6030],{"class":3455,"line":111},[1115,6025,3571],{"class":3458},[1115,6027,3551],{"class":3462},[1115,6029,3576],{"class":3466},[1115,6031,3579],{"class":3470},[1115,6033,6034,6037,6039,6041,6043,6046,6048,6051,6053],{"class":3455,"line":96},[1115,6035,6036],{"class":3458},"                 pred",[1115,6038,3551],{"class":3462},[1115,6040,3589],{"class":3466},[1115,6042,1626],{"class":3470},[1115,6044,6045],{"class":3594},"\"nezverejnuje\"",[1115,6047,1547],{"class":3462},[1115,6049,6050],{"class":3594}," \"zverejnuje\"",[1115,6052,1637],{"class":3470},[1115,6054,3491],{"class":3462},[1115,6056,6057,6060,6062,6064,6066,6068,6070,6072],{"class":3455,"line":89},[1115,6058,6059],{"class":3458},"                 po",[1115,6061,3984],{"class":3462},[1115,6063,3589],{"class":3466},[1115,6065,1626],{"class":3470},[1115,6067,6045],{"class":3594},[1115,6069,1547],{"class":3462},[1115,6071,6050],{"class":3594},[1115,6073,3642],{"class":3470},[1115,6075,6076,6079,6081,6083,6085,6088,6090,6093],{"class":3455,"line":82},[1115,6077,6078],{"class":3466},"mcnemar.test",[1115,6080,1626],{"class":3470},[1115,6082,5970],{"class":3458},[1115,6084,1547],{"class":3462},[1115,6086,6087],{"class":3458}," correct",[1115,6089,3551],{"class":3462},[1115,6091,6092],{"class":3478}," FALSE",[1115,6094,3655],{"class":3470},[3447,6096,6099],{"className":6097,"code":6098,"language":3677,"meta":1229},[3675],"    McNemar's Chi-squared test\n\ndata:  tab3\nMcNemar's chi-squared = 16.667, df = 1, p-value = 4.456e-05\n",[3223,6100,6098],{"__ignoreMap":1229},[1110,6102,6103,6104,3742,6123,6140,6141,6158],{},"P-hodnota ",[1115,6105,6107],{"className":6106},[1292],[1294,6108,6109],{"xmlns":1296},[1298,6110,6111,6120],{},[1301,6112,6113,6116,6118],{},[1311,6114,6115],{},"0,00004456",[1437,6117,4086],{},[1311,6119,3738],{},[1315,6121,6122],{"encoding":1317},"0{,}00004456 \u003C 0{,}05",[1115,6124,6126],{"className":6125},[1292],[1294,6127,6128],{"xmlns":1296},[1298,6129,6130,6138],{},[1301,6131,6132],{},[1304,6133,6134,6136],{},[1307,6135,1309],{},[1311,6137,1313],{},[1315,6139,1318],{"encoding":1317}," zamítáme, přijímáme ",[1115,6142,6144],{"className":6143},[1292],[1294,6145,6146],{"xmlns":1296},[1298,6147,6148,6156],{},[1301,6149,6150],{},[1304,6151,6152,6154],{},[1307,6153,1309],{},[1311,6155,1544],{},[1315,6157,2749],{"encoding":1317}," — informační kampaň měla vliv na změnu\nchování studentů ve zveřejňování údajů na Facebooku.",[1136,6160,6162],{"id":6161},"časté-chyby","Časté chyby",[1103,6164,6168,6176],{"className":6165,"dataCallout":6167},[1106,6166],"callout-warning","warning",[1110,6169,6171,6175],{"className":6170},[1113],[1115,6172],{"className":6173,"ariaHidden":1121},[1118,6174,1120],"i-lucide:triangle-alert","Test nezávislosti na párovaných datech",[1110,6177,6178,6179,6181],{},"Tabulka před\u002Fpo vypadá jako obyčejná kontingenční tabulka, ale ",[3223,6180,3225],{}," 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.",[3447,6183,6185],{"className":3449,"code":6184,"language":71,"meta":1229,"style":1229},"chisq.test(tab3)\n",[3223,6186,6187],{"__ignoreMap":1229},[1115,6188,6189,6191,6193,6195],{"class":3455,"line":10},[1115,6190,3648],{"class":3466},[1115,6192,1626],{"class":3470},[1115,6194,5970],{"class":3458},[1115,6196,3655],{"class":3470},[3447,6198,6201],{"className":6199,"code":6200,"language":3677,"meta":1229},[3675],"    Pearson's Chi-squared test with Yates' continuity correction\n\ndata:  tab3\nX-squared = 1.4793, df = 1, p-value = 0.2239\n",[3223,6202,6200],{"__ignoreMap":1229},[1110,6204,6103,6205,6224,6225,6242,6243,6245,6246,1417],{},[1115,6206,6208],{"className":6207},[1292],[1294,6209,6210],{"xmlns":1296},[1298,6211,6212,6221],{},[1301,6213,6214,6217,6219],{},[1311,6215,6216],{},"0,224",[1437,6218,1439],{},[1311,6220,3738],{},[1315,6222,6223],{"encoding":1317},"0{,}224 > 0{,}05"," by vedla k nezamítnutí ",[1115,6226,6228],{"className":6227},[1292],[1294,6229,6230],{"xmlns":1296},[1298,6231,6232,6240],{},[1301,6233,6234],{},[1304,6235,6236,6238],{},[1307,6237,1309],{},[1311,6239,1313],{},[1315,6241,1318],{"encoding":1317}," — opačný závěr než správný McNemarův test. Na\npárovaná data (stejné prvky měřené dvakrát) vždy patří ",[3223,6244,5803],{},", nikdy ",[3223,6247,3225],{},[1103,6249,6251,6260],{"className":6250,"dataCallout":6167},[1106,6166],[1110,6252,6254,6257,6258],{"className":6253},[1113],[1115,6255],{"className":6256,"ariaHidden":1121},[1118,6174,1120],"Výchozí korekce na kontinuitu v ",[3223,6259,5803],{},[1110,6261,6262,6263,6266],{},"Bez argumentu ",[3223,6264,6265],{},"correct"," R ve výchozím nastavení použije Yatesovu korekci na kontinuitu, která dá jinou\np-hodnotu než nekorigovaný vzorec uvedený výše.",[3447,6268,6270],{"className":3449,"code":6269,"language":71,"meta":1229,"style":1229},"mcnemar.test(tab3)\n",[3223,6271,6272],{"__ignoreMap":1229},[1115,6273,6274,6276,6278,6280],{"class":3455,"line":10},[1115,6275,6078],{"class":3466},[1115,6277,1626],{"class":3470},[1115,6279,5970],{"class":3458},[1115,6281,3655],{"class":3470},[3447,6283,6286],{"className":6284,"code":6285,"language":3677,"meta":1229},[3675],"    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",[3223,6287,6285],{"__ignoreMap":1229},[1110,6289,6290,6291,6309,6310,6329,6330,6343,6344,1417],{},"Oproti nekorigované hodnotě ",[1115,6292,6294],{"className":6293},[1292],[1294,6295,6296],{"xmlns":1296},[1298,6297,6298,6306],{},[1301,6299,6300,6302,6304],{},[1307,6301,1110],{},[1437,6303,1733],{},[1311,6305,6115],{},[1315,6307,6308],{"encoding":1317},"p = 0{,}00004456"," vyjde ",[1115,6311,6313],{"className":6312},[1292],[1294,6314,6315],{"xmlns":1296},[1298,6316,6317,6326],{},[1301,6318,6319,6321,6323],{},[1307,6320,1110],{},[1437,6322,1733],{},[1311,6324,6325],{},"0,00006879",[1315,6327,6328],{"encoding":1317},"p = 0{,}00006879"," — v tomto příkladu obě vedou ke\nstejnému rozhodnutí, ale u hodnot blíž hranici ",[1115,6331,6333],{"className":6332},[1292],[1294,6334,6335],{"xmlns":1296},[1298,6336,6337,6341],{},[1301,6338,6339],{},[1307,6340,3118],{},[1315,6342,3181],{"encoding":1317}," by korekce mohla rozhodnutí změnit. Aby R reprodukovalo\nnekorigovaný vzorec, je třeba vždy volat ",[3223,6345,6346],{},"mcnemar.test(x, correct = FALSE)",[1136,6348,1189],{"id":1188},[1191,6350,6351,6356,6362,6370,6378,6383,6391],{},[1194,6352,6353],{},[1127,6354,1133],{"className":6355,"dataFsResolvedFilePath":1131,"href":1132},[1130],[1194,6357,6358],{},[1127,6359,6361],{"className":6360,"dataFsResolvedFilePath":1471,"href":1472},[1130],"Testování statistických hypotéz",[1194,6363,6364],{},[1127,6365,6369],{"className":6366,"dataFsResolvedFilePath":6367,"href":6368},[1130],"topics\u002Fpopisna-statistika.md","\u002Fwiki\u002Fpopisna-statistika","Popisná statistika a datové soubory",[1194,6371,6372],{},[1127,6373,6377],{"className":6374,"dataFsResolvedFilePath":6375,"href":6376},[1130],"topics\u002Fnahodne-veliciny-a-rozdeleni.md","\u002Fwiki\u002Fnahodne-veliciny-a-rozdeleni","Náhodné veličiny a rozdělení pravděpodobnosti",[1194,6379,6380],{},[1127,6381,1169],{"className":6382,"dataFsResolvedFilePath":1167,"href":1168},[1130],[1194,6384,6385],{},[1127,6386,6390],{"className":6387,"dataFsResolvedFilePath":6388,"href":6389},[1130],"topics\u002Fregulacni-diagramy-a-indexy-zpusobilosti.md","\u002Fwiki\u002Fregulacni-diagramy-a-indexy-zpusobilosti","Regulační diagramy a indexy způsobilosti",[1194,6392,6393],{},[1127,6394,6396],{"className":6395,"dataFsResolvedFilePath":1214,"href":1215},[1130],"Tahák pro R",[1136,6398,1219],{"id":934},[1110,6400,1222,6401,1227],{},[1224,6402,1226],{},[6404,6405,6406],"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: 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var(--shiki-dark-text-decoration);}",{"title":1229,"searchDepth":27,"depth":27,"links":6408},[6409,6410,6411,6412,6413,6414,6415,6416],{"id":1459,"depth":27,"text":1460},{"id":2578,"depth":27,"text":2579},{"id":4186,"depth":27,"text":1401},{"id":4564,"depth":27,"text":1422},{"id":5195,"depth":27,"text":1455},{"id":6161,"depth":27,"text":6162},{"id":1188,"depth":27,"text":1189},{"id":934,"depth":27,"text":1219},{},"\u002Ftopics\u002Fkontingencni-tabulky",{"title":1182,"description":1229},[1244,1246],"topics\u002Fkontingencni-tabulky",[23,67,714,486,768,71],"topic","E-gDO0c3LOdVy6YB6I-h8KKMQKlrqjomMSQWFmOANZE",{"id":6426,"title":6377,"body":6427,"course":23,"courses":1234,"created":1235,"description":1229,"extension":1236,"meta":10881,"navigation":1238,"path":10882,"seo":10883,"sources":10884,"stem":10888,"tags":10889,"type":6423,"updated":1235,"__hash__":10890},"topics\u002Ftopics\u002Fnahodne-veliciny-a-rozdeleni.md",{"type":1096,"value":6428,"toc":10869},[6429,6432,6719,6723,6956,6959,7027,7031,7038,7045,7204,7243,7246,7480,7483,7561,7615,7713,7717,7819,7822,7826,7832,7888,7891,7899,8050,8057,8110,8140,8259,8262,8310,8472,8527,8534,8641,8703,8707,8810,8813,8850,8856,8915,8964,8971,9007,9013,9016,9064,9071,9133,9139,9142,9206,9213,9252,9258,9261,9265,9291,9622,9660,9715,9845,9851,9855,9862,9881,9987,10031,10050,10145,10162,10204,10379,10386,10389,10392,10546,10549,10625,10631,10633,10819,10821,10860,10862,10866],[1099,6430,6377],{"id":6431},"náhodné-veličiny-a-rozdělení-pravděpodobnosti",[1103,6433,6435,6441],{"className":6434,"dataCallout":1264},[1106,1263],[1110,6436,6438,1272],{"className":6437},[1113],[1115,6439],{"className":6440,"ariaHidden":1121},[1118,1271,1120],[1191,6442,6443,6454,6559,6626,6707],{},[1194,6444,6445,6446,6449,6450,6453],{},"Náhodná veličina je funkce, která výsledkům pokusu přiřazuje reálná čísla; rozlišujeme ",[1279,6447,6448],{},"diskrétní"," (izolované hodnoty s nenulovou pravděpodobností) a ",[1279,6451,6452],{},"spojité"," (hodnoty z intervalu, každý bod má nulovou pravděpodobnost).",[1194,6455,6456,6457,1402,6460,6499,6500,6537,6538,6558],{},"Každou náhodnou veličinu popisuje ",[1279,6458,6459],{},"distribuční funkce",[1115,6461,6463],{"className":6462},[1292],[1294,6464,6465],{"xmlns":1296},[1298,6466,6467,6496],{},[1301,6468,6469,6472,6474,6477,6479,6481,6484,6486,6489,6492,6494],{},[1307,6470,6471],{},"F",[1437,6473,1626],{"stretchy":1625},[1307,6475,6476],{},"x",[1437,6478,1637],{"stretchy":1625},[1437,6480,1733],{},[1307,6482,6483],{},"P",[1437,6485,1626],{"stretchy":1625},[1307,6487,6488],{},"X",[1437,6490,6491],{},"≤",[1307,6493,6476],{},[1437,6495,1637],{"stretchy":1625},[1315,6497,6498],{"encoding":1317},"F(x) = P(X \\le x)","; u spojité veličiny platí ",[1115,6501,6503],{"className":6502},[1292],[1294,6504,6505],{"xmlns":1296},[1298,6506,6507,6534],{},[1301,6508,6509,6517,6519,6521,6523,6525,6528,6530,6532],{},[1330,6510,6511,6513],{},[1307,6512,6471],{},[1437,6514,6516],{"mathvariant":1872,"lspace":6515,"rspace":6515},"0em","′",[1437,6518,1626],{"stretchy":1625},[1307,6520,6476],{},[1437,6522,1637],{"stretchy":1625},[1437,6524,1733],{},[1307,6526,6527],{},"f",[1437,6529,1626],{"stretchy":1625},[1307,6531,6476],{},[1437,6533,1637],{"stretchy":1625},[1315,6535,6536],{"encoding":1317},"F'(x) = f(x)",", kde ",[1115,6539,6541],{"className":6540},[1292],[1294,6542,6543],{"xmlns":1296},[1298,6544,6545,6555],{},[1301,6546,6547,6549,6551,6553],{},[1307,6548,6527],{},[1437,6550,1626],{"stretchy":1625},[1307,6552,6476],{},[1437,6554,1637],{"stretchy":1625},[1315,6556,6557],{"encoding":1317},"f(x)"," je hustota pravděpodobnosti.",[1194,6560,6561,6562,1417],{},"Pravděpodobnost na intervalu se počítá jako ",[1115,6563,6565],{"className":6564},[1292],[1294,6566,6567],{"xmlns":1296},[1298,6568,6569,6623],{},[1301,6570,6571,6573,6575,6581,6583,6585,6587,6593,6595,6597,6599,6601,6607,6609,6611,6613,6615,6621],{},[1307,6572,6483],{},[1437,6574,1626],{"stretchy":1625},[1304,6576,6577,6579],{},[1307,6578,6476],{},[1311,6580,1544],{},[1437,6582,4086],{},[1307,6584,6488],{},[1437,6586,4086],{},[1304,6588,6589,6591],{},[1307,6590,6476],{},[1311,6592,1337],{},[1437,6594,1637],{"stretchy":1625},[1437,6596,1733],{},[1307,6598,6471],{},[1437,6600,1626],{"stretchy":1625},[1304,6602,6603,6605],{},[1307,6604,6476],{},[1311,6606,1337],{},[1437,6608,1637],{"stretchy":1625},[1437,6610,2817],{},[1307,6612,6471],{},[1437,6614,1626],{"stretchy":1625},[1304,6616,6617,6619],{},[1307,6618,6476],{},[1311,6620,1544],{},[1437,6622,1637],{"stretchy":1625},[1315,6624,6625],{"encoding":1317},"P(x_1 \u003C X \u003C x_2) = F(x_2) - F(x_1)",[1194,6627,6628,1402,6631,6663,6664,2704,6667,2704,6670,6673,6674,6688,6689,1417],{},[1279,6629,6630],{},"Normální rozdělení",[1115,6632,6634],{"className":6633},[1292],[1294,6635,6636],{"xmlns":1296},[1298,6637,6638,6660],{},[1301,6639,6640,6643,6645,6648,6651,6658],{},[1307,6641,6642],{},"N",[1437,6644,1626],{"stretchy":1625},[1307,6646,6647],{},"μ",[1437,6649,6650],{"separator":1121},";",[1330,6652,6653,6656],{},[1307,6654,6655],{},"σ",[1311,6657,1337],{},[1437,6659,1637],{"stretchy":1625},[1315,6661,6662],{"encoding":1317},"N(\\mu; \\sigma^2)"," je nejdůležitější spojité rozdělení; v R ho počítáme funkcemi ",[3223,6665,6666],{},"dnorm",[3223,6668,6669],{},"pnorm",[3223,6671,6672],{},"qnorm"," — R jako parametr očekává směrodatnou odchylku ",[1115,6675,6677],{"className":6676},[1292],[1294,6678,6679],{"xmlns":1296},[1298,6680,6681,6685],{},[1301,6682,6683],{},[1307,6684,6655],{},[1315,6686,6687],{"encoding":1317},"\\sigma",", ne rozptyl ",[1115,6690,6692],{"className":6691},[1292],[1294,6693,6694],{"xmlns":1296},[1298,6695,6696,6704],{},[1301,6697,6698],{},[1330,6699,6700,6702],{},[1307,6701,6655],{},[1311,6703,1337],{},[1315,6705,6706],{"encoding":1317},"\\sigma^2",[1194,6708,6709,2704,6712,5495,6715,6718],{},[1279,6710,6711],{},"Studentovo",[1279,6713,6714],{},"Pearsonovo (χ²)",[1279,6716,6717],{},"Fisherovo-Snedecorovo"," rozdělení slouží jako nástroj pro pozdější konstrukci intervalů spolehlivosti a testování hypotéz.",[1136,6720,6722],{"id":6721},"náhodná-veličina","Náhodná veličina",[1110,6724,6725,6728,6729,6744,6745,1402,6747,6760,6761,6781,6782,6537,6795,6819,6820,2704,6833,2704,6847,6861,6862,2704,6875,2704,6889,6903,6904,6917,6918,6931,6932,1417],{},[1127,6726,1133],{"className":6727,"dataFsResolvedFilePath":1131,"href":1132},[1130]," pracuje s veličinami, jejichž hodnota závisí na náhodě. Formálně: uvažujeme základní prostor ",[1115,6730,6732],{"className":6731},[1292],[1294,6733,6734],{"xmlns":1296},[1298,6735,6736,6741],{},[1301,6737,6738],{},[1307,6739,6740],{"mathvariant":1872},"Ω",[1315,6742,6743],{"encoding":1317},"\\Omega"," přiřazený výsledkům pokusu. ",[1279,6746,6722],{},[1115,6748,6750],{"className":6749},[1292],[1294,6751,6752],{"xmlns":1296},[1298,6753,6754,6758],{},[1301,6755,6756],{},[1307,6757,6488],{},[1315,6759,6488],{"encoding":1317}," je funkce, která prvkům ",[1115,6762,6764],{"className":6763},[1292],[1294,6765,6766],{"xmlns":1296},[1298,6767,6768,6778],{},[1301,6769,6770,6773,6776],{},[1307,6771,6772],{},"ω",[1437,6774,6775],{},"∈",[1307,6777,6740],{"mathvariant":1872},[1315,6779,6780],{"encoding":1317},"\\omega \\in \\Omega"," přiřazuje reálná čísla ",[1115,6783,6785],{"className":6784},[1292],[1294,6786,6787],{"xmlns":1296},[1298,6788,6789,6793],{},[1301,6790,6791],{},[1307,6792,6476],{},[1315,6794,6476],{"encoding":1317},[1115,6796,6798],{"className":6797},[1292],[1294,6799,6800],{"xmlns":1296},[1298,6801,6802,6816],{},[1301,6803,6804,6806,6808,6810,6812,6814],{},[1307,6805,6476],{},[1437,6807,1733],{},[1307,6809,6488],{},[1437,6811,1626],{"stretchy":1625},[1307,6813,6772],{},[1437,6815,1637],{"stretchy":1625},[1315,6817,6818],{"encoding":1317},"x = X(\\omega)",". Náhodné veličiny značíme velkými písmeny (",[1115,6821,6823],{"className":6822},[1292],[1294,6824,6825],{"xmlns":1296},[1298,6826,6827,6831],{},[1301,6828,6829],{},[1307,6830,6488],{},[1315,6832,6488],{"encoding":1317},[1115,6834,6836],{"className":6835},[1292],[1294,6837,6838],{"xmlns":1296},[1298,6839,6840,6845],{},[1301,6841,6842],{},[1307,6843,6844],{},"Y",[1315,6846,6844],{"encoding":1317},[1115,6848,6850],{"className":6849},[1292],[1294,6851,6852],{"xmlns":1296},[1298,6853,6854,6859],{},[1301,6855,6856],{},[1307,6857,6858],{},"T",[1315,6860,6858],{"encoding":1317},"), jejich konkrétní hodnoty odpovídajícími malými písmeny (",[1115,6863,6865],{"className":6864},[1292],[1294,6866,6867],{"xmlns":1296},[1298,6868,6869,6873],{},[1301,6870,6871],{},[1307,6872,6476],{},[1315,6874,6476],{"encoding":1317},[1115,6876,6878],{"className":6877},[1292],[1294,6879,6880],{"xmlns":1296},[1298,6881,6882,6887],{},[1301,6883,6884],{},[1307,6885,6886],{},"y",[1315,6888,6886],{"encoding":1317},[1115,6890,6892],{"className":6891},[1292],[1294,6893,6894],{"xmlns":1296},[1298,6895,6896,6901],{},[1301,6897,6898],{},[1307,6899,6900],{},"t",[1315,6902,6900],{"encoding":1317},"); pravděpodobnost, že ",[1115,6905,6907],{"className":6906},[1292],[1294,6908,6909],{"xmlns":1296},[1298,6910,6911,6915],{},[1301,6912,6913],{},[1307,6914,6488],{},[1315,6916,6488],{"encoding":1317}," nabyla hodnoty ",[1115,6919,6921],{"className":6920},[1292],[1294,6922,6923],{"xmlns":1296},[1298,6924,6925,6929],{},[1301,6926,6927],{},[1307,6928,6476],{},[1315,6930,6476],{"encoding":1317},", zapisujeme ",[1115,6933,6935],{"className":6934},[1292],[1294,6936,6937],{"xmlns":1296},[1298,6938,6939,6953],{},[1301,6940,6941,6943,6945,6947,6949,6951],{},[1307,6942,6483],{},[1437,6944,1626],{"stretchy":1625},[1307,6946,6488],{},[1437,6948,1733],{},[1307,6950,6476],{},[1437,6952,1637],{"stretchy":1625},[1315,6954,6955],{"encoding":1317},"P(X = x)",[1110,6957,6958],{},"Podle typu hodnot, kterých náhodná veličina nabývá, rozlišujeme dva typy:",[1191,6960,6961,7021],{},[1194,6962,6963,6966,6967,6980,6981,7020],{},[1279,6964,6965],{},"Diskrétní náhodná veličina"," — prvky ",[1115,6968,6970],{"className":6969},[1292],[1294,6971,6972],{"xmlns":1296},[1298,6973,6974,6978],{},[1301,6975,6976],{},[1307,6977,6740],{"mathvariant":1872},[1315,6979,6743],{"encoding":1317}," se zobrazí na osu reálných čísel jako izolované body ",[1115,6982,6984],{"className":6983},[1292],[1294,6985,6986],{"xmlns":1296},[1298,6987,6988,7017],{},[1301,6989,6990,6996,6998,7004,7006,7008,7010],{},[1304,6991,6992,6994],{},[1307,6993,6476],{},[1311,6995,1544],{},[1437,6997,1547],{"separator":1121},[1304,6999,7000,7002],{},[1307,7001,6476],{},[1311,7003,1337],{},[1437,7005,1547],{"separator":1121},[1437,7007,1550],{},[1437,7009,1547],{"separator":1121},[1304,7011,7012,7014],{},[1307,7013,6476],{},[1307,7015,7016],{},"k",[1315,7018,7019],{"encoding":1317},"x_1, x_2, \\dots, x_k",", přičemž každý z nich má nenulovou pravděpodobnost. Příklad: počet bodů při hodu kostkou, počet studentů na cvičení.",[1194,7022,7023,7026],{},[1279,7024,7025],{},"Spojitá náhodná veličina"," — hodnoty tvoří interval na ose reálných čísel, přičemž každý bod intervalu má nulovou pravděpodobnost. Příklad: velikost výrobku, doba psaní testu, výška dětí v populaci.",[1136,7028,7030],{"id":7029},"distribuční-funkce","Distribuční funkce",[1110,7032,7033,7034,7037],{},"Náhodná veličina nabývá při pokusu určité hodnoty, aniž bychom předem věděli, které. Při opakování pokusu se ale projevují zákonitosti, které popisují ",[1279,7035,7036],{},"zákony rozdělení",". Nejobecnějším z nich je distribuční funkce.",[1110,7039,7040],{},[4137,7041],{"alt":7042,"className":7043,"src":7044},"mask-nv-distribucni-funkce",[1130,4141],"\u002Fwiki-assets\u002Fmask-nv-distribucni-funkce.png",[1103,7046,7049,7056],{"className":7047,"dataCallout":654},[1106,7048],"callout-info",[1110,7050,7052,7055],{"className":7051},[1113],[1115,7053],{"className":7054,"ariaHidden":1121},[1118,1271,1120],"Definice",[1110,7057,7058,7059,7072,7073,7093,7094,7107,7108,7144,7163,7164,7177,7178,1417],{},"Distribuční funkcí náhodné veličiny ",[1115,7060,7062],{"className":7061},[1292],[1294,7063,7064],{"xmlns":1296},[1298,7065,7066,7070],{},[1301,7067,7068],{},[1307,7069,6488],{},[1315,7071,6488],{"encoding":1317}," nazýváme reálnou funkci ",[1115,7074,7076],{"className":7075},[1292],[1294,7077,7078],{"xmlns":1296},[1298,7079,7080,7090],{},[1301,7081,7082,7084,7086,7088],{},[1307,7083,6471],{},[1437,7085,1626],{"stretchy":1625},[1307,7087,6476],{},[1437,7089,1637],{"stretchy":1625},[1315,7091,7092],{"encoding":1317},"F(x)"," definovanou pro každé reálné číslo ",[1115,7095,7097],{"className":7096},[1292],[1294,7098,7099],{"xmlns":1296},[1298,7100,7101,7105],{},[1301,7102,7103],{},[1307,7104,6476],{},[1315,7106,6476],{"encoding":1317}," jako\n",[1115,7109,7111],{"className":7110},[1292],[1294,7112,7113],{"xmlns":1296},[1298,7114,7115,7141],{},[1301,7116,7117,7119,7121,7123,7125,7127,7129,7131,7133,7135,7137,7139],{},[1307,7118,6471],{},[1437,7120,1626],{"stretchy":1625},[1307,7122,6476],{},[1437,7124,1637],{"stretchy":1625},[1437,7126,1733],{},[1307,7128,6483],{},[1437,7130,1626],{"stretchy":1625},[1307,7132,6488],{},[1437,7134,6491],{},[1307,7136,6476],{},[1437,7138,1637],{"stretchy":1625},[1307,7140,1417],{"mathvariant":1872},[1315,7142,7143],{"encoding":1317},"F(x) = P(X \\le x).",[1115,7145,7147],{"className":7146},[1292],[1294,7148,7149],{"xmlns":1296},[1298,7150,7151,7161],{},[1301,7152,7153,7155,7157,7159],{},[1307,7154,6471],{},[1437,7156,1626],{"stretchy":1625},[1307,7158,6476],{},[1437,7160,1637],{"stretchy":1625},[1315,7162,7092],{"encoding":1317}," tedy vyjadřuje pravděpodobnost, s jakou ",[1115,7165,7167],{"className":7166},[1292],[1294,7168,7169],{"xmlns":1296},[1298,7170,7171,7175],{},[1301,7172,7173],{},[1307,7174,6488],{},[1315,7176,6488],{"encoding":1317}," nabude hodnoty z intervalu ",[1115,7179,7181],{"className":7180},[1292],[1294,7182,7183],{"xmlns":1296},[1298,7184,7185,7201],{},[1301,7186,7187,7189,7191,7194,7196,7198],{},[1437,7188,1626],{"stretchy":1625},[1437,7190,2817],{},[1307,7192,7193],{"mathvariant":1872},"∞",[1437,7195,1547],{"separator":1121},[1307,7197,6476],{},[1437,7199,7200],{"stretchy":1625},"⟩",[1315,7202,7203],{"encoding":1317},"(-\\infty, x\\rangle",[1110,7205,7206,7207,7220,7221,7242],{},"Značí-li například ",[1115,7208,7210],{"className":7209},[1292],[1294,7211,7212],{"xmlns":1296},[1298,7213,7214,7218],{},[1301,7215,7216],{},[1307,7217,6488],{},[1315,7219,6488],{"encoding":1317}," výšku mužů v populaci, pak ",[1115,7222,7224],{"className":7223},[1292],[1294,7225,7226],{"xmlns":1296},[1298,7227,7228,7239],{},[1301,7229,7230,7232,7234,7237],{},[1307,7231,6471],{},[1437,7233,1626],{"stretchy":1625},[1311,7235,7236],{},"175",[1437,7238,1637],{"stretchy":1625},[1315,7240,7241],{"encoding":1317},"F(175)"," je pravděpodobnost, že muž měří nejvýše 175 cm.",[1110,7244,7245],{},"Pro distribuční funkci vždy platí:",[1191,7247,7248,7278,7336,7396],{},[1194,7249,7250,1547],{},[1115,7251,7253],{"className":7252},[1292],[1294,7254,7255],{"xmlns":1296},[1298,7256,7257,7275],{},[1301,7258,7259,7261,7263,7265,7267,7269,7271,7273],{},[1311,7260,1313],{},[1437,7262,6491],{},[1307,7264,6471],{},[1437,7266,1626],{"stretchy":1625},[1307,7268,6476],{},[1437,7270,1637],{"stretchy":1625},[1437,7272,6491],{},[1311,7274,1544],{},[1315,7276,7277],{"encoding":1317},"0 \\le F(x) \\le 1",[1194,7279,7280,7281,1547],{},"je neklesající: ",[1115,7282,7284],{"className":7283},[1292],[1294,7285,7286],{"xmlns":1296},[1298,7287,7288,7333],{},[1301,7289,7290,7296,7298,7304,7307,7309,7311,7317,7319,7321,7323,7325,7331],{},[1304,7291,7292,7294],{},[1307,7293,6476],{},[1311,7295,1544],{},[1437,7297,6491],{},[1304,7299,7300,7302],{},[1307,7301,6476],{},[1311,7303,1337],{},[1437,7305,7306],{},"⇒",[1307,7308,6471],{},[1437,7310,1626],{"stretchy":1625},[1304,7312,7313,7315],{},[1307,7314,6476],{},[1311,7316,1544],{},[1437,7318,1637],{"stretchy":1625},[1437,7320,6491],{},[1307,7322,6471],{},[1437,7324,1626],{"stretchy":1625},[1304,7326,7327,7329],{},[1307,7328,6476],{},[1311,7330,1337],{},[1437,7332,1637],{"stretchy":1625},[1315,7334,7335],{"encoding":1317},"x_1 \\le x_2 \\Rightarrow F(x_1) \\le F(x_2)",[1194,7337,7338,7339,1547],{},"je spojitá zprava: ",[1115,7340,7342],{"className":7341},[1292],[1294,7343,7344],{"xmlns":1296},[1298,7345,7346,7393],{},[1301,7347,7348,7371,7373,7375,7377,7379,7381,7383,7385,7387,7389,7391],{},[1304,7349,7350,7357],{},[1301,7351,7352,7355],{},[1307,7353,7354],{},"lim",[1437,7356,4245],{},[1301,7358,7359,7362,7365],{},[1307,7360,7361],{},"h",[1437,7363,7364],{},"→",[1330,7366,7367,7369],{},[1311,7368,1313],{},[1437,7370,5231],{},[1307,7372,6471],{},[1437,7374,1626],{"stretchy":1625},[1307,7376,6476],{},[1437,7378,5231],{},[1307,7380,7361],{},[1437,7382,1637],{"stretchy":1625},[1437,7384,1733],{},[1307,7386,6471],{},[1437,7388,1626],{"stretchy":1625},[1307,7390,6476],{},[1437,7392,1637],{"stretchy":1625},[1315,7394,7395],{"encoding":1317},"\\lim_{h \\to 0^+} F(x+h) = F(x)",[1194,7397,7398,2704,7440,1417],{},[1115,7399,7401],{"className":7400},[1292],[1294,7402,7403],{"xmlns":1296},[1298,7404,7405,7437],{},[1301,7406,7407,7425,7427,7429,7431,7433,7435],{},[1304,7408,7409,7415],{},[1301,7410,7411,7413],{},[1307,7412,7354],{},[1437,7414,4245],{},[1301,7416,7417,7419,7421,7423],{},[1307,7418,6476],{},[1437,7420,7364],{},[1437,7422,2817],{},[1307,7424,7193],{"mathvariant":1872},[1307,7426,6471],{},[1437,7428,1626],{"stretchy":1625},[1307,7430,6476],{},[1437,7432,1637],{"stretchy":1625},[1437,7434,1733],{},[1311,7436,1313],{},[1315,7438,7439],{"encoding":1317},"\\lim_{x \\to -\\infty} F(x) = 0",[1115,7441,7443],{"className":7442},[1292],[1294,7444,7445],{"xmlns":1296},[1298,7446,7447,7477],{},[1301,7448,7449,7465,7467,7469,7471,7473,7475],{},[1304,7450,7451,7457],{},[1301,7452,7453,7455],{},[1307,7454,7354],{},[1437,7456,4245],{},[1301,7458,7459,7461,7463],{},[1307,7460,6476],{},[1437,7462,7364],{},[1307,7464,7193],{"mathvariant":1872},[1307,7466,6471],{},[1437,7468,1626],{"stretchy":1625},[1307,7470,6476],{},[1437,7472,1637],{"stretchy":1625},[1437,7474,1733],{},[1311,7476,1544],{},[1315,7478,7479],{"encoding":1317},"\\lim_{x \\to \\infty} F(x) = 1",[1110,7481,7482],{},"U spojité náhodné veličiny je distribuční funkce svázaná s hustotou pravděpodobnosti vztahem",[1115,7484,7486],{"className":7485},[1292],[1294,7487,7488],{"xmlns":1296,"display":1715},[1298,7489,7490,7558],{},[1301,7491,7492,7498,7500,7502,7504,7506,7508,7510,7512,7514,7516,7518,7520,7522,7524,7526,7528,7541,7543,7545,7547,7549,7551,7554,7556],{},[1330,7493,7494,7496],{},[1307,7495,6471],{},[1437,7497,6516],{"mathvariant":1872,"lspace":6515,"rspace":6515},[1437,7499,1626],{"stretchy":1625},[1307,7501,6476],{},[1437,7503,1637],{"stretchy":1625},[1437,7505,1733],{},[1307,7507,6527],{},[1437,7509,1626],{"stretchy":1625},[1307,7511,6476],{},[1437,7513,1637],{"stretchy":1625},[1437,7515,1547],{"separator":1121},[1763,7517],{"width":1765},[1307,7519,6471],{},[1437,7521,1626],{"stretchy":1625},[1307,7523,6476],{},[1437,7525,1637],{"stretchy":1625},[1437,7527,1733],{},[3106,7529,7530,7533,7539],{},[1437,7531,7532],{},"∫",[1301,7534,7535,7537],{},[1437,7536,2817],{},[1307,7538,7193],{"mathvariant":1872},[1307,7540,6476],{},[1307,7542,6527],{},[1437,7544,1626],{"stretchy":1625},[1307,7546,6900],{},[1437,7548,1637],{"stretchy":1625},[2661,7550,2663],{},[1307,7552,7553],{},"d",[1307,7555,6900],{},[1307,7557,1417],{"mathvariant":1872},[1315,7559,7560],{"encoding":1317},"F'(x) = f(x), \\qquad F(x) = \\int_{-\\infty}^{x} f(t)\\,dt.",[1110,7562,7563,7564,7577,7578,5495,7596,7614],{},"Pravděpodobnost, že ",[1115,7565,7567],{"className":7566},[1292],[1294,7568,7569],{"xmlns":1296},[1298,7570,7571,7575],{},[1301,7572,7573],{},[1307,7574,6488],{},[1315,7576,6488],{"encoding":1317}," padne mezi body ",[1115,7579,7581],{"className":7580},[1292],[1294,7582,7583],{"xmlns":1296},[1298,7584,7585,7593],{},[1301,7586,7587],{},[1304,7588,7589,7591],{},[1307,7590,6476],{},[1311,7592,1544],{},[1315,7594,7595],{"encoding":1317},"x_1",[1115,7597,7599],{"className":7598},[1292],[1294,7600,7601],{"xmlns":1296},[1298,7602,7603,7611],{},[1301,7604,7605],{},[1304,7606,7607,7609],{},[1307,7608,6476],{},[1311,7610,1337],{},[1315,7612,7613],{"encoding":1317},"x_2",", se pak počítá jako",[1115,7616,7618],{"className":7617},[1292],[1294,7619,7620],{"xmlns":1296,"display":1715},[1298,7621,7622,7710],{},[1301,7623,7624,7626,7628,7634,7636,7638,7640,7646,7648,7650,7666,7668,7670,7672,7674,7676,7678,7680,7682,7684,7686,7692,7694,7696,7698,7700,7706,7708],{},[1307,7625,6483],{},[1437,7627,1626],{"stretchy":1625},[1304,7629,7630,7632],{},[1307,7631,6476],{},[1311,7633,1544],{},[1437,7635,4086],{},[1307,7637,6488],{},[1437,7639,4086],{},[1304,7641,7642,7644],{},[1307,7643,6476],{},[1311,7645,1337],{},[1437,7647,1637],{"stretchy":1625},[1437,7649,1733],{},[3106,7651,7652,7654,7660],{},[1437,7653,7532],{},[1304,7655,7656,7658],{},[1307,7657,6476],{},[1311,7659,1544],{},[1304,7661,7662,7664],{},[1307,7663,6476],{},[1311,7665,1337],{},[1307,7667,6527],{},[1437,7669,1626],{"stretchy":1625},[1307,7671,6900],{},[1437,7673,1637],{"stretchy":1625},[2661,7675,2663],{},[1307,7677,7553],{},[1307,7679,6900],{},[1437,7681,1733],{},[1307,7683,6471],{},[1437,7685,1626],{"stretchy":1625},[1304,7687,7688,7690],{},[1307,7689,6476],{},[1311,7691,1337],{},[1437,7693,1637],{"stretchy":1625},[1437,7695,2817],{},[1307,7697,6471],{},[1437,7699,1626],{"stretchy":1625},[1304,7701,7702,7704],{},[1307,7703,6476],{},[1311,7705,1544],{},[1437,7707,1637],{"stretchy":1625},[1307,7709,1417],{"mathvariant":1872},[1315,7711,7712],{"encoding":1317},"P(x_1 \u003C X \u003C x_2) = \\int_{x_1}^{x_2} f(t)\\,dt = F(x_2) - F(x_1).",[1136,7714,7716],{"id":7715},"hustota-pravděpodobnosti","Hustota pravděpodobnosti",[1103,7718,7720,7726],{"className":7719,"dataCallout":654},[1106,7048],[1110,7721,7723,7055],{"className":7722},[1113],[1115,7724],{"className":7725,"ariaHidden":1121},[1118,1271,1120],[1110,7727,7728,7729,7748,7749,7762,7763,7776,7777,1417],{},"Hustota pravděpodobnosti ",[1115,7730,7732],{"className":7731},[1292],[1294,7733,7734],{"xmlns":1296},[1298,7735,7736,7746],{},[1301,7737,7738,7740,7742,7744],{},[1307,7739,6527],{},[1437,7741,1626],{"stretchy":1625},[1307,7743,6476],{},[1437,7745,1637],{"stretchy":1625},[1315,7747,6557],{"encoding":1317}," určuje, jak jsou hodnoty spojité náhodné veličiny ",[1115,7750,7752],{"className":7751},[1292],[1294,7753,7754],{"xmlns":1296},[1298,7755,7756,7760],{},[1301,7757,7758],{},[1307,7759,6488],{},[1315,7761,6488],{"encoding":1317}," nahuštěny v okolí bodu ",[1115,7764,7766],{"className":7765},[1292],[1294,7767,7768],{"xmlns":1296},[1298,7769,7770,7774],{},[1301,7771,7772],{},[1307,7773,6476],{},[1315,7775,6476],{"encoding":1317},". Je vždy nezáporná a platí pro ni ",[1115,7778,7780],{"className":7779},[1292],[1294,7781,7782],{"xmlns":1296},[1298,7783,7784,7816],{},[1301,7785,7786,7798,7800,7802,7804,7806,7808,7810,7812,7814],{},[3106,7787,7788,7790,7796],{},[1437,7789,7532],{},[1301,7791,7792,7794],{},[1437,7793,2817],{},[1307,7795,7193],{"mathvariant":1872},[1307,7797,7193],{"mathvariant":1872},[1307,7799,6527],{},[1437,7801,1626],{"stretchy":1625},[1307,7803,6476],{},[1437,7805,1637],{"stretchy":1625},[2661,7807,2663],{},[1307,7809,7553],{},[1307,7811,6476],{},[1437,7813,1733],{},[1311,7815,1544],{},[1315,7817,7818],{"encoding":1317},"\\int_{-\\infty}^{\\infty} f(x)\\,dx = 1",[1110,7820,7821],{},"Intuitivně: rozdělíme-li hodnoty náhodné veličiny (např. výšku mužů v populaci) do stejně širokých intervalů, bude v intervalech blízko průměru nahuštěno víc pozorování než v krajních intervalech — hustota tam bude vyšší.",[1136,7823,7825],{"id":7824},"charakteristiky-spojité-náhodné-veličiny","Charakteristiky spojité náhodné veličiny",[1110,7827,7828,7831],{},[1279,7829,7830],{},"Střední hodnota"," je nejdůležitější charakteristika náhodné veličiny:",[1115,7833,7835],{"className":7834},[1292],[1294,7836,7837],{"xmlns":1296,"display":1715},[1298,7838,7839,7885],{},[1301,7840,7841,7844,7846,7848,7850,7852,7864,7866,7869,7871,7873,7875,7877,7879,7881,7883],{},[1307,7842,7843],{},"E",[1437,7845,1626],{"stretchy":1625},[1307,7847,6488],{},[1437,7849,1637],{"stretchy":1625},[1437,7851,1733],{},[3106,7853,7854,7856,7862],{},[1437,7855,7532],{},[1301,7857,7858,7860],{},[1437,7859,2817],{},[1307,7861,7193],{"mathvariant":1872},[1307,7863,7193],{"mathvariant":1872},[1307,7865,6476],{},[1437,7867,7868],{},"⋅",[1307,7870,6527],{},[1437,7872,1626],{"stretchy":1625},[1307,7874,6476],{},[1437,7876,1637],{"stretchy":1625},[2661,7878,2663],{},[1307,7880,7553],{},[1307,7882,6476],{},[1307,7884,1417],{"mathvariant":1872},[1315,7886,7887],{"encoding":1317},"E(X) = \\int_{-\\infty}^{\\infty} x \\cdot f(x)\\,dx.",[1110,7889,7890],{},"Je to číslo, kolem něhož kolísají výběrové průměry vypočtené ze sérií pozorovaných hodnot náhodné veličiny.",[1110,7892,7893,5495,7896,1709],{},[1279,7894,7895],{},"Rozptyl",[1279,7897,7898],{},"směrodatná odchylka",[1115,7900,7902],{"className":7901},[1292],[1294,7903,7904],{"xmlns":1296,"display":1715},[1298,7905,7906,8047],{},[1301,7907,7908,7911,7913,7915,7917,7919,7931,7934,7936,7938,7940,7942,7944,7946,7953,7955,7957,7959,7961,7963,7965,7967,7969,7981,7987,7989,7991,7993,7995,7997,7999,8001,8003,8005,8007,8009,8011,8013,8019,8021,8023,8025,8027,8029,8031,8033,8045],{},[1307,7909,7910],{},"D",[1437,7912,1626],{"stretchy":1625},[1307,7914,6488],{},[1437,7916,1637],{"stretchy":1625},[1437,7918,1733],{},[3106,7920,7921,7923,7929],{},[1437,7922,7532],{},[1301,7924,7925,7927],{},[1437,7926,2817],{},[1307,7928,7193],{"mathvariant":1872},[1307,7930,7193],{"mathvariant":1872},[1437,7932,7933],{"stretchy":1625},"[",[1307,7935,6476],{},[1437,7937,2817],{},[1307,7939,7843],{},[1437,7941,1626],{"stretchy":1625},[1307,7943,6488],{},[1437,7945,1637],{"stretchy":1625},[1330,7947,7948,7951],{},[1437,7949,7950],{"stretchy":1625},"]",[1311,7952,1337],{},[1307,7954,6527],{},[1437,7956,1626],{"stretchy":1625},[1307,7958,6476],{},[1437,7960,1637],{"stretchy":1625},[2661,7962,2663],{},[1307,7964,7553],{},[1307,7966,6476],{},[1437,7968,1733],{},[3106,7970,7971,7973,7979],{},[1437,7972,7532],{},[1301,7974,7975,7977],{},[1437,7976,2817],{},[1307,7978,7193],{"mathvariant":1872},[1307,7980,7193],{"mathvariant":1872},[1330,7982,7983,7985],{},[1307,7984,6476],{},[1311,7986,1337],{},[1307,7988,6527],{},[1437,7990,1626],{"stretchy":1625},[1307,7992,6476],{},[1437,7994,1637],{"stretchy":1625},[2661,7996,2663],{},[1307,7998,7553],{},[1307,8000,6476],{},[1437,8002,2817],{},[1437,8004,7933],{"stretchy":1625},[1307,8006,7843],{},[1437,8008,1626],{"stretchy":1625},[1307,8010,6488],{},[1437,8012,1637],{"stretchy":1625},[1330,8014,8015,8017],{},[1437,8016,7950],{"stretchy":1625},[1311,8018,1337],{},[1437,8020,1547],{"separator":1121},[1763,8022],{"width":1765},[1307,8024,6655],{},[1437,8026,1626],{"stretchy":1625},[1307,8028,6488],{},[1437,8030,1637],{"stretchy":1625},[1437,8032,1733],{},[4207,8034,8035],{},[1301,8036,8037,8039,8041,8043],{},[1307,8038,7910],{},[1437,8040,1626],{"stretchy":1625},[1307,8042,6488],{},[1437,8044,1637],{"stretchy":1625},[1307,8046,1417],{"mathvariant":1872},[1315,8048,8049],{"encoding":1317},"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)}.",[1110,8051,8052,8053,8056],{},"Směrodatná odchylka udává, jak moc jsou hodnoty náhodné veličiny rozptýlené kolem střední hodnoty. (Pro odhad těchto charakteristik z naměřených dat viz empirické protějšky v ",[1127,8054,886],{"className":8055,"dataFsResolvedFilePath":6367,"href":6368},[1130],".)",[1110,8058,8059,8062,8063,8076,8077,8095,8096,8109],{},[1279,8060,8061],{},"Kvantily"," udávají, jak jsou hodnoty náhodné veličiny ",[1115,8064,8066],{"className":8065},[1292],[1294,8067,8068],{"xmlns":1296},[1298,8069,8070,8074],{},[1301,8071,8072],{},[1307,8073,6488],{},[1315,8075,6488],{"encoding":1317}," rozděleny na ose reálných čísel v určitém pravděpodobnostním poměru. 100p%-ní kvantil ",[1115,8078,8080],{"className":8079},[1292],[1294,8081,8082],{"xmlns":1296},[1298,8083,8084,8092],{},[1301,8085,8086],{},[1304,8087,8088,8090],{},[1307,8089,6476],{},[1307,8091,1110],{},[1315,8093,8094],{"encoding":1317},"x_p"," je číslo, pro které při zvolené pravděpodobnosti ",[1115,8097,8099],{"className":8098},[1292],[1294,8100,8101],{"xmlns":1296},[1298,8102,8103,8107],{},[1301,8104,8105],{},[1307,8106,1110],{},[1315,8108,1110],{"encoding":1317}," platí",[1115,8111,8113],{"className":8112},[1292],[1294,8114,8115],{"xmlns":1296,"display":1715},[1298,8116,8117,8137],{},[1301,8118,8119,8121,8123,8129,8131,8133,8135],{},[1307,8120,6471],{},[1437,8122,1626],{"stretchy":1625},[1304,8124,8125,8127],{},[1307,8126,6476],{},[1307,8128,1110],{},[1437,8130,1637],{"stretchy":1625},[1437,8132,1733],{},[1307,8134,1110],{},[1307,8136,1417],{"mathvariant":1872},[1315,8138,8139],{"encoding":1317},"F(x_p) = p.",[1110,8141,8142,8143,8171,8172,8199,8200,8219,8220,8239,8240,1417],{},"V intervalu ",[1115,8144,8146],{"className":8145},[1292],[1294,8147,8148],{"xmlns":1296},[1298,8149,8150,8168],{},[1301,8151,8152,8154,8156,8158,8160,8166],{},[1437,8153,1626],{"stretchy":1625},[1437,8155,2817],{},[1307,8157,7193],{"mathvariant":1872},[1437,8159,6650],{"separator":1121},[1304,8161,8162,8164],{},[1307,8163,6476],{},[1307,8165,1110],{},[1437,8167,1637],{"stretchy":1625},[1315,8169,8170],{"encoding":1317},"(-\\infty; x_p)"," leží 100p % hodnot, v intervalu ",[1115,8173,8175],{"className":8174},[1292],[1294,8176,8177],{"xmlns":1296},[1298,8178,8179,8196],{},[1301,8180,8181,8184,8190,8192,8194],{},[1437,8182,8183],{"stretchy":1625},"⟨",[1304,8185,8186,8188],{},[1307,8187,6476],{},[1307,8189,1110],{},[1437,8191,6650],{"separator":1121},[1307,8193,7193],{"mathvariant":1872},[1437,8195,1637],{"stretchy":1625},[1315,8197,8198],{"encoding":1317},"\\langle x_p; \\infty)"," leží 100(1-p) % hodnot. Nejdůležitější kvantily jsou medián ",[1115,8201,8203],{"className":8202},[1292],[1294,8204,8205],{"xmlns":1296},[1298,8206,8207,8216],{},[1301,8208,8209],{},[1304,8210,8211,8213],{},[1307,8212,6476],{},[1311,8214,8215],{},"0,5",[1315,8217,8218],{"encoding":1317},"x_{0{,}5}",", dolní kvartil ",[1115,8221,8223],{"className":8222},[1292],[1294,8224,8225],{"xmlns":1296},[1298,8226,8227,8236],{},[1301,8228,8229],{},[1304,8230,8231,8233],{},[1307,8232,6476],{},[1311,8234,8235],{},"0,25",[1315,8237,8238],{"encoding":1317},"x_{0{,}25}"," a horní kvartil ",[1115,8241,8243],{"className":8242},[1292],[1294,8244,8245],{"xmlns":1296},[1298,8246,8247,8256],{},[1301,8248,8249],{},[1304,8250,8251,8253],{},[1307,8252,6476],{},[1311,8254,8255],{},"0,75",[1315,8257,8258],{"encoding":1317},"x_{0{,}75}",[1136,8260,6630],{"id":8261},"normální-rozdělení",[1110,8263,8264,8265,8278,8279,1402,8282,8309],{},"Spojitá náhodná veličina ",[1115,8266,8268],{"className":8267},[1292],[1294,8269,8270],{"xmlns":1296},[1298,8271,8272,8276],{},[1301,8273,8274],{},[1307,8275,6488],{},[1315,8277,6488],{"encoding":1317}," má ",[1279,8280,8281],{},"normální rozdělení",[1115,8283,8285],{"className":8284},[1292],[1294,8286,8287],{"xmlns":1296},[1298,8288,8289,8307],{},[1301,8290,8291,8293,8295,8297,8299,8305],{},[1307,8292,6642],{},[1437,8294,1626],{"stretchy":1625},[1307,8296,6647],{},[1437,8298,6650],{"separator":1121},[1330,8300,8301,8303],{},[1307,8302,6655],{},[1311,8304,1337],{},[1437,8306,1637],{"stretchy":1625},[1315,8308,6662],{"encoding":1317},", jestliže její hustota pravděpodobnosti a distribuční funkce jsou dány předpisy",[1115,8311,8313],{"className":8312},[1292],[1294,8314,8315],{"xmlns":1296,"display":1715},[1298,8316,8317,8469],{},[1301,8318,8319,8321,8323,8325,8327,8329,8346,8383,8385,8387,8389,8391,8393,8395,8397,8413,8425,8461,8463,8465,8467],{},[1307,8320,6527],{},[1437,8322,1626],{"stretchy":1625},[1307,8324,6476],{},[1437,8326,1637],{"stretchy":1625},[1437,8328,1733],{},[2491,8330,8331,8333],{},[1311,8332,1544],{},[1301,8334,8335,8337],{},[1307,8336,6655],{},[4207,8338,8339],{},[1301,8340,8341,8343],{},[1311,8342,1337],{},[1307,8344,8345],{},"π",[1330,8347,8348,8351],{},[1307,8349,8350],{},"e",[1301,8352,8353,8355],{},[1437,8354,2817],{},[2491,8356,8357,8373],{},[1301,8358,8359,8361,8363,8365,8367],{},[1437,8360,1626],{"stretchy":1625},[1307,8362,6476],{},[1437,8364,2817],{},[1307,8366,6647],{},[1330,8368,8369,8371],{},[1437,8370,1637],{"stretchy":1625},[1311,8372,1337],{},[1301,8374,8375,8377],{},[1311,8376,1337],{},[1330,8378,8379,8381],{},[1307,8380,6655],{},[1311,8382,1337],{},[1437,8384,1547],{"separator":1121},[1763,8386],{"width":1765},[1307,8388,6471],{},[1437,8390,1626],{"stretchy":1625},[1307,8392,6476],{},[1437,8394,1637],{"stretchy":1625},[1437,8396,1733],{},[2491,8398,8399,8401],{},[1311,8400,1544],{},[1301,8402,8403,8405],{},[1307,8404,6655],{},[4207,8406,8407],{},[1301,8408,8409,8411],{},[1311,8410,1337],{},[1307,8412,8345],{},[3106,8414,8415,8417,8423],{},[1437,8416,7532],{},[1301,8418,8419,8421],{},[1437,8420,2817],{},[1307,8422,7193],{"mathvariant":1872},[1307,8424,6476],{},[1330,8426,8427,8429],{},[1307,8428,8350],{},[1301,8430,8431,8433],{},[1437,8432,2817],{},[2491,8434,8435,8451],{},[1301,8436,8437,8439,8441,8443,8445],{},[1437,8438,1626],{"stretchy":1625},[1307,8440,6900],{},[1437,8442,2817],{},[1307,8444,6647],{},[1330,8446,8447,8449],{},[1437,8448,1637],{"stretchy":1625},[1311,8450,1337],{},[1301,8452,8453,8455],{},[1311,8454,1337],{},[1330,8456,8457,8459],{},[1307,8458,6655],{},[1311,8460,1337],{},[2661,8462,2663],{},[1307,8464,7553],{},[1307,8466,6900],{},[1437,8468,1547],{"separator":1121},[1315,8470,8471],{"encoding":1317},"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,",[1110,8473,8474,8475,2704,8499,1417],{},"přičemž ",[1115,8476,8478],{"className":8477},[1292],[1294,8479,8480],{"xmlns":1296},[1298,8481,8482,8496],{},[1301,8483,8484,8486,8488,8490,8492,8494],{},[1307,8485,7843],{},[1437,8487,1626],{"stretchy":1625},[1307,8489,6488],{},[1437,8491,1637],{"stretchy":1625},[1437,8493,1733],{},[1307,8495,6647],{},[1315,8497,8498],{"encoding":1317},"E(X) = \\mu",[1115,8500,8502],{"className":8501},[1292],[1294,8503,8504],{"xmlns":1296},[1298,8505,8506,8524],{},[1301,8507,8508,8510,8512,8514,8516,8518],{},[1307,8509,7910],{},[1437,8511,1626],{"stretchy":1625},[1307,8513,6488],{},[1437,8515,1637],{"stretchy":1625},[1437,8517,1733],{},[1330,8519,8520,8522],{},[1307,8521,6655],{},[1311,8523,1337],{},[1315,8525,8526],{"encoding":1317},"D(X) = \\sigma^2",[1110,8528,8529],{},[4137,8530],{"alt":8531,"className":8532,"src":8533},"mask-nv-normalni",[1130,4141],"\u002Fwiki-assets\u002Fmask-nv-normalni.png",[1110,8535,8536,8537,8540,8541,8555,8556,8575,8576,8592,8593,8606,8607,1417],{},"Křivka hustoty se nazývá ",[1279,8538,8539],{},"Gaussova křivka",": je symetrická kolem svislé přímky procházející ",[1115,8542,8544],{"className":8543},[1292],[1294,8545,8546],{"xmlns":1296},[1298,8547,8548,8552],{},[1301,8549,8550],{},[1307,8551,6647],{},[1315,8553,8554],{"encoding":1317},"\\mu",", kde má ",[1115,8557,8559],{"className":8558},[1292],[1294,8560,8561],{"xmlns":1296},[1298,8562,8563,8573],{},[1301,8564,8565,8567,8569,8571],{},[1307,8566,6527],{},[1437,8568,1626],{"stretchy":1625},[1307,8570,6476],{},[1437,8572,1637],{"stretchy":1625},[1315,8574,6557],{"encoding":1317}," globální maximum, a ve vzdálenosti ",[1115,8577,8579],{"className":8578},[1292],[1294,8580,8581],{"xmlns":1296},[1298,8582,8583,8589],{},[1301,8584,8585,8587],{},[1311,8586,3345],{},[1307,8588,6655],{},[1315,8590,8591],{"encoding":1317},"3\\sigma"," od ",[1115,8594,8596],{"className":8595},[1292],[1294,8597,8598],{"xmlns":1296},[1298,8599,8600,8604],{},[1301,8601,8602],{},[1307,8603,6647],{},[1315,8605,8554],{"encoding":1317}," se téměř dotýká osy x — zhruba 99,73 % hodnot leží v intervalu ",[1115,8608,8610],{"className":8609},[1292],[1294,8611,8612],{"xmlns":1296},[1298,8613,8614,8638],{},[1301,8615,8616,8618,8620,8622,8624,8626,8628,8630,8632,8634,8636],{},[1437,8617,1626],{"stretchy":1625},[1307,8619,6647],{},[1437,8621,2817],{},[1311,8623,3345],{},[1307,8625,6655],{},[1437,8627,6650],{"separator":1121},[1307,8629,6647],{},[1437,8631,5231],{},[1311,8633,3345],{},[1307,8635,6655],{},[1437,8637,1637],{"stretchy":1625},[1315,8639,8640],{"encoding":1317},"(\\mu - 3\\sigma; \\mu + 3\\sigma)",[1110,8642,8643,8644,1402,8647,8671,8672,1417],{},"Zvláštní postavení má ",[1279,8645,8646],{},"normované normální rozdělení",[1115,8648,8650],{"className":8649},[1292],[1294,8651,8652],{"xmlns":1296},[1298,8653,8654,8668],{},[1301,8655,8656,8658,8660,8662,8664,8666],{},[1307,8657,6642],{},[1437,8659,1626],{"stretchy":1625},[1311,8661,1313],{},[1437,8663,6650],{"separator":1121},[1311,8665,1544],{},[1437,8667,1637],{"stretchy":1625},[1315,8669,8670],{"encoding":1317},"N(0; 1)",", na které se dá libovolné normální rozdělení převést standardizací ",[1115,8673,8675],{"className":8674},[1292],[1294,8676,8677],{"xmlns":1296},[1298,8678,8679,8700],{},[1301,8680,8681,8684,8686,8688,8690,8692,8694,8696,8698],{},[1307,8682,8683],{},"Z",[1437,8685,1733],{},[1437,8687,1626],{"stretchy":1625},[1307,8689,6488],{},[1437,8691,2817],{},[1307,8693,6647],{},[1437,8695,1637],{"stretchy":1625},[1307,8697,4358],{"mathvariant":1872},[1307,8699,6655],{},[1315,8701,8702],{"encoding":1317},"Z = (X-\\mu)\u002F\\sigma",[8704,8705],"graph-mount",{"spec":8706},"{\"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\"}]}",[1103,8708,8710,8717],{"className":8709,"dataCallout":6167},[1106,6166],[1110,8711,8713,8716],{"className":8712},[1113],[1115,8714],{"className":8715,"ariaHidden":1121},[1118,6174,1120],"R očekává směrodatnou odchylku, ne rozptyl",[1110,8718,8719,8720,8747,8748,8751,8752,2704,8754,5495,8756,8758,8759,1402,8762,8775,8776,8802,8803,8806,8807,1417],{},"Zápis ",[1115,8721,8723],{"className":8722},[1292],[1294,8724,8725],{"xmlns":1296},[1298,8726,8727,8745],{},[1301,8728,8729,8731,8733,8735,8737,8743],{},[1307,8730,6642],{},[1437,8732,1626],{"stretchy":1625},[1307,8734,6647],{},[1437,8736,6650],{"separator":1121},[1330,8738,8739,8741],{},[1307,8740,6655],{},[1311,8742,1337],{},[1437,8744,1637],{"stretchy":1625},[1315,8746,6662],{"encoding":1317}," v definici používá ",[1279,8749,8750],{},"rozptyl",". Funkce ",[3223,8753,6666],{},[3223,8755,6669],{},[3223,8757,6672],{}," v R ale jako třetí argument berou ",[1279,8760,8761],{},"směrodatnou odchylku",[1115,8763,8765],{"className":8764},[1292],[1294,8766,8767],{"xmlns":1296},[1298,8768,8769,8773],{},[1301,8770,8771],{},[1307,8772,6655],{},[1315,8774,6687],{"encoding":1317},". Má-li náhodná veličina rozdělení ",[1115,8777,8779],{"className":8778},[1292],[1294,8780,8781],{"xmlns":1296},[1298,8782,8783,8799],{},[1301,8784,8785,8787,8789,8792,8794,8797],{},[1307,8786,6642],{},[1437,8788,1626],{"stretchy":1625},[1311,8790,8791],{},"10",[1437,8793,6650],{"separator":1121},[1311,8795,8796],{},"0,12",[1437,8798,1637],{"stretchy":1625},[1315,8800,8801],{"encoding":1317},"N(10; 0{,}12)",", je ",[3223,8804,8805],{},"sd = sqrt(0.12)",", ne ",[3223,8808,8809],{},"sd = 0.12",[1110,8811,8812],{},"V R:",[3447,8814,8816],{"className":3449,"code":8815,"language":71,"meta":1229,"style":1229},"dnorm(0)\npnorm(1.96)\nqnorm(0.975)\n",[3223,8817,8818,8828,8839],{"__ignoreMap":1229},[1115,8819,8820,8822,8824,8826],{"class":3455,"line":10},[1115,8821,6666],{"class":3466},[1115,8823,1626],{"class":3470},[1115,8825,1313],{"class":3478},[1115,8827,3655],{"class":3470},[1115,8829,8830,8832,8834,8837],{"class":3455,"line":27},[1115,8831,6669],{"class":3466},[1115,8833,1626],{"class":3470},[1115,8835,8836],{"class":3478},"1.96",[1115,8838,3655],{"class":3470},[1115,8840,8841,8843,8845,8848],{"class":3455,"line":148},[1115,8842,6672],{"class":3466},[1115,8844,1626],{"class":3470},[1115,8846,8847],{"class":3478},"0.975",[1115,8849,3655],{"class":3470},[3447,8851,8854],{"className":8852,"code":8853,"language":3677,"meta":1229},[3675],"[1] 0.3989423\n[1] 0.9750021\n[1] 1.959964\n",[3223,8855,8853],{"__ignoreMap":1229},[1110,8857,8858,8861,8862,8886,8887,1641,8890,5495,8911,8914],{},[3223,8859,8860],{},"dnorm(0)"," je hodnota hustoty ",[1115,8863,8865],{"className":8864},[1292],[1294,8866,8867],{"xmlns":1296},[1298,8868,8869,8883],{},[1301,8870,8871,8873,8875,8877,8879,8881],{},[1307,8872,6642],{},[1437,8874,1626],{"stretchy":1625},[1311,8876,1313],{},[1437,8878,6650],{"separator":1121},[1311,8880,1544],{},[1437,8882,1637],{"stretchy":1625},[1315,8884,8885],{"encoding":1317},"N(0;1)"," v bodě 0, ",[3223,8888,8889],{},"pnorm(1.96)",[1115,8891,8893],{"className":8892},[1292],[1294,8894,8895],{"xmlns":1296},[1298,8896,8897,8908],{},[1301,8898,8899,8901,8903,8906],{},[1307,8900,6471],{},[1437,8902,1626],{"stretchy":1625},[1311,8904,8905],{},"1,96",[1437,8907,1637],{"stretchy":1625},[1315,8909,8910],{"encoding":1317},"F(1{,}96)",[3223,8912,8913],{},"qnorm(0.975)"," je 97,5%-ní kvantil — hodnota, pod kterou leží 97,5 % pravděpodobnosti.",[1103,8916,8918,8925],{"className":8917,"dataCallout":3230},[1106,3229],[1110,8919,8921,8924],{"className":8920},[1113],[1115,8922],{"className":8923,"ariaHidden":1121},[1118,3237,1120],"Příklad: Návštěvnost zábavního parku",[1110,8926,8927,8928,8963],{},"Denní návštěvnost zábavního parku je náhodná veličina s normálním rozdělením, průměrnou hodnotou 230 a směrodatnou odchylkou 27,5 návštěvníků: ",[1115,8929,8931],{"className":8930},[1292],[1294,8932,8933],{"xmlns":1296},[1298,8934,8935,8960],{},[1301,8936,8937,8939,8942,8944,8946,8949,8951,8958],{},[1307,8938,6488],{},[1437,8940,8941],{},"∼",[1307,8943,6642],{},[1437,8945,1626],{"stretchy":1625},[1311,8947,8948],{},"230",[1437,8950,6650],{"separator":1121},[1330,8952,8953,8956],{},[1311,8954,8955],{},"27,5",[1311,8957,1337],{},[1437,8959,1637],{"stretchy":1625},[1315,8961,8962],{"encoding":1317},"X \\sim N(230; 27{,}5^2)",". Přijde-li za den méně než 180 návštěvníků, je park ztrátový. Kolik procent dní je ztrátových?",[1110,8965,8966],{},[4137,8967],{"alt":8968,"className":8969,"src":8970},"mask-nv-priklad-park",[1130,4141],"\u002Fwiki-assets\u002Fmask-nv-priklad-park.png",[3447,8972,8974],{"className":3449,"code":8973,"language":71,"meta":1229,"style":1229},"pnorm(180, mean = 230, sd = 27.5)\n",[3223,8975,8976],{"__ignoreMap":1229},[1115,8977,8978,8980,8982,8985,8987,8990,8992,8995,8997,9000,9002,9005],{"class":3455,"line":10},[1115,8979,6669],{"class":3466},[1115,8981,1626],{"class":3470},[1115,8983,8984],{"class":3478},"180",[1115,8986,1547],{"class":3462},[1115,8988,8989],{"class":3458}," mean",[1115,8991,3551],{"class":3462},[1115,8993,8994],{"class":3478}," 230",[1115,8996,1547],{"class":3462},[1115,8998,8999],{"class":3458}," sd",[1115,9001,3551],{"class":3462},[1115,9003,9004],{"class":3478}," 27.5",[1115,9006,3655],{"class":3470},[3447,9008,9011],{"className":9009,"code":9010,"language":3677,"meta":1229},[3675],"[1] 0.03451817\n",[3223,9012,9010],{"__ignoreMap":1229},[1110,9014,9015],{},"Park je ztrátový přibližně v 3,45 % dní.",[1103,9017,9019,9026],{"className":9018,"dataCallout":3230},[1106,3229],[1110,9020,9022,9025],{"className":9021},[1113],[1115,9023],{"className":9024,"ariaHidden":1121},[1118,3237,1120],"Příklad: Délka výrobku",[1110,9027,9028,9029,9063],{},"Automat je seřízen tak, aby střední hodnota délky výrobku byla 42 mm, s přesností charakterizovanou směrodatnou odchylkou 1,2 mm: ",[1115,9030,9032],{"className":9031},[1292],[1294,9033,9034],{"xmlns":1296},[1298,9035,9036,9060],{},[1301,9037,9038,9040,9042,9044,9046,9049,9051,9058],{},[1307,9039,6488],{},[1437,9041,8941],{},[1307,9043,6642],{},[1437,9045,1626],{"stretchy":1625},[1311,9047,9048],{},"42",[1437,9050,6650],{"separator":1121},[1330,9052,9053,9056],{},[1311,9054,9055],{},"1,2",[1311,9057,1337],{},[1437,9059,1637],{"stretchy":1625},[1315,9061,9062],{"encoding":1317},"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?",[1110,9065,9066],{},[4137,9067],{"alt":9068,"className":9069,"src":9070},"mask-nv-priklad-delka",[1130,4141],"\u002Fwiki-assets\u002Fmask-nv-priklad-delka.png",[3447,9072,9074],{"className":3449,"code":9073,"language":71,"meta":1229,"style":1229},"pnorm(43, mean = 42, sd = 1.2) - pnorm(41, mean = 42, sd = 1.2)\n",[3223,9075,9076],{"__ignoreMap":1229},[1115,9077,9078,9080,9082,9085,9087,9089,9091,9094,9096,9098,9100,9103,9105,9107,9110,9112,9115,9117,9119,9121,9123,9125,9127,9129,9131],{"class":3455,"line":10},[1115,9079,6669],{"class":3466},[1115,9081,1626],{"class":3470},[1115,9083,9084],{"class":3478},"43",[1115,9086,1547],{"class":3462},[1115,9088,8989],{"class":3458},[1115,9090,3551],{"class":3462},[1115,9092,9093],{"class":3478}," 42",[1115,9095,1547],{"class":3462},[1115,9097,8999],{"class":3458},[1115,9099,3551],{"class":3462},[1115,9101,9102],{"class":3478}," 1.2",[1115,9104,4355],{"class":3470},[1115,9106,4392],{"class":3462},[1115,9108,9109],{"class":3466}," pnorm",[1115,9111,1626],{"class":3470},[1115,9113,9114],{"class":3478},"41",[1115,9116,1547],{"class":3462},[1115,9118,8989],{"class":3458},[1115,9120,3551],{"class":3462},[1115,9122,9093],{"class":3478},[1115,9124,1547],{"class":3462},[1115,9126,8999],{"class":3458},[1115,9128,3551],{"class":3462},[1115,9130,9102],{"class":3478},[1115,9132,3655],{"class":3470},[3447,9134,9137],{"className":9135,"code":9136,"language":3677,"meta":1229},[3675],"[1] 0.5953432\n",[3223,9138,9136],{"__ignoreMap":1229},[1110,9140,9141],{},"Do 1. jakostní třídy spadá přibližně 59,53 % výrobků.",[1103,9143,9145,9152],{"className":9144,"dataCallout":3230},[1106,3229],[1110,9146,9148,9151],{"className":9147},[1113],[1115,9149],{"className":9150,"ariaHidden":1121},[1118,3237,1120],"Příklad: Obsah ampulky",[1110,9153,9154,9155,9178,9179,9205],{},"Obsah ampulky s lékem (v cm³) má rozdělení ",[1115,9156,9158],{"className":9157},[1292],[1294,9159,9160],{"xmlns":1296},[1298,9161,9162,9176],{},[1301,9163,9164,9166,9168,9170,9172,9174],{},[1307,9165,6642],{},[1437,9167,1626],{"stretchy":1625},[1311,9169,8791],{},[1437,9171,6650],{"separator":1121},[1311,9173,8796],{},[1437,9175,1637],{"stretchy":1625},[1315,9177,8801],{"encoding":1317},", tedy střední hodnota 10 a rozptyl 0,12 (",[1115,9180,9182],{"className":9181},[1292],[1294,9183,9184],{"xmlns":1296},[1298,9185,9186,9202],{},[1301,9187,9188,9190,9192,9196,9199],{},[1307,9189,6655],{},[1437,9191,1733],{},[4207,9193,9194],{},[1311,9195,8796],{},[1437,9197,9198],{},"≈",[1311,9200,9201],{},"0,346",[1315,9203,9204],{"encoding":1317},"\\sigma = \\sqrt{0{,}12} \\approx 0{,}346","). Kolik procent ampulek má obsah menší než 9,8 cm³?",[1110,9207,9208],{},[4137,9209],{"alt":9210,"className":9211,"src":9212},"mask-nv-priklad-ampulka",[1130,4141],"\u002Fwiki-assets\u002Fmask-nv-priklad-ampulka.png",[3447,9214,9216],{"className":3449,"code":9215,"language":71,"meta":1229,"style":1229},"pnorm(9.8, mean = 10, sd = sqrt(0.12))\n",[3223,9217,9218],{"__ignoreMap":1229},[1115,9219,9220,9222,9224,9227,9229,9231,9233,9236,9238,9240,9242,9244,9246,9249],{"class":3455,"line":10},[1115,9221,6669],{"class":3466},[1115,9223,1626],{"class":3470},[1115,9225,9226],{"class":3478},"9.8",[1115,9228,1547],{"class":3462},[1115,9230,8989],{"class":3458},[1115,9232,3551],{"class":3462},[1115,9234,9235],{"class":3478}," 10",[1115,9237,1547],{"class":3462},[1115,9239,8999],{"class":3458},[1115,9241,3551],{"class":3462},[1115,9243,4332],{"class":3466},[1115,9245,1626],{"class":3470},[1115,9247,9248],{"class":3478},"0.12",[1115,9250,9251],{"class":3470},"))\n",[3447,9253,9256],{"className":9254,"code":9255,"language":3677,"meta":1229},[3675],"[1] 0.2818514\n",[3223,9257,9255],{"__ignoreMap":1229},[1110,9259,9260],{},"Obsah menší než 9,8 cm³ má přibližně 28,19 % ampulek.",[1136,9262,9264],{"id":9263},"další-rozdělení-dostupná-v-r","Další rozdělení dostupná v R",[1110,9266,9267,9268,9271,9272,9275,9276,9279,9280,4358,9283,9286,9287,9290],{},"Vedle normálního rozdělení R přímo nabízí hustotu, distribuční funkci a kvantilovou funkci i pro další běžná rozdělení. Pojmenování funkcí je jednotné: ",[3223,9269,9270],{},"d*"," je hustota\u002Fpravděpodobnostní funkce, ",[3223,9273,9274],{},"p*"," distribuční funkce (s ",[3223,9277,9278],{},"lower.tail = FALSE",", případně čtvrtým argumentem ",[3223,9281,9282],{},"TRUE",[3223,9284,9285],{},"FALSE",", pro horní chvost) a ",[3223,9288,9289],{},"q*"," kvantilová funkce.",[1141,9292,9293,9399],{},[1144,9294,9295],{},[1147,9296,9297,9300,9346,9372],{},[1150,9298,9299],{},"Rozdělení",[1150,9301,9302,9326,9327],{},[1115,9303,9305],{"className":9304},[1292],[1294,9306,9307],{"xmlns":1296},[1298,9308,9309,9323],{},[1301,9310,9311,9313,9315,9317,9319,9321],{},[1307,9312,6483],{},[1437,9314,1626],{"stretchy":1625},[1307,9316,6488],{},[1437,9318,1733],{},[1307,9320,7016],{},[1437,9322,1637],{"stretchy":1625},[1315,9324,9325],{"encoding":1317},"P(X=k)"," \u002F ",[1115,9328,9330],{"className":9329},[1292],[1294,9331,9332],{"xmlns":1296},[1298,9333,9334,9344],{},[1301,9335,9336,9338,9340,9342],{},[1307,9337,6527],{},[1437,9339,1626],{"stretchy":1625},[1307,9341,6476],{},[1437,9343,1637],{"stretchy":1625},[1315,9345,6557],{"encoding":1317},[1150,9347,9348],{},[1115,9349,9351],{"className":9350},[1292],[1294,9352,9353],{"xmlns":1296},[1298,9354,9355,9369],{},[1301,9356,9357,9359,9361,9363,9365,9367],{},[1307,9358,6483],{},[1437,9360,1626],{"stretchy":1625},[1307,9362,6488],{},[1437,9364,6491],{},[1307,9366,7016],{},[1437,9368,1637],{"stretchy":1625},[1315,9370,9371],{"encoding":1317},"P(X \\le k)",[1150,9373,9374,9375],{},"horní chvost ",[1115,9376,9378],{"className":9377},[1292],[1294,9379,9380],{"xmlns":1296},[1298,9381,9382,9396],{},[1301,9383,9384,9386,9388,9390,9392,9394],{},[1307,9385,6483],{},[1437,9387,1626],{"stretchy":1625},[1307,9389,6488],{},[1437,9391,1439],{},[1307,9393,7016],{},[1437,9395,1637],{"stretchy":1625},[1315,9397,9398],{"encoding":1317},"P(X>k)",[1157,9400,9401,9447,9491,9532,9581],{},[1147,9402,9403,9432,9437,9442],{},[1162,9404,9405,9406],{},"Binomické ",[1115,9407,9409],{"className":9408},[1292],[1294,9410,9411],{"xmlns":1296},[1298,9412,9413,9429],{},[1301,9414,9415,9417,9419,9421,9423,9425,9427],{},[1307,9416,1574],{},[1307,9418,1629],{},[1437,9420,1626],{"stretchy":1625},[1307,9422,1435],{},[1437,9424,1547],{"separator":1121},[1307,9426,1110],{},[1437,9428,1637],{"stretchy":1625},[1315,9430,9431],{"encoding":1317},"Bi(n,p)",[1162,9433,9434],{},[3223,9435,9436],{},"dbinom(k, n, p)",[1162,9438,9439],{},[3223,9440,9441],{},"pbinom(k, n, p)",[1162,9443,9444],{},[3223,9445,9446],{},"pbinom(k, n, p, FALSE)",[1147,9448,9449,9476,9481,9486],{},[1162,9450,9451,9452],{},"Poissonovo ",[1115,9453,9455],{"className":9454},[1292],[1294,9456,9457],{"xmlns":1296},[1298,9458,9459,9473],{},[1301,9460,9461,9463,9466,9468,9471],{},[1307,9462,6483],{},[1307,9464,9465],{},"o",[1437,9467,1626],{"stretchy":1625},[1307,9469,9470],{},"λ",[1437,9472,1637],{"stretchy":1625},[1315,9474,9475],{"encoding":1317},"Po(\\lambda)",[1162,9477,9478],{},[3223,9479,9480],{},"dpois(k, lambda)",[1162,9482,9483],{},[3223,9484,9485],{},"ppois(k, lambda)",[1162,9487,9488],{},[3223,9489,9490],{},"ppois(k, lambda, FALSE)",[1147,9492,9493,9517,9522,9527],{},[1162,9494,9495,9496],{},"Geometrické ",[1115,9497,9499],{"className":9498},[1292],[1294,9500,9501],{"xmlns":1296},[1298,9502,9503,9514],{},[1301,9504,9505,9508,9510,9512],{},[1307,9506,9507],{},"G",[1437,9509,1626],{"stretchy":1625},[1307,9511,1110],{},[1437,9513,1637],{"stretchy":1625},[1315,9515,9516],{"encoding":1317},"G(p)",[1162,9518,9519],{},[3223,9520,9521],{},"dgeom(k, p)",[1162,9523,9524],{},[3223,9525,9526],{},"pgeom(k, p)",[1162,9528,9529],{},[3223,9530,9531],{},"pgeom(k, p, FALSE)",[1147,9533,9534,9566,9571,9576],{},[1162,9535,9536,9537],{},"Hypergeometrické ",[1115,9538,9540],{"className":9539},[1292],[1294,9541,9542],{"xmlns":1296},[1298,9543,9544,9563],{},[1301,9545,9546,9548,9550,9552,9554,9557,9559,9561],{},[1307,9547,1309],{},[1437,9549,1626],{"stretchy":1625},[1307,9551,6642],{},[1437,9553,1547],{"separator":1121},[1307,9555,9556],{},"M",[1437,9558,1547],{"separator":1121},[1307,9560,1435],{},[1437,9562,1637],{"stretchy":1625},[1315,9564,9565],{"encoding":1317},"H(N,M,n)",[1162,9567,9568],{},[3223,9569,9570],{},"dhyper(k, M, N-M, n)",[1162,9572,9573],{},[3223,9574,9575],{},"phyper(k, M, N-M, n)",[1162,9577,9578],{},[3223,9579,9580],{},"phyper(k, M, N-M, n, FALSE)",[1147,9582,9583,9607,9612,9617],{},[1162,9584,9585,9586],{},"Exponenciální ",[1115,9587,9589],{"className":9588},[1292],[1294,9590,9591],{"xmlns":1296},[1298,9592,9593,9604],{},[1301,9594,9595,9597,9599,9602],{},[1307,9596,7843],{},[1437,9598,1626],{"stretchy":1625},[1307,9600,9601],{},"δ",[1437,9603,1637],{"stretchy":1625},[1315,9605,9606],{"encoding":1317},"E(\\delta)",[1162,9608,9609],{},[3223,9610,9611],{},"dexp(k, 1\u002Fdelta)",[1162,9613,9614],{},[3223,9615,9616],{},"pexp(k, 1\u002Fdelta)",[1162,9618,9619],{},[3223,9620,9621],{},"pexp(k, 1\u002Fdelta, FALSE)",[1103,9623,9625,9632],{"className":9624,"dataCallout":6167},[1106,6166],[1110,9626,9628,9631],{"className":9627},[1113],[1115,9629],{"className":9630,"ariaHidden":1121},[1118,6174,1120],"Exponenciální rozdělení: R bere intenzitu, ne střední hodnotu",[1110,9633,9634,9635,9638,9639,9653,9654,8806,9657,1417],{},"R parametrizuje exponenciální rozdělení intenzitou (",[3223,9636,9637],{},"rate","). Je-li ",[1115,9640,9642],{"className":9641},[1292],[1294,9643,9644],{"xmlns":1296},[1298,9645,9646,9650],{},[1301,9647,9648],{},[1307,9649,9601],{},[1315,9651,9652],{"encoding":1317},"\\delta"," střední doba do události, do R se dosazuje ",[3223,9655,9656],{},"1\u002Fdelta",[3223,9658,9659],{},"delta",[1110,9661,9662,9663,9695,9696,9714],{},"V R (pravděpodobnostní a distribuční funkce diskrétní náhodné veličiny ",[1115,9664,9666],{"className":9665},[1292],[1294,9667,9668],{"xmlns":1296},[1298,9669,9670,9692],{},[1301,9671,9672,9674,9676,9678,9680,9682,9685,9687,9690],{},[1307,9673,6488],{},[1437,9675,8941],{},[1307,9677,1574],{},[1307,9679,1629],{},[1437,9681,1626],{"stretchy":1625},[1311,9683,9684],{},"5",[1437,9686,6650],{"separator":1121},[1311,9688,9689],{},"0,95",[1437,9691,1637],{"stretchy":1625},[1315,9693,9694],{"encoding":1317},"X \\sim Bi(5; 0{,}95)",", a pravděpodobnost, že u exponenciálního rozdělení se střední hodnotou ",[1115,9697,9699],{"className":9698},[1292],[1294,9700,9701],{"xmlns":1296},[1298,9702,9703,9711],{},[1301,9704,9705,9707,9709],{},[1307,9706,9601],{},[1437,9708,1733],{},[1311,9710,9684],{},[1315,9712,9713],{"encoding":1317},"\\delta = 5"," nastane událost do 3 jednotek času):",[3447,9716,9718],{"className":3449,"code":9717,"language":71,"meta":1229,"style":1229},"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",[3223,9719,9720,9734,9766,9795,9800,9809],{"__ignoreMap":1229},[1115,9721,9722,9724,9726,9729,9731],{"class":3455,"line":10},[1115,9723,6476],{"class":3458},[1115,9725,3463],{"class":3462},[1115,9727,9728],{"class":3478}," 0",[1115,9730,1709],{"class":3462},[1115,9732,9733],{"class":3478},"5\n",[1115,9735,9736,9739,9741,9744,9746,9748,9750,9753,9755,9758,9760,9762,9764],{"class":3455,"line":27},[1115,9737,9738],{"class":3466},"round",[1115,9740,1626],{"class":3470},[1115,9742,9743],{"class":3466},"dbinom",[1115,9745,1626],{"class":3470},[1115,9747,6476],{"class":3458},[1115,9749,1547],{"class":3462},[1115,9751,9752],{"class":3478}," 5",[1115,9754,1547],{"class":3462},[1115,9756,9757],{"class":3478}," 0.95",[1115,9759,1637],{"class":3470},[1115,9761,1547],{"class":3462},[1115,9763,3554],{"class":3478},[1115,9765,3655],{"class":3470},[1115,9767,9768,9770,9772,9775,9777,9779,9781,9783,9785,9787,9789,9791,9793],{"class":3455,"line":148},[1115,9769,9738],{"class":3466},[1115,9771,1626],{"class":3470},[1115,9773,9774],{"class":3466},"pbinom",[1115,9776,1626],{"class":3470},[1115,9778,6476],{"class":3458},[1115,9780,1547],{"class":3462},[1115,9782,9752],{"class":3478},[1115,9784,1547],{"class":3462},[1115,9786,9757],{"class":3478},[1115,9788,1637],{"class":3470},[1115,9790,1547],{"class":3462},[1115,9792,3554],{"class":3478},[1115,9794,3655],{"class":3470},[1115,9796,9797],{"class":3455,"line":111},[1115,9798,9799],{"emptyLinePlaceholder":1238},"\n",[1115,9801,9802,9804,9806],{"class":3455,"line":96},[1115,9803,9659],{"class":3458},[1115,9805,3463],{"class":3462},[1115,9807,9808],{"class":3478}," 5\n",[1115,9810,9811,9813,9815,9818,9820,9822,9824,9827,9829,9831,9834,9837,9839,9841,9843],{"class":3455,"line":89},[1115,9812,9738],{"class":3466},[1115,9814,1626],{"class":3470},[1115,9816,9817],{"class":3466},"pexp",[1115,9819,1626],{"class":3470},[1115,9821,3345],{"class":3478},[1115,9823,1547],{"class":3462},[1115,9825,9826],{"class":3458}," rate",[1115,9828,3551],{"class":3462},[1115,9830,4395],{"class":3478},[1115,9832,9833],{"class":3462}," \u002F",[1115,9835,9836],{"class":3458}," delta",[1115,9838,1637],{"class":3470},[1115,9840,1547],{"class":3462},[1115,9842,3554],{"class":3478},[1115,9844,3655],{"class":3470},[3447,9846,9849],{"className":9847,"code":9848,"language":3677,"meta":1229},[3675],"[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",[3223,9850,9848],{"__ignoreMap":1229},[1136,9852,9854],{"id":9853},"studentovo-pearsonovo-a-fisherovo-snedecorovo-rozdělení","Studentovo, Pearsonovo a Fisherovo-Snedecorovo rozdělení",[1110,9856,9857,9858,9861],{},"Tato tři rozdělení mají statistiky, které se dále používají při konstrukci intervalů spolehlivosti a testování hypotéz (viz ",[1127,9859,141],{"className":9860,"dataFsResolvedFilePath":1471,"href":1472},[1130],") — na rozdíl od normálního rozdělení se v příkladech této kapitoly samostatně nepočítají, jsou to nástroje pro další kapitoly.",[1110,9863,9864,3706,9867,9880],{},[1279,9865,9866],{},"Studentovo rozdělení",[1115,9868,9870],{"className":9869},[1292],[1294,9871,9872],{"xmlns":1296},[1298,9873,9874,9878],{},[1301,9875,9876],{},[1307,9877,7016],{},[1315,9879,7016],{"encoding":1317}," stupni volnosti má hustotu pravděpodobnosti",[1115,9882,9884],{"className":9883},[1292],[1294,9885,9886],{"xmlns":1296,"display":1715},[1298,9887,9888,9984],{},[1301,9889,9890,9892,9894,9896,9898,9900,9932,9970,9972,9974,9976,9978,9982],{},[1307,9891,6527],{},[1437,9893,1626],{"stretchy":1625},[1307,9895,6476],{},[1437,9897,1637],{"stretchy":1625},[1437,9899,1733],{},[2491,9901,9902,9904],{},[1311,9903,1544],{},[1301,9905,9906,9908,9928],{},[1307,9907,1574],{},[1301,9909,9910,9912,9918,9920,9926],{},[1437,9911,1626],{"fence":1121},[2491,9913,9914,9916],{},[1311,9915,1544],{},[1311,9917,1337],{},[1437,9919,1547],{"separator":1121},[2491,9921,9922,9924],{},[1307,9923,7016],{},[1311,9925,1337],{},[1437,9927,1637],{"fence":1121},[4207,9929,9930],{},[1307,9931,7016],{},[1330,9933,9934,9954],{},[1301,9935,9936,9938,9940,9942,9952],{},[1437,9937,1626],{"fence":1121},[1311,9939,1544],{},[1437,9941,5231],{},[2491,9943,9944,9950],{},[1330,9945,9946,9948],{},[1307,9947,6476],{},[1311,9949,1337],{},[1307,9951,7016],{},[1437,9953,1637],{"fence":1121},[1301,9955,9956,9958],{},[1437,9957,2817],{},[2491,9959,9960,9968],{},[1301,9961,9962,9964,9966],{},[1307,9963,7016],{},[1437,9965,5231],{},[1311,9967,1544],{},[1311,9969,1337],{},[1437,9971,1547],{"separator":1121},[1763,9973],{"width":1765},[1307,9975,6476],{},[1437,9977,6775],{},[1307,9979,9981],{"mathvariant":9980},"double-struck","R",[1437,9983,1547],{"separator":1121},[1315,9985,9986],{"encoding":1317},"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},",[1110,9988,4261,9989,10002,10003,10016,10017,10030],{},[1115,9990,9992],{"className":9991},[1292],[1294,9993,9994],{"xmlns":1296},[1298,9995,9996,10000],{},[1301,9997,9998],{},[1307,9999,1574],{},[1315,10001,1574],{"encoding":1317}," je funkce beta. Je symetrické kolem nuly; číslo ",[1115,10004,10006],{"className":10005},[1292],[1294,10007,10008],{"xmlns":1296},[1298,10009,10010,10014],{},[1301,10011,10012],{},[1307,10013,7016],{},[1315,10015,7016],{"encoding":1317}," určuje tvar křivky — s rostoucím ",[1115,10018,10020],{"className":10019},[1292],[1294,10021,10022],{"xmlns":1296},[1298,10023,10024,10028],{},[1301,10025,10026],{},[1307,10027,7016],{},[1315,10029,7016],{"encoding":1317}," se rozdělení blíží normálnímu.",[1110,10032,10033,3706,10036,10049],{},[1279,10034,10035],{},"Pearsonovo (chí-kvadrát) rozdělení",[1115,10037,10039],{"className":10038},[1292],[1294,10040,10041],{"xmlns":1296},[1298,10042,10043,10047],{},[1301,10044,10045],{},[1307,10046,7016],{},[1315,10048,7016],{"encoding":1317}," stupni volnosti:",[1115,10051,10053],{"className":10052},[1292],[1294,10054,10055],{"xmlns":1296,"display":1715},[1298,10056,10057,10142],{},[1301,10058,10059,10061,10063,10065,10067,10069,10100,10116,10130,10132,10134,10136,10138,10140],{},[1307,10060,6527],{},[1437,10062,1626],{"stretchy":1625},[1307,10064,6476],{},[1437,10066,1637],{"stretchy":1625},[1437,10068,1733],{},[2491,10070,10071,10073],{},[1311,10072,1544],{},[1301,10074,10075,10087,10090,10092,10094,10096,10098],{},[1330,10076,10077,10079],{},[1311,10078,1337],{},[1301,10080,10081,10083,10085],{},[1307,10082,7016],{},[1307,10084,4358],{"mathvariant":1872},[1311,10086,1337],{},[1307,10088,10089],{"mathvariant":1872},"Γ",[1437,10091,1626],{"stretchy":1625},[1307,10093,7016],{},[1307,10095,4358],{"mathvariant":1872},[1311,10097,1337],{},[1437,10099,1637],{"stretchy":1625},[1330,10101,10102,10104],{},[1307,10103,6476],{},[1301,10105,10106,10108,10110,10112,10114],{},[1307,10107,7016],{},[1307,10109,4358],{"mathvariant":1872},[1311,10111,1337],{},[1437,10113,2817],{},[1311,10115,1544],{},[1330,10117,10118,10120],{},[1307,10119,8350],{},[1301,10121,10122,10124,10126,10128],{},[1437,10123,2817],{},[1307,10125,6476],{},[1307,10127,4358],{"mathvariant":1872},[1311,10129,1337],{},[1437,10131,1547],{"separator":1121},[1763,10133],{"width":1765},[1307,10135,6476],{},[1437,10137,1439],{},[1311,10139,1313],{},[1437,10141,1547],{"separator":1121},[1315,10143,10144],{"encoding":1317},"f(x) = \\frac{1}{2^{k\u002F2}\\Gamma(k\u002F2)} x^{k\u002F2-1} e^{-x\u002F2}, \\qquad x > 0,",[1110,10146,4261,10147,10161],{},[1115,10148,10150],{"className":10149},[1292],[1294,10151,10152],{"xmlns":1296},[1298,10153,10154,10158],{},[1301,10155,10156],{},[1307,10157,10089],{"mathvariant":1872},[1315,10159,10160],{"encoding":1317},"\\Gamma"," je funkce gama.",[1110,10163,10164,10167,10168,5495,10186,1709],{},[1279,10165,10166],{},"Fisherovo-Snedecorovo rozdělení"," se stupni volnosti ",[1115,10169,10171],{"className":10170},[1292],[1294,10172,10173],{"xmlns":1296},[1298,10174,10175,10183],{},[1301,10176,10177],{},[1304,10178,10179,10181],{},[1307,10180,7016],{},[1311,10182,1544],{},[1315,10184,10185],{"encoding":1317},"k_1",[1115,10187,10189],{"className":10188},[1292],[1294,10190,10191],{"xmlns":1296},[1298,10192,10193,10201],{},[1301,10194,10195],{},[1304,10196,10197,10199],{},[1307,10198,7016],{},[1311,10200,1337],{},[1315,10202,10203],{"encoding":1317},"k_2",[1115,10205,10207],{"className":10206},[1292],[1294,10208,10209],{"xmlns":1296,"display":1715},[1298,10210,10211,10376],{},[1301,10212,10213,10215,10217,10219,10221,10223,10259,10293,10313,10365,10367,10369,10371,10373],{},[1307,10214,6527],{},[1437,10216,1626],{"stretchy":1625},[1307,10218,6476],{},[1437,10220,1637],{"stretchy":1625},[1437,10222,1733],{},[2491,10224,10225,10227],{},[1311,10226,1544],{},[1301,10228,10229,10231],{},[1307,10230,1574],{},[1301,10232,10233,10235,10245,10247,10257],{},[1437,10234,1626],{"fence":1121},[2491,10236,10237,10243],{},[1304,10238,10239,10241],{},[1307,10240,7016],{},[1311,10242,1544],{},[1311,10244,1337],{},[1437,10246,1547],{"separator":1121},[2491,10248,10249,10255],{},[1304,10250,10251,10253],{},[1307,10252,7016],{},[1311,10254,1337],{},[1311,10256,1337],{},[1437,10258,1637],{"fence":1121},[1330,10260,10261,10281],{},[1301,10262,10263,10265,10279],{},[1437,10264,1626],{"fence":1121},[2491,10266,10267,10273],{},[1304,10268,10269,10271],{},[1307,10270,7016],{},[1311,10272,1544],{},[1304,10274,10275,10277],{},[1307,10276,7016],{},[1311,10278,1337],{},[1437,10280,1637],{"fence":1121},[1301,10282,10283,10289,10291],{},[1304,10284,10285,10287],{},[1307,10286,7016],{},[1311,10288,1544],{},[1307,10290,4358],{"mathvariant":1872},[1311,10292,1337],{},[1330,10294,10295,10297],{},[1307,10296,6476],{},[1301,10298,10299,10305,10307,10309,10311],{},[1304,10300,10301,10303],{},[1307,10302,7016],{},[1311,10304,1544],{},[1307,10306,4358],{"mathvariant":1872},[1311,10308,1337],{},[1437,10310,2817],{},[1311,10312,1544],{},[1330,10314,10315,10341],{},[1301,10316,10317,10319,10321,10323,10337,10339],{},[1437,10318,1626],{"fence":1121},[1311,10320,1544],{},[1437,10322,5231],{},[2491,10324,10325,10331],{},[1304,10326,10327,10329],{},[1307,10328,7016],{},[1311,10330,1544],{},[1304,10332,10333,10335],{},[1307,10334,7016],{},[1311,10336,1337],{},[1307,10338,6476],{},[1437,10340,1637],{"fence":1121},[1301,10342,10343,10345],{},[1437,10344,2817],{},[2491,10346,10347,10363],{},[1301,10348,10349,10355,10357],{},[1304,10350,10351,10353],{},[1307,10352,7016],{},[1311,10354,1544],{},[1437,10356,5231],{},[1304,10358,10359,10361],{},[1307,10360,7016],{},[1311,10362,1337],{},[1311,10364,1337],{},[1437,10366,1547],{"separator":1121},[1763,10368],{"width":1765},[1307,10370,6476],{},[1437,10372,1439],{},[1311,10374,10375],{},"0.",[1315,10377,10378],{"encoding":1317},"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.",[1110,10380,10381],{},[4137,10382],{"alt":10383,"className":10384,"src":10385},"mask-nv-specialni-rozdeleni",[1130,4141],"\u002Fwiki-assets\u002Fmask-nv-specialni-rozdeleni.png",[8704,10387],{"spec":10388},"{\"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\":[]}",[1110,10390,10391],{},"R funkce pro tato tři rozdělení:",[1141,10393,10394,10408],{},[1144,10395,10396],{},[1147,10397,10398,10400,10403,10405],{},[1150,10399,9299],{},[1150,10401,10402],{},"hustota",[1150,10404,6459],{},[1150,10406,10407],{},"kvantil",[1157,10409,10410,10450,10494],{},[1147,10411,10412,10435,10440,10445],{},[1162,10413,10414,10415],{},"Studentovo ",[1115,10416,10418],{"className":10417},[1292],[1294,10419,10420],{"xmlns":1296},[1298,10421,10422,10432],{},[1301,10423,10424,10426,10428,10430],{},[1307,10425,6900],{},[1437,10427,1626],{"stretchy":1625},[1307,10429,7016],{},[1437,10431,1637],{"stretchy":1625},[1315,10433,10434],{"encoding":1317},"t(k)",[1162,10436,10437],{},[3223,10438,10439],{},"dt(x, df = k)",[1162,10441,10442],{},[3223,10443,10444],{},"pt(x, df = k)",[1162,10446,10447],{},[3223,10448,10449],{},"qt(p, df = k)",[1147,10451,10452,10479,10484,10489],{},[1162,10453,10454,10455],{},"Pearsonovo ",[1115,10456,10458],{"className":10457},[1292],[1294,10459,10460],{"xmlns":1296},[1298,10461,10462,10476],{},[1301,10463,10464,10470,10472,10474],{},[1330,10465,10466,10468],{},[1307,10467,1334],{},[1311,10469,1337],{},[1437,10471,1626],{"stretchy":1625},[1307,10473,7016],{},[1437,10475,1637],{"stretchy":1625},[1315,10477,10478],{"encoding":1317},"\\chi^2(k)",[1162,10480,10481],{},[3223,10482,10483],{},"dchisq(x, df = k)",[1162,10485,10486],{},[3223,10487,10488],{},"pchisq(x, df = k)",[1162,10490,10491],{},[3223,10492,10493],{},"qchisq(p, df = k)",[1147,10495,10496,10531,10536,10541],{},[1162,10497,10498,10499],{},"Fisherovo-Snedecorovo ",[1115,10500,10502],{"className":10501},[1292],[1294,10503,10504],{"xmlns":1296},[1298,10505,10506,10528],{},[1301,10507,10508,10510,10512,10518,10520,10526],{},[1307,10509,6471],{},[1437,10511,1626],{"stretchy":1625},[1304,10513,10514,10516],{},[1307,10515,7016],{},[1311,10517,1544],{},[1437,10519,1547],{"separator":1121},[1304,10521,10522,10524],{},[1307,10523,7016],{},[1311,10525,1337],{},[1437,10527,1637],{"stretchy":1625},[1315,10529,10530],{"encoding":1317},"F(k_1, k_2)",[1162,10532,10533],{},[3223,10534,10535],{},"df(x, df1 = k1, df2 = k2)",[1162,10537,10538],{},[3223,10539,10540],{},"pf(x, df1 = k1, df2 = k2)",[1162,10542,10543],{},[3223,10544,10545],{},"qf(p, df1 = k1, df2 = k2)",[1110,10547,10548],{},"V R (97,5%-ní kvantil Studentova rozdělení s 9 stupni volnosti, 95%-ní kvantily Pearsonova a Fisherova-Snedecorova rozdělení):",[3447,10550,10552],{"className":3449,"code":10551,"language":71,"meta":1229,"style":1229},"qt(0.975, df = 9)\nqchisq(0.95, df = 9)\nqf(0.95, df1 = 3, df2 = 10)\n",[3223,10553,10554,10575,10595],{"__ignoreMap":1229},[1115,10555,10556,10559,10561,10563,10565,10568,10570,10573],{"class":3455,"line":10},[1115,10557,10558],{"class":3466},"qt",[1115,10560,1626],{"class":3470},[1115,10562,8847],{"class":3478},[1115,10564,1547],{"class":3462},[1115,10566,10567],{"class":3458}," df",[1115,10569,3551],{"class":3462},[1115,10571,10572],{"class":3478}," 9",[1115,10574,3655],{"class":3470},[1115,10576,10577,10580,10582,10585,10587,10589,10591,10593],{"class":3455,"line":27},[1115,10578,10579],{"class":3466},"qchisq",[1115,10581,1626],{"class":3470},[1115,10583,10584],{"class":3478},"0.95",[1115,10586,1547],{"class":3462},[1115,10588,10567],{"class":3458},[1115,10590,3551],{"class":3462},[1115,10592,10572],{"class":3478},[1115,10594,3655],{"class":3470},[1115,10596,10597,10600,10602,10604,10606,10609,10611,10614,10616,10619,10621,10623],{"class":3455,"line":148},[1115,10598,10599],{"class":3466},"qf",[1115,10601,1626],{"class":3470},[1115,10603,10584],{"class":3478},[1115,10605,1547],{"class":3462},[1115,10607,10608],{"class":3458}," df1",[1115,10610,3551],{"class":3462},[1115,10612,10613],{"class":3478}," 3",[1115,10615,1547],{"class":3462},[1115,10617,10618],{"class":3458}," df2",[1115,10620,3551],{"class":3462},[1115,10622,9235],{"class":3478},[1115,10624,3655],{"class":3470},[3447,10626,10629],{"className":10627,"code":10628,"language":3677,"meta":1229},[3675],"[1] 2.262157\n[1] 16.91898\n[1] 3.708265\n",[3223,10630,10628],{"__ignoreMap":1229},[1136,10632,6162],{"id":6161},[1191,10634,10635,10721,10771],{},[1194,10636,10637,10640,10641,10668,10669,4358,10671,4358,10673,10675,10676,10696,10697,10720],{},[1279,10638,10639],{},"Rozptyl vs. směrodatná odchylka v R."," Zápis ",[1115,10642,10644],{"className":10643},[1292],[1294,10645,10646],{"xmlns":1296},[1298,10647,10648,10666],{},[1301,10649,10650,10652,10654,10656,10658,10664],{},[1307,10651,6642],{},[1437,10653,1626],{"stretchy":1625},[1307,10655,6647],{},[1437,10657,6650],{"separator":1121},[1330,10659,10660,10662],{},[1307,10661,6655],{},[1311,10663,1337],{},[1437,10665,1637],{"stretchy":1625},[1315,10667,6662],{"encoding":1317}," používá rozptyl, ale ",[3223,10670,6666],{},[3223,10672,6669],{},[3223,10674,6672],{}," očekávají směrodatnou odchylku. Dosazení rozptylu místo ",[1115,10677,10679],{"className":10678},[1292],[1294,10680,10681],{"xmlns":1296},[1298,10682,10683,10693],{},[1301,10684,10685],{},[4207,10686,10687],{},[1330,10688,10689,10691],{},[1307,10690,6655],{},[1311,10692,1337],{},[1315,10694,10695],{"encoding":1317},"\\sqrt{\\sigma^2}"," dává jiný — a pro ",[1115,10698,10700],{"className":10699},[1292],[1294,10701,10702],{"xmlns":1296},[1298,10703,10704,10717],{},[1301,10705,10706,10712,10715],{},[1330,10707,10708,10710],{},[1307,10709,6655],{},[1311,10711,1337],{},[1437,10713,10714],{"mathvariant":1872},"≠",[1311,10716,1544],{},[1315,10718,10719],{"encoding":1317},"\\sigma^2 \\ne 1"," výrazně odlišný — výsledek (viz příklad s ampulkou).",[1194,10722,10723,10750,10751,10770],{},[1279,10724,10725,10749],{},[1115,10726,10728],{"className":10727},[1292],[1294,10729,10730],{"xmlns":1296},[1298,10731,10732,10746],{},[1301,10733,10734,10736,10738,10740,10742,10744],{},[1307,10735,6483],{},[1437,10737,1626],{"stretchy":1625},[1307,10739,6488],{},[1437,10741,1733],{},[1307,10743,6476],{},[1437,10745,1637],{"stretchy":1625},[1315,10747,10748],{"encoding":1317},"P(X=x)"," u spojité veličiny je vždy 0."," Hustota ",[1115,10752,10754],{"className":10753},[1292],[1294,10755,10756],{"xmlns":1296},[1298,10757,10758,10768],{},[1301,10759,10760,10762,10764,10766],{},[1307,10761,6527],{},[1437,10763,1626],{"stretchy":1625},[1307,10765,6476],{},[1437,10767,1637],{"stretchy":1625},[1315,10769,6557],{"encoding":1317}," sama o sobě pravděpodobnost neudává — pravděpodobnost dává až plocha pod křivkou na intervalu.",[1194,10772,10773,1402,10776,10793,10794,10811,10812,10815,10816,1417],{},[1279,10774,10775],{},"Záměna stupňů volnosti u Fisherova-Snedecorova rozdělení.",[1115,10777,10779],{"className":10778},[1292],[1294,10780,10781],{"xmlns":1296},[1298,10782,10783,10791],{},[1301,10784,10785],{},[1304,10786,10787,10789],{},[1307,10788,7016],{},[1311,10790,1544],{},[1315,10792,10185],{"encoding":1317}," (čitatel) a ",[1115,10795,10797],{"className":10796},[1292],[1294,10798,10799],{"xmlns":1296},[1298,10800,10801,10809],{},[1301,10802,10803],{},[1304,10804,10805,10807],{},[1307,10806,7016],{},[1311,10808,1337],{},[1315,10810,10203],{"encoding":1317}," (jmenovatel) nejsou zaměnitelné — ",[3223,10813,10814],{},"qf(p, df1, df2)"," dá jiný výsledek než ",[3223,10817,10818],{},"qf(p, df2, df1)",[1136,10820,1189],{"id":1188},[1191,10822,10823,10828,10833,10838,10844,10849,10855],{},[1194,10824,10825],{},[1127,10826,1133],{"className":10827,"dataFsResolvedFilePath":1131,"href":1132},[1130],[1194,10829,10830],{},[1127,10831,886],{"className":10832,"dataFsResolvedFilePath":6367,"href":6368},[1130],[1194,10834,10835],{},[1127,10836,141],{"className":10837,"dataFsResolvedFilePath":1471,"href":1472},[1130],[1194,10839,10840],{},[1127,10841,10843],{"className":10842,"dataFsResolvedFilePath":1167,"href":1168},[1130],"regresni-a-korelacni-analyza",[1194,10845,10846],{},[1127,10847,716],{"className":10848,"dataFsResolvedFilePath":1180,"href":1181},[1130],[1194,10850,10851],{},[1127,10852,10854],{"className":10853,"dataFsResolvedFilePath":6388,"href":6389},[1130],"regulacni-diagramy-a-indexy-zpusobilosti",[1194,10856,10857],{},[1127,10858,6396],{"className":10859,"dataFsResolvedFilePath":1214,"href":1215},[1130],[1136,10861,1219],{"id":934},[1110,10863,1222,10864,1227],{},[1224,10865,1226],{},[6404,10867,10868],{},"html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .sP4rz, html code.shiki .sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}",{"title":1229,"searchDepth":27,"depth":27,"links":10870},[10871,10872,10873,10874,10875,10876,10877,10878,10879,10880],{"id":6721,"depth":27,"text":6722},{"id":7029,"depth":27,"text":7030},{"id":7715,"depth":27,"text":7716},{"id":7824,"depth":27,"text":7825},{"id":8261,"depth":27,"text":6630},{"id":9263,"depth":27,"text":9264},{"id":9853,"depth":27,"text":9854},{"id":6161,"depth":27,"text":6162},{"id":1188,"depth":27,"text":1189},{"id":934,"depth":27,"text":1219},{},"\u002Ftopics\u002Fnahodne-veliciny-a-rozdeleni",{"title":6377,"description":1229},[10885,10886,10887],"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":10892,"title":6369,"body":10893,"course":23,"courses":1234,"created":1235,"description":1229,"extension":1236,"meta":15644,"navigation":1238,"path":15645,"seo":15646,"sources":15647,"stem":15654,"tags":15655,"type":6423,"updated":1235,"__hash__":15656},"topics\u002Ftopics\u002Fpopisna-statistika.md",{"type":1096,"value":10894,"toc":15635},[10895,10898,10992,10996,11006,11132,11139,11150,11154,11197,11202,11304,11314,11319,11458,11534,11538,11639,11720,11727,11798,11817,11819,12035,12041,12051,12058,12061,12115,12121,12131,12144,12290,12293,12306,12625,12631,12634,12638,12717,12751,12780,12782,12860,12866,12927,12934,12947,13024,13140,13190,13203,13358,13364,13391,13395,13420,13423,13636,13704,13805,13812,13825,14328,14334,14366,14626,14779,14890,14919,14925,14932,14938,14951,15381,15387,15390,15392,15587,15589,15626,15628,15632],[1099,10896,6369],{"id":10897},"popisná-statistika-a-datové-soubory",[1103,10899,10901,10907],{"className":10900,"dataCallout":1264},[1106,1263],[1110,10902,10904,1272],{"className":10903},[1113],[1115,10905],{"className":10906,"ariaHidden":1121},[1118,1271,1120],[1191,10908,10909,10912,10915,10942,10989],{},[1194,10910,10911],{},"Rozlišit základní a výběrový soubor, typ statistického znaku (kvantitativní\u002Fkvalitativní, diskrétní\u002Fspojitý) a požadavek reprezentativity a nezávislého výběru.",[1194,10913,10914],{},"Spočítat výběrový průměr, rozptyl, směrodatnou odchylku a variační rozpětí; interpretovat je jako bodové odhady charakteristik náhodné veličiny.",[1194,10916,10917,10918,1417],{},"Určit medián a kvartily a číst empirickou distribuční funkci ",[1115,10919,10921],{"className":10920},[1292],[1294,10922,10923],{"xmlns":1296},[1298,10924,10925,10939],{},[1301,10926,10927,10933,10935,10937],{},[1304,10928,10929,10931],{},[1307,10930,6471],{},[1307,10932,1435],{},[1437,10934,1626],{"stretchy":1625},[1307,10936,6476],{},[1437,10938,1637],{"stretchy":1625},[1315,10940,10941],{"encoding":1317},"F_n(x)",[1194,10943,10944,10945,10988],{},"Roztřídit velký datový soubor do tříd (intervalové rozdělení četností), sestavit tabulku ",[1115,10946,10948],{"className":10947},[1292],[1294,10949,10950],{"xmlns":1296},[1298,10951,10952,10985],{},[1301,10953,10954,10961,10963,10969,10971,10977,10979],{},[1304,10955,10956,10959],{},[1307,10957,10958],{},"I",[1307,10960,1634],{},[1437,10962,1547],{"separator":1121},[1304,10964,10965,10967],{},[1307,10966,8683],{},[1307,10968,1634],{},[1437,10970,1547],{"separator":1121},[1304,10972,10973,10975],{},[1307,10974,6527],{},[1307,10976,1634],{},[1437,10978,1547],{"separator":1121},[1304,10980,10981,10983],{},[1307,10982,1110],{},[1307,10984,1634],{},[1315,10986,10987],{"encoding":1317},"I_j, Z_j, f_j, p_j"," a nakreslit histogram.",[1194,10990,10991],{},"Z histogramu odhadnout zákon rozdělení dat; formální test shody patří do testování hypotéz.",[1136,10993,10995],{"id":10994},"základní-pojmy","Základní pojmy",[1110,10997,10998,11001,11002,11005],{},[1127,10999,1133],{"className":11000,"dataFsResolvedFilePath":1131,"href":1132},[1130]," pracuje s ",[1279,11003,11004],{},"datovými soubory"," — konkrétními hodnotami, které popisují vlastnost zkoumaných prvků.",[1191,11007,11008,11014,11038,11044,11119],{},[1194,11009,11010,11013],{},[1279,11011,11012],{},"Základní soubor"," — množina prvků, na nichž provádíme šetření (např. všichni výdělečně činní obyvatelé ČR).",[1194,11015,11016,11019,11020],{},[1279,11017,11018],{},"Statistický znak"," — funkce, která vyjadřuje určitou vlastnost prvku (např. velikost platu). Znaky dělíme na:\n",[1191,11021,11022,11033],{},[1194,11023,11024,11026,11027,11029,11030,11032],{},[1279,11025,1484],{}," (vyjádřitelné číslem) — dále ",[1279,11028,6448],{}," (spočetně mnoho hodnot) nebo ",[1279,11031,6452],{}," (libovolná hodnota v intervalu);",[1194,11034,11035,11037],{},[1279,11036,1477],{}," (vyjádřitelné slovně).",[1194,11039,11040,11043],{},[1279,11041,11042],{},"Výběrový soubor"," — podmnožina prvků základního souboru, na níž znak skutečně zjišťujeme (např. 5 náhodně vybraných obyvatel).",[1194,11045,11046,11049,11050,1417],{},[1279,11047,11048],{},"Datový soubor"," — n-tice naměřených hodnot zkoumaného znaku, např. ",[1115,11051,11053],{"className":11052},[1292],[1294,11054,11055],{"xmlns":1296},[1298,11056,11057,11116],{},[1301,11058,11059,11061,11063,11065,11068,11070,11073,11076,11078,11081,11083,11085,11088,11090,11093,11095,11097,11099,11101,11103,11105,11107,11109,11111,11114],{},[1437,11060,1626],{"stretchy":1625},[1311,11062,3303],{},[2661,11064,2663],{},[1311,11066,11067],{},"500",[1437,11069,1547],{"separator":1121},[2661,11071,11072],{}," ",[1311,11074,11075],{},"38",[2661,11077,2663],{},[1311,11079,11080],{},"000",[1437,11082,1547],{"separator":1121},[2661,11084,11072],{},[1311,11086,11087],{},"37",[2661,11089,2663],{},[1311,11091,11092],{},"800",[1437,11094,1547],{"separator":1121},[2661,11096,11072],{},[1311,11098,9114],{},[2661,11100,2663],{},[1311,11102,11080],{},[1437,11104,1547],{"separator":1121},[2661,11106,11072],{},[1311,11108,3311],{},[2661,11110,2663],{},[1311,11112,11113],{},"200",[1437,11115,1637],{"stretchy":1625},[1315,11117,11118],{"encoding":1317},"(29\\,500,\\ 38\\,000,\\ 37\\,800,\\ 41\\,000,\\ 31\\,200)",[1194,11120,11121,11122,2704,11125,5495,11128,11131],{},"Podle počtu sledovaných znaků rozlišujeme ",[1279,11123,11124],{},"jednorozměrné",[1279,11126,11127],{},"dvourozměrné",[1279,11129,11130],{},"vícerozměrné"," datové soubory.",[1110,11133,11134],{},[4137,11135],{"alt":11136,"className":11137,"src":11138},"mask-ilu-zakladni-soubor-vyber",[1130,4141],"\u002Fwiki-assets\u002Fmask-ilu-zakladni-soubor-vyber.png",[1110,11140,11141,11142,11145,11146,11149],{},"Aby výběrový soubor dobře vypovídal o základním souboru, měl by být ",[1279,11143,11144],{},"reprezentativní"," (podobný základnímu souboru svým složením). Není-li to možné zajistit přímo, volí se prvky do výběru náhodně — ",[1279,11147,11148],{},"nezávislý výběr",". Bez náhodnosti výběru nelze vlastnosti základního souboru správně vystihnout.",[1136,11151,11153],{"id":11152},"empirické-charakteristiky","Empirické charakteristiky",[1110,11155,11156,11157,11160,11161,11164,11165,11178,11179,11182,11183,11196],{},"Zpracováním datového souboru získáme ",[1279,11158,11159],{},"empirické charakteristiky"," a odhad ",[1279,11162,11163],{},"zákona rozdělení"," zkoumané náhodné veličiny ",[1115,11166,11168],{"className":11167},[1292],[1294,11169,11170],{"xmlns":1296},[1298,11171,11172,11176],{},[1301,11173,11174],{},[1307,11175,6488],{},[1315,11177,6488],{"encoding":1317},". Jde o ",[1279,11180,11181],{},"bodové odhady"," charakteristik ",[1115,11184,11186],{"className":11185},[1292],[1294,11187,11188],{"xmlns":1296},[1298,11189,11190,11194],{},[1301,11191,11192],{},[1307,11193,6488],{},[1315,11195,6488],{"encoding":1317},"; ruční výpočet podle vzorců níže je potřeba jen bez dostupného softwaru.",[1110,11198,11199],{},[1279,11200,11201],{},"Míry polohy",[1115,11203,11205],{"className":11204},[1292],[1294,11206,11207],{"xmlns":1296,"display":1715},[1298,11208,11209,11301],{},[1301,11210,11211,11218,11220,11226,11240,11246,11248],{},[2475,11212,11213,11215],{"accent":1121},[1307,11214,6476],{},[1437,11216,11217],{},"ˉ",[1437,11219,1733],{},[2491,11221,11222,11224],{},[1311,11223,1544],{},[1307,11225,1435],{},[1735,11227,11228,11230,11238],{},[1437,11229,1739],{},[1301,11231,11232,11234,11236],{},[1307,11233,1629],{},[1437,11235,1733],{},[1311,11237,1544],{},[1307,11239,1435],{},[1304,11241,11242,11244],{},[1307,11243,6476],{},[1307,11245,1629],{},[1763,11247],{"width":1765},[1301,11249,11250,11253,11260,11263,11270,11273,11279,11282,11290,11292,11298],{},[2661,11251,11252],{},"(v",[2475,11254,11255,11257],{"accent":1121},[2661,11256,6886],{},[1437,11258,11259],{},"ˊ",[2661,11261,11262],{},"b",[2475,11264,11265,11267],{"accent":1121},[2661,11266,8350],{},[1437,11268,11269],{},"ˇ",[2661,11271,11272],{},"rov",[2475,11274,11275,11277],{"accent":1121},[2661,11276,6886],{},[1437,11278,11259],{},[2661,11280,11281],{}," pr",[2475,11283,11284,11287],{"accent":1121},[2661,11285,11286],{},"u",[1437,11288,11289],{},"˚",[2661,11291,4225],{},[2475,11293,11294,11296],{"accent":1121},[2661,11295,8350],{},[1437,11297,11269],{},[2661,11299,11300],{},"r)",[1315,11302,11303],{"encoding":1317},"\\bar{x} = \\frac{1}{n}\\sum_{i=1}^{n} x_i \\qquad \\text{(výběrový průměr)}",[1110,11305,11306,11307,5495,11310,11313],{},"Dalšími mírami polohy jsou ",[1279,11308,11309],{},"medián",[1279,11311,11312],{},"modus"," (nejčetnější hodnota výběru).",[1110,11315,11316],{},[1279,11317,11318],{},"Míry variability",[1115,11320,11322],{"className":11321},[1292],[1294,11323,11324],{"xmlns":1296,"display":1715},[1298,11325,11326,11455],{},[1301,11327,11328,11334,11336,11348,11390,11392,11394,11396,11398,11406,11408],{},[1330,11329,11330,11332],{},[1307,11331,1605],{},[1311,11333,1337],{},[1437,11335,1733],{},[2491,11337,11338,11340],{},[1311,11339,1544],{},[1301,11341,11342,11344,11346],{},[1307,11343,1435],{},[1437,11345,2817],{},[1311,11347,1544],{},[1301,11349,11350,11352,11366,11374,11376,11378,11388],{},[1437,11351,1626],{"fence":1121},[1735,11353,11354,11356,11364],{},[1437,11355,1739],{},[1301,11357,11358,11360,11362],{},[1307,11359,1629],{},[1437,11361,1733],{},[1311,11363,1544],{},[1307,11365,1435],{},[3106,11367,11368,11370,11372],{},[1307,11369,6476],{},[1307,11371,1629],{},[1311,11373,1337],{},[1437,11375,2817],{},[1307,11377,1435],{},[1330,11379,11380,11386],{},[2475,11381,11382,11384],{"accent":1121},[1307,11383,6476],{},[1437,11385,11217],{},[1311,11387,1337],{},[1437,11389,1637],{"fence":1121},[1437,11391,1547],{"separator":1121},[1763,11393],{"width":1765},[1307,11395,1605],{},[1437,11397,1733],{},[4207,11399,11400],{},[1330,11401,11402,11404],{},[1307,11403,1605],{},[1311,11405,1337],{},[1763,11407],{"width":1765},[1301,11409,11410,11412,11418,11420,11426,11428,11434,11437,11443,11446,11452],{},[2661,11411,11252],{},[2475,11413,11414,11416],{"accent":1121},[2661,11415,6886],{},[1437,11417,11259],{},[2661,11419,11262],{},[2475,11421,11422,11424],{"accent":1121},[2661,11423,8350],{},[1437,11425,11269],{},[2661,11427,11272],{},[2475,11429,11430,11432],{"accent":1121},[2661,11431,6886],{},[1437,11433,11259],{},[2661,11435,11436],{}," rozptyl, sm",[2475,11438,11439,11441],{"accent":1121},[2661,11440,8350],{},[1437,11442,11269],{},[2661,11444,11445],{},"rodatn",[2475,11447,11448,11450],{"accent":1121},[2661,11449,1127],{},[1437,11451,11259],{},[2661,11453,11454],{}," odchylka)",[1315,11456,11457],{"encoding":1317},"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)}",[1115,11459,11461],{"className":11460},[1292],[1294,11462,11463],{"xmlns":1296,"display":1715},[1298,11464,11465,11531],{},[1301,11466,11467,11469,11471,11480,11482,11490,11492],{},[1307,11468,9981],{},[1437,11470,1733],{},[1304,11472,11473,11475,11478],{},[1307,11474,6476],{},[1307,11476,11477],{},"max",[1437,11479,4245],{},[1437,11481,2817],{},[1304,11483,11484,11486,11488],{},[1307,11485,6476],{},[1307,11487,4242],{},[1437,11489,4245],{},[1763,11491],{"width":1765},[1301,11493,11494,11497,11503,11505,11512,11515,11521,11523,11529],{},[2661,11495,11496],{},"(varia",[2475,11498,11499,11501],{"accent":1121},[2661,11500,3473],{},[1437,11502,11269],{},[2661,11504,1435],{},[2475,11506,11507,11510],{"accent":1121},[2661,11508,11509],{},"ı",[1437,11511,11259],{},[2661,11513,11514],{}," rozp",[2475,11516,11517,11519],{"accent":1121},[2661,11518,8350],{},[1437,11520,11269],{},[2661,11522,6900],{},[2475,11524,11525,11527],{"accent":1121},[2661,11526,11509],{},[1437,11528,11259],{},[2661,11530,1637],{},[1315,11532,11533],{"encoding":1317},"R = x_{\\max} - x_{\\min} \\qquad \\text{(variační rozpětí)}",[1110,11535,11536],{},[1279,11537,8061],{},[1110,11539,11540,11541,11564,11565,11587,11588,11609,11610,11638],{},"Kvantil ",[1115,11542,11544],{"className":11543},[1292],[1294,11545,11546],{"xmlns":1296},[1298,11547,11548,11561],{},[1301,11549,11550],{},[1304,11551,11552,11559],{},[2475,11553,11554,11556],{"accent":1121},[1307,11555,6476],{},[1437,11557,11558],{},"~",[1307,11560,1110],{},[1315,11562,11563],{"encoding":1317},"\\tilde{x}_p"," dělí hodnoty datového souboru na dvě části: ",[1115,11566,11568],{"className":11567},[1292],[1294,11569,11570],{"xmlns":1296},[1298,11571,11572,11584],{},[1301,11573,11574,11577,11579,11581],{},[1311,11575,11576],{},"100",[1307,11578,1110],{},[2661,11580,2663],{},[1307,11582,11583],{"mathvariant":1872},"%",[1315,11585,11586],{"encoding":1317},"100p\\,\\%"," hodnot je menších nebo rovných ",[1115,11589,11591],{"className":11590},[1292],[1294,11592,11593],{"xmlns":1296},[1298,11594,11595,11607],{},[1301,11596,11597],{},[1304,11598,11599,11605],{},[2475,11600,11601,11603],{"accent":1121},[1307,11602,6476],{},[1437,11604,11558],{},[1307,11606,1110],{},[1315,11608,11563],{"encoding":1317},", zbylých ",[1115,11611,11613],{"className":11612},[1292],[1294,11614,11615],{"xmlns":1296},[1298,11616,11617,11635],{},[1301,11618,11619,11621,11623,11625,11627,11629,11631,11633],{},[1311,11620,11576],{},[1437,11622,1626],{"stretchy":1625},[1311,11624,1544],{},[1437,11626,2817],{},[1307,11628,1110],{},[1437,11630,1637],{"stretchy":1625},[2661,11632,2663],{},[1307,11634,11583],{"mathvariant":1872},[1315,11636,11637],{"encoding":1317},"100(1-p)\\,\\%"," je větších. Nejdůležitější kvantily:",[1191,11640,11641,11668],{},[1194,11642,11643,1402,11645,11667],{},[1279,11644,11309],{},[1115,11646,11648],{"className":11647},[1292],[1294,11649,11650],{"xmlns":1296},[1298,11651,11652,11664],{},[1301,11653,11654],{},[1304,11655,11656,11662],{},[2475,11657,11658,11660],{"accent":1121},[1307,11659,6476],{},[1437,11661,11558],{},[1311,11663,8215],{},[1315,11665,11666],{"encoding":1317},"\\tilde{x}_{0{,}5}"," — pro lichý počet prvků uspořádaného souboru prostřední prvek, pro sudý počet průměr dvou prostředních prvků;",[1194,11669,11670,1402,11673,5495,11695,1402,11698,1417],{},[1279,11671,11672],{},"dolní kvartil",[1115,11674,11676],{"className":11675},[1292],[1294,11677,11678],{"xmlns":1296},[1298,11679,11680,11692],{},[1301,11681,11682],{},[1304,11683,11684,11690],{},[2475,11685,11686,11688],{"accent":1121},[1307,11687,6476],{},[1437,11689,11558],{},[1311,11691,8235],{},[1315,11693,11694],{"encoding":1317},"\\tilde{x}_{0{,}25}",[1279,11696,11697],{},"horní kvartil",[1115,11699,11701],{"className":11700},[1292],[1294,11702,11703],{"xmlns":1296},[1298,11704,11705,11717],{},[1301,11706,11707],{},[1304,11708,11709,11715],{},[2475,11710,11711,11713],{"accent":1121},[1307,11712,6476],{},[1437,11714,11558],{},[1311,11716,8255],{},[1315,11718,11719],{"encoding":1317},"\\tilde{x}_{0{,}75}",[1110,11721,11722,11723,11726],{},"Datový soubor se do R zadává buď přímo (",[3223,11724,11725],{},"x \u003C- c(...)","), nebo načtením ze souboru:",[3447,11728,11730],{"className":3449,"code":11729,"language":71,"meta":1229,"style":1229},"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",[3223,11731,11732,11793],{"__ignoreMap":1229},[1115,11733,11734,11736,11738,11740,11742,11745,11747,11750,11752,11755,11757,11760,11762,11764,11766,11768,11770,11773,11775,11778,11780,11782,11784,11786,11789],{"class":3455,"line":10},[1115,11735,6476],{"class":3458},[1115,11737,3463],{"class":3462},[1115,11739,3589],{"class":3466},[1115,11741,1626],{"class":3470},[1115,11743,11744],{"class":3478},"4.1",[1115,11746,1547],{"class":3462},[1115,11748,11749],{"class":3478}," 4.0",[1115,11751,1547],{"class":3462},[1115,11753,11754],{"class":3478}," 3.8",[1115,11756,1547],{"class":3462},[1115,11758,11759],{"class":3478}," 3.9",[1115,11761,1547],{"class":3462},[1115,11763,11754],{"class":3478},[1115,11765,1547],{"class":3462},[1115,11767,11754],{"class":3478},[1115,11769,1547],{"class":3462},[1115,11771,11772],{"class":3478}," 3.5",[1115,11774,1547],{"class":3462},[1115,11776,11777],{"class":3478}," 3.7",[1115,11779,1547],{"class":3462},[1115,11781,11749],{"class":3478},[1115,11783,1547],{"class":3462},[1115,11785,11749],{"class":3478},[1115,11787,11788],{"class":3470},")   ",[1115,11790,11792],{"class":11791},"sCsY4","# přímé zadání hodnot\n",[1115,11794,11795],{"class":3455,"line":27},[1115,11796,11797],{"class":11791},"# x \u003C- read.table(\"data.txt\")[, 1]                       # načtení prvního sloupce ze souboru\n",[1110,11799,11800,11801,11804,11805,11808,11809,11812,11813,11816],{},"Řádek s načtením ze souboru je zakomentovaný znakem ",[3223,11802,11803],{},"#",": soubor musí ležet v pracovním adresáři R. ",[3223,11806,11807],{},"read.table()"," vrací datovou tabulku (",[3223,11810,11811],{},"data.frame","), proto ",[3223,11814,11815],{},"[, 1]"," vybere její první sloupec jako vektor.",[1110,11818,8812],{},[3447,11820,11822],{"className":3449,"code":11821,"language":71,"meta":1229,"style":1229},"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",[3223,11823,11824,11881,11892,11903,11914,11925,11963,11989,12012],{"__ignoreMap":1229},[1115,11825,11826,11828,11830,11832,11834,11837,11839,11842,11844,11847,11849,11852,11854,11856,11858,11861,11863,11865,11867,11870,11872,11875,11877,11879],{"class":3455,"line":10},[1115,11827,6476],{"class":3458},[1115,11829,3463],{"class":3462},[1115,11831,3589],{"class":3466},[1115,11833,1626],{"class":3470},[1115,11835,11836],{"class":3478},"11.1",[1115,11838,1547],{"class":3462},[1115,11840,11841],{"class":3478}," 12.7",[1115,11843,1547],{"class":3462},[1115,11845,11846],{"class":3478}," 10.8",[1115,11848,1547],{"class":3462},[1115,11850,11851],{"class":3478}," 13.2",[1115,11853,1547],{"class":3462},[1115,11855,11841],{"class":3478},[1115,11857,1547],{"class":3462},[1115,11859,11860],{"class":3478}," 13.4",[1115,11862,1547],{"class":3462},[1115,11864,11841],{"class":3478},[1115,11866,1547],{"class":3462},[1115,11868,11869],{"class":3478}," 14.4",[1115,11871,1547],{"class":3462},[1115,11873,11874],{"class":3478}," 14.7",[1115,11876,1547],{"class":3462},[1115,11878,11869],{"class":3478},[1115,11880,3655],{"class":3470},[1115,11882,11883,11886,11888,11890],{"class":3455,"line":27},[1115,11884,11885],{"class":3466},"length",[1115,11887,1626],{"class":3470},[1115,11889,6476],{"class":3458},[1115,11891,3655],{"class":3470},[1115,11893,11894,11897,11899,11901],{"class":3455,"line":148},[1115,11895,11896],{"class":3466},"mean",[1115,11898,1626],{"class":3470},[1115,11900,6476],{"class":3458},[1115,11902,3655],{"class":3470},[1115,11904,11905,11908,11910,11912],{"class":3455,"line":111},[1115,11906,11907],{"class":3466},"var",[1115,11909,1626],{"class":3470},[1115,11911,6476],{"class":3458},[1115,11913,3655],{"class":3470},[1115,11915,11916,11919,11921,11923],{"class":3455,"line":96},[1115,11917,11918],{"class":3466},"sd",[1115,11920,1626],{"class":3470},[1115,11922,6476],{"class":3458},[1115,11924,3655],{"class":3470},[1115,11926,11927,11929,11931,11933,11936,11938,11940,11942,11944,11946,11948,11950,11952,11954,11957,11959,11961],{"class":3455,"line":89},[1115,11928,4242],{"class":3466},[1115,11930,1626],{"class":3470},[1115,11932,6476],{"class":3458},[1115,11934,11935],{"class":3470},"); ",[1115,11937,11477],{"class":3466},[1115,11939,1626],{"class":3470},[1115,11941,6476],{"class":3458},[1115,11943,11935],{"class":3470},[1115,11945,11477],{"class":3466},[1115,11947,1626],{"class":3470},[1115,11949,6476],{"class":3458},[1115,11951,4355],{"class":3470},[1115,11953,4392],{"class":3462},[1115,11955,11956],{"class":3466}," min",[1115,11958,1626],{"class":3470},[1115,11960,6476],{"class":3458},[1115,11962,3655],{"class":3470},[1115,11964,11965,11968,11970,11972,11974,11977,11979,11982,11984,11987],{"class":3455,"line":82},[1115,11966,11967],{"class":3466},"quantile",[1115,11969,1626],{"class":3470},[1115,11971,6476],{"class":3458},[1115,11973,1547],{"class":3462},[1115,11975,11976],{"class":3478}," 0.5",[1115,11978,1547],{"class":3462},[1115,11980,11981],{"class":3458}," type",[1115,11983,3551],{"class":3462},[1115,11985,11986],{"class":3478}," 6",[1115,11988,3655],{"class":3470},[1115,11990,11991,11993,11995,11997,11999,12002,12004,12006,12008,12010],{"class":3455,"line":75},[1115,11992,11967],{"class":3466},[1115,11994,1626],{"class":3470},[1115,11996,6476],{"class":3458},[1115,11998,1547],{"class":3462},[1115,12000,12001],{"class":3478}," 0.25",[1115,12003,1547],{"class":3462},[1115,12005,11981],{"class":3458},[1115,12007,3551],{"class":3462},[1115,12009,11986],{"class":3478},[1115,12011,3655],{"class":3470},[1115,12013,12014,12016,12018,12020,12022,12025,12027,12029,12031,12033],{"class":3455,"line":3645},[1115,12015,11967],{"class":3466},[1115,12017,1626],{"class":3470},[1115,12019,6476],{"class":3458},[1115,12021,1547],{"class":3462},[1115,12023,12024],{"class":3478}," 0.75",[1115,12026,1547],{"class":3462},[1115,12028,11981],{"class":3458},[1115,12030,3551],{"class":3462},[1115,12032,11986],{"class":3478},[1115,12034,3655],{"class":3470},[3447,12036,12039],{"className":12037,"code":12038,"language":3677,"meta":1229},[3675],"[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",[3223,12040,12038],{"__ignoreMap":1229},[1110,12042,12043,12046,12047,12050],{},[3223,12044,12045],{},"quantile(x, p, type = 6)"," je potřeba zadat explicitně — výchozí typ v R (",[3223,12048,12049],{},"type = 7",") by u některých souborů dal mírně odlišné hodnoty kvantilů než ruční výpočet použitý v této kapitole.",[1110,12052,12053],{},[4137,12054],{"alt":12055,"className":12056,"src":12057},"mask-ps-kvantily",[1130,4141],"\u002Fwiki-assets\u002Fmask-ps-kvantily.png",[1110,12059,12060],{},"Seřazení souboru a krabicový graf:",[3447,12062,12064],{"className":3449,"code":12063,"language":71,"meta":1229,"style":1229},"sort(x)                     # vzestupně\nsort(x, decreasing = TRUE)  # sestupně\nboxplot(x)\n",[3223,12065,12066,12081,12104],{"__ignoreMap":1229},[1115,12067,12068,12071,12073,12075,12078],{"class":3455,"line":10},[1115,12069,12070],{"class":3466},"sort",[1115,12072,1626],{"class":3470},[1115,12074,6476],{"class":3458},[1115,12076,12077],{"class":3470},")                     ",[1115,12079,12080],{"class":11791},"# vzestupně\n",[1115,12082,12083,12085,12087,12089,12091,12094,12096,12098,12101],{"class":3455,"line":27},[1115,12084,12070],{"class":3466},[1115,12086,1626],{"class":3470},[1115,12088,6476],{"class":3458},[1115,12090,1547],{"class":3462},[1115,12092,12093],{"class":3458}," decreasing",[1115,12095,3551],{"class":3462},[1115,12097,3564],{"class":3478},[1115,12099,12100],{"class":3470},")  ",[1115,12102,12103],{"class":11791},"# sestupně\n",[1115,12105,12106,12109,12111,12113],{"class":3455,"line":148},[1115,12107,12108],{"class":3466},"boxplot",[1115,12110,1626],{"class":3470},[1115,12112,6476],{"class":3458},[1115,12114,3655],{"class":3470},[3447,12116,12119],{"className":12117,"code":12118,"language":3677,"meta":1229},[3675]," [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",[3223,12120,12118],{"__ignoreMap":1229},[1110,12122,12123,12126,12127,12130],{},[3223,12124,12125],{},"boxplot()"," kreslí krabici mezi hodnotami ",[3223,12128,12129],{},"fivenum(x)"," (zde 12,7 a 14,4), které se od kvartilů typu 6 mohou mírně lišit.",[1103,12132,12134,12141],{"className":12133,"dataCallout":3230},[1106,3229],[1110,12135,12137,12140],{"className":12136},[1113],[1115,12138],{"className":12139,"ariaHidden":1121},[1118,3237,1120],"Příklad: Empirické charakteristiky",[1110,12142,12143],{},"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.",[1110,12145,12146,12147,2704,12170,2704,12193,2704,12212,12231,12232,8219,12259,12274,12275,1417],{},"Výstup R kódu výše dává ",[1115,12148,12150],{"className":12149},[1292],[1294,12151,12152],{"xmlns":1296},[1298,12153,12154,12167],{},[1301,12155,12156,12162,12164],{},[2475,12157,12158,12160],{"accent":1121},[1307,12159,6476],{},[1437,12161,11217],{},[1437,12163,1733],{},[1311,12165,12166],{},"13,01",[1315,12168,12169],{"encoding":1317},"\\bar{x}=13{,}01",[1115,12171,12173],{"className":12172},[1292],[1294,12174,12175],{"xmlns":1296},[1298,12176,12177,12190],{},[1301,12178,12179,12185,12187],{},[1330,12180,12181,12183],{},[1307,12182,1605],{},[1311,12184,1337],{},[1437,12186,1733],{},[1311,12188,12189],{},"1,75",[1315,12191,12192],{"encoding":1317},"s^2=1{,}75",[1115,12194,12196],{"className":12195},[1292],[1294,12197,12198],{"xmlns":1296},[1298,12199,12200,12209],{},[1301,12201,12202,12204,12206],{},[1307,12203,1605],{},[1437,12205,1733],{},[1311,12207,12208],{},"1,32",[1315,12210,12211],{"encoding":1317},"s=1{,}32",[1115,12213,12215],{"className":12214},[1292],[1294,12216,12217],{"xmlns":1296},[1298,12218,12219,12228],{},[1301,12220,12221,12223,12225],{},[1307,12222,9981],{},[1437,12224,1733],{},[1311,12226,12227],{},"3,9",[1315,12229,12230],{"encoding":1317},"R=3{,}9",", medián ",[1115,12233,12235],{"className":12234},[1292],[1294,12236,12237],{"xmlns":1296},[1298,12238,12239,12256],{},[1301,12240,12241,12251,12253],{},[1304,12242,12243,12249],{},[2475,12244,12245,12247],{"accent":1121},[1307,12246,6476],{},[1437,12248,11558],{},[1311,12250,8215],{},[1437,12252,1733],{},[1311,12254,12255],{},"12,95",[1315,12257,12258],{"encoding":1317},"\\tilde{x}_{0{,}5}=12{,}95",[1115,12260,12262],{"className":12261},[1292],[1294,12263,12264],{"xmlns":1296},[1298,12265,12266,12271],{},[1301,12267,12268],{},[1311,12269,12270],{},"12,3",[1315,12272,12273],{"encoding":1317},"12{,}3",", horní kvartil ",[1115,12276,12278],{"className":12277},[1292],[1294,12279,12280],{"xmlns":1296},[1298,12281,12282,12287],{},[1301,12283,12284],{},[1311,12285,12286],{},"14,4",[1315,12288,12289],{"encoding":1317},"14{,}4",[1110,12291,12292],{},"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.",[1103,12294,12296,12303],{"className":12295,"dataCallout":3230},[1106,3229],[1110,12297,12299,12302],{"className":12298},[1113],[1115,12300],{"className":12301,"ariaHidden":1121},[1118,3237,1120],"Příklad: Doba oprav televizorů",[1110,12304,12305],{},"Při 50 opravách určité závady televizoru byly naměřeny časy (v minutách). Určete empirické charakteristiky.",[3447,12307,12309],{"className":3449,"code":12308,"language":71,"meta":1229,"style":1229},"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",[3223,12310,12311,12371,12422,12469,12516,12564,12574,12584,12594,12614],{"__ignoreMap":1229},[1115,12312,12313,12316,12318,12320,12322,12324,12326,12329,12331,12334,12336,12339,12341,12344,12346,12349,12351,12354,12356,12359,12361,12364,12366,12369],{"class":3455,"line":10},[1115,12314,12315],{"class":3458},"x6",[1115,12317,3463],{"class":3462},[1115,12319,3589],{"class":3466},[1115,12321,1626],{"class":3470},[1115,12323,3328],{"class":3478},[1115,12325,1547],{"class":3462},[1115,12327,12328],{"class":3478}," 40.2",[1115,12330,1547],{"class":3462},[1115,12332,12333],{"class":3478}," 41.9",[1115,12335,1547],{"class":3462},[1115,12337,12338],{"class":3478}," 43.4",[1115,12340,1547],{"class":3462},[1115,12342,12343],{"class":3478}," 42.8",[1115,12345,1547],{"class":3462},[1115,12347,12348],{"class":3478}," 42.3",[1115,12350,1547],{"class":3462},[1115,12352,12353],{"class":3478}," 43.2",[1115,12355,1547],{"class":3462},[1115,12357,12358],{"class":3478}," 45",[1115,12360,1547],{"class":3462},[1115,12362,12363],{"class":3478}," 41.5",[1115,12365,1547],{"class":3462},[1115,12367,12368],{"class":3478}," 42.7",[1115,12370,3491],{"class":3462},[1115,12372,12373,12376,12378,12381,12383,12386,12388,12391,12393,12396,12398,12401,12403,12406,12408,12411,12413,12415,12417,12420],{"class":3455,"line":27},[1115,12374,12375],{"class":3478},"        43.9",[1115,12377,1547],{"class":3462},[1115,12379,12380],{"class":3478}," 40.1",[1115,12382,1547],{"class":3462},[1115,12384,12385],{"class":3478}," 43.3",[1115,12387,1547],{"class":3462},[1115,12389,12390],{"class":3478}," 41.1",[1115,12392,1547],{"class":3462},[1115,12394,12395],{"class":3478}," 42.5",[1115,12397,1547],{"class":3462},[1115,12399,12400],{"class":3478}," 42.4",[1115,12402,1547],{"class":3462},[1115,12404,12405],{"class":3478}," 41.4",[1115,12407,1547],{"class":3462},[1115,12409,12410],{"class":3478}," 40.8",[1115,12412,1547],{"class":3462},[1115,12414,9093],{"class":3478},[1115,12416,1547],{"class":3462},[1115,12418,12419],{"class":3478}," 44.7",[1115,12421,3491],{"class":3462},[1115,12423,12424,12427,12429,12431,12433,12435,12437,12440,12442,12445,12447,12450,12452,12454,12456,12459,12461,12463,12465,12467],{"class":3455,"line":148},[1115,12425,12426],{"class":3478},"        41.2",[1115,12428,1547],{"class":3462},[1115,12430,12333],{"class":3478},[1115,12432,1547],{"class":3462},[1115,12434,12400],{"class":3478},[1115,12436,1547],{"class":3462},[1115,12438,12439],{"class":3478}," 44.4",[1115,12441,1547],{"class":3462},[1115,12443,12444],{"class":3478}," 40.5",[1115,12446,1547],{"class":3462},[1115,12448,12449],{"class":3478}," 39.7",[1115,12451,1547],{"class":3462},[1115,12453,12390],{"class":3478},[1115,12455,1547],{"class":3462},[1115,12457,12458],{"class":3478}," 41",[1115,12460,1547],{"class":3462},[1115,12462,12333],{"class":3478},[1115,12464,1547],{"class":3462},[1115,12466,12410],{"class":3478},[1115,12468,3491],{"class":3462},[1115,12470,12471,12474,12476,12478,12480,12483,12485,12487,12489,12491,12493,12496,12498,12501,12503,12505,12507,12510,12512,12514],{"class":3455,"line":111},[1115,12472,12473],{"class":3478},"        43",[1115,12475,1547],{"class":3462},[1115,12477,12343],{"class":3478},[1115,12479,1547],{"class":3462},[1115,12481,12482],{"class":3478}," 42.9",[1115,12484,1547],{"class":3462},[1115,12486,12368],{"class":3478},[1115,12488,1547],{"class":3462},[1115,12490,12385],{"class":3478},[1115,12492,1547],{"class":3462},[1115,12494,12495],{"class":3478}," 42.2",[1115,12497,1547],{"class":3462},[1115,12499,12500],{"class":3478}," 39.2",[1115,12502,1547],{"class":3462},[1115,12504,12363],{"class":3478},[1115,12506,1547],{"class":3462},[1115,12508,12509],{"class":3478}," 41.6",[1115,12511,1547],{"class":3462},[1115,12513,12368],{"class":3478},[1115,12515,3491],{"class":3462},[1115,12517,12518,12521,12523,12525,12527,12530,12532,12534,12536,12539,12541,12544,12546,12549,12551,12553,12555,12558,12560,12562],{"class":3455,"line":96},[1115,12519,12520],{"class":3478},"        45",[1115,12522,1547],{"class":3462},[1115,12524,12348],{"class":3478},[1115,12526,1547],{"class":3462},[1115,12528,12529],{"class":3478}," 43.6",[1115,12531,1547],{"class":3462},[1115,12533,12353],{"class":3478},[1115,12535,1547],{"class":3462},[1115,12537,12538],{"class":3478}," 38.8",[1115,12540,1547],{"class":3462},[1115,12542,12543],{"class":3478}," 43",[1115,12545,1547],{"class":3462},[1115,12547,12548],{"class":3478}," 44.2",[1115,12550,1547],{"class":3462},[1115,12552,12543],{"class":3478},[1115,12554,1547],{"class":3462},[1115,12556,12557],{"class":3478}," 40",[1115,12559,1547],{"class":3462},[1115,12561,12439],{"class":3478},[1115,12563,3655],{"class":3470},[1115,12565,12566,12568,12570,12572],{"class":3455,"line":89},[1115,12567,11885],{"class":3466},[1115,12569,1626],{"class":3470},[1115,12571,12315],{"class":3458},[1115,12573,3655],{"class":3470},[1115,12575,12576,12578,12580,12582],{"class":3455,"line":82},[1115,12577,11896],{"class":3466},[1115,12579,1626],{"class":3470},[1115,12581,12315],{"class":3458},[1115,12583,3655],{"class":3470},[1115,12585,12586,12588,12590,12592],{"class":3455,"line":75},[1115,12587,11918],{"class":3466},[1115,12589,1626],{"class":3470},[1115,12591,12315],{"class":3458},[1115,12593,3655],{"class":3470},[1115,12595,12596,12598,12600,12602,12604,12606,12608,12610,12612],{"class":3455,"line":3645},[1115,12597,11477],{"class":3466},[1115,12599,1626],{"class":3470},[1115,12601,12315],{"class":3458},[1115,12603,4355],{"class":3470},[1115,12605,4392],{"class":3462},[1115,12607,11956],{"class":3466},[1115,12609,1626],{"class":3470},[1115,12611,12315],{"class":3458},[1115,12613,3655],{"class":3470},[1115,12615,12616,12619,12621,12623],{"class":3455,"line":72},[1115,12617,12618],{"class":3466},"median",[1115,12620,1626],{"class":3470},[1115,12622,12315],{"class":3458},[1115,12624,3655],{"class":3470},[3447,12626,12629],{"className":12627,"code":12628,"language":3677,"meta":1229},[3675],"[1] 50\n[1] 42.27\n[1] 1.48052\n[1] 6.2\n[1] 42.4\n",[3223,12630,12628],{"__ignoreMap":1229},[1110,12632,12633],{},"Průměrná doba opravy je 42,27 minuty se směrodatnou odchylkou 1,48 minuty a mediánem 42,4 minuty; průměr a medián téměř splývají, data jsou kolem středu rozložena souměrně.",[1136,12635,12637],{"id":12636},"empirická-distribuční-funkce","Empirická distribuční funkce",[1110,12639,12640,12641,12654,12655,1402,12658,12681,12682,12716],{},"Pro libovolný rozsah datového souboru, diskrétní i spojitou náhodnou veličinu ",[1115,12642,12644],{"className":12643},[1292],[1294,12645,12646],{"xmlns":1296},[1298,12647,12648,12652],{},[1301,12649,12650],{},[1307,12651,6488],{},[1315,12653,6488],{"encoding":1317},", lze sestrojit ",[1279,12656,12657],{},"empirickou distribuční funkci",[1115,12659,12661],{"className":12660},[1292],[1294,12662,12663],{"xmlns":1296},[1298,12664,12665,12679],{},[1301,12666,12667,12673,12675,12677],{},[1304,12668,12669,12671],{},[1307,12670,6471],{},[1307,12672,1435],{},[1437,12674,1626],{"stretchy":1625},[1307,12676,6476],{},[1437,12678,1637],{"stretchy":1625},[1315,12680,10941],{"encoding":1317},". Pro datový soubor ",[1115,12683,12685],{"className":12684},[1292],[1294,12686,12687],{"xmlns":1296},[1298,12688,12689,12713],{},[1301,12690,12691,12693,12699,12701,12703,12705,12711],{},[1437,12692,1626],{"stretchy":1625},[1304,12694,12695,12697],{},[1307,12696,6476],{},[1311,12698,1544],{},[1437,12700,1547],{"separator":1121},[1437,12702,1550],{},[1437,12704,1547],{"separator":1121},[1304,12706,12707,12709],{},[1307,12708,6476],{},[1307,12710,1435],{},[1437,12712,1637],{"stretchy":1625},[1315,12714,12715],{"encoding":1317},"(x_1,\\dots,x_n)"," je",[1115,12718,12720],{"className":12719},[1292],[1294,12721,12722],{"xmlns":1296,"display":1715},[1298,12723,12724,12748],{},[1301,12725,12726,12732,12734,12736,12738,12740,12746],{},[1304,12727,12728,12730],{},[1307,12729,6471],{},[1307,12731,1435],{},[1437,12733,1626],{"stretchy":1625},[1307,12735,6476],{},[1437,12737,1637],{"stretchy":1625},[1437,12739,1733],{},[2491,12741,12742,12744],{},[1307,12743,7016],{},[1307,12745,1435],{},[1437,12747,1547],{"separator":1121},[1315,12749,12750],{"encoding":1317},"F_n(x) = \\frac{k}{n},",[1110,12752,4261,12753,12766,12767,1417],{},[1115,12754,12756],{"className":12755},[1292],[1294,12757,12758],{"xmlns":1296},[1298,12759,12760,12764],{},[1301,12761,12762],{},[1307,12763,7016],{},[1315,12765,7016],{"encoding":1317}," je počet prvků datového souboru menších nebo rovných číslu ",[1115,12768,12770],{"className":12769},[1292],[1294,12771,12772],{"xmlns":1296},[1298,12773,12774,12778],{},[1301,12775,12776],{},[1307,12777,6476],{},[1315,12779,6476],{"encoding":1317},[1110,12781,8812],{},[3447,12783,12785],{"className":3449,"code":12784,"language":71,"meta":1229,"style":1229},"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",[3223,12786,12787,12802,12817,12835,12849],{"__ignoreMap":1229},[1115,12788,12789,12791,12793,12796,12798,12800],{"class":3455,"line":10},[1115,12790,6527],{"class":3458},[1115,12792,3463],{"class":3462},[1115,12794,12795],{"class":3466}," ecdf",[1115,12797,1626],{"class":3470},[1115,12799,6476],{"class":3458},[1115,12801,3655],{"class":3470},[1115,12803,12804,12807,12809,12811,12814],{"class":3455,"line":27},[1115,12805,12806],{"class":3466},"knots",[1115,12808,1626],{"class":3470},[1115,12810,6527],{"class":3458},[1115,12812,12813],{"class":3470},")        ",[1115,12815,12816],{"class":11791},"# vzestupně seřazené různé hodnoty datového souboru\n",[1115,12818,12819,12821,12823,12825,12827,12829,12832],{"class":3455,"line":148},[1115,12820,6527],{"class":3466},[1115,12822,1626],{"class":3470},[1115,12824,12806],{"class":3466},[1115,12826,1626],{"class":3470},[1115,12828,6527],{"class":3458},[1115,12830,12831],{"class":3470},"))      ",[1115,12833,12834],{"class":11791},"# hodnoty Fn(x) v těchto bodech\n",[1115,12836,12837,12839,12841,12843,12846],{"class":3455,"line":111},[1115,12838,6527],{"class":3466},[1115,12840,1626],{"class":3470},[1115,12842,3298],{"class":3478},[1115,12844,12845],{"class":3470},")            ",[1115,12847,12848],{"class":11791},"# Fn v libovolném bodě\n",[1115,12850,12851,12854,12856,12858],{"class":3455,"line":96},[1115,12852,12853],{"class":3466},"plot",[1115,12855,1626],{"class":3470},[1115,12857,6527],{"class":3458},[1115,12859,3655],{"class":3470},[3447,12861,12864],{"className":12862,"code":12863,"language":3677,"meta":1229},[3675],"[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",[3223,12865,12863],{"__ignoreMap":1229},[1110,12867,12868,12871,12872,12890,12891,12894,12895,12908,12909,1417],{},[3223,12869,12870],{},"knots()"," vrací jen různé hodnoty (opakující se hodnota 12,7 je ve výpočtu ",[1115,12873,12875],{"className":12874},[1292],[1294,12876,12877],{"xmlns":1296},[1298,12878,12879,12887],{},[1301,12880,12881],{},[1304,12882,12883,12885],{},[1307,12884,6471],{},[1307,12886,1435],{},[1315,12888,12889],{"encoding":1317},"F_n"," započtena třikrát, v seznamu uzlů je ale jen jednou); ",[3223,12892,12893],{},"plot(f)"," nakreslí schodovitý graf, který v každém uzlu skáče o ",[1115,12896,12898],{"className":12897},[1292],[1294,12899,12900],{"xmlns":1296},[1298,12901,12902,12906],{},[1301,12903,12904],{},[1307,12905,7016],{},[1315,12907,7016],{"encoding":1317},"-násobek ",[1115,12910,12912],{"className":12911},[1292],[1294,12913,12914],{"xmlns":1296},[1298,12915,12916,12924],{},[1301,12917,12918,12920,12922],{},[1311,12919,1544],{},[1307,12921,4358],{"mathvariant":1872},[1307,12923,1435],{},[1315,12925,12926],{"encoding":1317},"1\u002Fn",[1110,12928,12929],{},[4137,12930],{"alt":12931,"className":12932,"src":12933},"mask-ps-ecdf",[1130,4141],"\u002Fwiki-assets\u002Fmask-ps-ecdf.png",[1103,12935,12937,12944],{"className":12936,"dataCallout":3230},[1106,3229],[1110,12938,12940,12943],{"className":12939},[1113],[1115,12941],{"className":12942,"ariaHidden":1121},[1118,3237,1120],"Příklad: Empirická distribuční funkce",[1110,12945,12946],{},"Pro předchozí datový soubor (doba opravy součástky) určete empirickou distribuční funkci.",[1110,12948,12949,12950,1417],{},"Uspořádaný soubor je ",[1115,12951,12953],{"className":12952},[1292],[1294,12954,12955],{"xmlns":1296},[1298,12956,12957,13021],{},[1301,12958,12959,12962,12964,12966,12969,12971,12973,12976,12978,12980,12982,12984,12986,12988,12990,12992,12995,12997,12999,13002,13004,13006,13008,13010,13012,13014,13016,13018],{},[1311,12960,12961],{},"10,8",[1437,12963,6650],{"separator":1121},[2661,12965,11072],{},[1311,12967,12968],{},"11,1",[1437,12970,6650],{"separator":1121},[2661,12972,11072],{},[1311,12974,12975],{},"12,7",[1437,12977,6650],{"separator":1121},[2661,12979,11072],{},[1311,12981,12975],{},[1437,12983,6650],{"separator":1121},[2661,12985,11072],{},[1311,12987,12975],{},[1437,12989,6650],{"separator":1121},[2661,12991,11072],{},[1311,12993,12994],{},"13,2",[1437,12996,6650],{"separator":1121},[2661,12998,11072],{},[1311,13000,13001],{},"13,4",[1437,13003,6650],{"separator":1121},[2661,13005,11072],{},[1311,13007,12286],{},[1437,13009,6650],{"separator":1121},[2661,13011,11072],{},[1311,13013,12286],{},[1437,13015,6650],{"separator":1121},[2661,13017,11072],{},[1311,13019,13020],{},"14,7",[1315,13022,13023],{"encoding":1317},"10{,}8;\\ 11{,}1;\\ 12{,}7;\\ 12{,}7;\\ 12{,}7;\\ 13{,}2;\\ 13{,}4;\\ 14{,}4;\\ 14{,}4;\\ 14{,}7",[1141,13025,13026,13059],{},[1144,13027,13028],{},[1147,13029,13030,13045,13047,13049,13051,13053,13055,13057],{},[1150,13031,13032],{},[1115,13033,13035],{"className":13034},[1292],[1294,13036,13037],{"xmlns":1296},[1298,13038,13039,13043],{},[1301,13040,13041],{},[1307,13042,6476],{},[1315,13044,6476],{"encoding":1317},[1150,13046,12961],{},[1150,13048,12968],{},[1150,13050,12975],{},[1150,13052,12994],{},[1150,13054,13001],{},[1150,13056,12286],{},[1150,13058,13020],{},[1157,13060,13061,13093],{},[1147,13062,13063,13078,13080,13082,13084,13086,13089,13091],{},[1162,13064,13065],{},[1115,13066,13068],{"className":13067},[1292],[1294,13069,13070],{"xmlns":1296},[1298,13071,13072,13076],{},[1301,13073,13074],{},[1307,13075,7016],{},[1315,13077,7016],{"encoding":1317},[1162,13079,1544],{},[1162,13081,1337],{},[1162,13083,9684],{},[1162,13085,3718],{},[1162,13087,13088],{},"7",[1162,13090,3348],{},[1162,13092,8791],{},[1147,13094,13095,13120,13123,13126,13128,13131,13134,13137],{},[1162,13096,13097],{},[1115,13098,13100],{"className":13099},[1292],[1294,13101,13102],{"xmlns":1296},[1298,13103,13104,13118],{},[1301,13105,13106,13112,13114,13116],{},[1304,13107,13108,13110],{},[1307,13109,6471],{},[1307,13111,1435],{},[1437,13113,1626],{"stretchy":1625},[1307,13115,6476],{},[1437,13117,1637],{"stretchy":1625},[1315,13119,10941],{"encoding":1317},[1162,13121,13122],{},"0,1",[1162,13124,13125],{},"0,2",[1162,13127,8215],{},[1162,13129,13130],{},"0,6",[1162,13132,13133],{},"0,7",[1162,13135,13136],{},"0,9",[1162,13138,13139],{},"1,0",[1110,13141,13142,13143,13165,13166,13189],{},"Graf (levý panel výše) odpovídá tabulce: funkce je nulová pod 10,8, skáče o ",[1115,13144,13146],{"className":13145},[1292],[1294,13147,13148],{"xmlns":1296},[1298,13149,13150,13162],{},[1301,13151,13152,13154,13156,13158,13160],{},[1311,13153,1544],{},[1307,13155,4358],{"mathvariant":1872},[1307,13157,1435],{},[1437,13159,1733],{},[1311,13161,13122],{},[1315,13163,13164],{"encoding":1317},"1\u002Fn = 0{,}1"," v každé jednoduché hodnotě a o ",[1115,13167,13169],{"className":13168},[1292],[1294,13170,13171],{"xmlns":1296},[1298,13172,13173,13186],{},[1301,13174,13175,13177,13179,13181,13183],{},[1311,13176,3345],{},[1307,13178,4358],{"mathvariant":1872},[1307,13180,1435],{},[1437,13182,1733],{},[1311,13184,13185],{},"0,3",[1315,13187,13188],{"encoding":1317},"3\u002Fn = 0{,}3"," v bodě 12,7, kde se hodnota opakuje třikrát.",[1103,13191,13193,13200],{"className":13192,"dataCallout":3230},[1106,3229],[1110,13194,13196,13199],{"className":13195},[1113],[1115,13197],{"className":13198,"ariaHidden":1121},[1118,3237,1120],"Příklad: Odpad materiálu",[1110,13201,13202],{},"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.",[3447,13204,13206],{"className":3449,"code":13205,"language":71,"meta":1229,"style":1229},"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",[3223,13207,13208,13259,13269,13279,13289,13309,13319,13334,13344],{"__ignoreMap":1229},[1115,13209,13210,13213,13215,13217,13219,13221,13223,13225,13227,13229,13231,13233,13235,13237,13239,13241,13243,13245,13247,13249,13251,13253,13255,13257],{"class":3455,"line":10},[1115,13211,13212],{"class":3458},"x4",[1115,13214,3463],{"class":3462},[1115,13216,3589],{"class":3466},[1115,13218,1626],{"class":3470},[1115,13220,11744],{"class":3478},[1115,13222,1547],{"class":3462},[1115,13224,11749],{"class":3478},[1115,13226,1547],{"class":3462},[1115,13228,11754],{"class":3478},[1115,13230,1547],{"class":3462},[1115,13232,11759],{"class":3478},[1115,13234,1547],{"class":3462},[1115,13236,11754],{"class":3478},[1115,13238,1547],{"class":3462},[1115,13240,11754],{"class":3478},[1115,13242,1547],{"class":3462},[1115,13244,11772],{"class":3478},[1115,13246,1547],{"class":3462},[1115,13248,11777],{"class":3478},[1115,13250,1547],{"class":3462},[1115,13252,11749],{"class":3478},[1115,13254,1547],{"class":3462},[1115,13256,11749],{"class":3478},[1115,13258,3655],{"class":3470},[1115,13260,13261,13263,13265,13267],{"class":3455,"line":27},[1115,13262,11885],{"class":3466},[1115,13264,1626],{"class":3470},[1115,13266,13212],{"class":3458},[1115,13268,3655],{"class":3470},[1115,13270,13271,13273,13275,13277],{"class":3455,"line":148},[1115,13272,11896],{"class":3466},[1115,13274,1626],{"class":3470},[1115,13276,13212],{"class":3458},[1115,13278,3655],{"class":3470},[1115,13280,13281,13283,13285,13287],{"class":3455,"line":111},[1115,13282,11918],{"class":3466},[1115,13284,1626],{"class":3470},[1115,13286,13212],{"class":3458},[1115,13288,3655],{"class":3470},[1115,13290,13291,13293,13295,13297,13299,13301,13303,13305,13307],{"class":3455,"line":96},[1115,13292,11477],{"class":3466},[1115,13294,1626],{"class":3470},[1115,13296,13212],{"class":3458},[1115,13298,4355],{"class":3470},[1115,13300,4392],{"class":3462},[1115,13302,11956],{"class":3466},[1115,13304,1626],{"class":3470},[1115,13306,13212],{"class":3458},[1115,13308,3655],{"class":3470},[1115,13310,13311,13313,13315,13317],{"class":3455,"line":89},[1115,13312,12618],{"class":3466},[1115,13314,1626],{"class":3470},[1115,13316,13212],{"class":3458},[1115,13318,3655],{"class":3470},[1115,13320,13321,13324,13326,13328,13330,13332],{"class":3455,"line":82},[1115,13322,13323],{"class":3458},"f4",[1115,13325,3463],{"class":3462},[1115,13327,12795],{"class":3466},[1115,13329,1626],{"class":3470},[1115,13331,13212],{"class":3458},[1115,13333,3655],{"class":3470},[1115,13335,13336,13338,13340,13342],{"class":3455,"line":75},[1115,13337,12806],{"class":3466},[1115,13339,1626],{"class":3470},[1115,13341,13323],{"class":3458},[1115,13343,3655],{"class":3470},[1115,13345,13346,13348,13350,13352,13354,13356],{"class":3455,"line":3645},[1115,13347,13323],{"class":3466},[1115,13349,1626],{"class":3470},[1115,13351,12806],{"class":3466},[1115,13353,1626],{"class":3470},[1115,13355,13323],{"class":3458},[1115,13357,9251],{"class":3470},[3447,13359,13362],{"className":13360,"code":13361,"language":3677,"meta":1229},[3675],"[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",[3223,13363,13361],{"__ignoreMap":1229},[1110,13365,13366,13367,13390],{},"Průměrný odpad je 3,86 % se směrodatnou odchylkou 0,18 % a mediánem 3,85 %. Pravý panel obrázku výše ukazuje tvar ",[1115,13368,13370],{"className":13369},[1292],[1294,13371,13372],{"xmlns":1296},[1298,13373,13374,13388],{},[1301,13375,13376,13382,13384,13386],{},[1304,13377,13378,13380],{},[1307,13379,6471],{},[1307,13381,1435],{},[1437,13383,1626],{"stretchy":1625},[1307,13385,6476],{},[1437,13387,1637],{"stretchy":1625},[1315,13389,10941],{"encoding":1317},": hodnota 3,8 se v souboru opakuje třikrát, proto zde funkce skáče o 0,3 najednou, stejně jako hodnota 4,0.",[1136,13392,13394],{"id":13393},"třídění-datového-souboru-do-tříd","Třídění datového souboru do tříd",[1110,13396,13397,13398,13401,13402,13415,13416,13419],{},"Je-li rozsah datového souboru velký (řádově přes 30 až 50 pozorování), hodnoty se před dalším zpracováním ",[1279,13399,13400],{},"roztřídí",": variační rozpětí ",[1115,13403,13405],{"className":13404},[1292],[1294,13406,13407],{"xmlns":1296},[1298,13408,13409,13413],{},[1301,13410,13411],{},[1307,13412,9981],{},[1315,13414,9981],{"encoding":1317}," se rozdělí na určitý počet ",[1279,13417,13418],{},"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.",[1110,13421,13422],{},"Výsledkem je tabulka četností se sloupci:",[1191,13424,13425,13505,13526,13547],{},[1194,13426,13427,13445,13446,13459,13460,13504],{},[1115,13428,13430],{"className":13429},[1292],[1294,13431,13432],{"xmlns":1296},[1298,13433,13434,13442],{},[1301,13435,13436],{},[1304,13437,13438,13440],{},[1307,13439,10958],{},[1307,13441,1634],{},[1315,13443,13444],{"encoding":1317},"I_j"," — ",[1115,13447,13449],{"className":13448},[1292],[1294,13450,13451],{"xmlns":1296},[1298,13452,13453,13457],{},[1301,13454,13455],{},[1307,13456,1634],{},[1315,13458,1634],{"encoding":1317},"-tý interval (v této kapitole vždy zleva uzavřený a zprava otevřený, ",[1115,13461,13463],{"className":13462},[1292],[1294,13464,13465],{"xmlns":1296},[1298,13466,13467,13501],{},[1301,13468,13469,13475,13477,13479,13485,13487,13499],{},[1304,13470,13471,13473],{},[1307,13472,10958],{},[1307,13474,1634],{},[1437,13476,1733],{},[1437,13478,8183],{"stretchy":1625},[1304,13480,13481,13483],{},[1307,13482,3473],{},[1307,13484,1634],{},[1437,13486,6650],{"separator":1121},[1304,13488,13489,13491],{},[1307,13490,3473],{},[1301,13492,13493,13495,13497],{},[1307,13494,1634],{},[1437,13496,5231],{},[1311,13498,1544],{},[1437,13500,1637],{"stretchy":1625},[1315,13502,13503],{"encoding":1317},"I_j = \\langle c_j; c_{j+1})","),",[1194,13506,13507,13525],{},[1115,13508,13510],{"className":13509},[1292],[1294,13511,13512],{"xmlns":1296},[1298,13513,13514,13522],{},[1301,13515,13516],{},[1304,13517,13518,13520],{},[1307,13519,8683],{},[1307,13521,1634],{},[1315,13523,13524],{"encoding":1317},"Z_j"," — střed (reprezentant) intervalu,",[1194,13527,13528,13546],{},[1115,13529,13531],{"className":13530},[1292],[1294,13532,13533],{"xmlns":1296},[1298,13534,13535,13543],{},[1301,13536,13537],{},[1304,13538,13539,13541],{},[1307,13540,6527],{},[1307,13542,1634],{},[1315,13544,13545],{"encoding":1317},"f_j"," — četnost, počet hodnot v intervalu,",[1194,13548,13549,13579,13580,5495,13608,1417],{},[1115,13550,13552],{"className":13551},[1292],[1294,13553,13554],{"xmlns":1296},[1298,13555,13556,13576],{},[1301,13557,13558,13564,13566,13572,13574],{},[1304,13559,13560,13562],{},[1307,13561,1110],{},[1307,13563,1634],{},[1437,13565,1733],{},[1304,13567,13568,13570],{},[1307,13569,6527],{},[1307,13571,1634],{},[1307,13573,4358],{"mathvariant":1872},[1307,13575,1435],{},[1315,13577,13578],{"encoding":1317},"p_j = f_j\u002Fn"," — relativní četnost, přičemž ",[1115,13581,13583],{"className":13582},[1292],[1294,13584,13585],{"xmlns":1296},[1298,13586,13587,13605],{},[1301,13588,13589,13595,13601,13603],{},[1304,13590,13591,13593],{},[1437,13592,1739],{},[1307,13594,1634],{},[1304,13596,13597,13599],{},[1307,13598,6527],{},[1307,13600,1634],{},[1437,13602,1733],{},[1307,13604,1435],{},[1315,13606,13607],{"encoding":1317},"\\sum_j f_j = n",[1115,13609,13611],{"className":13610},[1292],[1294,13612,13613],{"xmlns":1296},[1298,13614,13615,13633],{},[1301,13616,13617,13623,13629,13631],{},[1304,13618,13619,13621],{},[1437,13620,1739],{},[1307,13622,1634],{},[1304,13624,13625,13627],{},[1307,13626,1110],{},[1307,13628,1634],{},[1437,13630,1733],{},[1311,13632,1544],{},[1315,13634,13635],{"encoding":1317},"\\sum_j p_j = 1",[1110,13637,13638,13639,13642,13643,13646,13647,13650,13651,13654,13655,4361,13658,13675,13676,13679,13680,4361,13683,1562,13700,13703],{},"V R se třídění provádí příkazem ",[3223,13640,13641],{},"hist()"," — buď necháme R zvolit třídy samo (",[3223,13644,13645],{},"hist(x)","), nebo zadáme hranice přímo (",[3223,13648,13649],{},"hist(x, br = seq(0, 550, by = 50))","). Uložením výsledku do proměnné (",[3223,13652,13653],{},"y \u003C- hist(...)",") získáme jednotlivé sloupce tabulky: ",[3223,13656,13657],{},"y$counts",[1115,13659,13661],{"className":13660},[1292],[1294,13662,13663],{"xmlns":1296},[1298,13664,13665,13673],{},[1301,13666,13667],{},[1304,13668,13669,13671],{},[1307,13670,6527],{},[1307,13672,1634],{},[1315,13674,13545],{"encoding":1317},"), ",[3223,13677,13678],{},"y$breaks"," (hranice tříd), ",[3223,13681,13682],{},"y$mids",[1115,13684,13686],{"className":13685},[1292],[1294,13687,13688],{"xmlns":1296},[1298,13689,13690,13698],{},[1301,13691,13692],{},[1304,13693,13694,13696],{},[1307,13695,8683],{},[1307,13697,1634],{},[1315,13699,13524],{"encoding":1317},[3223,13701,13702],{},"y$density"," (relativní četnosti na škále hustoty).",[1110,13705,13706,13707,13724,13725,13727,13728,13764,13765,13768,13769,1417],{},"Interval ",[1115,13708,13710],{"className":13709},[1292],[1294,13711,13712],{"xmlns":1296},[1298,13713,13714,13722],{},[1301,13715,13716],{},[1304,13717,13718,13720],{},[1307,13719,10958],{},[1307,13721,1634],{},[1315,13723,13444],{"encoding":1317}," je ve výchozím nastavení ",[3223,13726,13641],{}," zleva otevřený a zprava uzavřený, ",[1115,13729,13731],{"className":13730},[1292],[1294,13732,13733],{"xmlns":1296},[1298,13734,13735,13761],{},[1301,13736,13737,13739,13745,13747,13759],{},[1437,13738,1626],{"stretchy":1625},[1304,13740,13741,13743],{},[1307,13742,3473],{},[1307,13744,1634],{},[1437,13746,6650],{"separator":1121},[1304,13748,13749,13751],{},[1307,13750,3473],{},[1301,13752,13753,13755,13757],{},[1307,13754,1634],{},[1437,13756,5231],{},[1311,13758,1544],{},[1437,13760,7200],{"stretchy":1625},[1315,13762,13763],{"encoding":1317},"(c_j; c_{j+1}\\rangle"," — opačně, než jak třídy zapisujeme v této kapitole. Parametr ",[3223,13766,13767],{},"right = FALSE"," třídy obrátí na ",[1115,13770,13772],{"className":13771},[1292],[1294,13773,13774],{"xmlns":1296},[1298,13775,13776,13802],{},[1301,13777,13778,13780,13786,13788,13800],{},[1437,13779,8183],{"stretchy":1625},[1304,13781,13782,13784],{},[1307,13783,3473],{},[1307,13785,1634],{},[1437,13787,6650],{"separator":1121},[1304,13789,13790,13792],{},[1307,13791,3473],{},[1301,13793,13794,13796,13798],{},[1307,13795,1634],{},[1437,13797,5231],{},[1311,13799,1544],{},[1437,13801,1637],{"stretchy":1625},[1315,13803,13804],{"encoding":1317},"\\langle c_j; c_{j+1})",[1110,13806,13807],{},[4137,13808],{"alt":13809,"className":13810,"src":13811},"mask-ps-histogram-trideni",[1130,4141],"\u002Fwiki-assets\u002Fmask-ps-histogram-trideni.png",[1103,13813,13815,13822],{"className":13814,"dataCallout":3230},[1106,3229],[1110,13816,13818,13821],{"className":13817},[1113],[1115,13819],{"className":13820,"ariaHidden":1121},[1118,3237,1120],"Příklad: Třídění datového souboru",[1110,13823,13824],{},"Byly provedeny zkoušky životnosti nového výrobku. Datový soubor obsahuje 68 hodnot doby do poruchy (v minutách). Určete odhady charakteristik a zákona rozdělení.",[3447,13826,13828],{"className":3449,"code":13827,"language":71,"meta":1229,"style":1229},"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",[3223,13829,13830,13887,13938,13988,14039,14089,14137,14177,14187,14207,14271,14280,14310],{"__ignoreMap":1229},[1115,13831,13832,13835,13837,13839,13841,13844,13846,13849,13851,13854,13856,13859,13861,13863,13865,13867,13869,13871,13873,13876,13878,13880,13882,13885],{"class":3455,"line":10},[1115,13833,13834],{"class":3458},"x9",[1115,13836,3463],{"class":3462},[1115,13838,3589],{"class":3466},[1115,13840,1626],{"class":3470},[1115,13842,13843],{"class":3478},"101",[1115,13845,1547],{"class":3462},[1115,13847,13848],{"class":3478}," 338",[1115,13850,1547],{"class":3462},[1115,13852,13853],{"class":3478}," 150",[1115,13855,1547],{"class":3462},[1115,13857,13858],{"class":3478}," 47",[1115,13860,1547],{"class":3462},[1115,13862,9235],{"class":3478},[1115,13864,1547],{"class":3462},[1115,13866,3934],{"class":3478},[1115,13868,1547],{"class":3462},[1115,13870,3488],{"class":3478},[1115,13872,1547],{"class":3462},[1115,13874,13875],{"class":3478}," 392",[1115,13877,1547],{"class":3462},[1115,13879,9752],{"class":3478},[1115,13881,1547],{"class":3462},[1115,13883,13884],{"class":3478}," 73",[1115,13886,3491],{"class":3462},[1115,13888,13889,13892,13894,13897,13899,13902,13904,13907,13909,13911,13913,13916,13918,13921,13923,13926,13928,13931,13933,13936],{"class":3455,"line":27},[1115,13890,13891],{"class":3478},"        367",[1115,13893,1547],{"class":3462},[1115,13895,13896],{"class":3478}," 54",[1115,13898,1547],{"class":3462},[1115,13900,13901],{"class":3478}," 114",[1115,13903,1547],{"class":3462},[1115,13905,13906],{"class":3478}," 213",[1115,13908,1547],{"class":3462},[1115,13910,3506],{"class":3478},[1115,13912,1547],{"class":3462},[1115,13914,13915],{"class":3478}," 341",[1115,13917,1547],{"class":3462},[1115,13919,13920],{"class":3478}," 313",[1115,13922,1547],{"class":3462},[1115,13924,13925],{"class":3478}," 112",[1115,13927,1547],{"class":3462},[1115,13929,13930],{"class":3478}," 343",[1115,13932,1547],{"class":3462},[1115,13934,13935],{"class":3478}," 151",[1115,13937,3491],{"class":3462},[1115,13939,13940,13943,13945,13948,13950,13953,13955,13958,13960,13963,13965,13967,13969,13972,13974,13976,13978,13981,13983,13986],{"class":3455,"line":148},[1115,13941,13942],{"class":3478},"        9",[1115,13944,1547],{"class":3462},[1115,13946,13947],{"class":3478}," 160",[1115,13949,1547],{"class":3462},[1115,13951,13952],{"class":3478}," 18",[1115,13954,1547],{"class":3462},[1115,13956,13957],{"class":3478}," 113",[1115,13959,1547],{"class":3462},[1115,13961,13962],{"class":3478}," 77",[1115,13964,1547],{"class":3462},[1115,13966,3506],{"class":3478},[1115,13968,1547],{"class":3462},[1115,13970,13971],{"class":3478}," 159",[1115,13973,1547],{"class":3462},[1115,13975,3488],{"class":3478},[1115,13977,1547],{"class":3462},[1115,13979,13980],{"class":3478}," 119",[1115,13982,1547],{"class":3462},[1115,13984,13985],{"class":3478}," 130",[1115,13987,3491],{"class":3462},[1115,13989,13990,13993,13995,13998,14000,14003,14005,14007,14009,14012,14014,14017,14019,14022,14024,14027,14029,14032,14034,14037],{"class":3455,"line":111},[1115,13991,13992],{"class":3478},"        140",[1115,13994,1547],{"class":3462},[1115,13996,13997],{"class":3478}," 161",[1115,13999,1547],{"class":3462},[1115,14001,14002],{"class":3478}," 379",[1115,14004,1547],{"class":3462},[1115,14006,13896],{"class":3478},[1115,14008,1547],{"class":3462},[1115,14010,14011],{"class":3478}," 373",[1115,14013,1547],{"class":3462},[1115,14015,14016],{"class":3478}," 168",[1115,14018,1547],{"class":3462},[1115,14020,14021],{"class":3478}," 365",[1115,14023,1547],{"class":3462},[1115,14025,14026],{"class":3478}," 110",[1115,14028,1547],{"class":3462},[1115,14030,14031],{"class":3478}," 145",[1115,14033,1547],{"class":3462},[1115,14035,14036],{"class":3478}," 88",[1115,14038,3491],{"class":3462},[1115,14040,14041,14044,14046,14049,14051,14054,14056,14059,14061,14064,14066,14068,14070,14073,14075,14077,14079,14082,14084,14087],{"class":3455,"line":96},[1115,14042,14043],{"class":3478},"        74",[1115,14045,1547],{"class":3462},[1115,14047,14048],{"class":3478}," 46",[1115,14050,1547],{"class":3462},[1115,14052,14053],{"class":3478}," 246",[1115,14055,1547],{"class":3462},[1115,14057,14058],{"class":3478}," 259",[1115,14060,1547],{"class":3462},[1115,14062,14063],{"class":3478}," 19",[1115,14065,1547],{"class":3462},[1115,14067,13980],{"class":3478},[1115,14069,1547],{"class":3462},[1115,14071,14072],{"class":3478}," 48",[1115,14074,1547],{"class":3462},[1115,14076,10613],{"class":3478},[1115,14078,1547],{"class":3462},[1115,14080,14081],{"class":3478}," 163",[1115,14083,1547],{"class":3462},[1115,14085,14086],{"class":3478}," 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91",[1115,14176,3655],{"class":3470},[1115,14178,14179,14181,14183,14185],{"class":3455,"line":75},[1115,14180,11885],{"class":3466},[1115,14182,1626],{"class":3470},[1115,14184,13834],{"class":3458},[1115,14186,3655],{"class":3470},[1115,14188,14189,14191,14193,14195,14197,14199,14201,14203,14205],{"class":3455,"line":3645},[1115,14190,11477],{"class":3466},[1115,14192,1626],{"class":3470},[1115,14194,13834],{"class":3458},[1115,14196,4355],{"class":3470},[1115,14198,4392],{"class":3462},[1115,14200,11956],{"class":3466},[1115,14202,1626],{"class":3470},[1115,14204,13834],{"class":3458},[1115,14206,3655],{"class":3470},[1115,14208,14209,14212,14214,14217,14219,14221,14223,14226,14228,14231,14233,14235,14237,14240,14242,14245,14247,14249,14251,14253,14256,14258,14260,14262,14265,14267,14269],{"class":3455,"line":72},[1115,14210,14211],{"class":3458},"y9",[1115,14213,3463],{"class":3462},[1115,14215,14216],{"class":3466}," hist",[1115,14218,1626],{"class":3470},[1115,14220,13834],{"class":3458},[1115,14222,1547],{"class":3462},[1115,14224,14225],{"class":3458}," br",[1115,14227,3551],{"class":3462},[1115,14229,14230],{"class":3466}," seq",[1115,14232,1626],{"class":3470},[1115,14234,1313],{"class":3478},[1115,14236,1547],{"class":3462},[1115,14238,14239],{"class":3478}," 550",[1115,14241,1547],{"class":3462},[1115,14243,14244],{"class":3458}," by",[1115,14246,3551],{"class":3462},[1115,14248,5999],{"class":3478},[1115,14250,1637],{"class":3470},[1115,14252,1547],{"class":3462},[1115,14254,14255],{"class":3458}," right",[1115,14257,3551],{"class":3462},[1115,14259,6092],{"class":3478},[1115,14261,1547],{"class":3462},[1115,14263,14264],{"class":3458}," plot",[1115,14266,3551],{"class":3462},[1115,14268,6092],{"class":3478},[1115,14270,3655],{"class":3470},[1115,14272,14273,14275,14277],{"class":3455,"line":25},[1115,14274,14211],{"class":3458},[1115,14276,3668],{"class":3462},[1115,14278,14279],{"class":3458},"counts\n",[1115,14281,14282,14284,14286,14288,14290,14293,14295,14298,14300,14302,14304,14306,14308],{"class":3455,"line":65},[1115,14283,9738],{"class":3466},[1115,14285,1626],{"class":3470},[1115,14287,14211],{"class":3458},[1115,14289,3668],{"class":3462},[1115,14291,14292],{"class":3458},"counts",[1115,14294,9833],{"class":3462},[1115,14296,14297],{"class":3466}," length",[1115,14299,1626],{"class":3470},[1115,14301,13834],{"class":3458},[1115,14303,1637],{"class":3470},[1115,14305,1547],{"class":3462},[1115,14307,10613],{"class":3478},[1115,14309,3655],{"class":3470},[1115,14311,14312,14314,14316,14318,14320,14322,14324,14326],{"class":3455,"line":63},[1115,14313,11896],{"class":3466},[1115,14315,1626],{"class":3470},[1115,14317,13834],{"class":3458},[1115,14319,11935],{"class":3470},[1115,14321,11918],{"class":3466},[1115,14323,1626],{"class":3470},[1115,14325,13834],{"class":3458},[1115,14327,3655],{"class":3470},[3447,14329,14332],{"className":14330,"code":14331,"language":3677,"meta":1229},[3675],"[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",[3223,14333,14331],{"__ignoreMap":1229},[1110,14335,14336,14337,14365],{},"Variační rozpětí je ",[1115,14338,14340],{"className":14339},[1292],[1294,14341,14342],{"xmlns":1296},[1298,14343,14344,14362],{},[1301,14345,14346,14348,14350,14353,14355,14357,14359],{},[1307,14347,9981],{},[1437,14349,1733],{},[1311,14351,14352],{},"501",[1437,14354,2817],{},[1311,14356,1337],{},[1437,14358,1733],{},[1311,14360,14361],{},"499",[1315,14363,14364],{"encoding":1317},"R = 501 - 2 = 499"," minut; rozdělit je na 11 tříd po 50 minutách je rozumná volba (ani moc málo, ani moc tříd). Výsledná tabulka četností:",[1141,14367,14368,14464],{},[1144,14369,14370],{},[1147,14371,14372,14387,14406,14425,14444],{},[1150,14373,14374],{},[1115,14375,14377],{"className":14376},[1292],[1294,14378,14379],{"xmlns":1296},[1298,14380,14381,14385],{},[1301,14382,14383],{},[1307,14384,1634],{},[1315,14386,1634],{"encoding":1317},[1150,14388,14389],{},[1115,14390,14392],{"className":14391},[1292],[1294,14393,14394],{"xmlns":1296},[1298,14395,14396,14404],{},[1301,14397,14398],{},[1304,14399,14400,14402],{},[1307,14401,10958],{},[1307,14403,1634],{},[1315,14405,13444],{"encoding":1317},[1150,14407,14408],{},[1115,14409,14411],{"className":14410},[1292],[1294,14412,14413],{"xmlns":1296},[1298,14414,14415,14423],{},[1301,14416,14417],{},[1304,14418,14419,14421],{},[1307,14420,8683],{},[1307,14422,1634],{},[1315,14424,13524],{"encoding":1317},[1150,14426,14427],{},[1115,14428,14430],{"className":14429},[1292],[1294,14431,14432],{"xmlns":1296},[1298,14433,14434,14442],{},[1301,14435,14436],{},[1304,14437,14438,14440],{},[1307,14439,6527],{},[1307,14441,1634],{},[1315,14443,13545],{"encoding":1317},[1150,14445,14446],{},[1115,14447,14449],{"className":14448},[1292],[1294,14450,14451],{"xmlns":1296},[1298,14452,14453,14461],{},[1301,14454,14455],{},[1304,14456,14457,14459],{},[1307,14458,1110],{},[1307,14460,1634],{},[1315,14462,14463],{"encoding":1317},"p_j",[1157,14465,14466,14481,14496,14511,14524,14539,14554,14568,14583,14597,14612],{},[1147,14467,14468,14470,14473,14475,14478],{},[1162,14469,1544],{},[1162,14471,14472],{},"⟨0; 50)",[1162,14474,3812],{},[1162,14476,14477],{},"19",[1162,14479,14480],{},"0,279",[1147,14482,14483,14485,14488,14491,14493],{},[1162,14484,1337],{},[1162,14486,14487],{},"⟨50; 100)",[1162,14489,14490],{},"75",[1162,14492,2006],{},[1162,14494,14495],{},"0,162",[1147,14497,14498,14500,14503,14506,14508],{},[1162,14499,3345],{},[1162,14501,14502],{},"⟨100; 150)",[1162,14504,14505],{},"125",[1162,14507,8791],{},[1162,14509,14510],{},"0,147",[1147,14512,14513,14515,14518,14520,14522],{},[1162,14514,3295],{},[1162,14516,14517],{},"⟨150; 200)",[1162,14519,7236],{},[1162,14521,8791],{},[1162,14523,14510],{},[1147,14525,14526,14528,14531,14534,14536],{},[1162,14527,9684],{},[1162,14529,14530],{},"⟨200; 250)",[1162,14532,14533],{},"225",[1162,14535,9684],{},[1162,14537,14538],{},"0,074",[1147,14540,14541,14543,14546,14549,14551],{},[1162,14542,3718],{},[1162,14544,14545],{},"⟨250; 300)",[1162,14547,14548],{},"275",[1162,14550,1544],{},[1162,14552,14553],{},"0,015",[1147,14555,14556,14558,14561,14564,14566],{},[1162,14557,13088],{},[1162,14559,14560],{},"⟨300; 350)",[1162,14562,14563],{},"325",[1162,14565,9684],{},[1162,14567,14538],{},[1147,14569,14570,14573,14576,14579,14581],{},[1162,14571,14572],{},"8",[1162,14574,14575],{},"⟨350; 400)",[1162,14577,14578],{},"375",[1162,14580,9684],{},[1162,14582,14538],{},[1147,14584,14585,14587,14590,14593,14595],{},[1162,14586,3348],{},[1162,14588,14589],{},"⟨400; 450)",[1162,14591,14592],{},"425",[1162,14594,1544],{},[1162,14596,14553],{},[1147,14598,14599,14601,14604,14607,14609],{},[1162,14600,8791],{},[1162,14602,14603],{},"⟨450; 500)",[1162,14605,14606],{},"475",[1162,14608,1313],{},[1162,14610,14611],{},"0,000",[1147,14613,14614,14616,14619,14622,14624],{},[1162,14615,2006],{},[1162,14617,14618],{},"⟨500; ∞)",[1162,14620,14621],{},"525",[1162,14623,1544],{},[1162,14625,14553],{},[1110,14627,14628,14629,14646,14647,14664,14665,2704,14688,2704,14716,14735,14736,2704,14759,14778],{},"Asi 27,9 % výrobků vydrželo méně než 50 minut, jen asi 1,5 % mezi 250 a 300 minutami. Charakteristiky spočtené ze středů tříd ",[1115,14630,14632],{"className":14631},[1292],[1294,14633,14634],{"xmlns":1296},[1298,14635,14636,14644],{},[1301,14637,14638],{},[1304,14639,14640,14642],{},[1307,14641,8683],{},[1307,14643,1634],{},[1315,14645,13524],{"encoding":1317}," (vážený průměr a rozptyl se střední hodnotou nahrazenou ",[1115,14648,14650],{"className":14649},[1292],[1294,14651,14652],{"xmlns":1296},[1298,14653,14654,14662],{},[1301,14655,14656],{},[1304,14657,14658,14660],{},[1307,14659,8683],{},[1307,14661,1634],{},[1315,14663,13524],{"encoding":1317},") vycházejí ",[1115,14666,14668],{"className":14667},[1292],[1294,14669,14670],{"xmlns":1296},[1298,14671,14672,14685],{},[1301,14673,14674,14680,14682],{},[2475,14675,14676,14678],{"accent":1121},[1307,14677,6476],{},[1437,14679,11217],{},[1437,14681,9198],{},[1311,14683,14684],{},"149,26",[1315,14686,14687],{"encoding":1317},"\\bar{x} \\approx 149{,}26",[1115,14689,14691],{"className":14690},[1292],[1294,14692,14693],{"xmlns":1296},[1298,14694,14695,14713],{},[1301,14696,14697,14703,14705,14708,14710],{},[1330,14698,14699,14701],{},[1307,14700,1605],{},[1311,14702,1337],{},[1437,14704,9198],{},[1311,14706,14707],{},"15",[2661,14709,2663],{},[1311,14711,14712],{},"484,5",[1315,14714,14715],{"encoding":1317},"s^2 \\approx 15\\,484{,}5",[1115,14717,14719],{"className":14718},[1292],[1294,14720,14721],{"xmlns":1296},[1298,14722,14723,14732],{},[1301,14724,14725,14727,14729],{},[1307,14726,1605],{},[1437,14728,9198],{},[1311,14730,14731],{},"124,44",[1315,14733,14734],{"encoding":1317},"s \\approx 124{,}44"," — blízko hodnotám ",[1115,14737,14739],{"className":14738},[1292],[1294,14740,14741],{"xmlns":1296},[1298,14742,14743,14756],{},[1301,14744,14745,14751,14753],{},[2475,14746,14747,14749],{"accent":1121},[1307,14748,6476],{},[1437,14750,11217],{},[1437,14752,1733],{},[1311,14754,14755],{},"145,44",[1315,14757,14758],{"encoding":1317},"\\bar{x}=145{,}44",[1115,14760,14762],{"className":14761},[1292],[1294,14763,14764],{"xmlns":1296},[1298,14765,14766,14775],{},[1301,14767,14768,14770,14772],{},[1307,14769,1605],{},[1437,14771,1733],{},[1311,14773,14774],{},"126,13",[1315,14776,14777],{"encoding":1317},"s=126{,}13"," spočteným přímo z nerozdělených dat; malý rozdíl vzniká tím, že třídění nahrazuje skutečné hodnoty středy tříd.",[1110,14780,14781,14782,14785,14786,14822,14823,14841,14842,14856,14857,14883,14884,14886,14887,4620],{},"Tvar histogramu — vysoká četnost u krátkých dob, rychlý pokles — odpovídá ",[1279,14783,14784],{},"exponenciálnímu rozdělení",", které se pro dobu do poruchy používá nejčastěji. Jeho hustota je ",[1115,14787,14789],{"className":14788},[1292],[1294,14790,14791],{"xmlns":1296},[1298,14792,14793,14819],{},[1301,14794,14795,14797,14799,14801,14803,14805,14807],{},[1307,14796,6527],{},[1437,14798,1626],{"stretchy":1625},[1307,14800,6476],{},[1437,14802,1637],{"stretchy":1625},[1437,14804,1733],{},[1307,14806,9470],{},[1330,14808,14809,14811],{},[1307,14810,8350],{},[1301,14812,14813,14815,14817],{},[1437,14814,2817],{},[1307,14816,9470],{},[1307,14818,6476],{},[1315,14820,14821],{"encoding":1317},"f(x) = \\lambda e^{-\\lambda x}"," pro ",[1115,14824,14826],{"className":14825},[1292],[1294,14827,14828],{"xmlns":1296},[1298,14829,14830,14838],{},[1301,14831,14832,14834,14836],{},[1307,14833,6476],{},[1437,14835,3104],{},[1311,14837,1313],{},[1315,14839,14840],{"encoding":1317},"x \\ge 0",", s parametrem ",[1115,14843,14845],{"className":14844},[1292],[1294,14846,14847],{"xmlns":1296},[1298,14848,14849,14853],{},[1301,14850,14851],{},[1307,14852,9470],{},[1315,14854,14855],{"encoding":1317},"\\lambda"," odhadnutým jako ",[1115,14858,14860],{"className":14859},[1292],[1294,14861,14862],{"xmlns":1296},[1298,14863,14864,14880],{},[1301,14865,14866,14868,14870,14872,14874],{},[1307,14867,9470],{},[1437,14869,1733],{},[1311,14871,1544],{},[1307,14873,4358],{"mathvariant":1872},[2475,14875,14876,14878],{"accent":1121},[1307,14877,6476],{},[1437,14879,11217],{},[1315,14881,14882],{"encoding":1317},"\\lambda = 1\u002F\\bar{x}"," (v R je ",[3223,14885,9637],{}," parametrem ",[3223,14888,14889],{},"dexp()",[3447,14891,14893],{"className":3449,"code":14892,"language":71,"meta":1229,"style":1229},"rate9 \u003C- 1 \u002F mean(x9)\nrate9\n",[3223,14894,14895,14914],{"__ignoreMap":1229},[1115,14896,14897,14900,14902,14904,14906,14908,14910,14912],{"class":3455,"line":10},[1115,14898,14899],{"class":3458},"rate9",[1115,14901,3463],{"class":3462},[1115,14903,4395],{"class":3478},[1115,14905,9833],{"class":3462},[1115,14907,8989],{"class":3466},[1115,14909,1626],{"class":3470},[1115,14911,13834],{"class":3458},[1115,14913,3655],{"class":3470},[1115,14915,14916],{"class":3455,"line":27},[1115,14917,14918],{"class":3458},"rate9\n",[3447,14920,14923],{"className":14921,"code":14922,"language":3677,"meta":1229},[3675],"[1] 0.006875632\n",[3223,14924,14922],{"__ignoreMap":1229},[1110,14926,14927],{},[4137,14928],{"alt":14929,"className":14930,"src":14931},"mask-ps-hustota-fit",[1130,4141],"\u002Fwiki-assets\u002Fmask-ps-hustota-fit.png",[1110,14933,14934,14935,1417],{},"Proložená křivka dobře sleduje tvar sloupců. Zda data odpovídají exponenciálnímu rozdělení formálně, posuzuje test dobré shody popsaný v ",[1127,14936,6361],{"className":14937,"dataFsResolvedFilePath":1471,"href":1472},[1130],[1103,14939,14941,14948],{"className":14940,"dataCallout":3230},[1106,3229],[1110,14942,14944,14947],{"className":14943},[1113],[1115,14945],{"className":14946,"ariaHidden":1121},[1118,3237,1120],"Příklad: Doba života výrobku",[1110,14949,14950],{},"Sledováním doby života výrobku bylo naměřeno 50 hodnot (v minutách). Určete empirické charakteristiky, roztřiďte datový soubor a nakreslete histogram četností.",[3447,14952,14954],{"className":3449,"code":14953,"language":71,"meta":1229,"style":1229},"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",[3223,14955,14956,15017,15068,15119,15170,15222,15232,15258,15278,15336,15345,15353],{"__ignoreMap":1229},[1115,14957,14958,14961,14963,14965,14967,14970,14972,14975,14977,14980,14982,14985,14987,14990,14992,14995,14997,15000,15002,15005,15007,15010,15012,15015],{"class":3455,"line":10},[1115,14959,14960],{"class":3458},"x5",[1115,14962,3463],{"class":3462},[1115,14964,3589],{"class":3466},[1115,14966,1626],{"class":3470},[1115,14968,14969],{"class":3478},"63",[1115,14971,1547],{"class":3462},[1115,14973,14974],{"class":3478}," 156",[1115,14976,1547],{"class":3462},[1115,14978,14979],{"class":3478}," 184",[1115,14981,1547],{"class":3462},[1115,14983,14984],{"class":3478}," 786",[1115,14986,1547],{"class":3462},[1115,14988,14989],{"class":3478}," 822",[1115,14991,1547],{"class":3462},[1115,14993,14994],{"class":3478}," 278",[1115,14996,1547],{"class":3462},[1115,14998,14999],{"class":3478}," 15",[1115,15001,1547],{"class":3462},[1115,15003,15004],{"class":3478}," 561",[1115,15006,1547],{"class":3462},[1115,15008,15009],{"class":3478}," 229",[1115,15011,1547],{"class":3462},[1115,15013,15014],{"class":3478}," 8",[1115,15016,3491],{"class":3462},[1115,15018,15019,15022,15024,15027,15029,15031,15033,15036,15038,15041,15043,15046,15048,15051,15053,15056,15058,15061,15063,15066],{"class":3455,"line":27},[1115,15020,15021],{"class":3478},"        4",[1115,15023,1547],{"class":3462},[1115,15025,15026],{"class":3478}," 35",[1115,15028,1547],{"class":3462},[1115,15030,13884],{"class":3478},[1115,15032,1547],{"class":3462},[1115,15034,15035],{"class":3478}," 203",[1115,15037,1547],{"class":3462},[1115,15039,15040],{"class":3478}," 178",[1115,15042,1547],{"class":3462},[1115,15044,15045],{"class":3478}," 323",[1115,15047,1547],{"class":3462},[1115,15049,15050],{"class":3478}," 275",[1115,15052,1547],{"class":3462},[1115,15054,15055],{"class":3478}," 176",[1115,15057,1547],{"class":3462},[1115,15059,15060],{"class":3478}," 427",[1115,15062,1547],{"class":3462},[1115,15064,15065],{"class":3478}," 196",[1115,15067,3491],{"class":3462},[1115,15069,15070,15073,15075,15078,15080,15083,15085,15088,15090,15093,15095,15098,15100,15103,15105,15107,15109,15112,15114,15117],{"class":3455,"line":148},[1115,15071,15072],{"class":3478},"        415",[1115,15074,1547],{"class":3462},[1115,15076,15077],{"class":3478}," 140",[1115,15079,1547],{"class":3462},[1115,15081,15082],{"class":3478}," 17",[1115,15084,1547],{"class":3462},[1115,15086,15087],{"class":3478}," 293",[1115,15089,1547],{"class":3462},[1115,15091,15092],{"class":3478}," 991",[1115,15094,1547],{"class":3462},[1115,15096,15097],{"class":3478}," 100",[1115,15099,1547],{"class":3462},[1115,15101,15102],{"class":3478}," 189",[1115,15104,1547],{"class":3462},[1115,15106,15055],{"class":3478},[1115,15108,1547],{"class":3462},[1115,15110,15111],{"class":3478}," 672",[1115,15113,1547],{"class":3462},[1115,15115,15116],{"class":3478}," 134",[1115,15118,3491],{"class":3462},[1115,15120,15121,15124,15126,15129,15131,15134,15136,15139,15141,15143,15145,15148,15150,15153,15155,15158,15160,15163,15165,15168],{"class":3455,"line":111},[1115,15122,15123],{"class":3478},"        529",[1115,15125,1547],{"class":3462},[1115,15127,15128],{"class":3478}," 310",[1115,15130,1547],{"class":3462},[1115,15132,15133],{"class":3478}," 22",[1115,15135,1547],{"class":3462},[1115,15137,15138],{"class":3478}," 69",[1115,15140,1547],{"class":3462},[1115,15142,13985],{"class":3478},[1115,15144,1547],{"class":3462},[1115,15146,15147],{"class":3478}," 272",[1115,15149,1547],{"class":3462},[1115,15151,15152],{"class":3478}," 117",[1115,15154,1547],{"class":3462},[1115,15156,15157],{"class":3478}," 169",[1115,15159,1547],{"class":3462},[1115,15161,15162],{"class":3478}," 466",[1115,15164,1547],{"class":3462},[1115,15166,15167],{"class":3478}," 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1050",[1115,15309,1547],{"class":3462},[1115,15311,14244],{"class":3458},[1115,15313,3551],{"class":3462},[1115,15315,13853],{"class":3478},[1115,15317,1637],{"class":3470},[1115,15319,1547],{"class":3462},[1115,15321,14255],{"class":3458},[1115,15323,3551],{"class":3462},[1115,15325,6092],{"class":3478},[1115,15327,1547],{"class":3462},[1115,15329,14264],{"class":3458},[1115,15331,3551],{"class":3462},[1115,15333,6092],{"class":3478},[1115,15335,3655],{"class":3470},[1115,15337,15338,15340,15342],{"class":3455,"line":72},[1115,15339,15282],{"class":3458},[1115,15341,3668],{"class":3462},[1115,15343,15344],{"class":3458},"mids\n",[1115,15346,15347,15349,15351],{"class":3455,"line":25},[1115,15348,15282],{"class":3458},[1115,15350,3668],{"class":3462},[1115,15352,14279],{"class":3458},[1115,15354,15355,15357,15359,15361,15363,15365,15367,15369,15371,15373,15375,15377,15379],{"class":3455,"line":65},[1115,15356,9738],{"class":3466},[1115,15358,1626],{"class":3470},[1115,15360,15282],{"class":3458},[1115,15362,3668],{"class":3462},[1115,15364,14292],{"class":3458},[1115,15366,9833],{"class":3462},[1115,15368,14297],{"class":3466},[1115,15370,1626],{"class":3470},[1115,15372,14960],{"class":3458},[1115,15374,1637],{"class":3470},[1115,15376,1547],{"class":3462},[1115,15378,10613],{"class":3478},[1115,15380,3655],{"class":3470},[3447,15382,15385],{"className":15383,"code":15384,"language":3677,"meta":1229},[3675],"[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",[3223,15386,15384],{"__ignoreMap":1229},[1110,15388,15389],{},"Variační rozpětí 987 minut rozdělené do 7 tříd po 150 minutách dává podobný tvar jako u předchozího příkladu: 74 % výrobků vydrželo méně než 300 minut, ojedinělé hodnoty sahají až k 991 minutám. Průměr 246,4 minuty leží výrazně nad mediánem 181 minut — rozdělení je zešikmené k vyšším hodnotám stejně jako u doby do poruchy výše.",[1136,15391,6162],{"id":6161},[1191,15393,15394,15412,15513,15581],{},[1194,15395,15396,1402,15399,15402,15403,15406,15407,15409,15410,1417],{},[1279,15397,15398],{},"Výchozí typ kvantilu v R.",[3223,15400,15401],{},"quantile()"," bez argumentu ",[3223,15404,15405],{},"type"," používá jiný výpočetní vzorec (",[3223,15408,12049],{},") než ruční postup v této kapitole — u některých souborů se hodnoty liší. Pro shodu s ručním výpočtem zadávejte ",[3223,15411,12045],{},[1194,15413,15414,15419,15420,15422,15423,15458,15459,15494,15495,15512],{},[1279,15415,15416,15417,1417],{},"Výchozí ohraničení tříd v ",[3223,15418,13641],{}," Bez ",[3223,15421,13767],{}," jsou třídy zprava uzavřené, ",[1115,15424,15426],{"className":15425},[1292],[1294,15427,15428],{"xmlns":1296},[1298,15429,15430,15456],{},[1301,15431,15432,15434,15440,15442,15454],{},[1437,15433,1626],{"stretchy":1625},[1304,15435,15436,15438],{},[1307,15437,3473],{},[1307,15439,1634],{},[1437,15441,6650],{"separator":1121},[1304,15443,15444,15446],{},[1307,15445,3473],{},[1301,15447,15448,15450,15452],{},[1307,15449,1634],{},[1437,15451,5231],{},[1311,15453,1544],{},[1437,15455,7200],{"stretchy":1625},[1315,15457,13763],{"encoding":1317}," — opačně než konvence ",[1115,15460,15462],{"className":15461},[1292],[1294,15463,15464],{"xmlns":1296},[1298,15465,15466,15492],{},[1301,15467,15468,15470,15476,15478,15490],{},[1437,15469,8183],{"stretchy":1625},[1304,15471,15472,15474],{},[1307,15473,3473],{},[1307,15475,1634],{},[1437,15477,6650],{"separator":1121},[1304,15479,15480,15482],{},[1307,15481,3473],{},[1301,15483,15484,15486,15488],{},[1307,15485,1634],{},[1437,15487,5231],{},[1311,15489,1544],{},[1437,15491,1637],{"stretchy":1625},[1315,15493,13804],{"encoding":1317}," použitá v tabulkách výše. Hodnota ležící přesně na hranici pak spadne do jiné třídy a četnosti ",[1115,15496,15498],{"className":15497},[1292],[1294,15499,15500],{"xmlns":1296},[1298,15501,15502,15510],{},[1301,15503,15504],{},[1304,15505,15506,15508],{},[1307,15507,6527],{},[1307,15509,1634],{},[1315,15511,13545],{"encoding":1317}," vyjdou jinak.",[1194,15514,15515,1402,15518,15536,15537,15550,15551,8806,15564,1417],{},[1279,15516,15517],{},"Rozptyl vs. směrodatná odchylka.",[1115,15519,15521],{"className":15520},[1292],[1294,15522,15523],{"xmlns":1296},[1298,15524,15525,15533],{},[1301,15526,15527],{},[1330,15528,15529,15531],{},[1307,15530,1605],{},[1311,15532,1337],{},[1315,15534,15535],{"encoding":1317},"s^2"," se udává v jednotkách znaku na druhou, ",[1115,15538,15540],{"className":15539},[1292],[1294,15541,15542],{"xmlns":1296},[1298,15543,15544,15548],{},[1301,15545,15546],{},[1307,15547,1605],{},[1315,15549,1605],{"encoding":1317}," ve stejných jednotkách jako data — pro interpretaci (např. „kolísání kolem průměru\") patří vždy ",[1115,15552,15554],{"className":15553},[1292],[1294,15555,15556],{"xmlns":1296},[1298,15557,15558,15562],{},[1301,15559,15560],{},[1307,15561,1605],{},[1315,15563,1605],{"encoding":1317},[1115,15565,15567],{"className":15566},[1292],[1294,15568,15569],{"xmlns":1296},[1298,15570,15571,15579],{},[1301,15572,15573],{},[1330,15574,15575,15577],{},[1307,15576,1605],{},[1311,15578,1337],{},[1315,15580,15535],{"encoding":1317},[1194,15582,15583,15586],{},[1279,15584,15585],{},"Příliš mnoho nebo příliš málo tříd."," Málo tříd skryje tvar rozdělení, moc tříd rozmělní četnosti na jednotky a histogram je nečitelný; volí se kompromis, ne pevné pravidlo.",[1136,15588,1189],{"id":1188},[1191,15590,15591,15596,15601,15606,15611,15616,15621],{},[1194,15592,15593],{},[1127,15594,1133],{"className":15595,"dataFsResolvedFilePath":1131,"href":1132},[1130],[1194,15597,15598],{},[1127,15599,6377],{"className":15600,"dataFsResolvedFilePath":6375,"href":6376},[1130],[1194,15602,15603],{},[1127,15604,6361],{"className":15605,"dataFsResolvedFilePath":1471,"href":1472},[1130],[1194,15607,15608],{},[1127,15609,1169],{"className":15610,"dataFsResolvedFilePath":1167,"href":1168},[1130],[1194,15612,15613],{},[1127,15614,1182],{"className":15615,"dataFsResolvedFilePath":1180,"href":1181},[1130],[1194,15617,15618],{},[1127,15619,6390],{"className":15620,"dataFsResolvedFilePath":6388,"href":6389},[1130],[1194,15622,15623],{},[1127,15624,6396],{"className":15625,"dataFsResolvedFilePath":1214,"href":1215},[1130],[1136,15627,1219],{"id":934},[1110,15629,1222,15630,1227],{},[1224,15631,1226],{},[6404,15633,15634],{},"html pre.shiki code .sP4rz, html 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analýza"," zkoumá jednostrannou závislost vysvětlované proměnné ",[1115,15682,15684],{"className":15683},[1292],[1294,15685,15686],{"xmlns":1296},[1298,15687,15688,15692],{},[1301,15689,15690],{},[1307,15691,6886],{},[1315,15693,6886],{"encoding":1317}," na vysvětlujících proměnných ",[1115,15696,15698],{"className":15697},[1292],[1294,15699,15700],{"xmlns":1296},[1298,15701,15702,15706],{},[1301,15703,15704],{},[1307,15705,6476],{},[1315,15707,6476],{"encoding":1317}," (příčina → následek); ",[1279,15710,15711],{},"korelační analýza"," měří intenzitu (těsnost) vzájemné závislosti.",[1194,15714,15715,15716,15719,15720,1417],{},"Parametry regresní funkce se odhadují ",[1279,15717,15718],{},"metodou nejmenších čtverců"," — minimalizací součtu čtverců reziduí ",[1115,15721,15723],{"className":15722},[1292],[1294,15724,15725],{"xmlns":1296},[1298,15726,15727,15757],{},[1301,15728,15729,15731,15733,15739,15741,15751],{},[1437,15730,1739],{},[1437,15732,1626],{"stretchy":1625},[1304,15734,15735,15737],{},[1307,15736,6886],{},[1307,15738,1629],{},[1437,15740,2817],{},[1304,15742,15743,15749],{},[2475,15744,15745,15747],{"accent":1121},[1307,15746,6886],{},[1437,15748,2481],{},[1307,15750,1629],{},[1330,15752,15753,15755],{},[1437,15754,1637],{"stretchy":1625},[1311,15756,1337],{},[1315,15758,15759],{"encoding":1317},"\\sum(y_i-\\hat y_i)^2",[1194,15761,15762,15763,1402,15766,15784,15785,1402,15788,15812,15813,1402,15816,1417],{},"Kvalitu fitu měří ",[1279,15764,15765],{},"index determinace",[1115,15767,15769],{"className":15768},[1292],[1294,15770,15771],{"xmlns":1296},[1298,15772,15773,15781],{},[1301,15774,15775],{},[1330,15776,15777,15779],{},[1307,15778,9981],{},[1311,15780,1337],{},[1315,15782,15783],{"encoding":1317},"R^2","; obecnou těsnost závislosti ",[1279,15786,15787],{},"index korelace",[1115,15789,15791],{"className":15790},[1292],[1294,15792,15793],{"xmlns":1296},[1298,15794,15795,15809],{},[1301,15796,15797,15799,15801],{},[1307,15798,10958],{},[1437,15800,1733],{},[4207,15802,15803],{},[1330,15804,15805,15807],{},[1307,15806,9981],{},[1311,15808,1337],{},[1315,15810,15811],{"encoding":1317},"I=\\sqrt{R^2}",", který je pro regresní přímku roven ",[1279,15814,15815],{},"koeficientu korelace",[1115,15817,15819],{"className":15818},[1292],[1294,15820,15821],{"xmlns":1296},[1298,15822,15823,15835],{},[1301,15824,15825],{},[1304,15826,15827,15829],{},[1307,15828,71],{},[1301,15830,15831,15833],{},[1307,15832,6476],{},[1307,15834,6886],{},[1315,15836,15837],{"encoding":1317},"r_{xy}",[1194,15839,15840,15841,15844,15845,15848,15849,15852],{},"Když přímka nestačí, volí se ",[1279,15842,15843],{},"parabolická, polynomická, hyperbolická nebo logaritmická"," regrese (stále lineární v parametrech, odhad metodou nejmenších čtverců) nebo ",[1279,15846,15847],{},"exponenciální"," regrese (nelineární v parametrech, odhad přes ",[3223,15850,15851],{},"nls2",").",[1194,15854,15855,15858],{},[1279,15856,15857],{},"Vícenásobná regrese"," rozšiřuje model o více regresorů; vyžaduje výběr proměnných (ENTER\u002Fstepwise), ověření šesti předpokladů modelu a kontrolu multikolinearity přes VIF.",[1194,15860,15861,15862,2704,15865,2704,15868,2704,15871,2704,15874,2704,15877,2704,15880,2704,15883,2704,15886,2704,15889,1417],{},"V R: ",[3223,15863,15864],{},"lm()",[3223,15866,15867],{},"nls2()",[3223,15869,15870],{},"summary()",[3223,15872,15873],{},"confint()",[3223,15875,15876],{},"predict()",[3223,15878,15879],{},"step()",[3223,15881,15882],{},"car::vif()",[3223,15884,15885],{},"lmtest::dwtest()",[3223,15887,15888],{},"whitestrap::white_test()",[3223,15890,15891],{},"shapiro.test()",[1136,15893,10995],{"id":10994},[1110,15895,15896,15899,15900,5495,15913,15926,15927,15929,15930,15943,15944,15957,15958,15961],{},[1127,15897,1133],{"className":15898,"dataFsResolvedFilePath":1131,"href":1132},[1130]," pracuje se dvěma znaky ",[1115,15901,15903],{"className":15902},[1292],[1294,15904,15905],{"xmlns":1296},[1298,15906,15907,15911],{},[1301,15908,15909],{},[1307,15910,6476],{},[1315,15912,6476],{"encoding":1317},[1115,15914,15916],{"className":15915},[1292],[1294,15917,15918],{"xmlns":1296},[1298,15919,15920,15924],{},[1301,15921,15922],{},[1307,15923,6886],{},[1315,15925,6886],{"encoding":1317}," zjištěnými na stejných jednotkách. ",[1279,15928,15679],{}," se zabývá jednostrannými závislostmi, kdy proti sobě stojí vysvětlující (nezávisle) proměnná ",[1115,15931,15933],{"className":15932},[1292],[1294,15934,15935],{"xmlns":1296},[1298,15936,15937,15941],{},[1301,15938,15939],{},[1307,15940,6476],{},[1315,15942,6476],{"encoding":1317}," v úloze příčiny a vysvětlovaná (závisle) proměnná ",[1115,15945,15947],{"className":15946},[1292],[1294,15948,15949],{"xmlns":1296},[1298,15950,15951,15955],{},[1301,15952,15953],{},[1307,15954,6886],{},[1315,15956,6886],{"encoding":1317}," v úloze následku. ",[1279,15959,15960],{},"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.",[1110,15963,15964,15965,15852],{},"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 (",[1279,15966,15967],{},"regresní funkce",[1110,15969,15970],{},"Druh regresní analýzy určuje struktura datového souboru:",[1191,15972,15973,16010],{},[1194,15974,15975,15978,15979,15992,15993,16006,16007,1547],{},[1279,15976,15977],{},"dvourozměrný datový soubor"," (jedna ",[1115,15980,15982],{"className":15981},[1292],[1294,15983,15984],{"xmlns":1296},[1298,15985,15986,15990],{},[1301,15987,15988],{},[1307,15989,6476],{},[1315,15991,6476],{"encoding":1317},", jedna ",[1115,15994,15996],{"className":15995},[1292],[1294,15997,15998],{"xmlns":1296},[1298,15999,16000,16004],{},[1301,16001,16002],{},[1307,16003,6886],{},[1315,16005,6886],{"encoding":1317},") → ",[1279,16008,16009],{},"regresní analýza dvou proměnných",[1194,16011,16012,16015,16016,16006,16046,1417],{},[1279,16013,16014],{},"vícerozměrný datový soubor"," (více ",[1115,16017,16019],{"className":16018},[1292],[1294,16020,16021],{"xmlns":1296},[1298,16022,16023,16043],{},[1301,16024,16025,16031,16033,16035,16037],{},[1304,16026,16027,16029],{},[1307,16028,6476],{},[1311,16030,1544],{},[1437,16032,1547],{"separator":1121},[1437,16034,1550],{},[1437,16036,1547],{"separator":1121},[1304,16038,16039,16041],{},[1307,16040,6476],{},[1307,16042,1110],{},[1315,16044,16045],{"encoding":1317},"x_1,\\dots,x_p",[1279,16047,16048],{},"vícenásobná regresní analýza",[1110,16050,16051,16052,16055,16056,16059],{},"Volba konkrétní regresní funkce by měla vycházet jak z ",[1279,16053,16054],{},"ekonomické teorie"," (ta napovídá, zda závislost roste, nebo klesá, zda je přímková, nebo zakřivená), tak z ",[1279,16057,16058],{},"grafické a matematicko-statistické analýzy"," dat — oba přístupy je vhodné kombinovat.",[1136,16061,16063],{"id":16062},"metoda-nejmenších-čtverců","Metoda nejmenších čtverců",[1110,16065,16066,16067,1402,16070,16124,16125,16143,16144,1402,16147,16203,16204,16222,16223,16240,16241,16279,16280,1417],{},"Rozlišují se ",[1279,16068,16069],{},"teoretická regresní funkce",[1115,16071,16073],{"className":16072},[1292],[1294,16074,16075],{"xmlns":1296},[1298,16076,16077,16121],{},[1301,16078,16079,16082,16084,16086,16088,16090,16092,16099,16101,16107,16109,16111,16113,16119],{},[1307,16080,16081],{},"η",[1437,16083,1733],{},[1307,16085,6527],{},[1437,16087,1626],{"stretchy":1625},[1307,16089,6476],{},[1437,16091,6650],{"separator":1121},[1304,16093,16094,16097],{},[1307,16095,16096],{},"β",[1311,16098,1313],{},[1437,16100,1547],{"separator":1121},[1304,16102,16103,16105],{},[1307,16104,16096],{},[1311,16106,1544],{},[1437,16108,1547],{"separator":1121},[1437,16110,1550],{},[1437,16112,1547],{"separator":1121},[1304,16114,16115,16117],{},[1307,16116,16096],{},[1307,16118,1110],{},[1437,16120,1637],{"stretchy":1625},[1315,16122,16123],{"encoding":1317},"\\eta = f(x;\\beta_0,\\beta_1,\\dots,\\beta_p)"," — neznámá, populační, daná neznámými parametry ",[1115,16126,16128],{"className":16127},[1292],[1294,16129,16130],{"xmlns":1296},[1298,16131,16132,16140],{},[1301,16133,16134],{},[1304,16135,16136,16138],{},[1307,16137,16096],{},[1307,16139,1629],{},[1315,16141,16142],{"encoding":1317},"\\beta_i"," — a ",[1279,16145,16146],{},"empirická regresní funkce",[1115,16148,16150],{"className":16149},[1292],[1294,16151,16152],{"xmlns":1296},[1298,16153,16154,16200],{},[1301,16155,16156,16162,16164,16166,16168,16170,16172,16178,16180,16186,16188,16190,16192,16198],{},[2475,16157,16158,16160],{"accent":1121},[1307,16159,6886],{},[1437,16161,2481],{},[1437,16163,1733],{},[1307,16165,6527],{},[1437,16167,1626],{"stretchy":1625},[1307,16169,6476],{},[1437,16171,6650],{"separator":1121},[1304,16173,16174,16176],{},[1307,16175,11262],{},[1311,16177,1313],{},[1437,16179,1547],{"separator":1121},[1304,16181,16182,16184],{},[1307,16183,11262],{},[1311,16185,1544],{},[1437,16187,1547],{"separator":1121},[1437,16189,1550],{},[1437,16191,1547],{"separator":1121},[1304,16193,16194,16196],{},[1307,16195,11262],{},[1307,16197,1110],{},[1437,16199,1637],{"stretchy":1625},[1315,16201,16202],{"encoding":1317},"\\hat y = f(x; b_0,b_1,\\dots,b_p)",", jejíž odhadnuté parametry ",[1115,16205,16207],{"className":16206},[1292],[1294,16208,16209],{"xmlns":1296},[1298,16210,16211,16219],{},[1301,16212,16213],{},[1304,16214,16215,16217],{},[1307,16216,11262],{},[1307,16218,1629],{},[1315,16220,16221],{"encoding":1317},"b_i"," jsou odhadem ",[1115,16224,16226],{"className":16225},[1292],[1294,16227,16228],{"xmlns":1296},[1298,16229,16230,16238],{},[1301,16231,16232],{},[1304,16233,16234,16236],{},[1307,16235,16096],{},[1307,16237,1629],{},[1315,16239,16142],{"encoding":1317}," vypočteným z konkrétních dat. Odchylky skutečných hodnot od empirické funkce, ",[1115,16242,16244],{"className":16243},[1292],[1294,16245,16246],{"xmlns":1296},[1298,16247,16248,16276],{},[1301,16249,16250,16256,16258,16264,16266],{},[1304,16251,16252,16254],{},[1307,16253,8350],{},[1307,16255,1629],{},[1437,16257,1733],{},[1304,16259,16260,16262],{},[1307,16261,6886],{},[1307,16263,1629],{},[1437,16265,2817],{},[1304,16267,16268,16274],{},[2475,16269,16270,16272],{"accent":1121},[1307,16271,6886],{},[1437,16273,2481],{},[1307,16275,1629],{},[1315,16277,16278],{"encoding":1317},"e_i=y_i-\\hat y_i",", se nazývají ",[1279,16281,16282],{},"rezidua",[1110,16284,16285,16286,16289],{},"Nejpoužívanější metodou odhadu parametrů je ",[1279,16287,16288],{},"metoda nejmenších čtverců (OLS)",": hledají se takové parametry, pro které je součet čtverců reziduí minimální,",[1115,16291,16293],{"className":16292},[1292],[1294,16294,16295],{"xmlns":1296,"display":1715},[1298,16296,16297,16347],{},[1301,16298,16299,16313,16315,16321,16323,16333,16339,16341,16343,16345],{},[1735,16300,16301,16303,16311],{},[1437,16302,1739],{},[1301,16304,16305,16307,16309],{},[1307,16306,1629],{},[1437,16308,1733],{},[1311,16310,1544],{},[1307,16312,1435],{},[1437,16314,1626],{"stretchy":1625},[1304,16316,16317,16319],{},[1307,16318,6886],{},[1307,16320,1629],{},[1437,16322,2817],{},[1304,16324,16325,16331],{},[2475,16326,16327,16329],{"accent":1121},[1307,16328,6886],{},[1437,16330,2481],{},[1307,16332,1629],{},[1330,16334,16335,16337],{},[1437,16336,1637],{"stretchy":1625},[1311,16338,1337],{},[1437,16340,7364],{},[1307,16342,4242],{},[1437,16344,4245],{},[1307,16346,1417],{"mathvariant":1872},[1315,16348,16349],{"encoding":1317},"\\sum_{i=1}^n (y_i - \\hat y_i)^2 \\to \\min.",[1110,16351,16352],{},"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.",[1110,16354,16355],{},[4137,16356],{"alt":16357,"className":16358,"src":16359},"mask-ra-primka-rezidua",[1130,4141],"\u002Fwiki-assets\u002Fmask-ra-primka-rezidua.png",[1110,16361,16362,16363,16381],{},"Obrázek ukazuje přesně to, co metoda minimalizuje: délky červených úseček jsou rezidua ",[1115,16364,16366],{"className":16365},[1292],[1294,16367,16368],{"xmlns":1296},[1298,16369,16370,16378],{},[1301,16371,16372],{},[1304,16373,16374,16376],{},[1307,16375,8350],{},[1307,16377,1629],{},[1315,16379,16380],{"encoding":1317},"e_i",", metoda nejmenších čtverců volí přímku tak, aby součet jejich čtverců byl nejmenší možný.",[1136,16383,16385],{"id":16384},"regresní-přímka","Regresní přímka",[1110,16387,16388,16389,1709],{},"Nejjednodušší regresní funkcí je ",[1279,16390,16391],{},"regresní přímka",[1115,16393,16395],{"className":16394},[1292],[1294,16396,16397],{"xmlns":1296,"display":1715},[1298,16398,16399,16451],{},[1301,16400,16401,16403,16405,16411,16413,16419,16421,16423,16425,16431,16433,16439,16441,16447,16449],{},[1307,16402,16081],{},[1437,16404,1733],{},[1304,16406,16407,16409],{},[1307,16408,16096],{},[1311,16410,1313],{},[1437,16412,5231],{},[1304,16414,16415,16417],{},[1307,16416,16096],{},[1311,16418,1544],{},[1307,16420,6476],{},[1437,16422,1547],{"separator":1121},[1763,16424],{"width":1765},[2475,16426,16427,16429],{"accent":1121},[1307,16428,6886],{},[1437,16430,2481],{},[1437,16432,1733],{},[1304,16434,16435,16437],{},[1307,16436,11262],{},[1311,16438,1313],{},[1437,16440,5231],{},[1304,16442,16443,16445],{},[1307,16444,11262],{},[1311,16446,1544],{},[1307,16448,6476],{},[1307,16450,1417],{"mathvariant":1872},[1315,16452,16453],{"encoding":1317},"\\eta = \\beta_0 + \\beta_1 x, \\qquad \\hat y = b_0 + b_1 x.",[1110,16455,16456,16457,16475,16476,16489,16490,16503],{},"Koeficient ",[1115,16458,16460],{"className":16459},[1292],[1294,16461,16462],{"xmlns":1296},[1298,16463,16464,16472],{},[1301,16465,16466],{},[1304,16467,16468,16470],{},[1307,16469,11262],{},[1311,16471,1544],{},[1315,16473,16474],{"encoding":1317},"b_1"," udává změnu průměru ",[1115,16477,16479],{"className":16478},[1292],[1294,16480,16481],{"xmlns":1296},[1298,16482,16483,16487],{},[1301,16484,16485],{},[1307,16486,6886],{},[1315,16488,6886],{"encoding":1317}," při jednotkové změně ",[1115,16491,16493],{"className":16492},[1292],[1294,16494,16495],{"xmlns":1296},[1298,16496,16497,16501],{},[1301,16498,16499],{},[1307,16500,6476],{},[1315,16502,6476],{"encoding":1317},"; jeho znaménko určuje, zda je závislost přímá, nebo nepřímá.",[16505,16506,16508],"h3",{"id":16507},"v-r","V R",[1110,16510,16511,16512,16515,16516,16519],{},"Vstupní data se nahrají buď ze souboru (",[3223,16513,16514],{},"d \u003C- read.table(\"data.txt\")",", případně ",[3223,16517,16518],{},"d \u003C- read.table(file.choose())","), nebo zapíší přímo jako vektory. Na šesti domácnostech sledujeme počet členů domácnosti a jejich týdenní výdaje:",[3447,16521,16523],{"className":3449,"code":16522,"language":71,"meta":1229,"style":1229},"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",[3223,16524,16525,16560,16601,16622],{"__ignoreMap":1229},[1115,16526,16527,16530,16532,16534,16536,16538,16540,16542,16544,16546,16548,16550,16552,16554,16556,16558],{"class":3455,"line":10},[1115,16528,16529],{"class":3458},"pocet_clenu",[1115,16531,3463],{"class":3462},[1115,16533,3589],{"class":3466},[1115,16535,1626],{"class":3470},[1115,16537,1544],{"class":3478},[1115,16539,1547],{"class":3462},[1115,16541,3934],{"class":3478},[1115,16543,1547],{"class":3462},[1115,16545,10613],{"class":3478},[1115,16547,1547],{"class":3462},[1115,16549,3554],{"class":3478},[1115,16551,1547],{"class":3462},[1115,16553,9752],{"class":3478},[1115,16555,1547],{"class":3462},[1115,16557,11986],{"class":3478},[1115,16559,3655],{"class":3470},[1115,16561,16562,16565,16567,16569,16571,16574,16576,16579,16581,16584,16586,16589,16591,16594,16596,16599],{"class":3455,"line":27},[1115,16563,16564],{"class":3458},"tydenni_vydaje",[1115,16566,3463],{"class":3462},[1115,16568,3589],{"class":3466},[1115,16570,1626],{"class":3470},[1115,16572,16573],{"class":3478},"490",[1115,16575,1547],{"class":3462},[1115,16577,16578],{"class":3478}," 820",[1115,16580,1547],{"class":3462},[1115,16582,16583],{"class":3478}," 1230",[1115,16585,1547],{"class":3462},[1115,16587,16588],{"class":3478}," 1570",[1115,16590,1547],{"class":3462},[1115,16592,16593],{"class":3478}," 1950",[1115,16595,1547],{"class":3462},[1115,16597,16598],{"class":3478}," 2320",[1115,16600,3655],{"class":3470},[1115,16602,16603,16605,16607,16610,16612,16614,16617,16620],{"class":3455,"line":148},[1115,16604,786],{"class":3458},[1115,16606,3463],{"class":3462},[1115,16608,16609],{"class":3466}," lm",[1115,16611,1626],{"class":3470},[1115,16613,16564],{"class":3458},[1115,16615,16616],{"class":3462}," ~",[1115,16618,16619],{"class":3458}," pocet_clenu",[1115,16621,3655],{"class":3470},[1115,16623,16624,16626,16628,16630],{"class":3455,"line":111},[1115,16625,1249],{"class":3466},[1115,16627,1626],{"class":3470},[1115,16629,786],{"class":3458},[1115,16631,3655],{"class":3470},[3447,16633,16636],{"className":16634,"code":16635,"language":3677,"meta":1229},[3675],"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",[3223,16637,16635],{"__ignoreMap":1229},[1110,16639,16640,16641,16673,16674,16677,16678,16708,16709,16739,16740,16743,16744,16767],{},"Odhadnutý model je ",[1115,16642,16644],{"className":16643},[1292],[1294,16645,16646],{"xmlns":1296},[1298,16647,16648,16670],{},[1301,16649,16650,16656,16658,16661,16663,16666,16668],{},[2475,16651,16652,16654],{"accent":1121},[1307,16653,6886],{},[1437,16655,2481],{},[1437,16657,1733],{},[1311,16659,16660],{},"108,7",[1437,16662,5231],{},[1311,16664,16665],{},"368,0",[2661,16667,2663],{},[1307,16669,6476],{},[1315,16671,16672],{"encoding":1317},"\\hat y = 108{,}7 + 368{,}0\\,x",". Sloupec ",[3223,16675,16676],{},"Pr(>|t|)"," je p-hodnota t-testu ",[1115,16679,16681],{"className":16680},[1292],[1294,16682,16683],{"xmlns":1296},[1298,16684,16685,16705],{},[1301,16686,16687,16693,16695,16701,16703],{},[1304,16688,16689,16691],{},[1307,16690,1309],{},[1311,16692,1313],{},[1437,16694,1709],{},[1304,16696,16697,16699],{},[1307,16698,16096],{},[1307,16700,1629],{},[1437,16702,1733],{},[1311,16704,1313],{},[1315,16706,16707],{"encoding":1317},"H_0:\\beta_i=0"," proti ",[1115,16710,16712],{"className":16711},[1292],[1294,16713,16714],{"xmlns":1296},[1298,16715,16716,16736],{},[1301,16717,16718,16724,16726,16732,16734],{},[1304,16719,16720,16722],{},[1307,16721,1309],{},[1311,16723,1544],{},[1437,16725,1709],{},[1304,16727,16728,16730],{},[1307,16729,16096],{},[1307,16731,1629],{},[1437,16733,10714],{"mathvariant":1872},[1311,16735,1313],{},[1315,16737,16738],{"encoding":1317},"H_1:\\beta_i\\neq0"," pro každý parametr — obě p-hodnoty jsou hluboko pod 0,05, oba parametry jsou tedy statisticky významné. ",[3223,16741,16742],{},"Multiple R-squared"," je index determinace ",[1115,16745,16747],{"className":16746},[1292],[1294,16748,16749],{"xmlns":1296},[1298,16750,16751,16764],{},[1301,16752,16753,16759,16761],{},[1330,16754,16755,16757],{},[1307,16756,9981],{},[1311,16758,1337],{},[1437,16760,1733],{},[1311,16762,16763],{},"0,9995",[1315,16765,16766],{"encoding":1317},"R^2=0{,}9995",": model vysvětluje 99,95 % rozptylu výdajů.",[1110,16769,16770],{},"Pro doplňkový přehled slouží přímé přístupové funkce:",[3447,16772,16774],{"className":3449,"code":16773,"language":71,"meta":1229,"style":1229},"coef(model)\nfitted(model)\nresiduals(model)\n",[3223,16775,16776,16787,16798],{"__ignoreMap":1229},[1115,16777,16778,16781,16783,16785],{"class":3455,"line":10},[1115,16779,16780],{"class":3466},"coef",[1115,16782,1626],{"class":3470},[1115,16784,786],{"class":3458},[1115,16786,3655],{"class":3470},[1115,16788,16789,16792,16794,16796],{"class":3455,"line":27},[1115,16790,16791],{"class":3466},"fitted",[1115,16793,1626],{"class":3470},[1115,16795,786],{"class":3458},[1115,16797,3655],{"class":3470},[1115,16799,16800,16803,16805,16807],{"class":3455,"line":148},[1115,16801,16802],{"class":3466},"residuals",[1115,16804,1626],{"class":3470},[1115,16806,786],{"class":3458},[1115,16808,3655],{"class":3470},[3447,16810,16813],{"className":16811,"code":16812,"language":3677,"meta":1229},[3675],"(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",[3223,16814,16812],{"__ignoreMap":1229},[1110,16816,16817,16820,16821,2704,16847,16850,16851,16873,16874,2704,16892,16895,16896,16933],{},[3223,16818,16819],{},"coef()"," vrací odhadnuté parametry ",[1115,16822,16824],{"className":16823},[1292],[1294,16825,16826],{"xmlns":1296},[1298,16827,16828,16844],{},[1301,16829,16830,16836,16838],{},[1304,16831,16832,16834],{},[1307,16833,11262],{},[1311,16835,1313],{},[1437,16837,1547],{"separator":1121},[1304,16839,16840,16842],{},[1307,16841,11262],{},[1311,16843,1544],{},[1315,16845,16846],{"encoding":1317},"b_0,b_1",[3223,16848,16849],{},"fitted()"," predikce ",[1115,16852,16854],{"className":16853},[1292],[1294,16855,16856],{"xmlns":1296},[1298,16857,16858,16870],{},[1301,16859,16860],{},[1304,16861,16862,16868],{},[2475,16863,16864,16866],{"accent":1121},[1307,16865,6886],{},[1437,16867,2481],{},[1307,16869,1629],{},[1315,16871,16872],{"encoding":1317},"\\hat y_i"," pro pozorované ",[1115,16875,16877],{"className":16876},[1292],[1294,16878,16879],{"xmlns":1296},[1298,16880,16881,16889],{},[1301,16882,16883],{},[1304,16884,16885,16887],{},[1307,16886,6476],{},[1307,16888,1629],{},[1315,16890,16891],{"encoding":1317},"x_i",[3223,16893,16894],{},"residuals()"," rezidua ",[1115,16897,16899],{"className":16898},[1292],[1294,16900,16901],{"xmlns":1296},[1298,16902,16903,16931],{},[1301,16904,16905,16911,16913,16919,16921],{},[1304,16906,16907,16909],{},[1307,16908,8350],{},[1307,16910,1629],{},[1437,16912,1733],{},[1304,16914,16915,16917],{},[1307,16916,6886],{},[1307,16918,1629],{},[1437,16920,2817],{},[1304,16922,16923,16929],{},[2475,16924,16925,16927],{"accent":1121},[1307,16926,6886],{},[1437,16928,2481],{},[1307,16930,1629],{},[1315,16932,16278],{"encoding":1317}," — stejná čísla, která na obrázku výše tvoří délky červených úseček.",[1110,16935,16936,16937,16950],{},"Intervaly spolehlivosti pro parametry a pro predikci v nových bodech ",[1115,16938,16940],{"className":16939},[1292],[1294,16941,16942],{"xmlns":1296},[1298,16943,16944,16948],{},[1301,16945,16946],{},[1307,16947,6476],{},[1315,16949,6476],{"encoding":1317}," (zde 7 a 8 členů domácnosti):",[3447,16952,16954],{"className":3449,"code":16953,"language":71,"meta":1229,"style":1229},"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",[3223,16955,16956,16976,17004,17043],{"__ignoreMap":1229},[1115,16957,16958,16961,16963,16965,16967,16970,16972,16974],{"class":3455,"line":10},[1115,16959,16960],{"class":3466},"confint",[1115,16962,1626],{"class":3470},[1115,16964,786],{"class":3458},[1115,16966,1547],{"class":3462},[1115,16968,16969],{"class":3458}," level",[1115,16971,3551],{"class":3462},[1115,16973,9757],{"class":3478},[1115,16975,3655],{"class":3470},[1115,16977,16978,16981,16983,16986,16988,16990,16992,16994,16996,16998,17000,17002],{"class":3455,"line":27},[1115,16979,16980],{"class":3458},"nove",[1115,16982,3463],{"class":3462},[1115,16984,16985],{"class":3466}," data.frame",[1115,16987,1626],{"class":3470},[1115,16989,16529],{"class":3458},[1115,16991,3551],{"class":3462},[1115,16993,3589],{"class":3466},[1115,16995,1626],{"class":3470},[1115,16997,13088],{"class":3478},[1115,16999,1547],{"class":3462},[1115,17001,15014],{"class":3478},[1115,17003,9251],{"class":3470},[1115,17005,17006,17009,17011,17013,17015,17018,17020,17023,17025,17028,17030,17033,17035,17037,17039,17041],{"class":3455,"line":148},[1115,17007,17008],{"class":3466},"predict",[1115,17010,1626],{"class":3470},[1115,17012,786],{"class":3458},[1115,17014,1547],{"class":3462},[1115,17016,17017],{"class":3458}," newdata",[1115,17019,3551],{"class":3462},[1115,17021,17022],{"class":3458}," nove",[1115,17024,1547],{"class":3462},[1115,17026,17027],{"class":3458}," interval",[1115,17029,3551],{"class":3462},[1115,17031,17032],{"class":3594}," \"confidence\"",[1115,17034,1547],{"class":3462},[1115,17036,16969],{"class":3458},[1115,17038,3551],{"class":3462},[1115,17040,9757],{"class":3478},[1115,17042,3655],{"class":3470},[1115,17044,17045,17047,17049,17051,17053,17055,17057,17059,17061,17063,17065,17068,17070,17072,17074,17076],{"class":3455,"line":111},[1115,17046,17008],{"class":3466},[1115,17048,1626],{"class":3470},[1115,17050,786],{"class":3458},[1115,17052,1547],{"class":3462},[1115,17054,17017],{"class":3458},[1115,17056,3551],{"class":3462},[1115,17058,17022],{"class":3458},[1115,17060,1547],{"class":3462},[1115,17062,17027],{"class":3458},[1115,17064,3551],{"class":3462},[1115,17066,17067],{"class":3594}," \"prediction\"",[1115,17069,1547],{"class":3462},[1115,17071,16969],{"class":3458},[1115,17073,3551],{"class":3462},[1115,17075,9757],{"class":3478},[1115,17077,3655],{"class":3470},[3447,17079,17082],{"className":17080,"code":17081,"language":3677,"meta":1229},[3675],"                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",[3223,17083,17081],{"__ignoreMap":1229},[1110,17085,17086,17089,17090,1402,17093,17106,17107,2704,17120,17123,17124,17127],{},[3223,17087,17088],{},"interval = \"confidence\""," dává interval spolehlivosti pro ",[1279,17091,17092],{},"střední hodnotu",[1115,17094,17096],{"className":17095},[1292],[1294,17097,17098],{"xmlns":1296},[1298,17099,17100,17104],{},[1301,17101,17102],{},[1307,17103,6886],{},[1315,17105,6886],{"encoding":1317}," při daném ",[1115,17108,17110],{"className":17109},[1292],[1294,17111,17112],{"xmlns":1296},[1298,17113,17114,17118],{},[1301,17115,17116],{},[1307,17117,6476],{},[1315,17119,6476],{"encoding":1317},[3223,17121,17122],{},"interval = \"prediction\""," širší interval pro ",[1279,17125,17126],{},"jednotlivé budoucí pozorování"," — ten musí zahrnout i rozptyl kolem regresní přímky, proto je vždy širší.",[16505,17129,17131],{"id":17130},"diagnostika-modelu","Diagnostika modelu",[1110,17133,17134,17135,2704,17138,5495,17141,17144],{},"Platnost závěrů z regresní přímky stojí na předpokladech o reziduích: ",[1279,17136,17137],{},"absenci autokorelace",[1279,17139,17140],{},"stálosti rozptylu (homoskedasticitě)",[1279,17142,17143],{},"normalitě",". V R se ověřují takto:",[3447,17146,17148],{"className":3449,"code":17147,"language":71,"meta":1229,"style":1229},"library(lmtest)\ndwtest(model)\n",[3223,17149,17150,17162],{"__ignoreMap":1229},[1115,17151,17152,17155,17157,17160],{"class":3455,"line":10},[1115,17153,17154],{"class":3462},"library",[1115,17156,1626],{"class":3470},[1115,17158,17159],{"class":3458},"lmtest",[1115,17161,3655],{"class":3470},[1115,17163,17164,17167,17169,17171],{"class":3455,"line":27},[1115,17165,17166],{"class":3466},"dwtest",[1115,17168,1626],{"class":3470},[1115,17170,786],{"class":3458},[1115,17172,3655],{"class":3470},[3447,17174,17177],{"className":17175,"code":17176,"language":3677,"meta":1229},[3675],"    Durbin-Watson test\n\ndata:  model\nDW = 3.4121, p-value = 0.9555\nalternative hypothesis: true autocorrelation is greater than 0\n",[3223,17178,17176],{"__ignoreMap":1229},[1110,17180,17181,17182,17199,17200,17217,17218,17235],{},"Durbinův–Watsonův test má ",[1115,17183,17185],{"className":17184},[1292],[1294,17186,17187],{"xmlns":1296},[1298,17188,17189,17197],{},[1301,17190,17191],{},[1304,17192,17193,17195],{},[1307,17194,1309],{},[1311,17196,1313],{},[1315,17198,1318],{"encoding":1317},": v modelu není problém s autokorelací, proti ",[1115,17201,17203],{"className":17202},[1292],[1294,17204,17205],{"xmlns":1296},[1298,17206,17207,17215],{},[1301,17208,17209],{},[1304,17210,17211,17213],{},[1307,17212,1309],{},[1311,17214,1544],{},[1315,17216,2749],{"encoding":1317},": 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, ",[1115,17219,17221],{"className":17220},[1292],[1294,17222,17223],{"xmlns":1296},[1298,17224,17225,17233],{},[1301,17226,17227],{},[1304,17228,17229,17231],{},[1307,17230,1309],{},[1311,17232,1313],{},[1315,17234,1318],{"encoding":1317}," se nezamítá.",[3447,17237,17239],{"className":3449,"code":17238,"language":71,"meta":1229,"style":1229},"library(whitestrap)\nwhite_test(model)\n",[3223,17240,17241,17252],{"__ignoreMap":1229},[1115,17242,17243,17245,17247,17250],{"class":3455,"line":10},[1115,17244,17154],{"class":3462},[1115,17246,1626],{"class":3470},[1115,17248,17249],{"class":3458},"whitestrap",[1115,17251,3655],{"class":3470},[1115,17253,17254,17257,17259,17261],{"class":3455,"line":27},[1115,17255,17256],{"class":3466},"white_test",[1115,17258,1626],{"class":3470},[1115,17260,786],{"class":3458},[1115,17262,3655],{"class":3470},[3447,17264,17267],{"className":17265,"code":17266,"language":3677,"meta":1229},[3675],"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",[3223,17268,17266],{"__ignoreMap":1229},[1110,17270,17271,17272,17289,17290,17307,17308,17235],{},"Whiteův test má ",[1115,17273,17275],{"className":17274},[1292],[1294,17276,17277],{"xmlns":1296},[1298,17278,17279,17287],{},[1301,17280,17281],{},[1304,17282,17283,17285],{},[1307,17284,1309],{},[1311,17286,1313],{},[1315,17288,1318],{"encoding":1317},": rozptyl reziduí je stálý (homoskedasticita), proti ",[1115,17291,17293],{"className":17292},[1292],[1294,17294,17295],{"xmlns":1296},[1298,17296,17297,17305],{},[1301,17298,17299],{},[1304,17300,17301,17303],{},[1307,17302,1309],{},[1311,17304,1544],{},[1315,17306,2749],{"encoding":1317},": rozptyl není stálý (heteroskedasticita). P-hodnota 0,21 je nad 0,05, ",[1115,17309,17311],{"className":17310},[1292],[1294,17312,17313],{"xmlns":1296},[1298,17314,17315,17323],{},[1301,17316,17317],{},[1304,17318,17319,17321],{},[1307,17320,1309],{},[1311,17322,1313],{},[1315,17324,1318],{"encoding":1317},[3447,17326,17328],{"className":3449,"code":17327,"language":71,"meta":1229,"style":1229},"shapiro.test(residuals(model))\n",[3223,17329,17330],{"__ignoreMap":1229},[1115,17331,17332,17335,17337,17339,17341,17343],{"class":3455,"line":10},[1115,17333,17334],{"class":3466},"shapiro.test",[1115,17336,1626],{"class":3470},[1115,17338,16802],{"class":3466},[1115,17340,1626],{"class":3470},[1115,17342,786],{"class":3458},[1115,17344,9251],{"class":3470},[3447,17346,17349],{"className":17347,"code":17348,"language":3677,"meta":1229},[3675],"    Shapiro-Wilk normality test\n\ndata:  residuals(model)\nW = 0.94818, p-value = 0.7255\n",[3223,17350,17348],{"__ignoreMap":1229},[1110,17352,17353,17354,17371],{},"Shapiro–Wilkův test má ",[1115,17355,17357],{"className":17356},[1292],[1294,17358,17359],{"xmlns":1296},[1298,17360,17361,17369],{},[1301,17362,17363],{},[1304,17364,17365,17367],{},[1307,17366,1309],{},[1311,17368,1313],{},[1315,17370,1318],{"encoding":1317},": rezidua pocházejí z normálního rozdělení. P-hodnota 0,73 opět nevede k zamítnutí — všechny tři předpoklady model splňuje.",[1110,17373,17374],{},[4137,17375],{"alt":17376,"className":17377,"src":17378},"mask-ra-diagnostika-rezidui",[1130,4141],"\u002Fwiki-assets\u002Fmask-ra-diagnostika-rezidui.png",[1110,17380,17381],{},"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.",[1103,17383,17385,17392,17423,17458,17523],{"className":17384,"dataCallout":3230},[1106,3229],[1110,17386,17388,17391],{"className":17387},[1113],[1115,17389],{"className":17390,"ariaHidden":1121},[1118,3237,1120],"Příklad: Regresní přímka",[1110,17393,17394,17395,17408,17409,17422],{},"V souboru s údaji o hodnotě produkce (v milionech Kč, proměnná ",[1115,17396,17398],{"className":17397},[1292],[1294,17399,17400],{"xmlns":1296},[1298,17401,17402,17406],{},[1301,17403,17404],{},[1307,17405,6886],{},[1315,17407,6886],{"encoding":1317},") a výši investic (ve stovkách tisíc Kč, proměnná ",[1115,17410,17412],{"className":17411},[1292],[1294,17413,17414],{"xmlns":1296},[1298,17415,17416,17420],{},[1301,17417,17418],{},[1307,17419,6476],{},[1315,17421,6476],{"encoding":1317},") 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.",[1110,17424,17425,17426,1417],{},"Výsledek: ",[1115,17427,17429],{"className":17428},[1292],[1294,17430,17431],{"xmlns":1296},[1298,17432,17433,17455],{},[1301,17434,17435,17441,17443,17446,17448,17451,17453],{},[2475,17436,17437,17439],{"accent":1121},[1307,17438,6886],{},[1437,17440,2481],{},[1437,17442,1733],{},[1311,17444,17445],{},"32,74",[1437,17447,5231],{},[1311,17449,17450],{},"2,15",[2661,17452,2663],{},[1307,17454,6476],{},[1315,17456,17457],{"encoding":1317},"\\hat y = 32{,}74 + 2{,}15\\,x",[1110,17459,16456,17460,17482,17483,17522],{},[1115,17461,17463],{"className":17462},[1292],[1294,17464,17465],{"xmlns":1296},[1298,17466,17467,17479],{},[1301,17468,17469,17475,17477],{},[1304,17470,17471,17473],{},[1307,17472,11262],{},[1311,17474,1544],{},[1437,17476,1733],{},[1311,17478,17450],{},[1315,17480,17481],{"encoding":1317},"b_1=2{,}15"," říká, že se zvýšením investic o 100 000 Kč vzroste produkce v průměru o ",[1115,17484,17486],{"className":17485},[1292],[1294,17487,17488],{"xmlns":1296},[1298,17489,17490,17519],{},[1301,17491,17492,17494,17496,17498,17500,17502,17504,17506,17508,17510,17512,17515,17517],{},[1311,17493,17450],{},[1437,17495,7868],{},[1311,17497,1544],{},[2661,17499,2663],{},[1311,17501,11080],{},[2661,17503,2663],{},[1311,17505,11080],{},[1437,17507,1733],{},[1311,17509,1337],{},[2661,17511,2663],{},[1311,17513,17514],{},"150",[2661,17516,2663],{},[1311,17518,11080],{},[1315,17520,17521],{"encoding":1317},"2{,}15\\cdot 1\\,000\\,000=2\\,150\\,000"," Kč.",[1110,17524,17525,17526,3742,17545,17593,17594,15852],{},"Dosazením libovolné hodnoty investic do empirické regresní funkce dostaneme predikci produkce, například pro třináctou firmu s investicemi ",[1115,17527,17529],{"className":17528},[1292],[1294,17530,17531],{"xmlns":1296},[1298,17532,17533,17542],{},[1301,17534,17535,17537,17539],{},[1307,17536,6476],{},[1437,17538,1733],{},[1311,17540,17541],{},"34",[1315,17543,17544],{"encoding":1317},"x=34",[1115,17546,17548],{"className":17547},[1292],[1294,17549,17550],{"xmlns":1296},[1298,17551,17552,17590],{},[1301,17553,17554,17564,17566,17572,17574,17580,17582,17584,17587],{},[1304,17555,17556,17562],{},[2475,17557,17558,17560],{"accent":1121},[1307,17559,6886],{},[1437,17561,2481],{},[1311,17563,3298],{},[1437,17565,1733],{},[1304,17567,17568,17570],{},[1307,17569,11262],{},[1311,17571,1313],{},[1437,17573,5231],{},[1304,17575,17576,17578],{},[1307,17577,11262],{},[1311,17579,1544],{},[1437,17581,7868],{},[1311,17583,17541],{},[1437,17585,17586],{},"≐",[1311,17588,17589],{},"105,81",[1315,17591,17592],{"encoding":1317},"\\hat y_{13} = b_0 + b_1\\cdot 34 \\doteq 105{,}81"," milionu Kč (se zaokrouhlenými koeficienty ",[1115,17595,17597],{"className":17596},[1292],[1294,17598,17599],{"xmlns":1296},[1298,17600,17601,17618],{},[1301,17602,17603,17605,17607,17609,17611,17613,17615],{},[1311,17604,17445],{},[1437,17606,5231],{},[1311,17608,17450],{},[1437,17610,7868],{},[1311,17612,17541],{},[1437,17614,17586],{},[1311,17616,17617],{},"105,8",[1315,17619,17620],{"encoding":1317},"32{,}74 + 2{,}15\\cdot 34 \\doteq 105{,}8",[1136,17622,17624],{"id":17623},"nelineární-a-vyšší-řády-regresních-funkcí","Nelineární a vyšší řády regresních funkcí",[1110,17626,17627,17628,17631,17632,17699,17700,17718,17719,17736],{},"Když přímka závislost nevystihuje, nabízí se další ",[1279,17629,17630],{},"lineární funkce"," — tedy funkce lineární ve svých parametrech, zapsatelné ve tvaru ",[1115,17633,17635],{"className":17634},[1292],[1294,17636,17637],{"xmlns":1296},[1298,17638,17639,17696],{},[1301,17640,17641,17643,17645,17651,17653,17659,17665,17667,17669,17671,17673,17676,17678,17684,17690,17692,17694],{},[1307,17642,16081],{},[1437,17644,1733],{},[1304,17646,17647,17649],{},[1307,17648,16096],{},[1311,17650,1313],{},[1437,17652,5231],{},[1304,17654,17655,17657],{},[1307,17656,16096],{},[1311,17658,1544],{},[1304,17660,17661,17663],{},[1307,17662,6527],{},[1311,17664,1544],{},[1437,17666,1626],{"stretchy":1625},[1307,17668,6476],{},[1437,17670,1637],{"stretchy":1625},[1437,17672,5231],{},[1437,17674,17675],{},"⋯",[1437,17677,5231],{},[1304,17679,17680,17682],{},[1307,17681,16096],{},[1307,17683,1110],{},[1304,17685,17686,17688],{},[1307,17687,6527],{},[1307,17689,1110],{},[1437,17691,1626],{"stretchy":1625},[1307,17693,6476],{},[1437,17695,1637],{"stretchy":1625},[1315,17697,17698],{"encoding":1317},"\\eta=\\beta_0+\\beta_1 f_1(x)+\\dots+\\beta_p f_p(x)"," se známými funkcemi ",[1115,17701,17703],{"className":17702},[1292],[1294,17704,17705],{"xmlns":1296},[1298,17706,17707,17715],{},[1301,17708,17709],{},[1304,17710,17711,17713],{},[1307,17712,6527],{},[1307,17714,1629],{},[1315,17716,17717],{"encoding":1317},"f_i"," a neznámými parametry ",[1115,17720,17722],{"className":17721},[1292],[1294,17723,17724],{"xmlns":1296},[1298,17725,17726,17734],{},[1301,17727,17728],{},[1304,17729,17730,17732],{},[1307,17731,16096],{},[1307,17733,1629],{},[1315,17735,16142],{"encoding":1317},". I tyto parametry se odhadují metodou nejmenších čtverců, stejně jako u přímky:",[1115,17738,17740],{"className":17739},[1292],[1294,17741,17742],{"xmlns":1296,"display":1715},[1298,17743,17744,18054],{},[17745,17746,17749,17822,17935,17994],"mtable",{"rowspacing":17747,"columnalign":17748,"columnspacing":6515},"0.25em","right left",[17750,17751,17752,17776],"mtr",{},[17753,17754,17755],"mtd",{},[2994,17756,17757],{"scriptlevel":1313,"displaystyle":1121},[1301,17758,17759,17773],{},[1301,17760,17761,17764,17770],{},[2661,17762,17763],{},"parabolick",[2475,17765,17766,17768],{"accent":1121},[2661,17767,1127],{},[1437,17769,11259],{},[2661,17771,17772],{}," regrese: ",[1763,17774],{"width":17775},"1em",[17753,17777,17778],{},[2994,17779,17780],{"scriptlevel":1313,"displaystyle":1121},[1301,17781,17782,17784,17790,17792,17798,17800,17806,17808,17810,17816],{},[1301,17783],{},[2475,17785,17786,17788],{"accent":1121},[1307,17787,6886],{},[1437,17789,2481],{},[1437,17791,1733],{},[1304,17793,17794,17796],{},[1307,17795,11262],{},[1311,17797,1313],{},[1437,17799,5231],{},[1304,17801,17802,17804],{},[1307,17803,11262],{},[1311,17805,1544],{},[1307,17807,6476],{},[1437,17809,5231],{},[1304,17811,17812,17814],{},[1307,17813,11262],{},[1311,17815,1337],{},[1330,17817,17818,17820],{},[1307,17819,6476],{},[1311,17821,1337],{},[17750,17823,17824,17871],{},[17753,17825,17826],{},[2994,17827,17828],{"scriptlevel":1313,"displaystyle":1121},[1301,17829,17830,17869],{},[1301,17831,17832,17835,17841,17844,17848,17851,17857,17860,17866],{},[2661,17833,17834],{},"polynomick",[2475,17836,17837,17839],{"accent":1121},[2661,17838,1127],{},[1437,17840,11259],{},[2661,17842,17843],{}," regrese ",[2994,17845,17846],{"scriptlevel":1313,"displaystyle":1625},[1307,17847,1110],{},[2661,17849,17850],{},"-t",[2475,17852,17853,17855],{"accent":1121},[2661,17854,8350],{},[1437,17856,11259],{},[2661,17858,17859],{},"ho stupn",[2475,17861,17862,17864],{"accent":1121},[2661,17863,8350],{},[1437,17865,11269],{},[2661,17867,17868],{},": ",[1763,17870],{"width":17775},[17753,17872,17873],{},[2994,17874,17875],{"scriptlevel":1313,"displaystyle":1121},[1301,17876,17877,17879,17885,17887,17893,17895,17901,17903,17905,17911,17917,17919,17921,17923,17929],{},[1301,17878],{},[2475,17880,17881,17883],{"accent":1121},[1307,17882,6886],{},[1437,17884,2481],{},[1437,17886,1733],{},[1304,17888,17889,17891],{},[1307,17890,11262],{},[1311,17892,1313],{},[1437,17894,5231],{},[1304,17896,17897,17899],{},[1307,17898,11262],{},[1311,17900,1544],{},[1307,17902,6476],{},[1437,17904,5231],{},[1304,17906,17907,17909],{},[1307,17908,11262],{},[1311,17910,1337],{},[1330,17912,17913,17915],{},[1307,17914,6476],{},[1311,17916,1337],{},[1437,17918,5231],{},[1437,17920,17675],{},[1437,17922,5231],{},[1304,17924,17925,17927],{},[1307,17926,11262],{},[1307,17928,1110],{},[1330,17930,17931,17933],{},[1307,17932,6476],{},[1307,17934,1110],{},[17750,17936,17937,17958],{},[17753,17938,17939],{},[2994,17940,17941],{"scriptlevel":1313,"displaystyle":1121},[1301,17942,17943,17956],{},[1301,17944,17945,17948,17954],{},[2661,17946,17947],{},"hyperbolick",[2475,17949,17950,17952],{"accent":1121},[2661,17951,1127],{},[1437,17953,11259],{},[2661,17955,17772],{},[1763,17957],{"width":17775},[17753,17959,17960],{},[2994,17961,17962],{"scriptlevel":1313,"displaystyle":1121},[1301,17963,17964,17966,17972,17974,17980,17982,17988],{},[1301,17965],{},[2475,17967,17968,17970],{"accent":1121},[1307,17969,6886],{},[1437,17971,2481],{},[1437,17973,1733],{},[1304,17975,17976,17978],{},[1307,17977,11262],{},[1311,17979,1313],{},[1437,17981,5231],{},[1304,17983,17984,17986],{},[1307,17985,11262],{},[1311,17987,1544],{},[2491,17989,17990,17992],{},[1311,17991,1544],{},[1307,17993,6476],{},[17750,17995,17996,18017],{},[17753,17997,17998],{},[2994,17999,18000],{"scriptlevel":1313,"displaystyle":1121},[1301,18001,18002,18015],{},[1301,18003,18004,18007,18013],{},[2661,18005,18006],{},"logaritmick",[2475,18008,18009,18011],{"accent":1121},[2661,18010,1127],{},[1437,18012,11259],{},[2661,18014,17772],{},[1763,18016],{"width":17775},[17753,18018,18019],{},[2994,18020,18021],{"scriptlevel":1313,"displaystyle":1121},[1301,18022,18023,18025,18031,18033,18039,18041,18047,18050,18052],{},[1301,18024],{},[2475,18026,18027,18029],{"accent":1121},[1307,18028,6886],{},[1437,18030,2481],{},[1437,18032,1733],{},[1304,18034,18035,18037],{},[1307,18036,11262],{},[1311,18038,1313],{},[1437,18040,5231],{},[1304,18042,18043,18045],{},[1307,18044,11262],{},[1311,18046,1544],{},[1307,18048,18049],{},"ln",[1437,18051,4245],{},[1307,18053,6476],{},[1315,18055,18056],{"encoding":1317},"\\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}",[1110,18058,18059,18060,18063,18064,18110,18111,1709],{},"Naproti tomu ",[1279,18061,18062],{},"nelineární funkce"," nelze do tvaru ",[1115,18065,18067],{"className":18066},[1292],[1294,18068,18069],{"xmlns":1296},[1298,18070,18071,18107],{},[1301,18072,18073,18075,18077,18083,18085,18091,18097,18099,18101,18103,18105],{},[1307,18074,16081],{},[1437,18076,1733],{},[1304,18078,18079,18081],{},[1307,18080,16096],{},[1311,18082,1313],{},[1437,18084,5231],{},[1304,18086,18087,18089],{},[1307,18088,16096],{},[1311,18090,1544],{},[1304,18092,18093,18095],{},[1307,18094,6527],{},[1311,18096,1544],{},[1437,18098,1626],{"stretchy":1625},[1307,18100,6476],{},[1437,18102,1637],{"stretchy":1625},[1437,18104,5231],{},[1437,18106,1550],{},[1315,18108,18109],{"encoding":1317},"\\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 ",[1279,18112,18113],{},"exponenciální regrese",[1115,18115,18117],{"className":18116},[1292],[1294,18118,18119],{"xmlns":1296,"display":1715},[1298,18120,18121,18153],{},[1301,18122,18123,18129,18131,18137,18139,18151],{},[2475,18124,18125,18127],{"accent":1121},[1307,18126,6886],{},[1437,18128,2481],{},[1437,18130,1733],{},[1304,18132,18133,18135],{},[1307,18134,11262],{},[1311,18136,1313],{},[1437,18138,7868],{},[3106,18140,18141,18143,18145],{},[1307,18142,11262],{},[1311,18144,1544],{},[1301,18146,18147,18149],{},[2661,18148,2663],{},[1307,18150,6476],{},[1307,18152,1417],{"mathvariant":1872},[1315,18154,18155],{"encoding":1317},"\\hat y = b_0 \\cdot b_1^{\\,x}.",[1110,18157,18158],{},[4137,18159],{"alt":18160,"className":18161,"src":18162},"mask-ra-nelinearni-krivky",[1130,4141],"\u002Fwiki-assets\u002Fmask-ra-nelinearni-krivky.png",[16505,18164,18166],{"id":18165},"v-r-parabolická-regrese","V R — parabolická regrese",[1110,18168,18169,18170,1709],{},"Na ročních ziscích firmy (šest let) se parabolická regrese odhadne přidáním kvadratického členu ",[3223,18171,18172],{},"I(x^2)",[3447,18174,18176],{"className":3449,"code":18175,"language":71,"meta":1229,"style":1229},"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",[3223,18177,18178,18213,18253,18287],{"__ignoreMap":1229},[1115,18179,18180,18183,18185,18187,18189,18191,18193,18195,18197,18199,18201,18203,18205,18207,18209,18211],{"class":3455,"line":10},[1115,18181,18182],{"class":3458},"rok",[1115,18184,3463],{"class":3462},[1115,18186,3589],{"class":3466},[1115,18188,1626],{"class":3470},[1115,18190,1544],{"class":3478},[1115,18192,1547],{"class":3462},[1115,18194,3934],{"class":3478},[1115,18196,1547],{"class":3462},[1115,18198,10613],{"class":3478},[1115,18200,1547],{"class":3462},[1115,18202,3554],{"class":3478},[1115,18204,1547],{"class":3462},[1115,18206,9752],{"class":3478},[1115,18208,1547],{"class":3462},[1115,18210,11986],{"class":3478},[1115,18212,3655],{"class":3470},[1115,18214,18215,18217,18219,18221,18223,18226,18228,18231,18233,18236,18238,18241,18243,18246,18248,18251],{"class":3455,"line":27},[1115,18216,1088],{"class":3458},[1115,18218,3463],{"class":3462},[1115,18220,3589],{"class":3466},[1115,18222,1626],{"class":3470},[1115,18224,18225],{"class":3478},"112",[1115,18227,1547],{"class":3462},[1115,18229,18230],{"class":3478}," 149",[1115,18232,1547],{"class":3462},[1115,18234,18235],{"class":3478}," 238",[1115,18237,1547],{"class":3462},[1115,18239,18240],{"class":3478}," 354",[1115,18242,1547],{"class":3462},[1115,18244,18245],{"class":3478}," 580",[1115,18247,1547],{"class":3462},[1115,18249,18250],{"class":3478}," 867",[1115,18252,3655],{"class":3470},[1115,18254,18255,18258,18260,18262,18264,18266,18268,18271,18274,18277,18279,18281,18283,18285],{"class":3455,"line":148},[1115,18256,18257],{"class":3458},"model_parabola",[1115,18259,3463],{"class":3462},[1115,18261,16609],{"class":3466},[1115,18263,1626],{"class":3470},[1115,18265,1088],{"class":3458},[1115,18267,16616],{"class":3462},[1115,18269,18270],{"class":3458}," rok",[1115,18272,18273],{"class":3462}," +",[1115,18275,18276],{"class":3466}," I",[1115,18278,1626],{"class":3470},[1115,18280,18182],{"class":3458},[1115,18282,2481],{"class":3462},[1115,18284,1337],{"class":3478},[1115,18286,9251],{"class":3470},[1115,18288,18289,18291,18293,18295],{"class":3455,"line":111},[1115,18290,1249],{"class":3466},[1115,18292,1626],{"class":3470},[1115,18294,18257],{"class":3458},[1115,18296,3655],{"class":3470},[3447,18298,18301],{"className":18299,"code":18300,"language":3677,"meta":1229},[3675],"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",[3223,18302,18300],{"__ignoreMap":1229},[1110,18304,18305,18306,18351],{},"Odhadnutá parabola ",[1115,18307,18309],{"className":18308},[1292],[1294,18310,18311],{"xmlns":1296},[1298,18312,18313,18348],{},[1301,18314,18315,18321,18323,18326,18328,18331,18333,18335,18337,18340,18342],{},[2475,18316,18317,18319],{"accent":1121},[1307,18318,6886],{},[1437,18320,2481],{},[1437,18322,1733],{},[1311,18324,18325],{},"164,6",[1437,18327,2817],{},[1311,18329,18330],{},"76,6",[2661,18332,2663],{},[1307,18334,6476],{},[1437,18336,5231],{},[1311,18338,18339],{},"32,1",[2661,18341,2663],{},[1330,18343,18344,18346],{},[1307,18345,6476],{},[1311,18347,1337],{},[1315,18349,18350],{"encoding":1317},"\\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.",[16505,18353,18355],{"id":18354},"v-r-exponenciální-regrese","V R — exponenciální regrese",[1110,18357,18358,18359,18361],{},"Nelineární funkce se v R odhadují funkcí ",[3223,18360,15867],{}," ze stejnojmenného balíčku. Bez zadaných počátečních hodnot R upozorní, že parametry nastavil na 1, a odhad dopočítá iteračně:",[3447,18363,18365],{"className":3449,"code":18364,"language":71,"meta":1229,"style":1229},"library(nls2)\nmodel_exp \u003C- nls2(zisk ~ b1 * exp(b2 * rok))\nsummary(model_exp)\n",[3223,18366,18367,18377,18413],{"__ignoreMap":1229},[1115,18368,18369,18371,18373,18375],{"class":3455,"line":10},[1115,18370,17154],{"class":3462},[1115,18372,1626],{"class":3470},[1115,18374,15851],{"class":3458},[1115,18376,3655],{"class":3470},[1115,18378,18379,18382,18384,18387,18389,18391,18393,18396,18399,18402,18404,18407,18409,18411],{"class":3455,"line":27},[1115,18380,18381],{"class":3458},"model_exp",[1115,18383,3463],{"class":3462},[1115,18385,18386],{"class":3466}," nls2",[1115,18388,1626],{"class":3470},[1115,18390,1088],{"class":3458},[1115,18392,16616],{"class":3462},[1115,18394,18395],{"class":3458}," b1",[1115,18397,18398],{"class":3462}," *",[1115,18400,18401],{"class":3466}," exp",[1115,18403,1626],{"class":3470},[1115,18405,18406],{"class":3458},"b2",[1115,18408,18398],{"class":3462},[1115,18410,18270],{"class":3458},[1115,18412,9251],{"class":3470},[1115,18414,18415,18417,18419,18421],{"class":3455,"line":148},[1115,18416,1249],{"class":3466},[1115,18418,1626],{"class":3470},[1115,18420,18381],{"class":3458},[1115,18422,3655],{"class":3470},[3447,18424,18427],{"className":18425,"code":18426,"language":3677,"meta":1229},[3675],"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",[3223,18428,18426],{"__ignoreMap":1229},[1110,18430,18431,18432,1709],{},"Stejnou křivku lze zapsat i v mocninném tvaru ",[1115,18433,18435],{"className":18434},[1292],[1294,18436,18437],{"xmlns":1296},[1298,18438,18439,18465],{},[1301,18440,18441,18447,18449,18455,18457],{},[2475,18442,18443,18445],{"accent":1121},[1307,18444,6886],{},[1437,18446,2481],{},[1437,18448,1733],{},[1304,18450,18451,18453],{},[1307,18452,11262],{},[1311,18454,1544],{},[1437,18456,7868],{},[3106,18458,18459,18461,18463],{},[1307,18460,11262],{},[1311,18462,1337],{},[1307,18464,6476],{},[1315,18466,18467],{"encoding":1317},"\\hat y=b_1\\cdot b_2^{x}",[3447,18469,18471],{"className":3449,"code":18470,"language":71,"meta":1229,"style":1229},"model_pow \u003C- nls2(zisk ~ b1 * (b2^rok))\nsummary(model_pow)\n",[3223,18472,18473,18502],{"__ignoreMap":1229},[1115,18474,18475,18478,18480,18482,18484,18486,18488,18490,18492,18494,18496,18498,18500],{"class":3455,"line":10},[1115,18476,18477],{"class":3458},"model_pow",[1115,18479,3463],{"class":3462},[1115,18481,18386],{"class":3466},[1115,18483,1626],{"class":3470},[1115,18485,1088],{"class":3458},[1115,18487,16616],{"class":3462},[1115,18489,18395],{"class":3458},[1115,18491,18398],{"class":3462},[1115,18493,4361],{"class":3470},[1115,18495,18406],{"class":3458},[1115,18497,2481],{"class":3462},[1115,18499,18182],{"class":3458},[1115,18501,9251],{"class":3470},[1115,18503,18504,18506,18508,18510],{"class":3455,"line":27},[1115,18505,1249],{"class":3466},[1115,18507,1626],{"class":3470},[1115,18509,18477],{"class":3458},[1115,18511,3655],{"class":3470},[3447,18513,18516],{"className":18514,"code":18515,"language":3677,"meta":1229},[3675],"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",[3223,18517,18515],{"__ignoreMap":1229},[1110,18519,18520,18521,18585,18586,18610],{},"Obě varianty popisují stejnou křivku (",[1115,18522,18524],{"className":18523},[1292],[1294,18525,18526],{"xmlns":1296},[1298,18527,18528,18582],{},[1301,18529,18530,18547,18549],{},[3106,18531,18532,18534,18536],{},[1307,18533,11262],{},[1311,18535,1337],{},[1301,18537,18538,18541],{},[2661,18539,18540],{},"mocninn",[2475,18542,18543,18545],{"accent":1121},[2661,18544,6886],{},[1437,18546,11259],{},[1437,18548,1733],{},[1330,18550,18551,18553],{},[1307,18552,8350],{},[1301,18554,18555,18557],{},[2661,18556,2663],{},[3106,18558,18559,18561,18563],{},[1307,18560,11262],{},[1311,18562,1337],{},[1301,18564,18565,18568,18574,18576],{},[2661,18566,18567],{},"exponenci",[2475,18569,18570,18572],{"accent":1121},[2661,18571,1127],{},[1437,18573,11259],{},[2661,18575,18049],{},[2475,18577,18578,18580],{"accent":1121},[2661,18579,11509],{},[1437,18581,11259],{},[1315,18583,18584],{"encoding":1317},"b_2^{\\text{mocninný}} = e^{\\,b_2^{\\text{exponenciální}}}",", zde ",[1115,18587,18589],{"className":18588},[1292],[1294,18590,18591],{"xmlns":1296},[1298,18592,18593,18607],{},[1301,18594,18595,18602,18604],{},[1330,18596,18597,18599],{},[1307,18598,8350],{},[1311,18600,18601],{},"0,4316",[1437,18603,9198],{},[1311,18605,18606],{},"1,540",[1315,18608,18609],{"encoding":1317},"e^{0{,}4316}\\approx 1{,}540",") a mají totožnou reziduální chybu — je to jen otázka parametrizace.",[16505,18612,18614],{"id":18613},"v-r-hyperbolická-regrese","V R — hyperbolická regrese",[1110,18616,18617,18618,1709],{},"Hyperbolická regrese se odhadne jako obyčejná lineární regrese na transformované proměnné ",[3223,18619,18620],{},"I(1\u002Fx)",[3447,18622,18624],{"className":3449,"code":18623,"language":71,"meta":1229,"style":1229},"model_hyperbola \u003C- lm(tydenni_vydaje ~ I(1 \u002F pocet_clenu))\nsummary(model_hyperbola)\n",[3223,18625,18626,18653],{"__ignoreMap":1229},[1115,18627,18628,18631,18633,18635,18637,18639,18641,18643,18645,18647,18649,18651],{"class":3455,"line":10},[1115,18629,18630],{"class":3458},"model_hyperbola",[1115,18632,3463],{"class":3462},[1115,18634,16609],{"class":3466},[1115,18636,1626],{"class":3470},[1115,18638,16564],{"class":3458},[1115,18640,16616],{"class":3462},[1115,18642,18276],{"class":3466},[1115,18644,1626],{"class":3470},[1115,18646,1544],{"class":3478},[1115,18648,9833],{"class":3462},[1115,18650,16619],{"class":3458},[1115,18652,9251],{"class":3470},[1115,18654,18655,18657,18659,18661],{"class":3455,"line":27},[1115,18656,1249],{"class":3466},[1115,18658,1626],{"class":3470},[1115,18660,18630],{"class":3458},[1115,18662,3655],{"class":3470},[3447,18664,18667],{"className":18665,"code":18666,"language":3677,"meta":1229},[3675],"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",[3223,18668,18666],{"__ignoreMap":1229},[1110,18670,18671,18672,18706,18707,18728],{},"Model ",[1115,18673,18675],{"className":18674},[1292],[1294,18676,18677],{"xmlns":1296},[1298,18678,18679,18703],{},[1301,18680,18681,18687,18689,18692,18694],{},[2475,18682,18683,18685],{"accent":1121},[1307,18684,6886],{},[1437,18686,2481],{},[1437,18688,1733],{},[1311,18690,18691],{},"2180,7",[1437,18693,2817],{},[2994,18695,18696],{"scriptlevel":1313,"displaystyle":1121},[2491,18697,18698,18701],{},[1311,18699,18700],{},"1920,0",[1307,18702,6476],{},[1315,18704,18705],{"encoding":1317},"\\hat y = 2180{,}7 - \\dfrac{1920{,}0}{x}"," vysvětluje jen 76,3 % rozptylu — u těchto dat je hyperbola podstatně horší volbou než přímka (",[1115,18708,18710],{"className":18709},[1292],[1294,18711,18712],{"xmlns":1296},[1298,18713,18714,18726],{},[1301,18715,18716,18722,18724],{},[1330,18717,18718,18720],{},[1307,18719,9981],{},[1311,18721,1337],{},[1437,18723,1733],{},[1311,18725,16763],{},[1315,18727,16766],{"encoding":1317},"). Právě k takovému porovnání slouží index determinace: nízká hodnota signalizuje, že zvolený typ funkce k datům nesedí.",[1103,18730,18732,18739,18770,18818],{"className":18731,"dataCallout":3230},[1106,3229],[1110,18733,18735,18738],{"className":18734},[1113],[1115,18736],{"className":18737,"ariaHidden":1121},[1118,3237,1120],"Příklad: Parabolická regrese",[1110,18740,18741,18742,18755,18756,18769],{},"Prodejna počítačových her nechala prodavače absolvovat kurz prodejních dovedností. Při dvaceti měřeních sledovala, kolik zákazníků navštíví prodejnu během prodejní doby (proměnná ",[1115,18743,18745],{"className":18744},[1292],[1294,18746,18747],{"xmlns":1296},[1298,18748,18749,18753],{},[1301,18750,18751],{},[1307,18752,6476],{},[1315,18754,6476],{"encoding":1317},") a jaká je toho dne tržba v tisících Kč (proměnná ",[1115,18757,18759],{"className":18758},[1292],[1294,18760,18761],{"xmlns":1296},[1298,18762,18763,18767],{},[1301,18764,18765],{},[1307,18766,6886],{},[1315,18768,6886],{"encoding":1317},"). Zároveň chtěla zjistit, zda při rostoucím počtu zákazníků stačí stávající počet prodavačů.",[1110,18771,17425,18772,1417],{},[1115,18773,18775],{"className":18774},[1292],[1294,18776,18777],{"xmlns":1296},[1298,18778,18779,18815],{},[1301,18780,18781,18787,18789,18791,18794,18796,18799,18801,18803,18805,18807,18809],{},[2475,18782,18783,18785],{"accent":1121},[1307,18784,6886],{},[1437,18786,2481],{},[1437,18788,1733],{},[1437,18790,2817],{},[1311,18792,18793],{},"60,3",[1437,18795,5231],{},[1311,18797,18798],{},"4,55",[2661,18800,2663],{},[1307,18802,6476],{},[1437,18804,2817],{},[1311,18806,3738],{},[2661,18808,2663],{},[1330,18810,18811,18813],{},[1307,18812,6476],{},[1311,18814,1337],{},[1315,18816,18817],{"encoding":1317},"\\hat y = -60{,}3 + 4{,}55\\,x - 0{,}05\\,x^2",[1110,18819,18820,18821,18839],{},"Záporný koeficient ",[1115,18822,18824],{"className":18823},[1292],[1294,18825,18826],{"xmlns":1296},[1298,18827,18828,18836],{},[1301,18829,18830],{},[1304,18831,18832,18834],{},[1307,18833,11262],{},[1311,18835,1337],{},[1315,18837,18838],{"encoding":1317},"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.",[1103,18841,18843,18850,18880,18925],{"className":18842,"dataCallout":3230},[1106,3229],[1110,18844,18846,18849],{"className":18845},[1113],[1115,18847],{"className":18848,"ariaHidden":1121},[1118,3237,1120],"Příklad: Hyperbolická regrese",[1110,18851,18852,18853,18866,18867,15852],{},"V podniku se podle interního účetnictví sledovala závislost vlastních nákladů na jednotku produkce v Kč (proměnná ",[1115,18854,18856],{"className":18855},[1292],[1294,18857,18858],{"xmlns":1296},[1298,18859,18860,18864],{},[1301,18861,18862],{},[1307,18863,6886],{},[1315,18865,6886],{"encoding":1317},") na objemu produkce v tisících kusů (proměnná ",[1115,18868,18870],{"className":18869},[1292],[1294,18871,18872],{"xmlns":1296},[1298,18873,18874,18878],{},[1301,18875,18876],{},[1307,18877,6476],{},[1315,18879,6476],{"encoding":1317},[1110,18881,17425,18882,1417],{},[1115,18883,18885],{"className":18884},[1292],[1294,18886,18887],{"xmlns":1296},[1298,18888,18889,18922],{},[1301,18890,18891,18897,18899,18901,18904,18906],{},[2475,18892,18893,18895],{"accent":1121},[1307,18894,6886],{},[1437,18896,2481],{},[1437,18898,1733],{},[1437,18900,2817],{},[1311,18902,18903],{},"96,78",[1437,18905,5231],{},[2994,18907,18908],{"scriptlevel":1313,"displaystyle":1121},[2491,18909,18910,18920],{},[1301,18911,18912,18915,18917],{},[1311,18913,18914],{},"250",[2661,18916,2663],{},[1311,18918,18919],{},"528,88",[1307,18921,6476],{},[1315,18923,18924],{"encoding":1317},"\\hat y = -96{,}78 + \\dfrac{250\\,528{,}88}{x}",[1110,18926,18927,18928,18945],{},"Záporná hodnota ",[1115,18929,18931],{"className":18930},[1292],[1294,18932,18933],{"xmlns":1296},[1298,18934,18935,18943],{},[1301,18936,18937],{},[1304,18938,18939,18941],{},[1307,18940,11262],{},[1311,18942,1544],{},[1315,18944,16474],{"encoding":1317}," v čitateli ukazuje klesající náklady na jednotku s rostoucím objemem produkce — typický projev úspor z rozsahu, který hyperbola dobře zachycuje.",[1136,18947,18949],{"id":18948},"kvalita-regresní-funkce-a-korelační-analýza","Kvalita regresní funkce a korelační analýza",[1110,18951,18952,18953,1709],{},"Kvalitu odhadnuté regresní funkce vyjadřuje ",[1279,18954,15765],{},[1115,18956,18958],{"className":18957},[1292],[1294,18959,18960],{"xmlns":1296,"display":1715},[1298,18961,18962,19030],{},[1301,18963,18964,18970,18972,18994,18996,18998,19000,19028],{},[1330,18965,18966,18968],{},[1307,18967,9981],{},[1311,18969,1337],{},[1437,18971,1733],{},[2491,18973,18974,18986],{},[3106,18975,18976,18978,18984],{},[1307,18977,1605],{},[2475,18979,18980,18982],{"accent":1121},[1307,18981,6886],{},[1437,18983,2481],{},[1311,18985,1337],{},[3106,18987,18988,18990,18992],{},[1307,18989,1605],{},[1307,18991,6886],{},[1311,18993,1337],{},[1437,18995,1733],{},[1311,18997,1544],{},[1437,18999,2817],{},[2491,19001,19002,19020],{},[3106,19003,19004,19006,19018],{},[1307,19005,1605],{},[1301,19007,19008,19010,19012],{},[1307,19009,6886],{},[1437,19011,2817],{},[2475,19013,19014,19016],{"accent":1121},[1307,19015,6886],{},[1437,19017,2481],{},[1311,19019,1337],{},[3106,19021,19022,19024,19026],{},[1307,19023,1605],{},[1307,19025,6886],{},[1311,19027,1337],{},[1307,19029,1417],{"mathvariant":1872},[1315,19031,19032],{"encoding":1317},"R^2 = \\frac{s^2_{\\hat y}}{s^2_y} = 1 - \\frac{s^2_{y-\\hat y}}{s^2_y}.",[1110,19034,19035,19036,19053,19054,19067],{},"Čím blíž je ",[1115,19037,19039],{"className":19038},[1292],[1294,19040,19041],{"xmlns":1296},[1298,19042,19043,19051],{},[1301,19044,19045],{},[1330,19046,19047,19049],{},[1307,19048,9981],{},[1311,19050,1337],{},[1315,19052,15783],{"encoding":1317}," k 1, tím silnější je závislost; v procentech udává, jakou část rozptylu závisle proměnné ",[1115,19055,19057],{"className":19056},[1292],[1294,19058,19059],{"xmlns":1296},[1298,19060,19061,19065],{},[1301,19062,19063],{},[1307,19064,6886],{},[1315,19066,6886],{"encoding":1317}," se podařilo vysvětlit zvolenou regresní funkcí. Nízký index determinace může signalizovat špatně zvolený typ regresní funkce, ne nutně absenci závislosti.",[1110,19069,19070,19071,1402,19073,19096,19097,1709],{},"Obecnou mírou těsnosti závislosti — platnou pro libovolný typ regresní funkce — je ",[1279,19072,15787],{},[1115,19074,19076],{"className":19075},[1292],[1294,19077,19078],{"xmlns":1296},[1298,19079,19080,19094],{},[1301,19081,19082,19084,19086],{},[1307,19083,10958],{},[1437,19085,1733],{},[4207,19087,19088],{},[1330,19089,19090,19092],{},[1307,19091,9981],{},[1311,19093,1337],{},[1315,19095,15811],{"encoding":1317},". Je-li zvolenou funkcí regresní přímka, index korelace je roven (až na znaménko) ",[1279,19098,15815],{},[1115,19100,19102],{"className":19101},[1292],[1294,19103,19104],{"xmlns":1296,"display":1715},[1298,19105,19106,19156],{},[1301,19107,19108,19118,19120,19154],{},[1304,19109,19110,19112],{},[1307,19111,71],{},[1301,19113,19114,19116],{},[1307,19115,6476],{},[1307,19117,6886],{},[1437,19119,1733],{},[2491,19121,19122,19132],{},[1304,19123,19124,19126],{},[1307,19125,1605],{},[1301,19127,19128,19130],{},[1307,19129,6476],{},[1307,19131,6886],{},[4207,19133,19134],{},[1301,19135,19136,19144,19146],{},[3106,19137,19138,19140,19142],{},[1307,19139,1605],{},[1307,19141,6476],{},[1311,19143,1337],{},[1437,19145,7868],{},[3106,19147,19148,19150,19152],{},[1307,19149,1605],{},[1307,19151,6886],{},[1311,19153,1337],{},[1307,19155,1417],{"mathvariant":1872},[1315,19157,19158],{"encoding":1317},"r_{xy} = \\frac{s_{xy}}{\\sqrt{s^2_x\\cdot s^2_y}}.",[1110,19160,19161,19162,19178,19179,19195],{},"Koeficient korelace nabývá hodnot od ",[1115,19163,19165],{"className":19164},[1292],[1294,19166,19167],{"xmlns":1296},[1298,19168,19169,19175],{},[1301,19170,19171,19173],{},[1437,19172,2817],{},[1311,19174,1544],{},[1315,19176,19177],{"encoding":1317},"-1"," do ",[1115,19180,19182],{"className":19181},[1292],[1294,19183,19184],{"xmlns":1296},[1298,19185,19186,19192],{},[1301,19187,19188,19190],{},[1437,19189,5231],{},[1311,19191,1544],{},[1315,19193,19194],{"encoding":1317},"+1",": znaménko určuje typ závislosti (pozitivní, nebo negativní), absolutní hodnota její sílu — čím blíž k 0, tím je závislost slabší.",[1110,19197,19198],{},[4137,19199],{"alt":19200,"className":19201,"src":19202},"mask-ra-korelace-sila",[1130,4141],"\u002Fwiki-assets\u002Fmask-ra-korelace-sila.png",[1110,19204,19205,19206,19219,19220,19238,19239,5495,19252,19265],{},"S rostoucí absolutní hodnotou ",[1115,19207,19209],{"className":19208},[1292],[1294,19210,19211],{"xmlns":1296},[1298,19212,19213,19217],{},[1301,19214,19215],{},[1307,19216,71],{},[1315,19218,71],{"encoding":1317}," se body v rozptylovém grafu víc blíží přímce; kolem ",[1115,19221,19223],{"className":19222},[1292],[1294,19224,19225],{"xmlns":1296},[1298,19226,19227,19235],{},[1301,19228,19229,19231,19233],{},[1307,19230,71],{},[1437,19232,9198],{},[1311,19234,1313],{},[1315,19236,19237],{"encoding":1317},"r\\approx 0"," je mezi ",[1115,19240,19242],{"className":19241},[1292],[1294,19243,19244],{"xmlns":1296},[1298,19245,19246,19250],{},[1301,19247,19248],{},[1307,19249,6476],{},[1315,19251,6476],{"encoding":1317},[1115,19253,19255],{"className":19254},[1292],[1294,19256,19257],{"xmlns":1296},[1298,19258,19259,19263],{},[1301,19260,19261],{},[1307,19262,6886],{},[1315,19264,6886],{"encoding":1317}," patrná jen náhodná rozptýlenost bez lineárního trendu.",[16505,19267,16508],{"id":19268},"v-r-1",[3447,19270,19272],{"className":3449,"code":19271,"language":71,"meta":1229,"style":1229},"cor(pocet_clenu, tydenni_vydaje)\n",[3223,19273,19274],{"__ignoreMap":1229},[1115,19275,19276,19279,19281,19283,19285,19288],{"class":3455,"line":10},[1115,19277,19278],{"class":3466},"cor",[1115,19280,1626],{"class":3470},[1115,19282,16529],{"class":3458},[1115,19284,1547],{"class":3462},[1115,19286,19287],{"class":3458}," tydenni_vydaje",[1115,19289,3655],{"class":3470},[3447,19291,19294],{"className":19292,"code":19293,"language":3677,"meta":1229},[3675],"[1] 0.9997441\n",[3223,19295,19293],{"__ignoreMap":1229},[1110,19297,19298,19299,19325],{},"Hodnota 0,9997 odpovídá ",[1115,19300,19302],{"className":19301},[1292],[1294,19303,19304],{"xmlns":1296},[1298,19305,19306,19322],{},[1301,19307,19308,19316,19318],{},[4207,19309,19310],{},[1330,19311,19312,19314],{},[1307,19313,9981],{},[1311,19315,1337],{},[1437,19317,1733],{},[4207,19319,19320],{},[1311,19321,16763],{},[1315,19323,19324],{"encoding":1317},"\\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.",[1103,19327,19329,19336,19339],{"className":19328,"dataCallout":3230},[1106,3229],[1110,19330,19332,19335],{"className":19331},[1113],[1115,19333],{"className":19334,"ariaHidden":1121},[1118,3237,1120],"Příklad: Koeficient korelace",[1110,19337,19338],{},"Pro stejná data o hodnotě produkce a výši investic dvanácti firem jako u regresní přímky byl spočten koeficient korelace mezi oběma proměnnými.",[1110,19340,17425,19341,19368],{},[1115,19342,19344],{"className":19343},[1292],[1294,19345,19346],{"xmlns":1296},[1298,19347,19348,19365],{},[1301,19349,19350,19360,19362],{},[1304,19351,19352,19354],{},[1307,19353,71],{},[1301,19355,19356,19358],{},[1307,19357,6476],{},[1307,19359,6886],{},[1437,19361,1733],{},[1311,19363,19364],{},"0,739",[1315,19366,19367],{"encoding":1317},"r_{xy} = 0{,}739"," — silná kladná závislost hodnoty produkce na výši investic.",[1136,19370,19372],{"id":19371},"vícenásobná-regrese-a-korelace","Vícenásobná regrese a korelace",[1110,19374,19375,19376,19389],{},"Pokud na závisle proměnnou ",[1115,19377,19379],{"className":19378},[1292],[1294,19380,19381],{"xmlns":1296},[1298,19382,19383,19387],{},[1301,19384,19385],{},[1307,19386,6886],{},[1315,19388,6886],{"encoding":1317}," působí víc vysvětlujících proměnných současně, analyzuje se zvlášť vliv každé z nich a výsledná regresní funkce se konstruuje jako součet jednoduchých regresních funkcí:",[1115,19391,19393],{"className":19392},[1292],[1294,19394,19395],{"xmlns":1296,"display":1715},[1298,19396,19397,19507],{},[1301,19398,19399,19401,19403,19409,19411,19417,19423,19425,19431,19437,19439,19441,19443,19449,19455,19457,19459,19465,19467,19473,19475,19481,19487,19489,19491,19493,19499,19505],{},[1307,19400,16081],{},[1437,19402,1733],{},[1304,19404,19405,19407],{},[1307,19406,16096],{},[1311,19408,1313],{},[1437,19410,5231],{},[1304,19412,19413,19415],{},[1307,19414,16096],{},[1311,19416,1544],{},[1304,19418,19419,19421],{},[1307,19420,6476],{},[1311,19422,1544],{},[1437,19424,5231],{},[1304,19426,19427,19429],{},[1307,19428,16096],{},[1311,19430,1337],{},[1304,19432,19433,19435],{},[1307,19434,6476],{},[1311,19436,1337],{},[1437,19438,5231],{},[1437,19440,17675],{},[1437,19442,5231],{},[1304,19444,19445,19447],{},[1307,19446,16096],{},[1307,19448,1110],{},[1304,19450,19451,19453],{},[1307,19452,6476],{},[1307,19454,1110],{},[1437,19456,1547],{"separator":1121},[1763,19458],{"width":1765},[2475,19460,19461,19463],{"accent":1121},[1307,19462,6886],{},[1437,19464,2481],{},[1437,19466,1733],{},[1304,19468,19469,19471],{},[1307,19470,11262],{},[1311,19472,1313],{},[1437,19474,5231],{},[1304,19476,19477,19479],{},[1307,19478,11262],{},[1311,19480,1544],{},[1304,19482,19483,19485],{},[1307,19484,6476],{},[1311,19486,1544],{},[1437,19488,5231],{},[1437,19490,17675],{},[1437,19492,5231],{},[1304,19494,19495,19497],{},[1307,19496,11262],{},[1307,19498,1110],{},[1304,19500,19501,19503],{},[1307,19502,6476],{},[1307,19504,1110],{},[1307,19506,1417],{"mathvariant":1872},[1315,19508,19509],{"encoding":1317},"\\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.",[16505,19511,19513],{"id":19512},"výběr-proměnných","Výběr proměnných",[1191,19515,19516,19522],{},[1194,19517,19518,19521],{},[1279,19519,19520],{},"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.",[1194,19523,19524,19527,19528,19531,19532,19535],{},[1279,19525,19526],{},"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 ",[1279,19529,19530],{},"forward"," proměnné postupně přidává, varianta ",[1279,19533,19534],{},"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.",[16505,19537,19539],{"id":19538},"postup-odhadu","Postup odhadu",[2617,19541,19542,19545,19548],{},[1194,19543,19544],{},"ověření předpokladů regresního modelu,",[1194,19546,19547],{},"samotný odhad parametrů,",[1194,19549,19550],{},"reziduální analýza výsledného modelu.",[1110,19552,19553,19554,19571,19572,3742,19574,19603,19604,19633,19634,19651],{},"Důležitost každého parametru ",[1115,19555,19557],{"className":19556},[1292],[1294,19558,19559],{"xmlns":1296},[1298,19560,19561,19569],{},[1301,19562,19563],{},[1304,19564,19565,19567],{},[1307,19566,11262],{},[1307,19568,1629],{},[1315,19570,16221],{"encoding":1317}," v modelu ověřuje ",[1279,19573,992],{},[1115,19575,19577],{"className":19576},[1292],[1294,19578,19579],{"xmlns":1296},[1298,19580,19581,19601],{},[1301,19582,19583,19589,19591,19597,19599],{},[1304,19584,19585,19587],{},[1307,19586,1309],{},[1311,19588,1313],{},[1437,19590,1709],{},[1304,19592,19593,19595],{},[1307,19594,16096],{},[1307,19596,1629],{},[1437,19598,1733],{},[1311,19600,1313],{},[1315,19602,16707],{"encoding":1317}," (proměnná je v modelu nevýznamná) proti ",[1115,19605,19607],{"className":19606},[1292],[1294,19608,19609],{"xmlns":1296},[1298,19610,19611,19631],{},[1301,19612,19613,19619,19621,19627,19629],{},[1304,19614,19615,19617],{},[1307,19616,1309],{},[1311,19618,1544],{},[1437,19620,1709],{},[1304,19622,19623,19625],{},[1307,19624,16096],{},[1307,19626,1629],{},[1437,19628,10714],{"mathvariant":1872},[1311,19630,1313],{},[1315,19632,16738],{"encoding":1317}," (proměnná je významná). Při nezamítnutí ",[1115,19635,19637],{"className":19636},[1292],[1294,19638,19639],{"xmlns":1296},[1298,19640,19641,19649],{},[1301,19642,19643],{},[1304,19644,19645,19647],{},[1307,19646,1309],{},[1311,19648,1313],{},[1315,19650,1318],{"encoding":1317}," by proměnná — a s ní spojený regresor — v modelu neměla zůstat.",[16505,19653,19655],{"id":19654},"předpoklady-modelu","Předpoklady modelu",[2617,19657,19658,19675,19708,19714,19717,19720],{},[1194,19659,19660,19661,19674],{},"Závisle proměnná ",[1115,19662,19664],{"className":19663},[1292],[1294,19665,19666],{"xmlns":1296},[1298,19667,19668,19672],{},[1301,19669,19670],{},[1307,19671,6886],{},[1315,19673,6886],{"encoding":1317}," musí být aspoň intervalového typu (ne binární, diskrétní s málo hodnotami apod.) — jinak je na místě logistická regrese.",[1194,19676,19677,19678,19707],{},"Nezávislé proměnné ",[1115,19679,19681],{"className":19680},[1292],[1294,19682,19683],{"xmlns":1296},[1298,19684,19685,19705],{},[1301,19686,19687,19693,19695,19697,19699],{},[1304,19688,19689,19691],{},[1307,19690,6476],{},[1311,19692,1544],{},[1437,19694,1547],{"separator":1121},[1437,19696,1550],{},[1437,19698,1547],{"separator":1121},[1304,19700,19701,19703],{},[1307,19702,6476],{},[1307,19704,1110],{},[1315,19706,16045],{"encoding":1317}," jsou rovněž aspoň intervalového typu, mohou být i alternativní.",[1194,19709,19710,19711,1417],{},"Nezávislé proměnné by mezi sebou neměly být příliš vysoce korelované — ",[1279,19712,19713],{},"multikolinearita",[1194,19715,19716],{},"V datech nesmí být odlehlé či extrémní hodnoty; regresní analýza je na ně citlivá a mohou vážně narušit kvalitu odhadů.",[1194,19718,19719],{},"Proměnné musí být ve vzájemně lineárním vztahu — vícenásobná lineární regrese je založená na Pearsonově koeficientu korelace, takže nelineární vztahy mezi proměnnými zůstanou neodhalené.",[1194,19721,19722,19723,19727],{},"Proměnné mají mít ",[1127,19724,19726],{"className":19725,"dataFsResolvedFilePath":6375,"href":6376},[1130],"normální rozložení","; význam tohoto předpokladu ustupuje do pozadí u dostatečně velkého datového souboru díky centrální limitní větě.",[1110,19729,19730,19731,19734],{},"Normalita se u menšího počtu pozorování ověřuje stejnými testy jako u jiných znaků (viz ",[1127,19732,1473],{"className":19733,"dataFsResolvedFilePath":1471,"href":1472},[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.",[16505,19736,19737],{"id":19713},"Multikolinearita",[1110,19739,19740],{},"Multikolinearita vzniká, když vysvětlující proměnné silně závisejí jedna na druhé. Je nežádoucí, protože:",[1191,19742,19743,19746,19749],{},[1194,19744,19745],{},"výsledky regrese jsou pak nespolehlivé,",[1194,19747,19748],{},"zvyšuje pravděpodobnost, že se důležitá proměnná jeví jako statisticky nevýznamná a bude z modelu vyřazena,",[1194,19750,19751],{},"směrodatné odchylky odhadnutých parametrů jsou vysoké, testová kritéria t-testů nízká, p-hodnoty vysoké.",[1110,19753,19754,19755,19758,19759,19782,19783,19801,19802,19818],{},"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 ",[1279,19756,19757],{},"VIF (Variance Inflation Factor)",": hodnoty ",[1115,19760,19762],{"className":19761},[1292],[1294,19763,19764],{"xmlns":1296},[1298,19765,19766,19779],{},[1301,19767,19768,19770,19772,19775,19777],{},[1311,19769,1544],{},[1437,19771,4086],{},[2661,19773,19774],{},"VIF",[1437,19776,4086],{},[1311,19778,9684],{},[1315,19780,19781],{"encoding":1317},"1\u003C\\text{VIF}\u003C5"," jsou varující, ",[1115,19784,19786],{"className":19785},[1292],[1294,19787,19788],{"xmlns":1296},[1298,19789,19790,19798],{},[1301,19791,19792,19794,19796],{},[2661,19793,19774],{},[1437,19795,1439],{},[1311,19797,9684],{},[1315,19799,19800],{"encoding":1317},"\\text{VIF}>5"," (přísněji ",[1115,19803,19805],{"className":19804},[1292],[1294,19806,19807],{"xmlns":1296},[1298,19808,19809,19815],{},[1301,19810,19811,19813],{},[1437,19812,1439],{},[1311,19814,8791],{},[1315,19816,19817],{"encoding":1317},">10",") značí vysokou multikolinearitu.",[1110,19820,19821],{},"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.",[16505,19823,19825],{"id":19824},"další-ukazatele-kvality-modelu","Další ukazatele kvality modelu",[1191,19827,19828,19834,19840],{},[1194,19829,19830,19833],{},[1279,19831,19832],{},"F-test"," — testuje hypotézu, že všechny regresní koeficienty jsou rovny nule, proti alternativě, že aspoň jeden v modelu být má (celková významnost modelu).",[1194,19835,19836,19839],{},[1279,19837,19838],{},"RMSE"," (odmocnina z reziduálního rozptylu) — absolutní měřítko vhodnosti funkce (na rozdíl od indexu determinace, který je relativní); nižší hodnota znamená lepší fit.",[1194,19841,19842,19845,19846,19849],{},[1279,19843,19844],{},"AIC"," (Akaikeho informační kritérium) a ",[1279,19847,19848],{},"BIC"," (Bayesovo informační kritérium) — čím nižší hodnoty obou kritérií, tím lepší model; používají se hlavně při stepwise výběru proměnných.",[16505,19851,16508],{"id":19852},"v-r-2",[1110,19854,19855],{},"Pro vícenásobnou regresi je postup v R rozšířením postupu pro regresní přímku — přibývá výběr proměnných a kontrola multikolinearity:",[3447,19857,19859],{"className":3449,"code":19858,"language":71,"meta":1229,"style":1229},"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",[3223,19860,19861,19887,19931,19957,19967,19971,19982,19993,19997,20007,20017,20021,20031,20041,20046],{"__ignoreMap":1229},[1115,19862,19863,19866,19868,19871,19873,19876,19878,19881,19883,19885],{"class":3455,"line":10},[1115,19864,19865],{"class":3458},"data",[1115,19867,3463],{"class":3462},[1115,19869,19870],{"class":3466}," read.table",[1115,19872,1626],{"class":3470},[1115,19874,19875],{"class":3594},"\"4_4.txt\"",[1115,19877,1547],{"class":3462},[1115,19879,19880],{"class":3458}," header",[1115,19882,3551],{"class":3462},[1115,19884,3564],{"class":3478},[1115,19886,3655],{"class":3470},[1115,19888,19889,19892,19894,19896,19898,19900,19902,19905,19907,19910,19912,19915,19917,19920,19922,19925,19927,19929],{"class":3455,"line":27},[1115,19890,19891],{"class":3458},"model_plny",[1115,19893,3463],{"class":3462},[1115,19895,16609],{"class":3466},[1115,19897,1626],{"class":3470},[1115,19899,6886],{"class":3458},[1115,19901,16616],{"class":3462},[1115,19903,19904],{"class":3458}," x1",[1115,19906,18273],{"class":3462},[1115,19908,19909],{"class":3458}," x2",[1115,19911,18273],{"class":3462},[1115,19913,19914],{"class":3458}," x3",[1115,19916,18273],{"class":3462},[1115,19918,19919],{"class":3458}," x4",[1115,19921,1547],{"class":3462},[1115,19923,19924],{"class":3458}," data",[1115,19926,3551],{"class":3462},[1115,19928,19924],{"class":3458},[1115,19930,3655],{"class":3470},[1115,19932,19933,19936,19938,19941,19943,19945,19947,19950,19952,19955],{"class":3455,"line":148},[1115,19934,19935],{"class":3458},"model_krok",[1115,19937,3463],{"class":3462},[1115,19939,19940],{"class":3466}," step",[1115,19942,1626],{"class":3470},[1115,19944,19891],{"class":3458},[1115,19946,1547],{"class":3462},[1115,19948,19949],{"class":3458}," direction",[1115,19951,3551],{"class":3462},[1115,19953,19954],{"class":3594}," \"both\"",[1115,19956,3655],{"class":3470},[1115,19958,19959,19961,19963,19965],{"class":3455,"line":111},[1115,19960,1249],{"class":3466},[1115,19962,1626],{"class":3470},[1115,19964,19935],{"class":3458},[1115,19966,3655],{"class":3470},[1115,19968,19969],{"class":3455,"line":96},[1115,19970,9799],{"emptyLinePlaceholder":1238},[1115,19972,19973,19975,19977,19980],{"class":3455,"line":89},[1115,19974,17154],{"class":3462},[1115,19976,1626],{"class":3470},[1115,19978,19979],{"class":3458},"car",[1115,19981,3655],{"class":3470},[1115,19983,19984,19987,19989,19991],{"class":3455,"line":82},[1115,19985,19986],{"class":3466},"vif",[1115,19988,1626],{"class":3470},[1115,19990,19935],{"class":3458},[1115,19992,3655],{"class":3470},[1115,19994,19995],{"class":3455,"line":75},[1115,19996,9799],{"emptyLinePlaceholder":1238},[1115,19998,19999,20001,20003,20005],{"class":3455,"line":3645},[1115,20000,17154],{"class":3462},[1115,20002,1626],{"class":3470},[1115,20004,17159],{"class":3458},[1115,20006,3655],{"class":3470},[1115,20008,20009,20011,20013,20015],{"class":3455,"line":72},[1115,20010,17166],{"class":3466},[1115,20012,1626],{"class":3470},[1115,20014,19935],{"class":3458},[1115,20016,3655],{"class":3470},[1115,20018,20019],{"class":3455,"line":25},[1115,20020,9799],{"emptyLinePlaceholder":1238},[1115,20022,20023,20025,20027,20029],{"class":3455,"line":65},[1115,20024,17154],{"class":3462},[1115,20026,1626],{"class":3470},[1115,20028,17249],{"class":3458},[1115,20030,3655],{"class":3470},[1115,20032,20033,20035,20037,20039],{"class":3455,"line":63},[1115,20034,17256],{"class":3466},[1115,20036,1626],{"class":3470},[1115,20038,19935],{"class":3458},[1115,20040,3655],{"class":3470},[1115,20042,20044],{"class":3455,"line":20043},14,[1115,20045,9799],{"emptyLinePlaceholder":1238},[1115,20047,20048,20050,20052,20054,20056,20058],{"class":3455,"line":60},[1115,20049,17334],{"class":3466},[1115,20051,1626],{"class":3470},[1115,20053,16802],{"class":3466},[1115,20055,1626],{"class":3470},[1115,20057,19935],{"class":3458},[1115,20059,9251],{"class":3470},[1110,20061,20062,20064,20065,20068],{},[3223,20063,15879],{}," provádí stepwise výběr podle AIC, ",[3223,20066,20067],{},"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.",[1103,20070,20072,20079,20082,20085],{"className":20071,"dataCallout":3230},[1106,3229],[1110,20073,20075,20078],{"className":20074},[1113],[1115,20076],{"className":20077,"ariaHidden":1121},[1118,3237,1120],"Příklad: Vícenásobná regrese",[1110,20080,20081],{},"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.",[1110,20083,20084],{},"Postup: odhad plného modelu → stepwise analýza podle AIC → ověření předpokladů.",[1110,20086,20087,20088,20091,20092,20094,20095,20098],{},"Diagnostika odhaleného modelu ukázala tři problémy: (1) ",[1279,20089,20090],{},"nelinearita"," — mezi některými vysvětlujícími proměnnými a cenou je zjevně jiný než lineární vztah, řešením je zkusit u nich druhou mocninu; (2) ",[1279,20093,19713],{}," mezi dvojicí proměnných popisujících vzdálenost (k silnici a ke spalovně) — doporučeno jednu z nich vynechat; (3) ",[1279,20096,20097],{},"odlehlá pozorování"," — vhodné je provést ještě test a případně je vyřadit. Výsledný model obsahoval i nevýznamné proměnné, jako celek však byl statisticky významný s přibližně průměrným indexem determinace; dalšího zlepšení šlo dosáhnout snížením AIC pomocí stepwise regrese.",[1136,20100,6162],{"id":6161},[1103,20102,20104,20111],{"className":20103,"dataCallout":6167},[1106,6166],[1110,20105,20107,20110],{"className":20106},[1113],[1115,20108],{"className":20109,"ariaHidden":1121},[1118,6174,1120],"Koeficient korelace jen pro přímku",[1110,20112,20113,20114,20170,20171,20188,20189,20209,20210,5495,20223,1417],{},"Vzorec ",[1115,20115,20117],{"className":20116},[1292],[1294,20118,20119],{"xmlns":1296},[1298,20120,20121,20167],{},[1301,20122,20123,20133,20135,20145,20147],{},[1304,20124,20125,20127],{},[1307,20126,71],{},[1301,20128,20129,20131],{},[1307,20130,6476],{},[1307,20132,6886],{},[1437,20134,1733],{},[1304,20136,20137,20139],{},[1307,20138,1605],{},[1301,20140,20141,20143],{},[1307,20142,6476],{},[1307,20144,6886],{},[1307,20146,4358],{"mathvariant":1872},[4207,20148,20149],{},[1301,20150,20151,20159],{},[3106,20152,20153,20155,20157],{},[1307,20154,1605],{},[1307,20156,6476],{},[1311,20158,1337],{},[3106,20160,20161,20163,20165],{},[1307,20162,1605],{},[1307,20164,6886],{},[1311,20166,1337],{},[1315,20168,20169],{"encoding":1317},"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 ",[1115,20172,20174],{"className":20173},[1292],[1294,20175,20176],{"xmlns":1296},[1298,20177,20178,20186],{},[1301,20179,20180],{},[1330,20181,20182,20184],{},[1307,20183,9981],{},[1311,20185,1337],{},[1315,20187,15783],{"encoding":1317},", případně obecným indexem korelace ",[1115,20190,20192],{"className":20191},[1292],[1294,20193,20194],{"xmlns":1296},[1298,20195,20196,20206],{},[1301,20197,20198],{},[4207,20199,20200],{},[1330,20201,20202,20204],{},[1307,20203,9981],{},[1311,20205,1337],{},[1315,20207,20208],{"encoding":1317},"\\sqrt{R^2}"," — ne koeficientem korelace mezi ",[1115,20211,20213],{"className":20212},[1292],[1294,20214,20215],{"xmlns":1296},[1298,20216,20217,20221],{},[1301,20218,20219],{},[1307,20220,6476],{},[1315,20222,6476],{"encoding":1317},[1115,20224,20226],{"className":20225},[1292],[1294,20227,20228],{"xmlns":1296},[1298,20229,20230,20234],{},[1301,20231,20232],{},[1307,20233,6886],{},[1315,20235,6886],{"encoding":1317},[1103,20237,20239,20246],{"className":20238,"dataCallout":6167},[1106,6166],[1110,20240,20242,20245],{"className":20241},[1113],[1115,20243],{"className":20244,"ariaHidden":1121},[1118,6174,1120],"Významný F-test, nevýznamné t-testy",[1110,20247,20248],{},"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.",[1103,20250,20252,20259],{"className":20251,"dataCallout":6167},[1106,6166],[1110,20253,20255,20258],{"className":20254},[1113],[1115,20256],{"className":20257,"ariaHidden":1121},[1118,6174,1120],"Durbin-Watsonova statistika mimo okolí 2",[1110,20260,20261],{},"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.",[1103,20263,20265,20272],{"className":20264,"dataCallout":6167},[1106,6166],[1110,20266,20268,20271],{"className":20267},[1113],[1115,20269],{"className":20270,"ariaHidden":1121},[1118,6174,1120],"Nízký počet pozorování při stepwise výběru",[1110,20273,20274],{},"Metoda ENTER potřebuje aspoň 20 pozorování na proměnnou, stepwise regrese aspoň 40. Při menším vzorku jsou výsledky výběru proměnných nespolehlivé bez ohledu na to, jak hezky vychází AIC.",[1136,20276,1189],{"id":1188},[1191,20278,20279,20284,20289,20294,20299,20304,20309],{},[1194,20280,20281],{},[1127,20282,1133],{"className":20283,"dataFsResolvedFilePath":1131,"href":1132},[1130],[1194,20285,20286],{},[1127,20287,6377],{"className":20288,"dataFsResolvedFilePath":6375,"href":6376},[1130],[1194,20290,20291],{},[1127,20292,6369],{"className":20293,"dataFsResolvedFilePath":6367,"href":6368},[1130],[1194,20295,20296],{},[1127,20297,6361],{"className":20298,"dataFsResolvedFilePath":1471,"href":1472},[1130],[1194,20300,20301],{},[1127,20302,1182],{"className":20303,"dataFsResolvedFilePath":1180,"href":1181},[1130],[1194,20305,20306],{},[1127,20307,6390],{"className":20308,"dataFsResolvedFilePath":6388,"href":6389},[1130],[1194,20310,20311],{},[1127,20312,6396],{"className":20313,"dataFsResolvedFilePath":1214,"href":1215},[1130],[1136,20315,1219],{"id":934},[1110,20317,1222,20318,1227],{},[1224,20319,1226],{},[6404,20321,20322],{},"html pre.shiki code .sP4rz, html 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.sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}",{"title":1229,"searchDepth":27,"depth":27,"links":20324},[20325,20326,20327,20331,20336,20339,20347,20348,20349],{"id":10994,"depth":27,"text":10995},{"id":16062,"depth":27,"text":16063},{"id":16384,"depth":27,"text":16385,"children":20328},[20329,20330],{"id":16507,"depth":148,"text":16508},{"id":17130,"depth":148,"text":17131},{"id":17623,"depth":27,"text":17624,"children":20332},[20333,20334,20335],{"id":18165,"depth":148,"text":18166},{"id":18354,"depth":148,"text":18355},{"id":18613,"depth":148,"text":18614},{"id":18948,"depth":27,"text":18949,"children":20337},[20338],{"id":19268,"depth":148,"text":16508},{"id":19371,"depth":27,"text":19372,"children":20340},[20341,20342,20343,20344,20345,20346],{"id":19512,"depth":148,"text":19513},{"id":19538,"depth":148,"text":19539},{"id":19654,"depth":148,"text":19655},{"id":19713,"depth":148,"text":19737},{"id":19824,"depth":148,"text":19825},{"id":19852,"depth":148,"text":16508},{"id":6161,"depth":27,"text":6162},{"id":1188,"depth":27,"text":1189},{"id":934,"depth":27,"text":1219},{},"\u002Ftopics\u002Fregresni-a-korelacni-analyza",{"title":1169,"description":1229},[1242,1243],"topics\u002Fregresni-a-korelacni-analyza",[23,67,135,294,71],"qS8RwxtzOoJHO1BXdLvvzGC9r7PL779FUTYQspgRw5k",{"id":20358,"title":6390,"body":20359,"course":23,"courses":1234,"created":1235,"description":1229,"extension":1236,"meta":25801,"navigation":1238,"path":25802,"seo":25803,"sources":25804,"stem":25809,"tags":25810,"type":6423,"updated":1235,"__hash__":25811},"topics\u002Ftopics\u002Fregulacni-diagramy-a-indexy-zpusobilosti.md",{"type":1096,"value":20360,"toc":25766},[20361,20364,20655,20659,20668,20675,20724,20735,20742,20745,20769,20773,20779,20799,20802,20809,20815,20826,20829,20858,20862,20865,20929,21020,21049,21094,21205,21208,21327,21416,21658,21700,21847,22075,22291,22410,22417,22426,22509,22516,22544,22613,22682,22722,22754,22891,22982,23037,23041,23044,23133,23149,23225,23269,23403,23409,23489,23496,23512,23568,23575,23649,23667,23699,23715,23781,23797,23837,23842,23914,23918,23960,23981,24000,24046,24097,24100,24284,24309,24312,24392,24479,24527,24615,24737,24741,24873,24913,24920,24927,24931,24998,25126,25196,25469,25471,25696,25698,25736,25738,25742,25749,25756,25763],[1099,20362,6390],{"id":20363},"regulační-diagramy-a-indexy-způsobilosti",[1103,20365,20367,20373],{"className":20366,"dataCallout":1264},[1106,1263],[1110,20368,20370,1272],{"className":20369},[1113],[1115,20371],{"className":20372,"ariaHidden":1121},[1118,1271,1120],[1191,20374,20375,20378,20472,20534,20537,20650],{},[1194,20376,20377],{},"Regulační diagram zobrazuje vývoj variability procesu v čase a dává signál, že na proces začala působit vymezitelná příčina: bod mimo akční meze UCL a LCL.",[1194,20379,20380,20381,2704,20407,5495,20433,1417],{},"Regulace měřením (spojitá veličina s normálním rozdělením): diagramy ",[1115,20382,20384],{"className":20383},[1292],[1294,20385,20386],{"xmlns":1296},[1298,20387,20388,20404],{},[1301,20389,20390,20392,20398,20400,20402],{},[1437,20391,1626],{"stretchy":1625},[2475,20393,20394,20396],{"accent":1121},[1307,20395,6476],{},[1437,20397,11217],{},[1437,20399,1547],{"separator":1121},[1307,20401,9981],{},[1437,20403,1637],{"stretchy":1625},[1315,20405,20406],{"encoding":1317},"(\\bar{x}, R)",[1115,20408,20410],{"className":20409},[1292],[1294,20411,20412],{"xmlns":1296},[1298,20413,20414,20430],{},[1301,20415,20416,20418,20424,20426,20428],{},[1437,20417,1626],{"stretchy":1625},[2475,20419,20420,20422],{"accent":1121},[1307,20421,6476],{},[1437,20423,11217],{},[1437,20425,1547],{"separator":1121},[1307,20427,1605],{},[1437,20429,1637],{"stretchy":1625},[1315,20431,20432],{"encoding":1317},"(\\bar{x}, s)",[1115,20434,20436],{"className":20435},[1292],[1294,20437,20438],{"xmlns":1296},[1298,20439,20440,20469],{},[1301,20441,20442,20444,20450,20452,20467],{},[1437,20443,1626],{"stretchy":1625},[1304,20445,20446,20448],{},[1307,20447,6476],{},[1307,20449,1629],{},[1437,20451,1547],{"separator":1121},[1304,20453,20454,20456],{},[1307,20455,9981],{},[1301,20457,20458,20460,20463,20465],{},[1307,20459,7016],{},[1307,20461,20462],{},"l",[1437,20464,1547],{"separator":1121},[1307,20466,1629],{},[1437,20468,1637],{"stretchy":1625},[1315,20470,20471],{"encoding":1317},"(x_i, R_{kl,i})",[1194,20473,20474,20475,20488,20489,20502,20503,20519,20520,20533],{},"Regulace srovnáváním (diskrétní veličina): počet neshod ",[1115,20476,20478],{"className":20477},[1292],[1294,20479,20480],{"xmlns":1296},[1298,20481,20482,20486],{},[1301,20483,20484],{},[1307,20485,3473],{},[1315,20487,3473],{"encoding":1317}," (konstantní rozsah) a ",[1115,20490,20492],{"className":20491},[1292],[1294,20493,20494],{"xmlns":1296},[1298,20495,20496,20500],{},[1301,20497,20498],{},[1307,20499,11286],{},[1315,20501,11286],{"encoding":1317}," (nekonstantní rozsah), počet neshodných produktů ",[1115,20504,20506],{"className":20505},[1292],[1294,20507,20508],{"xmlns":1296},[1298,20509,20510,20516],{},[1301,20511,20512,20514],{},[1307,20513,1435],{},[1307,20515,1110],{},[1315,20517,20518],{"encoding":1317},"np"," (konstantní rozsah) a jejich podíl ",[1115,20521,20523],{"className":20522},[1292],[1294,20524,20525],{"xmlns":1296},[1298,20526,20527,20531],{},[1301,20528,20529],{},[1307,20530,1110],{},[1315,20532,1110],{"encoding":1317}," (nekonstantní rozsah).",[1194,20535,20536],{},"Podskupiny s vymezitelnou příčinou se po jejím odstranění z výpočtu vyřadí a meze se přepočítají, dokud jsou všechny body uvnitř mezí.",[1194,20538,20539,20540,2704,20559,2704,20581,2704,20603,20627,20628,20649],{},"Indexy způsobilosti ",[1115,20541,20543],{"className":20542},[1292],[1294,20544,20545],{"xmlns":1296},[1298,20546,20547,20556],{},[1301,20548,20549],{},[1304,20550,20551,20554],{},[1307,20552,20553],{},"C",[1307,20555,1110],{},[1315,20557,20558],{"encoding":1317},"C_p",[1115,20560,20562],{"className":20561},[1292],[1294,20563,20564],{"xmlns":1296},[1298,20565,20566,20578],{},[1301,20567,20568],{},[1304,20569,20570,20572],{},[1307,20571,20553],{},[1301,20573,20574,20576],{},[1307,20575,1110],{},[1307,20577,7016],{},[1315,20579,20580],{"encoding":1317},"C_{pk}",[1115,20582,20584],{"className":20583},[1292],[1294,20585,20586],{"xmlns":1296},[1298,20587,20588,20600],{},[1301,20589,20590],{},[1304,20591,20592,20594],{},[1307,20593,20553],{},[1301,20595,20596,20598],{},[1307,20597,1110],{},[1307,20599,4225],{},[1315,20601,20602],{"encoding":1317},"C_{pm}",[1115,20604,20606],{"className":20605},[1292],[1294,20607,20608],{"xmlns":1296},[1298,20609,20610,20624],{},[1301,20611,20612],{},[1304,20613,20614,20616],{},[1307,20615,20553],{},[1301,20617,20618,20620,20622],{},[1307,20619,1110],{},[1307,20621,4225],{},[1307,20623,7016],{},[1315,20625,20626],{"encoding":1317},"C_{pmk}"," posuzují, zda statisticky zvládnutý proces vyhovuje tolerančním mezím; ",[1115,20629,20631],{"className":20630},[1292],[1294,20632,20633],{"xmlns":1296},[1298,20634,20635,20647],{},[1301,20636,20637],{},[1304,20638,20639,20641],{},[1307,20640,20553],{},[1301,20642,20643,20645],{},[1307,20644,1110],{},[1307,20646,7016],{},[1315,20648,20580],{"encoding":1317}," navíc zohledňuje vychýlení střední hodnoty.",[1194,20651,20652,20653,1417],{},"V R diagramy i indexy počítá balíček ",[3223,20654,360],{},[1136,20656,20658],{"id":20657},"statistická-regulace-procesu","Statistická regulace procesu",[1110,20660,20661,20662,20664,20665,1417],{},"Tradiční zabezpečování jakosti kontroluje výrobky až po jejich vyrobení, což je neekonomické. ",[1279,20663,20658],{}," 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 ",[1279,20666,20667],{},"statisticky zvládnutém stavu",[1110,20669,20670,20671,20674],{},"Teorie regulace vychází z ",[1279,20672,20673],{},"variability"," procesu, kterou způsobují dva druhy příčin:",[1141,20676,20677,20689],{},[1144,20678,20679],{},[1147,20680,20681,20683,20686],{},[1150,20682],{},[1150,20684,20685],{},"Náhodné příčiny",[1150,20687,20688],{},"Vymezitelné příčiny",[1157,20690,20691,20702,20713],{},[1147,20692,20693,20696,20699],{},[1162,20694,20695],{},"Povaha",[1162,20697,20698],{},"široká skupina neidentifikovatelných vlivů, každý přispívá k variabilitě malou měrou",[1162,20700,20701],{},"vlivy, které za běžných podmínek na proces nepůsobí; vyvolají nepřirozené kolísání údajů",[1147,20703,20704,20707,20710],{},[1162,20705,20706],{},"Stav procesu",[1162,20708,20709],{},"ustálený, jakost výstupů je předvídatelná, není nutné zasahovat — statisticky zvládnutý",[1162,20711,20712],{},"jakost výstupů není předvídatelná, je nutné zasáhnout — proces není statisticky zvládnutý",[1147,20714,20715,20718,20721],{},[1162,20716,20717],{},"Příklady",[1162,20719,20720],{},"psychický stav pracovníka, chvění stroje, teplota ovzduší",[1162,20722,20723],{},"změna materiálu, nezaškolená obsluha",[1110,20725,20726,20727,20730,20731,20734],{},"Vymezitelné příčiny jsou ",[1279,20728,20729],{},"sporadické"," (vznikají náhle, změny trvají krátce) nebo ",[1279,20732,20733],{},"přetrvávající"," (trvají stále nebo se mění).",[1110,20736,20737],{},[4137,20738],{"alt":20739,"className":20740,"src":20741},"mask-ilu-pricin-variability",[1130,4141],"\u002Fwiki-assets\u002Fmask-ilu-pricin-variability.png",[1110,20743,20744],{},"Regulace probíhá ve třech fázích:",[2617,20746,20747,20757,20763],{},[1194,20748,20749,20752,20753,20756],{},[1279,20750,20751],{},"Fáze přípravná"," — stanoví se sledované znaky jakosti (rozměr, hmotnost, počet vad…), délka časového intervalu mezi měřeními, ",[1279,20754,20755],{},"logická podskupina"," (skupina měření, v níž se předpokládá působení pouze náhodných příčin), typ regulačního diagramu a místa kontroly v procesu.",[1194,20758,20759,20762],{},[1279,20760,20761],{},"Fáze zabezpečování statistické zvládnutosti"," — pomocí regulačních diagramů se identifikují vymezitelné příčiny a odstraní se jejich působení.",[1194,20764,20765,20768],{},[1279,20766,20767],{},"Fáze analýzy a zabezpečení způsobilosti"," — zkoumá se, zda statisticky zvládnutý proces vyhovuje požadavkům zákazníka; k tomu slouží indexy způsobilosti (níže).",[1136,20770,20772],{"id":20771},"princip-regulačního-diagramu","Princip regulačního diagramu",[1110,20774,20775,20778],{},[1279,20776,20777],{},"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.",[1191,20780,20781,20787,20793],{},[1194,20782,20783,20786],{},[1279,20784,20785],{},"CL"," — střední přímka, odpovídá požadované (referenční) hodnotě použité charakteristiky,",[1194,20788,20789,20792],{},[1279,20790,20791],{},"UCL"," — horní akční regulační mez,",[1194,20794,20795,20798],{},[1279,20796,20797],{},"LCL"," — dolní akční regulační mez.",[1110,20800,20801],{},"Akční meze vymezují pásmo působení pouze náhodných příčin variability.",[1110,20803,20804],{},[4137,20805],{"alt":20806,"className":20807,"src":20808},"mask-rd-schema",[1130,4141],"\u002Fwiki-assets\u002Fmask-rd-schema.png",[1110,20810,20811,20814],{},[1279,20812,20813],{},"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.",[1110,20816,20817,20818,20821,20822,20825],{},"Podle charakteru regulované veličiny se diagramy dělí na diagramy pro ",[1279,20819,20820],{},"regulaci měřením"," (regulovaná veličina je spojitá náhodná veličina) a pro ",[1279,20823,20824],{},"regulaci srovnáváním"," (diskrétní náhodná veličina).",[1110,20827,20828],{},"Postup při konstrukci regulačního diagramu:",[2617,20830,20831,20834,20837,20840,20843,20846,20849,20852,20855],{},[1194,20832,20833],{},"volba regulované veličiny,",[1194,20835,20836],{},"sběr a záznam dat,",[1194,20838,20839],{},"ověření požadovaných předpokladů o datech,",[1194,20841,20842],{},"volba rozsahu logických podskupin,",[1194,20844,20845],{},"volba vhodného regulačního diagramu,",[1194,20847,20848],{},"výpočet hodnot zvoleného testového kritéria pro jednotlivé výběry,",[1194,20850,20851],{},"ověření a zajištění statistické zvládnutosti procesu,",[1194,20853,20854],{},"ověření způsobilosti procesu,",[1194,20856,20857],{},"vlastní regulace procesu.",[1136,20859,20861],{"id":20860},"regulace-měřením","Regulace měřením",[1110,20863,20864],{},"Diagramy pro regulaci měřením se používají, když je regulovaná veličina měřitelná. Požaduje se, aby:",[1191,20866,20867,20870],{},[1194,20868,20869],{},"jednotlivá měření byla vzájemně nezávislá,",[1194,20871,20872,20873,20886,20887,20900,20901,20914,20915,20928],{},"regulovaná veličina byla spojitá náhodná veličina s normálním rozdělením se střední hodnotou ",[1115,20874,20876],{"className":20875},[1292],[1294,20877,20878],{"xmlns":1296},[1298,20879,20880,20884],{},[1301,20881,20882],{},[1307,20883,6647],{},[1315,20885,8554],{"encoding":1317}," a směrodatnou odchylkou ",[1115,20888,20890],{"className":20889},[1292],[1294,20891,20892],{"xmlns":1296},[1298,20893,20894,20898],{},[1301,20895,20896],{},[1307,20897,6655],{},[1315,20899,6687],{"encoding":1317}," — tyto dva parametry charakterizují statistickou stabilitu procesu; ",[1115,20902,20904],{"className":20903},[1292],[1294,20905,20906],{"xmlns":1296},[1298,20907,20908,20912],{},[1301,20909,20910],{},[1307,20911,6647],{},[1315,20913,8554],{"encoding":1317}," je hodnota, na niž je proces nastaven, ",[1115,20916,20918],{"className":20917},[1292],[1294,20919,20920],{"xmlns":1296},[1298,20921,20922,20926],{},[1301,20923,20924],{},[1307,20925,6655],{},[1315,20927,6687],{"encoding":1317}," charakterizuje jeho přesnost.",[1110,20930,20931,20932,2704,20957,5495,20982,21019],{},"Jsou-li předpoklady splněny, volí se diagramy, které současně sledují stabilitu polohy i stabilitu rozptylu: ",[1115,20933,20935],{"className":20934},[1292],[1294,20936,20937],{"xmlns":1296},[1298,20938,20939,20955],{},[1301,20940,20941,20943,20949,20951,20953],{},[1437,20942,1626],{"stretchy":1625},[2475,20944,20945,20947],{"accent":1121},[1307,20946,6476],{},[1437,20948,11217],{},[1437,20950,1547],{"separator":1121},[1307,20952,9981],{},[1437,20954,1637],{"stretchy":1625},[1315,20956,20406],{"encoding":1317},[1115,20958,20960],{"className":20959},[1292],[1294,20961,20962],{"xmlns":1296},[1298,20963,20964,20980],{},[1301,20965,20966,20968,20974,20976,20978],{},[1437,20967,1626],{"stretchy":1625},[2475,20969,20970,20972],{"accent":1121},[1307,20971,6476],{},[1437,20973,11217],{},[1437,20975,1547],{"separator":1121},[1307,20977,1605],{},[1437,20979,1637],{"stretchy":1625},[1315,20981,20432],{"encoding":1317},[1115,20983,20985],{"className":20984},[1292],[1294,20986,20987],{"xmlns":1296},[1298,20988,20989,21017],{},[1301,20990,20991,20993,20999,21001,21015],{},[1437,20992,1626],{"stretchy":1625},[1304,20994,20995,20997],{},[1307,20996,6476],{},[1307,20998,1629],{},[1437,21000,1547],{"separator":1121},[1304,21002,21003,21005],{},[1307,21004,9981],{},[1301,21006,21007,21009,21011,21013],{},[1307,21008,7016],{},[1307,21010,20462],{},[1437,21012,1547],{"separator":1121},[1307,21014,1629],{},[1437,21016,1637],{"stretchy":1625},[1315,21018,20471],{"encoding":1317},". Výsledkem jsou vždy dva diagramy.",[16505,21021,21023,21024],{"id":21022},"diagram-xˉrbarx-r","Diagram ",[1115,21025,21027],{"className":21026},[1292],[1294,21028,21029],{"xmlns":1296},[1298,21030,21031,21047],{},[1301,21032,21033,21035,21041,21043,21045],{},[1437,21034,1626],{"stretchy":1625},[2475,21036,21037,21039],{"accent":1121},[1307,21038,6476],{},[1437,21040,11217],{},[1437,21042,1547],{"separator":1121},[1307,21044,9981],{},[1437,21046,1637],{"stretchy":1625},[1315,21048,20406],{"encoding":1317},[1110,21050,21051,21052,21074,21075,21093],{},"Regulované veličiny jsou výběrové průměry ",[1115,21053,21055],{"className":21054},[1292],[1294,21056,21057],{"xmlns":1296},[1298,21058,21059,21071],{},[1301,21060,21061],{},[1304,21062,21063,21069],{},[2475,21064,21065,21067],{"accent":1121},[1307,21066,6476],{},[1437,21068,11217],{},[1307,21070,1629],{},[1315,21072,21073],{"encoding":1317},"\\bar{x}_i"," a výběrová rozpětí ",[1115,21076,21078],{"className":21077},[1292],[1294,21079,21080],{"xmlns":1296},[1298,21081,21082,21090],{},[1301,21083,21084],{},[1304,21085,21086,21088],{},[1307,21087,9981],{},[1307,21089,1629],{},[1315,21091,21092],{"encoding":1317},"R_i"," v logických podskupinách:",[1115,21095,21097],{"className":21096},[1292],[1294,21098,21099],{"xmlns":1296,"display":1715},[1298,21100,21101,21202],{},[1301,21102,21103,21113,21115,21121,21135,21145,21147,21149,21155,21157,21168,21178,21180,21190,21200],{},[1304,21104,21105,21111],{},[2475,21106,21107,21109],{"accent":1121},[1307,21108,6476],{},[1437,21110,11217],{},[1307,21112,1629],{},[1437,21114,1733],{},[2491,21116,21117,21119],{},[1311,21118,1544],{},[1307,21120,1435],{},[1735,21122,21123,21125,21133],{},[1437,21124,1739],{},[1301,21126,21127,21129,21131],{},[1307,21128,1634],{},[1437,21130,1733],{},[1311,21132,1544],{},[1307,21134,1435],{},[1304,21136,21137,21139],{},[1307,21138,6476],{},[1301,21140,21141,21143],{},[1307,21142,1629],{},[1307,21144,1634],{},[1437,21146,1547],{"separator":1121},[1763,21148],{"width":1765},[1304,21150,21151,21153],{},[1307,21152,9981],{},[1307,21154,1629],{},[1437,21156,1733],{},[21158,21159,21160,21166],"munder",{},[1301,21161,21162,21164],{},[1307,21163,11477],{},[1437,21165,4245],{},[1307,21167,1634],{},[1304,21169,21170,21172],{},[1307,21171,6476],{},[1301,21173,21174,21176],{},[1307,21175,1629],{},[1307,21177,1634],{},[1437,21179,2817],{},[21158,21181,21182,21188],{},[1301,21183,21184,21186],{},[1307,21185,4242],{},[1437,21187,4245],{},[1307,21189,1634],{},[1304,21191,21192,21194],{},[1307,21193,6476],{},[1301,21195,21196,21198],{},[1307,21197,1629],{},[1307,21199,1634],{},[1307,21201,1417],{"mathvariant":1872},[1315,21203,21204],{"encoding":1317},"\\bar{x}_i = \\frac{1}{n}\\sum_{j=1}^n x_{ij}, \\qquad R_i = \\max_j x_{ij} - \\min_j x_{ij}.",[1110,21206,21207],{},"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.",[1110,21209,21210,21211,21237,21238,21251,21252,5495,21273,21290,21291,21304,21305,21323,21324,1417],{},"Data se zapisují do tabulky: řádek ",[1115,21212,21214],{"className":21213},[1292],[1294,21215,21216],{"xmlns":1296},[1298,21217,21218,21234],{},[1301,21219,21220,21222,21224,21226,21228,21230,21232],{},[1307,21221,1629],{},[1437,21223,1733],{},[1311,21225,1544],{},[1437,21227,1547],{"separator":1121},[1437,21229,1550],{},[1437,21231,1547],{"separator":1121},[1307,21233,7016],{},[1315,21235,21236],{"encoding":1317},"i = 1, \\dots, k"," je logická podskupina v pořadí, v jakém byla získána, sloupce obsahují ",[1115,21239,21241],{"className":21240},[1292],[1294,21242,21243],{"xmlns":1296},[1298,21244,21245,21249],{},[1301,21246,21247],{},[1307,21248,1435],{},[1315,21250,1435],{"encoding":1317}," naměřených hodnot a poslední dva sloupce ",[1115,21253,21255],{"className":21254},[1292],[1294,21256,21257],{"xmlns":1296},[1298,21258,21259,21271],{},[1301,21260,21261],{},[1304,21262,21263,21269],{},[2475,21264,21265,21267],{"accent":1121},[1307,21266,6476],{},[1437,21268,11217],{},[1307,21270,1629],{},[1315,21272,21073],{"encoding":1317},[1115,21274,21276],{"className":21275},[1292],[1294,21277,21278],{"xmlns":1296},[1298,21279,21280,21288],{},[1301,21281,21282],{},[1304,21283,21284,21286],{},[1307,21285,9981],{},[1307,21287,1629],{},[1315,21289,21092],{"encoding":1317},". Pro sestrojení diagramu je potřeba aspoň 20 podskupin. Nejprve se určí diagram ",[1115,21292,21294],{"className":21293},[1292],[1294,21295,21296],{"xmlns":1296},[1298,21297,21298,21302],{},[1301,21299,21300],{},[1307,21301,9981],{},[1315,21303,9981],{"encoding":1317},", potom diagram ",[1115,21306,21308],{"className":21307},[1292],[1294,21309,21310],{"xmlns":1296},[1298,21311,21312,21320],{},[1301,21313,21314],{},[2475,21315,21316,21318],{"accent":1121},[1307,21317,6476],{},[1437,21319,11217],{},[1315,21321,21322],{"encoding":1317},"\\bar{x}"," — u obou střední přímka a akční meze. V R se diagramy konstruují funkcí ",[3223,21325,21326],{},"qcc()",[1103,21328,21330,21337],{"className":21329,"dataCallout":3230},[1106,3229],[1110,21331,21333,21336],{"className":21332},[1113],[1115,21334],{"className":21335,"ariaHidden":1121},[1118,3237,1120],"Příklad: kontrola rozměru dílu ve 20 logických podskupinách",[1110,21338,21339,21340,21353,21354,2704,21372,21390,21391,1417],{},"Naměřená data znaku jakosti ",[1115,21341,21343],{"className":21342},[1292],[1294,21344,21345],{"xmlns":1296},[1298,21346,21347,21351],{},[1301,21348,21349],{},[1307,21350,6488],{},[1315,21352,6488],{"encoding":1317}," byla získána ve 20 logických podskupinách po 4 měřeních (",[1115,21355,21357],{"className":21356},[1292],[1294,21358,21359],{"xmlns":1296},[1298,21360,21361,21369],{},[1301,21362,21363,21365,21367],{},[1307,21364,7016],{},[1437,21366,1733],{},[1311,21368,3799],{},[1315,21370,21371],{"encoding":1317},"k=20",[1115,21373,21375],{"className":21374},[1292],[1294,21376,21377],{"xmlns":1296},[1298,21378,21379,21387],{},[1301,21380,21381,21383,21385],{},[1307,21382,1435],{},[1437,21384,1733],{},[1311,21386,3295],{},[1315,21388,21389],{"encoding":1317},"n=4","); znak je měřitelný a má normální rozdělení. Sestrojte regulační diagram ",[1115,21392,21394],{"className":21393},[1292],[1294,21395,21396],{"xmlns":1296},[1298,21397,21398,21414],{},[1301,21399,21400,21402,21408,21410,21412],{},[1437,21401,1626],{"stretchy":1625},[2475,21403,21404,21406],{"accent":1121},[1307,21405,6476],{},[1437,21407,11217],{},[1437,21409,1547],{"separator":1121},[1307,21411,9981],{},[1437,21413,1637],{"stretchy":1625},[1315,21415,20406],{"encoding":1317},[1141,21417,21418,21533],{},[1144,21419,21420],{},[1147,21421,21422,21437,21461,21485,21509],{},[1150,21423,21424],{},[1115,21425,21427],{"className":21426},[1292],[1294,21428,21429],{"xmlns":1296},[1298,21430,21431,21435],{},[1301,21432,21433],{},[1307,21434,1629],{},[1315,21436,1629],{"encoding":1317},[1150,21438,21439],{},[1115,21440,21442],{"className":21441},[1292],[1294,21443,21444],{"xmlns":1296},[1298,21445,21446,21458],{},[1301,21447,21448],{},[1304,21449,21450,21452],{},[1307,21451,6476],{},[1301,21453,21454,21456],{},[1307,21455,1629],{},[1311,21457,1544],{},[1315,21459,21460],{"encoding":1317},"x_{i1}",[1150,21462,21463],{},[1115,21464,21466],{"className":21465},[1292],[1294,21467,21468],{"xmlns":1296},[1298,21469,21470,21482],{},[1301,21471,21472],{},[1304,21473,21474,21476],{},[1307,21475,6476],{},[1301,21477,21478,21480],{},[1307,21479,1629],{},[1311,21481,1337],{},[1315,21483,21484],{"encoding":1317},"x_{i2}",[1150,21486,21487],{},[1115,21488,21490],{"className":21489},[1292],[1294,21491,21492],{"xmlns":1296},[1298,21493,21494,21506],{},[1301,21495,21496],{},[1304,21497,21498,21500],{},[1307,21499,6476],{},[1301,21501,21502,21504],{},[1307,21503,1629],{},[1311,21505,3345],{},[1315,21507,21508],{"encoding":1317},"x_{i3}",[1150,21510,21511],{},[1115,21512,21514],{"className":21513},[1292],[1294,21515,21516],{"xmlns":1296},[1298,21517,21518,21530],{},[1301,21519,21520],{},[1304,21521,21522,21524],{},[1307,21523,6476],{},[1301,21525,21526,21528],{},[1307,21527,1629],{},[1311,21529,3295],{},[1315,21531,21532],{"encoding":1317},"x_{i4}",[1157,21534,21535,21549,21564,21580,21595,21607,21621,21633,21646],{},[1147,21536,21537,21539,21542,21545,21547],{},[1162,21538,1544],{},[1162,21540,21541],{},"106",[1162,21543,21544],{},"98",[1162,21546,13843],{},[1162,21548,13843],{},[1147,21550,21551,21553,21556,21559,21562],{},[1162,21552,1337],{},[1162,21554,21555],{},"95",[1162,21557,21558],{},"94",[1162,21560,21561],{},"108",[1162,21563,5878],{},[1147,21565,21566,21568,21571,21574,21577],{},[1162,21567,3345],{},[1162,21569,21570],{},"122",[1162,21572,21573],{},"105",[1162,21575,21576],{},"103",[1162,21578,21579],{},"133",[1147,21581,21582,21584,21587,21589,21592],{},[1162,21583,3295],{},[1162,21585,21586],{},"113",[1162,21588,3317],{},[1162,21590,21591],{},"128",[1162,21593,21594],{},"135",[1147,21596,21597,21599,21601,21603,21605],{},[1162,21598,9684],{},[1162,21600,13843],{},[1162,21602,5878],{},[1162,21604,21576],{},[1162,21606,5878],{},[1147,21608,21609,21611,21613,21615,21618],{},[1162,21610,3718],{},[1162,21612,21544],{},[1162,21614,21576],{},[1162,21616,21617],{},"97",[1162,21619,21620],{},"99",[1147,21622,21623,21625,21627,21629,21631],{},[1162,21624,1550],{},[1162,21626,1550],{},[1162,21628,1550],{},[1162,21630,1550],{},[1162,21632,1550],{},[1147,21634,21635,21637,21639,21641,21644],{},[1162,21636,14477],{},[1162,21638,21591],{},[1162,21640,21579],{},[1162,21642,21643],{},"120",[1162,21645,14505],{},[1147,21647,21648,21650,21652,21654,21656],{},[1162,21649,3799],{},[1162,21651,21544],{},[1162,21653,21576],{},[1162,21655,21617],{},[1162,21657,21620],{},[1110,21659,21660,21661,21682,21683,1709],{},"Pro každou podskupinu se dopočítá výběrový průměr ",[1115,21662,21664],{"className":21663},[1292],[1294,21665,21666],{"xmlns":1296},[1298,21667,21668,21680],{},[1301,21669,21670],{},[1304,21671,21672,21678],{},[2475,21673,21674,21676],{"accent":1121},[1307,21675,6476],{},[1437,21677,11217],{},[1307,21679,1629],{},[1315,21681,21073],{"encoding":1317}," a rozpětí ",[1115,21684,21686],{"className":21685},[1292],[1294,21687,21688],{"xmlns":1296},[1298,21689,21690,21698],{},[1301,21691,21692],{},[1304,21693,21694,21696],{},[1307,21695,9981],{},[1307,21697,1629],{},[1315,21699,21092],{"encoding":1317},[1141,21701,21702,21763],{},[1144,21703,21704],{},[1147,21705,21706,21721,21744],{},[1150,21707,21708],{},[1115,21709,21711],{"className":21710},[1292],[1294,21712,21713],{"xmlns":1296},[1298,21714,21715,21719],{},[1301,21716,21717],{},[1307,21718,1629],{},[1315,21720,1629],{"encoding":1317},[1150,21722,21723],{},[1115,21724,21726],{"className":21725},[1292],[1294,21727,21728],{"xmlns":1296},[1298,21729,21730,21742],{},[1301,21731,21732],{},[1304,21733,21734,21740],{},[2475,21735,21736,21738],{"accent":1121},[1307,21737,6476],{},[1437,21739,11217],{},[1307,21741,1629],{},[1315,21743,21073],{"encoding":1317},[1150,21745,21746],{},[1115,21747,21749],{"className":21748},[1292],[1294,21750,21751],{"xmlns":1296},[1298,21752,21753,21761],{},[1301,21754,21755],{},[1304,21756,21757,21759],{},[1307,21758,9981],{},[1307,21760,1629],{},[1315,21762,21092],{"encoding":1317},[1157,21764,21765,21774,21784,21794,21804,21813,21822,21830,21839],{},[1147,21766,21767,21769,21772],{},[1162,21768,1544],{},[1162,21770,21771],{},"101,50",[1162,21773,14572],{},[1147,21775,21776,21778,21781],{},[1162,21777,1337],{},[1162,21779,21780],{},"97,25",[1162,21782,21783],{},"16",[1147,21785,21786,21788,21791],{},[1162,21787,3345],{},[1162,21789,21790],{},"115,75",[1162,21792,21793],{},"30",[1147,21795,21796,21798,21801],{},[1162,21797,3295],{},[1162,21799,21800],{},"111,75",[1162,21802,21803],{},"64",[1147,21805,21806,21808,21811],{},[1162,21807,9684],{},[1162,21809,21810],{},"97,00",[1162,21812,2006],{},[1147,21814,21815,21817,21820],{},[1162,21816,3718],{},[1162,21818,21819],{},"99,25",[1162,21821,3718],{},[1147,21823,21824,21826,21828],{},[1162,21825,1550],{},[1162,21827,1550],{},[1162,21829,1550],{},[1147,21831,21832,21834,21837],{},[1162,21833,14477],{},[1162,21835,21836],{},"126,50",[1162,21838,3298],{},[1147,21840,21841,21843,21845],{},[1162,21842,3799],{},[1162,21844,21819],{},[1162,21846,3718],{},[1110,21848,21849,21850,21863,21864,2704,21892,2704,21922,21950,21951,21973,21974,2704,22001,2704,22030,22057,22058,1417],{},"Nejprve se posoudí diagram ",[1115,21851,21853],{"className":21852},[1292],[1294,21854,21855],{"xmlns":1296},[1298,21856,21857,21861],{},[1301,21858,21859],{},[1307,21860,9981],{},[1315,21862,9981],{"encoding":1317}," na všech 20 podskupinách: ",[1115,21865,21867],{"className":21866},[1292],[1294,21868,21869],{"xmlns":1296},[1298,21870,21871,21889],{},[1301,21872,21873,21875,21878,21880,21882,21884,21886],{},[1307,21874,20553],{},[1307,21876,21877],{},"L",[1437,21879,1626],{"stretchy":1625},[1307,21881,9981],{},[1437,21883,1637],{"stretchy":1625},[1437,21885,1733],{},[1311,21887,21888],{},"15,8",[1315,21890,21891],{"encoding":1317},"CL(R)=15{,}8",[1115,21893,21895],{"className":21894},[1292],[1294,21896,21897],{"xmlns":1296},[1298,21898,21899,21919],{},[1301,21900,21901,21904,21906,21908,21910,21912,21914,21916],{},[1307,21902,21903],{},"U",[1307,21905,20553],{},[1307,21907,21877],{},[1437,21909,1626],{"stretchy":1625},[1307,21911,9981],{},[1437,21913,1637],{"stretchy":1625},[1437,21915,1733],{},[1311,21917,21918],{},"36,06",[1315,21920,21921],{"encoding":1317},"UCL(R)=36{,}06",[1115,21923,21925],{"className":21924},[1292],[1294,21926,21927],{"xmlns":1296},[1298,21928,21929,21947],{},[1301,21930,21931,21933,21935,21937,21939,21941,21943,21945],{},[1307,21932,21877],{},[1307,21934,20553],{},[1307,21936,21877],{},[1437,21938,1626],{"stretchy":1625},[1307,21940,9981],{},[1437,21942,1637],{"stretchy":1625},[1437,21944,1733],{},[1311,21946,1313],{},[1315,21948,21949],{"encoding":1317},"LCL(R)=0",". Rozpětí čtvrté podskupiny (",[1115,21952,21954],{"className":21953},[1292],[1294,21955,21956],{"xmlns":1296},[1298,21957,21958,21970],{},[1301,21959,21960,21966,21968],{},[1304,21961,21962,21964],{},[1307,21963,9981],{},[1311,21965,3295],{},[1437,21967,1733],{},[1311,21969,21803],{},[1315,21971,21972],{"encoding":1317},"R_4=64",") mez překračuje; po potvrzení vymezitelné příčiny se podskupina 4 z výpočtu vyřadí a meze se přepočítají — ",[1115,21975,21977],{"className":21976},[1292],[1294,21978,21979],{"xmlns":1296},[1298,21980,21981,21998],{},[1301,21982,21983,21985,21987,21989,21991,21993,21995],{},[1307,21984,20553],{},[1307,21986,21877],{},[1437,21988,1626],{"stretchy":1625},[1307,21990,9981],{},[1437,21992,1637],{"stretchy":1625},[1437,21994,1733],{},[1311,21996,21997],{},"13,26",[1315,21999,22000],{"encoding":1317},"CL(R)=13{,}26",[1115,22002,22004],{"className":22003},[1292],[1294,22005,22006],{"xmlns":1296},[1298,22007,22008,22027],{},[1301,22009,22010,22012,22014,22016,22018,22020,22022,22024],{},[1307,22011,21903],{},[1307,22013,20553],{},[1307,22015,21877],{},[1437,22017,1626],{"stretchy":1625},[1307,22019,9981],{},[1437,22021,1637],{"stretchy":1625},[1437,22023,1733],{},[1311,22025,22026],{},"30,27",[1315,22028,22029],{"encoding":1317},"UCL(R)=30{,}27",[1115,22031,22033],{"className":22032},[1292],[1294,22034,22035],{"xmlns":1296},[1298,22036,22037,22055],{},[1301,22038,22039,22041,22043,22045,22047,22049,22051,22053],{},[1307,22040,21877],{},[1307,22042,20553],{},[1307,22044,21877],{},[1437,22046,1626],{"stretchy":1625},[1307,22048,9981],{},[1437,22050,1637],{"stretchy":1625},[1437,22052,1733],{},[1311,22054,1313],{},[1315,22056,21949],{"encoding":1317},". Diagram rozpětí je teď zvládnutý, lze tedy posoudit diagram ",[1115,22059,22061],{"className":22060},[1292],[1294,22062,22063],{"xmlns":1296},[1298,22064,22065,22073],{},[1301,22066,22067],{},[2475,22068,22069,22071],{"accent":1121},[1307,22070,6476],{},[1437,22072,11217],{},[1315,22074,21322],{"encoding":1317},[1110,22076,21023,22077,22094,22095,2704,22126,2704,22159,22192,22193,22206,22207,2704,22234,2704,22263,22290],{},[1115,22078,22080],{"className":22079},[1292],[1294,22081,22082],{"xmlns":1296},[1298,22083,22084,22092],{},[1301,22085,22086],{},[2475,22087,22088,22090],{"accent":1121},[1307,22089,6476],{},[1437,22091,11217],{},[1315,22093,21322],{"encoding":1317}," bez čtvrté podskupiny dává ",[1115,22096,22098],{"className":22097},[1292],[1294,22099,22100],{"xmlns":1296},[1298,22101,22102,22123],{},[1301,22103,22104,22106,22108,22110,22116,22118,22120],{},[1307,22105,20553],{},[1307,22107,21877],{},[1437,22109,1626],{"stretchy":1625},[2475,22111,22112,22114],{"accent":1121},[1307,22113,6476],{},[1437,22115,11217],{},[1437,22117,1637],{"stretchy":1625},[1437,22119,1733],{},[1311,22121,22122],{},"102,01",[1315,22124,22125],{"encoding":1317},"CL(\\bar{x})=102{,}01",[1115,22127,22129],{"className":22128},[1292],[1294,22130,22131],{"xmlns":1296},[1298,22132,22133,22156],{},[1301,22134,22135,22137,22139,22141,22143,22149,22151,22153],{},[1307,22136,21903],{},[1307,22138,20553],{},[1307,22140,21877],{},[1437,22142,1626],{"stretchy":1625},[2475,22144,22145,22147],{"accent":1121},[1307,22146,6476],{},[1437,22148,11217],{},[1437,22150,1637],{"stretchy":1625},[1437,22152,1733],{},[1311,22154,22155],{},"111,68",[1315,22157,22158],{"encoding":1317},"UCL(\\bar{x})=111{,}68",[1115,22160,22162],{"className":22161},[1292],[1294,22163,22164],{"xmlns":1296},[1298,22165,22166,22189],{},[1301,22167,22168,22170,22172,22174,22176,22182,22184,22186],{},[1307,22169,21877],{},[1307,22171,20553],{},[1307,22173,21877],{},[1437,22175,1626],{"stretchy":1625},[2475,22177,22178,22180],{"accent":1121},[1307,22179,6476],{},[1437,22181,11217],{},[1437,22183,1637],{"stretchy":1625},[1437,22185,1733],{},[1311,22187,22188],{},"92,34",[1315,22190,22191],{"encoding":1317},"LCL(\\bar{x})=92{,}34",". Mez teď překračují průměry podskupin 3 a 19. Po potvrzení vymezitelné příčiny se vyřadí obě najednou a meze diagramu ",[1115,22194,22196],{"className":22195},[1292],[1294,22197,22198],{"xmlns":1296},[1298,22199,22200,22204],{},[1301,22201,22202],{},[1307,22203,9981],{},[1315,22205,9981],{"encoding":1317}," se přepočítají bez podskupin 3, 4 a 19: ",[1115,22208,22210],{"className":22209},[1292],[1294,22211,22212],{"xmlns":1296},[1298,22213,22214,22231],{},[1301,22215,22216,22218,22220,22222,22224,22226,22228],{},[1307,22217,20553],{},[1307,22219,21877],{},[1437,22221,1626],{"stretchy":1625},[1307,22223,9981],{},[1437,22225,1637],{"stretchy":1625},[1437,22227,1733],{},[1311,22229,22230],{},"12,29",[1315,22232,22233],{"encoding":1317},"CL(R)=12{,}29",[1115,22235,22237],{"className":22236},[1292],[1294,22238,22239],{"xmlns":1296},[1298,22240,22241,22260],{},[1301,22242,22243,22245,22247,22249,22251,22253,22255,22257],{},[1307,22244,21903],{},[1307,22246,20553],{},[1307,22248,21877],{},[1437,22250,1626],{"stretchy":1625},[1307,22252,9981],{},[1437,22254,1637],{"stretchy":1625},[1437,22256,1733],{},[1311,22258,22259],{},"28,06",[1315,22261,22262],{"encoding":1317},"UCL(R)=28{,}06",[1115,22264,22266],{"className":22265},[1292],[1294,22267,22268],{"xmlns":1296},[1298,22269,22270,22288],{},[1301,22271,22272,22274,22276,22278,22280,22282,22284,22286],{},[1307,22273,21877],{},[1307,22275,20553],{},[1307,22277,21877],{},[1437,22279,1626],{"stretchy":1625},[1307,22281,9981],{},[1437,22283,1637],{"stretchy":1625},[1437,22285,1733],{},[1311,22287,1313],{},[1315,22289,21949],{"encoding":1317}," — žádná z 17 zbývajících podskupin mez nepřekračuje.",[1110,22292,22293,22294,22311,22312,2704,22343,2704,22376,22409],{},"Konečný diagram ",[1115,22295,22297],{"className":22296},[1292],[1294,22298,22299],{"xmlns":1296},[1298,22300,22301,22309],{},[1301,22302,22303],{},[2475,22304,22305,22307],{"accent":1121},[1307,22306,6476],{},[1437,22308,11217],{},[1315,22310,21322],{"encoding":1317}," na stejných 17 podskupinách má ",[1115,22313,22315],{"className":22314},[1292],[1294,22316,22317],{"xmlns":1296},[1298,22318,22319,22340],{},[1301,22320,22321,22323,22325,22327,22333,22335,22337],{},[1307,22322,20553],{},[1307,22324,21877],{},[1437,22326,1626],{"stretchy":1625},[2475,22328,22329,22331],{"accent":1121},[1307,22330,6476],{},[1437,22332,11217],{},[1437,22334,1637],{"stretchy":1625},[1437,22336,1733],{},[1311,22338,22339],{},"99,76",[1315,22341,22342],{"encoding":1317},"CL(\\bar{x})=99{,}76",[1115,22344,22346],{"className":22345},[1292],[1294,22347,22348],{"xmlns":1296},[1298,22349,22350,22373],{},[1301,22351,22352,22354,22356,22358,22360,22366,22368,22370],{},[1307,22353,21903],{},[1307,22355,20553],{},[1307,22357,21877],{},[1437,22359,1626],{"stretchy":1625},[2475,22361,22362,22364],{"accent":1121},[1307,22363,6476],{},[1437,22365,11217],{},[1437,22367,1637],{"stretchy":1625},[1437,22369,1733],{},[1311,22371,22372],{},"108,73",[1315,22374,22375],{"encoding":1317},"UCL(\\bar{x})=108{,}73",[1115,22377,22379],{"className":22378},[1292],[1294,22380,22381],{"xmlns":1296},[1298,22382,22383,22406],{},[1301,22384,22385,22387,22389,22391,22393,22399,22401,22403],{},[1307,22386,21877],{},[1307,22388,20553],{},[1307,22390,21877],{},[1437,22392,1626],{"stretchy":1625},[2475,22394,22395,22397],{"accent":1121},[1307,22396,6476],{},[1437,22398,11217],{},[1437,22400,1637],{"stretchy":1625},[1437,22402,1733],{},[1311,22404,22405],{},"90,80",[1315,22407,22408],{"encoding":1317},"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.",[1110,22411,22412],{},[4137,22413],{"alt":22414,"className":22415,"src":22416},"mask-rd-priklad1-meze",[1130,4141],"\u002Fwiki-assets\u002Fmask-rd-priklad1-meze.png",[1110,22418,22419,22420,22422,22423,22425],{},"V R se diagramy sestrojí funkcí ",[3223,22421,21326],{}," z balíčku ",[3223,22424,360],{},". Data jsou tabulka, v níž řádek odpovídá logické podskupině a sloupce jednotlivým měřením:",[3447,22427,22429],{"className":3449,"code":22428,"language":71,"meta":1229,"style":1229},"library(qcc)\ndata \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"R\")      # diagram R\nqcc(data, type = \"xbar\")   # diagram x̄\n",[3223,22430,22431,22441,22464,22487],{"__ignoreMap":1229},[1115,22432,22433,22435,22437,22439],{"class":3455,"line":10},[1115,22434,17154],{"class":3462},[1115,22436,1626],{"class":3470},[1115,22438,360],{"class":3458},[1115,22440,3655],{"class":3470},[1115,22442,22443,22445,22447,22449,22451,22454,22456,22458,22460,22462],{"class":3455,"line":27},[1115,22444,19865],{"class":3458},[1115,22446,3463],{"class":3462},[1115,22448,19870],{"class":3466},[1115,22450,1626],{"class":3470},[1115,22452,22453],{"class":3594},"\"3_2.txt\"",[1115,22455,1547],{"class":3462},[1115,22457,19880],{"class":3458},[1115,22459,3551],{"class":3462},[1115,22461,3564],{"class":3478},[1115,22463,3655],{"class":3470},[1115,22465,22466,22468,22470,22472,22474,22476,22478,22481,22484],{"class":3455,"line":148},[1115,22467,360],{"class":3466},[1115,22469,1626],{"class":3470},[1115,22471,19865],{"class":3458},[1115,22473,1547],{"class":3462},[1115,22475,11981],{"class":3458},[1115,22477,3551],{"class":3462},[1115,22479,22480],{"class":3594}," \"R\"",[1115,22482,22483],{"class":3470},")      ",[1115,22485,22486],{"class":11791},"# diagram R\n",[1115,22488,22489,22491,22493,22495,22497,22499,22501,22504,22506],{"class":3455,"line":111},[1115,22490,360],{"class":3466},[1115,22492,1626],{"class":3470},[1115,22494,19865],{"class":3458},[1115,22496,1547],{"class":3462},[1115,22498,11981],{"class":3458},[1115,22500,3551],{"class":3462},[1115,22502,22503],{"class":3594}," \"xbar\"",[1115,22505,11788],{"class":3470},[1115,22507,22508],{"class":11791},"# diagram x̄\n",[1110,22510,22511,22512,22515],{},"Funkce vykreslí diagram se střední přímkou a akčními mezemi a body mimo meze zvýrazní. Podskupina s potvrzenou vymezitelnou příčinou se vyřadí z dat (například ",[3223,22513,22514],{},"data[-4, ]",") a diagram se sestrojí znovu.",[16505,22517,21023,22519],{"id":22518},"diagram-xˉsbarx-s",[1115,22520,22522],{"className":22521},[1292],[1294,22523,22524],{"xmlns":1296},[1298,22525,22526,22542],{},[1301,22527,22528,22530,22536,22538,22540],{},[1437,22529,1626],{"stretchy":1625},[2475,22531,22532,22534],{"accent":1121},[1307,22533,6476],{},[1437,22535,11217],{},[1437,22537,1547],{"separator":1121},[1307,22539,1605],{},[1437,22541,1637],{"stretchy":1625},[1315,22543,20432],{"encoding":1317},[1110,22545,21051,22546,22567,22568,22586,22587,22612],{},[1115,22547,22549],{"className":22548},[1292],[1294,22550,22551],{"xmlns":1296},[1298,22552,22553,22565],{},[1301,22554,22555],{},[1304,22556,22557,22563],{},[2475,22558,22559,22561],{"accent":1121},[1307,22560,6476],{},[1437,22562,11217],{},[1307,22564,1629],{},[1315,22566,21073],{"encoding":1317}," a výběrové směrodatné odchylky ",[1115,22569,22571],{"className":22570},[1292],[1294,22572,22573],{"xmlns":1296},[1298,22574,22575,22583],{},[1301,22576,22577],{},[1304,22578,22579,22581],{},[1307,22580,1605],{},[1307,22582,1629],{},[1315,22584,22585],{"encoding":1317},"s_i"," v logických podskupinách. Podmínky použití jsou stejné jako u ",[1115,22588,22590],{"className":22589},[1292],[1294,22591,22592],{"xmlns":1296},[1298,22593,22594,22610],{},[1301,22595,22596,22598,22604,22606,22608],{},[1437,22597,1626],{"stretchy":1625},[2475,22599,22600,22602],{"accent":1121},[1307,22601,6476],{},[1437,22603,11217],{},[1437,22605,1547],{"separator":1121},[1307,22607,9981],{},[1437,22609,1637],{"stretchy":1625},[1315,22611,20406],{"encoding":1317},", logické podskupiny ale sestávají z většího počtu měření. Data se zapisují do obdobné tabulky.",[3447,22614,22616],{"className":3449,"code":22615,"language":71,"meta":1229,"style":1229},"data \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"S\")      # diagram s\nqcc(data, type = \"xbar\")   # diagram x̄\n",[3223,22617,22618,22640,22662],{"__ignoreMap":1229},[1115,22619,22620,22622,22624,22626,22628,22630,22632,22634,22636,22638],{"class":3455,"line":10},[1115,22621,19865],{"class":3458},[1115,22623,3463],{"class":3462},[1115,22625,19870],{"class":3466},[1115,22627,1626],{"class":3470},[1115,22629,22453],{"class":3594},[1115,22631,1547],{"class":3462},[1115,22633,19880],{"class":3458},[1115,22635,3551],{"class":3462},[1115,22637,3564],{"class":3478},[1115,22639,3655],{"class":3470},[1115,22641,22642,22644,22646,22648,22650,22652,22654,22657,22659],{"class":3455,"line":27},[1115,22643,360],{"class":3466},[1115,22645,1626],{"class":3470},[1115,22647,19865],{"class":3458},[1115,22649,1547],{"class":3462},[1115,22651,11981],{"class":3458},[1115,22653,3551],{"class":3462},[1115,22655,22656],{"class":3594}," \"S\"",[1115,22658,22483],{"class":3470},[1115,22660,22661],{"class":11791},"# diagram s\n",[1115,22663,22664,22666,22668,22670,22672,22674,22676,22678,22680],{"class":3455,"line":148},[1115,22665,360],{"class":3466},[1115,22667,1626],{"class":3470},[1115,22669,19865],{"class":3458},[1115,22671,1547],{"class":3462},[1115,22673,11981],{"class":3458},[1115,22675,3551],{"class":3462},[1115,22677,22503],{"class":3594},[1115,22679,11788],{"class":3470},[1115,22681,22508],{"class":11791},[16505,22683,21023,22685],{"id":22684},"diagram-xirklix_i-r_kli",[1115,22686,22688],{"className":22687},[1292],[1294,22689,22690],{"xmlns":1296},[1298,22691,22692,22720],{},[1301,22693,22694,22696,22702,22704,22718],{},[1437,22695,1626],{"stretchy":1625},[1304,22697,22698,22700],{},[1307,22699,6476],{},[1307,22701,1629],{},[1437,22703,1547],{"separator":1121},[1304,22705,22706,22708],{},[1307,22707,9981],{},[1301,22709,22710,22712,22714,22716],{},[1307,22711,7016],{},[1307,22713,20462],{},[1437,22715,1547],{"separator":1121},[1307,22717,1629],{},[1437,22719,1637],{"stretchy":1625},[1315,22721,20471],{"encoding":1317},[1110,22723,22724,22725,22750,22751,1709],{},"Používá se za stejných podmínek jako ",[1115,22726,22728],{"className":22727},[1292],[1294,22729,22730],{"xmlns":1296},[1298,22731,22732,22748],{},[1301,22733,22734,22736,22742,22744,22746],{},[1437,22735,1626],{"stretchy":1625},[2475,22737,22738,22740],{"accent":1121},[1307,22739,6476],{},[1437,22741,11217],{},[1437,22743,1547],{"separator":1121},[1307,22745,9981],{},[1437,22747,1637],{"stretchy":1625},[1315,22749,20406],{"encoding":1317},", 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 ",[1279,22752,22753],{},"klouzavé rozpětí",[1115,22755,22757],{"className":22756},[1292],[1294,22758,22759],{"xmlns":1296,"display":1715},[1298,22760,22761,22888],{},[1301,22762,22763,22777,22779,22782,22788,22790,22802,22804,22806,22808,22810,22812,22814,22816,22818,22820,22822,22824,22826,22828,22830,22844,22846,22858,22872,22886],{},[1304,22764,22765,22767],{},[1307,22766,9981],{},[1301,22768,22769,22771,22773,22775],{},[1307,22770,7016],{},[1307,22772,20462],{},[1437,22774,1547],{"separator":1121},[1307,22776,1629],{},[1437,22778,1733],{},[1307,22780,22781],{"mathvariant":1872},"∣",[1304,22783,22784,22786],{},[1307,22785,6476],{},[1307,22787,1629],{},[1437,22789,2817],{},[1304,22791,22792,22794],{},[1307,22793,6476],{},[1301,22795,22796,22798,22800],{},[1307,22797,1629],{},[1437,22799,2817],{},[1311,22801,1544],{},[1307,22803,22781],{"mathvariant":1872},[1437,22805,1547],{"separator":1121},[1763,22807],{"width":17775},[1307,22809,1629],{},[1437,22811,1733],{},[1311,22813,1337],{},[1437,22815,1547],{"separator":1121},[1311,22817,3345],{},[1437,22819,1547],{"separator":1121},[1437,22821,1550],{},[1437,22823,1547],{"separator":1121},[1307,22825,7016],{},[1437,22827,1547],{"separator":1121},[1763,22829],{"width":1765},[1304,22831,22832,22838],{},[2475,22833,22834,22836],{"accent":1121},[1307,22835,9981],{},[1437,22837,11217],{},[1301,22839,22840,22842],{},[1307,22841,7016],{},[1307,22843,20462],{},[1437,22845,1733],{},[2491,22847,22848,22850],{},[1311,22849,1544],{},[1301,22851,22852,22854,22856],{},[1307,22853,7016],{},[1437,22855,2817],{},[1311,22857,1544],{},[1735,22859,22860,22862,22870],{},[1437,22861,1739],{},[1301,22863,22864,22866,22868],{},[1307,22865,1629],{},[1437,22867,1733],{},[1311,22869,1337],{},[1307,22871,7016],{},[1304,22873,22874,22876],{},[1307,22875,9981],{},[1301,22877,22878,22880,22882,22884],{},[1307,22879,7016],{},[1307,22881,20462],{},[1437,22883,1547],{"separator":1121},[1307,22885,1629],{},[1307,22887,1417],{"mathvariant":1872},[1315,22889,22890],{"encoding":1317},"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}.",[1110,22892,22893,22894,5495,22911,22937,22938,22963,22964,22981],{},"Regulované veličiny jsou hodnoty ",[1115,22895,22897],{"className":22896},[1292],[1294,22898,22899],{"xmlns":1296},[1298,22900,22901,22909],{},[1301,22902,22903],{},[1304,22904,22905,22907],{},[1307,22906,6476],{},[1307,22908,1629],{},[1315,22910,16891],{"encoding":1317},[1115,22912,22914],{"className":22913},[1292],[1294,22915,22916],{"xmlns":1296},[1298,22917,22918,22934],{},[1301,22919,22920],{},[1304,22921,22922,22924],{},[1307,22923,9981],{},[1301,22925,22926,22928,22930,22932],{},[1307,22927,7016],{},[1307,22929,20462],{},[1437,22931,1547],{"separator":1121},[1307,22933,1629],{},[1315,22935,22936],{"encoding":1317},"R_{kl,i}","; nejdříve se určí střední přímka a meze diagramu ",[1115,22939,22941],{"className":22940},[1292],[1294,22942,22943],{"xmlns":1296},[1298,22944,22945,22961],{},[1301,22946,22947],{},[1304,22948,22949,22951],{},[1307,22950,9981],{},[1301,22952,22953,22955,22957,22959],{},[1307,22954,7016],{},[1307,22956,20462],{},[1437,22958,1547],{"separator":1121},[1307,22960,1629],{},[1315,22962,22936],{"encoding":1317},", potom diagramu ",[1115,22965,22967],{"className":22966},[1292],[1294,22968,22969],{"xmlns":1296},[1298,22970,22971,22979],{},[1301,22972,22973],{},[1304,22974,22975,22977],{},[1307,22976,6476],{},[1307,22978,1629],{},[1315,22980,16891],{"encoding":1317},". Data jsou jeden vektor naměřených hodnot:",[3447,22983,22985],{"className":3449,"code":22984,"language":71,"meta":1229,"style":1229},"data \u003C- read.table(\"3_3.txt\", header = TRUE)\nqcc(data[, 1], type = \"xbar.one\")\n",[3223,22986,22987,23010],{"__ignoreMap":1229},[1115,22988,22989,22991,22993,22995,22997,23000,23002,23004,23006,23008],{"class":3455,"line":10},[1115,22990,19865],{"class":3458},[1115,22992,3463],{"class":3462},[1115,22994,19870],{"class":3466},[1115,22996,1626],{"class":3470},[1115,22998,22999],{"class":3594},"\"3_3.txt\"",[1115,23001,1547],{"class":3462},[1115,23003,19880],{"class":3458},[1115,23005,3551],{"class":3462},[1115,23007,3564],{"class":3478},[1115,23009,3655],{"class":3470},[1115,23011,23012,23014,23016,23018,23020,23022,23024,23026,23028,23030,23032,23035],{"class":3455,"line":27},[1115,23013,360],{"class":3466},[1115,23015,1626],{"class":3470},[1115,23017,19865],{"class":3458},[1115,23019,7933],{"class":3470},[1115,23021,1547],{"class":3462},[1115,23023,4395],{"class":3478},[1115,23025,7950],{"class":3470},[1115,23027,1547],{"class":3462},[1115,23029,11981],{"class":3458},[1115,23031,3551],{"class":3462},[1115,23033,23034],{"class":3594}," \"xbar.one\"",[1115,23036,3655],{"class":3470},[1136,23038,23040],{"id":23039},"regulace-srovnáváním","Regulace srovnáváním",[1110,23042,23043],{},"Diagramy pro regulaci srovnáváním se používají, sledují-li se počty neshodných produktů nebo počty neshod na produktech — regulovaná veličina je diskrétní náhodná veličina.",[1141,23045,23046,23059],{},[1144,23047,23048],{},[1147,23049,23050,23053,23056],{},[1150,23051,23052],{},"Sleduje se",[1150,23054,23055],{},"Konstantní rozsah podskupin",[1150,23057,23058],{},"Nekonstantní rozsah podskupin",[1157,23060,23061,23096],{},[1147,23062,23063,23066,23081],{},[1162,23064,23065],{},"počet neshod na produktech (např. vady na stejných tabulích skla)",[1162,23067,23068],{},[1115,23069,23071],{"className":23070},[1292],[1294,23072,23073],{"xmlns":1296},[1298,23074,23075,23079],{},[1301,23076,23077],{},[1307,23078,3473],{},[1315,23080,3473],{"encoding":1317},[1162,23082,23083],{},[1115,23084,23086],{"className":23085},[1292],[1294,23087,23088],{"xmlns":1296},[1298,23089,23090,23094],{},[1301,23091,23092],{},[1307,23093,11286],{},[1315,23095,11286],{"encoding":1317},[1147,23097,23098,23101,23118],{},[1162,23099,23100],{},"počet neshodných produktů ve výběru (např. neshodné kusy ze série na výrobní lince)",[1162,23102,23103],{},[1115,23104,23106],{"className":23105},[1292],[1294,23107,23108],{"xmlns":1296},[1298,23109,23110,23116],{},[1301,23111,23112,23114],{},[1307,23113,1435],{},[1307,23115,1110],{},[1315,23117,20518],{"encoding":1317},[1162,23119,23120],{},[1115,23121,23123],{"className":23122},[1292],[1294,23124,23125],{"xmlns":1296},[1298,23126,23127,23131],{},[1301,23128,23129],{},[1307,23130,1110],{},[1315,23132,1110],{"encoding":1317},[16505,23134,21023,23136],{"id":23135},"diagram-cc",[1115,23137,23139],{"className":23138},[1292],[1294,23140,23141],{"xmlns":1296},[1298,23142,23143,23147],{},[1301,23144,23145],{},[1307,23146,3473],{},[1315,23148,3473],{"encoding":1317},[1110,23150,23151,23152,23170,23171,23184,23185,23210,23211,23224],{},"Regulovanou veličinou ",[1115,23153,23155],{"className":23154},[1292],[1294,23156,23157],{"xmlns":1296},[1298,23158,23159,23167],{},[1301,23160,23161],{},[1304,23162,23163,23165],{},[1307,23164,3473],{},[1307,23166,1629],{},[1315,23168,23169],{"encoding":1317},"c_i"," je počet neshod na produktech v ",[1115,23172,23174],{"className":23173},[1292],[1294,23175,23176],{"xmlns":1296},[1298,23177,23178,23182],{},[1301,23179,23180],{},[1307,23181,1629],{},[1315,23183,1629],{"encoding":1317},"-té logické podskupině, ",[1115,23186,23188],{"className":23187},[1292],[1294,23189,23190],{"xmlns":1296},[1298,23191,23192,23208],{},[1301,23193,23194,23196,23198,23200,23202,23204,23206],{},[1307,23195,1629],{},[1437,23197,1733],{},[1311,23199,1544],{},[1437,23201,1547],{"separator":1121},[1437,23203,1550],{},[1437,23205,1547],{"separator":1121},[1307,23207,7016],{},[1315,23209,21236],{"encoding":1317},"; v každé podskupině je stejný počet ",[1115,23212,23214],{"className":23213},[1292],[1294,23215,23216],{"xmlns":1296},[1298,23217,23218,23222],{},[1301,23219,23220],{},[1307,23221,1435],{},[1315,23223,1435],{"encoding":1317}," 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.",[1103,23226,23228,23235],{"className":23227,"dataCallout":3230},[1106,3229],[1110,23229,23231,23234],{"className":23230},[1113],[1115,23232],{"className":23233,"ariaHidden":1121},[1118,3237,1120],"Příklad: bodové vady na pásech látky",[1110,23236,23237,23238,23255,23256,1417],{},"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 ",[1115,23239,23241],{"className":23240},[1292],[1294,23242,23243],{"xmlns":1296},[1298,23244,23245,23253],{},[1301,23246,23247],{},[1304,23248,23249,23251],{},[1307,23250,3473],{},[1307,23252,1629],{},[1315,23254,23169],{"encoding":1317},". Sestrojte regulační diagram ",[1115,23257,23259],{"className":23258},[1292],[1294,23260,23261],{"xmlns":1296},[1298,23262,23263,23267],{},[1301,23264,23265],{},[1307,23266,3473],{},[1315,23268,3473],{"encoding":1317},[3447,23270,23272],{"className":3449,"code":23271,"language":71,"meta":1229,"style":1229},"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",[3223,23273,23274,23364,23368,23393],{"__ignoreMap":1229},[1115,23275,23276,23278,23280,23282,23284,23286,23288,23290,23292,23294,23296,23298,23300,23302,23304,23306,23308,23310,23312,23314,23316,23318,23320,23322,23324,23326,23328,23330,23332,23334,23336,23338,23340,23342,23344,23346,23348,23350,23352,23354,23356,23358,23360,23362],{"class":3455,"line":10},[1115,23277,23169],{"class":3458},[1115,23279,3463],{"class":3462},[1115,23281,3589],{"class":3466},[1115,23283,1626],{"class":3470},[1115,23285,13088],{"class":3478},[1115,23287,1547],{"class":3462},[1115,23289,4395],{"class":3478},[1115,23291,1547],{"class":3462},[1115,23293,3934],{"class":3478},[1115,23295,1547],{"class":3462},[1115,23297,9752],{"class":3478},[1115,23299,1547],{"class":3462},[1115,23301,9728],{"class":3478},[1115,23303,1547],{"class":3462},[1115,23305,11986],{"class":3478},[1115,23307,1547],{"class":3462},[1115,23309,3934],{"class":3478},[1115,23311,1547],{"class":3462},[1115,23313,9728],{"class":3478},[1115,23315,1547],{"class":3462},[1115,23317,3554],{"class":3478},[1115,23319,1547],{"class":3462},[1115,23321,3554],{"class":3478},[1115,23323,1547],{"class":3462},[1115,23325,11986],{"class":3478},[1115,23327,1547],{"class":3462},[1115,23329,10613],{"class":3478},[1115,23331,1547],{"class":3462},[1115,23333,10613],{"class":3478},[1115,23335,1547],{"class":3462},[1115,23337,10613],{"class":3478},[1115,23339,1547],{"class":3462},[1115,23341,4395],{"class":3478},[1115,23343,1547],{"class":3462},[1115,23345,11986],{"class":3478},[1115,23347,1547],{"class":3462},[1115,23349,10613],{"class":3478},[1115,23351,1547],{"class":3462},[1115,23353,4395],{"class":3478},[1115,23355,1547],{"class":3462},[1115,23357,9752],{"class":3478},[1115,23359,1547],{"class":3462},[1115,23361,11986],{"class":3478},[1115,23363,3655],{"class":3470},[1115,23365,23366],{"class":3455,"line":27},[1115,23367,9799],{"emptyLinePlaceholder":1238},[1115,23369,23370,23373,23375,23378,23380,23382,23384,23386,23388,23391],{"class":3455,"line":148},[1115,23371,23372],{"class":3458},"q_c",[1115,23374,3463],{"class":3462},[1115,23376,23377],{"class":3466}," qcc",[1115,23379,1626],{"class":3470},[1115,23381,23169],{"class":3458},[1115,23383,1547],{"class":3462},[1115,23385,11981],{"class":3458},[1115,23387,3551],{"class":3462},[1115,23389,23390],{"class":3594}," \"c\"",[1115,23392,3655],{"class":3470},[1115,23394,23395,23397,23399,23401],{"class":3455,"line":111},[1115,23396,1249],{"class":3466},[1115,23398,1626],{"class":3470},[1115,23400,23372],{"class":3458},[1115,23402,3655],{"class":3470},[3447,23404,23407],{"className":23405,"code":23406,"language":3677,"meta":1229},[3675],"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",[3223,23408,23406],{"__ignoreMap":1229},[1110,23410,23411,23412,23441,23442,23465,23466,23488],{},"Průměrný počet vad na pás je ",[1115,23413,23415],{"className":23414},[1292],[1294,23416,23417],{"xmlns":1296},[1298,23418,23419,23438],{},[1301,23420,23421,23423,23425,23427,23433,23435],{},[1307,23422,20553],{},[1307,23424,21877],{},[1437,23426,1733],{},[2475,23428,23429,23431],{"accent":1121},[1307,23430,3473],{},[1437,23432,11217],{},[1437,23434,1733],{},[1311,23436,23437],{},"3,4",[1315,23439,23440],{"encoding":1317},"CL = \\bar{c} = 3{,}4",", horní mez ",[1115,23443,23445],{"className":23444},[1292],[1294,23446,23447],{"xmlns":1296},[1298,23448,23449,23462],{},[1301,23450,23451,23453,23455,23457,23459],{},[1307,23452,21903],{},[1307,23454,20553],{},[1307,23456,21877],{},[1437,23458,1733],{},[1311,23460,23461],{},"8,93",[1315,23463,23464],{"encoding":1317},"UCL = 8{,}93"," a dolní mez ",[1115,23467,23469],{"className":23468},[1292],[1294,23470,23471],{"xmlns":1296},[1298,23472,23473,23485],{},[1301,23474,23475,23477,23479,23481,23483],{},[1307,23476,21877],{},[1307,23478,20553],{},[1307,23480,21877],{},[1437,23482,1733],{},[1311,23484,1313],{},[1315,23486,23487],{"encoding":1317},"LCL = 0",". Žádný pás meze nepřekračuje — proces je zvládnutý.",[1110,23490,23491],{},[4137,23492],{"alt":23493,"className":23494,"src":23495},"mask-rd-priklad2-c",[1130,4141],"\u002Fwiki-assets\u002Fmask-rd-priklad2-c.png",[16505,23497,21023,23499],{"id":23498},"diagram-uu",[1115,23500,23502],{"className":23501},[1292],[1294,23503,23504],{"xmlns":1296},[1298,23505,23506,23510],{},[1301,23507,23508],{},[1307,23509,11286],{},[1315,23511,11286],{"encoding":1317},[1110,23513,23151,23514,23548,23549,23567],{},[1115,23515,23517],{"className":23516},[1292],[1294,23518,23519],{"xmlns":1296},[1298,23520,23521,23545],{},[1301,23522,23523,23529,23531,23537,23539],{},[1304,23524,23525,23527],{},[1307,23526,11286],{},[1307,23528,1629],{},[1437,23530,1733],{},[1304,23532,23533,23535],{},[1307,23534,3473],{},[1307,23536,1629],{},[1307,23538,4358],{"mathvariant":1872},[1304,23540,23541,23543],{},[1307,23542,1435],{},[1307,23544,1629],{},[1315,23546,23547],{"encoding":1317},"u_i = c_i\u002Fn_i"," je průměrný počet neshod přepočítaný na jeden produkt z logické podskupiny; rozsah podskupin ",[1115,23550,23552],{"className":23551},[1292],[1294,23553,23554],{"xmlns":1296},[1298,23555,23556,23564],{},[1301,23557,23558],{},[1304,23559,23560,23562],{},[1307,23561,1435],{},[1307,23563,1629],{},[1315,23565,23566],{"encoding":1317},"n_i"," není konstantní, a proto se bod od bodu mění i meze.",[1110,23569,23570,23571,23574],{},"Za ",[3223,23572,23573],{},"sizes"," se dosadí vektor rozsahů jednotlivých logických podskupin, resp. rozměr jejich jednotek:",[3447,23576,23578],{"className":3449,"code":23577,"language":71,"meta":1229,"style":1229},"data \u003C- read.table(\"3_4.txt\", header = TRUE)   # počty suků a rozměry prken\nqcc(data[, 1], type = \"u\", sizes = data[, 2])\n",[3223,23579,23580,23606],{"__ignoreMap":1229},[1115,23581,23582,23584,23586,23588,23590,23593,23595,23597,23599,23601,23603],{"class":3455,"line":10},[1115,23583,19865],{"class":3458},[1115,23585,3463],{"class":3462},[1115,23587,19870],{"class":3466},[1115,23589,1626],{"class":3470},[1115,23591,23592],{"class":3594},"\"3_4.txt\"",[1115,23594,1547],{"class":3462},[1115,23596,19880],{"class":3458},[1115,23598,3551],{"class":3462},[1115,23600,3564],{"class":3478},[1115,23602,11788],{"class":3470},[1115,23604,23605],{"class":11791},"# počty suků a rozměry prken\n",[1115,23607,23608,23610,23612,23614,23616,23618,23620,23622,23624,23626,23628,23631,23633,23636,23638,23640,23642,23644,23646],{"class":3455,"line":27},[1115,23609,360],{"class":3466},[1115,23611,1626],{"class":3470},[1115,23613,19865],{"class":3458},[1115,23615,7933],{"class":3470},[1115,23617,1547],{"class":3462},[1115,23619,4395],{"class":3478},[1115,23621,7950],{"class":3470},[1115,23623,1547],{"class":3462},[1115,23625,11981],{"class":3458},[1115,23627,3551],{"class":3462},[1115,23629,23630],{"class":3594}," \"u\"",[1115,23632,1547],{"class":3462},[1115,23634,23635],{"class":3458}," sizes",[1115,23637,3551],{"class":3462},[1115,23639,19924],{"class":3458},[1115,23641,7933],{"class":3470},[1115,23643,1547],{"class":3462},[1115,23645,3934],{"class":3478},[1115,23647,23648],{"class":3470},"])\n",[16505,23650,21023,23652],{"id":23651},"diagram-npnp",[1115,23653,23655],{"className":23654},[1292],[1294,23656,23657],{"xmlns":1296},[1298,23658,23659,23665],{},[1301,23660,23661,23663],{},[1307,23662,1435],{},[1307,23664,1110],{},[1315,23666,20518],{"encoding":1317},[1110,23668,23669,23670,6537,23685,23698],{},"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 ",[1115,23671,23673],{"className":23672},[1292],[1294,23674,23675],{"xmlns":1296},[1298,23676,23677,23683],{},[1301,23678,23679,23681],{},[1307,23680,1435],{},[1307,23682,1110],{},[1315,23684,20518],{"encoding":1317},[1115,23686,23688],{"className":23687},[1292],[1294,23689,23690],{"xmlns":1296},[1298,23691,23692,23696],{},[1301,23693,23694],{},[1307,23695,1110],{},[1315,23697,1110],{"encoding":1317}," je pravděpodobnost, že vyrobený produkt je neshodný.",[1110,23700,23701,23702,1709],{},"Pro konstantní rozsah ",[1115,23703,23705],{"className":23704},[1292],[1294,23706,23707],{"xmlns":1296},[1298,23708,23709,23713],{},[1301,23710,23711],{},[1307,23712,1435],{},[1315,23714,1435],{"encoding":1317},[3447,23716,23718],{"className":3449,"code":23717,"language":71,"meta":1229,"style":1229},"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",[3223,23719,23720,23746],{"__ignoreMap":1229},[1115,23721,23722,23724,23726,23728,23730,23733,23735,23737,23739,23741,23743],{"class":3455,"line":10},[1115,23723,19865],{"class":3458},[1115,23725,3463],{"class":3462},[1115,23727,19870],{"class":3466},[1115,23729,1626],{"class":3470},[1115,23731,23732],{"class":3594},"\"3_7.txt\"",[1115,23734,1547],{"class":3462},[1115,23736,19880],{"class":3458},[1115,23738,3551],{"class":3462},[1115,23740,3564],{"class":3478},[1115,23742,11788],{"class":3470},[1115,23744,23745],{"class":11791},"# počty vadných tabletů v sériích po 100 kusech\n",[1115,23747,23748,23750,23752,23754,23756,23758,23760,23762,23764,23766,23768,23771,23773,23775,23777,23779],{"class":3455,"line":27},[1115,23749,360],{"class":3466},[1115,23751,1626],{"class":3470},[1115,23753,19865],{"class":3458},[1115,23755,7933],{"class":3470},[1115,23757,1547],{"class":3462},[1115,23759,4395],{"class":3478},[1115,23761,7950],{"class":3470},[1115,23763,1547],{"class":3462},[1115,23765,11981],{"class":3458},[1115,23767,3551],{"class":3462},[1115,23769,23770],{"class":3594}," \"np\"",[1115,23772,1547],{"class":3462},[1115,23774,23635],{"class":3458},[1115,23776,3551],{"class":3462},[1115,23778,15097],{"class":3478},[1115,23780,3655],{"class":3470},[16505,23782,21023,23784],{"id":23783},"diagram-pp",[1115,23785,23787],{"className":23786},[1292],[1294,23788,23789],{"xmlns":1296},[1298,23790,23791,23795],{},[1301,23792,23793],{},[1307,23794,1110],{},[1315,23796,1110],{"encoding":1317},[1110,23798,23799,23800,23836],{},"Regulovanou veličinou je počet neshodných produktů v logické podskupině přepočtený na jednotku, ",[1115,23801,23803],{"className":23802},[1292],[1294,23804,23805],{"xmlns":1296},[1298,23806,23807,23833],{},[1301,23808,23809,23815,23817,23819,23825,23827],{},[1304,23810,23811,23813],{},[1307,23812,1110],{},[1307,23814,1629],{},[1437,23816,1733],{},[1307,23818,1435],{},[1304,23820,23821,23823],{},[1307,23822,1110],{},[1307,23824,1629],{},[1307,23826,4358],{"mathvariant":1872},[1304,23828,23829,23831],{},[1307,23830,1435],{},[1307,23832,1629],{},[1315,23834,23835],{"encoding":1317},"p_i = np_i\u002Fn_i","; rozsahy podskupin nemusí být konstantní.",[1110,23838,23570,23839,23841],{},[3223,23840,23573],{}," se dosadí vektor rozsahů logických podskupin:",[3447,23843,23845],{"className":3449,"code":23844,"language":71,"meta":1229,"style":1229},"data \u003C- read.table(\"3_6.txt\", header = TRUE)   # počty vadných tabletů a rozsahy sérií\nqcc(data[, 1], type = \"p\", sizes = data[, 2])\n",[3223,23846,23847,23873],{"__ignoreMap":1229},[1115,23848,23849,23851,23853,23855,23857,23860,23862,23864,23866,23868,23870],{"class":3455,"line":10},[1115,23850,19865],{"class":3458},[1115,23852,3463],{"class":3462},[1115,23854,19870],{"class":3466},[1115,23856,1626],{"class":3470},[1115,23858,23859],{"class":3594},"\"3_6.txt\"",[1115,23861,1547],{"class":3462},[1115,23863,19880],{"class":3458},[1115,23865,3551],{"class":3462},[1115,23867,3564],{"class":3478},[1115,23869,11788],{"class":3470},[1115,23871,23872],{"class":11791},"# počty vadných tabletů a rozsahy sérií\n",[1115,23874,23875,23877,23879,23881,23883,23885,23887,23889,23891,23893,23895,23898,23900,23902,23904,23906,23908,23910,23912],{"class":3455,"line":27},[1115,23876,360],{"class":3466},[1115,23878,1626],{"class":3470},[1115,23880,19865],{"class":3458},[1115,23882,7933],{"class":3470},[1115,23884,1547],{"class":3462},[1115,23886,4395],{"class":3478},[1115,23888,7950],{"class":3470},[1115,23890,1547],{"class":3462},[1115,23892,11981],{"class":3458},[1115,23894,3551],{"class":3462},[1115,23896,23897],{"class":3594}," \"p\"",[1115,23899,1547],{"class":3462},[1115,23901,23635],{"class":3458},[1115,23903,3551],{"class":3462},[1115,23905,19924],{"class":3458},[1115,23907,7933],{"class":3470},[1115,23909,1547],{"class":3462},[1115,23911,3934],{"class":3478},[1115,23913,23648],{"class":3470},[1136,23915,23917],{"id":23916},"indexy-způsobilosti","Indexy způsobilosti",[1110,23919,23920,23921,23940,23941,23959],{},"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 ",[1115,23922,23924],{"className":23923},[1292],[1294,23925,23926],{"xmlns":1296},[1298,23927,23928,23937],{},[1301,23929,23930,23932,23935],{},[1307,23931,21877],{},[1307,23933,23934],{},"S",[1307,23936,21877],{},[1315,23938,23939],{"encoding":1317},"LSL"," a horní meze ",[1115,23942,23944],{"className":23943},[1292],[1294,23945,23946],{"xmlns":1296},[1298,23947,23948,23956],{},[1301,23949,23950,23952,23954],{},[1307,23951,21903],{},[1307,23953,23934],{},[1307,23955,21877],{},[1315,23957,23958],{"encoding":1317},"USL",". Způsobilost se zkoumá až pro proces, který je podle regulačních diagramů statisticky zvládnutý (třetí fáze regulace).",[16505,23961,23963,23980],{"id":23962},"cpc_p-index-způsobilosti",[1115,23964,23966],{"className":23965},[1292],[1294,23967,23968],{"xmlns":1296},[1298,23969,23970,23978],{},[1301,23971,23972],{},[1304,23973,23974,23976],{},[1307,23975,20553],{},[1307,23977,1110],{},[1315,23979,20558],{"encoding":1317}," — index způsobilosti",[1110,23982,23983,23984,1709],{},"Podíl mezi délkou tolerančního intervalu a délkou intervalu, ve kterém by za normálního rozdělení mělo ležet skoro všech 99,73 % hodnot znaku, tedy ",[1115,23985,23987],{"className":23986},[1292],[1294,23988,23989],{"xmlns":1296},[1298,23990,23991,23997],{},[1301,23992,23993,23995],{},[1311,23994,3718],{},[1307,23996,6655],{},[1315,23998,23999],{"encoding":1317},"6\\sigma",[1115,24001,24003],{"className":24002},[1292],[1294,24004,24005],{"xmlns":1296,"display":1715},[1298,24006,24007,24043],{},[1301,24008,24009,24015,24017,24041],{},[1304,24010,24011,24013],{},[1307,24012,20553],{},[1307,24014,1110],{},[1437,24016,1733],{},[2491,24018,24019,24035],{},[1301,24020,24021,24023,24025,24027,24029,24031,24033],{},[1307,24022,21903],{},[1307,24024,23934],{},[1307,24026,21877],{},[1437,24028,2817],{},[1307,24030,21877],{},[1307,24032,23934],{},[1307,24034,21877],{},[1301,24036,24037,24039],{},[1311,24038,3718],{},[1307,24040,6655],{},[1307,24042,1417],{"mathvariant":1872},[1315,24044,24045],{"encoding":1317},"C_p = \\frac{USL - LSL}{6\\sigma}.",[1110,24047,24048,24065,24066,24079,24080,1417],{},[1115,24049,24051],{"className":24050},[1292],[1294,24052,24053],{"xmlns":1296},[1298,24054,24055,24063],{},[1301,24056,24057],{},[1304,24058,24059,24061],{},[1307,24060,20553],{},[1307,24062,1110],{},[1315,24064,20558],{"encoding":1317}," srovnává jen délky, nevšímá si, kde uprostřed tolerance proces leží — centrovaný i silně vychýlený proces se stejným ",[1115,24067,24069],{"className":24068},[1292],[1294,24070,24071],{"xmlns":1296},[1298,24072,24073,24077],{},[1301,24074,24075],{},[1307,24076,6655],{},[1315,24078,6687],{"encoding":1317}," mají stejné ",[1115,24081,24083],{"className":24082},[1292],[1294,24084,24085],{"xmlns":1296},[1298,24086,24087,24095],{},[1301,24088,24089],{},[1304,24090,24091,24093],{},[1307,24092,20553],{},[1307,24094,1110],{},[1315,24096,20558],{"encoding":1317},[1110,24098,24099],{},"Doplňkové charakteristiky využití tolerančního intervalu:",[1191,24101,24102,24136,24224],{},[1194,24103,24104,3742,24107,24135],{},[1279,24105,24106],{},"míra využití tolerančního intervalu",[1115,24108,24110],{"className":24109},[1292],[1294,24111,24112],{"xmlns":1296},[1298,24113,24114,24132],{},[1301,24115,24116,24128,24130],{},[2994,24117,24118],{"scriptlevel":1313,"displaystyle":1121},[2491,24119,24120,24122],{},[1311,24121,11576],{},[1304,24123,24124,24126],{},[1307,24125,20553],{},[1307,24127,1110],{},[2661,24129,2663],{},[1307,24131,11583],{"mathvariant":1872},[1315,24133,24134],{"encoding":1317},"\\dfrac{100}{C_p}\\,\\%"," — na kolik procent je toleranční interval využíván sledovaným znakem,",[1194,24137,24138,24141,24142,24159,24160,5495,24192,1547],{},[1279,24139,24140],{},"robustnost procesu",": rezerva, kterou máme v tolerančních mezích, než index ",[1115,24143,24145],{"className":24144},[1292],[1294,24146,24147],{"xmlns":1296},[1298,24148,24149,24157],{},[1301,24150,24151],{},[1304,24152,24153,24155],{},[1307,24154,20553],{},[1307,24156,1110],{},[1315,24158,20558],{"encoding":1317}," nabyde hodnotu 1 — rovná se menší hodnotě z výrazů ",[1115,24161,24163],{"className":24162},[1292],[1294,24164,24165],{"xmlns":1296},[1298,24166,24167,24189],{},[1301,24168,24169,24171,24173,24175,24177,24179,24181,24183,24185,24187],{},[1307,24170,21903],{},[1307,24172,23934],{},[1307,24174,21877],{},[1437,24176,2817],{},[1437,24178,1626],{"stretchy":1625},[1307,24180,6647],{},[1437,24182,5231],{},[1311,24184,3345],{},[1307,24186,6655],{},[1437,24188,1637],{"stretchy":1625},[1315,24190,24191],{"encoding":1317},"USL-(\\mu+3\\sigma)",[1115,24193,24195],{"className":24194},[1292],[1294,24196,24197],{"xmlns":1296},[1298,24198,24199,24221],{},[1301,24200,24201,24203,24205,24207,24209,24211,24213,24215,24217,24219],{},[1437,24202,1626],{"stretchy":1625},[1307,24204,6647],{},[1437,24206,2817],{},[1311,24208,3345],{},[1307,24210,6655],{},[1437,24212,1637],{"stretchy":1625},[1437,24214,2817],{},[1307,24216,21877],{},[1307,24218,23934],{},[1307,24220,21877],{},[1315,24222,24223],{"encoding":1317},"(\\mu-3\\sigma)-LSL",[1194,24225,24226,3742,24229,6537,24269,24283],{},[1279,24227,24228],{},"podíl zmetků",[1115,24230,24232],{"className":24231},[1292],[1294,24233,24234],{"xmlns":1296},[1298,24235,24236,24266],{},[1301,24237,24238,24245,24247,24249,24252,24254,24256,24258,24264],{},[1304,24239,24240,24242],{},[1307,24241,6483],{},[1307,24243,24244],{},"z",[1437,24246,1733],{},[1311,24248,1337],{},[1307,24250,24251],{"mathvariant":1872},"Φ",[1437,24253,1626],{"stretchy":1625},[1437,24255,2817],{},[1311,24257,3345],{},[1304,24259,24260,24262],{},[1307,24261,20553],{},[1307,24263,1110],{},[1437,24265,1637],{"stretchy":1625},[1315,24267,24268],{"encoding":1317},"P_z = 2\\Phi(-3C_p)",[1115,24270,24272],{"className":24271},[1292],[1294,24273,24274],{"xmlns":1296},[1298,24275,24276,24280],{},[1301,24277,24278],{},[1307,24279,24251],{"mathvariant":1872},[1315,24281,24282],{"encoding":1317},"\\Phi"," je distribuční funkce normovaného normálního rozdělení.",[16505,24285,24287,24308],{"id":24286},"cpkc_pk-index-způsobilosti-s-ohledem-na-vychýlení",[1115,24288,24290],{"className":24289},[1292],[1294,24291,24292],{"xmlns":1296},[1298,24293,24294,24306],{},[1301,24295,24296],{},[1304,24297,24298,24300],{},[1307,24299,20553],{},[1301,24301,24302,24304],{},[1307,24303,1110],{},[1307,24305,7016],{},[1315,24307,20580],{"encoding":1317}," — index způsobilosti s ohledem na vychýlení",[1110,24310,24311],{},"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:",[1115,24313,24315],{"className":24314},[1292],[1294,24316,24317],{"xmlns":1296,"display":1715},[1298,24318,24319,24389],{},[1301,24320,24321,24331,24333,24335,24337,24387],{},[1304,24322,24323,24325],{},[1307,24324,20553],{},[1301,24326,24327,24329],{},[1307,24328,1110],{},[1307,24330,7016],{},[1437,24332,1733],{},[1307,24334,4242],{},[1437,24336,4245],{},[1301,24338,24339,24341,24361,24363,24365,24385],{},[1437,24340,1626],{"fence":1121},[2491,24342,24343,24355],{},[1301,24344,24345,24347,24349,24351,24353],{},[1307,24346,21903],{},[1307,24348,23934],{},[1307,24350,21877],{},[1437,24352,2817],{},[1307,24354,6647],{},[1301,24356,24357,24359],{},[1311,24358,3345],{},[1307,24360,6655],{},[1437,24362,1547],{"separator":1121},[2661,24364,11072],{},[2491,24366,24367,24379],{},[1301,24368,24369,24371,24373,24375,24377],{},[1307,24370,6647],{},[1437,24372,2817],{},[1307,24374,21877],{},[1307,24376,23934],{},[1307,24378,21877],{},[1301,24380,24381,24383],{},[1311,24382,3345],{},[1307,24384,6655],{},[1437,24386,1637],{"fence":1121},[1307,24388,1417],{"mathvariant":1872},[1315,24390,24391],{"encoding":1317},"C_{pk} = \\min\\left(\\frac{USL-\\mu}{3\\sigma},\\ \\frac{\\mu-LSL}{3\\sigma}\\right).",[1110,24393,24394,24395,24408,24409,24439,24440,24461,24462,1417],{},"Vyjde-li některý z obou podílů záporný, položí se roven nule; to nastane, když střední hodnota ",[1115,24396,24398],{"className":24397},[1292],[1294,24399,24400],{"xmlns":1296},[1298,24401,24402,24406],{},[1301,24403,24404],{},[1307,24405,6647],{},[1315,24407,8554],{"encoding":1317}," leží mimo toleranční interval, a proces pak není pod statistickou kontrolou. U centrovaného procesu jsou oba podíly stejné a ",[1115,24410,24412],{"className":24411},[1292],[1294,24413,24414],{"xmlns":1296},[1298,24415,24416,24436],{},[1301,24417,24418,24428,24430],{},[1304,24419,24420,24422],{},[1307,24421,20553],{},[1301,24423,24424,24426],{},[1307,24425,1110],{},[1307,24427,7016],{},[1437,24429,1733],{},[1304,24431,24432,24434],{},[1307,24433,20553],{},[1307,24435,1110],{},[1315,24437,24438],{"encoding":1317},"C_{pk} = C_p","; čím víc je proces vychýlený, tím víc je ",[1115,24441,24443],{"className":24442},[1292],[1294,24444,24445],{"xmlns":1296},[1298,24446,24447,24459],{},[1301,24448,24449],{},[1304,24450,24451,24453],{},[1307,24452,20553],{},[1301,24454,24455,24457],{},[1307,24456,1110],{},[1307,24458,7016],{},[1315,24460,20580],{"encoding":1317}," menší než ",[1115,24463,24465],{"className":24464},[1292],[1294,24466,24467],{"xmlns":1296},[1298,24468,24469,24477],{},[1301,24470,24471],{},[1304,24472,24473,24475],{},[1307,24474,20553],{},[1307,24476,1110],{},[1315,24478,20558],{"encoding":1317},[16505,24480,24482,5495,24503,24526],{"id":24481},"cpmc_pm-a-cpmkc_pmk-indexy-vztažené-k-cíli",[1115,24483,24485],{"className":24484},[1292],[1294,24486,24487],{"xmlns":1296},[1298,24488,24489,24501],{},[1301,24490,24491],{},[1304,24492,24493,24495],{},[1307,24494,20553],{},[1301,24496,24497,24499],{},[1307,24498,1110],{},[1307,24500,4225],{},[1315,24502,20602],{"encoding":1317},[1115,24504,24506],{"className":24505},[1292],[1294,24507,24508],{"xmlns":1296},[1298,24509,24510,24524],{},[1301,24511,24512],{},[1304,24513,24514,24516],{},[1307,24515,20553],{},[1301,24517,24518,24520,24522],{},[1307,24519,1110],{},[1307,24521,4225],{},[1307,24523,7016],{},[1315,24525,20626],{"encoding":1317}," — indexy vztažené k cíli",[1110,24528,24529,24530,24543,24544,24557,24558,24601,24602,1709],{},"Pokud má proces zadaný cílový střed ",[1115,24531,24533],{"className":24532},[1292],[1294,24534,24535],{"xmlns":1296},[1298,24536,24537,24541],{},[1301,24538,24539],{},[1307,24540,6858],{},[1315,24542,6858],{"encoding":1317}," (ne nutně střed tolerance), nahradí se ",[1115,24545,24547],{"className":24546},[1292],[1294,24548,24549],{"xmlns":1296},[1298,24550,24551,24555],{},[1301,24552,24553],{},[1307,24554,6655],{},[1315,24556,6687],{"encoding":1317}," odmocninou ze střední čtvercové odchylky od cíle ",[1115,24559,24561],{"className":24560},[1292],[1294,24562,24563],{"xmlns":1296},[1298,24564,24565,24598],{},[1301,24566,24567,24570,24572],{},[1307,24568,24569],{},"τ",[1437,24571,1733],{},[4207,24573,24574],{},[1301,24575,24576,24582,24584,24586,24588,24590,24592],{},[1330,24577,24578,24580],{},[1307,24579,6655],{},[1311,24581,1337],{},[1437,24583,5231],{},[1437,24585,1626],{"stretchy":1625},[1307,24587,6647],{},[1437,24589,2817],{},[1307,24591,6858],{},[1330,24593,24594,24596],{},[1437,24595,1637],{"stretchy":1625},[1311,24597,1337],{},[1315,24599,24600],{"encoding":1317},"\\tau = \\sqrt{\\sigma^2+(\\mu-T)^2}",", která trestá i vychýlení od ",[1115,24603,24605],{"className":24604},[1292],[1294,24606,24607],{"xmlns":1296},[1298,24608,24609,24613],{},[1301,24610,24611],{},[1307,24612,6858],{},[1315,24614,6858],{"encoding":1317},[1115,24616,24618],{"className":24617},[1292],[1294,24619,24620],{"xmlns":1296,"display":1715},[1298,24621,24622,24734],{},[1301,24623,24624,24634,24636,24660,24662,24664,24676,24678,24680,24682,24732],{},[1304,24625,24626,24628],{},[1307,24627,20553],{},[1301,24629,24630,24632],{},[1307,24631,1110],{},[1307,24633,4225],{},[1437,24635,1733],{},[2491,24637,24638,24654],{},[1301,24639,24640,24642,24644,24646,24648,24650,24652],{},[1307,24641,21903],{},[1307,24643,23934],{},[1307,24645,21877],{},[1437,24647,2817],{},[1307,24649,21877],{},[1307,24651,23934],{},[1307,24653,21877],{},[1301,24655,24656,24658],{},[1311,24657,3718],{},[1307,24659,24569],{},[1437,24661,1547],{"separator":1121},[1763,24663],{"width":1765},[1304,24665,24666,24668],{},[1307,24667,20553],{},[1301,24669,24670,24672,24674],{},[1307,24671,1110],{},[1307,24673,4225],{},[1307,24675,7016],{},[1437,24677,1733],{},[1307,24679,4242],{},[1437,24681,4245],{},[1301,24683,24684,24686,24706,24708,24710,24730],{},[1437,24685,1626],{"fence":1121},[2491,24687,24688,24700],{},[1301,24689,24690,24692,24694,24696,24698],{},[1307,24691,21903],{},[1307,24693,23934],{},[1307,24695,21877],{},[1437,24697,2817],{},[1307,24699,6647],{},[1301,24701,24702,24704],{},[1311,24703,3345],{},[1307,24705,24569],{},[1437,24707,1547],{"separator":1121},[2661,24709,11072],{},[2491,24711,24712,24724],{},[1301,24713,24714,24716,24718,24720,24722],{},[1307,24715,6647],{},[1437,24717,2817],{},[1307,24719,21877],{},[1307,24721,23934],{},[1307,24723,21877],{},[1301,24725,24726,24728],{},[1311,24727,3345],{},[1307,24729,24569],{},[1437,24731,1637],{"fence":1121},[1307,24733,1417],{"mathvariant":1872},[1315,24735,24736],{"encoding":1317},"C_{pm} = \\frac{USL-LSL}{6\\tau}, \\qquad C_{pmk} = \\min\\left(\\frac{USL-\\mu}{3\\tau},\\ \\frac{\\mu-LSL}{3\\tau}\\right).",[16505,24738,24740],{"id":24739},"interpretace","Interpretace",[1141,24742,24743,24770],{},[1144,24744,24745],{},[1147,24746,24747,24767],{},[1150,24748,24749,24750],{},"Hodnota ",[1115,24751,24753],{"className":24752},[1292],[1294,24754,24755],{"xmlns":1296},[1298,24756,24757,24765],{},[1301,24758,24759],{},[1304,24760,24761,24763],{},[1307,24762,20553],{},[1307,24764,1110],{},[1315,24766,20558],{"encoding":1317},[1150,24768,24769],{},"Způsobilost procesu",[1157,24771,24772,24801,24844],{},[1147,24773,24774,24798],{},[1162,24775,24776],{},[1115,24777,24779],{"className":24778},[1292],[1294,24780,24781],{"xmlns":1296},[1298,24782,24783,24795],{},[1301,24784,24785,24791,24793],{},[1304,24786,24787,24789],{},[1307,24788,20553],{},[1307,24790,1110],{},[1437,24792,4086],{},[1311,24794,1544],{},[1315,24796,24797],{"encoding":1317},"C_p \u003C 1",[1162,24799,24800],{},"dosahovaná přesnost je menší než předepsaná — proces je nezpůsobilý",[1147,24802,24803,24827],{},[1162,24804,24805],{},[1115,24806,24808],{"className":24807},[1292],[1294,24809,24810],{"xmlns":1296},[1298,24811,24812,24824],{},[1301,24813,24814,24820,24822],{},[1304,24815,24816,24818],{},[1307,24817,20553],{},[1307,24819,1110],{},[1437,24821,1733],{},[1311,24823,1544],{},[1315,24825,24826],{"encoding":1317},"C_p = 1",[1162,24828,24829,24830,24843],{},"dosahovaná přesnost je rovna předepsané — proces je způsobilý, ale sebemenší zvětšení ",[1115,24831,24833],{"className":24832},[1292],[1294,24834,24835],{"xmlns":1296},[1298,24836,24837,24841],{},[1301,24838,24839],{},[1307,24840,6655],{},[1315,24842,6687],{"encoding":1317}," jej posune na nezpůsobilý",[1147,24845,24846,24870],{},[1162,24847,24848],{},[1115,24849,24851],{"className":24850},[1292],[1294,24852,24853],{"xmlns":1296},[1298,24854,24855,24867],{},[1301,24856,24857,24863,24865],{},[1304,24858,24859,24861],{},[1307,24860,20553],{},[1307,24862,1110],{},[1437,24864,1439],{},[1311,24866,1544],{},[1315,24868,24869],{"encoding":1317},"C_p > 1",[1162,24871,24872],{},"dosahovaná přesnost je větší než předepsaná — proces je způsobilý",[1110,24874,24875,24876,24897,24898,1417],{},"U indexu ",[1115,24877,24879],{"className":24878},[1292],[1294,24880,24881],{"xmlns":1296},[1298,24882,24883,24895],{},[1301,24884,24885],{},[1304,24886,24887,24889],{},[1307,24888,20553],{},[1301,24890,24891,24893],{},[1307,24892,1110],{},[1307,24894,7016],{},[1315,24896,20580],{"encoding":1317}," se v praxi požaduje víc než jen hodnota nad 1: s rozvojem technologií roste nárok na rezervu, a běžně se dnes vyžaduje hodnota alespoň ",[1115,24899,24901],{"className":24900},[1292],[1294,24902,24903],{"xmlns":1296},[1298,24904,24905,24910],{},[1301,24906,24907],{},[1311,24908,24909],{},"1,5",[1315,24911,24912],{"encoding":1317},"1{,}5",[1110,24914,24915],{},[4137,24916],{"alt":24917,"className":24918,"src":24919},"mask-rd-cp-panely",[1130,4141],"\u002Fwiki-assets\u002Fmask-rd-cp-panely.png",[1110,24921,24922],{},[4137,24923],{"alt":24924,"className":24925,"src":24926},"mask-rd-cpk-off-centre",[1130,4141],"\u002Fwiki-assets\u002Fmask-rd-cpk-off-centre.png",[16505,24928,24930],{"id":24929},"výpočet-v-r","Výpočet v R",[1110,24932,24933,24934,24937,24938,24941,24942,24945,24946,5495,24963,2704,24980,24983,24984,24997],{},"Indexy způsobilosti počítá ",[3223,24935,24936],{},"process.capability()"," z výstupu regulačního diagramu ",[3223,24939,24940],{},"q","; ",[3223,24943,24944],{},"spec.limits"," jsou toleranční meze ",[1115,24947,24949],{"className":24948},[1292],[1294,24950,24951],{"xmlns":1296},[1298,24952,24953,24961],{},[1301,24954,24955,24957,24959],{},[1307,24956,21877],{},[1307,24958,23934],{},[1307,24960,21877],{},[1315,24962,23939],{"encoding":1317},[1115,24964,24966],{"className":24965},[1292],[1294,24967,24968],{"xmlns":1296},[1298,24969,24970,24978],{},[1301,24971,24972,24974,24976],{},[1307,24973,21903],{},[1307,24975,23934],{},[1307,24977,21877],{},[1315,24979,23958],{"encoding":1317},[3223,24981,24982],{},"target"," cílová hodnota ",[1115,24985,24987],{"className":24986},[1292],[1294,24988,24989],{"xmlns":1296},[1298,24990,24991,24995],{},[1301,24992,24993],{},[1307,24994,6858],{},[1315,24996,6858],{"encoding":1317},". Pro velikost výrobku v mm s tolerančními mezemi 100 a 110 mm a cílovou hodnotou 105 mm:",[3447,24999,25001],{"className":3449,"code":25000,"language":71,"meta":1229,"style":1229},"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",[3223,25002,25003,25013,25036,25051,25073],{"__ignoreMap":1229},[1115,25004,25005,25007,25009,25011],{"class":3455,"line":10},[1115,25006,17154],{"class":3462},[1115,25008,1626],{"class":3470},[1115,25010,360],{"class":3458},[1115,25012,3655],{"class":3470},[1115,25014,25015,25017,25019,25021,25023,25026,25028,25030,25032,25034],{"class":3455,"line":27},[1115,25016,19865],{"class":3458},[1115,25018,3463],{"class":3462},[1115,25020,19870],{"class":3466},[1115,25022,1626],{"class":3470},[1115,25024,25025],{"class":3594},"\"3_8.txt\"",[1115,25027,1547],{"class":3462},[1115,25029,19880],{"class":3458},[1115,25031,3551],{"class":3462},[1115,25033,3564],{"class":3478},[1115,25035,3655],{"class":3470},[1115,25037,25038,25040,25042,25045,25047,25049],{"class":3455,"line":148},[1115,25039,6476],{"class":3458},[1115,25041,3463],{"class":3462},[1115,25043,25044],{"class":3466}," as.matrix",[1115,25046,1626],{"class":3470},[1115,25048,19865],{"class":3458},[1115,25050,3655],{"class":3470},[1115,25052,25053,25055,25057,25059,25061,25063,25065,25067,25069,25071],{"class":3455,"line":111},[1115,25054,24940],{"class":3458},[1115,25056,3463],{"class":3462},[1115,25058,23377],{"class":3466},[1115,25060,1626],{"class":3470},[1115,25062,6476],{"class":3458},[1115,25064,1547],{"class":3462},[1115,25066,11981],{"class":3458},[1115,25068,3551],{"class":3462},[1115,25070,22503],{"class":3594},[1115,25072,3655],{"class":3470},[1115,25074,25075,25078,25080,25082,25084,25087,25089,25091,25093,25095,25097,25099,25101,25103,25106,25108,25111,25113,25116,25118,25120,25122,25124],{"class":3455,"line":96},[1115,25076,25077],{"class":3466},"process.capability",[1115,25079,1626],{"class":3470},[1115,25081,24940],{"class":3458},[1115,25083,1547],{"class":3462},[1115,25085,25086],{"class":3458}," spec.limits",[1115,25088,3551],{"class":3462},[1115,25090,3589],{"class":3466},[1115,25092,1626],{"class":3470},[1115,25094,11576],{"class":3478},[1115,25096,1547],{"class":3462},[1115,25098,14026],{"class":3478},[1115,25100,1637],{"class":3470},[1115,25102,1547],{"class":3462},[1115,25104,25105],{"class":3458}," target",[1115,25107,3551],{"class":3462},[1115,25109,25110],{"class":3478}," 105",[1115,25112,1547],{"class":3462},[1115,25114,25115],{"class":3458}," std.dev",[1115,25117,3551],{"class":3462},[1115,25119,8999],{"class":3466},[1115,25121,1626],{"class":3470},[1115,25123,6476],{"class":3458},[1115,25125,9251],{"class":3470},[1110,25127,25128,25129,2704,25132,2704,25135,2704,25138,5495,25141,25144,25145,5495,25147,25149,25150,25171,25172,25195],{},"Výpis obsahuje řádky ",[3223,25130,25131],{},"Cp",[3223,25133,25134],{},"Cp_l",[3223,25136,25137],{},"Cp_u",[3223,25139,25140],{},"Cp_k",[3223,25142,25143],{},"Cpm"," s hodnotou indexu a 95% intervalem spolehlivosti. ",[3223,25146,25134],{},[3223,25148,25137],{}," jsou dílčí poměry k dolní a horní mezi, jejich minimum je ",[1115,25151,25153],{"className":25152},[1292],[1294,25154,25155],{"xmlns":1296},[1298,25156,25157,25169],{},[1301,25158,25159],{},[1304,25160,25161,25163],{},[1307,25162,20553],{},[1301,25164,25165,25167],{},[1307,25166,1110],{},[1307,25168,7016],{},[1315,25170,20580],{"encoding":1317},". Index ",[1115,25173,25175],{"className":25174},[1292],[1294,25176,25177],{"xmlns":1296},[1298,25178,25179,25193],{},[1301,25180,25181],{},[1304,25182,25183,25185],{},[1307,25184,20553],{},[1301,25186,25187,25189,25191],{},[1307,25188,1110],{},[1307,25190,4225],{},[1307,25192,7016],{},[1315,25194,20626],{"encoding":1317}," a doplňkové charakteristiky se dopočítají ze vzorců výše:",[3447,25197,25199],{"className":3449,"code":25198,"language":71,"meta":1229,"style":1229},"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",[3223,25200,25201,25228,25253,25290,25320,25378,25392,25443],{"__ignoreMap":1229},[1115,25202,25203,25206,25208,25210,25212,25214,25216,25218,25220,25222,25224,25226],{"class":3455,"line":10},[1115,25204,25205],{"class":3458},"mu",[1115,25207,3463],{"class":3462},[1115,25209,8989],{"class":3466},[1115,25211,1626],{"class":3470},[1115,25213,6476],{"class":3458},[1115,25215,11935],{"class":3470},[1115,25217,380],{"class":3458},[1115,25219,3463],{"class":3462},[1115,25221,8999],{"class":3466},[1115,25223,1626],{"class":3470},[1115,25225,6476],{"class":3458},[1115,25227,3655],{"class":3470},[1115,25229,25230,25232,25234,25236,25238,25240,25242,25244,25246,25248,25250],{"class":3455,"line":27},[1115,25231,23939],{"class":3458},[1115,25233,3463],{"class":3462},[1115,25235,15097],{"class":3478},[1115,25237,24941],{"class":3470},[1115,25239,23958],{"class":3458},[1115,25241,3463],{"class":3462},[1115,25243,14026],{"class":3478},[1115,25245,24941],{"class":3470},[1115,25247,6858],{"class":3458},[1115,25249,3463],{"class":3462},[1115,25251,25252],{"class":3478}," 105\n",[1115,25254,25255,25258,25260,25262,25264,25266,25268,25270,25272,25274,25276,25279,25282,25284,25286,25288],{"class":3455,"line":148},[1115,25256,25257],{"class":3458},"tau",[1115,25259,3463],{"class":3462},[1115,25261,4332],{"class":3466},[1115,25263,1626],{"class":3470},[1115,25265,380],{"class":3458},[1115,25267,2481],{"class":3462},[1115,25269,1337],{"class":3478},[1115,25271,18273],{"class":3462},[1115,25273,4361],{"class":3470},[1115,25275,25205],{"class":3458},[1115,25277,25278],{"class":3462}," -",[1115,25280,25281],{"class":3458}," T",[1115,25283,1637],{"class":3470},[1115,25285,2481],{"class":3462},[1115,25287,1337],{"class":3478},[1115,25289,3655],{"class":3470},[1115,25291,25292,25294,25296,25298,25300,25302,25305,25307,25309,25311,25313,25315,25318],{"class":3455,"line":111},[1115,25293,25131],{"class":3458},[1115,25295,3463],{"class":3462},[1115,25297,4361],{"class":3470},[1115,25299,23958],{"class":3458},[1115,25301,25278],{"class":3462},[1115,25303,25304],{"class":3458}," LSL",[1115,25306,4355],{"class":3470},[1115,25308,4358],{"class":3462},[1115,25310,4361],{"class":3470},[1115,25312,3718],{"class":3478},[1115,25314,18398],{"class":3462},[1115,25316,25317],{"class":3458}," sigma",[1115,25319,3655],{"class":3470},[1115,25321,25322,25325,25327,25329,25332,25334,25336,25339,25341,25343,25345,25347,25349,25352,25354,25356,25358,25360,25362,25364,25366,25368,25370,25372,25374,25376],{"class":3455,"line":96},[1115,25323,25324],{"class":3458},"Cpmk",[1115,25326,3463],{"class":3462},[1115,25328,11956],{"class":3466},[1115,25330,25331],{"class":3470},"((",[1115,25333,23958],{"class":3458},[1115,25335,25278],{"class":3462},[1115,25337,25338],{"class":3458}," mu",[1115,25340,4355],{"class":3470},[1115,25342,4358],{"class":3462},[1115,25344,4361],{"class":3470},[1115,25346,3345],{"class":3478},[1115,25348,18398],{"class":3462},[1115,25350,25351],{"class":3458}," tau",[1115,25353,1637],{"class":3470},[1115,25355,1547],{"class":3462},[1115,25357,4361],{"class":3470},[1115,25359,25205],{"class":3458},[1115,25361,25278],{"class":3462},[1115,25363,25304],{"class":3458},[1115,25365,4355],{"class":3470},[1115,25367,4358],{"class":3462},[1115,25369,4361],{"class":3470},[1115,25371,3345],{"class":3478},[1115,25373,18398],{"class":3462},[1115,25375,25351],{"class":3458},[1115,25377,9251],{"class":3470},[1115,25379,25380,25383,25385,25387,25389],{"class":3455,"line":89},[1115,25381,25382],{"class":3458},"miravyuziti",[1115,25384,3463],{"class":3462},[1115,25386,15097],{"class":3478},[1115,25388,9833],{"class":3462},[1115,25390,25391],{"class":3458}," Cp\n",[1115,25393,25394,25397,25399,25401,25403,25405,25407,25409,25411,25413,25415,25417,25419,25421,25423,25425,25427,25429,25431,25433,25435,25437,25439,25441],{"class":3455,"line":82},[1115,25395,25396],{"class":3458},"robustnost",[1115,25398,3463],{"class":3462},[1115,25400,11956],{"class":3466},[1115,25402,1626],{"class":3470},[1115,25404,23958],{"class":3458},[1115,25406,25278],{"class":3462},[1115,25408,4361],{"class":3470},[1115,25410,25205],{"class":3458},[1115,25412,18273],{"class":3462},[1115,25414,10613],{"class":3478},[1115,25416,18398],{"class":3462},[1115,25418,25317],{"class":3458},[1115,25420,1637],{"class":3470},[1115,25422,1547],{"class":3462},[1115,25424,4361],{"class":3470},[1115,25426,25205],{"class":3458},[1115,25428,25278],{"class":3462},[1115,25430,10613],{"class":3478},[1115,25432,18398],{"class":3462},[1115,25434,25317],{"class":3458},[1115,25436,4355],{"class":3470},[1115,25438,4392],{"class":3462},[1115,25440,25304],{"class":3458},[1115,25442,3655],{"class":3470},[1115,25444,25445,25448,25450,25452,25454,25456,25458,25460,25462,25464,25467],{"class":3455,"line":75},[1115,25446,25447],{"class":3458},"Pz",[1115,25449,3463],{"class":3462},[1115,25451,3934],{"class":3478},[1115,25453,18398],{"class":3462},[1115,25455,9109],{"class":3466},[1115,25457,1626],{"class":3470},[1115,25459,4392],{"class":3462},[1115,25461,3345],{"class":3478},[1115,25463,18398],{"class":3462},[1115,25465,25466],{"class":3458}," Cp",[1115,25468,3655],{"class":3470},[1136,25470,6162],{"id":6161},[1191,25472,25473,25476,25536,25627,25693],{},[1194,25474,25475],{},"Počítat indexy způsobilosti pro proces, který není statisticky zvládnutý — způsobilost se zkoumá až ve třetí fázi regulace.",[1194,25477,25478,25479,25496,25497,25514,25515,1417],{},"Posuzovat jen ",[1115,25480,25482],{"className":25481},[1292],[1294,25483,25484],{"xmlns":1296},[1298,25485,25486,25494],{},[1301,25487,25488],{},[1304,25489,25490,25492],{},[1307,25491,20553],{},[1307,25493,1110],{},[1315,25495,20558],{"encoding":1317}," u vychýleného procesu — ",[1115,25498,25500],{"className":25499},[1292],[1294,25501,25502],{"xmlns":1296},[1298,25503,25504,25512],{},[1301,25505,25506],{},[1304,25507,25508,25510],{},[1307,25509,20553],{},[1307,25511,1110],{},[1315,25513,20558],{"encoding":1317}," polohu střední hodnoty nezohledňuje, vychýlení zachytí až ",[1115,25516,25518],{"className":25517},[1292],[1294,25519,25520],{"xmlns":1296},[1298,25521,25522,25534],{},[1301,25523,25524],{},[1304,25525,25526,25528],{},[1307,25527,20553],{},[1301,25529,25530,25532],{},[1307,25531,1110],{},[1307,25533,7016],{},[1315,25535,20580],{"encoding":1317},[1194,25537,25538,25539,25552,25553,25566,25567,25552,25582,25595,25596,25609,25610,25623,25624,25626],{},"Zaměnit diagram ",[1115,25540,25542],{"className":25541},[1292],[1294,25543,25544],{"xmlns":1296},[1298,25545,25546,25550],{},[1301,25547,25548],{},[1307,25549,3473],{},[1315,25551,3473],{"encoding":1317}," s diagramem ",[1115,25554,25556],{"className":25555},[1292],[1294,25557,25558],{"xmlns":1296},[1298,25559,25560,25564],{},[1301,25561,25562],{},[1307,25563,11286],{},[1315,25565,11286],{"encoding":1317}," nebo diagram ",[1115,25568,25570],{"className":25569},[1292],[1294,25571,25572],{"xmlns":1296},[1298,25573,25574,25580],{},[1301,25575,25576,25578],{},[1307,25577,1435],{},[1307,25579,1110],{},[1315,25581,20518],{"encoding":1317},[1115,25583,25585],{"className":25584},[1292],[1294,25586,25587],{"xmlns":1296},[1298,25588,25589,25593],{},[1301,25590,25591],{},[1307,25592,1110],{},[1315,25594,1110],{"encoding":1317}," — při nekonstantním rozsahu podskupin se volí ",[1115,25597,25599],{"className":25598},[1292],[1294,25600,25601],{"xmlns":1296},[1298,25602,25603,25607],{},[1301,25604,25605],{},[1307,25606,11286],{},[1315,25608,11286],{"encoding":1317},", resp. ",[1115,25611,25613],{"className":25612},[1292],[1294,25614,25615],{"xmlns":1296},[1298,25616,25617,25621],{},[1301,25618,25619],{},[1307,25620,1110],{},[1315,25622,1110],{"encoding":1317},", a do ",[3223,25625,23573],{}," se zadává vektor rozsahů.",[1194,25628,25629,25630,25647,25648,25661,25662,25675,25676,1417],{},"Posuzovat diagram ",[1115,25631,25633],{"className":25632},[1292],[1294,25634,25635],{"xmlns":1296},[1298,25636,25637,25645],{},[1301,25638,25639],{},[2475,25640,25641,25643],{"accent":1121},[1307,25642,6476],{},[1437,25644,11217],{},[1315,25646,21322],{"encoding":1317}," dřív než diagram rozpětí — nejprve se určí a stabilizuje diagram ",[1115,25649,25651],{"className":25650},[1292],[1294,25652,25653],{"xmlns":1296},[1298,25654,25655,25659],{},[1301,25656,25657],{},[1307,25658,9981],{},[1315,25660,9981],{"encoding":1317}," (resp. ",[1115,25663,25665],{"className":25664},[1292],[1294,25666,25667],{"xmlns":1296},[1298,25668,25669,25673],{},[1301,25670,25671],{},[1307,25672,1605],{},[1315,25674,1605],{"encoding":1317},"), potom diagram ",[1115,25677,25679],{"className":25678},[1292],[1294,25680,25681],{"xmlns":1296},[1298,25682,25683,25691],{},[1301,25684,25685],{},[2475,25686,25687,25689],{"accent":1121},[1307,25688,6476],{},[1437,25690,11217],{},[1315,25692,21322],{"encoding":1317},[1194,25694,25695],{},"Vyřadit podskupinu jen podle polohy bodu — vyřazuje se až po zjištění a odstranění vymezitelné příčiny.",[1136,25697,1189],{"id":1188},[1191,25699,25700,25705,25710,25716,25721,25726,25731],{},[1194,25701,25702],{},[1127,25703,1133],{"className":25704,"dataFsResolvedFilePath":1131,"href":1132},[1130],[1194,25706,25707],{},[1127,25708,886],{"className":25709,"dataFsResolvedFilePath":6367,"href":6368},[1130],[1194,25711,25712],{},[1127,25713,25715],{"className":25714,"dataFsResolvedFilePath":6375,"href":6376},[1130],"nahodne-veliciny-a-rozdeleni",[1194,25717,25718],{},[1127,25719,141],{"className":25720,"dataFsResolvedFilePath":1471,"href":1472},[1130],[1194,25722,25723],{},[1127,25724,10843],{"className":25725,"dataFsResolvedFilePath":1167,"href":1168},[1130],[1194,25727,25728],{},[1127,25729,716],{"className":25730,"dataFsResolvedFilePath":1180,"href":1181},[1130],[1194,25732,25733],{},[1127,25734,6396],{"className":25735,"dataFsResolvedFilePath":1214,"href":1215},[1130],[1136,25737,1219],{"id":934},[1110,25739,1222,25740,1227],{},[1224,25741,1226],{},[1110,25743,25744,25745,25748],{},"MONTGOMERY, D. C. ",[1224,25746,25747],{},"Introduction to Statistical Quality Control",". 6. vyd. John Wiley & Sons, 2005.",[1110,25750,25751,25752,25755],{},"ČSN ISO 8258. ",[1224,25753,25754],{},"Shewhartovy regulační diagramy",". Praha: Český normalizační institut, 1994.",[1110,25757,25758,25759,25762],{},"KUPKA, K. ",[1224,25760,25761],{},"Statistické řízení jakosti",". Pardubice: TriloByte, 1997.",[6404,25764,25765],{},"html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sP4rz, html code.shiki .sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sCsY4, html code.shiki .sCsY4{--shiki-light:#6A737D;--shiki-default:#6A737D;--shiki-dark:#6A737D}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: 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pp",{"id":23916,"depth":27,"text":23917,"children":25789},[25790,25792,25794,25796,25797],{"id":23962,"depth":148,"text":25791},"CpC_p — index způsobilosti",{"id":24286,"depth":148,"text":25793},"CpkC_{pk} — index způsobilosti s ohledem na vychýlení",{"id":24481,"depth":148,"text":25795},"CpmC_{pm} a CpmkC_{pmk} — indexy vztažené k cíli",{"id":24739,"depth":148,"text":24740},{"id":24929,"depth":148,"text":24930},{"id":6161,"depth":27,"text":6162},{"id":1188,"depth":27,"text":1189},{"id":934,"depth":27,"text":1219},{},"\u002Ftopics\u002Fregulacni-diagramy-a-indexy-zpusobilosti",{"title":6390,"description":1229},[25805,25806,25807,25808],"raw\u002Fmask\u002F06 regulační diagramy.pdf","raw\u002Fmask\u002F07 indexy způsobilosti.pdf","raw\u002Fmask\u002Fnávod 06 a 07.pdf","raw\u002Fmask\u002Fpříklady 06 a 07.pdf","topics\u002Fregulacni-diagramy-a-indexy-zpusobilosti",[23,137,274,360,67,71],"bwtPTtx6g53SO_ovQdrK_C3d6vq9rKG9Vb8jM13_yag",{"id":25813,"title":6361,"body":25814,"course":23,"courses":1234,"created":1235,"description":1229,"extension":1236,"meta":35625,"navigation":1238,"path":35626,"seo":35627,"sources":35628,"stem":35634,"tags":35635,"type":6423,"updated":1235,"__hash__":35636},"topics\u002Ftopics\u002Ftestovani-hypotez.md",{"type":1096,"value":25815,"toc":35598},[25816,25819,26018,26062,26066,26076,26079,26145,26195,26348,26352,26355,26449,26599,26618,26625,26714,26718,26753,26790,26828,26863,26867,26874,27092,27211,27215,27347,27401,27423,27765,27772,27860,27866,27907,28192,28201,28316,28322,28329,28334,28340,28434,28440,28466,28472,28564,28570,28620,28624,28820,28880,29242,29581,29680,29686,29914,29918,30184,30188,30191,30257,30304,30760,30764,30767,30954,30987,31209,31528,31567,31574,32231,32370,32376,32532,32538,32545,32598,32604,32777,32783,32847,32852,33037,33043,33088,33092,33095,33099,33146,33374,33390,33479,33485,33511,33515,33518,33590,33683,33752,33758,33781,34228,34235,34239,34269,34273,34523,34542,34603,34612,34768,34774,34800,34975,34979,35000,35031,35035,35059,35089,35093,35153,35211,35215,35222,35395,35397,35550,35552,35589,35591,35595],[1099,25817,6361],{"id":25818},"testování-statistických-hypotéz",[1103,25820,25822,25828],{"className":25821,"dataCallout":1264},[1106,1263],[1110,25823,25825,1272],{"className":25824},[1113],[1115,25826],{"className":25827,"ariaHidden":1121},[1118,1271,1120],[1191,25829,25830,25900,25982,25985,25988],{},[1194,25831,25832,25833,25850,25851,25868,25869,2704,25882,25899],{},"Test porovnává tvrzení ",[1115,25834,25836],{"className":25835},[1292],[1294,25837,25838],{"xmlns":1296},[1298,25839,25840,25848],{},[1301,25841,25842],{},[1304,25843,25844,25846],{},[1307,25845,1309],{},[1311,25847,1313],{},[1315,25849,1318],{"encoding":1317}," s alternativou ",[1115,25852,25854],{"className":25853},[1292],[1294,25855,25856],{"xmlns":1296},[1298,25857,25858,25866],{},[1301,25859,25860],{},[1304,25861,25862,25864],{},[1307,25863,1309],{},[1311,25865,1544],{},[1315,25867,2749],{"encoding":1317}," pomocí testového kritéria spočteného z výběru; padne-li kritérium do kritického oboru ",[1115,25870,25872],{"className":25871},[1292],[1294,25873,25874],{"xmlns":1296},[1298,25875,25876,25880],{},[1301,25877,25878],{},[1307,25879,1353],{},[1315,25881,1353],{"encoding":1317},[1115,25883,25885],{"className":25884},[1292],[1294,25886,25887],{"xmlns":1296},[1298,25888,25889,25897],{},[1301,25890,25891],{},[1304,25892,25893,25895],{},[1307,25894,1309],{},[1311,25896,1313],{},[1315,25898,1318],{"encoding":1317}," zamítáme.",[1194,25901,25902,25903,25916,25917,25934,25935,25949,25950,25967,25968,25981],{},"Rozhodnutí nese dva typy chyb: chybu I. druhu (",[1115,25904,25906],{"className":25905},[1292],[1294,25907,25908],{"xmlns":1296},[1298,25909,25910,25914],{},[1301,25911,25912],{},[1307,25913,3118],{},[1315,25915,3181],{"encoding":1317},", zamítnutí platné ",[1115,25918,25920],{"className":25919},[1292],[1294,25921,25922],{"xmlns":1296},[1298,25923,25924,25932],{},[1301,25925,25926],{},[1304,25927,25928,25930],{},[1307,25929,1309],{},[1311,25931,1313],{},[1315,25933,1318],{"encoding":1317},") a chybu II. druhu (",[1115,25936,25938],{"className":25937},[1292],[1294,25939,25940],{"xmlns":1296},[1298,25941,25942,25946],{},[1301,25943,25944],{},[1307,25945,16096],{},[1315,25947,25948],{"encoding":1317},"\\beta",", přijetí neplatné ",[1115,25951,25953],{"className":25952},[1292],[1294,25954,25955],{"xmlns":1296},[1298,25956,25957,25965],{},[1301,25958,25959],{},[1304,25960,25961,25963],{},[1307,25962,1309],{},[1311,25964,1313],{},[1315,25966,1318],{"encoding":1317},"). Hladina významnosti ",[1115,25969,25971],{"className":25970},[1292],[1294,25972,25973],{"xmlns":1296},[1298,25974,25975,25979],{},[1301,25976,25977],{},[1307,25978,3118],{},[1315,25980,3181],{"encoding":1317}," se volí předem, obvykle 0,05.",[1194,25983,25984],{},"Pro střední hodnotu normálního rozdělení slouží jednovýběrový a párový t-test; pro srovnání dvou souborů F-test (rozptyly) a dvouvýběrový t-test (střední hodnoty).",[1194,25986,25987],{},"Normalitu ověřuje Shapiro-Wilkův test, shodu s libovolným rozdělením Kolmogorov-Smirnovův test; při porušené normalitě nastupují neparametrické testy (Wilcoxonovy, Kruskalův-Wallisův, mediánový, Friedmanův).",[1194,25989,25990,25991,26004,26005,1417],{},"Rozhodnutí lze číst dvěma rovnocennými způsoby — podle polohy kritéria vůči ",[1115,25992,25994],{"className":25993},[1292],[1294,25995,25996],{"xmlns":1296},[1298,25997,25998,26002],{},[1301,25999,26000],{},[1307,26001,1353],{},[1315,26003,1353],{"encoding":1317},", nebo podle p-hodnoty vůči ",[1115,26006,26008],{"className":26007},[1292],[1294,26009,26010],{"xmlns":1296},[1298,26011,26012,26016],{},[1301,26013,26014],{},[1307,26015,3118],{},[1315,26017,3181],{"encoding":1317},[1110,26019,26020,26021,26025,26026,26030,26031,26035,26036,2704,26049,15852],{},"Testy statistických hypotéz jsou nástroj ",[1127,26022,26024],{"className":26023,"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 ",[1127,26027,26029],{"className":26028,"dataFsResolvedFilePath":6367,"href":6368},[1130],"popisnou statistiku"," výběru, a z rozdělení uvedených u ",[1127,26032,26034],{"className":26033,"dataFsResolvedFilePath":6375,"href":6376},[1130],"náhodných veličin"," (normální, ",[1115,26037,26039],{"className":26038},[1292],[1294,26040,26041],{"xmlns":1296},[1298,26042,26043,26047],{},[1301,26044,26045],{},[1307,26046,6900],{},[1315,26048,6900],{"encoding":1317},[1115,26050,26052],{"className":26051},[1292],[1294,26053,26054],{"xmlns":1296},[1298,26055,26056,26060],{},[1301,26057,26058],{},[1307,26059,6471],{},[1315,26061,6471],{"encoding":1317},[1136,26063,26065],{"id":26064},"statistická-hypotéza-a-její-test","Statistická hypotéza a její test",[1110,26067,26068,26071,26072,26075],{},[1279,26069,26070],{},"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. ",[1279,26073,26074],{},"Testování hypotéz"," je proces ověření správnosti nebo nesprávnosti hypotézy pomocí výsledků získaných náhodným výběrem.",[1110,26077,26078],{},"Proti sobě stojí dvě hypotézy:",[1191,26080,26081,26104],{},[1194,26082,26083,26103],{},[1279,26084,26085,26086],{},"Nulová hypotéza ",[1115,26087,26089],{"className":26088},[1292],[1294,26090,26091],{"xmlns":1296},[1298,26092,26093,26101],{},[1301,26094,26095],{},[1304,26096,26097,26099],{},[1307,26098,1309],{},[1311,26100,1313],{},[1315,26102,1318],{"encoding":1317}," — tvrzení o parametru nebo rozdělení, které chceme ověřit.",[1194,26105,26106,26126,26127,26144],{},[1279,26107,26108,26109],{},"Alternativní hypotéza ",[1115,26110,26112],{"className":26111},[1292],[1294,26113,26114],{"xmlns":1296},[1298,26115,26116,26124],{},[1301,26117,26118],{},[1304,26119,26120,26122],{},[1307,26121,1309],{},[1311,26123,1544],{},[1315,26125,2749],{"encoding":1317}," — staví se proti ",[1115,26128,26130],{"className":26129},[1292],[1294,26131,26132],{"xmlns":1296},[1298,26133,26134,26142],{},[1301,26135,26136],{},[1304,26137,26138,26140],{},[1307,26139,1309],{},[1311,26141,1313],{},[1315,26143,1318],{"encoding":1317}," a určitým způsobem popírá její tvrzení.",[1110,26146,1448,26147,26177,26178,1709],{},[1115,26148,26150],{"className":26149},[1292],[1294,26151,26152],{"xmlns":1296},[1298,26153,26154,26174],{},[1301,26155,26156,26162,26164,26166,26168],{},[1304,26157,26158,26160],{},[1307,26159,1309],{},[1311,26161,1313],{},[1437,26163,1709],{},[1307,26165,6647],{},[1437,26167,1733],{},[1304,26169,26170,26172],{},[1307,26171,6647],{},[1311,26173,1313],{},[1315,26175,26176],{"encoding":1317},"H_0: \\mu = \\mu_0"," existují tři varianty ",[1115,26179,26181],{"className":26180},[1292],[1294,26182,26183],{"xmlns":1296},[1298,26184,26185,26193],{},[1301,26186,26187],{},[1304,26188,26189,26191],{},[1307,26190,1309],{},[1311,26192,1544],{},[1315,26194,2749],{"encoding":1317},[1141,26196,26197,26227],{},[1144,26198,26199],{},[1147,26200,26201,26221,26224],{},[1150,26202,26203,26204],{},"Tvar ",[1115,26205,26207],{"className":26206},[1292],[1294,26208,26209],{"xmlns":1296},[1298,26210,26211,26219],{},[1301,26212,26213],{},[1304,26214,26215,26217],{},[1307,26216,1309],{},[1311,26218,1544],{},[1315,26220,2749],{"encoding":1317},[1150,26222,26223],{},"Zápis",[1150,26225,26226],{},"Typ",[1157,26228,26229,26269,26309],{},[1147,26230,26231,26234,26266],{},[1162,26232,26233],{},"nerovnost",[1162,26235,26236],{},[1115,26237,26239],{"className":26238},[1292],[1294,26240,26241],{"xmlns":1296},[1298,26242,26243,26263],{},[1301,26244,26245,26251,26253,26255,26257],{},[1304,26246,26247,26249],{},[1307,26248,1309],{},[1311,26250,1544],{},[1437,26252,1709],{},[1307,26254,6647],{},[1437,26256,10714],{"mathvariant":1872},[1304,26258,26259,26261],{},[1307,26260,6647],{},[1311,26262,1313],{},[1315,26264,26265],{"encoding":1317},"H_1: \\mu \\neq \\mu_0",[1162,26267,26268],{},"dvoustranná",[1147,26270,26271,26274,26306],{},[1162,26272,26273],{},"větší",[1162,26275,26276],{},[1115,26277,26279],{"className":26278},[1292],[1294,26280,26281],{"xmlns":1296},[1298,26282,26283,26303],{},[1301,26284,26285,26291,26293,26295,26297],{},[1304,26286,26287,26289],{},[1307,26288,1309],{},[1311,26290,1544],{},[1437,26292,1709],{},[1307,26294,6647],{},[1437,26296,1439],{},[1304,26298,26299,26301],{},[1307,26300,6647],{},[1311,26302,1313],{},[1315,26304,26305],{"encoding":1317},"H_1: \\mu > \\mu_0",[1162,26307,26308],{},"jednostranná",[1147,26310,26311,26314,26346],{},[1162,26312,26313],{},"menší",[1162,26315,26316],{},[1115,26317,26319],{"className":26318},[1292],[1294,26320,26321],{"xmlns":1296},[1298,26322,26323,26343],{},[1301,26324,26325,26331,26333,26335,26337],{},[1304,26326,26327,26329],{},[1307,26328,1309],{},[1311,26330,1544],{},[1437,26332,1709],{},[1307,26334,6647],{},[1437,26336,4086],{},[1304,26338,26339,26341],{},[1307,26340,6647],{},[1311,26342,1313],{},[1315,26344,26345],{"encoding":1317},"H_1: \\mu \u003C \\mu_0",[1162,26347,26308],{},[16505,26349,26351],{"id":26350},"chyba-i-a-ii-druhu","Chyba I. a II. druhu",[1110,26353,26354],{},"Protože je úsudek odvozen z náhodného výběru, může vést ke dvěma typům chybného rozhodnutí:",[1191,26356,26357,26394],{},[1194,26358,26359,26362,26363,26380,26381,1417],{},[1279,26360,26361],{},"Chyba I. druhu"," — zamítnutí ",[1115,26364,26366],{"className":26365},[1292],[1294,26367,26368],{"xmlns":1296},[1298,26369,26370,26378],{},[1301,26371,26372],{},[1304,26373,26374,26376],{},[1307,26375,1309],{},[1311,26377,1313],{},[1315,26379,1318],{"encoding":1317},", ačkoliv ve skutečnosti platí. Pravděpodobnost ",[1115,26382,26384],{"className":26383},[1292],[1294,26385,26386],{"xmlns":1296},[1298,26387,26388,26392],{},[1301,26389,26390],{},[1307,26391,3118],{},[1315,26393,3181],{"encoding":1317},[1194,26395,26396,26399,26400,26417,26418,26435,26436,1417],{},[1279,26397,26398],{},"Chyba II. druhu"," — přijetí ",[1115,26401,26403],{"className":26402},[1292],[1294,26404,26405],{"xmlns":1296},[1298,26406,26407,26415],{},[1301,26408,26409],{},[1304,26410,26411,26413],{},[1307,26412,1309],{},[1311,26414,1313],{},[1315,26416,1318],{"encoding":1317},", ačkoliv platí ",[1115,26419,26421],{"className":26420},[1292],[1294,26422,26423],{"xmlns":1296},[1298,26424,26425,26433],{},[1301,26426,26427],{},[1304,26428,26429,26431],{},[1307,26430,1309],{},[1311,26432,1544],{},[1315,26434,2749],{"encoding":1317},". Pravděpodobnost ",[1115,26437,26439],{"className":26438},[1292],[1294,26440,26441],{"xmlns":1296},[1298,26442,26443,26447],{},[1301,26444,26445],{},[1307,26446,16096],{},[1315,26448,25948],{"encoding":1317},[1141,26450,26451,26514],{},[1144,26452,26453],{},[1147,26454,26455,26475,26494],{},[1150,26456,26457,26458],{},"Úsudek o ",[1115,26459,26461],{"className":26460},[1292],[1294,26462,26463],{"xmlns":1296},[1298,26464,26465,26473],{},[1301,26466,26467],{},[1304,26468,26469,26471],{},[1307,26470,1309],{},[1311,26472,1313],{},[1315,26474,1318],{"encoding":1317},[1150,26476,26477,8109],{},[1115,26478,26480],{"className":26479},[1292],[1294,26481,26482],{"xmlns":1296},[1298,26483,26484,26492],{},[1301,26485,26486],{},[1304,26487,26488,26490],{},[1307,26489,1309],{},[1311,26491,1313],{},[1315,26493,1318],{"encoding":1317},[1150,26495,26496,26513],{},[1115,26497,26499],{"className":26498},[1292],[1294,26500,26501],{"xmlns":1296},[1298,26502,26503,26511],{},[1301,26504,26505],{},[1304,26506,26507,26509],{},[1307,26508,1309],{},[1311,26510,1313],{},[1315,26512,1318],{"encoding":1317}," neplatí",[1157,26515,26516,26558],{},[1147,26517,26518,26521,26542],{},[1162,26519,26520],{},"Nezamítá se",[1162,26522,26523,26524],{},"správné rozhodnutí, ",[1115,26525,26527],{"className":26526},[1292],[1294,26528,26529],{"xmlns":1296},[1298,26530,26531,26539],{},[1301,26532,26533,26535,26537],{},[1311,26534,1544],{},[1437,26536,2817],{},[1307,26538,3118],{},[1315,26540,26541],{"encoding":1317},"1-\\alpha",[1162,26543,26544,26545],{},"chyba II. druhu, ",[1115,26546,26548],{"className":26547},[1292],[1294,26549,26550],{"xmlns":1296},[1298,26551,26552,26556],{},[1301,26553,26554],{},[1307,26555,16096],{},[1315,26557,25948],{"encoding":1317},[1147,26559,26560,26563,26579],{},[1162,26561,26562],{},"Zamítá se",[1162,26564,26565,26566],{},"chyba I. druhu, ",[1115,26567,26569],{"className":26568},[1292],[1294,26570,26571],{"xmlns":1296},[1298,26572,26573,26577],{},[1301,26574,26575],{},[1307,26576,3118],{},[1315,26578,3181],{"encoding":1317},[1162,26580,26523,26581],{},[1115,26582,26584],{"className":26583},[1292],[1294,26585,26586],{"xmlns":1296},[1298,26587,26588,26596],{},[1301,26589,26590,26592,26594],{},[1311,26591,1544],{},[1437,26593,2817],{},[1307,26595,16096],{},[1315,26597,26598],{"encoding":1317},"1-\\beta",[1110,26600,26601,1402,26604,26617],{},[1279,26602,26603],{},"Hladina významnosti",[1115,26605,26607],{"className":26606},[1292],[1294,26608,26609],{"xmlns":1296},[1298,26610,26611,26615],{},[1301,26612,26613],{},[1307,26614,3118],{},[1315,26616,3181],{"encoding":1317}," 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.",[1110,26619,26620],{},[4137,26621],{"alt":26622,"className":26623,"src":26624},"mask-th-chyba-i-ii",[1130,4141],"\u002Fwiki-assets\u002Fmask-th-chyba-i-ii.png",[1110,26626,26627,26628,26641,26642,26655,26656,26669,26670,1641,26683,26696,26697,1417],{},"Obrázek ukazuje, proč jde o kompromis: posunutí kritické hodnoty ",[1115,26629,26631],{"className":26630},[1292],[1294,26632,26633],{"xmlns":1296},[1298,26634,26635,26639],{},[1301,26636,26637],{},[1307,26638,3473],{},[1315,26640,3473],{"encoding":1317}," doleva zmenší ",[1115,26643,26645],{"className":26644},[1292],[1294,26646,26647],{"xmlns":1296},[1298,26648,26649,26653],{},[1301,26650,26651],{},[1307,26652,16096],{},[1315,26654,25948],{"encoding":1317},", ale zvětší ",[1115,26657,26659],{"className":26658},[1292],[1294,26660,26661],{"xmlns":1296},[1298,26662,26663,26667],{},[1301,26664,26665],{},[1307,26666,3118],{},[1315,26668,3181],{"encoding":1317},", a naopak. Pro danou hladinu ",[1115,26671,26673],{"className":26672},[1292],[1294,26674,26675],{"xmlns":1296},[1298,26676,26677,26681],{},[1301,26678,26679],{},[1307,26680,3118],{},[1315,26682,3181],{"encoding":1317},[1115,26684,26686],{"className":26685},[1292],[1294,26687,26688],{"xmlns":1296},[1298,26689,26690,26694],{},[1301,26691,26692],{},[1307,26693,3473],{},[1315,26695,3473],{"encoding":1317}," jednoznačně určena rozdělením kritéria za platnosti ",[1115,26698,26700],{"className":26699},[1292],[1294,26701,26702],{"xmlns":1296},[1298,26703,26704,26712],{},[1301,26705,26706],{},[1304,26707,26708,26710],{},[1307,26709,1309],{},[1311,26711,1313],{},[1315,26713,1318],{"encoding":1317},[16505,26715,26717],{"id":26716},"testové-kritérium-a-kritický-obor","Testové kritérium a kritický obor",[1110,26719,26720,1402,26722,26735,26736,1417],{},[1279,26721,2753],{},[1115,26723,26725],{"className":26724},[1292],[1294,26726,26727],{"xmlns":1296},[1298,26728,26729,26733],{},[1301,26730,26731],{},[1307,26732,6858],{},[1315,26734,6858],{"encoding":1317}," je statistika spočtená z výběru; aby bylo možné test provést, musí být známo jeho rozdělení za platnosti ",[1115,26737,26739],{"className":26738},[1292],[1294,26740,26741],{"xmlns":1296},[1298,26742,26743,26751],{},[1301,26744,26745],{},[1304,26746,26747,26749],{},[1307,26748,1309],{},[1311,26750,1313],{},[1315,26752,1318],{"encoding":1317},[1110,26754,26755,1402,26758,26771,26772,26789],{},[1279,26756,26757],{},"Kritický obor",[1115,26759,26761],{"className":26760},[1292],[1294,26762,26763],{"xmlns":1296},[1298,26764,26765,26769],{},[1301,26766,26767],{},[1307,26768,1353],{},[1315,26770,1353],{"encoding":1317}," je množina hodnot svědčících pro ",[1115,26773,26775],{"className":26774},[1292],[1294,26776,26777],{"xmlns":1296},[1298,26778,26779,26787],{},[1301,26780,26781],{},[1304,26782,26783,26785],{},[1307,26784,1309],{},[1311,26786,1544],{},[1315,26788,2749],{"encoding":1317},". Je zkonstruován tak, aby",[1115,26791,26793],{"className":26792},[1292],[1294,26794,26795],{"xmlns":1296,"display":1715},[1298,26796,26797,26825],{},[1301,26798,26799,26801,26803,26805,26807,26809,26811,26817,26819,26821,26823],{},[1307,26800,6483],{},[1437,26802,1626],{"stretchy":1625},[1307,26804,6858],{},[1437,26806,6775],{},[1307,26808,1353],{},[1437,26810,22781],{},[1304,26812,26813,26815],{},[1307,26814,1309],{},[1311,26816,1313],{},[1437,26818,1637],{"stretchy":1625},[1437,26820,1733],{},[1307,26822,3118],{},[1437,26824,1547],{"separator":1121},[1315,26826,26827],{"encoding":1317},"P(T \\in W \\mid H_0) = \\alpha,",[1110,26829,26830,26831,26844,26845,26862],{},"tedy aby pravděpodobnost, že výběr dá hodnotu kritéria v ",[1115,26832,26834],{"className":26833},[1292],[1294,26835,26836],{"xmlns":1296},[1298,26837,26838,26842],{},[1301,26839,26840],{},[1307,26841,1353],{},[1315,26843,1353],{"encoding":1317}," i při platné ",[1115,26846,26848],{"className":26847},[1292],[1294,26849,26850],{"xmlns":1296},[1298,26851,26852,26860],{},[1301,26853,26854],{},[1304,26855,26856,26858],{},[1307,26857,1309],{},[1311,26859,1313],{},[1315,26861,1318],{"encoding":1317},", byla rovna zvolené hladině významnosti.",[16505,26864,26866],{"id":26865},"postup-testování-hypotézy","Postup testování hypotézy",[1110,26868,26869],{},[4137,26870],{"alt":26871,"className":26872,"src":26873},"mask-ilu-postup-testovani",[1130,4141],"\u002Fwiki-assets\u002Fmask-ilu-postup-testovani.png",[2617,26875,26876,26913,26916,26932],{},[1194,26877,26878,26879,5495,26896,1417],{},"Formulace hypotéz ",[1115,26880,26882],{"className":26881},[1292],[1294,26883,26884],{"xmlns":1296},[1298,26885,26886,26894],{},[1301,26887,26888],{},[1304,26889,26890,26892],{},[1307,26891,1309],{},[1311,26893,1313],{},[1315,26895,1318],{"encoding":1317},[1115,26897,26899],{"className":26898},[1292],[1294,26900,26901],{"xmlns":1296},[1298,26902,26903,26911],{},[1301,26904,26905],{},[1304,26906,26907,26909],{},[1307,26908,1309],{},[1311,26910,1544],{},[1315,26912,2749],{"encoding":1317},[1194,26914,26915],{},"Volba testového kritéria a výpočet jeho hodnoty.",[1194,26917,26918,26919,1417],{},"Volba hladiny významnosti a sestrojení příslušného kritického oboru ",[1115,26920,26922],{"className":26921},[1292],[1294,26923,26924],{"xmlns":1296},[1298,26925,26926,26930],{},[1301,26927,26928],{},[1307,26929,1353],{},[1315,26931,1353],{"encoding":1317},[1194,26933,26934,26935],{},"Formulace závěru:\n",[1191,26936,26937,27015],{},[1194,26938,26939,26940,3742,26958,26975,26976,26996,26997,27014],{},"pokud ",[1115,26941,26943],{"className":26942},[1292],[1294,26944,26945],{"xmlns":1296},[1298,26946,26947,26955],{},[1301,26948,26949,26951,26953],{},[1307,26950,6858],{},[1437,26952,6775],{},[1307,26954,1353],{},[1315,26956,26957],{"encoding":1317},"T \\in W",[1115,26959,26961],{"className":26960},[1292],[1294,26962,26963],{"xmlns":1296},[1298,26964,26965,26973],{},[1301,26966,26967],{},[1304,26968,26969,26971],{},[1307,26970,1309],{},[1311,26972,1544],{},[1315,26974,2749],{"encoding":1317}," je testem prokázána na hladině významnosti ",[1115,26977,26979],{"className":26978},[1292],[1294,26980,26981],{"xmlns":1296},[1298,26982,26983,26993],{},[1301,26984,26985,26987,26989,26991],{},[1311,26986,11576],{},[1307,26988,3118],{},[2661,26990,2663],{},[1307,26992,11583],{"mathvariant":1872},[1315,26994,26995],{"encoding":1317},"100\\alpha\\,\\%"," (zamítáme ",[1115,26998,27000],{"className":26999},[1292],[1294,27001,27002],{"xmlns":1296},[1298,27003,27004,27012],{},[1301,27005,27006],{},[1304,27007,27008,27010],{},[1307,27009,1309],{},[1311,27011,1313],{},[1315,27013,1318],{"encoding":1317},");",[1194,27016,26939,27017,3742,27036,27053,27054,27073,27074,27091],{},[1115,27018,27020],{"className":27019},[1292],[1294,27021,27022],{"xmlns":1296},[1298,27023,27024,27033],{},[1301,27025,27026,27028,27031],{},[1307,27027,6858],{},[1437,27029,27030],{"mathvariant":1872},"∉",[1307,27032,1353],{},[1315,27034,27035],{"encoding":1317},"T \\notin W",[1115,27037,27039],{"className":27038},[1292],[1294,27040,27041],{"xmlns":1296},[1298,27042,27043,27051],{},[1301,27044,27045],{},[1304,27046,27047,27049],{},[1307,27048,1309],{},[1311,27050,1544],{},[1315,27052,2749],{"encoding":1317}," není testem prokázána na hladině významnosti ",[1115,27055,27057],{"className":27056},[1292],[1294,27058,27059],{"xmlns":1296},[1298,27060,27061,27071],{},[1301,27062,27063,27065,27067,27069],{},[1311,27064,11576],{},[1307,27066,3118],{},[2661,27068,2663],{},[1307,27070,11583],{"mathvariant":1872},[1315,27072,26995],{"encoding":1317}," ; ",[1115,27075,27077],{"className":27076},[1292],[1294,27078,27079],{"xmlns":1296},[1298,27080,27081,27089],{},[1301,27082,27083],{},[1304,27084,27085,27087],{},[1307,27086,1309],{},[1311,27088,1313],{},[1315,27090,1318],{"encoding":1317}," nezamítáme.",[1110,27093,27094,27095,27098,27099,27116,27117,27134,27135,27155,27156,24941,27173,1402,27193,27210],{},"Rovnocennou alternativou je ",[1279,27096,27097],{},"p-hodnota",": udává, nakolik jsou data slučitelná s ",[1115,27100,27102],{"className":27101},[1292],[1294,27103,27104],{"xmlns":1296},[1298,27105,27106,27114],{},[1301,27107,27108],{},[1304,27109,27110,27112],{},[1307,27111,1309],{},[1311,27113,1313],{},[1315,27115,1318],{"encoding":1317},". Čím menší p-hodnota, tím více data svědčí proti ",[1115,27118,27120],{"className":27119},[1292],[1294,27121,27122],{"xmlns":1296},[1298,27123,27124,27132],{},[1301,27125,27126],{},[1304,27127,27128,27130],{},[1307,27129,1309],{},[1311,27131,1313],{},[1315,27133,1318],{"encoding":1317},". Rozhodovací pravidlo: ",[1115,27136,27138],{"className":27137},[1292],[1294,27139,27140],{"xmlns":1296},[1298,27141,27142,27152],{},[1301,27143,27144,27146,27148,27150],{},[1307,27145,1110],{},[1437,27147,6491],{},[1307,27149,3118],{},[1437,27151,7306],{},[1315,27153,27154],{"encoding":1317},"p \\le \\alpha \\Rightarrow"," zamítáme ",[1115,27157,27159],{"className":27158},[1292],[1294,27160,27161],{"xmlns":1296},[1298,27162,27163,27171],{},[1301,27164,27165],{},[1304,27166,27167,27169],{},[1307,27168,1309],{},[1311,27170,1313],{},[1315,27172,1318],{"encoding":1317},[1115,27174,27176],{"className":27175},[1292],[1294,27177,27178],{"xmlns":1296},[1298,27179,27180,27190],{},[1301,27181,27182,27184,27186,27188],{},[1307,27183,1110],{},[1437,27185,1439],{},[1307,27187,3118],{},[1437,27189,7306],{},[1315,27191,27192],{"encoding":1317},"p > \\alpha \\Rightarrow",[1115,27194,27196],{"className":27195},[1292],[1294,27197,27198],{"xmlns":1296},[1298,27199,27200,27208],{},[1301,27201,27202],{},[1304,27203,27204,27206],{},[1307,27205,1309],{},[1311,27207,1313],{},[1315,27209,1318],{"encoding":1317}," nezamítáme. Obě cesty — kritický obor i p-hodnota — vedou vždy ke stejnému závěru; R u všech testů vrací p-hodnotu přímo.",[1136,27212,27214],{"id":27213},"jednovýběrový-t-test","Jednovýběrový t-test",[1110,27216,27217,27218,27231,27232,27264,27265,27278,27279,5495,27296,27313,27314,27332,27333,27346],{},"Test o střední hodnotě ",[1115,27219,27221],{"className":27220},[1292],[1294,27222,27223],{"xmlns":1296},[1298,27224,27225,27229],{},[1301,27226,27227],{},[1307,27228,6647],{},[1315,27230,8554],{"encoding":1317}," rozdělení ",[1115,27233,27235],{"className":27234},[1292],[1294,27236,27237],{"xmlns":1296},[1298,27238,27239,27261],{},[1301,27240,27241,27243,27245,27247,27249,27251,27253,27259],{},[1307,27242,6488],{},[1437,27244,8941],{},[1307,27246,6642],{},[1437,27248,1626],{"stretchy":1625},[1307,27250,6647],{},[1437,27252,1547],{"separator":1121},[1330,27254,27255,27257],{},[1307,27256,6655],{},[1311,27258,1337],{},[1437,27260,1637],{"stretchy":1625},[1315,27262,27263],{"encoding":1317},"X \\sim N(\\mu, \\sigma^2)",". Z výběru o rozsahu ",[1115,27266,27268],{"className":27267},[1292],[1294,27269,27270],{"xmlns":1296},[1298,27271,27272,27276],{},[1301,27273,27274],{},[1307,27275,1435],{},[1315,27277,1435],{"encoding":1317}," se určí charakteristiky ",[1115,27280,27282],{"className":27281},[1292],[1294,27283,27284],{"xmlns":1296},[1298,27285,27286,27294],{},[1301,27287,27288],{},[2475,27289,27290,27292],{"accent":1121},[1307,27291,6476],{},[1437,27293,11217],{},[1315,27295,21322],{"encoding":1317},[1115,27297,27299],{"className":27298},[1292],[1294,27300,27301],{"xmlns":1296},[1298,27302,27303,27311],{},[1301,27304,27305],{},[1330,27306,27307,27309],{},[1307,27308,1605],{},[1311,27310,1337],{},[1315,27312,15535],{"encoding":1317},"; testem se posuzuje vztah mezi zvoleným číslem ",[1115,27315,27317],{"className":27316},[1292],[1294,27318,27319],{"xmlns":1296},[1298,27320,27321,27329],{},[1301,27322,27323],{},[1304,27324,27325,27327],{},[1307,27326,6647],{},[1311,27328,1313],{},[1315,27330,27331],{"encoding":1317},"\\mu_0"," a neznámou hodnotou ",[1115,27334,27336],{"className":27335},[1292],[1294,27337,27338],{"xmlns":1296},[1298,27339,27340,27344],{},[1301,27341,27342],{},[1307,27343,6647],{},[1315,27345,8554],{"encoding":1317},". Testové kritérium",[1115,27348,27350],{"className":27349},[1292],[1294,27351,27352],{"xmlns":1296,"display":1715},[1298,27353,27354,27398],{},[1301,27355,27356,27358,27360,27380,27384,27386],{},[1307,27357,6858],{},[1437,27359,1733],{},[2491,27361,27362,27378],{},[1301,27363,27364,27370,27372],{},[2475,27365,27366,27368],{"accent":1121},[1307,27367,6476],{},[1437,27369,11217],{},[1437,27371,2817],{},[1304,27373,27374,27376],{},[1307,27375,6647],{},[1311,27377,1313],{},[1307,27379,1605],{},[4207,27381,27382],{},[1307,27383,1435],{},[1437,27385,8941],{},[1304,27387,27388,27390],{},[1307,27389,6900],{},[1301,27391,27392,27394,27396],{},[1307,27393,1435],{},[1437,27395,2817],{},[1311,27397,1544],{},[1315,27399,27400],{"encoding":1317},"T = \\frac{\\bar{x} - \\mu_0}{s}\\sqrt{n} \\sim t_{n-1}",[1110,27402,27403,27404,27422],{},"má Studentovo rozdělení o ",[1115,27405,27407],{"className":27406},[1292],[1294,27408,27409],{"xmlns":1296},[1298,27410,27411,27419],{},[1301,27412,27413,27415,27417],{},[1307,27414,1435],{},[1437,27416,2817],{},[1311,27418,1544],{},[1315,27420,27421],{"encoding":1317},"n-1"," stupních volnosti.",[1141,27424,27425,27483],{},[1144,27426,27427],{},[1147,27428,27429,27448,27467],{},[1150,27430,27431],{},[1115,27432,27434],{"className":27433},[1292],[1294,27435,27436],{"xmlns":1296},[1298,27437,27438,27446],{},[1301,27439,27440],{},[1304,27441,27442,27444],{},[1307,27443,1309],{},[1311,27445,1313],{},[1315,27447,1318],{"encoding":1317},[1150,27449,27450],{},[1115,27451,27453],{"className":27452},[1292],[1294,27454,27455],{"xmlns":1296},[1298,27456,27457,27465],{},[1301,27458,27459],{},[1304,27460,27461,27463],{},[1307,27462,1309],{},[1311,27464,1544],{},[1315,27466,2749],{"encoding":1317},[1150,27468,27469,27470],{},"Kritický obor ",[1115,27471,27473],{"className":27472},[1292],[1294,27474,27475],{"xmlns":1296},[1298,27476,27477,27481],{},[1301,27478,27479],{},[1307,27480,1353],{},[1315,27482,1353],{"encoding":1317},[1157,27484,27485,27575,27673],{},[1147,27486,27487,27511,27535],{},[1162,27488,27489],{},[1115,27490,27492],{"className":27491},[1292],[1294,27493,27494],{"xmlns":1296},[1298,27495,27496,27508],{},[1301,27497,27498,27500,27502],{},[1307,27499,6647],{},[1437,27501,6491],{},[1304,27503,27504,27506],{},[1307,27505,6647],{},[1311,27507,1313],{},[1315,27509,27510],{"encoding":1317},"\\mu \\le \\mu_0",[1162,27512,27513],{},[1115,27514,27516],{"className":27515},[1292],[1294,27517,27518],{"xmlns":1296},[1298,27519,27520,27532],{},[1301,27521,27522,27524,27526],{},[1307,27523,6647],{},[1437,27525,1439],{},[1304,27527,27528,27530],{},[1307,27529,6647],{},[1311,27531,1313],{},[1315,27533,27534],{"encoding":1317},"\\mu > \\mu_0",[1162,27536,27537],{},[1115,27538,27540],{"className":27539},[1292],[1294,27541,27542],{"xmlns":1296},[1298,27543,27544,27572],{},[1301,27545,27546,27548,27550,27562,27564,27566,27568,27570],{},[1307,27547,6900],{},[1437,27549,3104],{},[1304,27551,27552,27554],{},[1307,27553,6900],{},[1301,27555,27556,27558,27560],{},[1311,27557,1544],{},[1437,27559,2817],{},[1307,27561,3118],{},[1437,27563,1626],{"stretchy":1625},[1307,27565,1435],{},[1437,27567,2817],{},[1311,27569,1544],{},[1437,27571,1637],{"stretchy":1625},[1315,27573,27574],{"encoding":1317},"t \\ge t_{1-\\alpha}(n-1)",[1147,27576,27577,27601,27625],{},[1162,27578,27579],{},[1115,27580,27582],{"className":27581},[1292],[1294,27583,27584],{"xmlns":1296},[1298,27585,27586,27598],{},[1301,27587,27588,27590,27592],{},[1307,27589,6647],{},[1437,27591,1733],{},[1304,27593,27594,27596],{},[1307,27595,6647],{},[1311,27597,1313],{},[1315,27599,27600],{"encoding":1317},"\\mu = \\mu_0",[1162,27602,27603],{},[1115,27604,27606],{"className":27605},[1292],[1294,27607,27608],{"xmlns":1296},[1298,27609,27610,27622],{},[1301,27611,27612,27614,27616],{},[1307,27613,6647],{},[1437,27615,10714],{"mathvariant":1872},[1304,27617,27618,27620],{},[1307,27619,6647],{},[1311,27621,1313],{},[1315,27623,27624],{"encoding":1317},"\\mu \\neq \\mu_0",[1162,27626,27627],{},[1115,27628,27630],{"className":27629},[1292],[1294,27631,27632],{"xmlns":1296},[1298,27633,27634,27670],{},[1301,27635,27636,27638,27640,27642,27644,27660,27662,27664,27666,27668],{},[1437,27637,22781],{"stretchy":1625},[1307,27639,6900],{},[1437,27641,22781],{"stretchy":1625},[1437,27643,3104],{},[1304,27645,27646,27648],{},[1307,27647,6900],{},[1301,27649,27650,27652,27654,27656,27658],{},[1311,27651,1544],{},[1437,27653,2817],{},[1307,27655,3118],{},[1307,27657,4358],{"mathvariant":1872},[1311,27659,1337],{},[1437,27661,1626],{"stretchy":1625},[1307,27663,1435],{},[1437,27665,2817],{},[1311,27667,1544],{},[1437,27669,1637],{"stretchy":1625},[1315,27671,27672],{"encoding":1317},"\\lvert t \\rvert \\ge t_{1-\\alpha\u002F2}(n-1)",[1147,27674,27675,27699,27723],{},[1162,27676,27677],{},[1115,27678,27680],{"className":27679},[1292],[1294,27681,27682],{"xmlns":1296},[1298,27683,27684,27696],{},[1301,27685,27686,27688,27690],{},[1307,27687,6647],{},[1437,27689,3104],{},[1304,27691,27692,27694],{},[1307,27693,6647],{},[1311,27695,1313],{},[1315,27697,27698],{"encoding":1317},"\\mu \\ge \\mu_0",[1162,27700,27701],{},[1115,27702,27704],{"className":27703},[1292],[1294,27705,27706],{"xmlns":1296},[1298,27707,27708,27720],{},[1301,27709,27710,27712,27714],{},[1307,27711,6647],{},[1437,27713,4086],{},[1304,27715,27716,27718],{},[1307,27717,6647],{},[1311,27719,1313],{},[1315,27721,27722],{"encoding":1317},"\\mu \u003C \\mu_0",[1162,27724,27725],{},[1115,27726,27728],{"className":27727},[1292],[1294,27729,27730],{"xmlns":1296},[1298,27731,27732,27762],{},[1301,27733,27734,27736,27738,27740,27752,27754,27756,27758,27760],{},[1307,27735,6900],{},[1437,27737,6491],{},[1437,27739,2817],{},[1304,27741,27742,27744],{},[1307,27743,6900],{},[1301,27745,27746,27748,27750],{},[1311,27747,1544],{},[1437,27749,2817],{},[1307,27751,3118],{},[1437,27753,1626],{"stretchy":1625},[1307,27755,1435],{},[1437,27757,2817],{},[1311,27759,1544],{},[1437,27761,1637],{"stretchy":1625},[1315,27763,27764],{"encoding":1317},"t \\le -t_{1-\\alpha}(n-1)",[1110,27766,27767,27768,27771],{},"V R test provádí ",[3223,27769,27770],{},"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?",[3447,27773,27775],{"className":3449,"code":27774,"language":71,"meta":1229,"style":1229},"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",[3223,27776,27777,27831],{"__ignoreMap":1229},[1115,27778,27779,27781,27783,27785,27787,27790,27792,27795,27797,27800,27802,27805,27807,27810,27812,27815,27817,27819,27821,27824,27826,27829],{"class":3455,"line":10},[1115,27780,6476],{"class":3458},[1115,27782,3463],{"class":3462},[1115,27784,3589],{"class":3466},[1115,27786,1626],{"class":3470},[1115,27788,27789],{"class":3478},"12.5",[1115,27791,1547],{"class":3462},[1115,27793,27794],{"class":3478}," 13.5",[1115,27796,1547],{"class":3462},[1115,27798,27799],{"class":3478}," 11.9",[1115,27801,1547],{"class":3462},[1115,27803,27804],{"class":3478}," 12.2",[1115,27806,1547],{"class":3462},[1115,27808,27809],{"class":3478}," 13.0",[1115,27811,1547],{"class":3462},[1115,27813,27814],{"class":3478}," 14.3",[1115,27816,1547],{"class":3462},[1115,27818,27804],{"class":3478},[1115,27820,1547],{"class":3462},[1115,27822,27823],{"class":3478}," 11.8",[1115,27825,1547],{"class":3462},[1115,27827,27828],{"class":3478}," 14.0",[1115,27830,3655],{"class":3470},[1115,27832,27833,27836,27838,27840,27842,27844,27846,27848,27850,27853,27855,27858],{"class":3455,"line":27},[1115,27834,27835],{"class":3466},"t.test",[1115,27837,1626],{"class":3470},[1115,27839,6476],{"class":3458},[1115,27841,1547],{"class":3462},[1115,27843,25338],{"class":3458},[1115,27845,3551],{"class":3462},[1115,27847,3488],{"class":3478},[1115,27849,1547],{"class":3462},[1115,27851,27852],{"class":3458}," alternative",[1115,27854,3551],{"class":3462},[1115,27856,27857],{"class":3594}," \"two.sided\"",[1115,27859,3655],{"class":3470},[3447,27861,27864],{"className":27862,"code":27863,"language":3677,"meta":1229},[3675],"    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",[3223,27865,27863],{"__ignoreMap":1229},[1110,27867,27868,27870,27871,27874,27875,27878,27879,27882,27883,27906],{},[3223,27869,6900],{}," je testové kritérium, ",[3223,27872,27873],{},"df"," stupně volnosti, ",[3223,27876,27877],{},"p-value"," p-hodnota pro zvolenou alternativu a ",[3223,27880,27881],{},"mean of x"," výběrový průměr. Zde ",[1115,27884,27886],{"className":27885},[1292],[1294,27887,27888],{"xmlns":1296},[1298,27889,27890,27903],{},[1301,27891,27892,27894,27896,27899,27901],{},[1307,27893,1110],{},[1437,27895,1733],{},[1311,27897,27898],{},"0,02843",[1437,27900,4086],{},[1311,27902,3738],{},[1315,27904,27905],{"encoding":1317},"p = 0{,}02843 \u003C 0{,}05",": úprava trasy průměrnou dobu jízdy (původně 12 minut) statisticky významně změnila.",[1103,27908,27910,27917,28005,28061,28153],{"className":27909,"dataCallout":3230},[1106,3229],[1110,27911,27913,27916],{"className":27912},[1113],[1115,27914],{"className":27915,"ariaHidden":1121},[1118,3237,1120],"Příklad: Kontrola objemu lahví",[1110,27918,27919,27920,27942,27943,27961,27962,27985,27986,28004],{},"Pivovar plní lahve, deklarovaný objem je ",[1115,27921,27923],{"className":27922},[1292],[1294,27924,27925],{"xmlns":1296},[1298,27926,27927,27939],{},[1301,27928,27929,27935,27937],{},[1304,27930,27931,27933],{},[1307,27932,6647],{},[1311,27934,1313],{},[1437,27936,1733],{},[1311,27938,8215],{},[1315,27940,27941],{"encoding":1317},"\\mu_0 = 0{,}5"," l. Náhodný výběr ",[1115,27944,27946],{"className":27945},[1292],[1294,27947,27948],{"xmlns":1296},[1298,27949,27950,27958],{},[1301,27951,27952,27954,27956],{},[1307,27953,1435],{},[1437,27955,1733],{},[1311,27957,3799],{},[1315,27959,27960],{"encoding":1317},"n = 20"," lahví dal ",[1115,27963,27965],{"className":27964},[1292],[1294,27966,27967],{"xmlns":1296},[1298,27968,27969,27982],{},[1301,27970,27971,27977,27979],{},[2475,27972,27973,27975],{"accent":1121},[1307,27974,6476],{},[1437,27976,11217],{},[1437,27978,1733],{},[1311,27980,27981],{},"0,492",[1315,27983,27984],{"encoding":1317},"\\bar{x} = 0{,}492"," l, ",[1115,27987,27989],{"className":27988},[1292],[1294,27990,27991],{"xmlns":1296},[1298,27992,27993,28001],{},[1301,27994,27995,27997,27999],{},[1307,27996,1605],{},[1437,27998,1733],{},[1311,28000,14553],{},[1315,28002,28003],{"encoding":1317},"s = 0{,}015"," l. Na hladině významnosti 5 % ověřte podezření, že pivovar lahve nedoplňuje.",[1110,28006,28007,28033,28034,28060],{},[1115,28008,28010],{"className":28009},[1292],[1294,28011,28012],{"xmlns":1296},[1298,28013,28014,28030],{},[1301,28015,28016,28022,28024,28026,28028],{},[1304,28017,28018,28020],{},[1307,28019,1309],{},[1311,28021,1313],{},[1437,28023,1709],{},[1307,28025,6647],{},[1437,28027,3104],{},[1311,28029,8215],{},[1315,28031,28032],{"encoding":1317},"H_0: \\mu \\ge 0{,}5"," l (objem je v pořádku nebo větší), ",[1115,28035,28037],{"className":28036},[1292],[1294,28038,28039],{"xmlns":1296},[1298,28040,28041,28057],{},[1301,28042,28043,28049,28051,28053,28055],{},[1304,28044,28045,28047],{},[1307,28046,1309],{},[1311,28048,1544],{},[1437,28050,1709],{},[1307,28052,6647],{},[1437,28054,4086],{},[1311,28056,8215],{},[1315,28058,28059],{"encoding":1317},"H_1: \\mu \u003C 0{,}5"," l (lahve jsou nedoplněné).",[1110,28062,28063],{},[1115,28064,28066],{"className":28065},[1292],[1294,28067,28068],{"xmlns":1296},[1298,28069,28070,28150],{},[1301,28071,28072,28074,28076,28088,28092,28094,28096,28099,28101,28103,28105,28107,28109,28111,28113,28115,28127,28129,28131,28133,28135,28137,28139,28141,28143,28145,28148],{},[1307,28073,6900],{},[1437,28075,1733],{},[2491,28077,28078,28086],{},[1301,28079,28080,28082,28084],{},[1311,28081,27981],{},[1437,28083,2817],{},[1311,28085,8215],{},[1311,28087,14553],{},[4207,28089,28090],{},[1311,28091,3799],{},[1437,28093,1733],{},[1437,28095,2817],{},[1311,28097,28098],{},"2,385",[1437,28100,1547],{"separator":1121},[1763,28102],{"width":1765},[1307,28104,1353],{},[1437,28106,1733],{},[1437,28108,3087],{"stretchy":1625},[1307,28110,6900],{},[1437,28112,6491],{},[1437,28114,2817],{},[1304,28116,28117,28119],{},[1307,28118,6900],{},[1301,28120,28121,28123,28125],{},[1311,28122,1313],{},[1437,28124,1547],{"separator":1121},[1311,28126,21555],{},[1437,28128,1626],{"stretchy":1625},[1311,28130,14477],{},[1437,28132,1637],{"stretchy":1625},[1437,28134,3147],{"stretchy":1625},[1437,28136,1733],{},[1437,28138,3087],{"stretchy":1625},[1307,28140,6900],{},[1437,28142,6491],{},[1437,28144,2817],{},[1311,28146,28147],{},"1,729",[1437,28149,3147],{"stretchy":1625},[1315,28151,28152],{"encoding":1317},"t = \\frac{0{,}492 - 0{,}5}{0{,}015}\\sqrt{20} = -2{,}385, \\qquad W = \\{t \\le -t_{0,95}(19)\\} = \\{t \\le -1{,}729\\}",[1110,28154,28155,28156,5761,28174,28191],{},"Protože ",[1115,28157,28159],{"className":28158},[1292],[1294,28160,28161],{"xmlns":1296},[1298,28162,28163,28171],{},[1301,28164,28165,28167,28169],{},[1307,28166,6900],{},[1437,28168,6775],{},[1307,28170,1353],{},[1315,28172,28173],{"encoding":1317},"t \\in W",[1115,28175,28177],{"className":28176},[1292],[1294,28178,28179],{"xmlns":1296},[1298,28180,28181,28189],{},[1301,28182,28183],{},[1304,28184,28185,28187],{},[1307,28186,1309],{},[1311,28188,1313],{},[1315,28190,1318],{"encoding":1317},": na hladině významnosti 5 % se potvrdilo, že pivovar plní lahve pod deklarovaný objem.",[1110,28193,28194,28195,28197,28198,1709],{},"Ze souhrnných charakteristik bez surových dat ",[3223,28196,27770],{}," spustit nelze — kritérium a kritická hodnota se dopočítají přímo z definice pomocí ",[3223,28199,28200],{},"qt()",[3447,28202,28204],{"className":3449,"code":28203,"language":71,"meta":1229,"style":1229},"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",[3223,28205,28206,28244,28276,28306,28311],{"__ignoreMap":1229},[1115,28207,28208,28211,28213,28216,28218,28220,28222,28225,28227,28229,28231,28234,28236,28239,28241],{"class":3455,"line":10},[1115,28209,28210],{"class":3458},"xbar",[1115,28212,3463],{"class":3462},[1115,28214,28215],{"class":3478}," 0.492",[1115,28217,24941],{"class":3470},[1115,28219,1605],{"class":3458},[1115,28221,3463],{"class":3462},[1115,28223,28224],{"class":3478}," 0.015",[1115,28226,24941],{"class":3470},[1115,28228,1435],{"class":3458},[1115,28230,3463],{"class":3462},[1115,28232,28233],{"class":3478}," 20",[1115,28235,24941],{"class":3470},[1115,28237,28238],{"class":3458},"mu0",[1115,28240,3463],{"class":3462},[1115,28242,28243],{"class":3478}," 0.5\n",[1115,28245,28246,28248,28250,28252,28254,28256,28259,28261,28263,28266,28268,28270,28272,28274],{"class":3455,"line":27},[1115,28247,6900],{"class":3458},[1115,28249,3463],{"class":3462},[1115,28251,4361],{"class":3470},[1115,28253,28210],{"class":3458},[1115,28255,25278],{"class":3462},[1115,28257,28258],{"class":3458}," mu0",[1115,28260,4355],{"class":3470},[1115,28262,4358],{"class":3462},[1115,28264,28265],{"class":3458}," s",[1115,28267,18398],{"class":3462},[1115,28269,4332],{"class":3466},[1115,28271,1626],{"class":3470},[1115,28273,1435],{"class":3458},[1115,28275,3655],{"class":3470},[1115,28277,28278,28281,28283,28286,28288,28291,28293,28295,28297,28300,28302,28304],{"class":3455,"line":148},[1115,28279,28280],{"class":3458},"t_krit",[1115,28282,3463],{"class":3462},[1115,28284,28285],{"class":3466}," qt",[1115,28287,1626],{"class":3470},[1115,28289,28290],{"class":3478},"0.05",[1115,28292,1547],{"class":3462},[1115,28294,10567],{"class":3458},[1115,28296,3551],{"class":3462},[1115,28298,28299],{"class":3458}," n",[1115,28301,25278],{"class":3462},[1115,28303,4395],{"class":3478},[1115,28305,3655],{"class":3470},[1115,28307,28308],{"class":3455,"line":111},[1115,28309,28310],{"class":3458},"t\n",[1115,28312,28313],{"class":3455,"line":96},[1115,28314,28315],{"class":3458},"t_krit\n",[3447,28317,28320],{"className":28318,"code":28319,"language":3677,"meta":1229},[3675],"[1] -2.385139\n[1] -1.729133\n",[3223,28321,28319],{"__ignoreMap":1229},[1110,28323,28324],{},[4137,28325],{"alt":28326,"className":28327,"src":28328},"mask-th-t-jednostranny",[1130,4141],"\u002Fwiki-assets\u002Fmask-th-t-jednostranny.png",[1110,28330,28331,28332,1709],{},"Další dva příklady mají k dispozici surová data, takže je lze otestovat přímo ",[3223,28333,27770],{},[1110,28335,28336,28339],{},[1279,28337,28338],{},"Životnost baterií."," Výrobce udává průměrnou životnost 10 hodin, na 11 bateriích byly naměřeny hodnoty v hodinách.",[3447,28341,28343],{"className":3449,"code":28342,"language":71,"meta":1229,"style":1229},"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",[3223,28344,28345,28408],{"__ignoreMap":1229},[1115,28346,28347,28350,28352,28354,28356,28359,28361,28364,28366,28369,28371,28374,28376,28379,28381,28384,28386,28388,28390,28393,28395,28397,28399,28402,28404,28406],{"class":3455,"line":10},[1115,28348,28349],{"class":3458},"x2",[1115,28351,3463],{"class":3462},[1115,28353,3589],{"class":3466},[1115,28355,1626],{"class":3470},[1115,28357,28358],{"class":3478},"9.5",[1115,28360,1547],{"class":3462},[1115,28362,28363],{"class":3478}," 10.5",[1115,28365,1547],{"class":3462},[1115,28367,28368],{"class":3478}," 8.9",[1115,28370,1547],{"class":3462},[1115,28372,28373],{"class":3478}," 9.2",[1115,28375,1547],{"class":3462},[1115,28377,28378],{"class":3478}," 10.0",[1115,28380,1547],{"class":3462},[1115,28382,28383],{"class":3478}," 8.5",[1115,28385,1547],{"class":3462},[1115,28387,28373],{"class":3478},[1115,28389,1547],{"class":3462},[1115,28391,28392],{"class":3478}," 8.8",[1115,28394,1547],{"class":3462},[1115,28396,28378],{"class":3478},[1115,28398,1547],{"class":3462},[1115,28400,28401],{"class":3478}," 9.5",[1115,28403,1547],{"class":3462},[1115,28405,28373],{"class":3478},[1115,28407,3655],{"class":3470},[1115,28409,28410,28412,28414,28416,28418,28420,28422,28424,28426,28428,28430,28432],{"class":3455,"line":27},[1115,28411,27835],{"class":3466},[1115,28413,1626],{"class":3470},[1115,28415,28349],{"class":3458},[1115,28417,1547],{"class":3462},[1115,28419,25338],{"class":3458},[1115,28421,3551],{"class":3462},[1115,28423,9235],{"class":3478},[1115,28425,1547],{"class":3462},[1115,28427,27852],{"class":3458},[1115,28429,3551],{"class":3462},[1115,28431,27857],{"class":3594},[1115,28433,3655],{"class":3470},[3447,28435,28438],{"className":28436,"code":28437,"language":3677,"meta":1229},[3675],"    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",[3223,28439,28437],{"__ignoreMap":1229},[1110,28441,28442,28465],{},[1115,28443,28445],{"className":28444},[1292],[1294,28446,28447],{"xmlns":1296},[1298,28448,28449,28462],{},[1301,28450,28451,28453,28455,28458,28460],{},[1307,28452,1110],{},[1437,28454,1733],{},[1311,28456,28457],{},"0,006548",[1437,28459,4086],{},[1311,28461,3738],{},[1315,28463,28464],{"encoding":1317},"p = 0{,}006548 \u003C 0{,}05",": skutečná životnost se od deklarovaných 10 hodin statisticky významně liší (baterie vydrží méně).",[1110,28467,28468,28471],{},[1279,28469,28470],{},"Odpad materiálu."," Na deseti obráběných kusech byl naměřen odpad materiálu v procentech; testuje se rozdíl proti 4 % a zároveň normalita dat.",[3447,28473,28475],{"className":3449,"code":28474,"language":71,"meta":1229,"style":1229},"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",[3223,28476,28477,28528,28554],{"__ignoreMap":1229},[1115,28478,28479,28482,28484,28486,28488,28490,28492,28494,28496,28498,28500,28502,28504,28506,28508,28510,28512,28514,28516,28518,28520,28522,28524,28526],{"class":3455,"line":10},[1115,28480,28481],{"class":3458},"x3",[1115,28483,3463],{"class":3462},[1115,28485,3589],{"class":3466},[1115,28487,1626],{"class":3470},[1115,28489,11744],{"class":3478},[1115,28491,1547],{"class":3462},[1115,28493,11749],{"class":3478},[1115,28495,1547],{"class":3462},[1115,28497,11754],{"class":3478},[1115,28499,1547],{"class":3462},[1115,28501,11759],{"class":3478},[1115,28503,1547],{"class":3462},[1115,28505,11754],{"class":3478},[1115,28507,1547],{"class":3462},[1115,28509,11754],{"class":3478},[1115,28511,1547],{"class":3462},[1115,28513,11772],{"class":3478},[1115,28515,1547],{"class":3462},[1115,28517,11777],{"class":3478},[1115,28519,1547],{"class":3462},[1115,28521,11749],{"class":3478},[1115,28523,1547],{"class":3462},[1115,28525,11749],{"class":3478},[1115,28527,3655],{"class":3470},[1115,28529,28530,28532,28534,28536,28538,28540,28542,28544,28546,28548,28550,28552],{"class":3455,"line":27},[1115,28531,27835],{"class":3466},[1115,28533,1626],{"class":3470},[1115,28535,28481],{"class":3458},[1115,28537,1547],{"class":3462},[1115,28539,25338],{"class":3458},[1115,28541,3551],{"class":3462},[1115,28543,3554],{"class":3478},[1115,28545,1547],{"class":3462},[1115,28547,27852],{"class":3458},[1115,28549,3551],{"class":3462},[1115,28551,27857],{"class":3594},[1115,28553,3655],{"class":3470},[1115,28555,28556,28558,28560,28562],{"class":3455,"line":148},[1115,28557,17334],{"class":3466},[1115,28559,1626],{"class":3470},[1115,28561,28481],{"class":3458},[1115,28563,3655],{"class":3470},[3447,28565,28568],{"className":28566,"code":28567,"language":3677,"meta":1229},[3675],"    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",[3223,28569,28567],{"__ignoreMap":1229},[1110,28571,28572,28595,28596,28619],{},[1115,28573,28575],{"className":28574},[1292],[1294,28576,28577],{"xmlns":1296},[1298,28578,28579,28592],{},[1301,28580,28581,28583,28585,28588,28590],{},[1307,28582,1110],{},[1437,28584,1733],{},[1311,28586,28587],{},"0,0343",[1437,28589,4086],{},[1311,28591,3738],{},[1315,28593,28594],{"encoding":1317},"p = 0{,}0343 \u003C 0{,}05",": průměrný odpad se od 4 % statisticky významně liší (výběrový průměr 3,86 %). Shapiro-Wilkův test dává ",[1115,28597,28599],{"className":28598},[1292],[1294,28600,28601],{"xmlns":1296},[1298,28602,28603,28616],{},[1301,28604,28605,28607,28609,28612,28614],{},[1307,28606,1110],{},[1437,28608,1733],{},[1311,28610,28611],{},"0,4634",[1437,28613,1439],{},[1311,28615,3738],{},[1315,28617,28618],{"encoding":1317},"p = 0{,}4634 > 0{,}05",", předpoklad normality pro t-test je v pořádku.",[1136,28621,28623],{"id":28622},"párový-t-test","Párový t-test",[1110,28625,28626,28627,28657,28658,6537,28692,28730,28731,28744,28745,5495,28763,28783,28784,28801,28802,27346],{},"Používá se, když jsou měření závislá — na stejných objektech se měří dvě hodnoty ",[1115,28628,28630],{"className":28629},[1292],[1294,28631,28632],{"xmlns":1296},[1298,28633,28634,28654],{},[1301,28635,28636,28638,28644,28646,28652],{},[1437,28637,1626],{"stretchy":1625},[1304,28639,28640,28642],{},[1307,28641,6488],{},[1307,28643,1629],{},[1437,28645,1547],{"separator":1121},[1304,28647,28648,28650],{},[1307,28649,6844],{},[1307,28651,1629],{},[1437,28653,1637],{"stretchy":1625},[1315,28655,28656],{"encoding":1317},"(X_i, Y_i)"," a vyhodnocují se jejich diference ",[1115,28659,28661],{"className":28660},[1292],[1294,28662,28663],{"xmlns":1296},[1298,28664,28665,28689],{},[1301,28666,28667,28673,28675,28681,28683],{},[1304,28668,28669,28671],{},[1307,28670,7910],{},[1307,28672,1629],{},[1437,28674,1733],{},[1304,28676,28677,28679],{},[1307,28678,6488],{},[1307,28680,1629],{},[1437,28682,2817],{},[1304,28684,28685,28687],{},[1307,28686,6844],{},[1307,28688,1629],{},[1315,28690,28691],{"encoding":1317},"D_i = X_i - Y_i",[1115,28693,28695],{"className":28694},[1292],[1294,28696,28697],{"xmlns":1296},[1298,28698,28699,28727],{},[1301,28700,28701,28703,28705,28707,28709,28715,28717,28725],{},[1307,28702,7910],{},[1437,28704,8941],{},[1307,28706,6642],{},[1437,28708,1626],{"stretchy":1625},[1304,28710,28711,28713],{},[1307,28712,6647],{},[1307,28714,7910],{},[1437,28716,1547],{"separator":1121},[3106,28718,28719,28721,28723],{},[1307,28720,6655],{},[1307,28722,7910],{},[1311,28724,1337],{},[1437,28726,1637],{"stretchy":1625},[1315,28728,28729],{"encoding":1317},"D \\sim N(\\mu_D, \\sigma_D^2)",". Z ",[1115,28732,28734],{"className":28733},[1292],[1294,28735,28736],{"xmlns":1296},[1298,28737,28738,28742],{},[1301,28739,28740],{},[1307,28741,1435],{},[1315,28743,1435],{"encoding":1317}," dvojic se určí ",[1115,28746,28748],{"className":28747},[1292],[1294,28749,28750],{"xmlns":1296},[1298,28751,28752,28760],{},[1301,28753,28754],{},[2475,28755,28756,28758],{"accent":1121},[1307,28757,7553],{},[1437,28759,11217],{},[1315,28761,28762],{"encoding":1317},"\\bar{d}",[1115,28764,28766],{"className":28765},[1292],[1294,28767,28768],{"xmlns":1296},[1298,28769,28770,28780],{},[1301,28771,28772],{},[3106,28773,28774,28776,28778],{},[1307,28775,1605],{},[1307,28777,7553],{},[1311,28779,1337],{},[1315,28781,28782],{"encoding":1317},"s_d^2","; testuje se vztah mezi zvoleným číslem ",[1115,28785,28787],{"className":28786},[1292],[1294,28788,28789],{"xmlns":1296},[1298,28790,28791,28799],{},[1301,28792,28793],{},[1304,28794,28795,28797],{},[1307,28796,6647],{},[1311,28798,1313],{},[1315,28800,27331],{"encoding":1317}," (obvykle 0) a ",[1115,28803,28805],{"className":28804},[1292],[1294,28806,28807],{"xmlns":1296},[1298,28808,28809,28817],{},[1301,28810,28811],{},[1304,28812,28813,28815],{},[1307,28814,6647],{},[1307,28816,7910],{},[1315,28818,28819],{"encoding":1317},"\\mu_D",[1115,28821,28823],{"className":28822},[1292],[1294,28824,28825],{"xmlns":1296,"display":1715},[1298,28826,28827,28877],{},[1301,28828,28829,28831,28833,28857,28861,28863,28875],{},[1307,28830,6858],{},[1437,28832,1733],{},[2491,28834,28835,28851],{},[1301,28836,28837,28843,28845],{},[2475,28838,28839,28841],{"accent":1121},[1307,28840,7553],{},[1437,28842,11217],{},[1437,28844,2817],{},[1304,28846,28847,28849],{},[1307,28848,6647],{},[1311,28850,1313],{},[1304,28852,28853,28855],{},[1307,28854,1605],{},[1307,28856,7553],{},[4207,28858,28859],{},[1307,28860,1435],{},[1437,28862,8941],{},[1304,28864,28865,28867],{},[1307,28866,6900],{},[1301,28868,28869,28871,28873],{},[1307,28870,1435],{},[1437,28872,2817],{},[1311,28874,1544],{},[1307,28876,1417],{"mathvariant":1872},[1315,28878,28879],{"encoding":1317},"T = \\frac{\\bar{d} - \\mu_0}{s_d}\\sqrt{n} \\sim t_{n-1}.",[1141,28881,28882,28939],{},[1144,28883,28884],{},[1147,28885,28886,28905,28924],{},[1150,28887,28888],{},[1115,28889,28891],{"className":28890},[1292],[1294,28892,28893],{"xmlns":1296},[1298,28894,28895,28903],{},[1301,28896,28897],{},[1304,28898,28899,28901],{},[1307,28900,1309],{},[1311,28902,1313],{},[1315,28904,1318],{"encoding":1317},[1150,28906,28907],{},[1115,28908,28910],{"className":28909},[1292],[1294,28911,28912],{"xmlns":1296},[1298,28913,28914,28922],{},[1301,28915,28916],{},[1304,28917,28918,28920],{},[1307,28919,1309],{},[1311,28921,1544],{},[1315,28923,2749],{"encoding":1317},[1150,28925,27469,28926],{},[1115,28927,28929],{"className":28928},[1292],[1294,28930,28931],{"xmlns":1296},[1298,28932,28933,28937],{},[1301,28934,28935],{},[1307,28936,1353],{},[1315,28938,1353],{"encoding":1317},[1157,28940,28941,29038,29143],{},[1147,28942,28943,28971,28999],{},[1162,28944,28945],{},[1115,28946,28948],{"className":28947},[1292],[1294,28949,28950],{"xmlns":1296},[1298,28951,28952,28968],{},[1301,28953,28954,28960,28962],{},[1304,28955,28956,28958],{},[1307,28957,6647],{},[1307,28959,7910],{},[1437,28961,6491],{},[1304,28963,28964,28966],{},[1307,28965,6647],{},[1311,28967,1313],{},[1315,28969,28970],{"encoding":1317},"\\mu_D \\le \\mu_0",[1162,28972,28973],{},[1115,28974,28976],{"className":28975},[1292],[1294,28977,28978],{"xmlns":1296},[1298,28979,28980,28996],{},[1301,28981,28982,28988,28990],{},[1304,28983,28984,28986],{},[1307,28985,6647],{},[1307,28987,7910],{},[1437,28989,1439],{},[1304,28991,28992,28994],{},[1307,28993,6647],{},[1311,28995,1313],{},[1315,28997,28998],{"encoding":1317},"\\mu_D > \\mu_0",[1162,29000,29001],{},[1115,29002,29004],{"className":29003},[1292],[1294,29005,29006],{"xmlns":1296},[1298,29007,29008,29036],{},[1301,29009,29010,29012,29014,29026,29028,29030,29032,29034],{},[1307,29011,6900],{},[1437,29013,3104],{},[1304,29015,29016,29018],{},[1307,29017,6900],{},[1301,29019,29020,29022,29024],{},[1311,29021,1544],{},[1437,29023,2817],{},[1307,29025,3118],{},[1437,29027,1626],{"stretchy":1625},[1307,29029,1435],{},[1437,29031,2817],{},[1311,29033,1544],{},[1437,29035,1637],{"stretchy":1625},[1315,29037,27574],{"encoding":1317},[1147,29039,29040,29068,29096],{},[1162,29041,29042],{},[1115,29043,29045],{"className":29044},[1292],[1294,29046,29047],{"xmlns":1296},[1298,29048,29049,29065],{},[1301,29050,29051,29057,29059],{},[1304,29052,29053,29055],{},[1307,29054,6647],{},[1307,29056,7910],{},[1437,29058,1733],{},[1304,29060,29061,29063],{},[1307,29062,6647],{},[1311,29064,1313],{},[1315,29066,29067],{"encoding":1317},"\\mu_D = \\mu_0",[1162,29069,29070],{},[1115,29071,29073],{"className":29072},[1292],[1294,29074,29075],{"xmlns":1296},[1298,29076,29077,29093],{},[1301,29078,29079,29085,29087],{},[1304,29080,29081,29083],{},[1307,29082,6647],{},[1307,29084,7910],{},[1437,29086,10714],{"mathvariant":1872},[1304,29088,29089,29091],{},[1307,29090,6647],{},[1311,29092,1313],{},[1315,29094,29095],{"encoding":1317},"\\mu_D \\neq \\mu_0",[1162,29097,29098],{},[1115,29099,29101],{"className":29100},[1292],[1294,29102,29103],{"xmlns":1296},[1298,29104,29105,29141],{},[1301,29106,29107,29109,29111,29113,29115,29131,29133,29135,29137,29139],{},[1437,29108,22781],{"stretchy":1625},[1307,29110,6900],{},[1437,29112,22781],{"stretchy":1625},[1437,29114,3104],{},[1304,29116,29117,29119],{},[1307,29118,6900],{},[1301,29120,29121,29123,29125,29127,29129],{},[1311,29122,1544],{},[1437,29124,2817],{},[1307,29126,3118],{},[1307,29128,4358],{"mathvariant":1872},[1311,29130,1337],{},[1437,29132,1626],{"stretchy":1625},[1307,29134,1435],{},[1437,29136,2817],{},[1311,29138,1544],{},[1437,29140,1637],{"stretchy":1625},[1315,29142,27672],{"encoding":1317},[1147,29144,29145,29173,29201],{},[1162,29146,29147],{},[1115,29148,29150],{"className":29149},[1292],[1294,29151,29152],{"xmlns":1296},[1298,29153,29154,29170],{},[1301,29155,29156,29162,29164],{},[1304,29157,29158,29160],{},[1307,29159,6647],{},[1307,29161,7910],{},[1437,29163,3104],{},[1304,29165,29166,29168],{},[1307,29167,6647],{},[1311,29169,1313],{},[1315,29171,29172],{"encoding":1317},"\\mu_D \\ge \\mu_0",[1162,29174,29175],{},[1115,29176,29178],{"className":29177},[1292],[1294,29179,29180],{"xmlns":1296},[1298,29181,29182,29198],{},[1301,29183,29184,29190,29192],{},[1304,29185,29186,29188],{},[1307,29187,6647],{},[1307,29189,7910],{},[1437,29191,4086],{},[1304,29193,29194,29196],{},[1307,29195,6647],{},[1311,29197,1313],{},[1315,29199,29200],{"encoding":1317},"\\mu_D \u003C \\mu_0",[1162,29202,29203],{},[1115,29204,29206],{"className":29205},[1292],[1294,29207,29208],{"xmlns":1296},[1298,29209,29210,29240],{},[1301,29211,29212,29214,29216,29218,29230,29232,29234,29236,29238],{},[1307,29213,6900],{},[1437,29215,6491],{},[1437,29217,2817],{},[1304,29219,29220,29222],{},[1307,29221,6900],{},[1301,29223,29224,29226,29228],{},[1311,29225,1544],{},[1437,29227,2817],{},[1307,29229,3118],{},[1437,29231,1626],{"stretchy":1625},[1307,29233,1435],{},[1437,29235,2817],{},[1311,29237,1544],{},[1437,29239,1637],{"stretchy":1625},[1315,29241,27764],{"encoding":1317},[1103,29243,29245,29252,29394,29458,29544],{"className":29244,"dataCallout":3230},[1106,3229],[1110,29246,29248,29251],{"className":29247},[1113],[1115,29249],{"className":29250,"ariaHidden":1121},[1118,3237,1120],"Příklad: Snížení spotřeby paliva aditivem",[1110,29253,29254,29255,29273,29274,29292,29293,29311,29312,29345,29346,29369,29370,29393],{},"U ",[1115,29256,29258],{"className":29257},[1292],[1294,29259,29260],{"xmlns":1296},[1298,29261,29262,29270],{},[1301,29263,29264,29266,29268],{},[1307,29265,1435],{},[1437,29267,1733],{},[1311,29269,8791],{},[1315,29271,29272],{"encoding":1317},"n = 10"," vozů se změřila spotřeba před přidáním aditiva (",[1115,29275,29277],{"className":29276},[1292],[1294,29278,29279],{"xmlns":1296},[1298,29280,29281,29289],{},[1301,29282,29283],{},[1304,29284,29285,29287],{},[1307,29286,6488],{},[1307,29288,1629],{},[1315,29290,29291],{"encoding":1317},"X_i",") a po něm (",[1115,29294,29296],{"className":29295},[1292],[1294,29297,29298],{"xmlns":1296},[1298,29299,29300,29308],{},[1301,29301,29302],{},[1304,29303,29304,29306],{},[1307,29305,6844],{},[1307,29307,1629],{},[1315,29309,29310],{"encoding":1317},"Y_i","), diference ",[1115,29313,29315],{"className":29314},[1292],[1294,29316,29317],{"xmlns":1296},[1298,29318,29319,29343],{},[1301,29320,29321,29327,29329,29335,29337],{},[1304,29322,29323,29325],{},[1307,29324,7910],{},[1307,29326,1629],{},[1437,29328,1733],{},[1304,29330,29331,29333],{},[1307,29332,6488],{},[1307,29334,1629],{},[1437,29336,2817],{},[1304,29338,29339,29341],{},[1307,29340,6844],{},[1307,29342,1629],{},[1315,29344,28691],{"encoding":1317}," představují úsporu paliva. Z dat vyšla průměrná úspora ",[1115,29347,29349],{"className":29348},[1292],[1294,29350,29351],{"xmlns":1296},[1298,29352,29353,29366],{},[1301,29354,29355,29361,29363],{},[2475,29356,29357,29359],{"accent":1121},[1307,29358,7553],{},[1437,29360,11217],{},[1437,29362,1733],{},[1311,29364,29365],{},"0,4",[1315,29367,29368],{"encoding":1317},"\\bar{d} = 0{,}4"," l\u002F100 km, ",[1115,29371,29373],{"className":29372},[1292],[1294,29374,29375],{"xmlns":1296},[1298,29376,29377,29390],{},[1301,29378,29379,29385,29387],{},[1304,29380,29381,29383],{},[1307,29382,1605],{},[1307,29384,7553],{},[1437,29386,1733],{},[1311,29388,29389],{},"0,35",[1315,29391,29392],{"encoding":1317},"s_d = 0{,}35"," l\u002F100 km. Ověřte, že aditivum spotřebu statisticky významně snižuje.",[1110,29395,29396,29426,29427,29457],{},[1115,29397,29399],{"className":29398},[1292],[1294,29400,29401],{"xmlns":1296},[1298,29402,29403,29423],{},[1301,29404,29405,29411,29413,29419,29421],{},[1304,29406,29407,29409],{},[1307,29408,1309],{},[1311,29410,1313],{},[1437,29412,1709],{},[1304,29414,29415,29417],{},[1307,29416,6647],{},[1307,29418,7910],{},[1437,29420,6491],{},[1311,29422,1313],{},[1315,29424,29425],{"encoding":1317},"H_0: \\mu_D \\le 0"," (aditivum nemá vliv nebo spotřebu zvyšuje), ",[1115,29428,29430],{"className":29429},[1292],[1294,29431,29432],{"xmlns":1296},[1298,29433,29434,29454],{},[1301,29435,29436,29442,29444,29450,29452],{},[1304,29437,29438,29440],{},[1307,29439,1309],{},[1311,29441,1544],{},[1437,29443,1709],{},[1304,29445,29446,29448],{},[1307,29447,6647],{},[1307,29449,7910],{},[1437,29451,1439],{},[1311,29453,1313],{},[1315,29455,29456],{"encoding":1317},"H_1: \\mu_D > 0"," (aditivum spotřebu snižuje).",[1110,29459,29460],{},[1115,29461,29463],{"className":29462},[1292],[1294,29464,29465],{"xmlns":1296},[1298,29466,29467,29541],{},[1301,29468,29469,29471,29473,29485,29489,29491,29494,29496,29498,29500,29502,29504,29506,29508,29520,29522,29524,29526,29528,29530,29532,29534,29536,29539],{},[1307,29470,6900],{},[1437,29472,1733],{},[2491,29474,29475,29483],{},[1301,29476,29477,29479,29481],{},[1311,29478,29365],{},[1437,29480,2817],{},[1311,29482,1313],{},[1311,29484,29389],{},[4207,29486,29487],{},[1311,29488,8791],{},[1437,29490,1733],{},[1311,29492,29493],{},"3,614",[1437,29495,1547],{"separator":1121},[1763,29497],{"width":1765},[1307,29499,1353],{},[1437,29501,1733],{},[1437,29503,3087],{"stretchy":1625},[1307,29505,6900],{},[1437,29507,3104],{},[1304,29509,29510,29512],{},[1307,29511,6900],{},[1301,29513,29514,29516,29518],{},[1311,29515,1313],{},[1437,29517,1547],{"separator":1121},[1311,29519,21555],{},[1437,29521,1626],{"stretchy":1625},[1311,29523,3348],{},[1437,29525,1637],{"stretchy":1625},[1437,29527,3147],{"stretchy":1625},[1437,29529,1733],{},[1437,29531,3087],{"stretchy":1625},[1307,29533,6900],{},[1437,29535,3104],{},[1311,29537,29538],{},"1,833",[1437,29540,3147],{"stretchy":1625},[1315,29542,29543],{"encoding":1317},"t = \\frac{0{,}4 - 0}{0{,}35}\\sqrt{10} = 3{,}614, \\qquad W = \\{t \\ge t_{0,95}(9)\\} = \\{t \\ge 1{,}833\\}",[1110,29545,28155,29546,5761,29563,29580],{},[1115,29547,29549],{"className":29548},[1292],[1294,29550,29551],{"xmlns":1296},[1298,29552,29553,29561],{},[1301,29554,29555,29557,29559],{},[1307,29556,6900],{},[1437,29558,6775],{},[1307,29560,1353],{},[1315,29562,28173],{"encoding":1317},[1115,29564,29566],{"className":29565},[1292],[1294,29567,29568],{"xmlns":1296},[1298,29569,29570,29578],{},[1301,29571,29572],{},[1304,29573,29574,29576],{},[1307,29575,1309],{},[1311,29577,1313],{},[1315,29579,1318],{"encoding":1317},": aditivum prokazatelně snižuje průměrnou spotřebu paliva.",[3447,29582,29584],{"className":3449,"code":29583,"language":71,"meta":1229,"style":1229},"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",[3223,29585,29586,29615,29646,29672,29676],{"__ignoreMap":1229},[1115,29587,29588,29591,29593,29596,29598,29601,29603,29606,29608,29610,29612],{"class":3455,"line":10},[1115,29589,29590],{"class":3458},"dbar",[1115,29592,3463],{"class":3462},[1115,29594,29595],{"class":3478}," 0.4",[1115,29597,24941],{"class":3470},[1115,29599,29600],{"class":3458},"sd_d",[1115,29602,3463],{"class":3462},[1115,29604,29605],{"class":3478}," 0.35",[1115,29607,24941],{"class":3470},[1115,29609,1435],{"class":3458},[1115,29611,3463],{"class":3462},[1115,29613,29614],{"class":3478}," 10\n",[1115,29616,29617,29619,29621,29623,29625,29627,29629,29631,29633,29636,29638,29640,29642,29644],{"class":3455,"line":27},[1115,29618,6900],{"class":3458},[1115,29620,3463],{"class":3462},[1115,29622,4361],{"class":3470},[1115,29624,29590],{"class":3458},[1115,29626,25278],{"class":3462},[1115,29628,9728],{"class":3478},[1115,29630,4355],{"class":3470},[1115,29632,4358],{"class":3462},[1115,29634,29635],{"class":3458}," sd_d",[1115,29637,18398],{"class":3462},[1115,29639,4332],{"class":3466},[1115,29641,1626],{"class":3470},[1115,29643,1435],{"class":3458},[1115,29645,3655],{"class":3470},[1115,29647,29648,29650,29652,29654,29656,29658,29660,29662,29664,29666,29668,29670],{"class":3455,"line":148},[1115,29649,28280],{"class":3458},[1115,29651,3463],{"class":3462},[1115,29653,28285],{"class":3466},[1115,29655,1626],{"class":3470},[1115,29657,10584],{"class":3478},[1115,29659,1547],{"class":3462},[1115,29661,10567],{"class":3458},[1115,29663,3551],{"class":3462},[1115,29665,28299],{"class":3458},[1115,29667,25278],{"class":3462},[1115,29669,4395],{"class":3478},[1115,29671,3655],{"class":3470},[1115,29673,29674],{"class":3455,"line":111},[1115,29675,28310],{"class":3458},[1115,29677,29678],{"class":3455,"line":96},[1115,29679,28315],{"class":3458},[3447,29681,29684],{"className":29682,"code":29683,"language":3677,"meta":1229},[3675],"[1] 3.614032\n[1] 1.833113\n",[3223,29685,29683],{"__ignoreMap":1229},[1103,29687,29689,29696,29699,29844,29850],{"className":29688,"dataCallout":6167},[1106,6166],[1110,29690,29692,29695],{"className":29691},[1113],[1115,29693],{"className":29694,"ariaHidden":1121},[1118,6174,1120],"Ověřte normalitu diferencí, ne jen výsledek testu",[1110,29697,29698],{},"Realitní kancelář nechala dva odhadce ocenit osm nemovitostí (tisíce Kč):",[3447,29700,29702],{"className":3449,"code":29701,"language":71,"meta":1229,"style":1229},"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",[3223,29703,29704,29755,29806,29830],{"__ignoreMap":1229},[1115,29705,29706,29709,29711,29713,29715,29718,29720,29723,29725,29728,29730,29733,29735,29738,29740,29743,29745,29748,29750,29753],{"class":3455,"line":10},[1115,29707,29708],{"class":3458},"estA",[1115,29710,3463],{"class":3462},[1115,29712,3589],{"class":3466},[1115,29714,1626],{"class":3470},[1115,29716,29717],{"class":3478},"3282",[1115,29719,1547],{"class":3462},[1115,29721,29722],{"class":3478}," 2506",[1115,29724,1547],{"class":3462},[1115,29726,29727],{"class":3478}," 2812",[1115,29729,1547],{"class":3462},[1115,29731,29732],{"class":3478}," 5453",[1115,29734,1547],{"class":3462},[1115,29736,29737],{"class":3478}," 3263",[1115,29739,1547],{"class":3462},[1115,29741,29742],{"class":3478}," 4571",[1115,29744,1547],{"class":3462},[1115,29746,29747],{"class":3478}," 3121",[1115,29749,1547],{"class":3462},[1115,29751,29752],{"class":3478}," 2963",[1115,29754,3655],{"class":3470},[1115,29756,29757,29760,29762,29764,29766,29769,29771,29774,29776,29779,29781,29784,29786,29789,29791,29794,29796,29799,29801,29804],{"class":3455,"line":27},[1115,29758,29759],{"class":3458},"estB",[1115,29761,3463],{"class":3462},[1115,29763,3589],{"class":3466},[1115,29765,1626],{"class":3470},[1115,29767,29768],{"class":3478},"3271",[1115,29770,1547],{"class":3462},[1115,29772,29773],{"class":3478}," 2531",[1115,29775,1547],{"class":3462},[1115,29777,29778],{"class":3478}," 2799",[1115,29780,1547],{"class":3462},[1115,29782,29783],{"class":3478}," 5471",[1115,29785,1547],{"class":3462},[1115,29787,29788],{"class":3478}," 3285",[1115,29790,1547],{"class":3462},[1115,29792,29793],{"class":3478}," 4557",[1115,29795,1547],{"class":3462},[1115,29797,29798],{"class":3478}," 3139",[1115,29800,1547],{"class":3462},[1115,29802,29803],{"class":3478}," 2976",[1115,29805,3655],{"class":3470},[1115,29807,29808,29810,29812,29814,29816,29819,29821,29824,29826,29828],{"class":3455,"line":148},[1115,29809,27835],{"class":3466},[1115,29811,1626],{"class":3470},[1115,29813,29708],{"class":3458},[1115,29815,1547],{"class":3462},[1115,29817,29818],{"class":3458}," estB",[1115,29820,1547],{"class":3462},[1115,29822,29823],{"class":3458}," paired",[1115,29825,3551],{"class":3462},[1115,29827,3564],{"class":3478},[1115,29829,3655],{"class":3470},[1115,29831,29832,29834,29836,29838,29840,29842],{"class":3455,"line":111},[1115,29833,17334],{"class":3466},[1115,29835,1626],{"class":3470},[1115,29837,29708],{"class":3458},[1115,29839,25278],{"class":3462},[1115,29841,29818],{"class":3458},[1115,29843,3655],{"class":3470},[3447,29845,29848],{"className":29846,"code":29847,"language":3677,"meta":1229},[3675],"    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",[3223,29849,29847],{"__ignoreMap":1229},[1110,29851,29852,29853,4361,29870,29889,29890,29913],{},"Párový t-test sám nezamítá ",[1115,29854,29856],{"className":29855},[1292],[1294,29857,29858],{"xmlns":1296},[1298,29859,29860,29868],{},[1301,29861,29862],{},[1304,29863,29864,29866],{},[1307,29865,1309],{},[1311,29867,1313],{},[1315,29869,1318],{"encoding":1317},[1115,29871,29873],{"className":29872},[1292],[1294,29874,29875],{"xmlns":1296},[1298,29876,29877,29886],{},[1301,29878,29879,29881,29883],{},[1307,29880,1110],{},[1437,29882,1733],{},[1311,29884,29885],{},"0,2635",[1315,29887,29888],{"encoding":1317},"p = 0{,}2635","): odhadci se podle něj neliší. Shapiro-Wilkův test na diferencích ale dává ",[1115,29891,29893],{"className":29892},[1292],[1294,29894,29895],{"xmlns":1296},[1298,29896,29897,29910],{},[1301,29898,29899,29901,29903,29906,29908],{},[1307,29900,1110],{},[1437,29902,1733],{},[1311,29904,29905],{},"0,03203",[1437,29907,4086],{},[1311,29909,3738],{},[1315,29911,29912],{"encoding":1317},"p = 0{,}03203 \u003C 0{,}05"," — předpoklad normality diferencí je porušen a výsledek t-testu proto není spolehlivý. Správný postup je ověřit normalitu diferencí dříve, než se párový t-test interpretuje, a při jejím porušení použít párový Wilcoxonův test (viz oddíl Neparametrické testy níže).",[1136,29915,29917],{"id":29916},"testy-o-dvou-základních-souborech","Testy o dvou základních souborech",[1110,29919,29920,29921,29947,29948,29986,29987,5495,30005,29986,30043,30061,30062,5495,30094,30126,30127,30153,30154,1417],{},"Uvažují se dva nezávislé základní soubory ",[1115,29922,29924],{"className":29923},[1292],[1294,29925,29926],{"xmlns":1296},[1298,29927,29928,29944],{},[1301,29929,29930,29936,29938],{},[1304,29931,29932,29934],{},[1307,29933,8683],{},[1311,29935,1544],{},[1437,29937,1547],{"separator":1121},[1304,29939,29940,29942],{},[1307,29941,8683],{},[1311,29943,1337],{},[1315,29945,29946],{"encoding":1317},"Z_1, Z_2"," se znakem ",[1115,29949,29951],{"className":29950},[1292],[1294,29952,29953],{"xmlns":1296},[1298,29954,29955,29983],{},[1301,29956,29957,29959,29961,29963,29965,29971,29973,29981],{},[1307,29958,6488],{},[1437,29960,8941],{},[1307,29962,6642],{},[1437,29964,1626],{"stretchy":1625},[1304,29966,29967,29969],{},[1307,29968,6647],{},[1311,29970,1544],{},[1437,29972,1547],{"separator":1121},[3106,29974,29975,29977,29979],{},[1307,29976,6655],{},[1311,29978,1544],{},[1311,29980,1337],{},[1437,29982,1637],{"stretchy":1625},[1315,29984,29985],{"encoding":1317},"X \\sim N(\\mu_1, \\sigma_1^2)"," v ",[1115,29988,29990],{"className":29989},[1292],[1294,29991,29992],{"xmlns":1296},[1298,29993,29994,30002],{},[1301,29995,29996],{},[1304,29997,29998,30000],{},[1307,29999,8683],{},[1311,30001,1544],{},[1315,30003,30004],{"encoding":1317},"Z_1",[1115,30006,30008],{"className":30007},[1292],[1294,30009,30010],{"xmlns":1296},[1298,30011,30012,30040],{},[1301,30013,30014,30016,30018,30020,30022,30028,30030,30038],{},[1307,30015,6488],{},[1437,30017,8941],{},[1307,30019,6642],{},[1437,30021,1626],{"stretchy":1625},[1304,30023,30024,30026],{},[1307,30025,6647],{},[1311,30027,1337],{},[1437,30029,1547],{"separator":1121},[3106,30031,30032,30034,30036],{},[1307,30033,6655],{},[1311,30035,1337],{},[1311,30037,1337],{},[1437,30039,1637],{"stretchy":1625},[1315,30041,30042],{"encoding":1317},"X \\sim N(\\mu_2, \\sigma_2^2)",[1115,30044,30046],{"className":30045},[1292],[1294,30047,30048],{"xmlns":1296},[1298,30049,30050,30058],{},[1301,30051,30052],{},[1304,30053,30054,30056],{},[1307,30055,8683],{},[1311,30057,1337],{},[1315,30059,30060],{"encoding":1317},"Z_2",". Z výběrů se určí ",[1115,30063,30065],{"className":30064},[1292],[1294,30066,30067],{"xmlns":1296},[1298,30068,30069,30091],{},[1301,30070,30071,30081,30083],{},[1304,30072,30073,30079],{},[2475,30074,30075,30077],{"accent":1121},[1307,30076,6476],{},[1437,30078,11217],{},[1311,30080,1544],{},[1437,30082,1547],{"separator":1121},[3106,30084,30085,30087,30089],{},[1307,30086,1605],{},[1311,30088,1544],{},[1311,30090,1337],{},[1315,30092,30093],{"encoding":1317},"\\bar{x}_1, s_1^2",[1115,30095,30097],{"className":30096},[1292],[1294,30098,30099],{"xmlns":1296},[1298,30100,30101,30123],{},[1301,30102,30103,30113,30115],{},[1304,30104,30105,30111],{},[2475,30106,30107,30109],{"accent":1121},[1307,30108,6476],{},[1437,30110,11217],{},[1311,30112,1337],{},[1437,30114,1547],{"separator":1121},[3106,30116,30117,30119,30121],{},[1307,30118,1605],{},[1311,30120,1337],{},[1311,30122,1337],{},[1315,30124,30125],{"encoding":1317},"\\bar{x}_2, s_2^2",". Testují se varianty vztahů mezi ",[1115,30128,30130],{"className":30129},[1292],[1294,30131,30132],{"xmlns":1296},[1298,30133,30134,30150],{},[1301,30135,30136,30142,30144],{},[1304,30137,30138,30140],{},[1307,30139,6647],{},[1311,30141,1544],{},[1437,30143,1547],{"separator":1121},[1304,30145,30146,30148],{},[1307,30147,6647],{},[1311,30149,1337],{},[1315,30151,30152],{"encoding":1317},"\\mu_1, \\mu_2",", resp. mezi ",[1115,30155,30157],{"className":30156},[1292],[1294,30158,30159],{"xmlns":1296},[1298,30160,30161,30181],{},[1301,30162,30163,30171,30173],{},[3106,30164,30165,30167,30169],{},[1307,30166,6655],{},[1311,30168,1544],{},[1311,30170,1337],{},[1437,30172,1547],{"separator":1121},[3106,30174,30175,30177,30179],{},[1307,30176,6655],{},[1311,30178,1337],{},[1311,30180,1337],{},[1315,30182,30183],{"encoding":1317},"\\sigma_1^2, \\sigma_2^2",[16505,30185,30187],{"id":30186},"f-test-o-rozptylech","F-test o rozptylech",[1110,30189,30190],{},"Statistika",[1115,30192,30194],{"className":30193},[1292],[1294,30195,30196],{"xmlns":1296,"display":1715},[1298,30197,30198,30254],{},[1301,30199,30200,30202,30204,30222,30224],{},[1307,30201,6471],{},[1437,30203,1733],{},[2491,30205,30206,30214],{},[3106,30207,30208,30210,30212],{},[1307,30209,1605],{},[1311,30211,1544],{},[1311,30213,1337],{},[3106,30215,30216,30218,30220],{},[1307,30217,1605],{},[1311,30219,1337],{},[1311,30221,1337],{},[1437,30223,8941],{},[1304,30225,30226,30228],{},[1307,30227,6471],{},[1301,30229,30230,30236,30238,30240,30242,30244,30250,30252],{},[1304,30231,30232,30234],{},[1307,30233,1435],{},[1311,30235,1544],{},[1437,30237,2817],{},[1311,30239,1544],{},[1437,30241,1547],{"separator":1121},[2661,30243,2663],{},[1304,30245,30246,30248],{},[1307,30247,1435],{},[1311,30249,1337],{},[1437,30251,2817],{},[1311,30253,1544],{},[1315,30255,30256],{"encoding":1317},"F = \\frac{s_1^2}{s_2^2} \\sim F_{n_1-1,\\,n_2-1}",[1110,30258,30259,30260,5495,30282,27422],{},"má Fisherovo-Snedecorovo rozdělení o ",[1115,30261,30263],{"className":30262},[1292],[1294,30264,30265],{"xmlns":1296},[1298,30266,30267,30279],{},[1301,30268,30269,30275,30277],{},[1304,30270,30271,30273],{},[1307,30272,1435],{},[1311,30274,1544],{},[1437,30276,2817],{},[1311,30278,1544],{},[1315,30280,30281],{"encoding":1317},"n_1-1",[1115,30283,30285],{"className":30284},[1292],[1294,30286,30287],{"xmlns":1296},[1298,30288,30289,30301],{},[1301,30290,30291,30297,30299],{},[1304,30292,30293,30295],{},[1307,30294,1435],{},[1311,30296,1337],{},[1437,30298,2817],{},[1311,30300,1544],{},[1315,30302,30303],{"encoding":1317},"n_2-1",[1141,30305,30306,30363],{},[1144,30307,30308],{},[1147,30309,30310,30329,30348],{},[1150,30311,30312],{},[1115,30313,30315],{"className":30314},[1292],[1294,30316,30317],{"xmlns":1296},[1298,30318,30319,30327],{},[1301,30320,30321],{},[1304,30322,30323,30325],{},[1307,30324,1309],{},[1311,30326,1313],{},[1315,30328,1318],{"encoding":1317},[1150,30330,30331],{},[1115,30332,30334],{"className":30333},[1292],[1294,30335,30336],{"xmlns":1296},[1298,30337,30338,30346],{},[1301,30339,30340],{},[1304,30341,30342,30344],{},[1307,30343,1309],{},[1311,30345,1544],{},[1315,30347,2749],{"encoding":1317},[1150,30349,27469,30350],{},[1115,30351,30353],{"className":30352},[1292],[1294,30354,30355],{"xmlns":1296},[1298,30356,30357,30361],{},[1301,30358,30359],{},[1307,30360,1353],{},[1315,30362,1353],{"encoding":1317},[1157,30364,30365,30479,30652],{},[1147,30366,30367,30395,30423],{},[1162,30368,30369],{},[1115,30370,30372],{"className":30371},[1292],[1294,30373,30374],{"xmlns":1296},[1298,30375,30376,30392],{},[1301,30377,30378,30384,30386],{},[1304,30379,30380,30382],{},[1307,30381,6655],{},[1311,30383,1544],{},[1437,30385,6491],{},[1304,30387,30388,30390],{},[1307,30389,6655],{},[1311,30391,1337],{},[1315,30393,30394],{"encoding":1317},"\\sigma_1 \\le \\sigma_2",[1162,30396,30397],{},[1115,30398,30400],{"className":30399},[1292],[1294,30401,30402],{"xmlns":1296},[1298,30403,30404,30420],{},[1301,30405,30406,30412,30414],{},[1304,30407,30408,30410],{},[1307,30409,6655],{},[1311,30411,1544],{},[1437,30413,1439],{},[1304,30415,30416,30418],{},[1307,30417,6655],{},[1311,30419,1337],{},[1315,30421,30422],{"encoding":1317},"\\sigma_1 > \\sigma_2",[1162,30424,30425],{},[1115,30426,30428],{"className":30427},[1292],[1294,30429,30430],{"xmlns":1296},[1298,30431,30432,30476],{},[1301,30433,30434,30436,30438,30450,30452,30458,30460,30462,30464,30470,30472,30474],{},[1307,30435,6471],{},[1437,30437,3104],{},[1304,30439,30440,30442],{},[1307,30441,6471],{},[1301,30443,30444,30446,30448],{},[1311,30445,1544],{},[1437,30447,2817],{},[1307,30449,3118],{},[1437,30451,1626],{"stretchy":1625},[1304,30453,30454,30456],{},[1307,30455,1435],{},[1311,30457,1544],{},[1437,30459,2817],{},[1311,30461,1544],{},[1437,30463,1547],{"separator":1121},[1304,30465,30466,30468],{},[1307,30467,1435],{},[1311,30469,1337],{},[1437,30471,2817],{},[1311,30473,1544],{},[1437,30475,1637],{"stretchy":1625},[1315,30477,30478],{"encoding":1317},"F \\ge F_{1-\\alpha}(n_1-1, n_2-1)",[1147,30480,30481,30509,30537],{},[1162,30482,30483],{},[1115,30484,30486],{"className":30485},[1292],[1294,30487,30488],{"xmlns":1296},[1298,30489,30490,30506],{},[1301,30491,30492,30498,30500],{},[1304,30493,30494,30496],{},[1307,30495,6655],{},[1311,30497,1544],{},[1437,30499,1733],{},[1304,30501,30502,30504],{},[1307,30503,6655],{},[1311,30505,1337],{},[1315,30507,30508],{"encoding":1317},"\\sigma_1 = \\sigma_2",[1162,30510,30511],{},[1115,30512,30514],{"className":30513},[1292],[1294,30515,30516],{"xmlns":1296},[1298,30517,30518,30534],{},[1301,30519,30520,30526,30528],{},[1304,30521,30522,30524],{},[1307,30523,6655],{},[1311,30525,1544],{},[1437,30527,10714],{"mathvariant":1872},[1304,30529,30530,30532],{},[1307,30531,6655],{},[1311,30533,1337],{},[1315,30535,30536],{"encoding":1317},"\\sigma_1 \\neq \\sigma_2",[1162,30538,30539,30593,30594],{},[1115,30540,30542],{"className":30541},[1292],[1294,30543,30544],{"xmlns":1296},[1298,30545,30546,30590],{},[1301,30547,30548,30550,30552,30564,30566,30572,30574,30576,30578,30584,30586,30588],{},[1307,30549,6471],{},[1437,30551,6491],{},[1304,30553,30554,30556],{},[1307,30555,6471],{},[1301,30557,30558,30560,30562],{},[1307,30559,3118],{},[1307,30561,4358],{"mathvariant":1872},[1311,30563,1337],{},[1437,30565,1626],{"stretchy":1625},[1304,30567,30568,30570],{},[1307,30569,1435],{},[1311,30571,1544],{},[1437,30573,2817],{},[1311,30575,1544],{},[1437,30577,1547],{"separator":1121},[1304,30579,30580,30582],{},[1307,30581,1435],{},[1311,30583,1337],{},[1437,30585,2817],{},[1311,30587,1544],{},[1437,30589,1637],{"stretchy":1625},[1315,30591,30592],{"encoding":1317},"F \\le F_{\\alpha\u002F2}(n_1-1, n_2-1)"," nebo ",[1115,30595,30597],{"className":30596},[1292],[1294,30598,30599],{"xmlns":1296},[1298,30600,30601,30649],{},[1301,30602,30603,30605,30607,30623,30625,30631,30633,30635,30637,30643,30645,30647],{},[1307,30604,6471],{},[1437,30606,3104],{},[1304,30608,30609,30611],{},[1307,30610,6471],{},[1301,30612,30613,30615,30617,30619,30621],{},[1311,30614,1544],{},[1437,30616,2817],{},[1307,30618,3118],{},[1307,30620,4358],{"mathvariant":1872},[1311,30622,1337],{},[1437,30624,1626],{"stretchy":1625},[1304,30626,30627,30629],{},[1307,30628,1435],{},[1311,30630,1544],{},[1437,30632,2817],{},[1311,30634,1544],{},[1437,30636,1547],{"separator":1121},[1304,30638,30639,30641],{},[1307,30640,1435],{},[1311,30642,1337],{},[1437,30644,2817],{},[1311,30646,1544],{},[1437,30648,1637],{"stretchy":1625},[1315,30650,30651],{"encoding":1317},"F \\ge F_{1-\\alpha\u002F2}(n_1-1, n_2-1)",[1147,30653,30654,30682,30710],{},[1162,30655,30656],{},[1115,30657,30659],{"className":30658},[1292],[1294,30660,30661],{"xmlns":1296},[1298,30662,30663,30679],{},[1301,30664,30665,30671,30673],{},[1304,30666,30667,30669],{},[1307,30668,6655],{},[1311,30670,1544],{},[1437,30672,3104],{},[1304,30674,30675,30677],{},[1307,30676,6655],{},[1311,30678,1337],{},[1315,30680,30681],{"encoding":1317},"\\sigma_1 \\ge \\sigma_2",[1162,30683,30684],{},[1115,30685,30687],{"className":30686},[1292],[1294,30688,30689],{"xmlns":1296},[1298,30690,30691,30707],{},[1301,30692,30693,30699,30701],{},[1304,30694,30695,30697],{},[1307,30696,6655],{},[1311,30698,1544],{},[1437,30700,4086],{},[1304,30702,30703,30705],{},[1307,30704,6655],{},[1311,30706,1337],{},[1315,30708,30709],{"encoding":1317},"\\sigma_1 \u003C \\sigma_2",[1162,30711,30712],{},[1115,30713,30715],{"className":30714},[1292],[1294,30716,30717],{"xmlns":1296},[1298,30718,30719,30757],{},[1301,30720,30721,30723,30725,30731,30733,30739,30741,30743,30745,30751,30753,30755],{},[1307,30722,6471],{},[1437,30724,6491],{},[1304,30726,30727,30729],{},[1307,30728,6471],{},[1307,30730,3118],{},[1437,30732,1626],{"stretchy":1625},[1304,30734,30735,30737],{},[1307,30736,1435],{},[1311,30738,1544],{},[1437,30740,2817],{},[1311,30742,1544],{},[1437,30744,1547],{"separator":1121},[1304,30746,30747,30749],{},[1307,30748,1435],{},[1311,30750,1337],{},[1437,30752,2817],{},[1311,30754,1544],{},[1437,30756,1637],{"stretchy":1625},[1315,30758,30759],{"encoding":1317},"F \\le F_{\\alpha}(n_1-1, n_2-1)",[16505,30761,30763],{"id":30762},"dvouvýběrový-t-test-o-středních-hodnotách","Dvouvýběrový t-test o středních hodnotách",[1110,30765,30766],{},"Volba statistiky závisí na tom, zda jsou rozptyly považovány za shodné:",[1115,30768,30770],{"className":30769},[1292],[1294,30771,30772],{"xmlns":1296,"display":1715},[1298,30773,30774,30951],{},[1301,30775,30776,30782,30784,30860,30908,30910,30912,30921,30923,30929,30931,30937,30939,30945,30947,30949],{},[1304,30777,30778,30780],{},[1307,30779,6858],{},[1311,30781,1544],{},[1437,30783,1733],{},[2491,30785,30786,30810],{},[1301,30787,30788,30798,30800],{},[1304,30789,30790,30796],{},[2475,30791,30792,30794],{"accent":1121},[1307,30793,6476],{},[1437,30795,11217],{},[1311,30797,1544],{},[1437,30799,2817],{},[1304,30801,30802,30808],{},[2475,30803,30804,30806],{"accent":1121},[1307,30805,6476],{},[1437,30807,11217],{},[1311,30809,1337],{},[4207,30811,30812],{},[1301,30813,30814,30816,30822,30824,30826,30828,30836,30838,30840,30846,30848,30850,30852],{},[1437,30815,1626],{"stretchy":1625},[1304,30817,30818,30820],{},[1307,30819,1435],{},[1311,30821,1544],{},[1437,30823,2817],{},[1311,30825,1544],{},[1437,30827,1637],{"stretchy":1625},[3106,30829,30830,30832,30834],{},[1307,30831,1605],{},[1311,30833,1544],{},[1311,30835,1337],{},[1437,30837,5231],{},[1437,30839,1626],{"stretchy":1625},[1304,30841,30842,30844],{},[1307,30843,1435],{},[1311,30845,1337],{},[1437,30847,2817],{},[1311,30849,1544],{},[1437,30851,1637],{"stretchy":1625},[3106,30853,30854,30856,30858],{},[1307,30855,1605],{},[1311,30857,1337],{},[1311,30859,1337],{},[4207,30861,30862],{},[2491,30863,30864,30884],{},[1301,30865,30866,30872,30874,30880,30882],{},[1304,30867,30868,30870],{},[1307,30869,1435],{},[1311,30871,1544],{},[1437,30873,5231],{},[1304,30875,30876,30878],{},[1307,30877,1435],{},[1311,30879,1337],{},[1437,30881,2817],{},[1311,30883,1337],{},[1301,30885,30886,30896,30898],{},[2491,30887,30888,30890],{},[1311,30889,1544],{},[1304,30891,30892,30894],{},[1307,30893,1435],{},[1311,30895,1544],{},[1437,30897,5231],{},[2491,30899,30900,30902],{},[1311,30901,1544],{},[1304,30903,30904,30906],{},[1307,30905,1435],{},[1311,30907,1337],{},[1437,30909,1547],{"separator":1121},[1763,30911],{"width":1765},[3106,30913,30914,30916,30918],{},[1307,30915,6900],{},[1307,30917,1110],{},[1437,30919,30920],{},"∗",[1437,30922,1733],{},[1304,30924,30925,30927],{},[1307,30926,6900],{},[1307,30928,1110],{},[1437,30930,1626],{"stretchy":1625},[1304,30932,30933,30935],{},[1307,30934,1435],{},[1311,30936,1544],{},[1437,30938,5231],{},[1304,30940,30941,30943],{},[1307,30942,1435],{},[1311,30944,1337],{},[1437,30946,2817],{},[1311,30948,1337],{},[1437,30950,1637],{"stretchy":1625},[1315,30952,30953],{"encoding":1317},"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)",[1110,30955,30956,30957,30986],{},"se použije, pokud jsou rozptyly ",[1115,30958,30960],{"className":30959},[1292],[1294,30961,30962],{"xmlns":1296},[1298,30963,30964,30984],{},[1301,30965,30966,30974,30976],{},[3106,30967,30968,30970,30972],{},[1307,30969,6655],{},[1311,30971,1544],{},[1311,30973,1337],{},[1437,30975,1547],{"separator":1121},[3106,30977,30978,30980,30982],{},[1307,30979,6655],{},[1311,30981,1337],{},[1311,30983,1337],{},[1315,30985,30183],{"encoding":1317}," alespoň přibližně shodné; při rozdílných rozptylech",[1115,30988,30990],{"className":30989},[1292],[1294,30991,30992],{"xmlns":1296,"display":1715},[1298,30993,30994,31206],{},[1301,30995,30996,31002,31004,31068,31070,31072,31080,31082,31204],{},[1304,30997,30998,31000],{},[1307,30999,6858],{},[1311,31001,1337],{},[1437,31003,1733],{},[2491,31005,31006,31030],{},[1301,31007,31008,31018,31020],{},[1304,31009,31010,31016],{},[2475,31011,31012,31014],{"accent":1121},[1307,31013,6476],{},[1437,31015,11217],{},[1311,31017,1544],{},[1437,31019,2817],{},[1304,31021,31022,31028],{},[2475,31023,31024,31026],{"accent":1121},[1307,31025,6476],{},[1437,31027,11217],{},[1311,31029,1337],{},[4207,31031,31032],{},[1301,31033,31034,31042,31044,31050,31052,31060,31062],{},[3106,31035,31036,31038,31040],{},[1307,31037,1605],{},[1311,31039,1544],{},[1311,31041,1337],{},[1307,31043,4358],{"mathvariant":1872},[1304,31045,31046,31048],{},[1307,31047,1435],{},[1311,31049,1544],{},[1437,31051,5231],{},[3106,31053,31054,31056,31058],{},[1307,31055,1605],{},[1311,31057,1337],{},[1311,31059,1337],{},[1307,31061,4358],{"mathvariant":1872},[1304,31063,31064,31066],{},[1307,31065,1435],{},[1311,31067,1337],{},[1437,31069,1547],{"separator":1121},[1763,31071],{"width":1765},[3106,31073,31074,31076,31078],{},[1307,31075,6900],{},[1307,31077,1110],{},[1437,31079,30920],{},[1437,31081,1733],{},[2491,31083,31084,31164],{},[1301,31085,31086,31104,31110,31112,31118,31120,31122,31124,31126,31144,31150,31152,31158,31160,31162],{},[2994,31087,31088],{"scriptlevel":1313,"displaystyle":1121},[2491,31089,31090,31098],{},[3106,31091,31092,31094,31096],{},[1307,31093,1605],{},[1311,31095,1544],{},[1311,31097,1337],{},[1304,31099,31100,31102],{},[1307,31101,1435],{},[1311,31103,1544],{},[1304,31105,31106,31108],{},[1307,31107,6900],{},[1307,31109,1110],{},[1437,31111,1626],{"stretchy":1625},[1304,31113,31114,31116],{},[1307,31115,1435],{},[1311,31117,1544],{},[1437,31119,2817],{},[1311,31121,1544],{},[1437,31123,1637],{"stretchy":1625},[1437,31125,5231],{},[2994,31127,31128],{"scriptlevel":1313,"displaystyle":1121},[2491,31129,31130,31138],{},[3106,31131,31132,31134,31136],{},[1307,31133,1605],{},[1311,31135,1337],{},[1311,31137,1337],{},[1304,31139,31140,31142],{},[1307,31141,1435],{},[1311,31143,1337],{},[1304,31145,31146,31148],{},[1307,31147,6900],{},[1307,31149,1110],{},[1437,31151,1626],{"stretchy":1625},[1304,31153,31154,31156],{},[1307,31155,1435],{},[1311,31157,1337],{},[1437,31159,2817],{},[1311,31161,1544],{},[1437,31163,1637],{"stretchy":1625},[1301,31165,31166,31184,31186],{},[2994,31167,31168],{"scriptlevel":1313,"displaystyle":1121},[2491,31169,31170,31178],{},[3106,31171,31172,31174,31176],{},[1307,31173,1605],{},[1311,31175,1544],{},[1311,31177,1337],{},[1304,31179,31180,31182],{},[1307,31181,1435],{},[1311,31183,1544],{},[1437,31185,5231],{},[2994,31187,31188],{"scriptlevel":1313,"displaystyle":1121},[2491,31189,31190,31198],{},[3106,31191,31192,31194,31196],{},[1307,31193,1605],{},[1311,31195,1337],{},[1311,31197,1337],{},[1304,31199,31200,31202],{},[1307,31201,1435],{},[1311,31203,1337],{},[1307,31205,1417],{"mathvariant":1872},[1315,31207,31208],{"encoding":1317},"T_2 = \\frac{\\bar{x}_1-\\bar{x}_2}{\\sqrt{s_1^2\u002Fn_1 + s_2^2\u002Fn_2}}, \\qquad t_p^* = \\frac{\\dfrac{s_1^2}{n_1}t_p(n_1-1) + \\dfrac{s_2^2}{n_2}t_p(n_2-1)}{\\dfrac{s_1^2}{n_1}+\\dfrac{s_2^2}{n_2}}.",[1141,31210,31211,31268],{},[1144,31212,31213],{},[1147,31214,31215,31234,31253],{},[1150,31216,31217],{},[1115,31218,31220],{"className":31219},[1292],[1294,31221,31222],{"xmlns":1296},[1298,31223,31224,31232],{},[1301,31225,31226],{},[1304,31227,31228,31230],{},[1307,31229,1309],{},[1311,31231,1313],{},[1315,31233,1318],{"encoding":1317},[1150,31235,31236],{},[1115,31237,31239],{"className":31238},[1292],[1294,31240,31241],{"xmlns":1296},[1298,31242,31243,31251],{},[1301,31244,31245],{},[1304,31246,31247,31249],{},[1307,31248,1309],{},[1311,31250,1544],{},[1315,31252,2749],{"encoding":1317},[1150,31254,27469,31255],{},[1115,31256,31258],{"className":31257},[1292],[1294,31259,31260],{"xmlns":1296},[1298,31261,31262,31266],{},[1301,31263,31264],{},[1307,31265,1353],{},[1315,31267,1353],{"encoding":1317},[1157,31269,31270,31354,31442],{},[1147,31271,31272,31300,31328],{},[1162,31273,31274],{},[1115,31275,31277],{"className":31276},[1292],[1294,31278,31279],{"xmlns":1296},[1298,31280,31281,31297],{},[1301,31282,31283,31289,31291],{},[1304,31284,31285,31287],{},[1307,31286,6647],{},[1311,31288,1544],{},[1437,31290,6491],{},[1304,31292,31293,31295],{},[1307,31294,6647],{},[1311,31296,1337],{},[1315,31298,31299],{"encoding":1317},"\\mu_1 \\le \\mu_2",[1162,31301,31302],{},[1115,31303,31305],{"className":31304},[1292],[1294,31306,31307],{"xmlns":1296},[1298,31308,31309,31325],{},[1301,31310,31311,31317,31319],{},[1304,31312,31313,31315],{},[1307,31314,6647],{},[1311,31316,1544],{},[1437,31318,1439],{},[1304,31320,31321,31323],{},[1307,31322,6647],{},[1311,31324,1337],{},[1315,31326,31327],{"encoding":1317},"\\mu_1 > \\mu_2",[1162,31329,31330],{},[1115,31331,31333],{"className":31332},[1292],[1294,31334,31335],{"xmlns":1296},[1298,31336,31337,31351],{},[1301,31338,31339,31341,31343],{},[1307,31340,6900],{},[1437,31342,3104],{},[3106,31344,31345,31347,31349],{},[1307,31346,6900],{},[1307,31348,1110],{},[1437,31350,30920],{},[1315,31352,31353],{"encoding":1317},"t \\ge t_p^*",[1147,31355,31356,31384,31412],{},[1162,31357,31358],{},[1115,31359,31361],{"className":31360},[1292],[1294,31362,31363],{"xmlns":1296},[1298,31364,31365,31381],{},[1301,31366,31367,31373,31375],{},[1304,31368,31369,31371],{},[1307,31370,6647],{},[1311,31372,1544],{},[1437,31374,1733],{},[1304,31376,31377,31379],{},[1307,31378,6647],{},[1311,31380,1337],{},[1315,31382,31383],{"encoding":1317},"\\mu_1 = \\mu_2",[1162,31385,31386],{},[1115,31387,31389],{"className":31388},[1292],[1294,31390,31391],{"xmlns":1296},[1298,31392,31393,31409],{},[1301,31394,31395,31401,31403],{},[1304,31396,31397,31399],{},[1307,31398,6647],{},[1311,31400,1544],{},[1437,31402,10714],{"mathvariant":1872},[1304,31404,31405,31407],{},[1307,31406,6647],{},[1311,31408,1337],{},[1315,31410,31411],{"encoding":1317},"\\mu_1 \\neq \\mu_2",[1162,31413,31414],{},[1115,31415,31417],{"className":31416},[1292],[1294,31418,31419],{"xmlns":1296},[1298,31420,31421,31439],{},[1301,31422,31423,31425,31427,31429,31431],{},[1437,31424,22781],{"stretchy":1625},[1307,31426,6900],{},[1437,31428,22781],{"stretchy":1625},[1437,31430,3104],{},[3106,31432,31433,31435,31437],{},[1307,31434,6900],{},[1307,31436,1110],{},[1437,31438,30920],{},[1315,31440,31441],{"encoding":1317},"\\lvert t \\rvert \\ge t_p^*",[1147,31443,31444,31472,31500],{},[1162,31445,31446],{},[1115,31447,31449],{"className":31448},[1292],[1294,31450,31451],{"xmlns":1296},[1298,31452,31453,31469],{},[1301,31454,31455,31461,31463],{},[1304,31456,31457,31459],{},[1307,31458,6647],{},[1311,31460,1544],{},[1437,31462,3104],{},[1304,31464,31465,31467],{},[1307,31466,6647],{},[1311,31468,1337],{},[1315,31470,31471],{"encoding":1317},"\\mu_1 \\ge \\mu_2",[1162,31473,31474],{},[1115,31475,31477],{"className":31476},[1292],[1294,31478,31479],{"xmlns":1296},[1298,31480,31481,31497],{},[1301,31482,31483,31489,31491],{},[1304,31484,31485,31487],{},[1307,31486,6647],{},[1311,31488,1544],{},[1437,31490,4086],{},[1304,31492,31493,31495],{},[1307,31494,6647],{},[1311,31496,1337],{},[1315,31498,31499],{"encoding":1317},"\\mu_1 \u003C \\mu_2",[1162,31501,31502],{},[1115,31503,31505],{"className":31504},[1292],[1294,31506,31507],{"xmlns":1296},[1298,31508,31509,31525],{},[1301,31510,31511,31513,31515,31517],{},[1307,31512,6900],{},[1437,31514,6491],{},[1437,31516,2817],{},[3106,31518,31519,31521,31523],{},[1307,31520,6900],{},[1307,31522,1110],{},[1437,31524,30920],{},[1315,31526,31527],{"encoding":1317},"t \\le -t_p^*",[1110,31529,31530,31531,30593,31549,1417],{},"Postup je dvoukrokový: nejprve F-test rozhodne o shodě rozptylů, pak se podle výsledku zvolí ",[1115,31532,31534],{"className":31533},[1292],[1294,31535,31536],{"xmlns":1296},[1298,31537,31538,31546],{},[1301,31539,31540],{},[1304,31541,31542,31544],{},[1307,31543,6858],{},[1311,31545,1544],{},[1315,31547,31548],{"encoding":1317},"T_1",[1115,31550,31552],{"className":31551},[1292],[1294,31553,31554],{"xmlns":1296},[1298,31555,31556,31564],{},[1301,31557,31558],{},[1304,31559,31560,31562],{},[1307,31561,6858],{},[1311,31563,1337],{},[1315,31565,31566],{"encoding":1317},"T_2",[1110,31568,31569],{},[4137,31570],{"alt":31571,"className":31572,"src":31573},"mask-th-f-kriticky-obor",[1130,4141],"\u002Fwiki-assets\u002Fmask-th-f-kriticky-obor.png",[1103,31575,31577,31584,31734,31815,31944,31982,32055,32194],{"className":31576,"dataCallout":3230},[1106,3229],[1110,31578,31580,31583],{"className":31579},[1113],[1115,31581],{"className":31582,"ariaHidden":1121},[1118,3237,1120],"Příklad: Porovnání dvou dodavatelů součástek",[1110,31585,31586,31587,2704,31609,31635,31636,31660,31661,2704,31683,31635,31709,31733],{},"Pevnost plastových dílů: dodavatel A (",[1115,31588,31590],{"className":31589},[1292],[1294,31591,31592],{"xmlns":1296},[1298,31593,31594,31606],{},[1301,31595,31596,31602,31604],{},[1304,31597,31598,31600],{},[1307,31599,1435],{},[1311,31601,1544],{},[1437,31603,1733],{},[1311,31605,8791],{},[1315,31607,31608],{"encoding":1317},"n_1 = 10",[1115,31610,31612],{"className":31611},[1292],[1294,31613,31614],{"xmlns":1296},[1298,31615,31616,31632],{},[1301,31617,31618,31628,31630],{},[1304,31619,31620,31626],{},[2475,31621,31622,31624],{"accent":1121},[1307,31623,6476],{},[1437,31625,11217],{},[1311,31627,1544],{},[1437,31629,1733],{},[1311,31631,3381],{},[1315,31633,31634],{"encoding":1317},"\\bar{x}_1 = 82"," MPa, ",[1115,31637,31639],{"className":31638},[1292],[1294,31640,31641],{"xmlns":1296},[1298,31642,31643,31657],{},[1301,31644,31645,31653,31655],{},[3106,31646,31647,31649,31651],{},[1307,31648,1605],{},[1311,31650,1544],{},[1311,31652,1337],{},[1437,31654,1733],{},[1311,31656,3812],{},[1315,31658,31659],{"encoding":1317},"s_1^2 = 25","), dodavatel B (",[1115,31662,31664],{"className":31663},[1292],[1294,31665,31666],{"xmlns":1296},[1298,31667,31668,31680],{},[1301,31669,31670,31676,31678],{},[1304,31671,31672,31674],{},[1307,31673,1435],{},[1311,31675,1337],{},[1437,31677,1733],{},[1311,31679,2027],{},[1315,31681,31682],{"encoding":1317},"n_2 = 12",[1115,31684,31686],{"className":31685},[1292],[1294,31687,31688],{"xmlns":1296},[1298,31689,31690,31706],{},[1301,31691,31692,31702,31704],{},[1304,31693,31694,31700],{},[2475,31695,31696,31698],{"accent":1121},[1307,31697,6476],{},[1437,31699,11217],{},[1311,31701,1337],{},[1437,31703,1733],{},[1311,31705,14490],{},[1315,31707,31708],{"encoding":1317},"\\bar{x}_2 = 75",[1115,31710,31712],{"className":31711},[1292],[1294,31713,31714],{"xmlns":1296},[1298,31715,31716,31730],{},[1301,31717,31718,31726,31728],{},[3106,31719,31720,31722,31724],{},[1307,31721,1605],{},[1311,31723,1337],{},[1311,31725,1337],{},[1437,31727,1733],{},[1311,31729,21783],{},[1315,31731,31732],{"encoding":1317},"s_2^2 = 16","). Předpokládá se normalita obou rozdělení.",[1110,31735,31736,1402,31739,2704,31777,1417],{},[1279,31737,31738],{},"Krok 1 — F-test rozptylů.",[1115,31740,31742],{"className":31741},[1292],[1294,31743,31744],{"xmlns":1296},[1298,31745,31746,31774],{},[1301,31747,31748,31754,31756,31764,31766],{},[1304,31749,31750,31752],{},[1307,31751,1309],{},[1311,31753,1313],{},[1437,31755,1709],{},[3106,31757,31758,31760,31762],{},[1307,31759,6655],{},[1311,31761,1544],{},[1311,31763,1337],{},[1437,31765,1733],{},[3106,31767,31768,31770,31772],{},[1307,31769,6655],{},[1311,31771,1337],{},[1311,31773,1337],{},[1315,31775,31776],{"encoding":1317},"H_0: \\sigma_1^2 = \\sigma_2^2",[1115,31778,31780],{"className":31779},[1292],[1294,31781,31782],{"xmlns":1296},[1298,31783,31784,31812],{},[1301,31785,31786,31792,31794,31802,31804],{},[1304,31787,31788,31790],{},[1307,31789,1309],{},[1311,31791,1544],{},[1437,31793,1709],{},[3106,31795,31796,31798,31800],{},[1307,31797,6655],{},[1311,31799,1544],{},[1311,31801,1337],{},[1437,31803,10714],{"mathvariant":1872},[3106,31805,31806,31808,31810],{},[1307,31807,6655],{},[1311,31809,1337],{},[1311,31811,1337],{},[1315,31813,31814],{"encoding":1317},"H_1: \\sigma_1^2 \\neq \\sigma_2^2",[1110,31816,31817],{},[1115,31818,31820],{"className":31819},[1292],[1294,31821,31822],{"xmlns":1296},[1298,31823,31824,31941],{},[1301,31825,31826,31828,31830,31836,31838,31841,31843,31845,31847,31849,31851,31853,31855,31868,31870,31872,31874,31876,31878,31881,31884,31886,31888,31890,31903,31905,31907,31909,31911,31913,31915,31917,31919,31921,31923,31926,31928,31930,31932,31934,31936,31939],{},[1307,31827,6471],{},[1437,31829,1733],{},[2491,31831,31832,31834],{},[1311,31833,3812],{},[1311,31835,21783],{},[1437,31837,1733],{},[1311,31839,31840],{},"1,5625",[1437,31842,1547],{"separator":1121},[1763,31844],{"width":1765},[1307,31846,1353],{},[1437,31848,1733],{},[1437,31850,3087],{"stretchy":1625},[1307,31852,6471],{},[1437,31854,6491],{},[1304,31856,31857,31859],{},[1307,31858,6471],{},[1301,31860,31861,31863,31865],{},[1311,31862,1313],{},[1437,31864,1547],{"separator":1121},[1311,31866,31867],{},"025",[1437,31869,1626],{"stretchy":1625},[1311,31871,3348],{},[1437,31873,1547],{"separator":1121},[1311,31875,2006],{},[1437,31877,1637],{"stretchy":1625},[2661,31879,31880],{},"  ",[2661,31882,31883],{},"nebo",[2661,31885,31880],{},[1307,31887,6471],{},[1437,31889,3104],{},[1304,31891,31892,31894],{},[1307,31893,6471],{},[1301,31895,31896,31898,31900],{},[1311,31897,1313],{},[1437,31899,1547],{"separator":1121},[1311,31901,31902],{},"975",[1437,31904,1626],{"stretchy":1625},[1311,31906,3348],{},[1437,31908,1547],{"separator":1121},[1311,31910,2006],{},[1437,31912,1637],{"stretchy":1625},[1437,31914,3147],{"stretchy":1625},[1437,31916,1733],{},[1437,31918,3087],{"stretchy":1625},[1307,31920,6471],{},[1437,31922,6491],{},[1311,31924,31925],{},"0,256",[2661,31927,31880],{},[2661,31929,31883],{},[2661,31931,31880],{},[1307,31933,6471],{},[1437,31935,3104],{},[1311,31937,31938],{},"3,588",[1437,31940,3147],{"stretchy":1625},[1315,31942,31943],{"encoding":1317},"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\\}",[1110,31945,31946,31964,31965,1417],{},[1115,31947,31949],{"className":31948},[1292],[1294,31950,31951],{"xmlns":1296},[1298,31952,31953,31961],{},[1301,31954,31955,31957,31959],{},[1307,31956,6471],{},[1437,31958,27030],{"mathvariant":1872},[1307,31960,1353],{},[1315,31962,31963],{"encoding":1317},"F \\notin W",", rozptyly nezamítáme jako shodné — pro t-test se použije ",[1115,31966,31968],{"className":31967},[1292],[1294,31969,31970],{"xmlns":1296},[1298,31971,31972,31980],{},[1301,31973,31974],{},[1304,31975,31976,31978],{},[1307,31977,6858],{},[1311,31979,1544],{},[1315,31981,31548],{"encoding":1317},[1110,31983,31984,1402,31987,2704,32021,1417],{},[1279,31985,31986],{},"Krok 2 — dvouvýběrový t-test středních hodnot.",[1115,31988,31990],{"className":31989},[1292],[1294,31991,31992],{"xmlns":1296},[1298,31993,31994,32018],{},[1301,31995,31996,32002,32004,32010,32012],{},[1304,31997,31998,32000],{},[1307,31999,1309],{},[1311,32001,1313],{},[1437,32003,1709],{},[1304,32005,32006,32008],{},[1307,32007,6647],{},[1311,32009,1544],{},[1437,32011,1733],{},[1304,32013,32014,32016],{},[1307,32015,6647],{},[1311,32017,1337],{},[1315,32019,32020],{"encoding":1317},"H_0: \\mu_1 = \\mu_2",[1115,32022,32024],{"className":32023},[1292],[1294,32025,32026],{"xmlns":1296},[1298,32027,32028,32052],{},[1301,32029,32030,32036,32038,32044,32046],{},[1304,32031,32032,32034],{},[1307,32033,1309],{},[1311,32035,1544],{},[1437,32037,1709],{},[1304,32039,32040,32042],{},[1307,32041,6647],{},[1311,32043,1544],{},[1437,32045,10714],{"mathvariant":1872},[1304,32047,32048,32050],{},[1307,32049,6647],{},[1311,32051,1337],{},[1315,32053,32054],{"encoding":1317},"H_1: \\mu_1 \\neq \\mu_2",[1110,32056,32057],{},[1115,32058,32060],{"className":32059},[1292],[1294,32061,32062],{"xmlns":1296},[1298,32063,32064,32191],{},[1301,32065,32066,32074,32076,32096,32098,32101,32103,32105,32107,32109,32123,32131,32133,32136,32138,32140,32142,32144,32146,32148,32150,32152,32154,32166,32168,32170,32172,32174,32176,32178,32180,32182,32184,32186,32189],{},[3106,32067,32068,32070,32072],{},[1307,32069,1605],{},[1307,32071,1110],{},[1311,32073,1337],{},[1437,32075,1733],{},[2491,32077,32078,32094],{},[1301,32079,32080,32082,32084,32086,32088,32090,32092],{},[1311,32081,3348],{},[1437,32083,7868],{},[1311,32085,3812],{},[1437,32087,5231],{},[1311,32089,2006],{},[1437,32091,7868],{},[1311,32093,21783],{},[1311,32095,3799],{},[1437,32097,1733],{},[1311,32099,32100],{},"20,05",[1437,32102,1547],{"separator":1121},[1763,32104],{"width":1765},[1307,32106,6900],{},[1437,32108,1733],{},[2491,32110,32111,32119],{},[1301,32112,32113,32115,32117],{},[1311,32114,3381],{},[1437,32116,2817],{},[1311,32118,14490],{},[4207,32120,32121],{},[1311,32122,32100],{},[4207,32124,32125],{},[2491,32126,32127,32129],{},[1311,32128,21643],{},[1311,32130,2141],{},[1437,32132,9198],{},[1311,32134,32135],{},"3,651",[1437,32137,1547],{"separator":1121},[1763,32139],{"width":1765},[1307,32141,1353],{},[1437,32143,1733],{},[1437,32145,3087],{"stretchy":1625},[1437,32147,22781],{"stretchy":1625},[1307,32149,6900],{},[1437,32151,22781],{"stretchy":1625},[1437,32153,3104],{},[1304,32155,32156,32158],{},[1307,32157,6900],{},[1301,32159,32160,32162,32164],{},[1311,32161,1313],{},[1437,32163,1547],{"separator":1121},[1311,32165,31902],{},[1437,32167,1626],{"stretchy":1625},[1311,32169,3799],{},[1437,32171,1637],{"stretchy":1625},[1437,32173,3147],{"stretchy":1625},[1437,32175,1733],{},[1437,32177,3087],{"stretchy":1625},[1437,32179,22781],{"stretchy":1625},[1307,32181,6900],{},[1437,32183,22781],{"stretchy":1625},[1437,32185,3104],{},[1311,32187,32188],{},"2,086",[1437,32190,3147],{"stretchy":1625},[1315,32192,32193],{"encoding":1317},"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\\}",[1110,32195,32196,5761,32213,32230],{},[1115,32197,32199],{"className":32198},[1292],[1294,32200,32201],{"xmlns":1296},[1298,32202,32203,32211],{},[1301,32204,32205,32207,32209],{},[1307,32206,6900],{},[1437,32208,6775],{},[1307,32210,1353],{},[1315,32212,28173],{"encoding":1317},[1115,32214,32216],{"className":32215},[1292],[1294,32217,32218],{"xmlns":1296},[1298,32219,32220,32228],{},[1301,32221,32222],{},[1304,32223,32224,32226],{},[1307,32225,1309],{},[1311,32227,1313],{},[1315,32229,1318],{"encoding":1317},": pevnost součástek od obou dodavatelů se statisticky významně liší.",[3447,32232,32234],{"className":3449,"code":32233,"language":71,"meta":1229,"style":1229},"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",[3223,32235,32236,32254,32274,32289,32324,32355,32360,32365],{"__ignoreMap":1229},[1115,32237,32238,32241,32243,32245,32247,32250,32252],{"class":3455,"line":10},[1115,32239,32240],{"class":3458},"s1",[1115,32242,3463],{"class":3462},[1115,32244,14160],{"class":3478},[1115,32246,24941],{"class":3470},[1115,32248,32249],{"class":3458},"n1",[1115,32251,3463],{"class":3462},[1115,32253,29614],{"class":3478},[1115,32255,32256,32259,32261,32264,32266,32269,32271],{"class":3455,"line":27},[1115,32257,32258],{"class":3458},"s2",[1115,32260,3463],{"class":3462},[1115,32262,32263],{"class":3478}," 16",[1115,32265,24941],{"class":3470},[1115,32267,32268],{"class":3458},"n2",[1115,32270,3463],{"class":3462},[1115,32272,32273],{"class":3478}," 12\n",[1115,32275,32276,32279,32281,32284,32286],{"class":3455,"line":148},[1115,32277,32278],{"class":3458},"Fstat",[1115,32280,3463],{"class":3462},[1115,32282,32283],{"class":3458}," s1",[1115,32285,9833],{"class":3462},[1115,32287,32288],{"class":3458}," s2\n",[1115,32290,32291,32294,32296,32299,32301,32304,32306,32309,32311,32313,32315,32318,32320,32322],{"class":3455,"line":111},[1115,32292,32293],{"class":3458},"F_dolni",[1115,32295,3463],{"class":3462},[1115,32297,32298],{"class":3466}," qf",[1115,32300,1626],{"class":3470},[1115,32302,32303],{"class":3478},"0.025",[1115,32305,1547],{"class":3462},[1115,32307,32308],{"class":3458}," n1",[1115,32310,25278],{"class":3462},[1115,32312,4395],{"class":3478},[1115,32314,1547],{"class":3462},[1115,32316,32317],{"class":3458}," n2",[1115,32319,25278],{"class":3462},[1115,32321,4395],{"class":3478},[1115,32323,3655],{"class":3470},[1115,32325,32326,32329,32331,32333,32335,32337,32339,32341,32343,32345,32347,32349,32351,32353],{"class":3455,"line":96},[1115,32327,32328],{"class":3458},"F_horni",[1115,32330,3463],{"class":3462},[1115,32332,32298],{"class":3466},[1115,32334,1626],{"class":3470},[1115,32336,8847],{"class":3478},[1115,32338,1547],{"class":3462},[1115,32340,32308],{"class":3458},[1115,32342,25278],{"class":3462},[1115,32344,4395],{"class":3478},[1115,32346,1547],{"class":3462},[1115,32348,32317],{"class":3458},[1115,32350,25278],{"class":3462},[1115,32352,4395],{"class":3478},[1115,32354,3655],{"class":3470},[1115,32356,32357],{"class":3455,"line":89},[1115,32358,32359],{"class":3458},"Fstat\n",[1115,32361,32362],{"class":3455,"line":82},[1115,32363,32364],{"class":3458},"F_dolni\n",[1115,32366,32367],{"class":3455,"line":75},[1115,32368,32369],{"class":3458},"F_horni\n",[3447,32371,32374],{"className":32372,"code":32373,"language":3677,"meta":1229},[3675],"[1] 1.5625\n[1] 0.2556189\n[1] 3.587899\n",[3223,32375,32373],{"__ignoreMap":1229},[3447,32377,32379],{"className":3449,"code":32378,"language":71,"meta":1229,"style":1229},"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",[3223,32380,32381,32438,32489,32519,32524,32528],{"__ignoreMap":1229},[1115,32382,32383,32386,32388,32391,32393,32395,32397,32399,32401,32403,32405,32407,32409,32411,32413,32415,32417,32420,32422,32424,32426,32428,32430,32432,32434,32436],{"class":3455,"line":10},[1115,32384,32385],{"class":3458},"sp2",[1115,32387,3463],{"class":3462},[1115,32389,32390],{"class":3470}," ((",[1115,32392,32249],{"class":3458},[1115,32394,25278],{"class":3462},[1115,32396,4395],{"class":3478},[1115,32398,4355],{"class":3470},[1115,32400,4373],{"class":3462},[1115,32402,32283],{"class":3458},[1115,32404,18273],{"class":3462},[1115,32406,4361],{"class":3470},[1115,32408,32268],{"class":3458},[1115,32410,25278],{"class":3462},[1115,32412,4395],{"class":3478},[1115,32414,4355],{"class":3470},[1115,32416,4373],{"class":3462},[1115,32418,32419],{"class":3458}," s2",[1115,32421,4355],{"class":3470},[1115,32423,4358],{"class":3462},[1115,32425,4361],{"class":3470},[1115,32427,32249],{"class":3458},[1115,32429,18273],{"class":3462},[1115,32431,32317],{"class":3458},[1115,32433,25278],{"class":3462},[1115,32435,3934],{"class":3478},[1115,32437,3655],{"class":3470},[1115,32439,32440,32442,32444,32446,32448,32450,32453,32455,32457,32459,32461,32463,32465,32467,32469,32471,32473,32475,32477,32479,32481,32483,32485,32487],{"class":3455,"line":27},[1115,32441,6900],{"class":3458},[1115,32443,3463],{"class":3462},[1115,32445,4361],{"class":3470},[1115,32447,3381],{"class":3478},[1115,32449,25278],{"class":3462},[1115,32451,32452],{"class":3478}," 75",[1115,32454,4355],{"class":3470},[1115,32456,4358],{"class":3462},[1115,32458,4332],{"class":3466},[1115,32460,1626],{"class":3470},[1115,32462,32385],{"class":3458},[1115,32464,4355],{"class":3470},[1115,32466,4373],{"class":3462},[1115,32468,4332],{"class":3466},[1115,32470,1626],{"class":3470},[1115,32472,32249],{"class":3458},[1115,32474,18398],{"class":3462},[1115,32476,32317],{"class":3458},[1115,32478,9833],{"class":3462},[1115,32480,4361],{"class":3470},[1115,32482,32249],{"class":3458},[1115,32484,18273],{"class":3462},[1115,32486,32317],{"class":3458},[1115,32488,9251],{"class":3470},[1115,32490,32491,32493,32495,32497,32499,32501,32503,32505,32507,32509,32511,32513,32515,32517],{"class":3455,"line":148},[1115,32492,28280],{"class":3458},[1115,32494,3463],{"class":3462},[1115,32496,28285],{"class":3466},[1115,32498,1626],{"class":3470},[1115,32500,8847],{"class":3478},[1115,32502,1547],{"class":3462},[1115,32504,10567],{"class":3458},[1115,32506,3551],{"class":3462},[1115,32508,32308],{"class":3458},[1115,32510,18273],{"class":3462},[1115,32512,32317],{"class":3458},[1115,32514,25278],{"class":3462},[1115,32516,3934],{"class":3478},[1115,32518,3655],{"class":3470},[1115,32520,32521],{"class":3455,"line":111},[1115,32522,32523],{"class":3458},"sp2\n",[1115,32525,32526],{"class":3455,"line":96},[1115,32527,28310],{"class":3458},[1115,32529,32530],{"class":3455,"line":89},[1115,32531,28315],{"class":3458},[3447,32533,32536],{"className":32534,"code":32535,"language":3677,"meta":1229},[3675],"[1] 20.05\n[1] 3.65107\n[1] 2.085963\n",[3223,32537,32535],{"__ignoreMap":1229},[1110,32539,32540],{},[4137,32541],{"alt":32542,"className":32543,"src":32544},"mask-th-t-dvoustranny",[1130,4141],"\u002Fwiki-assets\u002Fmask-th-t-dvoustranny.png",[1110,32546,32547,32548,5495,32551,32553,32554,32557,32558,5495,32575,3742,32592,32594,32595,32597],{},"V R provede obě kroky ",[3223,32549,32550],{},"var.test()",[3223,32552,27770],{},". Parametr ",[3223,32555,32556],{},"var.equal"," nastavuje volbu mezi ",[1115,32559,32561],{"className":32560},[1292],[1294,32562,32563],{"xmlns":1296},[1298,32564,32565,32573],{},[1301,32566,32567],{},[1304,32568,32569,32571],{},[1307,32570,6858],{},[1311,32572,1544],{},[1315,32574,31548],{"encoding":1317},[1115,32576,32578],{"className":32577},[1292],[1294,32579,32580],{"xmlns":1296},[1298,32581,32582,32590],{},[1301,32583,32584],{},[1304,32585,32586,32588],{},[1307,32587,6858],{},[1311,32589,1337],{},[1315,32591,31566],{"encoding":1317},[3223,32593,9282],{}," znamená předpoklad shodných rozptylů (podle výsledku F-testu), ",[3223,32596,9285],{}," předpoklad rozdílných rozptylů.",[1110,32599,32600,32603],{},[1279,32601,32602],{},"Kabely A\u002FB."," Pevnost v tahu dvou výrobců (MPa, 12 kabelů od každého):",[3447,32605,32607],{"className":3449,"code":32606,"language":71,"meta":1229,"style":1229},"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",[3223,32608,32609,32675,32738,32754],{"__ignoreMap":1229},[1115,32610,32611,32613,32615,32617,32619,32622,32624,32627,32629,32632,32634,32637,32639,32641,32643,32646,32648,32651,32653,32655,32657,32660,32662,32664,32666,32669,32671,32673],{"class":3455,"line":10},[1115,32612,1525],{"class":3458},[1115,32614,3463],{"class":3462},[1115,32616,3589],{"class":3466},[1115,32618,1626],{"class":3470},[1115,32620,32621],{"class":3478},"313",[1115,32623,1547],{"class":3462},[1115,32625,32626],{"class":3478}," 299",[1115,32628,1547],{"class":3462},[1115,32630,32631],{"class":3478}," 315",[1115,32633,1547],{"class":3462},[1115,32635,32636],{"class":3478}," 312",[1115,32638,1547],{"class":3462},[1115,32640,15128],{"class":3478},[1115,32642,1547],{"class":3462},[1115,32644,32645],{"class":3478}," 308",[1115,32647,1547],{"class":3462},[1115,32649,32650],{"class":3478}," 314",[1115,32652,1547],{"class":3462},[1115,32654,13920],{"class":3478},[1115,32656,1547],{"class":3462},[1115,32658,32659],{"class":3478}," 305",[1115,32661,1547],{"class":3462},[1115,32663,15128],{"class":3478},[1115,32665,1547],{"class":3462},[1115,32667,32668],{"class":3478}," 309",[1115,32670,1547],{"class":3462},[1115,32672,32650],{"class":3478},[1115,32674,3655],{"class":3470},[1115,32676,32677,32679,32681,32683,32685,32688,32690,32693,32695,32697,32699,32701,32703,32706,32708,32711,32713,32715,32717,32719,32721,32723,32725,32728,32730,32732,32734,32736],{"class":3455,"line":27},[1115,32678,1574],{"class":3458},[1115,32680,3463],{"class":3462},[1115,32682,3589],{"class":3466},[1115,32684,1626],{"class":3470},[1115,32686,32687],{"class":3478},"307",[1115,32689,1547],{"class":3462},[1115,32691,32692],{"class":3478}," 322",[1115,32694,1547],{"class":3462},[1115,32696,13920],{"class":3478},[1115,32698,1547],{"class":3462},[1115,32700,13920],{"class":3478},[1115,32702,1547],{"class":3462},[1115,32704,32705],{"class":3478}," 311",[1115,32707,1547],{"class":3462},[1115,32709,32710],{"class":3478}," 316",[1115,32712,1547],{"class":3462},[1115,32714,32631],{"class":3478},[1115,32716,1547],{"class":3462},[1115,32718,32650],{"class":3478},[1115,32720,1547],{"class":3462},[1115,32722,32645],{"class":3478},[1115,32724,1547],{"class":3462},[1115,32726,32727],{"class":3478}," 319",[1115,32729,1547],{"class":3462},[1115,32731,13920],{"class":3478},[1115,32733,1547],{"class":3462},[1115,32735,32636],{"class":3478},[1115,32737,3655],{"class":3470},[1115,32739,32740,32743,32745,32747,32749,32752],{"class":3455,"line":148},[1115,32741,32742],{"class":3466},"var.test",[1115,32744,1626],{"class":3470},[1115,32746,1525],{"class":3458},[1115,32748,1547],{"class":3462},[1115,32750,32751],{"class":3458}," B",[1115,32753,3655],{"class":3470},[1115,32755,32756,32758,32760,32762,32764,32766,32768,32771,32773,32775],{"class":3455,"line":111},[1115,32757,27835],{"class":3466},[1115,32759,1626],{"class":3470},[1115,32761,1525],{"class":3458},[1115,32763,1547],{"class":3462},[1115,32765,32751],{"class":3458},[1115,32767,1547],{"class":3462},[1115,32769,32770],{"class":3458}," var.equal",[1115,32772,3551],{"class":3462},[1115,32774,3564],{"class":3478},[1115,32776,3655],{"class":3470},[3447,32778,32781],{"className":32779,"code":32780,"language":3677,"meta":1229},[3675],"    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",[3223,32782,32780],{"__ignoreMap":1229},[1110,32784,32785,32786,11812,32805,32808,32809,32828,32829,32846],{},"F-test shodu rozptylů nezamítá (",[1115,32787,32789],{"className":32788},[1292],[1294,32790,32791],{"xmlns":1296},[1298,32792,32793,32802],{},[1301,32794,32795,32797,32799],{},[1307,32796,1110],{},[1437,32798,1733],{},[1311,32800,32801],{},"0,7776",[1315,32803,32804],{"encoding":1317},"p = 0{,}7776",[3223,32806,32807],{},"var.equal = TRUE",". Výsledný t-test dává ",[1115,32810,32812],{"className":32811},[1292],[1294,32813,32814],{"xmlns":1296},[1298,32815,32816,32825],{},[1301,32817,32818,32820,32822],{},[1307,32819,1110],{},[1437,32821,1733],{},[1311,32823,32824],{},"0,06932",[1315,32826,32827],{"encoding":1317},"p = 0{,}06932"," — na hladině 5 % se ",[1115,32830,32832],{"className":32831},[1292],[1294,32833,32834],{"xmlns":1296},[1298,32835,32836,32844],{},[1301,32837,32838],{},[1304,32839,32840,32842],{},[1307,32841,1309],{},[1311,32843,1313],{},[1315,32845,1318],{"encoding":1317}," nezamítá, ale hodnota je těsně nad hranicí.",[1110,32848,32849],{},[1279,32850,32851],{},"Výšky chlapců a dívek v páté třídě:",[3447,32853,32855],{"className":3449,"code":32854,"language":71,"meta":1229,"style":1229},"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",[3223,32856,32857,32937,33000,33015],{"__ignoreMap":1229},[1115,32858,32859,32862,32864,32866,32868,32871,32873,32875,32877,32880,32882,32885,32887,32890,32892,32895,32897,32899,32901,32903,32905,32907,32909,32911,32913,32916,32918,32921,32923,32926,32928,32930,32932,32935],{"class":3455,"line":10},[1115,32860,32861],{"class":3458},"boys",[1115,32863,3463],{"class":3462},[1115,32865,3589],{"class":3466},[1115,32867,1626],{"class":3470},[1115,32869,32870],{"class":3478},"130",[1115,32872,1547],{"class":3462},[1115,32874,15077],{"class":3478},[1115,32876,1547],{"class":3462},[1115,32878,32879],{"class":3478}," 136",[1115,32881,1547],{"class":3462},[1115,32883,32884],{"class":3478}," 141",[1115,32886,1547],{"class":3462},[1115,32888,32889],{"class":3478}," 139",[1115,32891,1547],{"class":3462},[1115,32893,32894],{"class":3478}," 133",[1115,32896,1547],{"class":3462},[1115,32898,18230],{"class":3478},[1115,32900,1547],{"class":3462},[1115,32902,13935],{"class":3478},[1115,32904,1547],{"class":3462},[1115,32906,32889],{"class":3478},[1115,32908,1547],{"class":3462},[1115,32910,32879],{"class":3478},[1115,32912,1547],{"class":3462},[1115,32914,32915],{"class":3478}," 138",[1115,32917,1547],{"class":3462},[1115,32919,32920],{"class":3478}," 142",[1115,32922,1547],{"class":3462},[1115,32924,32925],{"class":3478}," 127",[1115,32927,1547],{"class":3462},[1115,32929,32889],{"class":3478},[1115,32931,1547],{"class":3462},[1115,32933,32934],{"class":3478}," 147",[1115,32936,3655],{"class":3470},[1115,32938,32939,32942,32944,32946,32948,32950,32952,32954,32956,32959,32961,32964,32966,32969,32971,32973,32975,32977,32979,32981,32983,32985,32987,32990,32992,32994,32996,32998],{"class":3455,"line":27},[1115,32940,32941],{"class":3458},"girls",[1115,32943,3463],{"class":3462},[1115,32945,3589],{"class":3466},[1115,32947,1626],{"class":3470},[1115,32949,21594],{"class":3478},[1115,32951,1547],{"class":3462},[1115,32953,32884],{"class":3478},[1115,32955,1547],{"class":3462},[1115,32957,32958],{"class":3478}," 143",[1115,32960,1547],{"class":3462},[1115,32962,32963],{"class":3478}," 132",[1115,32965,1547],{"class":3462},[1115,32967,32968],{"class":3478}," 146",[1115,32970,1547],{"class":3462},[1115,32972,32968],{"class":3478},[1115,32974,1547],{"class":3462},[1115,32976,13935],{"class":3478},[1115,32978,1547],{"class":3462},[1115,32980,32884],{"class":3478},[1115,32982,1547],{"class":3462},[1115,32984,32884],{"class":3478},[1115,32986,1547],{"class":3462},[1115,32988,32989],{"class":3478}," 131",[1115,32991,1547],{"class":3462},[1115,32993,32920],{"class":3478},[1115,32995,1547],{"class":3462},[1115,32997,32884],{"class":3478},[1115,32999,3655],{"class":3470},[1115,33001,33002,33004,33006,33008,33010,33013],{"class":3455,"line":148},[1115,33003,32742],{"class":3466},[1115,33005,1626],{"class":3470},[1115,33007,32861],{"class":3458},[1115,33009,1547],{"class":3462},[1115,33011,33012],{"class":3458}," girls",[1115,33014,3655],{"class":3470},[1115,33016,33017,33019,33021,33023,33025,33027,33029,33031,33033,33035],{"class":3455,"line":111},[1115,33018,27835],{"class":3466},[1115,33020,1626],{"class":3470},[1115,33022,32861],{"class":3458},[1115,33024,1547],{"class":3462},[1115,33026,33012],{"class":3458},[1115,33028,1547],{"class":3462},[1115,33030,32770],{"class":3458},[1115,33032,3551],{"class":3462},[1115,33034,3564],{"class":3478},[1115,33036,3655],{"class":3470},[3447,33038,33041],{"className":33039,"code":33040,"language":3677,"meta":1229},[3675],"    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",[3223,33042,33040],{"__ignoreMap":1229},[1110,33044,32785,33045,33064,33065,33067,33068,33087],{},[1115,33046,33048],{"className":33047},[1292],[1294,33049,33050],{"xmlns":1296},[1298,33051,33052,33061],{},[1301,33053,33054,33056,33058],{},[1307,33055,1110],{},[1437,33057,1733],{},[1311,33059,33060],{},"0,6977",[1315,33062,33063],{"encoding":1317},"p = 0{,}6977","), t-test s ",[3223,33066,32807],{}," dává ",[1115,33069,33071],{"className":33070},[1292],[1294,33072,33073],{"xmlns":1296},[1298,33074,33075,33084],{},[1301,33076,33077,33079,33081],{},[1307,33078,1110],{},[1437,33080,1733],{},[1311,33082,33083],{},"0,4883",[1315,33085,33086],{"encoding":1317},"p = 0{,}4883",": na hladině 5 % se rozdíl průměrných výšek chlapců a dívek neprokázal.",[1136,33089,33091],{"id":33090},"testy-dobré-shody-a-normalita","Testy dobré shody a normalita",[1110,33093,33094],{},"Testy dobré shody ověřují, zda datový soubor pochází ze základního souboru s určitým typem rozdělení (normální, exponenciální apod.).",[16505,33096,33098],{"id":33097},"kolmogorovův-smirnovův-test","Kolmogorovův-Smirnovův test",[1110,33100,33101,33102,33125,33126,33145],{},"Univerzální test pro spojitá rozdělení. Porovnává empirickou distribuční funkci ",[1115,33103,33105],{"className":33104},[1292],[1294,33106,33107],{"xmlns":1296},[1298,33108,33109,33123],{},[1301,33110,33111,33117,33119,33121],{},[1304,33112,33113,33115],{},[1307,33114,6471],{},[1307,33116,1435],{},[1437,33118,1626],{"stretchy":1625},[1307,33120,6476],{},[1437,33122,1637],{"stretchy":1625},[1315,33124,10941],{"encoding":1317}," s teoretickou distribuční funkcí ",[1115,33127,33129],{"className":33128},[1292],[1294,33130,33131],{"xmlns":1296},[1298,33132,33133,33143],{},[1301,33134,33135,33137,33139,33141],{},[1307,33136,6471],{},[1437,33138,1626],{"stretchy":1625},[1307,33140,6476],{},[1437,33142,1637],{"stretchy":1625},[1315,33144,7092],{"encoding":1317}," testovaného rozdělení.",[1191,33147,33148,33211,33231,33287],{},[1194,33149,33150,33167,33168,5495,33191,33210],{},[1115,33151,33153],{"className":33152},[1292],[1294,33154,33155],{"xmlns":1296},[1298,33156,33157,33165],{},[1301,33158,33159],{},[1304,33160,33161,33163],{},[1307,33162,1309],{},[1311,33164,1313],{},[1315,33166,1318],{"encoding":1317},": odchylky mezi ",[1115,33169,33171],{"className":33170},[1292],[1294,33172,33173],{"xmlns":1296},[1298,33174,33175,33189],{},[1301,33176,33177,33183,33185,33187],{},[1304,33178,33179,33181],{},[1307,33180,6471],{},[1307,33182,1435],{},[1437,33184,1626],{"stretchy":1625},[1307,33186,6476],{},[1437,33188,1637],{"stretchy":1625},[1315,33190,10941],{"encoding":1317},[1115,33192,33194],{"className":33193},[1292],[1294,33195,33196],{"xmlns":1296},[1298,33197,33198,33208],{},[1301,33199,33200,33202,33204,33206],{},[1307,33201,6471],{},[1437,33203,1626],{"stretchy":1625},[1307,33205,6476],{},[1437,33207,1637],{"stretchy":1625},[1315,33209,7092],{"encoding":1317}," jsou náhodné (data mají dané rozdělení).",[1194,33212,33213,33230],{},[1115,33214,33216],{"className":33215},[1292],[1294,33217,33218],{"xmlns":1296},[1298,33219,33220,33228],{},[1301,33221,33222],{},[1304,33223,33224,33226],{},[1307,33225,1309],{},[1311,33227,1544],{},[1315,33229,2749],{"encoding":1317},": data nemají dané rozdělení.",[1194,33232,33233,33234,1417],{},"Testové kritérium: ",[1115,33235,33237],{"className":33236},[1292],[1294,33238,33239],{"xmlns":1296},[1298,33240,33241,33284],{},[1301,33242,33243,33245,33247,33258,33260,33266,33268,33270,33272,33274,33276,33278,33280,33282],{},[1307,33244,7910],{},[1437,33246,1733],{},[1304,33248,33249,33256],{},[1301,33250,33251,33254],{},[1307,33252,33253],{},"sup",[1437,33255,4245],{},[1307,33257,6476],{},[1437,33259,22781],{"stretchy":1625},[1304,33261,33262,33264],{},[1307,33263,6471],{},[1307,33265,1435],{},[1437,33267,1626],{"stretchy":1625},[1307,33269,6476],{},[1437,33271,1637],{"stretchy":1625},[1437,33273,2817],{},[1307,33275,6471],{},[1437,33277,1626],{"stretchy":1625},[1307,33279,6476],{},[1437,33281,1637],{"stretchy":1625},[1437,33283,22781],{"stretchy":1625},[1315,33285,33286],{"encoding":1317},"D = \\sup_x \\lvert F_n(x) - F(x) \\rvert",[1194,33288,3071,33289,33333,33334,33352,33353,1417],{},[1115,33290,33292],{"className":33291},[1292],[1294,33293,33294],{"xmlns":1296},[1298,33295,33296,33330],{},[1301,33297,33298,33304,33306,33308,33310,33312,33314,33316,33322,33324,33326,33328],{},[1304,33299,33300,33302],{},[1307,33301,1353],{},[1307,33303,3118],{},[1437,33305,1733],{},[1437,33307,3087],{"stretchy":1625},[1307,33309,7553],{},[1437,33311,1709],{},[1307,33313,7553],{},[1437,33315,1439],{},[1304,33317,33318,33320],{},[1307,33319,7910],{},[1307,33321,3118],{},[1437,33323,1626],{"stretchy":1625},[1307,33325,1435],{},[1437,33327,1637],{"stretchy":1625},[1437,33329,3147],{"stretchy":1625},[1315,33331,33332],{"encoding":1317},"W_\\alpha = \\{d : d > D_\\alpha(n)\\}","; pro ",[1115,33335,33337],{"className":33336},[1292],[1294,33338,33339],{"xmlns":1296},[1298,33340,33341,33349],{},[1301,33342,33343,33345,33347],{},[1307,33344,1435],{},[1437,33346,1439],{},[1311,33348,21793],{},[1315,33350,33351],{"encoding":1317},"n>30"," se kritická hodnota aproximuje zlomkem ",[1115,33354,33356],{"className":33355},[1292],[1294,33357,33358],{"xmlns":1296},[1298,33359,33360,33371],{},[1301,33361,33362,33365,33367],{},[1311,33363,33364],{},"1,36",[1307,33366,4358],{"mathvariant":1872},[4207,33368,33369],{},[1307,33370,1435],{},[1315,33372,33373],{"encoding":1317},"1{,}36\u002F\\sqrt{n}",[1110,33375,27767,33376,33379,33380,33382,33383,2704,33386,33389],{},[3223,33377,33378],{},"ks.test()",", kde se za ",[3223,33381,7092],{}," dosadí příslušná distribuční funkce (",[3223,33384,33385],{},"\"pnorm\"",[3223,33387,33388],{},"\"pexp\"",", …) s jejími parametry:",[3447,33391,33393],{"className":3449,"code":33392,"language":71,"meta":1229,"style":1229},"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",[3223,33394,33395,33445],{"__ignoreMap":1229},[1115,33396,33397,33399,33401,33403,33405,33407,33409,33411,33413,33415,33417,33419,33421,33423,33425,33427,33429,33431,33433,33435,33437,33439,33441,33443],{"class":3455,"line":10},[1115,33398,28481],{"class":3458},[1115,33400,3463],{"class":3462},[1115,33402,3589],{"class":3466},[1115,33404,1626],{"class":3470},[1115,33406,11744],{"class":3478},[1115,33408,1547],{"class":3462},[1115,33410,11749],{"class":3478},[1115,33412,1547],{"class":3462},[1115,33414,11754],{"class":3478},[1115,33416,1547],{"class":3462},[1115,33418,11759],{"class":3478},[1115,33420,1547],{"class":3462},[1115,33422,11754],{"class":3478},[1115,33424,1547],{"class":3462},[1115,33426,11754],{"class":3478},[1115,33428,1547],{"class":3462},[1115,33430,11772],{"class":3478},[1115,33432,1547],{"class":3462},[1115,33434,11777],{"class":3478},[1115,33436,1547],{"class":3462},[1115,33438,11749],{"class":3478},[1115,33440,1547],{"class":3462},[1115,33442,11749],{"class":3478},[1115,33444,3655],{"class":3470},[1115,33446,33447,33450,33452,33454,33456,33459,33461,33463,33465,33467,33469,33471,33473,33475,33477],{"class":3455,"line":27},[1115,33448,33449],{"class":3466},"ks.test",[1115,33451,1626],{"class":3470},[1115,33453,28481],{"class":3458},[1115,33455,1547],{"class":3462},[1115,33457,33458],{"class":3594}," \"pnorm\"",[1115,33460,1547],{"class":3462},[1115,33462,8989],{"class":3466},[1115,33464,1626],{"class":3470},[1115,33466,28481],{"class":3458},[1115,33468,1637],{"class":3470},[1115,33470,1547],{"class":3462},[1115,33472,8999],{"class":3466},[1115,33474,1626],{"class":3470},[1115,33476,28481],{"class":3458},[1115,33478,9251],{"class":3470},[3447,33480,33483],{"className":33481,"code":33482,"language":3677,"meta":1229},[3675],"    Asymptotic one-sample Kolmogorov-Smirnov test\n\ndata:  x3\nD = 0.18469, p-value = 0.8847\nalternative hypothesis: two-sided\n",[3223,33484,33482],{"__ignoreMap":1229},[1110,33486,33487,33510],{},[1115,33488,33490],{"className":33489},[1292],[1294,33491,33492],{"xmlns":1296},[1298,33493,33494,33507],{},[1301,33495,33496,33498,33500,33503,33505],{},[1307,33497,1110],{},[1437,33499,1733],{},[1311,33501,33502],{},"0,8847",[1437,33504,1439],{},[1311,33506,3738],{},[1315,33508,33509],{"encoding":1317},"p = 0{,}8847 > 0{,}05",": odpad materiálu je slučitelný s normálním rozdělením se stejným průměrem a směrodatnou odchylkou.",[16505,33512,33514],{"id":33513},"shapiro-wilkův-test","Shapiro-Wilkův test",[1110,33516,33517],{},"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.",[1191,33519,33520,33540,33560],{},[1194,33521,33522,33539],{},[1115,33523,33525],{"className":33524},[1292],[1294,33526,33527],{"xmlns":1296},[1298,33528,33529,33537],{},[1301,33530,33531],{},[1304,33532,33533,33535],{},[1307,33534,1309],{},[1311,33536,1313],{},[1315,33538,1318],{"encoding":1317},": data mají normální rozdělení.",[1194,33541,33542,33559],{},[1115,33543,33545],{"className":33544},[1292],[1294,33546,33547],{"xmlns":1296},[1298,33548,33549,33557],{},[1301,33550,33551],{},[1304,33552,33553,33555],{},[1307,33554,1309],{},[1311,33556,1544],{},[1315,33558,2749],{"encoding":1317},": data nemají normální rozdělení.",[1194,33561,33562,33563,33589],{},"Testová statistika ",[1115,33564,33566],{"className":33565},[1292],[1294,33567,33568],{"xmlns":1296},[1298,33569,33570,33586],{},[1301,33571,33572,33574,33576,33578,33580,33582,33584],{},[1307,33573,1353],{},[1437,33575,6775],{},[1437,33577,8183],{"stretchy":1625},[1311,33579,1313],{},[1437,33581,1547],{"separator":1121},[1311,33583,1544],{},[1437,33585,7200],{"stretchy":1625},[1315,33587,33588],{"encoding":1317},"W \\in \\langle 0,1 \\rangle","; hodnoty blízké 1 indikují shodu s normalitou.",[1110,33591,33592,33593,33606,33607,1402,33627,33644,33645,1402,33665,33682],{},"Na rozdíl od ostatních testů v této kapitole se Shapiro-Wilkův test v praxi vyhodnocuje pouze přes p-hodnotu (tabulka kritických hodnot pro ",[1115,33594,33596],{"className":33595},[1292],[1294,33597,33598],{"xmlns":1296},[1298,33599,33600,33604],{},[1301,33601,33602],{},[1307,33603,1353],{},[1315,33605,1353],{"encoding":1317}," se běžně neudává): ",[1115,33608,33610],{"className":33609},[1292],[1294,33611,33612],{"xmlns":1296},[1298,33613,33614,33624],{},[1301,33615,33616,33618,33620,33622],{},[1307,33617,1110],{},[1437,33619,3104],{},[1307,33621,3118],{},[1437,33623,7306],{},[1315,33625,33626],{"encoding":1317},"p \\ge \\alpha \\Rightarrow",[1115,33628,33630],{"className":33629},[1292],[1294,33631,33632],{"xmlns":1296},[1298,33633,33634,33642],{},[1301,33635,33636],{},[1304,33637,33638,33640],{},[1307,33639,1309],{},[1311,33641,1313],{},[1315,33643,1318],{"encoding":1317}," nezamítáme (normalitu lze předpokládat); ",[1115,33646,33648],{"className":33647},[1292],[1294,33649,33650],{"xmlns":1296},[1298,33651,33652,33662],{},[1301,33653,33654,33656,33658,33660],{},[1307,33655,1110],{},[1437,33657,4086],{},[1307,33659,3118],{},[1437,33661,7306],{},[1315,33663,33664],{"encoding":1317},"p \u003C \\alpha \\Rightarrow",[1115,33666,33668],{"className":33667},[1292],[1294,33669,33670],{"xmlns":1296},[1298,33671,33672,33680],{},[1301,33673,33674],{},[1304,33675,33676,33678],{},[1307,33677,1309],{},[1311,33679,1313],{},[1315,33681,1318],{"encoding":1317}," zamítáme (předpoklad normality je porušen).",[3447,33684,33686],{"className":3449,"code":33685,"language":71,"meta":1229,"style":1229},"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",[3223,33687,33688,33742],{"__ignoreMap":1229},[1115,33689,33690,33692,33694,33696,33698,33700,33702,33704,33706,33708,33710,33712,33714,33716,33718,33720,33722,33724,33726,33728,33730,33732,33734,33736,33738,33740],{"class":3455,"line":10},[1115,33691,28349],{"class":3458},[1115,33693,3463],{"class":3462},[1115,33695,3589],{"class":3466},[1115,33697,1626],{"class":3470},[1115,33699,28358],{"class":3478},[1115,33701,1547],{"class":3462},[1115,33703,28363],{"class":3478},[1115,33705,1547],{"class":3462},[1115,33707,28368],{"class":3478},[1115,33709,1547],{"class":3462},[1115,33711,28373],{"class":3478},[1115,33713,1547],{"class":3462},[1115,33715,28378],{"class":3478},[1115,33717,1547],{"class":3462},[1115,33719,28383],{"class":3478},[1115,33721,1547],{"class":3462},[1115,33723,28373],{"class":3478},[1115,33725,1547],{"class":3462},[1115,33727,28392],{"class":3478},[1115,33729,1547],{"class":3462},[1115,33731,28378],{"class":3478},[1115,33733,1547],{"class":3462},[1115,33735,28401],{"class":3478},[1115,33737,1547],{"class":3462},[1115,33739,28373],{"class":3478},[1115,33741,3655],{"class":3470},[1115,33743,33744,33746,33748,33750],{"class":3455,"line":27},[1115,33745,17334],{"class":3466},[1115,33747,1626],{"class":3470},[1115,33749,28349],{"class":3458},[1115,33751,3655],{"class":3470},[3447,33753,33756],{"className":33754,"code":33755,"language":3677,"meta":1229},[3675],"    Shapiro-Wilk normality test\n\ndata:  x2\nW = 0.96022, p-value = 0.7744\n",[3223,33757,33755],{"__ignoreMap":1229},[1110,33759,33760,33761,33780],{},"U dat o životnosti baterií se normalita nezamítá (",[1115,33762,33764],{"className":33763},[1292],[1294,33765,33766],{"xmlns":1296},[1298,33767,33768,33777],{},[1301,33769,33770,33772,33774],{},[1307,33771,1110],{},[1437,33773,1733],{},[1311,33775,33776],{},"0,7744",[1315,33778,33779],{"encoding":1317},"p = 0{,}7744","), předpoklad t-testu je tedy splněn.",[1103,33782,33784,33791,33794,34161,34167],{"className":33783,"dataCallout":3230},[1106,3229],[1110,33785,33787,33790],{"className":33786},[1113],[1115,33788],{"className":33789,"ariaHidden":1121},[1118,3237,1120],"Příklad: Doba do poruchy výrobku",[1110,33792,33793],{},"Zkoušky životnosti nového výrobku daly soubor 68 hodnot doby do poruchy (v minutách). Odhadněte charakteristiky a zákon rozdělení.",[3447,33795,33797],{"className":3449,"code":33796,"language":71,"meta":1229,"style":1229},"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",[3223,33798,33799,33890,33968,34056,34090,34100,34110,34120,34130],{"__ignoreMap":1229},[1115,33800,33801,33803,33805,33807,33809,33811,33813,33815,33817,33819,33821,33823,33825,33827,33829,33831,33833,33835,33837,33839,33841,33843,33845,33847,33849,33852,33854,33856,33858,33860,33862,33864,33866,33868,33870,33872,33874,33876,33878,33880,33882,33884,33886,33888],{"class":3455,"line":10},[1115,33802,13834],{"class":3458},[1115,33804,3463],{"class":3462},[1115,33806,3589],{"class":3466},[1115,33808,1626],{"class":3470},[1115,33810,13843],{"class":3478},[1115,33812,1547],{"class":3462},[1115,33814,13848],{"class":3478},[1115,33816,1547],{"class":3462},[1115,33818,13853],{"class":3478},[1115,33820,1547],{"class":3462},[1115,33822,13858],{"class":3478},[1115,33824,1547],{"class":3462},[1115,33826,9235],{"class":3478},[1115,33828,1547],{"class":3462},[1115,33830,3934],{"class":3478},[1115,33832,1547],{"class":3462},[1115,33834,3488],{"class":3478},[1115,33836,1547],{"class":3462},[1115,33838,13875],{"class":3478},[1115,33840,1547],{"class":3462},[1115,33842,9752],{"class":3478},[1115,33844,1547],{"class":3462},[1115,33846,13884],{"class":3478},[1115,33848,1547],{"class":3462},[1115,33850,33851],{"class":3478}," 367",[1115,33853,1547],{"class":3462},[1115,33855,13896],{"class":3478},[1115,33857,1547],{"class":3462},[1115,33859,13901],{"class":3478},[1115,33861,1547],{"class":3462},[1115,33863,13906],{"class":3478},[1115,33865,1547],{"class":3462},[1115,33867,3506],{"class":3478},[1115,33869,1547],{"class":3462},[1115,33871,13915],{"class":3478},[1115,33873,1547],{"class":3462},[1115,33875,13920],{"class":3478},[1115,33877,1547],{"class":3462},[1115,33879,13925],{"class":3478},[1115,33881,1547],{"class":3462},[1115,33883,13930],{"class":3478},[1115,33885,1547],{"class":3462},[1115,33887,13935],{"class":3478},[1115,33889,3491],{"class":3462},[1115,33891,33892,33894,33896,33898,33900,33902,33904,33906,33908,33910,33912,33914,33916,33918,33920,33922,33924,33926,33928,33930,33932,33934,33936,33938,33940,33942,33944,33946,33948,33950,33952,33954,33956,33958,33960,33962,33964,33966],{"class":3455,"line":27},[1115,33893,13942],{"class":3478},[1115,33895,1547],{"class":3462},[1115,33897,13947],{"class":3478},[1115,33899,1547],{"class":3462},[1115,33901,13952],{"class":3478},[1115,33903,1547],{"class":3462},[1115,33905,13957],{"class":3478},[1115,33907,1547],{"class":3462},[1115,33909,13962],{"class":3478},[1115,33911,1547],{"class":3462},[1115,33913,3506],{"class":3478},[1115,33915,1547],{"class":3462},[1115,33917,13971],{"class":3478},[1115,33919,1547],{"class":3462},[1115,33921,3488],{"class":3478},[1115,33923,1547],{"class":3462},[1115,33925,13980],{"class":3478},[1115,33927,1547],{"class":3462},[1115,33929,13985],{"class":3478},[1115,33931,1547],{"class":3462},[1115,33933,15077],{"class":3478},[1115,33935,1547],{"class":3462},[1115,33937,13997],{"class":3478},[1115,33939,1547],{"class":3462},[1115,33941,14002],{"class":3478},[1115,33943,1547],{"class":3462},[1115,33945,13896],{"class":3478},[1115,33947,1547],{"class":3462},[1115,33949,14011],{"class":3478},[1115,33951,1547],{"class":3462},[1115,33953,14016],{"class":3478},[1115,33955,1547],{"class":3462},[1115,33957,14021],{"class":3478},[1115,33959,1547],{"class":3462},[1115,33961,14026],{"class":3478},[1115,33963,1547],{"class":3462},[1115,33965,14031],{"class":3478},[1115,33967,3491],{"class":3462},[1115,33969,33970,33972,33974,33977,33979,33981,33983,33985,33987,33989,33991,33993,33995,33997,33999,34001,34003,34005,34007,34009,34011,34013,34015,34018,34020,34022,34024,34026,34028,34030,34032,34034,34036,34038,34040,34042,34044,34046,34048,34050,34052,34054],{"class":3455,"line":148},[1115,33971,14141],{"class":3478},[1115,33973,1547],{"class":3462},[1115,33975,33976],{"class":3478}," 74",[1115,33978,1547],{"class":3462},[1115,33980,14048],{"class":3478},[1115,33982,1547],{"class":3462},[1115,33984,14053],{"class":3478},[1115,33986,1547],{"class":3462},[1115,33988,14058],{"class":3478},[1115,33990,1547],{"class":3462},[1115,33992,14063],{"class":3478},[1115,33994,1547],{"class":3462},[1115,33996,13980],{"class":3478},[1115,33998,1547],{"class":3462},[1115,34000,14072],{"class":3478},[1115,34002,1547],{"class":3462},[1115,34004,10613],{"class":3478},[1115,34006,1547],{"class":3462},[1115,34008,14081],{"class":3478},[1115,34010,1547],{"class":3462},[1115,34012,14086],{"class":3478},[1115,34014,1547],{"class":3462},[1115,34016,34017],{"class":3478}," 194",[1115,34019,1547],{"class":3462},[1115,34021,3899],{"class":3478},[1115,34023,1547],{"class":3462},[1115,34025,14102],{"class":3478},[1115,34027,1547],{"class":3462},[1115,34029,14107],{"class":3478},[1115,34031,1547],{"class":3462},[1115,34033,14112],{"class":3478},[1115,34035,1547],{"class":3462},[1115,34037,14063],{"class":3478},[1115,34039,1547],{"class":3462},[1115,34041,9752],{"class":3478},[1115,34043,1547],{"class":3462},[1115,34045,3934],{"class":3478},[1115,34047,1547],{"class":3462},[1115,34049,14129],{"class":3478},[1115,34051,1547],{"class":3462},[1115,34053,14134],{"class":3478},[1115,34055,3491],{"class":3462},[1115,34057,34058,34060,34062,34064,34066,34068,34070,34072,34074,34076,34078,34080,34082,34084,34086,34088],{"class":3455,"line":111},[1115,34059,14141],{"class":3478},[1115,34061,1547],{"class":3462},[1115,34063,3483],{"class":3478},[1115,34065,1547],{"class":3462},[1115,34067,14150],{"class":3478},[1115,34069,1547],{"class":3462},[1115,34071,14155],{"class":3478},[1115,34073,1547],{"class":3462},[1115,34075,14160],{"class":3478},[1115,34077,1547],{"class":3462},[1115,34079,14165],{"class":3478},[1115,34081,1547],{"class":3462},[1115,34083,13896],{"class":3478},[1115,34085,1547],{"class":3462},[1115,34087,14174],{"class":3478},[1115,34089,3655],{"class":3470},[1115,34091,34092,34094,34096,34098],{"class":3455,"line":96},[1115,34093,11896],{"class":3466},[1115,34095,1626],{"class":3470},[1115,34097,13834],{"class":3458},[1115,34099,3655],{"class":3470},[1115,34101,34102,34104,34106,34108],{"class":3455,"line":89},[1115,34103,11918],{"class":3466},[1115,34105,1626],{"class":3470},[1115,34107,13834],{"class":3458},[1115,34109,3655],{"class":3470},[1115,34111,34112,34114,34116,34118],{"class":3455,"line":82},[1115,34113,12618],{"class":3466},[1115,34115,1626],{"class":3470},[1115,34117,13834],{"class":3458},[1115,34119,3655],{"class":3470},[1115,34121,34122,34124,34126,34128],{"class":3455,"line":75},[1115,34123,17334],{"class":3466},[1115,34125,1626],{"class":3470},[1115,34127,13834],{"class":3458},[1115,34129,3655],{"class":3470},[1115,34131,34132,34134,34136,34138,34140,34143,34145,34147,34149,34151,34153,34155,34157,34159],{"class":3455,"line":3645},[1115,34133,33449],{"class":3466},[1115,34135,1626],{"class":3470},[1115,34137,13834],{"class":3458},[1115,34139,1547],{"class":3462},[1115,34141,34142],{"class":3594}," \"pexp\"",[1115,34144,1547],{"class":3462},[1115,34146,9826],{"class":3458},[1115,34148,3551],{"class":3462},[1115,34150,4395],{"class":3478},[1115,34152,9833],{"class":3462},[1115,34154,8989],{"class":3466},[1115,34156,1626],{"class":3470},[1115,34158,13834],{"class":3458},[1115,34160,9251],{"class":3470},[3447,34162,34165],{"className":34163,"code":34164,"language":3677,"meta":1229},[3675],"[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",[3223,34166,34164],{"__ignoreMap":1229},[1110,34168,34169,34170,34189,34190,34207,34208,34227],{},"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 (",[1115,34171,34173],{"className":34172},[1292],[1294,34174,34175],{"xmlns":1296},[1298,34176,34177,34186],{},[1301,34178,34179,34181,34183],{},[1307,34180,1110],{},[1437,34182,4086],{},[1311,34184,34185],{},"0,0001",[1315,34187,34188],{"encoding":1317},"p \u003C 0{,}0001","), zatímco Kolmogorov-Smirnovův test proti exponenciálnímu rozdělení se střední hodnotou ",[1115,34191,34193],{"className":34192},[1292],[1294,34194,34195],{"xmlns":1296},[1298,34196,34197,34205],{},[1301,34198,34199],{},[2475,34200,34201,34203],{"accent":1121},[1307,34202,6476],{},[1437,34204,11217],{},[1315,34206,21322],{"encoding":1317}," shodu nezamítá (",[1115,34209,34211],{"className":34210},[1292],[1294,34212,34213],{"xmlns":1296},[1298,34214,34215,34224],{},[1301,34216,34217,34219,34221],{},[1307,34218,1110],{},[1437,34220,1733],{},[1311,34222,34223],{},"0,8421",[1315,34225,34226],{"encoding":1317},"p = 0{,}8421","): data odpovídají spíše exponenciálnímu rozdělení než normálnímu.",[1110,34229,34230],{},[4137,34231],{"alt":34232,"className":34233,"src":34234},"mask-th-exponencialni-shoda",[1130,4141],"\u002Fwiki-assets\u002Fmask-th-exponencialni-shoda.png",[1136,34236,34238],{"id":34237},"neparametrické-testy","Neparametrické testy",[1110,34240,34241,34242,4361,34244,34268],{},"Když předpoklad normality neplatí, nahrazují t-testy jejich neparametrické obdoby — Wilcoxonovy testy posuzují ",[1279,34243,11309],{},[1115,34245,34247],{"className":34246},[1292],[1294,34248,34249],{"xmlns":1296},[1298,34250,34251,34265],{},[1301,34252,34253],{},[1304,34254,34255,34257],{},[1307,34256,6476],{},[1301,34258,34259,34261,34263],{},[1311,34260,1313],{},[1437,34262,1547],{"separator":1121},[1311,34264,9684],{},[1315,34266,34267],{"encoding":1317},"x_{0,5}",") místo střední hodnoty a nevyžadují normalitu dat.",[16505,34270,34272],{"id":34271},"wilcoxonovy-testy","Wilcoxonovy testy",[1141,34274,34275,34320],{},[1144,34276,34277],{},[1147,34278,34279,34298,34317],{},[1150,34280,34281],{},[1115,34282,34284],{"className":34283},[1292],[1294,34285,34286],{"xmlns":1296},[1298,34287,34288,34296],{},[1301,34289,34290],{},[1304,34291,34292,34294],{},[1307,34293,1309],{},[1311,34295,1313],{},[1315,34297,1318],{"encoding":1317},[1150,34299,34300],{},[1115,34301,34303],{"className":34302},[1292],[1294,34304,34305],{"xmlns":1296},[1298,34306,34307,34315],{},[1301,34308,34309],{},[1304,34310,34311,34313],{},[1307,34312,1309],{},[1311,34314,1544],{},[1315,34316,2749],{"encoding":1317},[1150,34318,34319],{},"Příkaz v R",[1157,34321,34322,34389,34456],{},[1147,34323,34324,34354,34384],{},[1162,34325,34326],{},[1115,34327,34329],{"className":34328},[1292],[1294,34330,34331],{"xmlns":1296},[1298,34332,34333,34351],{},[1301,34334,34335,34347,34349],{},[1304,34336,34337,34339],{},[1307,34338,6476],{},[1301,34340,34341,34343,34345],{},[1311,34342,1313],{},[1437,34344,1547],{"separator":1121},[1311,34346,9684],{},[1437,34348,6491],{},[1307,34350,3473],{},[1315,34352,34353],{"encoding":1317},"x_{0,5} \\le c",[1162,34355,34356],{},[1115,34357,34359],{"className":34358},[1292],[1294,34360,34361],{"xmlns":1296},[1298,34362,34363,34381],{},[1301,34364,34365,34377,34379],{},[1304,34366,34367,34369],{},[1307,34368,6476],{},[1301,34370,34371,34373,34375],{},[1311,34372,1313],{},[1437,34374,1547],{"separator":1121},[1311,34376,9684],{},[1437,34378,1439],{},[1307,34380,3473],{},[1315,34382,34383],{"encoding":1317},"x_{0,5} > c",[1162,34385,34386],{},[3223,34387,34388],{},"wilcox.test(x, alternative = \"greater\", mu = c)",[1147,34390,34391,34421,34451],{},[1162,34392,34393],{},[1115,34394,34396],{"className":34395},[1292],[1294,34397,34398],{"xmlns":1296},[1298,34399,34400,34418],{},[1301,34401,34402,34414,34416],{},[1304,34403,34404,34406],{},[1307,34405,6476],{},[1301,34407,34408,34410,34412],{},[1311,34409,1313],{},[1437,34411,1547],{"separator":1121},[1311,34413,9684],{},[1437,34415,1733],{},[1307,34417,3473],{},[1315,34419,34420],{"encoding":1317},"x_{0,5} = c",[1162,34422,34423],{},[1115,34424,34426],{"className":34425},[1292],[1294,34427,34428],{"xmlns":1296},[1298,34429,34430,34448],{},[1301,34431,34432,34444,34446],{},[1304,34433,34434,34436],{},[1307,34435,6476],{},[1301,34437,34438,34440,34442],{},[1311,34439,1313],{},[1437,34441,1547],{"separator":1121},[1311,34443,9684],{},[1437,34445,10714],{"mathvariant":1872},[1307,34447,3473],{},[1315,34449,34450],{"encoding":1317},"x_{0,5} \\neq c",[1162,34452,34453],{},[3223,34454,34455],{},"wilcox.test(x, alternative = \"two.sided\", mu = c)",[1147,34457,34458,34488,34518],{},[1162,34459,34460],{},[1115,34461,34463],{"className":34462},[1292],[1294,34464,34465],{"xmlns":1296},[1298,34466,34467,34485],{},[1301,34468,34469,34481,34483],{},[1304,34470,34471,34473],{},[1307,34472,6476],{},[1301,34474,34475,34477,34479],{},[1311,34476,1313],{},[1437,34478,1547],{"separator":1121},[1311,34480,9684],{},[1437,34482,3104],{},[1307,34484,3473],{},[1315,34486,34487],{"encoding":1317},"x_{0,5} \\ge c",[1162,34489,34490],{},[1115,34491,34493],{"className":34492},[1292],[1294,34494,34495],{"xmlns":1296},[1298,34496,34497,34515],{},[1301,34498,34499,34511,34513],{},[1304,34500,34501,34503],{},[1307,34502,6476],{},[1301,34504,34505,34507,34509],{},[1311,34506,1313],{},[1437,34508,1547],{"separator":1121},[1311,34510,9684],{},[1437,34512,4086],{},[1307,34514,3473],{},[1315,34516,34517],{"encoding":1317},"x_{0,5} \u003C c",[1162,34519,34520],{},[3223,34521,34522],{},"wilcox.test(x, alternative = \"less\", mu = c)",[1110,34524,34525,34528,34529,1417],{},[1224,34526,34527],{},"Jednovýběrový Wilcoxonův test"," (obdoba t-testu) posuzuje odchylku mediánu od konstanty ",[1115,34530,34532],{"className":34531},[1292],[1294,34533,34534],{"xmlns":1296},[1298,34535,34536,34540],{},[1301,34537,34538],{},[1307,34539,3473],{},[1315,34541,3473],{"encoding":1317},[1110,34543,34544,34547,34548,8592,34586,34599,34600,1417],{},[1224,34545,34546],{},"Jednovýběrový Wilcoxonův test na diferencích"," (obdoba párového t-testu) posuzuje odchylku mediánu rozdílu ",[1115,34549,34551],{"className":34550},[1292],[1294,34552,34553],{"xmlns":1296},[1298,34554,34555,34583],{},[1301,34556,34557,34569,34571],{},[1304,34558,34559,34561],{},[1307,34560,6476],{},[1301,34562,34563,34565,34567],{},[1311,34564,1313],{},[1437,34566,1547],{"separator":1121},[1311,34568,9684],{},[1437,34570,2817],{},[1304,34572,34573,34575],{},[1307,34574,6886],{},[1301,34576,34577,34579,34581],{},[1311,34578,1313],{},[1437,34580,1547],{"separator":1121},[1311,34582,9684],{},[1315,34584,34585],{"encoding":1317},"x_{0,5}-y_{0,5}",[1115,34587,34589],{"className":34588},[1292],[1294,34590,34591],{"xmlns":1296},[1298,34592,34593,34597],{},[1301,34594,34595],{},[1307,34596,3473],{},[1315,34598,3473],{"encoding":1317},"; v R se volá se stejnými argumenty jako výše a navíc ",[3223,34601,34602],{},"paired = TRUE",[1110,34604,34605,34608,34609,34611],{},[1224,34606,34607],{},"Dvouvýběrový Wilcoxonův test"," (obdoba dvouvýběrového t-testu) posuzuje odchylku mediánů dvou nezávislých výběrů; argument ",[3223,34610,25205],{}," odpadá. Pro výšky chlapců a dívek z příkladu výše:",[3447,34613,34615],{"className":3449,"code":34614,"language":71,"meta":1229,"style":1229},"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",[3223,34616,34617,34687,34745],{"__ignoreMap":1229},[1115,34618,34619,34621,34623,34625,34627,34629,34631,34633,34635,34637,34639,34641,34643,34645,34647,34649,34651,34653,34655,34657,34659,34661,34663,34665,34667,34669,34671,34673,34675,34677,34679,34681,34683,34685],{"class":3455,"line":10},[1115,34620,32861],{"class":3458},[1115,34622,3463],{"class":3462},[1115,34624,3589],{"class":3466},[1115,34626,1626],{"class":3470},[1115,34628,32870],{"class":3478},[1115,34630,1547],{"class":3462},[1115,34632,15077],{"class":3478},[1115,34634,1547],{"class":3462},[1115,34636,32879],{"class":3478},[1115,34638,1547],{"class":3462},[1115,34640,32884],{"class":3478},[1115,34642,1547],{"class":3462},[1115,34644,32889],{"class":3478},[1115,34646,1547],{"class":3462},[1115,34648,32894],{"class":3478},[1115,34650,1547],{"class":3462},[1115,34652,18230],{"class":3478},[1115,34654,1547],{"class":3462},[1115,34656,13935],{"class":3478},[1115,34658,1547],{"class":3462},[1115,34660,32889],{"class":3478},[1115,34662,1547],{"class":3462},[1115,34664,32879],{"class":3478},[1115,34666,1547],{"class":3462},[1115,34668,32915],{"class":3478},[1115,34670,1547],{"class":3462},[1115,34672,32920],{"class":3478},[1115,34674,1547],{"class":3462},[1115,34676,32925],{"class":3478},[1115,34678,1547],{"class":3462},[1115,34680,32889],{"class":3478},[1115,34682,1547],{"class":3462},[1115,34684,32934],{"class":3478},[1115,34686,3655],{"class":3470},[1115,34688,34689,34691,34693,34695,34697,34699,34701,34703,34705,34707,34709,34711,34713,34715,34717,34719,34721,34723,34725,34727,34729,34731,34733,34735,34737,34739,34741,34743],{"class":3455,"line":27},[1115,34690,32941],{"class":3458},[1115,34692,3463],{"class":3462},[1115,34694,3589],{"class":3466},[1115,34696,1626],{"class":3470},[1115,34698,21594],{"class":3478},[1115,34700,1547],{"class":3462},[1115,34702,32884],{"class":3478},[1115,34704,1547],{"class":3462},[1115,34706,32958],{"class":3478},[1115,34708,1547],{"class":3462},[1115,34710,32963],{"class":3478},[1115,34712,1547],{"class":3462},[1115,34714,32968],{"class":3478},[1115,34716,1547],{"class":3462},[1115,34718,32968],{"class":3478},[1115,34720,1547],{"class":3462},[1115,34722,13935],{"class":3478},[1115,34724,1547],{"class":3462},[1115,34726,32884],{"class":3478},[1115,34728,1547],{"class":3462},[1115,34730,32884],{"class":3478},[1115,34732,1547],{"class":3462},[1115,34734,32989],{"class":3478},[1115,34736,1547],{"class":3462},[1115,34738,32920],{"class":3478},[1115,34740,1547],{"class":3462},[1115,34742,32884],{"class":3478},[1115,34744,3655],{"class":3470},[1115,34746,34747,34750,34752,34754,34756,34758,34760,34762,34764,34766],{"class":3455,"line":148},[1115,34748,34749],{"class":3466},"wilcox.test",[1115,34751,1626],{"class":3470},[1115,34753,32861],{"class":3458},[1115,34755,1547],{"class":3462},[1115,34757,33012],{"class":3458},[1115,34759,1547],{"class":3462},[1115,34761,27852],{"class":3458},[1115,34763,3551],{"class":3462},[1115,34765,27857],{"class":3594},[1115,34767,3655],{"class":3470},[3447,34769,34772],{"className":34770,"code":34771,"language":3677,"meta":1229},[3675],"    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",[3223,34773,34771],{"__ignoreMap":1229},[1110,34775,34776,34799],{},[1115,34777,34779],{"className":34778},[1292],[1294,34780,34781],{"xmlns":1296},[1298,34782,34783,34796],{},[1301,34784,34785,34787,34789,34792,34794],{},[1307,34786,1110],{},[1437,34788,1733],{},[1311,34790,34791],{},"0,315",[1437,34793,1439],{},[1311,34795,3738],{},[1315,34797,34798],{"encoding":1317},"p = 0{,}315 > 0{,}05",": mediány výšek chlapců a dívek se statisticky významně neliší — stejný závěr jako u dvouvýběrového t-testu.",[1103,34801,34803,34810,34832,34943,34949],{"className":34802,"dataCallout":3230},[1106,3229],[1110,34804,34806,34809],{"className":34805},[1113],[1115,34807],{"className":34808,"ariaHidden":1121},[1118,3237,1120],"Příklad: Realitní odhadci — neparametrická alternativa",[1110,34811,34812,34813,34831],{},"U odhadů cen z párového t-testu výše normalita diferencí neplatí (",[1115,34814,34816],{"className":34815},[1292],[1294,34817,34818],{"xmlns":1296},[1298,34819,34820,34828],{},[1301,34821,34822,34824,34826],{},[1307,34823,1110],{},[1437,34825,1733],{},[1311,34827,29905],{},[1315,34829,34830],{"encoding":1317},"p = 0{,}03203","). Správnou volbou je párový Wilcoxonův test:",[3447,34833,34835],{"className":3449,"code":34834,"language":71,"meta":1229,"style":1229},"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",[3223,34836,34837,34879,34921],{"__ignoreMap":1229},[1115,34838,34839,34841,34843,34845,34847,34849,34851,34853,34855,34857,34859,34861,34863,34865,34867,34869,34871,34873,34875,34877],{"class":3455,"line":10},[1115,34840,29708],{"class":3458},[1115,34842,3463],{"class":3462},[1115,34844,3589],{"class":3466},[1115,34846,1626],{"class":3470},[1115,34848,29717],{"class":3478},[1115,34850,1547],{"class":3462},[1115,34852,29722],{"class":3478},[1115,34854,1547],{"class":3462},[1115,34856,29727],{"class":3478},[1115,34858,1547],{"class":3462},[1115,34860,29732],{"class":3478},[1115,34862,1547],{"class":3462},[1115,34864,29737],{"class":3478},[1115,34866,1547],{"class":3462},[1115,34868,29742],{"class":3478},[1115,34870,1547],{"class":3462},[1115,34872,29747],{"class":3478},[1115,34874,1547],{"class":3462},[1115,34876,29752],{"class":3478},[1115,34878,3655],{"class":3470},[1115,34880,34881,34883,34885,34887,34889,34891,34893,34895,34897,34899,34901,34903,34905,34907,34909,34911,34913,34915,34917,34919],{"class":3455,"line":27},[1115,34882,29759],{"class":3458},[1115,34884,3463],{"class":3462},[1115,34886,3589],{"class":3466},[1115,34888,1626],{"class":3470},[1115,34890,29768],{"class":3478},[1115,34892,1547],{"class":3462},[1115,34894,29773],{"class":3478},[1115,34896,1547],{"class":3462},[1115,34898,29778],{"class":3478},[1115,34900,1547],{"class":3462},[1115,34902,29783],{"class":3478},[1115,34904,1547],{"class":3462},[1115,34906,29788],{"class":3478},[1115,34908,1547],{"class":3462},[1115,34910,29793],{"class":3478},[1115,34912,1547],{"class":3462},[1115,34914,29798],{"class":3478},[1115,34916,1547],{"class":3462},[1115,34918,29803],{"class":3478},[1115,34920,3655],{"class":3470},[1115,34922,34923,34925,34927,34929,34931,34933,34935,34937,34939,34941],{"class":3455,"line":148},[1115,34924,34749],{"class":3466},[1115,34926,1626],{"class":3470},[1115,34928,29708],{"class":3458},[1115,34930,1547],{"class":3462},[1115,34932,29818],{"class":3458},[1115,34934,1547],{"class":3462},[1115,34936,29823],{"class":3458},[1115,34938,3551],{"class":3462},[1115,34940,3564],{"class":3478},[1115,34942,3655],{"class":3470},[3447,34944,34947],{"className":34945,"code":34946,"language":3677,"meta":1229},[3675],"    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",[3223,34948,34946],{"__ignoreMap":1229},[1110,34950,34951,34974],{},[1115,34952,34954],{"className":34953},[1292],[1294,34955,34956],{"xmlns":1296},[1298,34957,34958,34971],{},[1301,34959,34960,34962,34964,34967,34969],{},[1307,34961,1110],{},[1437,34963,1733],{},[1311,34965,34966],{},"0,1484",[1437,34968,1439],{},[1311,34970,3738],{},[1315,34972,34973],{"encoding":1317},"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.",[16505,34976,34978],{"id":34977},"kruskalův-wallisův-test","Kruskalův-Wallisův test",[1110,34980,34981,34982,34999],{},"Zobecnění dvouvýběrového Wilcoxonova testu, neparametrická obdoba analýzy rozptylu jednoduchého třídění. ",[1115,34983,34985],{"className":34984},[1292],[1294,34986,34987],{"xmlns":1296},[1298,34988,34989,34997],{},[1301,34990,34991],{},[1304,34992,34993,34995],{},[1307,34994,1309],{},[1311,34996,1313],{},[1315,34998,1318],{"encoding":1317},": všechny výběry pocházejí ze stejného rozdělení.",[3447,35001,35003],{"className":3449,"code":35002,"language":71,"meta":1229,"style":1229},"kruskal.test(kvantitativní_proměnná ~ faktor, data = soubor)\n",[3223,35004,35005],{"__ignoreMap":1229},[1115,35006,35007,35010,35012,35015,35017,35020,35022,35024,35026,35029],{"class":3455,"line":10},[1115,35008,35009],{"class":3466},"kruskal.test",[1115,35011,1626],{"class":3470},[1115,35013,35014],{"class":3458},"kvantitativní_proměnná",[1115,35016,16616],{"class":3462},[1115,35018,35019],{"class":3458}," faktor",[1115,35021,1547],{"class":3462},[1115,35023,19924],{"class":3458},[1115,35025,3551],{"class":3462},[1115,35027,35028],{"class":3458}," soubor",[1115,35030,3655],{"class":3470},[16505,35032,35034],{"id":35033},"mediánový-test","Mediánový test",[1110,35036,35037,35038,35055,35056,1709],{},"Má stejný účel jako Kruskalův-Wallisův test (obdoba analýzy rozptylu jednoduchého třídění, ",[1115,35039,35041],{"className":35040},[1292],[1294,35042,35043],{"xmlns":1296},[1298,35044,35045,35053],{},[1301,35046,35047],{},[1304,35048,35049,35051],{},[1307,35050,1309],{},[1311,35052,1313],{},[1315,35054,1318],{"encoding":1317},": všechny výběry pocházejí ze stejného rozdělení) a je součástí balíčku ",[3223,35057,35058],{},"agricolae",[3447,35060,35062],{"className":3449,"code":35061,"language":71,"meta":1229,"style":1229},"library(agricolae)\nMedian.test(kvantitativní_proměnná, faktor)\n",[3223,35063,35064,35074],{"__ignoreMap":1229},[1115,35065,35066,35068,35070,35072],{"class":3455,"line":10},[1115,35067,17154],{"class":3462},[1115,35069,1626],{"class":3470},[1115,35071,35058],{"class":3458},[1115,35073,3655],{"class":3470},[1115,35075,35076,35079,35081,35083,35085,35087],{"class":3455,"line":27},[1115,35077,35078],{"class":3466},"Median.test",[1115,35080,1626],{"class":3470},[1115,35082,35014],{"class":3458},[1115,35084,1547],{"class":3462},[1115,35086,35019],{"class":3458},[1115,35088,3655],{"class":3470},[16505,35090,35092],{"id":35091},"friedmanův-test","Friedmanův test",[1110,35094,35095,35096,35113,35114,35152],{},"Neparametrická obdoba analýzy rozptylu dvojného třídění s jedním pozorováním v každé podtřídě. ",[1115,35097,35099],{"className":35098},[1292],[1294,35100,35101],{"xmlns":1296},[1298,35102,35103,35111],{},[1301,35104,35105],{},[1304,35106,35107,35109],{},[1307,35108,1309],{},[1311,35110,1313],{},[1315,35112,1318],{"encoding":1317},": distribuční funkce veličin ",[1115,35115,35117],{"className":35116},[1292],[1294,35118,35119],{"xmlns":1296},[1298,35120,35121,35149],{},[1301,35122,35123,35133,35135,35137,35139],{},[1304,35124,35125,35127],{},[1307,35126,6488],{},[1301,35128,35129,35131],{},[1307,35130,1629],{},[1311,35132,1544],{},[1437,35134,1547],{"separator":1121},[1437,35136,1550],{},[1437,35138,1547],{"separator":1121},[1304,35140,35141,35143],{},[1307,35142,6488],{},[1301,35144,35145,35147],{},[1307,35146,1629],{},[1307,35148,7016],{},[1315,35150,35151],{"encoding":1317},"X_{i1}, \\dots, X_{ik}"," jsou totožné.",[3447,35154,35156],{"className":3449,"code":35155,"language":71,"meta":1229,"style":1229},"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",[3223,35157,35158,35188,35193],{"__ignoreMap":1229},[1115,35159,35160,35163,35165,35167,35169,35172,35175,35178,35180,35182,35184,35186],{"class":3455,"line":10},[1115,35161,35162],{"class":3466},"friedman.test",[1115,35164,1626],{"class":3470},[1115,35166,35014],{"class":3458},[1115,35168,16616],{"class":3462},[1115,35170,35171],{"class":3458}," faktor_A",[1115,35173,35174],{"class":3462}," |",[1115,35176,35177],{"class":3458}," faktor_B",[1115,35179,1547],{"class":3462},[1115,35181,19924],{"class":3458},[1115,35183,3551],{"class":3462},[1115,35185,35028],{"class":3458},[1115,35187,3655],{"class":3470},[1115,35189,35190],{"class":3455,"line":27},[1115,35191,35192],{"class":11791},"# jsou-li proměnné samostatné vektory (bez argumentu data):\n",[1115,35194,35195,35197,35199,35201,35203,35205,35207,35209],{"class":3455,"line":148},[1115,35196,35162],{"class":3466},[1115,35198,1626],{"class":3470},[1115,35200,35014],{"class":3458},[1115,35202,1547],{"class":3462},[1115,35204,35171],{"class":3458},[1115,35206,1547],{"class":3462},[1115,35208,35177],{"class":3458},[1115,35210,3655],{"class":3470},[1136,35212,35214],{"id":35213},"přehled-testů","Přehled testů",[1110,35216,35217],{},[4137,35218],{"alt":35219,"className":35220,"src":35221},"mask-ilu-volba-testu",[1130,4141],"\u002Fwiki-assets\u002Fmask-ilu-volba-testu.png",[1141,35223,35224,35237],{},[1144,35225,35226],{},[1147,35227,35228,35231,35234],{},[1150,35229,35230],{},"Situace",[1150,35232,35233],{},"Test",[1150,35235,35236],{},"R funkce",[1157,35238,35239,35252,35265,35277,35290,35305,35317,35330,35343,35356,35368,35383],{},[1147,35240,35241,35244,35247],{},[1162,35242,35243],{},"Jedna střední hodnota vs. zadané číslo, normální data",[1162,35245,35246],{},"jednovýběrový t-test",[1162,35248,35249],{},[3223,35250,35251],{},"t.test(x, mu = ..., alternative = ...)",[1147,35253,35254,35257,35260],{},[1162,35255,35256],{},"Rozdíl dvou závislých měření, diference normální",[1162,35258,35259],{},"párový t-test",[1162,35261,35262],{},[3223,35263,35264],{},"t.test(x, y, paired = TRUE)",[1147,35266,35267,35270,35272],{},[1162,35268,35269],{},"Shoda rozptylů dvou nezávislých normálních výběrů",[1162,35271,19832],{},[1162,35273,35274],{},[3223,35275,35276],{},"var.test(x, y)",[1147,35278,35279,35282,35285],{},[1162,35280,35281],{},"Shoda středních hodnot dvou nezávislých normálních výběrů",[1162,35283,35284],{},"dvouvýběrový t-test",[1162,35286,35287],{},[3223,35288,35289],{},"t.test(x, y, var.equal = TRUE\u002FFALSE)",[1147,35291,35292,35295,35297],{},[1162,35293,35294],{},"Shoda dat se zadaným typem rozdělení (normální, exponenciální, …)",[1162,35296,33098],{},[1162,35298,35299,2704,35302],{},[3223,35300,35301],{},"ks.test(x, \"pnorm\", mu, sigma)",[3223,35303,35304],{},"ks.test(x, \"pexp\", 1\u002Fdelta)",[1147,35306,35307,35310,35312],{},[1162,35308,35309],{},"Normalita dat",[1162,35311,33514],{},[1162,35313,35314],{},[3223,35315,35316],{},"shapiro.test(x)",[1147,35318,35319,35322,35325],{},[1162,35320,35321],{},"Medián jednoho výběru vs. konstanta, data nejsou normální",[1162,35323,35324],{},"jednovýběrový Wilcoxonův test",[1162,35326,35327],{},[3223,35328,35329],{},"wilcox.test(x, mu = c, alternative = ...)",[1147,35331,35332,35335,35338],{},[1162,35333,35334],{},"Medián diferencí dvou závislých měření, data nejsou normální",[1162,35336,35337],{},"párový Wilcoxonův test",[1162,35339,35340],{},[3223,35341,35342],{},"wilcox.test(x, y, paired = TRUE, mu = c)",[1147,35344,35345,35348,35351],{},[1162,35346,35347],{},"Mediány dvou nezávislých výběrů, data nejsou normální",[1162,35349,35350],{},"dvouvýběrový Wilcoxonův test",[1162,35352,35353],{},[3223,35354,35355],{},"wilcox.test(x, y)",[1147,35357,35358,35361,35363],{},[1162,35359,35360],{},"Více než dva nezávislé výběry, data nejsou normální",[1162,35362,34978],{},[1162,35364,35365],{},[3223,35366,35367],{},"kruskal.test(y ~ faktor, data)",[1147,35369,35370,35373,35376],{},[1162,35371,35372],{},"Více než dva nezávislé výběry, data nejsou normální (alternativa)",[1162,35374,35375],{},"mediánový test",[1162,35377,35378,22422,35381],{},[3223,35379,35380],{},"Median.test(y, faktor)",[3223,35382,35058],{},[1147,35384,35385,35388,35390],{},[1162,35386,35387],{},"Více než dva závislé výběry (dvojné třídění, jedno pozorování na podtřídu)",[1162,35389,35092],{},[1162,35391,35392],{},[3223,35393,35394],{},"friedman.test(y ~ A | B, data)",[1136,35396,6162],{"id":6161},[1191,35398,35399,35476,35482,35499,35530],{},[1194,35400,35401,35440,35441,32828,35458,35475],{},[1279,35402,35403,35404,35421,35422,35439],{},"Nezamítnutí ",[1115,35405,35407],{"className":35406},[1292],[1294,35408,35409],{"xmlns":1296},[1298,35410,35411,35419],{},[1301,35412,35413],{},[1304,35414,35415,35417],{},[1307,35416,1309],{},[1311,35418,1313],{},[1315,35420,1318],{"encoding":1317}," není důkaz, že ",[1115,35423,35425],{"className":35424},[1292],[1294,35426,35427],{"xmlns":1296},[1298,35428,35429,35437],{},[1301,35430,35431],{},[1304,35432,35433,35435],{},[1307,35434,1309],{},[1311,35436,1313],{},[1315,35438,1318],{"encoding":1317}," platí."," U kabelů A\u002FB vyšlo ",[1115,35442,35444],{"className":35443},[1292],[1294,35445,35446],{"xmlns":1296},[1298,35447,35448,35456],{},[1301,35449,35450,35452,35454],{},[1307,35451,1110],{},[1437,35453,1733],{},[1311,35455,32824],{},[1315,35457,32827],{"encoding":1317},[1115,35459,35461],{"className":35460},[1292],[1294,35462,35463],{"xmlns":1296},[1298,35464,35465,35473],{},[1301,35466,35467],{},[1304,35468,35469,35471],{},[1307,35470,1309],{},[1311,35472,1313],{},[1315,35474,1318],{"encoding":1317}," nezamítá, ale hodnota je blízko hranice; správná interpretace je „data rovnost průměrů nevyvracejí“, ne „rovnost je prokázána“.",[1194,35477,35478,35481],{},[1279,35479,35480],{},"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.",[1194,35483,35484,35491,35492,35495,35496,35498],{},[1279,35485,35486,29986,35488,35490],{},[3223,35487,32556],{},[3223,35489,27770],{}," se volí podle F-testu, ne podle výchozí hodnoty."," Výchozí nastavení R je ",[3223,35493,35494],{},"var.equal = FALSE"," (Welchova varianta); pokud F-test potvrdí shodné rozptyly, je třeba explicitně napsat ",[3223,35497,32807],{},", jinak se použije jiná statistika a jiné stupně volnosti.",[1194,35500,35501,35504,35505,35508,35509,35526,35527,1417],{},[1279,35502,35503],{},"Jednostranná vs. dvoustranná alternativa mění kritický obor i závěr."," Volba ",[3223,35506,35507],{},"alternative = \"greater\"\u002F\"less\"\u002F\"two.sided\""," musí odpovídat formulaci ",[1115,35510,35512],{"className":35511},[1292],[1294,35513,35514],{"xmlns":1296},[1298,35515,35516,35524],{},[1301,35517,35518],{},[1304,35519,35520,35522],{},[1307,35521,1309],{},[1311,35523,1544],{},[1315,35525,2749],{"encoding":1317}," v zadání, ne být ponechána na výchozí hodnotě ",[3223,35528,35529],{},"\"two.sided\"",[1194,35531,35532,35535,35536,35549],{},[1279,35533,35534],{},"Shapiro-Wilkův test se vyhodnocuje jen přes p-hodnotu",", ne porovnáním ",[1115,35537,35539],{"className":35538},[1292],[1294,35540,35541],{"xmlns":1296},[1298,35542,35543,35547],{},[1301,35544,35545],{},[1307,35546,1353],{},[1315,35548,1353],{"encoding":1317}," s tabulkovou kritickou hodnotou jako u ostatních testů v této kapitole.",[1136,35551,1189],{"id":1188},[1191,35553,35554,35559,35564,35569,35574,35579,35584],{},[1194,35555,35556],{},[1127,35557,1133],{"className":35558,"dataFsResolvedFilePath":1131,"href":1132},[1130],[1194,35560,35561],{},[1127,35562,6377],{"className":35563,"dataFsResolvedFilePath":6375,"href":6376},[1130],[1194,35565,35566],{},[1127,35567,6369],{"className":35568,"dataFsResolvedFilePath":6367,"href":6368},[1130],[1194,35570,35571],{},[1127,35572,1169],{"className":35573,"dataFsResolvedFilePath":1167,"href":1168},[1130],[1194,35575,35576],{},[1127,35577,1182],{"className":35578,"dataFsResolvedFilePath":1180,"href":1181},[1130],[1194,35580,35581],{},[1127,35582,6390],{"className":35583,"dataFsResolvedFilePath":6388,"href":6389},[1130],[1194,35585,35586],{},[1127,35587,6396],{"className":35588,"dataFsResolvedFilePath":1214,"href":1215},[1130],[1136,35590,1219],{"id":934},[1110,35592,1222,35593,1227],{},[1224,35594,1226],{},[6404,35596,35597],{},"html pre.shiki code .sP4rz, html 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