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tabulky",{"type":1096,"value":1097,"toc":6284},"minimark",[1098,1102,1309,1314,1337,1355,1568,1709,2310,2327,2440,2444,2475,2480,3083,3090,3310,3537,3545,3626,3738,3891,3897,3978,3999,4008,4042,4049,4052,4058,4124,4183,4336,4342,4349,4427,4430,4486,4824,4845,4949,5058,5061,5082,5085,5340,5422,5429,5433,5663,5677,5826,5960,5966,6024,6028,6047,6062,6068,6113,6132,6147,6153,6212,6216,6269,6272,6280],[1099,1100,1094],"h1",{"id":1101},"kontingenční-tabulky",[1103,1104,1109,1123],"aside",{"className":1105,"dataCallout":1108},[1106,1107],"callout","callout-default","tldr",[1110,1111,1114,1122],"p",{"className":1112},[1113],"callout-title",[1115,1116],"span",{"className":1117,"ariaHidden":1121},[1118,1119,1120],"iconify","i-lucide:info","callout-icon","true","V kostce",[1124,1125,1126,1135,1209,1230,1270,1298],"ul",{},[1127,1128,1129,1130,1134],"li",{},"Kontingenční tabulka zaznamenává ",[1131,1132,1133],"strong",{},"simultánní četnosti"," dvou kvalitativních znaků naměřených na stejném souboru.",[1127,1136,1137,1140,1141,1171,1172,1193,1194,1208],{},[1131,1138,1139],{},"Test nezávislosti"," srovnává pozorované četnosti s očekávanými za platnosti ",[1115,1142,1145],{"className":1143},[1144],"katex",[1146,1147,1149],"math",{"xmlns":1148},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1150,1151,1152,1166],"semantics",{},[1153,1154,1155],"mrow",{},[1156,1157,1158,1162],"msub",{},[1159,1160,1161],"mi",{},"H",[1163,1164,1165],"mn",{},"0",[1167,1168,1170],"annotation",{"encoding":1169},"application\u002Fx-tex","H_0"," pomocí statistiky ",[1115,1173,1175],{"className":1174},[1144],[1146,1176,1177],{"xmlns":1148},[1150,1178,1179,1190],{},[1153,1180,1181],{},[1182,1183,1184,1187],"msup",{},[1159,1185,1186],{},"χ",[1163,1188,1189],{},"2",[1167,1191,1192],{"encoding":1169},"\\chi^2","; rozhoduje kritický obor ",[1115,1195,1197],{"className":1196},[1144],[1146,1198,1199],{"xmlns":1148},[1150,1200,1201,1206],{},[1153,1202,1203],{},[1159,1204,1205],{},"W",[1167,1207,1205],{"encoding":1169},", prakticky p-hodnota.",[1127,1210,1211,1212,1229],{},"Aproximace ",[1115,1213,1215],{"className":1214},[1144],[1146,1216,1217],{"xmlns":1148},[1150,1218,1219,1227],{},[1153,1220,1221],{},[1182,1222,1223,1225],{},[1159,1224,1186],{},[1163,1226,1189],{},[1167,1228,1192],{"encoding":1169}," rozdělením platí jen tehdy, když jsou očekávané četnosti dostatečně velké — proto se vždy kontrolují.",[1127,1231,1232,1233,1250,1251,1254,1255,1269],{},"Zamítnutí ",[1115,1234,1236],{"className":1235},[1144],[1146,1237,1238],{"xmlns":1148},[1150,1239,1240,1248],{},[1153,1241,1242],{},[1156,1243,1244,1246],{},[1159,1245,1161],{},[1163,1247,1165],{},[1167,1249,1170],{"encoding":1169}," samo o sobě neříká, jak silná závislost je — na to slouží ",[1131,1252,1253],{},"Cramérův koeficient kontingence"," ",[1115,1256,1258],{"className":1257},[1144],[1146,1259,1260],{"xmlns":1148},[1150,1261,1262,1267],{},[1153,1263,1264],{},[1159,1265,1266],{},"V",[1167,1268,1266],{"encoding":1169},".",[1127,1271,1272,1275,1276,1269],{},[1131,1273,1274],{},"Čtyřpolní tabulka"," (2×2) je speciální případ s vlastním zjednodušeným vzorcem pro ",[1115,1277,1279],{"className":1278},[1144],[1146,1280,1281],{"xmlns":1148},[1150,1282,1283,1295],{},[1153,1284,1285,1288,1292],{},[1159,1286,1287],{},"n",[1289,1290,1291],"mo",{},">",[1163,1293,1294],{},"40",[1167,1296,1297],{"encoding":1169},"n>40",[1127,1299,1300,1301,1304,1305,1308],{},"Pro ",[1131,1302,1303],{},"párová data"," (stejné prvky měřené dvakrát, např. před\u002Fpo zásahu) se používá ",[1131,1306,1307],{},"McNemarův test",", ne obyčejný test nezávislosti.",[1310,1311,1313],"h2",{"id":1312},"kontingenční-tabulka","Kontingenční tabulka",[1110,1315,1316,1317,1325,1326,1332,1333,1336],{},"V rámci ",[1318,1319,1324],"a",{"className":1320,"dataFsResolvedFilePath":1322,"href":1323},[1321],"wikilink","courses\u002Fmask.md","\u002Fwiki\u002Fmask","Metody aplikované statistiky"," navazují kontingenční tabulky na\n",[1318,1327,1331],{"className":1328,"dataFsResolvedFilePath":1329,"href":1330},[1321],"topics\u002Ftestovani-hypotez.md","\u002Fwiki\u002Ftestovani-hypotez","testování statistických hypotéz",": místo jedné náhodné veličiny teď sledujeme dva\n",[1131,1334,1335],{},"kvalitativní"," (kategoriální) znaky současně a ptáme se, zda spolu souvisí.",[1110,1338,1339,1340,1343,1344,1346,1347,1350,1351,1354],{},"Znak je ",[1131,1341,1342],{},"kvantitativní",", pokud nabývá číselných hodnot (stáří, stav tachometru), a ",[1131,1345,1335],{},"\n(kategoriální), pokud nabývá slovních variant (vzdělání, kuřák\u002Fnekuřák). Kvalitativní znaky dále dělíme na\n",[1131,1348,1349],{},"alternativní"," (dvě varianty, např. vada ano\u002Fne) a ",[1131,1352,1353],{},"množné"," (více než dvě varianty, např. svobodný\u002Frozvedený\u002Fženatý).",[1110,1356,1357,1358,1371,1372,1386,1387,1420,1421,1435,1436,1467,1468,1471,1472,1499,1500,1254,1503,1525,1526,1544,1545,1563,1564,1567],{},"Mějme ",[1115,1359,1361],{"className":1360},[1144],[1146,1362,1363],{"xmlns":1148},[1150,1364,1365,1369],{},[1153,1366,1367],{},[1159,1368,1287],{},[1167,1370,1287],{"encoding":1169}," opakování pokusu, při nichž sledujeme dva kvalitativní znaky ",[1115,1373,1375],{"className":1374},[1144],[1146,1376,1377],{"xmlns":1148},[1150,1378,1379,1384],{},[1153,1380,1381],{},[1159,1382,1383],{},"A",[1167,1385,1383],{"encoding":1169}," (varianty ",[1115,1388,1390],{"className":1389},[1144],[1146,1391,1392],{"xmlns":1148},[1150,1393,1394,1417],{},[1153,1395,1396,1403,1406,1409,1411],{},[1156,1397,1398,1400],{},[1159,1399,1383],{},[1163,1401,1402],{},"1",[1289,1404,1405],{"separator":1121},",",[1289,1407,1408],{},"…",[1289,1410,1405],{"separator":1121},[1156,1412,1413,1415],{},[1159,1414,1383],{},[1159,1416,71],{},[1167,1418,1419],{"encoding":1169},"A_1,\\dots,A_r",") a ",[1115,1422,1424],{"className":1423},[1144],[1146,1425,1426],{"xmlns":1148},[1150,1427,1428,1433],{},[1153,1429,1430],{},[1159,1431,1432],{},"B",[1167,1434,1432],{"encoding":1169},"\n(varianty ",[1115,1437,1439],{"className":1438},[1144],[1146,1440,1441],{"xmlns":1148},[1150,1442,1443,1464],{},[1153,1444,1445,1451,1453,1455,1457],{},[1156,1446,1447,1449],{},[1159,1448,1432],{},[1163,1450,1402],{},[1289,1452,1405],{"separator":1121},[1289,1454,1408],{},[1289,1456,1405],{"separator":1121},[1156,1458,1459,1461],{},[1159,1460,1432],{},[1159,1462,1463],{},"s",[1167,1465,1466],{"encoding":1169},"B_1,\\dots,B_s","). Výsledky zapíšeme do ",[1131,1469,1470],{},"kontingenční tabulky",": v políčku ",[1115,1473,1475],{"className":1474},[1144],[1146,1476,1477],{"xmlns":1148},[1150,1478,1479,1496],{},[1153,1480,1481,1485,1488,1490,1493],{},[1289,1482,1484],{"stretchy":1483},"false","(",[1159,1486,1487],{},"i",[1289,1489,1405],{"separator":1121},[1159,1491,1492],{},"j",[1289,1494,1495],{"stretchy":1483},")",[1167,1497,1498],{"encoding":1169},"(i,j)"," je ",[1131,1501,1502],{},"simultánní\nčetnost",[1115,1504,1506],{"className":1505},[1144],[1146,1507,1508],{"xmlns":1148},[1150,1509,1510,1522],{},[1153,1511,1512],{},[1156,1513,1514,1516],{},[1159,1515,1287],{},[1153,1517,1518,1520],{},[1159,1519,1487],{},[1159,1521,1492],{},[1167,1523,1524],{"encoding":1169},"n_{ij}",", tedy počet pokusů s variantou ",[1115,1527,1529],{"className":1528},[1144],[1146,1530,1531],{"xmlns":1148},[1150,1532,1533,1541],{},[1153,1534,1535],{},[1156,1536,1537,1539],{},[1159,1538,1383],{},[1159,1540,1487],{},[1167,1542,1543],{"encoding":1169},"A_i"," zároveň s variantou ",[1115,1546,1548],{"className":1547},[1144],[1146,1549,1550],{"xmlns":1148},[1150,1551,1552,1560],{},[1153,1553,1554],{},[1156,1555,1556,1558],{},[1159,1557,1432],{},[1159,1559,1492],{},[1167,1561,1562],{"encoding":1169},"B_j",". Řádkové a sloupcové součty\njsou ",[1131,1565,1566],{},"marginální četnosti",":",[1115,1569,1571],{"className":1570},[1144],[1146,1572,1574],{"xmlns":1148,"display":1573},"block",[1150,1575,1576,1706],{},[1153,1577,1578,1589,1592,1608,1618,1620,1624,1634,1636,1650,1660,1662,1664,1666,1668,1682,1696],{},[1156,1579,1580,1582],{},[1159,1581,1287],{},[1153,1583,1584,1586],{},[1159,1585,1487],{},[1289,1587,1588],{},"∙",[1289,1590,1591],{},"=",[1593,1594,1595,1598,1606],"munderover",{},[1289,1596,1597],{},"∑",[1153,1599,1600,1602,1604],{},[1159,1601,1492],{},[1289,1603,1591],{},[1163,1605,1402],{},[1159,1607,1463],{},[1156,1609,1610,1612],{},[1159,1611,1287],{},[1153,1613,1614,1616],{},[1159,1615,1487],{},[1159,1617,1492],{},[1289,1619,1405],{"separator":1121},[1621,1622],"mspace",{"width":1623},"2em",[1156,1625,1626,1628],{},[1159,1627,1287],{},[1153,1629,1630,1632],{},[1289,1631,1588],{},[1159,1633,1492],{},[1289,1635,1591],{},[1593,1637,1638,1640,1648],{},[1289,1639,1597],{},[1153,1641,1642,1644,1646],{},[1159,1643,1487],{},[1289,1645,1591],{},[1163,1647,1402],{},[1159,1649,71],{},[1156,1651,1652,1654],{},[1159,1653,1287],{},[1153,1655,1656,1658],{},[1159,1657,1487],{},[1159,1659,1492],{},[1289,1661,1405],{"separator":1121},[1621,1663],{"width":1623},[1159,1665,1287],{},[1289,1667,1591],{},[1593,1669,1670,1672,1680],{},[1289,1671,1597],{},[1153,1673,1674,1676,1678],{},[1159,1675,1487],{},[1289,1677,1591],{},[1163,1679,1402],{},[1159,1681,71],{},[1593,1683,1684,1686,1694],{},[1289,1685,1597],{},[1153,1687,1688,1690,1692],{},[1159,1689,1492],{},[1289,1691,1591],{},[1163,1693,1402],{},[1159,1695,1463],{},[1156,1697,1698,1700],{},[1159,1699,1287],{},[1153,1701,1702,1704],{},[1159,1703,1487],{},[1159,1705,1492],{},[1167,1707,1708],{"encoding":1169},"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}",[1710,1711,1712,1827],"table",{},[1713,1714,1715],"thead",{},[1716,1717,1718,1741,1761,1781,1783,1803],"tr",{},[1719,1720,1721],"th",{},[1115,1722,1724],{"className":1723},[1144],[1146,1725,1726],{"xmlns":1148},[1150,1727,1728,1738],{},[1153,1729,1730,1732,1736],{},[1159,1731,1383],{},[1159,1733,1735],{"mathvariant":1734},"normal","\\",[1159,1737,1432],{},[1167,1739,1740],{"encoding":1169},"A \\backslash B",[1719,1742,1743],{},[1115,1744,1746],{"className":1745},[1144],[1146,1747,1748],{"xmlns":1148},[1150,1749,1750,1758],{},[1153,1751,1752],{},[1156,1753,1754,1756],{},[1159,1755,1432],{},[1163,1757,1402],{},[1167,1759,1760],{"encoding":1169},"B_1",[1719,1762,1763],{},[1115,1764,1766],{"className":1765},[1144],[1146,1767,1768],{"xmlns":1148},[1150,1769,1770,1778],{},[1153,1771,1772],{},[1156,1773,1774,1776],{},[1159,1775,1432],{},[1163,1777,1189],{},[1167,1779,1780],{"encoding":1169},"B_2",[1719,1782,1408],{},[1719,1784,1785],{},[1115,1786,1788],{"className":1787},[1144],[1146,1789,1790],{"xmlns":1148},[1150,1791,1792,1800],{},[1153,1793,1794],{},[1156,1795,1796,1798],{},[1159,1797,1432],{},[1159,1799,1463],{},[1167,1801,1802],{"encoding":1169},"B_s",[1719,1804,1805],{},[1115,1806,1808],{"className":1807},[1144],[1146,1809,1810],{"xmlns":1148},[1150,1811,1812,1824],{},[1153,1813,1814],{},[1156,1815,1816,1818],{},[1159,1817,1287],{},[1153,1819,1820,1822],{},[1159,1821,1487],{},[1289,1823,1588],{},[1167,1825,1826],{"encoding":1169},"n_{i\\bullet}",[1828,1829,1830,1945,2059,2075,2195],"tbody",{},[1716,1831,1832,1853,1874,1895,1897,1921],{},[1833,1834,1835],"td",{},[1115,1836,1838],{"className":1837},[1144],[1146,1839,1840],{"xmlns":1148},[1150,1841,1842,1850],{},[1153,1843,1844],{},[1156,1845,1846,1848],{},[1159,1847,1383],{},[1163,1849,1402],{},[1167,1851,1852],{"encoding":1169},"A_1",[1833,1854,1855],{},[1115,1856,1858],{"className":1857},[1144],[1146,1859,1860],{"xmlns":1148},[1150,1861,1862,1871],{},[1153,1863,1864],{},[1156,1865,1866,1868],{},[1159,1867,1287],{},[1163,1869,1870],{},"11",[1167,1872,1873],{"encoding":1169},"n_{11}",[1833,1875,1876],{},[1115,1877,1879],{"className":1878},[1144],[1146,1880,1881],{"xmlns":1148},[1150,1882,1883,1892],{},[1153,1884,1885],{},[1156,1886,1887,1889],{},[1159,1888,1287],{},[1163,1890,1891],{},"12",[1167,1893,1894],{"encoding":1169},"n_{12}",[1833,1896,1408],{},[1833,1898,1899],{},[1115,1900,1902],{"className":1901},[1144],[1146,1903,1904],{"xmlns":1148},[1150,1905,1906,1918],{},[1153,1907,1908],{},[1156,1909,1910,1912],{},[1159,1911,1287],{},[1153,1913,1914,1916],{},[1163,1915,1402],{},[1159,1917,1463],{},[1167,1919,1920],{"encoding":1169},"n_{1s}",[1833,1922,1923],{},[1115,1924,1926],{"className":1925},[1144],[1146,1927,1928],{"xmlns":1148},[1150,1929,1930,1942],{},[1153,1931,1932],{},[1156,1933,1934,1936],{},[1159,1935,1287],{},[1153,1937,1938,1940],{},[1163,1939,1402],{},[1289,1941,1588],{},[1167,1943,1944],{"encoding":1169},"n_{1\\bullet}",[1716,1946,1947,1967,1988,2009,2011,2035],{},[1833,1948,1949],{},[1115,1950,1952],{"className":1951},[1144],[1146,1953,1954],{"xmlns":1148},[1150,1955,1956,1964],{},[1153,1957,1958],{},[1156,1959,1960,1962],{},[1159,1961,1383],{},[1163,1963,1189],{},[1167,1965,1966],{"encoding":1169},"A_2",[1833,1968,1969],{},[1115,1970,1972],{"className":1971},[1144],[1146,1973,1974],{"xmlns":1148},[1150,1975,1976,1985],{},[1153,1977,1978],{},[1156,1979,1980,1982],{},[1159,1981,1287],{},[1163,1983,1984],{},"21",[1167,1986,1987],{"encoding":1169},"n_{21}",[1833,1989,1990],{},[1115,1991,1993],{"className":1992},[1144],[1146,1994,1995],{"xmlns":1148},[1150,1996,1997,2006],{},[1153,1998,1999],{},[1156,2000,2001,2003],{},[1159,2002,1287],{},[1163,2004,2005],{},"22",[1167,2007,2008],{"encoding":1169},"n_{22}",[1833,2010,1408],{},[1833,2012,2013],{},[1115,2014,2016],{"className":2015},[1144],[1146,2017,2018],{"xmlns":1148},[1150,2019,2020,2032],{},[1153,2021,2022],{},[1156,2023,2024,2026],{},[1159,2025,1287],{},[1153,2027,2028,2030],{},[1163,2029,1189],{},[1159,2031,1463],{},[1167,2033,2034],{"encoding":1169},"n_{2s}",[1833,2036,2037],{},[1115,2038,2040],{"className":2039},[1144],[1146,2041,2042],{"xmlns":1148},[1150,2043,2044,2056],{},[1153,2045,2046],{},[1156,2047,2048,2050],{},[1159,2049,1287],{},[1153,2051,2052,2054],{},[1163,2053,1189],{},[1289,2055,1588],{},[1167,2057,2058],{"encoding":1169},"n_{2\\bullet}",[1716,2060,2061,2064,2066,2068,2071,2073],{},[1833,2062,2063],{},"⋮",[1833,2065,2063],{},[1833,2067,2063],{},[1833,2069,2070],{},"⋱",[1833,2072,2063],{},[1833,2074,2063],{},[1716,2076,2077,2097,2121,2145,2147,2171],{},[1833,2078,2079],{},[1115,2080,2082],{"className":2081},[1144],[1146,2083,2084],{"xmlns":1148},[1150,2085,2086,2094],{},[1153,2087,2088],{},[1156,2089,2090,2092],{},[1159,2091,1383],{},[1159,2093,71],{},[1167,2095,2096],{"encoding":1169},"A_r",[1833,2098,2099],{},[1115,2100,2102],{"className":2101},[1144],[1146,2103,2104],{"xmlns":1148},[1150,2105,2106,2118],{},[1153,2107,2108],{},[1156,2109,2110,2112],{},[1159,2111,1287],{},[1153,2113,2114,2116],{},[1159,2115,71],{},[1163,2117,1402],{},[1167,2119,2120],{"encoding":1169},"n_{r1}",[1833,2122,2123],{},[1115,2124,2126],{"className":2125},[1144],[1146,2127,2128],{"xmlns":1148},[1150,2129,2130,2142],{},[1153,2131,2132],{},[1156,2133,2134,2136],{},[1159,2135,1287],{},[1153,2137,2138,2140],{},[1159,2139,71],{},[1163,2141,1189],{},[1167,2143,2144],{"encoding":1169},"n_{r2}",[1833,2146,1408],{},[1833,2148,2149],{},[1115,2150,2152],{"className":2151},[1144],[1146,2153,2154],{"xmlns":1148},[1150,2155,2156,2168],{},[1153,2157,2158],{},[1156,2159,2160,2162],{},[1159,2161,1287],{},[1153,2163,2164,2166],{},[1159,2165,71],{},[1159,2167,1463],{},[1167,2169,2170],{"encoding":1169},"n_{rs}",[1833,2172,2173],{},[1115,2174,2176],{"className":2175},[1144],[1146,2177,2178],{"xmlns":1148},[1150,2179,2180,2192],{},[1153,2181,2182],{},[1156,2183,2184,2186],{},[1159,2185,1287],{},[1153,2187,2188,2190],{},[1159,2189,71],{},[1289,2191,1588],{},[1167,2193,2194],{"encoding":1169},"n_{r\\bullet}",[1716,2196,2197,2221,2245,2269,2271,2295],{},[1833,2198,2199],{},[1115,2200,2202],{"className":2201},[1144],[1146,2203,2204],{"xmlns":1148},[1150,2205,2206,2218],{},[1153,2207,2208],{},[1156,2209,2210,2212],{},[1159,2211,1287],{},[1153,2213,2214,2216],{},[1289,2215,1588],{},[1159,2217,1492],{},[1167,2219,2220],{"encoding":1169},"n_{\\bullet j}",[1833,2222,2223],{},[1115,2224,2226],{"className":2225},[1144],[1146,2227,2228],{"xmlns":1148},[1150,2229,2230,2242],{},[1153,2231,2232],{},[1156,2233,2234,2236],{},[1159,2235,1287],{},[1153,2237,2238,2240],{},[1289,2239,1588],{},[1163,2241,1402],{},[1167,2243,2244],{"encoding":1169},"n_{\\bullet 1}",[1833,2246,2247],{},[1115,2248,2250],{"className":2249},[1144],[1146,2251,2252],{"xmlns":1148},[1150,2253,2254,2266],{},[1153,2255,2256],{},[1156,2257,2258,2260],{},[1159,2259,1287],{},[1153,2261,2262,2264],{},[1289,2263,1588],{},[1163,2265,1189],{},[1167,2267,2268],{"encoding":1169},"n_{\\bullet 2}",[1833,2270,1408],{},[1833,2272,2273],{},[1115,2274,2276],{"className":2275},[1144],[1146,2277,2278],{"xmlns":1148},[1150,2279,2280,2292],{},[1153,2281,2282],{},[1156,2283,2284,2286],{},[1159,2285,1287],{},[1153,2287,2288,2290],{},[1289,2289,1588],{},[1159,2291,1463],{},[1167,2293,2294],{"encoding":1169},"n_{\\bullet s}",[1833,2296,2297],{},[1115,2298,2300],{"className":2299},[1144],[1146,2301,2302],{"xmlns":1148},[1150,2303,2304,2308],{},[1153,2305,2306],{},[1159,2307,1287],{},[1167,2309,1287],{"encoding":1169},[1110,2311,2312,2313,2326],{},"Vydělením četností počtem opakování ",[1115,2314,2316],{"className":2315},[1144],[1146,2317,2318],{"xmlns":1148},[1150,2319,2320,2324],{},[1153,2321,2322],{},[1159,2323,1287],{},[1167,2325,1287],{"encoding":1169}," dostaneme odhady pravděpodobností:",[1115,2328,2330],{"className":2329},[1144],[1146,2331,2332],{"xmlns":1148,"display":1573},[1150,2333,2334,2437],{},[1153,2335,2336,2352,2354,2369,2371,2373,2387,2389,2403,2405,2407,2421,2423],{},[1156,2337,2338,2346],{},[2339,2340,2341,2343],"mover",{"accent":1121},[1159,2342,1110],{},[1289,2344,2345],{},"^",[1153,2347,2348,2350],{},[1159,2349,1487],{},[1159,2351,1492],{},[1289,2353,1591],{},[2355,2356,2357,2367],"mfrac",{},[1156,2358,2359,2361],{},[1159,2360,1287],{},[1153,2362,2363,2365],{},[1159,2364,1487],{},[1159,2366,1492],{},[1159,2368,1287],{},[1289,2370,1405],{"separator":1121},[1621,2372],{"width":1623},[1156,2374,2375,2381],{},[2339,2376,2377,2379],{"accent":1121},[1159,2378,1110],{},[1289,2380,2345],{},[1153,2382,2383,2385],{},[1159,2384,1487],{},[1289,2386,1588],{},[1289,2388,1591],{},[2355,2390,2391,2401],{},[1156,2392,2393,2395],{},[1159,2394,1287],{},[1153,2396,2397,2399],{},[1159,2398,1487],{},[1289,2400,1588],{},[1159,2402,1287],{},[1289,2404,1405],{"separator":1121},[1621,2406],{"width":1623},[1156,2408,2409,2415],{},[2339,2410,2411,2413],{"accent":1121},[1159,2412,1110],{},[1289,2414,2345],{},[1153,2416,2417,2419],{},[1289,2418,1588],{},[1159,2420,1492],{},[1289,2422,1591],{},[2355,2424,2425,2435],{},[1156,2426,2427,2429],{},[1159,2428,1287],{},[1153,2430,2431,2433],{},[1289,2432,1588],{},[1159,2434,1492],{},[1159,2436,1287],{},[1167,2438,2439],{"encoding":1169},"\\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}",[1310,2441,2443],{"id":2442},"test-nezávislosti-dvou-kvalitativních-znaků","Test nezávislosti dvou kvalitativních znaků",[1110,2445,2446,2447,2460,2461,2474],{},"Test ověřuje, zda varianty znaku ",[1115,2448,2450],{"className":2449},[1144],[1146,2451,2452],{"xmlns":1148},[1150,2453,2454,2458],{},[1153,2455,2456],{},[1159,2457,1383],{},[1167,2459,1383],{"encoding":1169}," a varianty znaku ",[1115,2462,2464],{"className":2463},[1144],[1146,2465,2466],{"xmlns":1148},[1150,2467,2468,2472],{},[1153,2469,2470],{},[1159,2471,1432],{},[1167,2473,1432],{"encoding":1169}," jsou na sobě nezávislé, tedy zda simultánní\npravděpodobnost je součinem marginálních pravděpodobností.",[1110,2476,2477],{},[1131,2478,2479],{},"Postup testu:",[2481,2482,2483,2615,2933,3015],"ol",{},[1127,2484,2485,2541,2542,2568,2569,2595,2596,2614],{},[1115,2486,2488],{"className":2487},[1144],[1146,2489,2490],{"xmlns":1148},[1150,2491,2492,2538],{},[1153,2493,2494,2500,2502,2512,2514,2524,2528],{},[1156,2495,2496,2498],{},[1159,2497,1161],{},[1163,2499,1165],{},[1289,2501,1567],{},[1156,2503,2504,2506],{},[1159,2505,1110],{},[1153,2507,2508,2510],{},[1159,2509,1487],{},[1159,2511,1492],{},[1289,2513,1591],{},[1156,2515,2516,2518],{},[1159,2517,1110],{},[1153,2519,2520,2522],{},[1159,2521,1487],{},[1289,2523,1588],{},[2525,2526,2527],"mtext",{}," ",[1156,2529,2530,2532],{},[1159,2531,1110],{},[1153,2533,2534,2536],{},[1289,2535,1588],{},[1159,2537,1492],{},[1167,2539,2540],{"encoding":1169},"H_0: p_{ij} = p_{i\\bullet}\\,p_{\\bullet j}"," pro všechna ",[1115,2543,2545],{"className":2544},[1144],[1146,2546,2547],{"xmlns":1148},[1150,2548,2549,2565],{},[1153,2550,2551,2553,2555,2557,2559,2561,2563],{},[1159,2552,1487],{},[1289,2554,1591],{},[1163,2556,1402],{},[1289,2558,1405],{"separator":1121},[1289,2560,1408],{},[1289,2562,1405],{"separator":1121},[1159,2564,71],{},[1167,2566,2567],{"encoding":1169},"i = 1,\\dots,r",", ",[1115,2570,2572],{"className":2571},[1144],[1146,2573,2574],{"xmlns":1148},[1150,2575,2576,2592],{},[1153,2577,2578,2580,2582,2584,2586,2588,2590],{},[1159,2579,1492],{},[1289,2581,1591],{},[1163,2583,1402],{},[1289,2585,1405],{"separator":1121},[1289,2587,1408],{},[1289,2589,1405],{"separator":1121},[1159,2591,1463],{},[1167,2593,2594],{"encoding":1169},"j = 1,\\dots,s"," (znaky jsou na sobě\nnezávislé) proti ",[1115,2597,2599],{"className":2598},[1144],[1146,2600,2601],{"xmlns":1148},[1150,2602,2603,2611],{},[1153,2604,2605],{},[1156,2606,2607,2609],{},[1159,2608,1161],{},[1163,2610,1402],{},[1167,2612,2613],{"encoding":1169},"H_1",": znaky jsou závislé.",[1127,2616,2617,2618,2775,2778,2779,2796,2797,2829,2830,1499,2889,2892,2893,2914,2915,2932],{},"Testové kritérium",[1115,2619,2621],{"className":2620},[1144],[1146,2622,2623],{"xmlns":1148,"display":1573},[1150,2624,2625,2772],{},[1153,2626,2627,2633,2635,2649,2663,2722,2724,2726,2740,2742,2756,2758],{},[1182,2628,2629,2631],{},[1159,2630,1186],{},[1163,2632,1189],{},[1289,2634,1591],{},[1593,2636,2637,2639,2647],{},[1289,2638,1597],{},[1153,2640,2641,2643,2645],{},[1159,2642,1487],{},[1289,2644,1591],{},[1163,2646,1402],{},[1159,2648,71],{},[1593,2650,2651,2653,2661],{},[1289,2652,1597],{},[1153,2654,2655,2657,2659],{},[1159,2656,1492],{},[1289,2658,1591],{},[1163,2660,1402],{},[1159,2662,1463],{},[2355,2664,2665,2704],{},[1153,2666,2667,2669,2679,2682,2684,2698],{},[1289,2668,1484],{"stretchy":1483},[1156,2670,2671,2673],{},[1159,2672,1287],{},[1153,2674,2675,2677],{},[1159,2676,1487],{},[1159,2678,1492],{},[1289,2680,2681],{},"−",[1159,2683,1287],{},[1156,2685,2686,2692],{},[2339,2687,2688,2690],{"accent":1121},[1159,2689,1110],{},[1289,2691,2345],{},[1153,2693,2694,2696],{},[1159,2695,1487],{},[1159,2697,1492],{},[1182,2699,2700,2702],{},[1289,2701,1495],{"stretchy":1483},[1163,2703,1189],{},[1153,2705,2706,2708],{},[1159,2707,1287],{},[1156,2709,2710,2716],{},[2339,2711,2712,2714],{"accent":1121},[1159,2713,1110],{},[1289,2715,2345],{},[1153,2717,2718,2720],{},[1159,2719,1487],{},[1159,2721,1492],{},[1289,2723,1405],{"separator":1121},[1621,2725],{"width":1623},[1156,2727,2728,2734],{},[2339,2729,2730,2732],{"accent":1121},[1159,2731,1110],{},[1289,2733,2345],{},[1153,2735,2736,2738],{},[1159,2737,1487],{},[1159,2739,1492],{},[1289,2741,1591],{},[1156,2743,2744,2750],{},[2339,2745,2746,2748],{"accent":1121},[1159,2747,1110],{},[1289,2749,2345],{},[1153,2751,2752,2754],{},[1159,2753,1487],{},[1289,2755,1588],{},[2525,2757,2527],{},[1156,2759,2760,2766],{},[2339,2761,2762,2764],{"accent":1121},[1159,2763,1110],{},[1289,2765,2345],{},[1153,2767,2768,2770],{},[1289,2769,1588],{},[1159,2771,1492],{},[1167,2773,2774],{"encoding":1169},"\\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}",[2776,2777],"br",{},"má asymptoticky Pearsonovo (",[1115,2780,2782],{"className":2781},[1144],[1146,2783,2784],{"xmlns":1148},[1150,2785,2786,2794],{},[1153,2787,2788],{},[1182,2789,2790,2792],{},[1159,2791,1186],{},[1163,2793,1189],{},[1167,2795,1192],{"encoding":1169},") rozdělení o ",[1115,2798,2800],{"className":2799},[1144],[1146,2801,2802],{"xmlns":1148},[1150,2803,2804,2826],{},[1153,2805,2806,2808,2810,2812,2814,2816,2818,2820,2822,2824],{},[1289,2807,1484],{"stretchy":1483},[1159,2809,71],{},[1289,2811,2681],{},[1163,2813,1402],{},[1289,2815,1495],{"stretchy":1483},[1289,2817,1484],{"stretchy":1483},[1159,2819,1463],{},[1289,2821,2681],{},[1163,2823,1402],{},[1289,2825,1495],{"stretchy":1483},[1167,2827,2828],{"encoding":1169},"(r-1)(s-1)"," stupních volnosti. Hodnota ",[1115,2831,2833],{"className":2832},[1144],[1146,2834,2835],{"xmlns":1148},[1150,2836,2837,2886],{},[1153,2838,2839,2841,2855,2857],{},[1159,2840,1287],{},[1156,2842,2843,2849],{},[2339,2844,2845,2847],{"accent":1121},[1159,2846,1110],{},[1289,2848,2345],{},[1153,2850,2851,2853],{},[1159,2852,1487],{},[1159,2854,1492],{},[1289,2856,1591],{},[2858,2859,2860],"mstyle",{"scriptlevel":1165,"displaystyle":1121},[2355,2861,2862,2884],{},[1153,2863,2864,2874],{},[1156,2865,2866,2868],{},[1159,2867,1287],{},[1153,2869,2870,2872],{},[1159,2871,1487],{},[1289,2873,1588],{},[1156,2875,2876,2878],{},[1159,2877,1287],{},[1153,2879,2880,2882],{},[1289,2881,1588],{},[1159,2883,1492],{},[1159,2885,1287],{},[1167,2887,2888],{"encoding":1169},"n\\hat p_{ij} = \\dfrac{n_{i\\bullet}n_{\\bullet j}}{n}",[1131,2890,2891],{},"očekávaná četnost"," políčka ",[1115,2894,2896],{"className":2895},[1144],[1146,2897,2898],{"xmlns":1148},[1150,2899,2900,2912],{},[1153,2901,2902,2904,2906,2908,2910],{},[1289,2903,1484],{"stretchy":1483},[1159,2905,1487],{},[1289,2907,1405],{"separator":1121},[1159,2909,1492],{},[1289,2911,1495],{"stretchy":1483},[1167,2913,1498],{"encoding":1169}," — četnost, kterou bychom čekali, kdyby ",[1115,2916,2918],{"className":2917},[1144],[1146,2919,2920],{"xmlns":1148},[1150,2921,2922,2930],{},[1153,2923,2924],{},[1156,2925,2926,2928],{},[1159,2927,1161],{},[1163,2929,1165],{},[1167,2931,1170],{"encoding":1169}," platila.",[1127,2934,2935,2936,1269],{},"Kritický obor: ",[1115,2937,2939],{"className":2938},[1144],[1146,2940,2941],{"xmlns":1148},[1150,2942,2943,3012],{},[1153,2944,2945,2947,2949,2952,2958,2960,2966,2969,2985,2987,2989,2991,2993,2995,2997,2999,3001,3003,3005,3007,3009],{},[1159,2946,1205],{},[1289,2948,1591],{},[1289,2950,2951],{"stretchy":1483},"{",[1182,2953,2954,2956],{},[1159,2955,1186],{},[1163,2957,1189],{},[1289,2959,1567],{},[1182,2961,2962,2964],{},[1159,2963,1186],{},[1163,2965,1189],{},[1289,2967,2968],{},"≥",[2970,2971,2972,2974,2983],"msubsup",{},[1159,2973,1186],{},[1153,2975,2976,2978,2980],{},[1163,2977,1402],{},[1289,2979,2681],{},[1159,2981,2982],{},"α",[1163,2984,1189],{},[1289,2986,1484],{"stretchy":1483},[1289,2988,1484],{"stretchy":1483},[1159,2990,71],{},[1289,2992,2681],{},[1163,2994,1402],{},[1289,2996,1495],{"stretchy":1483},[1289,2998,1484],{"stretchy":1483},[1159,3000,1463],{},[1289,3002,2681],{},[1163,3004,1402],{},[1289,3006,1495],{"stretchy":1483},[1289,3008,1495],{"stretchy":1483},[1289,3010,3011],{"stretchy":1483},"}",[1167,3013,3014],{"encoding":1169},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}((r-1)(s-1))\\}",[1127,3016,3017,3018,3031,3032,3046,3047,3064,3065,3082],{},"Padne-li testové kritérium do ",[1115,3019,3021],{"className":3020},[1144],[1146,3022,3023],{"xmlns":1148},[1150,3024,3025,3029],{},[1153,3026,3027],{},[1159,3028,1205],{},[1167,3030,1205],{"encoding":1169},", zamítáme na hladině ",[1115,3033,3035],{"className":3034},[1144],[1146,3036,3037],{"xmlns":1148},[1150,3038,3039,3043],{},[1153,3040,3041],{},[1159,3042,2982],{},[1167,3044,3045],{"encoding":1169},"\\alpha"," nulovou hypotézu o nezávislosti a přijímáme\n",[1115,3048,3050],{"className":3049},[1144],[1146,3051,3052],{"xmlns":1148},[1150,3053,3054,3062],{},[1153,3055,3056],{},[1156,3057,3058,3060],{},[1159,3059,1161],{},[1163,3061,1402],{},[1167,3063,2613],{"encoding":1169},"; jinak nemáme důvod ",[1115,3066,3068],{"className":3067},[1144],[1146,3069,3070],{"xmlns":1148},[1150,3071,3072,3080],{},[1153,3073,3074],{},[1156,3075,3076,3078],{},[1159,3077,1161],{},[1163,3079,1165],{},[1167,3081,1170],{"encoding":1169}," zamítnout.",[1110,3084,3085,3086,1269],{},"V R počítá test i očekávané četnosti funkce ",[3087,3088,3089],"code",{},"chisq.test()",[1103,3091,3095,3103,3106,3109,3255],{"className":3092,"dataCallout":3094},[1106,3093],"callout-example","example",[1110,3096,3098,3102],{"className":3097},[1113],[1115,3099],{"className":3100,"ariaHidden":1121},[1118,3101,1120],"i-lucide:flask-conical","Příklad: nákup potravin na internetu a vzdělání",[1110,3104,3105],{},"Testujte hypotézu, zda se vzájemně ovlivňuje zkušenost s nákupem potravin na internetu a vzdělání respondenta\n(n = 385 respondentů).",[1110,3107,3108],{},"Základní soubor: respondenti; výběrový soubor: respondenti, kteří odpověděli; měřený znak A: vzdělání, měřený\nznak B: způsob nákupu.",[1710,3110,3111,3150],{},[1713,3112,3113],{},[1716,3114,3115,3118,3121,3124,3127],{},[1719,3116,3117],{},"vzdělání \\ nákup",[1719,3119,3120],{},"ano",[1719,3122,3123],{},"ne, ale plánuji",[1719,3125,3126],{},"ne, neplánuji",[1719,3128,3129],{},[1115,3130,3132],{"className":3131},[1144],[1146,3133,3134],{"xmlns":1148},[1150,3135,3136,3148],{},[1153,3137,3138],{},[1156,3139,3140,3142],{},[1159,3141,1287],{},[1153,3143,3144,3146],{},[1159,3145,1487],{},[1289,3147,1588],{},[1167,3149,1826],{"encoding":1169},[1828,3151,3152,3168,3185,3202,3218],{},[1716,3153,3154,3157,3160,3163,3165],{},[1833,3155,3156],{},"SŠ bez maturity",[1833,3158,3159],{},"4",[1833,3161,3162],{},"13",[1833,3164,1891],{},[1833,3166,3167],{},"29",[1716,3169,3170,3173,3176,3179,3182],{},[1833,3171,3172],{},"SŠ s maturitou, VOŠ",[1833,3174,3175],{},"31",[1833,3177,3178],{},"62",[1833,3180,3181],{},"71",[1833,3183,3184],{},"164",[1716,3186,3187,3190,3193,3196,3199],{},[1833,3188,3189],{},"VŠ",[1833,3191,3192],{},"44",[1833,3194,3195],{},"58",[1833,3197,3198],{},"66",[1833,3200,3201],{},"168",[1716,3203,3204,3207,3210,3213,3215],{},[1833,3205,3206],{},"ZŠ",[1833,3208,3209],{},"3",[1833,3211,3212],{},"9",[1833,3214,1891],{},[1833,3216,3217],{},"24",[1716,3219,3220,3243,3246,3249,3252],{},[1833,3221,3222],{},[1115,3223,3225],{"className":3224},[1144],[1146,3226,3227],{"xmlns":1148},[1150,3228,3229,3241],{},[1153,3230,3231],{},[1156,3232,3233,3235],{},[1159,3234,1287],{},[1153,3236,3237,3239],{},[1289,3238,1588],{},[1159,3240,1492],{},[1167,3242,2220],{"encoding":1169},[1833,3244,3245],{},"82",[1833,3247,3248],{},"142",[1833,3250,3251],{},"161",[1833,3253,3254],{},"385",[1110,3256,3257,3309],{},[1115,3258,3260],{"className":3259},[1144],[1146,3261,3262],{"xmlns":1148},[1150,3263,3264,3306],{},[1153,3265,3266,3272,3274,3284,3286,3296],{},[1156,3267,3268,3270],{},[1159,3269,1161],{},[1163,3271,1165],{},[1289,3273,1567],{},[1156,3275,3276,3278],{},[1159,3277,1110],{},[1153,3279,3280,3282],{},[1159,3281,1487],{},[1159,3283,1492],{},[1289,3285,1591],{},[1156,3287,3288,3290],{},[1159,3289,1110],{},[1153,3291,3292,3294],{},[1159,3293,1487],{},[1289,3295,1588],{},[1156,3297,3298,3300],{},[1159,3299,1110],{},[1153,3301,3302,3304],{},[1289,3303,1588],{},[1159,3305,1492],{},[1167,3307,3308],{"encoding":1169},"H_0: p_{ij} = p_{i\\bullet}p_{\\bullet j}"," — vzdělání a způsob nákupu jsou na sobě nezávislé.",[3311,3312,3316],"pre",{"className":3313,"code":3314,"language":71,"meta":3315,"style":3315},"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","",[3087,3317,3318,3357,3374,3391,3409,3432,3445,3480,3508,3521],{"__ignoreMap":3315},[1115,3319,3321,3325,3329,3333,3336,3339,3341,3344,3346,3349,3351,3354],{"class":3320,"line":10},"line",[1115,3322,3324],{"class":3323},"sP4rz","tab1",[1115,3326,3328],{"class":3327},"s8jYJ"," \u003C-",[1115,3330,3332],{"class":3331},"snPdu"," matrix",[1115,3334,1484],{"class":3335},"sxrX7",[1115,3337,3338],{"class":3331},"c",[1115,3340,1484],{"class":3335},[1115,3342,3159],{"class":3343},"sBjJW",[1115,3345,1405],{"class":3327},[1115,3347,3348],{"class":3343}," 13",[1115,3350,1405],{"class":3327},[1115,3352,3353],{"class":3343}," 12",[1115,3355,3356],{"class":3327},",\n",[1115,3358,3359,3362,3364,3367,3369,3372],{"class":3320,"line":27},[1115,3360,3361],{"class":3343},"                 31",[1115,3363,1405],{"class":3327},[1115,3365,3366],{"class":3343}," 62",[1115,3368,1405],{"class":3327},[1115,3370,3371],{"class":3343}," 71",[1115,3373,3356],{"class":3327},[1115,3375,3376,3379,3381,3384,3386,3389],{"class":3320,"line":148},[1115,3377,3378],{"class":3343},"                 44",[1115,3380,1405],{"class":3327},[1115,3382,3383],{"class":3343}," 58",[1115,3385,1405],{"class":3327},[1115,3387,3388],{"class":3343}," 66",[1115,3390,3356],{"class":3327},[1115,3392,3393,3396,3398,3401,3403,3405,3407],{"class":3320,"line":111},[1115,3394,3395],{"class":3343},"                 3",[1115,3397,1405],{"class":3327},[1115,3399,3400],{"class":3343},"  9",[1115,3402,1405],{"class":3327},[1115,3404,3353],{"class":3343},[1115,3406,1495],{"class":3335},[1115,3408,3356],{"class":3327},[1115,3410,3411,3414,3417,3420,3422,3425,3427,3430],{"class":3320,"line":96},[1115,3412,3413],{"class":3323},"               nrow",[1115,3415,3416],{"class":3327}," =",[1115,3418,3419],{"class":3343}," 4",[1115,3421,1405],{"class":3327},[1115,3423,3424],{"class":3323}," byrow",[1115,3426,3416],{"class":3327},[1115,3428,3429],{"class":3343}," TRUE",[1115,3431,3356],{"class":3327},[1115,3433,3434,3437,3439,3442],{"class":3320,"line":89},[1115,3435,3436],{"class":3323},"               dimnames",[1115,3438,3416],{"class":3327},[1115,3440,3441],{"class":3331}," list",[1115,3443,3444],{"class":3335},"(\n",[1115,3446,3447,3450,3452,3455,3457,3461,3463,3466,3468,3471,3473,3476,3478],{"class":3320,"line":82},[1115,3448,3449],{"class":3323},"                 vzdelani",[1115,3451,3416],{"class":3327},[1115,3453,3454],{"class":3331}," c",[1115,3456,1484],{"class":3335},[1115,3458,3460],{"class":3459},"sIIMD","\"SS bez maturity\"",[1115,3462,1405],{"class":3327},[1115,3464,3465],{"class":3459}," \"SS s maturitou nebo VOS\"",[1115,3467,1405],{"class":3327},[1115,3469,3470],{"class":3459}," \"VS\"",[1115,3472,1405],{"class":3327},[1115,3474,3475],{"class":3459}," \"ZS\"",[1115,3477,1495],{"class":3335},[1115,3479,3356],{"class":3327},[1115,3481,3482,3485,3488,3490,3492,3495,3497,3500,3502,3505],{"class":3320,"line":75},[1115,3483,3484],{"class":3323},"                 nakup",[1115,3486,3487],{"class":3327},"    =",[1115,3489,3454],{"class":3331},[1115,3491,1484],{"class":3335},[1115,3493,3494],{"class":3459},"\"ano\"",[1115,3496,1405],{"class":3327},[1115,3498,3499],{"class":3459}," \"ne, ale planuji\"",[1115,3501,1405],{"class":3327},[1115,3503,3504],{"class":3459}," \"ne, neplanuji\"",[1115,3506,3507],{"class":3335},")))\n",[1115,3509,3511,3514,3516,3518],{"class":3320,"line":3510},9,[1115,3512,3513],{"class":3331},"chisq.test",[1115,3515,1484],{"class":3335},[1115,3517,3324],{"class":3323},[1115,3519,3520],{"class":3335},")\n",[1115,3522,3523,3525,3527,3529,3531,3534],{"class":3320,"line":72},[1115,3524,3513],{"class":3331},[1115,3526,1484],{"class":3335},[1115,3528,3324],{"class":3323},[1115,3530,1495],{"class":3335},[1115,3532,3533],{"class":3327},"$",[1115,3535,3536],{"class":3323},"expected\n",[3311,3538,3543],{"className":3539,"code":3541,"language":3542,"meta":3315},[3540],"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",[3087,3544,3541],{"__ignoreMap":3315},[1110,3546,3547,3548,3571,3572,3586,3587,3607,3608,3625],{},"Všechny očekávané četnosti jsou nad 5, aproximace je v pořádku. Testové kritérium ",[1115,3549,3551],{"className":3550},[1144],[1146,3552,3553],{"xmlns":1148},[1150,3554,3555,3568],{},[1153,3556,3557,3563,3565],{},[1182,3558,3559,3561],{},[1159,3560,1186],{},[1163,3562,1189],{},[1289,3564,1591],{},[1163,3566,3567],{},"5,49",[1167,3569,3570],{"encoding":1169},"\\chi^2 = 5{,}49"," s ",[1115,3573,3575],{"className":3574},[1144],[1146,3576,3577],{"xmlns":1148},[1150,3578,3579,3584],{},[1153,3580,3581],{},[1163,3582,3583],{},"6",[1167,3585,3583],{"encoding":1169}," stupni\nvolnosti dává p-hodnotu ",[1115,3588,3590],{"className":3589},[1144],[1146,3591,3592],{"xmlns":1148},[1150,3593,3594,3604],{},[1153,3595,3596,3599,3601],{},[1163,3597,3598],{},"0,483",[1289,3600,1291],{},[1163,3602,3603],{},"0,05",[1167,3605,3606],{"encoding":1169},"0{,}483 > 0{,}05",": ",[1115,3609,3611],{"className":3610},[1144],[1146,3612,3613],{"xmlns":1148},[1150,3614,3615,3623],{},[1153,3616,3617],{},[1156,3618,3619,3621],{},[1159,3620,1161],{},[1163,3622,1165],{},[1167,3624,1170],{"encoding":1169}," nezamítáme, závislost mezi zkušeností s nákupem potravin na\ninternetu a vzděláním respondenta se neprokázala.",[1103,3627,3629,3636,3639,3684],{"className":3628,"dataCallout":3094},[1106,3093],[1110,3630,3632,3635],{"className":3631},[1113],[1115,3633],{"className":3634,"ariaHidden":1121},[1118,3101,1120],"Příklad: vzdělání a zveřejňování citlivých údajů na Facebooku",[1110,3637,3638],{},"Mezi 221 osobami bylo zaznamenáno vzdělání a zda zveřejňují na Facebooku citlivé údaje. Proveďte test\nnezávislosti.",[1710,3640,3641,3655],{},[1713,3642,3643],{},[1716,3644,3645,3648,3651,3653],{},[1719,3646,3647],{},"zveřejňuje \\ vzdělání",[1719,3649,3650],{},"SŠ",[1719,3652,3189],{},[1719,3654,3206],{},[1828,3656,3657,3671],{},[1716,3658,3659,3662,3665,3668],{},[1833,3660,3661],{},"ne",[1833,3663,3664],{},"20",[1833,3666,3667],{},"33",[1833,3669,3670],{},"39",[1716,3672,3673,3675,3678,3681],{},[1833,3674,3120],{},[1833,3676,3677],{},"25",[1833,3679,3680],{},"28",[1833,3682,3683],{},"76",[1110,3685,3686,3737],{},[1115,3687,3689],{"className":3688},[1144],[1146,3690,3691],{"xmlns":1148},[1150,3692,3693,3735],{},[1153,3694,3695,3701,3703,3713,3715,3725],{},[1156,3696,3697,3699],{},[1159,3698,1161],{},[1163,3700,1165],{},[1289,3702,1567],{},[1156,3704,3705,3707],{},[1159,3706,1110],{},[1153,3708,3709,3711],{},[1159,3710,1487],{},[1159,3712,1492],{},[1289,3714,1591],{},[1156,3716,3717,3719],{},[1159,3718,1110],{},[1153,3720,3721,3723],{},[1159,3722,1487],{},[1289,3724,1588],{},[1156,3726,3727,3729],{},[1159,3728,1110],{},[1153,3730,3731,3733],{},[1289,3732,1588],{},[1159,3734,1492],{},[1167,3736,3308],{"encoding":1169}," — vzdělání a zveřejňování citlivých údajů jsou na sobě nezávislé.",[3311,3739,3741],{"className":3313,"code":3740,"language":71,"meta":3315,"style":3315},"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",[3087,3742,3743,3772,3791,3810,3820,3843,3867,3877],{"__ignoreMap":3315},[1115,3744,3745,3748,3750,3752,3754,3756,3758,3760,3762,3765,3767,3770],{"class":3320,"line":10},[1115,3746,3747],{"class":3323},"tab2",[1115,3749,3328],{"class":3327},[1115,3751,3332],{"class":3331},[1115,3753,1484],{"class":3335},[1115,3755,3338],{"class":3331},[1115,3757,1484],{"class":3335},[1115,3759,3664],{"class":3343},[1115,3761,1405],{"class":3327},[1115,3763,3764],{"class":3343}," 33",[1115,3766,1405],{"class":3327},[1115,3768,3769],{"class":3343}," 39",[1115,3771,3356],{"class":3327},[1115,3773,3774,3777,3779,3782,3784,3787,3789],{"class":3320,"line":27},[1115,3775,3776],{"class":3343},"                 25",[1115,3778,1405],{"class":3327},[1115,3780,3781],{"class":3343}," 28",[1115,3783,1405],{"class":3327},[1115,3785,3786],{"class":3343}," 76",[1115,3788,1495],{"class":3335},[1115,3790,3356],{"class":3327},[1115,3792,3793,3795,3797,3800,3802,3804,3806,3808],{"class":3320,"line":148},[1115,3794,3413],{"class":3323},[1115,3796,3416],{"class":3327},[1115,3798,3799],{"class":3343}," 2",[1115,3801,1405],{"class":3327},[1115,3803,3424],{"class":3323},[1115,3805,3416],{"class":3327},[1115,3807,3429],{"class":3343},[1115,3809,3356],{"class":3327},[1115,3811,3812,3814,3816,3818],{"class":3320,"line":111},[1115,3813,3436],{"class":3323},[1115,3815,3416],{"class":3327},[1115,3817,3441],{"class":3331},[1115,3819,3444],{"class":3335},[1115,3821,3822,3825,3827,3829,3831,3834,3836,3839,3841],{"class":3320,"line":96},[1115,3823,3824],{"class":3323},"                 zverejnuje",[1115,3826,3416],{"class":3327},[1115,3828,3454],{"class":3331},[1115,3830,1484],{"class":3335},[1115,3832,3833],{"class":3459},"\"ne\"",[1115,3835,1405],{"class":3327},[1115,3837,3838],{"class":3459}," \"ano\"",[1115,3840,1495],{"class":3335},[1115,3842,3356],{"class":3327},[1115,3844,3845,3847,3850,3852,3854,3857,3859,3861,3863,3865],{"class":3320,"line":89},[1115,3846,3449],{"class":3323},[1115,3848,3849],{"class":3327},"   =",[1115,3851,3454],{"class":3331},[1115,3853,1484],{"class":3335},[1115,3855,3856],{"class":3459},"\"SS\"",[1115,3858,1405],{"class":3327},[1115,3860,3470],{"class":3459},[1115,3862,1405],{"class":3327},[1115,3864,3475],{"class":3459},[1115,3866,3507],{"class":3335},[1115,3868,3869,3871,3873,3875],{"class":3320,"line":82},[1115,3870,3513],{"class":3331},[1115,3872,1484],{"class":3335},[1115,3874,3747],{"class":3323},[1115,3876,3520],{"class":3335},[1115,3878,3879,3881,3883,3885,3887,3889],{"class":3320,"line":75},[1115,3880,3513],{"class":3331},[1115,3882,1484],{"class":3335},[1115,3884,3747],{"class":3323},[1115,3886,1495],{"class":3335},[1115,3888,3533],{"class":3327},[1115,3890,3536],{"class":3323},[3311,3892,3895],{"className":3893,"code":3894,"language":3542,"meta":3315},[3540],"    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",[3087,3896,3894],{"__ignoreMap":3315},[1110,3898,3899,3900,3571,3923,3936,3937,3607,3957,3974,3975,1269],{},"I zde jsou všechny očekávané četnosti nad 5. Testové kritérium ",[1115,3901,3903],{"className":3902},[1144],[1146,3904,3905],{"xmlns":1148},[1150,3906,3907,3920],{},[1153,3908,3909,3915,3917],{},[1182,3910,3911,3913],{},[1159,3912,1186],{},[1163,3914,1189],{},[1289,3916,1591],{},[1163,3918,3919],{},"6,87",[1167,3921,3922],{"encoding":1169},"\\chi^2 = 6{,}87",[1115,3924,3926],{"className":3925},[1144],[1146,3927,3928],{"xmlns":1148},[1150,3929,3930,3934],{},[1153,3931,3932],{},[1163,3933,1189],{},[1167,3935,1189],{"encoding":1169}," stupni volnosti dává\np-hodnotu ",[1115,3938,3940],{"className":3939},[1144],[1146,3941,3942],{"xmlns":1148},[1150,3943,3944,3954],{},[1153,3945,3946,3949,3952],{},[1163,3947,3948],{},"0,032",[1289,3950,3951],{},"\u003C",[1163,3953,3603],{},[1167,3955,3956],{"encoding":1169},"0{,}032 \u003C 0{,}05",[1115,3958,3960],{"className":3959},[1144],[1146,3961,3962],{"xmlns":1148},[1150,3963,3964,3972],{},[1153,3965,3966],{},[1156,3967,3968,3970],{},[1159,3969,1161],{},[1163,3971,1165],{},[1167,3973,1170],{"encoding":1169}," zamítáme — na rozdíl od předchozího příkladu tady vzdělání a zveřejňování\ncitlivých údajů na Facebooku na sobě ",[1131,3976,3977],{},"závisí",[1110,3979,3980,3981,3998],{},"Srovnání pozorovaných a očekávaných četností ukazuje, proč jeden příklad ",[1115,3982,3984],{"className":3983},[1144],[1146,3985,3986],{"xmlns":1148},[1150,3987,3988,3996],{},[1153,3989,3990],{},[1156,3991,3992,3994],{},[1159,3993,1161],{},[1163,3995,1165],{},[1167,3997,1170],{"encoding":1169}," nezamítá a druhý ano — ve druhém\nse pozorované sloupce (zejména u ZŠ) systematicky odchylují od očekávaných, v prvním kolísají jen náhodně kolem nich:",[1110,4000,4001],{},[4002,4003],"img",{"alt":4004,"className":4005,"src":4007},"mask-kt-observed-expected",[1321,4006],"wikilink-broken","\u002Fwiki-assets\u002Fmask-kt-observed-expected.png",[1110,4009,4010,4011,4028,4029,1567],{},"Totéž je vidět na rozdělení testového kritéria: u prvního příkladu leží ",[1115,4012,4014],{"className":4013},[1144],[1146,4015,4016],{"xmlns":1148},[1150,4017,4018,4026],{},[1153,4019,4020],{},[1182,4021,4022,4024],{},[1159,4023,1186],{},[1163,4025,1189],{},[1167,4027,1192],{"encoding":1169}," hluboko pod kritickou hodnotou,\nu druhého uvnitř kritického oboru ",[1115,4030,4032],{"className":4031},[1144],[1146,4033,4034],{"xmlns":1148},[1150,4035,4036,4040],{},[1153,4037,4038],{},[1159,4039,1205],{},[1167,4041,1205],{"encoding":1169},[1110,4043,4044],{},[4002,4045],{"alt":4046,"className":4047,"src":4048},"mask-kt-chi2-kriticky-obor",[1321,4006],"\u002Fwiki-assets\u002Fmask-kt-chi2-kriticky-obor.png",[1310,4050,1253],{"id":4051},"cramérův-koeficient-kontingence",[1110,4053,4054,4055,1567],{},"Test nezávislosti pouze rozhodne, zda jsou znaky závislé, nebo ne. Sílu závislosti měří ",[1131,4056,4057],{},"Cramérův koeficient\nkontingence",[1115,4059,4061],{"className":4060},[1144],[1146,4062,4063],{"xmlns":1148,"display":1573},[1150,4064,4065,4121],{},[1153,4066,4067,4069,4071,4097,4099,4101,4103,4105,4108,4111,4113,4115,4117,4119],{},[1159,4068,1266],{},[1289,4070,1591],{},[4072,4073,4074],"msqrt",{},[2355,4075,4076,4082],{},[1182,4077,4078,4080],{},[1159,4079,1186],{},[1163,4081,1189],{},[1153,4083,4084,4086,4088,4091,4093,4095],{},[1159,4085,1287],{},[1289,4087,1484],{"stretchy":1483},[1159,4089,4090],{},"m",[1289,4092,2681],{},[1163,4094,1402],{},[1289,4096,1495],{"stretchy":1483},[1289,4098,1405],{"separator":1121},[1621,4100],{"width":1623},[1159,4102,4090],{},[1289,4104,1591],{},[1159,4106,4107],{},"min",[1289,4109,4110],{},"⁡",[1289,4112,1484],{"stretchy":1483},[1159,4114,71],{},[1289,4116,1405],{"separator":1121},[1159,4118,1463],{},[1289,4120,1495],{"stretchy":1483},[1167,4122,4123],{"encoding":1169},"V = \\sqrt{\\frac{\\chi^2}{n(m-1)}}, \\qquad m = \\min(r, s)",[1110,4125,4126,4127,4144,4145,4163,4164,4182],{},"kde ",[1115,4128,4130],{"className":4129},[1144],[1146,4131,4132],{"xmlns":1148},[1150,4133,4134,4142],{},[1153,4135,4136],{},[1182,4137,4138,4140],{},[1159,4139,1186],{},[1163,4141,1189],{},[1167,4143,1192],{"encoding":1169}," je hodnota testového kritéria z testu nezávislosti. ",[1115,4146,4148],{"className":4147},[1144],[1146,4149,4150],{"xmlns":1148},[1150,4151,4152,4160],{},[1153,4153,4154,4156,4158],{},[1159,4155,1266],{},[1289,4157,1591],{},[1163,4159,1165],{},[1167,4161,4162],{"encoding":1169},"V = 0"," odpovídá úplné nezávislosti znaků,\n",[1115,4165,4167],{"className":4166},[1144],[1146,4168,4169],{"xmlns":1148},[1150,4170,4171,4179],{},[1153,4172,4173,4175,4177],{},[1159,4174,1266],{},[1289,4176,1591],{},[1163,4178,1402],{},[1167,4180,4181],{"encoding":1169},"V = 1"," jejich úplné závislosti.",[3311,4184,4186],{"className":3313,"code":4185,"language":71,"meta":3315,"style":3315},"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",[3087,4187,4188,4263,4326,4331],{"__ignoreMap":3315},[1115,4189,4190,4193,4195,4198,4200,4203,4205,4207,4209,4211,4213,4215,4218,4221,4224,4227,4230,4232,4234,4236,4239,4241,4243,4245,4248,4250,4252,4255,4258,4261],{"class":3320,"line":10},[1115,4191,4192],{"class":3323},"V1",[1115,4194,3328],{"class":3327},[1115,4196,4197],{"class":3331}," sqrt",[1115,4199,1484],{"class":3335},[1115,4201,4202],{"class":3331},"as.numeric",[1115,4204,1484],{"class":3335},[1115,4206,3513],{"class":3331},[1115,4208,1484],{"class":3335},[1115,4210,3324],{"class":3323},[1115,4212,1495],{"class":3335},[1115,4214,3533],{"class":3327},[1115,4216,4217],{"class":3323},"statistic",[1115,4219,4220],{"class":3335},") ",[1115,4222,4223],{"class":3327},"\u002F",[1115,4225,4226],{"class":3335}," (",[1115,4228,4229],{"class":3331},"sum",[1115,4231,1484],{"class":3335},[1115,4233,3324],{"class":3323},[1115,4235,4220],{"class":3335},[1115,4237,4238],{"class":3327},"*",[1115,4240,4226],{"class":3335},[1115,4242,4107],{"class":3331},[1115,4244,1484],{"class":3335},[1115,4246,4247],{"class":3331},"dim",[1115,4249,1484],{"class":3335},[1115,4251,3324],{"class":3323},[1115,4253,4254],{"class":3335},")) ",[1115,4256,4257],{"class":3327},"-",[1115,4259,4260],{"class":3343}," 1",[1115,4262,3507],{"class":3335},[1115,4264,4265,4268,4270,4272,4274,4276,4278,4280,4282,4284,4286,4288,4290,4292,4294,4296,4298,4300,4302,4304,4306,4308,4310,4312,4314,4316,4318,4320,4322,4324],{"class":3320,"line":27},[1115,4266,4267],{"class":3323},"V2",[1115,4269,3328],{"class":3327},[1115,4271,4197],{"class":3331},[1115,4273,1484],{"class":3335},[1115,4275,4202],{"class":3331},[1115,4277,1484],{"class":3335},[1115,4279,3513],{"class":3331},[1115,4281,1484],{"class":3335},[1115,4283,3747],{"class":3323},[1115,4285,1495],{"class":3335},[1115,4287,3533],{"class":3327},[1115,4289,4217],{"class":3323},[1115,4291,4220],{"class":3335},[1115,4293,4223],{"class":3327},[1115,4295,4226],{"class":3335},[1115,4297,4229],{"class":3331},[1115,4299,1484],{"class":3335},[1115,4301,3747],{"class":3323},[1115,4303,4220],{"class":3335},[1115,4305,4238],{"class":3327},[1115,4307,4226],{"class":3335},[1115,4309,4107],{"class":3331},[1115,4311,1484],{"class":3335},[1115,4313,4247],{"class":3331},[1115,4315,1484],{"class":3335},[1115,4317,3747],{"class":3323},[1115,4319,4254],{"class":3335},[1115,4321,4257],{"class":3327},[1115,4323,4260],{"class":3343},[1115,4325,3507],{"class":3335},[1115,4327,4328],{"class":3320,"line":148},[1115,4329,4330],{"class":3323},"V1\n",[1115,4332,4333],{"class":3320,"line":111},[1115,4334,4335],{"class":3323},"V2\n",[3311,4337,4340],{"className":4338,"code":4339,"language":3542,"meta":3315},[3540],"[1] 0.08441958\n[1] 0.1762822\n",[3087,4341,4339],{"__ignoreMap":3315},[1110,4343,4344],{},[4002,4345],{"alt":4346,"className":4347,"src":4348},"mask-kt-cramerovo-v",[1321,4006],"\u002Fwiki-assets\u002Fmask-kt-cramerovo-v.png",[1110,4350,4351,4352,4371,4372,4389,4390,3607,4409,4426],{},"U nákupu potravin je ",[1115,4353,4355],{"className":4354},[1144],[1146,4356,4357],{"xmlns":1148},[1150,4358,4359,4368],{},[1153,4360,4361,4363,4365],{},[1159,4362,1266],{},[1289,4364,1591],{},[1163,4366,4367],{},"0,084",[1167,4369,4370],{"encoding":1169},"V = 0{,}084"," zanedbatelné — ostatně ",[1115,4373,4375],{"className":4374},[1144],[1146,4376,4377],{"xmlns":1148},[1150,4378,4379,4387],{},[1153,4380,4381],{},[1156,4382,4383,4385],{},[1159,4384,1161],{},[1163,4386,1165],{},[1167,4388,1170],{"encoding":1169}," jsme ani nezamítli. U zveřejňování údajů je ",[1115,4391,4393],{"className":4392},[1144],[1146,4394,4395],{"xmlns":1148},[1150,4396,4397,4406],{},[1153,4398,4399,4401,4403],{},[1159,4400,1266],{},[1289,4402,1591],{},[1163,4404,4405],{},"0,176",[1167,4407,4408],{"encoding":1169},"V = 0{,}176",[1115,4410,4412],{"className":4411},[1144],[1146,4413,4414],{"xmlns":1148},[1150,4415,4416,4424],{},[1153,4417,4418],{},[1156,4419,4420,4422],{},[1159,4421,1161],{},[1163,4423,1165],{},[1167,4425,1170],{"encoding":1169},"\njsme zamítli, ale samotná závislost je stále slabá.",[1310,4428,1274],{"id":4429},"čtyřpolní-tabulka",[1110,4431,4432,4434,4435,4448,4449,4462,4463,4485],{},[1131,4433,1274],{}," je speciální případ kontingenční tabulky, kdy oba znaky ",[1115,4436,4438],{"className":4437},[1144],[1146,4439,4440],{"xmlns":1148},[1150,4441,4442,4446],{},[1153,4443,4444],{},[1159,4445,1383],{},[1167,4447,1383],{"encoding":1169}," i ",[1115,4450,4452],{"className":4451},[1144],[1146,4453,4454],{"xmlns":1148},[1150,4455,4456,4460],{},[1153,4457,4458],{},[1159,4459,1432],{},[1167,4461,1432],{"encoding":1169}," mají jen dvě varianty\n(",[1115,4464,4466],{"className":4465},[1144],[1146,4467,4468],{"xmlns":1148},[1150,4469,4470,4482],{},[1153,4471,4472,4474,4476,4478,4480],{},[1159,4473,71],{},[1289,4475,1591],{},[1159,4477,1463],{},[1289,4479,1591],{},[1163,4481,1189],{},[1167,4483,4484],{"encoding":1169},"r = s = 2","):",[1710,4487,4488,4572],{},[1713,4489,4490],{},[1716,4491,4492,4511,4530,4549],{},[1719,4493,4494],{},[1115,4495,4497],{"className":4496},[1144],[1146,4498,4499],{"xmlns":1148},[1150,4500,4501,4509],{},[1153,4502,4503,4505,4507],{},[1159,4504,1383],{},[1159,4506,1735],{"mathvariant":1734},[1159,4508,1432],{},[1167,4510,1740],{"encoding":1169},[1719,4512,4513],{},[1115,4514,4516],{"className":4515},[1144],[1146,4517,4518],{"xmlns":1148},[1150,4519,4520,4528],{},[1153,4521,4522],{},[1156,4523,4524,4526],{},[1159,4525,1432],{},[1163,4527,1402],{},[1167,4529,1760],{"encoding":1169},[1719,4531,4532],{},[1115,4533,4535],{"className":4534},[1144],[1146,4536,4537],{"xmlns":1148},[1150,4538,4539,4547],{},[1153,4540,4541],{},[1156,4542,4543,4545],{},[1159,4544,1432],{},[1163,4546,1189],{},[1167,4548,1780],{"encoding":1169},[1719,4550,4551],{},[1115,4552,4554],{"className":4553},[1144],[1146,4555,4556],{"xmlns":1148},[1150,4557,4558,4570],{},[1153,4559,4560],{},[1156,4561,4562,4564],{},[1159,4563,1287],{},[1153,4565,4566,4568],{},[1159,4567,1487],{},[1289,4569,1588],{},[1167,4571,1826],{"encoding":1169},[1828,4573,4574,4656,4738],{},[1716,4575,4576,4595,4614,4633],{},[1833,4577,4578],{},[1115,4579,4581],{"className":4580},[1144],[1146,4582,4583],{"xmlns":1148},[1150,4584,4585,4593],{},[1153,4586,4587],{},[1156,4588,4589,4591],{},[1159,4590,1383],{},[1163,4592,1402],{},[1167,4594,1852],{"encoding":1169},[1833,4596,4597],{},[1115,4598,4600],{"className":4599},[1144],[1146,4601,4602],{"xmlns":1148},[1150,4603,4604,4612],{},[1153,4605,4606],{},[1156,4607,4608,4610],{},[1159,4609,1287],{},[1163,4611,1870],{},[1167,4613,1873],{"encoding":1169},[1833,4615,4616],{},[1115,4617,4619],{"className":4618},[1144],[1146,4620,4621],{"xmlns":1148},[1150,4622,4623,4631],{},[1153,4624,4625],{},[1156,4626,4627,4629],{},[1159,4628,1287],{},[1163,4630,1891],{},[1167,4632,1894],{"encoding":1169},[1833,4634,4635],{},[1115,4636,4638],{"className":4637},[1144],[1146,4639,4640],{"xmlns":1148},[1150,4641,4642,4654],{},[1153,4643,4644],{},[1156,4645,4646,4648],{},[1159,4647,1287],{},[1153,4649,4650,4652],{},[1163,4651,1402],{},[1289,4653,1588],{},[1167,4655,1944],{"encoding":1169},[1716,4657,4658,4677,4696,4715],{},[1833,4659,4660],{},[1115,4661,4663],{"className":4662},[1144],[1146,4664,4665],{"xmlns":1148},[1150,4666,4667,4675],{},[1153,4668,4669],{},[1156,4670,4671,4673],{},[1159,4672,1383],{},[1163,4674,1189],{},[1167,4676,1966],{"encoding":1169},[1833,4678,4679],{},[1115,4680,4682],{"className":4681},[1144],[1146,4683,4684],{"xmlns":1148},[1150,4685,4686,4694],{},[1153,4687,4688],{},[1156,4689,4690,4692],{},[1159,4691,1287],{},[1163,4693,1984],{},[1167,4695,1987],{"encoding":1169},[1833,4697,4698],{},[1115,4699,4701],{"className":4700},[1144],[1146,4702,4703],{"xmlns":1148},[1150,4704,4705,4713],{},[1153,4706,4707],{},[1156,4708,4709,4711],{},[1159,4710,1287],{},[1163,4712,2005],{},[1167,4714,2008],{"encoding":1169},[1833,4716,4717],{},[1115,4718,4720],{"className":4719},[1144],[1146,4721,4722],{"xmlns":1148},[1150,4723,4724,4736],{},[1153,4725,4726],{},[1156,4727,4728,4730],{},[1159,4729,1287],{},[1153,4731,4732,4734],{},[1163,4733,1189],{},[1289,4735,1588],{},[1167,4737,2058],{"encoding":1169},[1716,4739,4740,4763,4786,4809],{},[1833,4741,4742],{},[1115,4743,4745],{"className":4744},[1144],[1146,4746,4747],{"xmlns":1148},[1150,4748,4749,4761],{},[1153,4750,4751],{},[1156,4752,4753,4755],{},[1159,4754,1287],{},[1153,4756,4757,4759],{},[1289,4758,1588],{},[1159,4760,1492],{},[1167,4762,2220],{"encoding":1169},[1833,4764,4765],{},[1115,4766,4768],{"className":4767},[1144],[1146,4769,4770],{"xmlns":1148},[1150,4771,4772,4784],{},[1153,4773,4774],{},[1156,4775,4776,4778],{},[1159,4777,1287],{},[1153,4779,4780,4782],{},[1289,4781,1588],{},[1163,4783,1402],{},[1167,4785,2244],{"encoding":1169},[1833,4787,4788],{},[1115,4789,4791],{"className":4790},[1144],[1146,4792,4793],{"xmlns":1148},[1150,4794,4795,4807],{},[1153,4796,4797],{},[1156,4798,4799,4801],{},[1159,4800,1287],{},[1153,4802,4803,4805],{},[1289,4804,1588],{},[1163,4806,1189],{},[1167,4808,2268],{"encoding":1169},[1833,4810,4811],{},[1115,4812,4814],{"className":4813},[1144],[1146,4815,4816],{"xmlns":1148},[1150,4817,4818,4822],{},[1153,4819,4820],{},[1159,4821,1287],{},[1167,4823,1287],{"encoding":1169},[1110,4825,1300,4826,4844],{},[1115,4827,4829],{"className":4828},[1144],[1146,4830,4831],{"xmlns":1148},[1150,4832,4833,4841],{},[1153,4834,4835,4837,4839],{},[1159,4836,1287],{},[1289,4838,1291],{},[1163,4840,1294],{},[1167,4842,4843],{"encoding":1169},"n > 40"," se místo obecného vzorce používá zjednodušená varianta testového kritéria:",[1115,4846,4848],{"className":4847},[1144],[1146,4849,4850],{"xmlns":1148,"display":1573},[1150,4851,4852,4946],{},[1153,4853,4854,4860,4862,4864,4866],{},[1182,4855,4856,4858],{},[1159,4857,1186],{},[1163,4859,1189],{},[1289,4861,1591],{},[1159,4863,1287],{},[2525,4865,2527],{},[2355,4867,4868,4904],{},[1153,4869,4870,4872,4878,4884,4886,4892,4898],{},[1289,4871,1484],{"stretchy":1483},[1156,4873,4874,4876],{},[1159,4875,1287],{},[1163,4877,1870],{},[1156,4879,4880,4882],{},[1159,4881,1287],{},[1163,4883,2005],{},[1289,4885,2681],{},[1156,4887,4888,4890],{},[1159,4889,1287],{},[1163,4891,1891],{},[1156,4893,4894,4896],{},[1159,4895,1287],{},[1163,4897,1984],{},[1182,4899,4900,4902],{},[1289,4901,1495],{"stretchy":1483},[1163,4903,1189],{},[1153,4905,4906,4916,4926,4936],{},[1156,4907,4908,4910],{},[1159,4909,1287],{},[1153,4911,4912,4914],{},[1163,4913,1402],{},[1289,4915,1588],{},[1156,4917,4918,4920],{},[1159,4919,1287],{},[1153,4921,4922,4924],{},[1163,4923,1189],{},[1289,4925,1588],{},[1156,4927,4928,4930],{},[1159,4929,1287],{},[1153,4931,4932,4934],{},[1289,4933,1588],{},[1163,4935,1402],{},[1156,4937,4938,4940],{},[1159,4939,1287],{},[1153,4941,4942,4944],{},[1289,4943,1588],{},[1163,4945,1189],{},[1167,4947,4948],{"encoding":1169},"\\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}}",[1110,4950,4951,4952,5012,5013,5049,5050,5053,5054,5057],{},"s kritickým oborem ",[1115,4953,4955],{"className":4954},[1144],[1146,4956,4957],{"xmlns":1148},[1150,4958,4959,5009],{},[1153,4960,4961,4967,4969,4971,4977,4979,4985,4987,5001,5003,5005,5007],{},[1156,4962,4963,4965],{},[1159,4964,1205],{},[1159,4966,2982],{},[1289,4968,1591],{},[1289,4970,2951],{"stretchy":1483},[1182,4972,4973,4975],{},[1159,4974,1186],{},[1163,4976,1189],{},[1289,4978,1567],{},[1182,4980,4981,4983],{},[1159,4982,1186],{},[1163,4984,1189],{},[1289,4986,2968],{},[2970,4988,4989,4991,4999],{},[1159,4990,1186],{},[1153,4992,4993,4995,4997],{},[1163,4994,1402],{},[1289,4996,2681],{},[1159,4998,2982],{},[1163,5000,1189],{},[1289,5002,1484],{"stretchy":1483},[1163,5004,1402],{},[1289,5006,1495],{"stretchy":1483},[1289,5008,3011],{"stretchy":1483},[1167,5010,5011],{"encoding":1169},"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 ",[1115,5014,5016],{"className":5015},[1144],[1146,5017,5018],{"xmlns":1148},[1150,5019,5020,5046],{},[1153,5021,5022,5024,5026,5028,5030,5032,5034,5036,5038,5040,5042,5044],{},[1289,5023,1484],{"stretchy":1483},[1159,5025,71],{},[1289,5027,2681],{},[1163,5029,1402],{},[1289,5031,1495],{"stretchy":1483},[1289,5033,1484],{"stretchy":1483},[1159,5035,1463],{},[1289,5037,2681],{},[1163,5039,1402],{},[1289,5041,1495],{"stretchy":1483},[1289,5043,1591],{},[1163,5045,1402],{},[1167,5047,5048],{"encoding":1169},"(r-1)(s-1) = 1"," stupeň volnosti. V R dává tuto hodnotu ",[3087,5051,5052],{},"chisq.test(tab, correct = FALSE)",". Bez ",[3087,5055,5056],{},"correct = FALSE"," R u tabulky 2 × 2 použije Yatesovu korekci na kontinuitu a testové kritérium vyjde menší.",[1310,5059,1307],{"id":5060},"mcnemarův-test",[1110,5062,5063,5064,5067,5068,5070,5071,5074,5075,5078,5079,5081],{},"Čtyřpolní tabulka z předchozí sekce porovnává dva ",[1131,5065,5066],{},"různé"," znaky na stejném souboru. ",[1131,5069,1307],{}," řeší\njinou situaci: na prvcích základního souboru se měří ",[1131,5072,5073],{},"jeden"," alternativní znak, a to ",[1131,5076,5077],{},"dvakrát"," — před a po\nnějakém zásahu. Cílem je zjistit, zda zásah změnil pravděpodobnostní rozdělení variant tohoto znaku. Jde tedy o\n",[1131,5080,1303],{}," (stejné prvky měřené opakovaně), ne o dva nezávisle naměřené znaky.",[1110,5083,5084],{},"Kontingenční tabulka před\u002Fpo má tvar:",[1710,5086,5087,5122],{},[1713,5088,5089],{},[1716,5090,5091,5094,5097,5099],{},[1719,5092,5093],{},"před \\ po",[1719,5095,5096],{},"+",[1719,5098,2681],{},[1719,5100,5101],{},[1115,5102,5104],{"className":5103},[1144],[1146,5105,5106],{"xmlns":1148},[1150,5107,5108,5120],{},[1153,5109,5110],{},[1156,5111,5112,5114],{},[1159,5113,1287],{},[1153,5115,5116,5118],{},[1159,5117,1487],{},[1289,5119,1588],{},[1167,5121,1826],{"encoding":1169},[1828,5123,5124,5189,5254],{},[1716,5125,5126,5128,5147,5166],{},[1833,5127,5096],{},[1833,5129,5130],{},[1115,5131,5133],{"className":5132},[1144],[1146,5134,5135],{"xmlns":1148},[1150,5136,5137,5145],{},[1153,5138,5139],{},[1156,5140,5141,5143],{},[1159,5142,1287],{},[1163,5144,1870],{},[1167,5146,1873],{"encoding":1169},[1833,5148,5149],{},[1115,5150,5152],{"className":5151},[1144],[1146,5153,5154],{"xmlns":1148},[1150,5155,5156,5164],{},[1153,5157,5158],{},[1156,5159,5160,5162],{},[1159,5161,1287],{},[1163,5163,1891],{},[1167,5165,1894],{"encoding":1169},[1833,5167,5168],{},[1115,5169,5171],{"className":5170},[1144],[1146,5172,5173],{"xmlns":1148},[1150,5174,5175,5187],{},[1153,5176,5177],{},[1156,5178,5179,5181],{},[1159,5180,1287],{},[1153,5182,5183,5185],{},[1163,5184,1402],{},[1289,5186,1588],{},[1167,5188,1944],{"encoding":1169},[1716,5190,5191,5193,5212,5231],{},[1833,5192,2681],{},[1833,5194,5195],{},[1115,5196,5198],{"className":5197},[1144],[1146,5199,5200],{"xmlns":1148},[1150,5201,5202,5210],{},[1153,5203,5204],{},[1156,5205,5206,5208],{},[1159,5207,1287],{},[1163,5209,1984],{},[1167,5211,1987],{"encoding":1169},[1833,5213,5214],{},[1115,5215,5217],{"className":5216},[1144],[1146,5218,5219],{"xmlns":1148},[1150,5220,5221,5229],{},[1153,5222,5223],{},[1156,5224,5225,5227],{},[1159,5226,1287],{},[1163,5228,2005],{},[1167,5230,2008],{"encoding":1169},[1833,5232,5233],{},[1115,5234,5236],{"className":5235},[1144],[1146,5237,5238],{"xmlns":1148},[1150,5239,5240,5252],{},[1153,5241,5242],{},[1156,5243,5244,5246],{},[1159,5245,1287],{},[1153,5247,5248,5250],{},[1163,5249,1189],{},[1289,5251,1588],{},[1167,5253,2058],{"encoding":1169},[1716,5255,5256,5279,5302,5325],{},[1833,5257,5258],{},[1115,5259,5261],{"className":5260},[1144],[1146,5262,5263],{"xmlns":1148},[1150,5264,5265,5277],{},[1153,5266,5267],{},[1156,5268,5269,5271],{},[1159,5270,1287],{},[1153,5272,5273,5275],{},[1289,5274,1588],{},[1159,5276,1492],{},[1167,5278,2220],{"encoding":1169},[1833,5280,5281],{},[1115,5282,5284],{"className":5283},[1144],[1146,5285,5286],{"xmlns":1148},[1150,5287,5288,5300],{},[1153,5289,5290],{},[1156,5291,5292,5294],{},[1159,5293,1287],{},[1153,5295,5296,5298],{},[1289,5297,1588],{},[1163,5299,1402],{},[1167,5301,2244],{"encoding":1169},[1833,5303,5304],{},[1115,5305,5307],{"className":5306},[1144],[1146,5308,5309],{"xmlns":1148},[1150,5310,5311,5323],{},[1153,5312,5313],{},[1156,5314,5315,5317],{},[1159,5316,1287],{},[1153,5318,5319,5321],{},[1289,5320,1588],{},[1163,5322,1189],{},[1167,5324,2268],{"encoding":1169},[1833,5326,5327],{},[1115,5328,5330],{"className":5329},[1144],[1146,5331,5332],{"xmlns":1148},[1150,5333,5334,5338],{},[1153,5335,5336],{},[1159,5337,1287],{},[1167,5339,1287],{"encoding":1169},[1110,5341,5342,5343,5360,5361,5378,5379,5382,5383,5360,5400,5417,5418,5421],{},"Pole ",[1115,5344,5346],{"className":5345},[1144],[1146,5347,5348],{"xmlns":1148},[1150,5349,5350,5358],{},[1153,5351,5352],{},[1156,5353,5354,5356],{},[1159,5355,1287],{},[1163,5357,1870],{},[1167,5359,1873],{"encoding":1169}," a ",[1115,5362,5364],{"className":5363},[1144],[1146,5365,5366],{"xmlns":1148},[1150,5367,5368,5376],{},[1153,5369,5370],{},[1156,5371,5372,5374],{},[1159,5373,1287],{},[1163,5375,2005],{},[1167,5377,2008],{"encoding":1169}," jsou ",[1131,5380,5381],{},"shodná"," (prvek zůstal ve stejné variantě), pole ",[1115,5384,5386],{"className":5385},[1144],[1146,5387,5388],{"xmlns":1148},[1150,5389,5390,5398],{},[1153,5391,5392],{},[1156,5393,5394,5396],{},[1159,5395,1287],{},[1163,5397,1891],{},[1167,5399,1894],{"encoding":1169},[1115,5401,5403],{"className":5402},[1144],[1146,5404,5405],{"xmlns":1148},[1150,5406,5407,5415],{},[1153,5408,5409],{},[1156,5410,5411,5413],{},[1159,5412,1287],{},[1163,5414,1984],{},[1167,5416,1987],{"encoding":1169}," jsou\n",[1131,5419,5420],{},"diskordantní"," (prvek mezi měřeními variantu změnil) — jen ta rozhodují o výsledku testu:",[1110,5423,5424],{},[4002,5425],{"alt":5426,"className":5427,"src":5428},"mask-kt-mcnemar-tabulka",[1321,4006],"\u002Fwiki-assets\u002Fmask-kt-mcnemar-tabulka.png",[1110,5430,5431],{},[1131,5432,2479],{},[2481,5434,5435,5472,5553,5611],{},[1127,5436,5437,5471],{},[1115,5438,5440],{"className":5439},[1144],[1146,5441,5442],{"xmlns":1148},[1150,5443,5444,5468],{},[1153,5445,5446,5452,5454,5460,5462],{},[1156,5447,5448,5450],{},[1159,5449,1161],{},[1163,5451,1165],{},[1289,5453,1567],{},[1156,5455,5456,5458],{},[1159,5457,1110],{},[1163,5459,1891],{},[1289,5461,1591],{},[1156,5463,5464,5466],{},[1159,5465,1110],{},[1163,5467,1984],{},[1167,5469,5470],{"encoding":1169},"H_0: p_{12} = p_{21}"," — pravděpodobnost přechodu z varianty (+) do (−) je stejná jako pravděpodobnost\npřechodu z (−) do (+); zásah tedy nemá na rozdělení variant žádný vliv.",[1127,5473,2617,5474,5536,5538,5539,5552],{},[1115,5475,5477],{"className":5476},[1144],[1146,5478,5479],{"xmlns":1148,"display":1573},[1150,5480,5481,5533],{},[1153,5482,5483,5489,5491],{},[1182,5484,5485,5487],{},[1159,5486,1186],{},[1163,5488,1189],{},[1289,5490,1591],{},[2355,5492,5493,5517],{},[1153,5494,5495,5497,5503,5505,5511],{},[1289,5496,1484],{"stretchy":1483},[1156,5498,5499,5501],{},[1159,5500,1287],{},[1163,5502,1891],{},[1289,5504,2681],{},[1156,5506,5507,5509],{},[1159,5508,1287],{},[1163,5510,1984],{},[1182,5512,5513,5515],{},[1289,5514,1495],{"stretchy":1483},[1163,5516,1189],{},[1153,5518,5519,5525,5527],{},[1156,5520,5521,5523],{},[1159,5522,1287],{},[1163,5524,1891],{},[1289,5526,5096],{},[1156,5528,5529,5531],{},[1159,5530,1287],{},[1163,5532,1984],{},[1167,5534,5535],{"encoding":1169},"\\chi^2 = \\frac{(n_{12} - n_{21})^2}{n_{12} + n_{21}}",[2776,5537],{},"má asymptoticky Pearsonovo rozdělení o ",[1115,5540,5542],{"className":5541},[1144],[1146,5543,5544],{"xmlns":1148},[1150,5545,5546,5550],{},[1153,5547,5548],{},[1163,5549,1402],{},[1167,5551,1402],{"encoding":1169}," stupni volnosti.",[1127,5554,2935,5555,1269],{},[1115,5556,5558],{"className":5557},[1144],[1146,5559,5560],{"xmlns":1148},[1150,5561,5562,5608],{},[1153,5563,5564,5566,5568,5570,5576,5578,5584,5586,5600,5602,5604,5606],{},[1159,5565,1205],{},[1289,5567,1591],{},[1289,5569,2951],{"stretchy":1483},[1182,5571,5572,5574],{},[1159,5573,1186],{},[1163,5575,1189],{},[1289,5577,1567],{},[1182,5579,5580,5582],{},[1159,5581,1186],{},[1163,5583,1189],{},[1289,5585,2968],{},[2970,5587,5588,5590,5598],{},[1159,5589,1186],{},[1153,5591,5592,5594,5596],{},[1163,5593,1402],{},[1289,5595,2681],{},[1159,5597,2982],{},[1163,5599,1189],{},[1289,5601,1484],{"stretchy":1483},[1163,5603,1402],{},[1289,5605,1495],{"stretchy":1483},[1289,5607,3011],{"stretchy":1483},[1167,5609,5610],{"encoding":1169},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}(1)\\}",[1127,5612,3017,5613,5626,5627,5644,5645,5662],{},[1115,5614,5616],{"className":5615},[1144],[1146,5617,5618],{"xmlns":1148},[1150,5619,5620,5624],{},[1153,5621,5622],{},[1159,5623,1205],{},[1167,5625,1205],{"encoding":1169},", zamítáme ",[1115,5628,5630],{"className":5629},[1144],[1146,5631,5632],{"xmlns":1148},[1150,5633,5634,5642],{},[1153,5635,5636],{},[1156,5637,5638,5640],{},[1159,5639,1161],{},[1163,5641,1165],{},[1167,5643,1170],{"encoding":1169}," a přijímáme ",[1115,5646,5648],{"className":5647},[1144],[1146,5649,5650],{"xmlns":1148},[1150,5651,5652,5660],{},[1153,5653,5654],{},[1156,5655,5656,5658],{},[1159,5657,1161],{},[1163,5659,1402],{},[1167,5661,2613],{"encoding":1169},": zásah rozdělení variant změnil.",[1110,5664,5665,5666,5669,5670,5673,5674,5676],{},"V R počítá tento test funkce ",[3087,5667,5668],{},"mcnemar.test()",". Vzorec výše ",[1131,5671,5672],{},"neobsahuje korekci na kontinuitu"," — aby R vrátilo\npřesně tuto hodnotu, musí se volat s ",[3087,5675,5056],{}," (viz Časté chyby níže).",[1103,5678,5680,5687,5690,5693,5790],{"className":5679,"dataCallout":3094},[1106,3093],[1110,5681,5683,5686],{"className":5682},[1113],[1115,5684],{"className":5685,"ariaHidden":1121},[1118,3101,1120],"Příklad: informační kampaň a zveřejňování na Facebooku",[1110,5688,5689],{},"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.",[1110,5691,5692],{},"Základní soubor: všichni studenti; výběrový soubor: vybraní studenti; měřený znak: zveřejňování (ano \u002F ne).",[1710,5694,5695,5730],{},[1713,5696,5697],{},[1716,5698,5699,5701,5704,5707],{},[1719,5700,5093],{},[1719,5702,5703],{},"nezveřejňuje",[1719,5705,5706],{},"zveřejňuje",[1719,5708,5709],{},[1115,5710,5712],{"className":5711},[1144],[1146,5713,5714],{"xmlns":1148},[1150,5715,5716,5728],{},[1153,5717,5718],{},[1156,5719,5720,5722],{},[1159,5721,1287],{},[1153,5723,5724,5726],{},[1159,5725,1487],{},[1289,5727,1588],{},[1167,5729,1826],{"encoding":1169},[1828,5731,5732,5744,5756],{},[1716,5733,5734,5736,5738,5741],{},[1833,5735,5703],{},[1833,5737,3217],{},[1833,5739,5740],{},"68",[1833,5742,5743],{},"92",[1716,5745,5746,5748,5750,5753],{},[1833,5747,5706],{},[1833,5749,3680],{},[1833,5751,5752],{},"50",[1833,5754,5755],{},"78",[1716,5757,5758,5781,5784,5787],{},[1833,5759,5760],{},[1115,5761,5763],{"className":5762},[1144],[1146,5764,5765],{"xmlns":1148},[1150,5766,5767,5779],{},[1153,5768,5769],{},[1156,5770,5771,5773],{},[1159,5772,1287],{},[1153,5774,5775,5777],{},[1289,5776,1588],{},[1159,5778,1492],{},[1167,5780,2220],{"encoding":1169},[1833,5782,5783],{},"52",[1833,5785,5786],{},"118",[1833,5788,5789],{},"170",[1110,5791,5792,5825],{},[1115,5793,5795],{"className":5794},[1144],[1146,5796,5797],{"xmlns":1148},[1150,5798,5799,5823],{},[1153,5800,5801,5807,5809,5815,5817],{},[1156,5802,5803,5805],{},[1159,5804,1161],{},[1163,5806,1165],{},[1289,5808,1567],{},[1156,5810,5811,5813],{},[1159,5812,1110],{},[1163,5814,1891],{},[1289,5816,1591],{},[1156,5818,5819,5821],{},[1159,5820,1110],{},[1163,5822,1984],{},[1167,5824,5470],{"encoding":1169}," — informační kampaň nemá na chování vliv.",[3311,5827,5829],{"className":3313,"code":5828,"language":71,"meta":3315,"style":3315},"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",[3087,5830,5831,5855,5869,5887,5897,5920,5939],{"__ignoreMap":3315},[1115,5832,5833,5836,5838,5840,5842,5844,5846,5848,5850,5853],{"class":3320,"line":10},[1115,5834,5835],{"class":3323},"tab3",[1115,5837,3328],{"class":3327},[1115,5839,3332],{"class":3331},[1115,5841,1484],{"class":3335},[1115,5843,3338],{"class":3331},[1115,5845,1484],{"class":3335},[1115,5847,3217],{"class":3343},[1115,5849,1405],{"class":3327},[1115,5851,5852],{"class":3343}," 68",[1115,5854,3356],{"class":3327},[1115,5856,5857,5860,5862,5865,5867],{"class":3320,"line":27},[1115,5858,5859],{"class":3343},"                 28",[1115,5861,1405],{"class":3327},[1115,5863,5864],{"class":3343}," 50",[1115,5866,1495],{"class":3335},[1115,5868,3356],{"class":3327},[1115,5870,5871,5873,5875,5877,5879,5881,5883,5885],{"class":3320,"line":148},[1115,5872,3413],{"class":3323},[1115,5874,3416],{"class":3327},[1115,5876,3799],{"class":3343},[1115,5878,1405],{"class":3327},[1115,5880,3424],{"class":3323},[1115,5882,3416],{"class":3327},[1115,5884,3429],{"class":3343},[1115,5886,3356],{"class":3327},[1115,5888,5889,5891,5893,5895],{"class":3320,"line":111},[1115,5890,3436],{"class":3323},[1115,5892,3416],{"class":3327},[1115,5894,3441],{"class":3331},[1115,5896,3444],{"class":3335},[1115,5898,5899,5902,5904,5906,5908,5911,5913,5916,5918],{"class":3320,"line":96},[1115,5900,5901],{"class":3323},"                 pred",[1115,5903,3416],{"class":3327},[1115,5905,3454],{"class":3331},[1115,5907,1484],{"class":3335},[1115,5909,5910],{"class":3459},"\"nezverejnuje\"",[1115,5912,1405],{"class":3327},[1115,5914,5915],{"class":3459}," \"zverejnuje\"",[1115,5917,1495],{"class":3335},[1115,5919,3356],{"class":3327},[1115,5921,5922,5925,5927,5929,5931,5933,5935,5937],{"class":3320,"line":89},[1115,5923,5924],{"class":3323},"                 po",[1115,5926,3849],{"class":3327},[1115,5928,3454],{"class":3331},[1115,5930,1484],{"class":3335},[1115,5932,5910],{"class":3459},[1115,5934,1405],{"class":3327},[1115,5936,5915],{"class":3459},[1115,5938,3507],{"class":3335},[1115,5940,5941,5944,5946,5948,5950,5953,5955,5958],{"class":3320,"line":82},[1115,5942,5943],{"class":3331},"mcnemar.test",[1115,5945,1484],{"class":3335},[1115,5947,5835],{"class":3323},[1115,5949,1405],{"class":3327},[1115,5951,5952],{"class":3323}," correct",[1115,5954,3416],{"class":3327},[1115,5956,5957],{"class":3343}," FALSE",[1115,5959,3520],{"class":3335},[3311,5961,5964],{"className":5962,"code":5963,"language":3542,"meta":3315},[3540],"    McNemar's Chi-squared test\n\ndata:  tab3\nMcNemar's chi-squared = 16.667, df = 1, p-value = 4.456e-05\n",[3087,5965,5963],{"__ignoreMap":3315},[1110,5967,5968,5969,3607,5988,6005,6006,6023],{},"P-hodnota ",[1115,5970,5972],{"className":5971},[1144],[1146,5973,5974],{"xmlns":1148},[1150,5975,5976,5985],{},[1153,5977,5978,5981,5983],{},[1163,5979,5980],{},"0,00004456",[1289,5982,3951],{},[1163,5984,3603],{},[1167,5986,5987],{"encoding":1169},"0{,}00004456 \u003C 0{,}05",[1115,5989,5991],{"className":5990},[1144],[1146,5992,5993],{"xmlns":1148},[1150,5994,5995,6003],{},[1153,5996,5997],{},[1156,5998,5999,6001],{},[1159,6000,1161],{},[1163,6002,1165],{},[1167,6004,1170],{"encoding":1169}," zamítáme, přijímáme ",[1115,6007,6009],{"className":6008},[1144],[1146,6010,6011],{"xmlns":1148},[1150,6012,6013,6021],{},[1153,6014,6015],{},[1156,6016,6017,6019],{},[1159,6018,1161],{},[1163,6020,1402],{},[1167,6022,2613],{"encoding":1169}," — informační kampaň měla vliv na změnu\nchování studentů ve zveřejňování údajů na Facebooku.",[1310,6025,6027],{"id":6026},"časté-chyby","Časté chyby",[1103,6029,6033,6041],{"className":6030,"dataCallout":6032},[1106,6031],"callout-warning","warning",[1110,6034,6036,6040],{"className":6035},[1113],[1115,6037],{"className":6038,"ariaHidden":1121},[1118,6039,1120],"i-lucide:triangle-alert","Test nezávislosti na párovaných datech",[1110,6042,6043,6044,6046],{},"Tabulka před\u002Fpo vypadá jako obyčejná kontingenční tabulka, ale ",[3087,6045,3089],{}," 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.",[3311,6048,6050],{"className":3313,"code":6049,"language":71,"meta":3315,"style":3315},"chisq.test(tab3)\n",[3087,6051,6052],{"__ignoreMap":3315},[1115,6053,6054,6056,6058,6060],{"class":3320,"line":10},[1115,6055,3513],{"class":3331},[1115,6057,1484],{"class":3335},[1115,6059,5835],{"class":3323},[1115,6061,3520],{"class":3335},[3311,6063,6066],{"className":6064,"code":6065,"language":3542,"meta":3315},[3540],"    Pearson's Chi-squared test with Yates' continuity correction\n\ndata:  tab3\nX-squared = 1.4793, df = 1, p-value = 0.2239\n",[3087,6067,6065],{"__ignoreMap":3315},[1110,6069,5968,6070,6089,6090,6107,6108,6110,6111,1269],{},[1115,6071,6073],{"className":6072},[1144],[1146,6074,6075],{"xmlns":1148},[1150,6076,6077,6086],{},[1153,6078,6079,6082,6084],{},[1163,6080,6081],{},"0,224",[1289,6083,1291],{},[1163,6085,3603],{},[1167,6087,6088],{"encoding":1169},"0{,}224 > 0{,}05"," by vedla k nezamítnutí ",[1115,6091,6093],{"className":6092},[1144],[1146,6094,6095],{"xmlns":1148},[1150,6096,6097,6105],{},[1153,6098,6099],{},[1156,6100,6101,6103],{},[1159,6102,1161],{},[1163,6104,1165],{},[1167,6106,1170],{"encoding":1169}," — opačný závěr než správný McNemarův test. Na\npárovaná data (stejné prvky měřené dvakrát) vždy patří ",[3087,6109,5668],{},", nikdy ",[3087,6112,3089],{},[1103,6114,6116,6125],{"className":6115,"dataCallout":6032},[1106,6031],[1110,6117,6119,6122,6123],{"className":6118},[1113],[1115,6120],{"className":6121,"ariaHidden":1121},[1118,6039,1120],"Výchozí korekce na kontinuitu v ",[3087,6124,5668],{},[1110,6126,6127,6128,6131],{},"Bez argumentu ",[3087,6129,6130],{},"correct"," R ve výchozím nastavení použije Yatesovu korekci na kontinuitu, která dá jinou\np-hodnotu než nekorigovaný vzorec uvedený výše.",[3311,6133,6135],{"className":3313,"code":6134,"language":71,"meta":3315,"style":3315},"mcnemar.test(tab3)\n",[3087,6136,6137],{"__ignoreMap":3315},[1115,6138,6139,6141,6143,6145],{"class":3320,"line":10},[1115,6140,5943],{"class":3331},[1115,6142,1484],{"class":3335},[1115,6144,5835],{"class":3323},[1115,6146,3520],{"class":3335},[3311,6148,6151],{"className":6149,"code":6150,"language":3542,"meta":3315},[3540],"    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",[3087,6152,6150],{"__ignoreMap":3315},[1110,6154,6155,6156,6174,6175,6194,6195,6208,6209,1269],{},"Oproti nekorigované hodnotě ",[1115,6157,6159],{"className":6158},[1144],[1146,6160,6161],{"xmlns":1148},[1150,6162,6163,6171],{},[1153,6164,6165,6167,6169],{},[1159,6166,1110],{},[1289,6168,1591],{},[1163,6170,5980],{},[1167,6172,6173],{"encoding":1169},"p = 0{,}00004456"," vyjde ",[1115,6176,6178],{"className":6177},[1144],[1146,6179,6180],{"xmlns":1148},[1150,6181,6182,6191],{},[1153,6183,6184,6186,6188],{},[1159,6185,1110],{},[1289,6187,1591],{},[1163,6189,6190],{},"0,00006879",[1167,6192,6193],{"encoding":1169},"p = 0{,}00006879"," — v tomto příkladu obě vedou ke\nstejnému rozhodnutí, ale u hodnot blíž hranici ",[1115,6196,6198],{"className":6197},[1144],[1146,6199,6200],{"xmlns":1148},[1150,6201,6202,6206],{},[1153,6203,6204],{},[1159,6205,2982],{},[1167,6207,3045],{"encoding":1169}," by korekce mohla rozhodnutí změnit. Aby R reprodukovalo\nnekorigovaný vzorec, je třeba vždy volat ",[3087,6210,6211],{},"mcnemar.test(x, correct = FALSE)",[1310,6213,6215],{"id":6214},"související-stránky","Související stránky",[1124,6217,6218,6223,6229,6237,6245,6253,6261],{},[1127,6219,6220],{},[1318,6221,1324],{"className":6222,"dataFsResolvedFilePath":1322,"href":1323},[1321],[1127,6224,6225],{},[1318,6226,6228],{"className":6227,"dataFsResolvedFilePath":1329,"href":1330},[1321],"Testování statistických hypotéz",[1127,6230,6231],{},[1318,6232,6236],{"className":6233,"dataFsResolvedFilePath":6234,"href":6235},[1321],"topics\u002Fpopisna-statistika.md","\u002Fwiki\u002Fpopisna-statistika","Popisná statistika a datové soubory",[1127,6238,6239],{},[1318,6240,6244],{"className":6241,"dataFsResolvedFilePath":6242,"href":6243},[1321],"topics\u002Fnahodne-veliciny-a-rozdeleni.md","\u002Fwiki\u002Fnahodne-veliciny-a-rozdeleni","Náhodné veličiny a rozdělení pravděpodobnosti",[1127,6246,6247],{},[1318,6248,6252],{"className":6249,"dataFsResolvedFilePath":6250,"href":6251},[1321],"topics\u002Fregresni-a-korelacni-analyza.md","\u002Fwiki\u002Fregresni-a-korelacni-analyza","Regresní a korelační analýza",[1127,6254,6255],{},[1318,6256,6260],{"className":6257,"dataFsResolvedFilePath":6258,"href":6259},[1321],"topics\u002Fregulacni-diagramy-a-indexy-zpusobilosti.md","\u002Fwiki\u002Fregulacni-diagramy-a-indexy-zpusobilosti","Regulační diagramy a indexy způsobilosti",[1127,6262,6263],{},[1318,6264,6268],{"className":6265,"dataFsResolvedFilePath":6266,"href":6267},[1321],"outputs\u002Fmask-r-tahak.md","\u002Fwiki\u002Fmask-r-tahak","Tahák pro R",[1310,6270,6271],{"id":934},"Reference",[1110,6273,6274,6275,6279],{},"KROPÁČ, J. ",[6276,6277,6278],"em",{},"Statistika A",". 4. vyd. 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veličina je funkce, která výsledkům pokusu přiřazuje reálná čísla; rozlišujeme ",[1131,10990,10991],{},"diskrétní"," (izolované hodnoty s nenulovou pravděpodobností) a ",[1131,10994,10995],{},"spojité"," (hodnoty z intervalu, každý bod má nulovou pravděpodobnost).",[1127,10998,10999,11000,1254,11003,11042,11043,11080,11081,11101],{},"Každou náhodnou veličinu popisuje ",[1131,11001,11002],{},"distribuční funkce",[1115,11004,11006],{"className":11005},[1144],[1146,11007,11008],{"xmlns":1148},[1150,11009,11010,11039],{},[1153,11011,11012,11015,11017,11020,11022,11024,11027,11029,11032,11035,11037],{},[1159,11013,11014],{},"F",[1289,11016,1484],{"stretchy":1483},[1159,11018,11019],{},"x",[1289,11021,1495],{"stretchy":1483},[1289,11023,1591],{},[1159,11025,11026],{},"P",[1289,11028,1484],{"stretchy":1483},[1159,11030,11031],{},"X",[1289,11033,11034],{},"≤",[1159,11036,11019],{},[1289,11038,1495],{"stretchy":1483},[1167,11040,11041],{"encoding":1169},"F(x) = P(X \\le x)","; u spojité veličiny platí ",[1115,11044,11046],{"className":11045},[1144],[1146,11047,11048],{"xmlns":1148},[1150,11049,11050,11077],{},[1153,11051,11052,11060,11062,11064,11066,11068,11071,11073,11075],{},[1182,11053,11054,11056],{},[1159,11055,11014],{},[1289,11057,11059],{"mathvariant":1734,"lspace":11058,"rspace":11058},"0em","′",[1289,11061,1484],{"stretchy":1483},[1159,11063,11019],{},[1289,11065,1495],{"stretchy":1483},[1289,11067,1591],{},[1159,11069,11070],{},"f",[1289,11072,1484],{"stretchy":1483},[1159,11074,11019],{},[1289,11076,1495],{"stretchy":1483},[1167,11078,11079],{"encoding":1169},"F'(x) = f(x)",", kde ",[1115,11082,11084],{"className":11083},[1144],[1146,11085,11086],{"xmlns":1148},[1150,11087,11088,11098],{},[1153,11089,11090,11092,11094,11096],{},[1159,11091,11070],{},[1289,11093,1484],{"stretchy":1483},[1159,11095,11019],{},[1289,11097,1495],{"stretchy":1483},[1167,11099,11100],{"encoding":1169},"f(x)"," je hustota pravděpodobnosti.",[1127,11103,11104,11105,1269],{},"Pravděpodobnost na intervalu se počítá jako ",[1115,11106,11108],{"className":11107},[1144],[1146,11109,11110],{"xmlns":1148},[1150,11111,11112,11166],{},[1153,11113,11114,11116,11118,11124,11126,11128,11130,11136,11138,11140,11142,11144,11150,11152,11154,11156,11158,11164],{},[1159,11115,11026],{},[1289,11117,1484],{"stretchy":1483},[1156,11119,11120,11122],{},[1159,11121,11019],{},[1163,11123,1402],{},[1289,11125,3951],{},[1159,11127,11031],{},[1289,11129,3951],{},[1156,11131,11132,11134],{},[1159,11133,11019],{},[1163,11135,1189],{},[1289,11137,1495],{"stretchy":1483},[1289,11139,1591],{},[1159,11141,11014],{},[1289,11143,1484],{"stretchy":1483},[1156,11145,11146,11148],{},[1159,11147,11019],{},[1163,11149,1189],{},[1289,11151,1495],{"stretchy":1483},[1289,11153,2681],{},[1159,11155,11014],{},[1289,11157,1484],{"stretchy":1483},[1156,11159,11160,11162],{},[1159,11161,11019],{},[1163,11163,1402],{},[1289,11165,1495],{"stretchy":1483},[1167,11167,11168],{"encoding":1169},"P(x_1 \u003C X \u003C x_2) = F(x_2) - F(x_1)",[1127,11170,11171,1254,11174,11206,11207,2568,11210,2568,11213,11216,11217,11231,11232,1269],{},[1131,11172,11173],{},"Normální rozdělení",[1115,11175,11177],{"className":11176},[1144],[1146,11178,11179],{"xmlns":1148},[1150,11180,11181,11203],{},[1153,11182,11183,11186,11188,11191,11194,11201],{},[1159,11184,11185],{},"N",[1289,11187,1484],{"stretchy":1483},[1159,11189,11190],{},"μ",[1289,11192,11193],{"separator":1121},";",[1182,11195,11196,11199],{},[1159,11197,11198],{},"σ",[1163,11200,1189],{},[1289,11202,1495],{"stretchy":1483},[1167,11204,11205],{"encoding":1169},"N(\\mu; \\sigma^2)"," je nejdůležitější spojité rozdělení; v R ho počítáme funkcemi ",[3087,11208,11209],{},"dnorm",[3087,11211,11212],{},"pnorm",[3087,11214,11215],{},"qnorm"," — R jako parametr očekává směrodatnou odchylku ",[1115,11218,11220],{"className":11219},[1144],[1146,11221,11222],{"xmlns":1148},[1150,11223,11224,11228],{},[1153,11225,11226],{},[1159,11227,11198],{},[1167,11229,11230],{"encoding":1169},"\\sigma",", ne rozptyl ",[1115,11233,11235],{"className":11234},[1144],[1146,11236,11237],{"xmlns":1148},[1150,11238,11239,11247],{},[1153,11240,11241],{},[1182,11242,11243,11245],{},[1159,11244,11198],{},[1163,11246,1189],{},[1167,11248,11249],{"encoding":1169},"\\sigma^2",[1127,11251,11252,2568,11255,5360,11258,11261],{},[1131,11253,11254],{},"Studentovo",[1131,11256,11257],{},"Pearsonovo (χ²)",[1131,11259,11260],{},"Fisherovo-Snedecorovo"," rozdělení slouží jako nástroj pro pozdější konstrukci intervalů spolehlivosti a testování hypotéz.",[1310,11263,11265],{"id":11264},"náhodná-veličina","Náhodná veličina",[1110,11267,11268,11271,11272,11287,11288,1254,11290,11303,11304,11324,11325,11080,11338,11362,11363,2568,11376,2568,11390,11404,11405,2568,11418,2568,11432,11446,11447,11460,11461,11474,11475,1269],{},[1318,11269,1324],{"className":11270,"dataFsResolvedFilePath":1322,"href":1323},[1321]," pracuje s veličinami, jejichž hodnota závisí na náhodě. Formálně: uvažujeme základní prostor ",[1115,11273,11275],{"className":11274},[1144],[1146,11276,11277],{"xmlns":1148},[1150,11278,11279,11284],{},[1153,11280,11281],{},[1159,11282,11283],{"mathvariant":1734},"Ω",[1167,11285,11286],{"encoding":1169},"\\Omega"," přiřazený výsledkům pokusu. ",[1131,11289,11265],{},[1115,11291,11293],{"className":11292},[1144],[1146,11294,11295],{"xmlns":1148},[1150,11296,11297,11301],{},[1153,11298,11299],{},[1159,11300,11031],{},[1167,11302,11031],{"encoding":1169}," je funkce, která prvkům ",[1115,11305,11307],{"className":11306},[1144],[1146,11308,11309],{"xmlns":1148},[1150,11310,11311,11321],{},[1153,11312,11313,11316,11319],{},[1159,11314,11315],{},"ω",[1289,11317,11318],{},"∈",[1159,11320,11283],{"mathvariant":1734},[1167,11322,11323],{"encoding":1169},"\\omega \\in \\Omega"," přiřazuje reálná čísla ",[1115,11326,11328],{"className":11327},[1144],[1146,11329,11330],{"xmlns":1148},[1150,11331,11332,11336],{},[1153,11333,11334],{},[1159,11335,11019],{},[1167,11337,11019],{"encoding":1169},[1115,11339,11341],{"className":11340},[1144],[1146,11342,11343],{"xmlns":1148},[1150,11344,11345,11359],{},[1153,11346,11347,11349,11351,11353,11355,11357],{},[1159,11348,11019],{},[1289,11350,1591],{},[1159,11352,11031],{},[1289,11354,1484],{"stretchy":1483},[1159,11356,11315],{},[1289,11358,1495],{"stretchy":1483},[1167,11360,11361],{"encoding":1169},"x = X(\\omega)",". Náhodné veličiny značíme velkými písmeny (",[1115,11364,11366],{"className":11365},[1144],[1146,11367,11368],{"xmlns":1148},[1150,11369,11370,11374],{},[1153,11371,11372],{},[1159,11373,11031],{},[1167,11375,11031],{"encoding":1169},[1115,11377,11379],{"className":11378},[1144],[1146,11380,11381],{"xmlns":1148},[1150,11382,11383,11388],{},[1153,11384,11385],{},[1159,11386,11387],{},"Y",[1167,11389,11387],{"encoding":1169},[1115,11391,11393],{"className":11392},[1144],[1146,11394,11395],{"xmlns":1148},[1150,11396,11397,11402],{},[1153,11398,11399],{},[1159,11400,11401],{},"T",[1167,11403,11401],{"encoding":1169},"), jejich konkrétní hodnoty odpovídajícími malými písmeny (",[1115,11406,11408],{"className":11407},[1144],[1146,11409,11410],{"xmlns":1148},[1150,11411,11412,11416],{},[1153,11413,11414],{},[1159,11415,11019],{},[1167,11417,11019],{"encoding":1169},[1115,11419,11421],{"className":11420},[1144],[1146,11422,11423],{"xmlns":1148},[1150,11424,11425,11430],{},[1153,11426,11427],{},[1159,11428,11429],{},"y",[1167,11431,11429],{"encoding":1169},[1115,11433,11435],{"className":11434},[1144],[1146,11436,11437],{"xmlns":1148},[1150,11438,11439,11444],{},[1153,11440,11441],{},[1159,11442,11443],{},"t",[1167,11445,11443],{"encoding":1169},"); pravděpodobnost, že ",[1115,11448,11450],{"className":11449},[1144],[1146,11451,11452],{"xmlns":1148},[1150,11453,11454,11458],{},[1153,11455,11456],{},[1159,11457,11031],{},[1167,11459,11031],{"encoding":1169}," nabyla hodnoty ",[1115,11462,11464],{"className":11463},[1144],[1146,11465,11466],{"xmlns":1148},[1150,11467,11468,11472],{},[1153,11469,11470],{},[1159,11471,11019],{},[1167,11473,11019],{"encoding":1169},", zapisujeme ",[1115,11476,11478],{"className":11477},[1144],[1146,11479,11480],{"xmlns":1148},[1150,11481,11482,11496],{},[1153,11483,11484,11486,11488,11490,11492,11494],{},[1159,11485,11026],{},[1289,11487,1484],{"stretchy":1483},[1159,11489,11031],{},[1289,11491,1591],{},[1159,11493,11019],{},[1289,11495,1495],{"stretchy":1483},[1167,11497,11498],{"encoding":1169},"P(X = x)",[1110,11500,11501],{},"Podle typu hodnot, kterých náhodná veličina nabývá, rozlišujeme dva typy:",[1124,11503,11504,11564],{},[1127,11505,11506,11509,11510,11523,11524,11563],{},[1131,11507,11508],{},"Diskrétní náhodná veličina"," — prvky ",[1115,11511,11513],{"className":11512},[1144],[1146,11514,11515],{"xmlns":1148},[1150,11516,11517,11521],{},[1153,11518,11519],{},[1159,11520,11283],{"mathvariant":1734},[1167,11522,11286],{"encoding":1169}," se zobrazí na osu reálných čísel jako izolované body ",[1115,11525,11527],{"className":11526},[1144],[1146,11528,11529],{"xmlns":1148},[1150,11530,11531,11560],{},[1153,11532,11533,11539,11541,11547,11549,11551,11553],{},[1156,11534,11535,11537],{},[1159,11536,11019],{},[1163,11538,1402],{},[1289,11540,1405],{"separator":1121},[1156,11542,11543,11545],{},[1159,11544,11019],{},[1163,11546,1189],{},[1289,11548,1405],{"separator":1121},[1289,11550,1408],{},[1289,11552,1405],{"separator":1121},[1156,11554,11555,11557],{},[1159,11556,11019],{},[1159,11558,11559],{},"k",[1167,11561,11562],{"encoding":1169},"x_1, x_2, \\dots, x_k",", přičemž každý z nich má nenulovou pravděpodobnost. Příklad: počet bodů při hodu kostkou, počet studentů na cvičení.",[1127,11565,11566,11569],{},[1131,11567,11568],{},"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.",[1310,11571,11573],{"id":11572},"distribuční-funkce","Distribuční funkce",[1110,11575,11576,11577,11580],{},"Náhodná veličina nabývá při pokusu určité hodnoty, aniž bychom předem věděli, které. Při opakování pokusu se ale projevují zákonitosti, které popisují ",[1131,11578,11579],{},"zákony rozdělení",". Nejobecnějším z nich je distribuční funkce.",[1110,11582,11583],{},[4002,11584],{"alt":11585,"className":11586,"src":11587},"mask-nv-distribucni-funkce",[1321,4006],"\u002Fwiki-assets\u002Fmask-nv-distribucni-funkce.png",[1103,11589,11592,11599],{"className":11590,"dataCallout":654},[1106,11591],"callout-info",[1110,11593,11595,11598],{"className":11594},[1113],[1115,11596],{"className":11597,"ariaHidden":1121},[1118,1119,1120],"Definice",[1110,11600,11601,11602,11615,11616,11636,11637,11650,11651,11687,11706,11707,11720,11721,1269],{},"Distribuční funkcí náhodné veličiny ",[1115,11603,11605],{"className":11604},[1144],[1146,11606,11607],{"xmlns":1148},[1150,11608,11609,11613],{},[1153,11610,11611],{},[1159,11612,11031],{},[1167,11614,11031],{"encoding":1169}," nazýváme reálnou funkci ",[1115,11617,11619],{"className":11618},[1144],[1146,11620,11621],{"xmlns":1148},[1150,11622,11623,11633],{},[1153,11624,11625,11627,11629,11631],{},[1159,11626,11014],{},[1289,11628,1484],{"stretchy":1483},[1159,11630,11019],{},[1289,11632,1495],{"stretchy":1483},[1167,11634,11635],{"encoding":1169},"F(x)"," definovanou pro každé reálné číslo ",[1115,11638,11640],{"className":11639},[1144],[1146,11641,11642],{"xmlns":1148},[1150,11643,11644,11648],{},[1153,11645,11646],{},[1159,11647,11019],{},[1167,11649,11019],{"encoding":1169}," jako\n",[1115,11652,11654],{"className":11653},[1144],[1146,11655,11656],{"xmlns":1148},[1150,11657,11658,11684],{},[1153,11659,11660,11662,11664,11666,11668,11670,11672,11674,11676,11678,11680,11682],{},[1159,11661,11014],{},[1289,11663,1484],{"stretchy":1483},[1159,11665,11019],{},[1289,11667,1495],{"stretchy":1483},[1289,11669,1591],{},[1159,11671,11026],{},[1289,11673,1484],{"stretchy":1483},[1159,11675,11031],{},[1289,11677,11034],{},[1159,11679,11019],{},[1289,11681,1495],{"stretchy":1483},[1159,11683,1269],{"mathvariant":1734},[1167,11685,11686],{"encoding":1169},"F(x) = P(X \\le x).",[1115,11688,11690],{"className":11689},[1144],[1146,11691,11692],{"xmlns":1148},[1150,11693,11694,11704],{},[1153,11695,11696,11698,11700,11702],{},[1159,11697,11014],{},[1289,11699,1484],{"stretchy":1483},[1159,11701,11019],{},[1289,11703,1495],{"stretchy":1483},[1167,11705,11635],{"encoding":1169}," tedy vyjadřuje pravděpodobnost, s jakou ",[1115,11708,11710],{"className":11709},[1144],[1146,11711,11712],{"xmlns":1148},[1150,11713,11714,11718],{},[1153,11715,11716],{},[1159,11717,11031],{},[1167,11719,11031],{"encoding":1169}," nabude hodnoty z intervalu ",[1115,11722,11724],{"className":11723},[1144],[1146,11725,11726],{"xmlns":1148},[1150,11727,11728,11744],{},[1153,11729,11730,11732,11734,11737,11739,11741],{},[1289,11731,1484],{"stretchy":1483},[1289,11733,2681],{},[1159,11735,11736],{"mathvariant":1734},"∞",[1289,11738,1405],{"separator":1121},[1159,11740,11019],{},[1289,11742,11743],{"stretchy":1483},"⟩",[1167,11745,11746],{"encoding":1169},"(-\\infty, x\\rangle",[1110,11748,11749,11750,11763,11764,11785],{},"Značí-li například ",[1115,11751,11753],{"className":11752},[1144],[1146,11754,11755],{"xmlns":1148},[1150,11756,11757,11761],{},[1153,11758,11759],{},[1159,11760,11031],{},[1167,11762,11031],{"encoding":1169}," výšku mužů v populaci, pak ",[1115,11765,11767],{"className":11766},[1144],[1146,11768,11769],{"xmlns":1148},[1150,11770,11771,11782],{},[1153,11772,11773,11775,11777,11780],{},[1159,11774,11014],{},[1289,11776,1484],{"stretchy":1483},[1163,11778,11779],{},"175",[1289,11781,1495],{"stretchy":1483},[1167,11783,11784],{"encoding":1169},"F(175)"," je pravděpodobnost, že muž měří nejvýše 175 cm.",[1110,11787,11788],{},"Pro distribuční funkci vždy platí:",[1124,11790,11791,11821,11879,11939],{},[1127,11792,11793,1405],{},[1115,11794,11796],{"className":11795},[1144],[1146,11797,11798],{"xmlns":1148},[1150,11799,11800,11818],{},[1153,11801,11802,11804,11806,11808,11810,11812,11814,11816],{},[1163,11803,1165],{},[1289,11805,11034],{},[1159,11807,11014],{},[1289,11809,1484],{"stretchy":1483},[1159,11811,11019],{},[1289,11813,1495],{"stretchy":1483},[1289,11815,11034],{},[1163,11817,1402],{},[1167,11819,11820],{"encoding":1169},"0 \\le F(x) \\le 1",[1127,11822,11823,11824,1405],{},"je neklesající: ",[1115,11825,11827],{"className":11826},[1144],[1146,11828,11829],{"xmlns":1148},[1150,11830,11831,11876],{},[1153,11832,11833,11839,11841,11847,11850,11852,11854,11860,11862,11864,11866,11868,11874],{},[1156,11834,11835,11837],{},[1159,11836,11019],{},[1163,11838,1402],{},[1289,11840,11034],{},[1156,11842,11843,11845],{},[1159,11844,11019],{},[1163,11846,1189],{},[1289,11848,11849],{},"⇒",[1159,11851,11014],{},[1289,11853,1484],{"stretchy":1483},[1156,11855,11856,11858],{},[1159,11857,11019],{},[1163,11859,1402],{},[1289,11861,1495],{"stretchy":1483},[1289,11863,11034],{},[1159,11865,11014],{},[1289,11867,1484],{"stretchy":1483},[1156,11869,11870,11872],{},[1159,11871,11019],{},[1163,11873,1189],{},[1289,11875,1495],{"stretchy":1483},[1167,11877,11878],{"encoding":1169},"x_1 \\le x_2 \\Rightarrow F(x_1) \\le F(x_2)",[1127,11880,11881,11882,1405],{},"je spojitá zprava: ",[1115,11883,11885],{"className":11884},[1144],[1146,11886,11887],{"xmlns":1148},[1150,11888,11889,11936],{},[1153,11890,11891,11914,11916,11918,11920,11922,11924,11926,11928,11930,11932,11934],{},[1156,11892,11893,11900],{},[1153,11894,11895,11898],{},[1159,11896,11897],{},"lim",[1289,11899,4110],{},[1153,11901,11902,11905,11908],{},[1159,11903,11904],{},"h",[1289,11906,11907],{},"→",[1182,11909,11910,11912],{},[1163,11911,1165],{},[1289,11913,5096],{},[1159,11915,11014],{},[1289,11917,1484],{"stretchy":1483},[1159,11919,11019],{},[1289,11921,5096],{},[1159,11923,11904],{},[1289,11925,1495],{"stretchy":1483},[1289,11927,1591],{},[1159,11929,11014],{},[1289,11931,1484],{"stretchy":1483},[1159,11933,11019],{},[1289,11935,1495],{"stretchy":1483},[1167,11937,11938],{"encoding":1169},"\\lim_{h \\to 0^+} F(x+h) = F(x)",[1127,11940,11941,2568,11983,1269],{},[1115,11942,11944],{"className":11943},[1144],[1146,11945,11946],{"xmlns":1148},[1150,11947,11948,11980],{},[1153,11949,11950,11968,11970,11972,11974,11976,11978],{},[1156,11951,11952,11958],{},[1153,11953,11954,11956],{},[1159,11955,11897],{},[1289,11957,4110],{},[1153,11959,11960,11962,11964,11966],{},[1159,11961,11019],{},[1289,11963,11907],{},[1289,11965,2681],{},[1159,11967,11736],{"mathvariant":1734},[1159,11969,11014],{},[1289,11971,1484],{"stretchy":1483},[1159,11973,11019],{},[1289,11975,1495],{"stretchy":1483},[1289,11977,1591],{},[1163,11979,1165],{},[1167,11981,11982],{"encoding":1169},"\\lim_{x \\to -\\infty} F(x) = 0",[1115,11984,11986],{"className":11985},[1144],[1146,11987,11988],{"xmlns":1148},[1150,11989,11990,12020],{},[1153,11991,11992,12008,12010,12012,12014,12016,12018],{},[1156,11993,11994,12000],{},[1153,11995,11996,11998],{},[1159,11997,11897],{},[1289,11999,4110],{},[1153,12001,12002,12004,12006],{},[1159,12003,11019],{},[1289,12005,11907],{},[1159,12007,11736],{"mathvariant":1734},[1159,12009,11014],{},[1289,12011,1484],{"stretchy":1483},[1159,12013,11019],{},[1289,12015,1495],{"stretchy":1483},[1289,12017,1591],{},[1163,12019,1402],{},[1167,12021,12022],{"encoding":1169},"\\lim_{x \\to \\infty} F(x) = 1",[1110,12024,12025],{},"U spojité náhodné veličiny je distribuční funkce svázaná s hustotou pravděpodobnosti vztahem",[1115,12027,12029],{"className":12028},[1144],[1146,12030,12031],{"xmlns":1148,"display":1573},[1150,12032,12033,12101],{},[1153,12034,12035,12041,12043,12045,12047,12049,12051,12053,12055,12057,12059,12061,12063,12065,12067,12069,12071,12084,12086,12088,12090,12092,12094,12097,12099],{},[1182,12036,12037,12039],{},[1159,12038,11014],{},[1289,12040,11059],{"mathvariant":1734,"lspace":11058,"rspace":11058},[1289,12042,1484],{"stretchy":1483},[1159,12044,11019],{},[1289,12046,1495],{"stretchy":1483},[1289,12048,1591],{},[1159,12050,11070],{},[1289,12052,1484],{"stretchy":1483},[1159,12054,11019],{},[1289,12056,1495],{"stretchy":1483},[1289,12058,1405],{"separator":1121},[1621,12060],{"width":1623},[1159,12062,11014],{},[1289,12064,1484],{"stretchy":1483},[1159,12066,11019],{},[1289,12068,1495],{"stretchy":1483},[1289,12070,1591],{},[2970,12072,12073,12076,12082],{},[1289,12074,12075],{},"∫",[1153,12077,12078,12080],{},[1289,12079,2681],{},[1159,12081,11736],{"mathvariant":1734},[1159,12083,11019],{},[1159,12085,11070],{},[1289,12087,1484],{"stretchy":1483},[1159,12089,11443],{},[1289,12091,1495],{"stretchy":1483},[2525,12093,2527],{},[1159,12095,12096],{},"d",[1159,12098,11443],{},[1159,12100,1269],{"mathvariant":1734},[1167,12102,12103],{"encoding":1169},"F'(x) = f(x), \\qquad F(x) = \\int_{-\\infty}^{x} f(t)\\,dt.",[1110,12105,12106,12107,12120,12121,5360,12139,12157],{},"Pravděpodobnost, že ",[1115,12108,12110],{"className":12109},[1144],[1146,12111,12112],{"xmlns":1148},[1150,12113,12114,12118],{},[1153,12115,12116],{},[1159,12117,11031],{},[1167,12119,11031],{"encoding":1169}," padne mezi body ",[1115,12122,12124],{"className":12123},[1144],[1146,12125,12126],{"xmlns":1148},[1150,12127,12128,12136],{},[1153,12129,12130],{},[1156,12131,12132,12134],{},[1159,12133,11019],{},[1163,12135,1402],{},[1167,12137,12138],{"encoding":1169},"x_1",[1115,12140,12142],{"className":12141},[1144],[1146,12143,12144],{"xmlns":1148},[1150,12145,12146,12154],{},[1153,12147,12148],{},[1156,12149,12150,12152],{},[1159,12151,11019],{},[1163,12153,1189],{},[1167,12155,12156],{"encoding":1169},"x_2",", se pak počítá jako",[1115,12159,12161],{"className":12160},[1144],[1146,12162,12163],{"xmlns":1148,"display":1573},[1150,12164,12165,12253],{},[1153,12166,12167,12169,12171,12177,12179,12181,12183,12189,12191,12193,12209,12211,12213,12215,12217,12219,12221,12223,12225,12227,12229,12235,12237,12239,12241,12243,12249,12251],{},[1159,12168,11026],{},[1289,12170,1484],{"stretchy":1483},[1156,12172,12173,12175],{},[1159,12174,11019],{},[1163,12176,1402],{},[1289,12178,3951],{},[1159,12180,11031],{},[1289,12182,3951],{},[1156,12184,12185,12187],{},[1159,12186,11019],{},[1163,12188,1189],{},[1289,12190,1495],{"stretchy":1483},[1289,12192,1591],{},[2970,12194,12195,12197,12203],{},[1289,12196,12075],{},[1156,12198,12199,12201],{},[1159,12200,11019],{},[1163,12202,1402],{},[1156,12204,12205,12207],{},[1159,12206,11019],{},[1163,12208,1189],{},[1159,12210,11070],{},[1289,12212,1484],{"stretchy":1483},[1159,12214,11443],{},[1289,12216,1495],{"stretchy":1483},[2525,12218,2527],{},[1159,12220,12096],{},[1159,12222,11443],{},[1289,12224,1591],{},[1159,12226,11014],{},[1289,12228,1484],{"stretchy":1483},[1156,12230,12231,12233],{},[1159,12232,11019],{},[1163,12234,1189],{},[1289,12236,1495],{"stretchy":1483},[1289,12238,2681],{},[1159,12240,11014],{},[1289,12242,1484],{"stretchy":1483},[1156,12244,12245,12247],{},[1159,12246,11019],{},[1163,12248,1402],{},[1289,12250,1495],{"stretchy":1483},[1159,12252,1269],{"mathvariant":1734},[1167,12254,12255],{"encoding":1169},"P(x_1 \u003C X \u003C x_2) = \\int_{x_1}^{x_2} f(t)\\,dt = F(x_2) - F(x_1).",[1310,12257,12259],{"id":12258},"hustota-pravděpodobnosti","Hustota pravděpodobnosti",[1103,12261,12263,12269],{"className":12262,"dataCallout":654},[1106,11591],[1110,12264,12266,11598],{"className":12265},[1113],[1115,12267],{"className":12268,"ariaHidden":1121},[1118,1119,1120],[1110,12270,12271,12272,12291,12292,12305,12306,12319,12320,1269],{},"Hustota pravděpodobnosti ",[1115,12273,12275],{"className":12274},[1144],[1146,12276,12277],{"xmlns":1148},[1150,12278,12279,12289],{},[1153,12280,12281,12283,12285,12287],{},[1159,12282,11070],{},[1289,12284,1484],{"stretchy":1483},[1159,12286,11019],{},[1289,12288,1495],{"stretchy":1483},[1167,12290,11100],{"encoding":1169}," určuje, jak jsou hodnoty spojité náhodné veličiny ",[1115,12293,12295],{"className":12294},[1144],[1146,12296,12297],{"xmlns":1148},[1150,12298,12299,12303],{},[1153,12300,12301],{},[1159,12302,11031],{},[1167,12304,11031],{"encoding":1169}," nahuštěny v okolí bodu ",[1115,12307,12309],{"className":12308},[1144],[1146,12310,12311],{"xmlns":1148},[1150,12312,12313,12317],{},[1153,12314,12315],{},[1159,12316,11019],{},[1167,12318,11019],{"encoding":1169},". Je vždy nezáporná a platí pro ni ",[1115,12321,12323],{"className":12322},[1144],[1146,12324,12325],{"xmlns":1148},[1150,12326,12327,12359],{},[1153,12328,12329,12341,12343,12345,12347,12349,12351,12353,12355,12357],{},[2970,12330,12331,12333,12339],{},[1289,12332,12075],{},[1153,12334,12335,12337],{},[1289,12336,2681],{},[1159,12338,11736],{"mathvariant":1734},[1159,12340,11736],{"mathvariant":1734},[1159,12342,11070],{},[1289,12344,1484],{"stretchy":1483},[1159,12346,11019],{},[1289,12348,1495],{"stretchy":1483},[2525,12350,2527],{},[1159,12352,12096],{},[1159,12354,11019],{},[1289,12356,1591],{},[1163,12358,1402],{},[1167,12360,12361],{"encoding":1169},"\\int_{-\\infty}^{\\infty} f(x)\\,dx = 1",[1110,12363,12364],{},"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.",[1310,12366,12368],{"id":12367},"charakteristiky-spojité-náhodné-veličiny","Charakteristiky spojité náhodné veličiny",[1110,12370,12371,12374],{},[1131,12372,12373],{},"Střední hodnota"," je nejdůležitější charakteristika náhodné veličiny:",[1115,12376,12378],{"className":12377},[1144],[1146,12379,12380],{"xmlns":1148,"display":1573},[1150,12381,12382,12428],{},[1153,12383,12384,12387,12389,12391,12393,12395,12407,12409,12412,12414,12416,12418,12420,12422,12424,12426],{},[1159,12385,12386],{},"E",[1289,12388,1484],{"stretchy":1483},[1159,12390,11031],{},[1289,12392,1495],{"stretchy":1483},[1289,12394,1591],{},[2970,12396,12397,12399,12405],{},[1289,12398,12075],{},[1153,12400,12401,12403],{},[1289,12402,2681],{},[1159,12404,11736],{"mathvariant":1734},[1159,12406,11736],{"mathvariant":1734},[1159,12408,11019],{},[1289,12410,12411],{},"⋅",[1159,12413,11070],{},[1289,12415,1484],{"stretchy":1483},[1159,12417,11019],{},[1289,12419,1495],{"stretchy":1483},[2525,12421,2527],{},[1159,12423,12096],{},[1159,12425,11019],{},[1159,12427,1269],{"mathvariant":1734},[1167,12429,12430],{"encoding":1169},"E(X) = \\int_{-\\infty}^{\\infty} x \\cdot f(x)\\,dx.",[1110,12432,12433],{},"Je to číslo, kolem něhož kolísají výběrové průměry vypočtené ze sérií pozorovaných hodnot náhodné veličiny.",[1110,12435,12436,5360,12439,1567],{},[1131,12437,12438],{},"Rozptyl",[1131,12440,12441],{},"směrodatná odchylka",[1115,12443,12445],{"className":12444},[1144],[1146,12446,12447],{"xmlns":1148,"display":1573},[1150,12448,12449,12590],{},[1153,12450,12451,12454,12456,12458,12460,12462,12474,12477,12479,12481,12483,12485,12487,12489,12496,12498,12500,12502,12504,12506,12508,12510,12512,12524,12530,12532,12534,12536,12538,12540,12542,12544,12546,12548,12550,12552,12554,12556,12562,12564,12566,12568,12570,12572,12574,12576,12588],{},[1159,12452,12453],{},"D",[1289,12455,1484],{"stretchy":1483},[1159,12457,11031],{},[1289,12459,1495],{"stretchy":1483},[1289,12461,1591],{},[2970,12463,12464,12466,12472],{},[1289,12465,12075],{},[1153,12467,12468,12470],{},[1289,12469,2681],{},[1159,12471,11736],{"mathvariant":1734},[1159,12473,11736],{"mathvariant":1734},[1289,12475,12476],{"stretchy":1483},"[",[1159,12478,11019],{},[1289,12480,2681],{},[1159,12482,12386],{},[1289,12484,1484],{"stretchy":1483},[1159,12486,11031],{},[1289,12488,1495],{"stretchy":1483},[1182,12490,12491,12494],{},[1289,12492,12493],{"stretchy":1483},"]",[1163,12495,1189],{},[1159,12497,11070],{},[1289,12499,1484],{"stretchy":1483},[1159,12501,11019],{},[1289,12503,1495],{"stretchy":1483},[2525,12505,2527],{},[1159,12507,12096],{},[1159,12509,11019],{},[1289,12511,1591],{},[2970,12513,12514,12516,12522],{},[1289,12515,12075],{},[1153,12517,12518,12520],{},[1289,12519,2681],{},[1159,12521,11736],{"mathvariant":1734},[1159,12523,11736],{"mathvariant":1734},[1182,12525,12526,12528],{},[1159,12527,11019],{},[1163,12529,1189],{},[1159,12531,11070],{},[1289,12533,1484],{"stretchy":1483},[1159,12535,11019],{},[1289,12537,1495],{"stretchy":1483},[2525,12539,2527],{},[1159,12541,12096],{},[1159,12543,11019],{},[1289,12545,2681],{},[1289,12547,12476],{"stretchy":1483},[1159,12549,12386],{},[1289,12551,1484],{"stretchy":1483},[1159,12553,11031],{},[1289,12555,1495],{"stretchy":1483},[1182,12557,12558,12560],{},[1289,12559,12493],{"stretchy":1483},[1163,12561,1189],{},[1289,12563,1405],{"separator":1121},[1621,12565],{"width":1623},[1159,12567,11198],{},[1289,12569,1484],{"stretchy":1483},[1159,12571,11031],{},[1289,12573,1495],{"stretchy":1483},[1289,12575,1591],{},[4072,12577,12578],{},[1153,12579,12580,12582,12584,12586],{},[1159,12581,12453],{},[1289,12583,1484],{"stretchy":1483},[1159,12585,11031],{},[1289,12587,1495],{"stretchy":1483},[1159,12589,1269],{"mathvariant":1734},[1167,12591,12592],{"encoding":1169},"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)}.",[1110,12594,12595,12596,12599],{},"Směrodatná odchylka udává, jak moc jsou hodnoty náhodné veličiny rozptýlené kolem střední hodnoty. (Pro odhad těchto charakteristik z naměřených dat viz empirické protějšky v ",[1318,12597,886],{"className":12598,"dataFsResolvedFilePath":6234,"href":6235},[1321],".)",[1110,12601,12602,12605,12606,12619,12620,12638,12639,12652],{},[1131,12603,12604],{},"Kvantily"," udávají, jak jsou hodnoty náhodné veličiny ",[1115,12607,12609],{"className":12608},[1144],[1146,12610,12611],{"xmlns":1148},[1150,12612,12613,12617],{},[1153,12614,12615],{},[1159,12616,11031],{},[1167,12618,11031],{"encoding":1169}," rozděleny na ose reálných čísel v určitém pravděpodobnostním poměru. 100p%-ní kvantil ",[1115,12621,12623],{"className":12622},[1144],[1146,12624,12625],{"xmlns":1148},[1150,12626,12627,12635],{},[1153,12628,12629],{},[1156,12630,12631,12633],{},[1159,12632,11019],{},[1159,12634,1110],{},[1167,12636,12637],{"encoding":1169},"x_p"," je číslo, pro které při zvolené pravděpodobnosti ",[1115,12640,12642],{"className":12641},[1144],[1146,12643,12644],{"xmlns":1148},[1150,12645,12646,12650],{},[1153,12647,12648],{},[1159,12649,1110],{},[1167,12651,1110],{"encoding":1169}," platí",[1115,12654,12656],{"className":12655},[1144],[1146,12657,12658],{"xmlns":1148,"display":1573},[1150,12659,12660,12680],{},[1153,12661,12662,12664,12666,12672,12674,12676,12678],{},[1159,12663,11014],{},[1289,12665,1484],{"stretchy":1483},[1156,12667,12668,12670],{},[1159,12669,11019],{},[1159,12671,1110],{},[1289,12673,1495],{"stretchy":1483},[1289,12675,1591],{},[1159,12677,1110],{},[1159,12679,1269],{"mathvariant":1734},[1167,12681,12682],{"encoding":1169},"F(x_p) = p.",[1110,12684,12685,12686,12714,12715,12742,12743,12762,12763,12782,12783,1269],{},"V intervalu ",[1115,12687,12689],{"className":12688},[1144],[1146,12690,12691],{"xmlns":1148},[1150,12692,12693,12711],{},[1153,12694,12695,12697,12699,12701,12703,12709],{},[1289,12696,1484],{"stretchy":1483},[1289,12698,2681],{},[1159,12700,11736],{"mathvariant":1734},[1289,12702,11193],{"separator":1121},[1156,12704,12705,12707],{},[1159,12706,11019],{},[1159,12708,1110],{},[1289,12710,1495],{"stretchy":1483},[1167,12712,12713],{"encoding":1169},"(-\\infty; x_p)"," leží 100p % hodnot, v intervalu ",[1115,12716,12718],{"className":12717},[1144],[1146,12719,12720],{"xmlns":1148},[1150,12721,12722,12739],{},[1153,12723,12724,12727,12733,12735,12737],{},[1289,12725,12726],{"stretchy":1483},"⟨",[1156,12728,12729,12731],{},[1159,12730,11019],{},[1159,12732,1110],{},[1289,12734,11193],{"separator":1121},[1159,12736,11736],{"mathvariant":1734},[1289,12738,1495],{"stretchy":1483},[1167,12740,12741],{"encoding":1169},"\\langle x_p; \\infty)"," leží 100(1-p) % hodnot. Nejdůležitější kvantily jsou medián ",[1115,12744,12746],{"className":12745},[1144],[1146,12747,12748],{"xmlns":1148},[1150,12749,12750,12759],{},[1153,12751,12752],{},[1156,12753,12754,12756],{},[1159,12755,11019],{},[1163,12757,12758],{},"0,5",[1167,12760,12761],{"encoding":1169},"x_{0{,}5}",", dolní kvartil ",[1115,12764,12766],{"className":12765},[1144],[1146,12767,12768],{"xmlns":1148},[1150,12769,12770,12779],{},[1153,12771,12772],{},[1156,12773,12774,12776],{},[1159,12775,11019],{},[1163,12777,12778],{},"0,25",[1167,12780,12781],{"encoding":1169},"x_{0{,}25}"," a horní kvartil ",[1115,12784,12786],{"className":12785},[1144],[1146,12787,12788],{"xmlns":1148},[1150,12789,12790,12799],{},[1153,12791,12792],{},[1156,12793,12794,12796],{},[1159,12795,11019],{},[1163,12797,12798],{},"0,75",[1167,12800,12801],{"encoding":1169},"x_{0{,}75}",[1310,12803,11173],{"id":12804},"normální-rozdělení",[1110,12806,12807,12808,12821,12822,1254,12825,12852],{},"Spojitá náhodná veličina ",[1115,12809,12811],{"className":12810},[1144],[1146,12812,12813],{"xmlns":1148},[1150,12814,12815,12819],{},[1153,12816,12817],{},[1159,12818,11031],{},[1167,12820,11031],{"encoding":1169}," má ",[1131,12823,12824],{},"normální rozdělení",[1115,12826,12828],{"className":12827},[1144],[1146,12829,12830],{"xmlns":1148},[1150,12831,12832,12850],{},[1153,12833,12834,12836,12838,12840,12842,12848],{},[1159,12835,11185],{},[1289,12837,1484],{"stretchy":1483},[1159,12839,11190],{},[1289,12841,11193],{"separator":1121},[1182,12843,12844,12846],{},[1159,12845,11198],{},[1163,12847,1189],{},[1289,12849,1495],{"stretchy":1483},[1167,12851,11205],{"encoding":1169},", jestliže její hustota pravděpodobnosti a distribuční funkce jsou dány předpisy",[1115,12854,12856],{"className":12855},[1144],[1146,12857,12858],{"xmlns":1148,"display":1573},[1150,12859,12860,13012],{},[1153,12861,12862,12864,12866,12868,12870,12872,12889,12926,12928,12930,12932,12934,12936,12938,12940,12956,12968,13004,13006,13008,13010],{},[1159,12863,11070],{},[1289,12865,1484],{"stretchy":1483},[1159,12867,11019],{},[1289,12869,1495],{"stretchy":1483},[1289,12871,1591],{},[2355,12873,12874,12876],{},[1163,12875,1402],{},[1153,12877,12878,12880],{},[1159,12879,11198],{},[4072,12881,12882],{},[1153,12883,12884,12886],{},[1163,12885,1189],{},[1159,12887,12888],{},"π",[1182,12890,12891,12894],{},[1159,12892,12893],{},"e",[1153,12895,12896,12898],{},[1289,12897,2681],{},[2355,12899,12900,12916],{},[1153,12901,12902,12904,12906,12908,12910],{},[1289,12903,1484],{"stretchy":1483},[1159,12905,11019],{},[1289,12907,2681],{},[1159,12909,11190],{},[1182,12911,12912,12914],{},[1289,12913,1495],{"stretchy":1483},[1163,12915,1189],{},[1153,12917,12918,12920],{},[1163,12919,1189],{},[1182,12921,12922,12924],{},[1159,12923,11198],{},[1163,12925,1189],{},[1289,12927,1405],{"separator":1121},[1621,12929],{"width":1623},[1159,12931,11014],{},[1289,12933,1484],{"stretchy":1483},[1159,12935,11019],{},[1289,12937,1495],{"stretchy":1483},[1289,12939,1591],{},[2355,12941,12942,12944],{},[1163,12943,1402],{},[1153,12945,12946,12948],{},[1159,12947,11198],{},[4072,12949,12950],{},[1153,12951,12952,12954],{},[1163,12953,1189],{},[1159,12955,12888],{},[2970,12957,12958,12960,12966],{},[1289,12959,12075],{},[1153,12961,12962,12964],{},[1289,12963,2681],{},[1159,12965,11736],{"mathvariant":1734},[1159,12967,11019],{},[1182,12969,12970,12972],{},[1159,12971,12893],{},[1153,12973,12974,12976],{},[1289,12975,2681],{},[2355,12977,12978,12994],{},[1153,12979,12980,12982,12984,12986,12988],{},[1289,12981,1484],{"stretchy":1483},[1159,12983,11443],{},[1289,12985,2681],{},[1159,12987,11190],{},[1182,12989,12990,12992],{},[1289,12991,1495],{"stretchy":1483},[1163,12993,1189],{},[1153,12995,12996,12998],{},[1163,12997,1189],{},[1182,12999,13000,13002],{},[1159,13001,11198],{},[1163,13003,1189],{},[2525,13005,2527],{},[1159,13007,12096],{},[1159,13009,11443],{},[1289,13011,1405],{"separator":1121},[1167,13013,13014],{"encoding":1169},"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,",[1110,13016,13017,13018,2568,13042,1269],{},"přičemž ",[1115,13019,13021],{"className":13020},[1144],[1146,13022,13023],{"xmlns":1148},[1150,13024,13025,13039],{},[1153,13026,13027,13029,13031,13033,13035,13037],{},[1159,13028,12386],{},[1289,13030,1484],{"stretchy":1483},[1159,13032,11031],{},[1289,13034,1495],{"stretchy":1483},[1289,13036,1591],{},[1159,13038,11190],{},[1167,13040,13041],{"encoding":1169},"E(X) = \\mu",[1115,13043,13045],{"className":13044},[1144],[1146,13046,13047],{"xmlns":1148},[1150,13048,13049,13067],{},[1153,13050,13051,13053,13055,13057,13059,13061],{},[1159,13052,12453],{},[1289,13054,1484],{"stretchy":1483},[1159,13056,11031],{},[1289,13058,1495],{"stretchy":1483},[1289,13060,1591],{},[1182,13062,13063,13065],{},[1159,13064,11198],{},[1163,13066,1189],{},[1167,13068,13069],{"encoding":1169},"D(X) = \\sigma^2",[1110,13071,13072],{},[4002,13073],{"alt":13074,"className":13075,"src":13076},"mask-nv-normalni",[1321,4006],"\u002Fwiki-assets\u002Fmask-nv-normalni.png",[1110,13078,13079,13080,13083,13084,13098,13099,13118,13119,13135,13136,13149,13150,1269],{},"Křivka hustoty se nazývá ",[1131,13081,13082],{},"Gaussova křivka",": je symetrická kolem svislé přímky procházející ",[1115,13085,13087],{"className":13086},[1144],[1146,13088,13089],{"xmlns":1148},[1150,13090,13091,13095],{},[1153,13092,13093],{},[1159,13094,11190],{},[1167,13096,13097],{"encoding":1169},"\\mu",", kde má ",[1115,13100,13102],{"className":13101},[1144],[1146,13103,13104],{"xmlns":1148},[1150,13105,13106,13116],{},[1153,13107,13108,13110,13112,13114],{},[1159,13109,11070],{},[1289,13111,1484],{"stretchy":1483},[1159,13113,11019],{},[1289,13115,1495],{"stretchy":1483},[1167,13117,11100],{"encoding":1169}," globální maximum, a ve vzdálenosti ",[1115,13120,13122],{"className":13121},[1144],[1146,13123,13124],{"xmlns":1148},[1150,13125,13126,13132],{},[1153,13127,13128,13130],{},[1163,13129,3209],{},[1159,13131,11198],{},[1167,13133,13134],{"encoding":1169},"3\\sigma"," od ",[1115,13137,13139],{"className":13138},[1144],[1146,13140,13141],{"xmlns":1148},[1150,13142,13143,13147],{},[1153,13144,13145],{},[1159,13146,11190],{},[1167,13148,13097],{"encoding":1169}," se téměř dotýká osy x — zhruba 99,73 % hodnot leží v intervalu ",[1115,13151,13153],{"className":13152},[1144],[1146,13154,13155],{"xmlns":1148},[1150,13156,13157,13181],{},[1153,13158,13159,13161,13163,13165,13167,13169,13171,13173,13175,13177,13179],{},[1289,13160,1484],{"stretchy":1483},[1159,13162,11190],{},[1289,13164,2681],{},[1163,13166,3209],{},[1159,13168,11198],{},[1289,13170,11193],{"separator":1121},[1159,13172,11190],{},[1289,13174,5096],{},[1163,13176,3209],{},[1159,13178,11198],{},[1289,13180,1495],{"stretchy":1483},[1167,13182,13183],{"encoding":1169},"(\\mu - 3\\sigma; \\mu + 3\\sigma)",[1110,13185,13186,13187,1254,13190,13214,13215,1269],{},"Zvláštní postavení má ",[1131,13188,13189],{},"normované normální rozdělení",[1115,13191,13193],{"className":13192},[1144],[1146,13194,13195],{"xmlns":1148},[1150,13196,13197,13211],{},[1153,13198,13199,13201,13203,13205,13207,13209],{},[1159,13200,11185],{},[1289,13202,1484],{"stretchy":1483},[1163,13204,1165],{},[1289,13206,11193],{"separator":1121},[1163,13208,1402],{},[1289,13210,1495],{"stretchy":1483},[1167,13212,13213],{"encoding":1169},"N(0; 1)",", na které se dá libovolné normální rozdělení převést standardizací ",[1115,13216,13218],{"className":13217},[1144],[1146,13219,13220],{"xmlns":1148},[1150,13221,13222,13243],{},[1153,13223,13224,13227,13229,13231,13233,13235,13237,13239,13241],{},[1159,13225,13226],{},"Z",[1289,13228,1591],{},[1289,13230,1484],{"stretchy":1483},[1159,13232,11031],{},[1289,13234,2681],{},[1159,13236,11190],{},[1289,13238,1495],{"stretchy":1483},[1159,13240,4223],{"mathvariant":1734},[1159,13242,11198],{},[1167,13244,13245],{"encoding":1169},"Z = (X-\\mu)\u002F\\sigma",[13247,13248],"graph-mount",{"spec":13249},"{\"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\"}]}",[1103,13251,13253,13260],{"className":13252,"dataCallout":6032},[1106,6031],[1110,13254,13256,13259],{"className":13255},[1113],[1115,13257],{"className":13258,"ariaHidden":1121},[1118,6039,1120],"R očekává směrodatnou odchylku, ne rozptyl",[1110,13261,13262,13263,13290,13291,13294,13295,2568,13297,5360,13299,13301,13302,1254,13305,13318,13319,13345,13346,13349,13350,1269],{},"Zápis ",[1115,13264,13266],{"className":13265},[1144],[1146,13267,13268],{"xmlns":1148},[1150,13269,13270,13288],{},[1153,13271,13272,13274,13276,13278,13280,13286],{},[1159,13273,11185],{},[1289,13275,1484],{"stretchy":1483},[1159,13277,11190],{},[1289,13279,11193],{"separator":1121},[1182,13281,13282,13284],{},[1159,13283,11198],{},[1163,13285,1189],{},[1289,13287,1495],{"stretchy":1483},[1167,13289,11205],{"encoding":1169}," v definici používá ",[1131,13292,13293],{},"rozptyl",". Funkce ",[3087,13296,11209],{},[3087,13298,11212],{},[3087,13300,11215],{}," v R ale jako třetí argument berou ",[1131,13303,13304],{},"směrodatnou odchylku",[1115,13306,13308],{"className":13307},[1144],[1146,13309,13310],{"xmlns":1148},[1150,13311,13312,13316],{},[1153,13313,13314],{},[1159,13315,11198],{},[1167,13317,11230],{"encoding":1169},". Má-li náhodná veličina rozdělení ",[1115,13320,13322],{"className":13321},[1144],[1146,13323,13324],{"xmlns":1148},[1150,13325,13326,13342],{},[1153,13327,13328,13330,13332,13335,13337,13340],{},[1159,13329,11185],{},[1289,13331,1484],{"stretchy":1483},[1163,13333,13334],{},"10",[1289,13336,11193],{"separator":1121},[1163,13338,13339],{},"0,12",[1289,13341,1495],{"stretchy":1483},[1167,13343,13344],{"encoding":1169},"N(10; 0{,}12)",", je ",[3087,13347,13348],{},"sd = sqrt(0.12)",", ne ",[3087,13351,13352],{},"sd = 0.12",[1110,13354,13355],{},"V R:",[3311,13357,13359],{"className":3313,"code":13358,"language":71,"meta":3315,"style":3315},"dnorm(0)\npnorm(1.96)\nqnorm(0.975)\n",[3087,13360,13361,13371,13382],{"__ignoreMap":3315},[1115,13362,13363,13365,13367,13369],{"class":3320,"line":10},[1115,13364,11209],{"class":3331},[1115,13366,1484],{"class":3335},[1115,13368,1165],{"class":3343},[1115,13370,3520],{"class":3335},[1115,13372,13373,13375,13377,13380],{"class":3320,"line":27},[1115,13374,11212],{"class":3331},[1115,13376,1484],{"class":3335},[1115,13378,13379],{"class":3343},"1.96",[1115,13381,3520],{"class":3335},[1115,13383,13384,13386,13388,13391],{"class":3320,"line":148},[1115,13385,11215],{"class":3331},[1115,13387,1484],{"class":3335},[1115,13389,13390],{"class":3343},"0.975",[1115,13392,3520],{"class":3335},[3311,13394,13397],{"className":13395,"code":13396,"language":3542,"meta":3315},[3540],"[1] 0.3989423\n[1] 0.9750021\n[1] 1.959964\n",[3087,13398,13396],{"__ignoreMap":3315},[1110,13400,13401,13404,13405,13429,13430,1499,13433,5360,13454,13457],{},[3087,13402,13403],{},"dnorm(0)"," je hodnota hustoty ",[1115,13406,13408],{"className":13407},[1144],[1146,13409,13410],{"xmlns":1148},[1150,13411,13412,13426],{},[1153,13413,13414,13416,13418,13420,13422,13424],{},[1159,13415,11185],{},[1289,13417,1484],{"stretchy":1483},[1163,13419,1165],{},[1289,13421,11193],{"separator":1121},[1163,13423,1402],{},[1289,13425,1495],{"stretchy":1483},[1167,13427,13428],{"encoding":1169},"N(0;1)"," v bodě 0, ",[3087,13431,13432],{},"pnorm(1.96)",[1115,13434,13436],{"className":13435},[1144],[1146,13437,13438],{"xmlns":1148},[1150,13439,13440,13451],{},[1153,13441,13442,13444,13446,13449],{},[1159,13443,11014],{},[1289,13445,1484],{"stretchy":1483},[1163,13447,13448],{},"1,96",[1289,13450,1495],{"stretchy":1483},[1167,13452,13453],{"encoding":1169},"F(1{,}96)",[3087,13455,13456],{},"qnorm(0.975)"," je 97,5%-ní kvantil — hodnota, pod kterou leží 97,5 % pravděpodobnosti.",[1103,13459,13461,13468],{"className":13460,"dataCallout":3094},[1106,3093],[1110,13462,13464,13467],{"className":13463},[1113],[1115,13465],{"className":13466,"ariaHidden":1121},[1118,3101,1120],"Příklad: Návštěvnost zábavního parku",[1110,13469,13470,13471,13506],{},"Denní návštěvnost zábavního parku je náhodná veličina s normálním rozdělením, průměrnou hodnotou 230 a směrodatnou odchylkou 27,5 návštěvníků: ",[1115,13472,13474],{"className":13473},[1144],[1146,13475,13476],{"xmlns":1148},[1150,13477,13478,13503],{},[1153,13479,13480,13482,13485,13487,13489,13492,13494,13501],{},[1159,13481,11031],{},[1289,13483,13484],{},"∼",[1159,13486,11185],{},[1289,13488,1484],{"stretchy":1483},[1163,13490,13491],{},"230",[1289,13493,11193],{"separator":1121},[1182,13495,13496,13499],{},[1163,13497,13498],{},"27,5",[1163,13500,1189],{},[1289,13502,1495],{"stretchy":1483},[1167,13504,13505],{"encoding":1169},"X \\sim N(230; 27{,}5^2)",". Přijde-li za den méně než 180 návštěvníků, je park ztrátový. Kolik procent dní je ztrátových?",[1110,13508,13509],{},[4002,13510],{"alt":13511,"className":13512,"src":13513},"mask-nv-priklad-park",[1321,4006],"\u002Fwiki-assets\u002Fmask-nv-priklad-park.png",[3311,13515,13517],{"className":3313,"code":13516,"language":71,"meta":3315,"style":3315},"pnorm(180, mean = 230, sd = 27.5)\n",[3087,13518,13519],{"__ignoreMap":3315},[1115,13520,13521,13523,13525,13528,13530,13533,13535,13538,13540,13543,13545,13548],{"class":3320,"line":10},[1115,13522,11212],{"class":3331},[1115,13524,1484],{"class":3335},[1115,13526,13527],{"class":3343},"180",[1115,13529,1405],{"class":3327},[1115,13531,13532],{"class":3323}," mean",[1115,13534,3416],{"class":3327},[1115,13536,13537],{"class":3343}," 230",[1115,13539,1405],{"class":3327},[1115,13541,13542],{"class":3323}," sd",[1115,13544,3416],{"class":3327},[1115,13546,13547],{"class":3343}," 27.5",[1115,13549,3520],{"class":3335},[3311,13551,13554],{"className":13552,"code":13553,"language":3542,"meta":3315},[3540],"[1] 0.03451817\n",[3087,13555,13553],{"__ignoreMap":3315},[1110,13557,13558],{},"Park je ztrátový přibližně v 3,45 % dní.",[1103,13560,13562,13569],{"className":13561,"dataCallout":3094},[1106,3093],[1110,13563,13565,13568],{"className":13564},[1113],[1115,13566],{"className":13567,"ariaHidden":1121},[1118,3101,1120],"Příklad: Délka výrobku",[1110,13570,13571,13572,13606],{},"Automat je seřízen tak, aby střední hodnota délky výrobku byla 42 mm, s přesností charakterizovanou směrodatnou odchylkou 1,2 mm: ",[1115,13573,13575],{"className":13574},[1144],[1146,13576,13577],{"xmlns":1148},[1150,13578,13579,13603],{},[1153,13580,13581,13583,13585,13587,13589,13592,13594,13601],{},[1159,13582,11031],{},[1289,13584,13484],{},[1159,13586,11185],{},[1289,13588,1484],{"stretchy":1483},[1163,13590,13591],{},"42",[1289,13593,11193],{"separator":1121},[1182,13595,13596,13599],{},[1163,13597,13598],{},"1,2",[1163,13600,1189],{},[1289,13602,1495],{"stretchy":1483},[1167,13604,13605],{"encoding":1169},"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?",[1110,13608,13609],{},[4002,13610],{"alt":13611,"className":13612,"src":13613},"mask-nv-priklad-delka",[1321,4006],"\u002Fwiki-assets\u002Fmask-nv-priklad-delka.png",[3311,13615,13617],{"className":3313,"code":13616,"language":71,"meta":3315,"style":3315},"pnorm(43, mean = 42, sd = 1.2) - pnorm(41, mean = 42, sd = 1.2)\n",[3087,13618,13619],{"__ignoreMap":3315},[1115,13620,13621,13623,13625,13628,13630,13632,13634,13637,13639,13641,13643,13646,13648,13650,13653,13655,13658,13660,13662,13664,13666,13668,13670,13672,13674],{"class":3320,"line":10},[1115,13622,11212],{"class":3331},[1115,13624,1484],{"class":3335},[1115,13626,13627],{"class":3343},"43",[1115,13629,1405],{"class":3327},[1115,13631,13532],{"class":3323},[1115,13633,3416],{"class":3327},[1115,13635,13636],{"class":3343}," 42",[1115,13638,1405],{"class":3327},[1115,13640,13542],{"class":3323},[1115,13642,3416],{"class":3327},[1115,13644,13645],{"class":3343}," 1.2",[1115,13647,4220],{"class":3335},[1115,13649,4257],{"class":3327},[1115,13651,13652],{"class":3331}," pnorm",[1115,13654,1484],{"class":3335},[1115,13656,13657],{"class":3343},"41",[1115,13659,1405],{"class":3327},[1115,13661,13532],{"class":3323},[1115,13663,3416],{"class":3327},[1115,13665,13636],{"class":3343},[1115,13667,1405],{"class":3327},[1115,13669,13542],{"class":3323},[1115,13671,3416],{"class":3327},[1115,13673,13645],{"class":3343},[1115,13675,3520],{"class":3335},[3311,13677,13680],{"className":13678,"code":13679,"language":3542,"meta":3315},[3540],"[1] 0.5953432\n",[3087,13681,13679],{"__ignoreMap":3315},[1110,13683,13684],{},"Do 1. jakostní třídy spadá přibližně 59,53 % výrobků.",[1103,13686,13688,13695],{"className":13687,"dataCallout":3094},[1106,3093],[1110,13689,13691,13694],{"className":13690},[1113],[1115,13692],{"className":13693,"ariaHidden":1121},[1118,3101,1120],"Příklad: Obsah ampulky",[1110,13696,13697,13698,13721,13722,13748],{},"Obsah ampulky s lékem (v cm³) má rozdělení ",[1115,13699,13701],{"className":13700},[1144],[1146,13702,13703],{"xmlns":1148},[1150,13704,13705,13719],{},[1153,13706,13707,13709,13711,13713,13715,13717],{},[1159,13708,11185],{},[1289,13710,1484],{"stretchy":1483},[1163,13712,13334],{},[1289,13714,11193],{"separator":1121},[1163,13716,13339],{},[1289,13718,1495],{"stretchy":1483},[1167,13720,13344],{"encoding":1169},", tedy střední hodnota 10 a rozptyl 0,12 (",[1115,13723,13725],{"className":13724},[1144],[1146,13726,13727],{"xmlns":1148},[1150,13728,13729,13745],{},[1153,13730,13731,13733,13735,13739,13742],{},[1159,13732,11198],{},[1289,13734,1591],{},[4072,13736,13737],{},[1163,13738,13339],{},[1289,13740,13741],{},"≈",[1163,13743,13744],{},"0,346",[1167,13746,13747],{"encoding":1169},"\\sigma = \\sqrt{0{,}12} \\approx 0{,}346","). Kolik procent ampulek má obsah menší než 9,8 cm³?",[1110,13750,13751],{},[4002,13752],{"alt":13753,"className":13754,"src":13755},"mask-nv-priklad-ampulka",[1321,4006],"\u002Fwiki-assets\u002Fmask-nv-priklad-ampulka.png",[3311,13757,13759],{"className":3313,"code":13758,"language":71,"meta":3315,"style":3315},"pnorm(9.8, mean = 10, sd = sqrt(0.12))\n",[3087,13760,13761],{"__ignoreMap":3315},[1115,13762,13763,13765,13767,13770,13772,13774,13776,13779,13781,13783,13785,13787,13789,13792],{"class":3320,"line":10},[1115,13764,11212],{"class":3331},[1115,13766,1484],{"class":3335},[1115,13768,13769],{"class":3343},"9.8",[1115,13771,1405],{"class":3327},[1115,13773,13532],{"class":3323},[1115,13775,3416],{"class":3327},[1115,13777,13778],{"class":3343}," 10",[1115,13780,1405],{"class":3327},[1115,13782,13542],{"class":3323},[1115,13784,3416],{"class":3327},[1115,13786,4197],{"class":3331},[1115,13788,1484],{"class":3335},[1115,13790,13791],{"class":3343},"0.12",[1115,13793,13794],{"class":3335},"))\n",[3311,13796,13799],{"className":13797,"code":13798,"language":3542,"meta":3315},[3540],"[1] 0.2818514\n",[3087,13800,13798],{"__ignoreMap":3315},[1110,13802,13803],{},"Obsah menší než 9,8 cm³ má přibližně 28,19 % ampulek.",[1310,13805,13807],{"id":13806},"další-rozdělení-dostupná-v-r","Další rozdělení dostupná v R",[1110,13809,13810,13811,13814,13815,13818,13819,13822,13823,4223,13826,13829,13830,13833],{},"Vedle normálního rozdělení R přímo nabízí hustotu, distribuční funkci a kvantilovou funkci i pro další běžná rozdělení. Pojmenování funkcí je jednotné: ",[3087,13812,13813],{},"d*"," je hustota\u002Fpravděpodobnostní funkce, ",[3087,13816,13817],{},"p*"," distribuční funkce (s ",[3087,13820,13821],{},"lower.tail = FALSE",", případně čtvrtým argumentem ",[3087,13824,13825],{},"TRUE",[3087,13827,13828],{},"FALSE",", pro horní chvost) a ",[3087,13831,13832],{},"q*"," kvantilová funkce.",[1710,13835,13836,13942],{},[1713,13837,13838],{},[1716,13839,13840,13843,13889,13915],{},[1719,13841,13842],{},"Rozdělení",[1719,13844,13845,13869,13870],{},[1115,13846,13848],{"className":13847},[1144],[1146,13849,13850],{"xmlns":1148},[1150,13851,13852,13866],{},[1153,13853,13854,13856,13858,13860,13862,13864],{},[1159,13855,11026],{},[1289,13857,1484],{"stretchy":1483},[1159,13859,11031],{},[1289,13861,1591],{},[1159,13863,11559],{},[1289,13865,1495],{"stretchy":1483},[1167,13867,13868],{"encoding":1169},"P(X=k)"," \u002F ",[1115,13871,13873],{"className":13872},[1144],[1146,13874,13875],{"xmlns":1148},[1150,13876,13877,13887],{},[1153,13878,13879,13881,13883,13885],{},[1159,13880,11070],{},[1289,13882,1484],{"stretchy":1483},[1159,13884,11019],{},[1289,13886,1495],{"stretchy":1483},[1167,13888,11100],{"encoding":1169},[1719,13890,13891],{},[1115,13892,13894],{"className":13893},[1144],[1146,13895,13896],{"xmlns":1148},[1150,13897,13898,13912],{},[1153,13899,13900,13902,13904,13906,13908,13910],{},[1159,13901,11026],{},[1289,13903,1484],{"stretchy":1483},[1159,13905,11031],{},[1289,13907,11034],{},[1159,13909,11559],{},[1289,13911,1495],{"stretchy":1483},[1167,13913,13914],{"encoding":1169},"P(X \\le k)",[1719,13916,13917,13918],{},"horní chvost ",[1115,13919,13921],{"className":13920},[1144],[1146,13922,13923],{"xmlns":1148},[1150,13924,13925,13939],{},[1153,13926,13927,13929,13931,13933,13935,13937],{},[1159,13928,11026],{},[1289,13930,1484],{"stretchy":1483},[1159,13932,11031],{},[1289,13934,1291],{},[1159,13936,11559],{},[1289,13938,1495],{"stretchy":1483},[1167,13940,13941],{"encoding":1169},"P(X>k)",[1828,13943,13944,13990,14034,14075,14124],{},[1716,13945,13946,13975,13980,13985],{},[1833,13947,13948,13949],{},"Binomické ",[1115,13950,13952],{"className":13951},[1144],[1146,13953,13954],{"xmlns":1148},[1150,13955,13956,13972],{},[1153,13957,13958,13960,13962,13964,13966,13968,13970],{},[1159,13959,1432],{},[1159,13961,1487],{},[1289,13963,1484],{"stretchy":1483},[1159,13965,1287],{},[1289,13967,1405],{"separator":1121},[1159,13969,1110],{},[1289,13971,1495],{"stretchy":1483},[1167,13973,13974],{"encoding":1169},"Bi(n,p)",[1833,13976,13977],{},[3087,13978,13979],{},"dbinom(k, n, p)",[1833,13981,13982],{},[3087,13983,13984],{},"pbinom(k, n, p)",[1833,13986,13987],{},[3087,13988,13989],{},"pbinom(k, n, p, FALSE)",[1716,13991,13992,14019,14024,14029],{},[1833,13993,13994,13995],{},"Poissonovo ",[1115,13996,13998],{"className":13997},[1144],[1146,13999,14000],{"xmlns":1148},[1150,14001,14002,14016],{},[1153,14003,14004,14006,14009,14011,14014],{},[1159,14005,11026],{},[1159,14007,14008],{},"o",[1289,14010,1484],{"stretchy":1483},[1159,14012,14013],{},"λ",[1289,14015,1495],{"stretchy":1483},[1167,14017,14018],{"encoding":1169},"Po(\\lambda)",[1833,14020,14021],{},[3087,14022,14023],{},"dpois(k, lambda)",[1833,14025,14026],{},[3087,14027,14028],{},"ppois(k, lambda)",[1833,14030,14031],{},[3087,14032,14033],{},"ppois(k, lambda, FALSE)",[1716,14035,14036,14060,14065,14070],{},[1833,14037,14038,14039],{},"Geometrické ",[1115,14040,14042],{"className":14041},[1144],[1146,14043,14044],{"xmlns":1148},[1150,14045,14046,14057],{},[1153,14047,14048,14051,14053,14055],{},[1159,14049,14050],{},"G",[1289,14052,1484],{"stretchy":1483},[1159,14054,1110],{},[1289,14056,1495],{"stretchy":1483},[1167,14058,14059],{"encoding":1169},"G(p)",[1833,14061,14062],{},[3087,14063,14064],{},"dgeom(k, p)",[1833,14066,14067],{},[3087,14068,14069],{},"pgeom(k, p)",[1833,14071,14072],{},[3087,14073,14074],{},"pgeom(k, p, FALSE)",[1716,14076,14077,14109,14114,14119],{},[1833,14078,14079,14080],{},"Hypergeometrické ",[1115,14081,14083],{"className":14082},[1144],[1146,14084,14085],{"xmlns":1148},[1150,14086,14087,14106],{},[1153,14088,14089,14091,14093,14095,14097,14100,14102,14104],{},[1159,14090,1161],{},[1289,14092,1484],{"stretchy":1483},[1159,14094,11185],{},[1289,14096,1405],{"separator":1121},[1159,14098,14099],{},"M",[1289,14101,1405],{"separator":1121},[1159,14103,1287],{},[1289,14105,1495],{"stretchy":1483},[1167,14107,14108],{"encoding":1169},"H(N,M,n)",[1833,14110,14111],{},[3087,14112,14113],{},"dhyper(k, M, N-M, n)",[1833,14115,14116],{},[3087,14117,14118],{},"phyper(k, M, N-M, n)",[1833,14120,14121],{},[3087,14122,14123],{},"phyper(k, M, N-M, n, FALSE)",[1716,14125,14126,14150,14155,14160],{},[1833,14127,14128,14129],{},"Exponenciální ",[1115,14130,14132],{"className":14131},[1144],[1146,14133,14134],{"xmlns":1148},[1150,14135,14136,14147],{},[1153,14137,14138,14140,14142,14145],{},[1159,14139,12386],{},[1289,14141,1484],{"stretchy":1483},[1159,14143,14144],{},"δ",[1289,14146,1495],{"stretchy":1483},[1167,14148,14149],{"encoding":1169},"E(\\delta)",[1833,14151,14152],{},[3087,14153,14154],{},"dexp(k, 1\u002Fdelta)",[1833,14156,14157],{},[3087,14158,14159],{},"pexp(k, 1\u002Fdelta)",[1833,14161,14162],{},[3087,14163,14164],{},"pexp(k, 1\u002Fdelta, FALSE)",[1103,14166,14168,14175],{"className":14167,"dataCallout":6032},[1106,6031],[1110,14169,14171,14174],{"className":14170},[1113],[1115,14172],{"className":14173,"ariaHidden":1121},[1118,6039,1120],"Exponenciální rozdělení: R bere intenzitu, ne střední hodnotu",[1110,14176,14177,14178,14181,14182,14196,14197,13349,14200,1269],{},"R parametrizuje exponenciální rozdělení intenzitou (",[3087,14179,14180],{},"rate","). Je-li ",[1115,14183,14185],{"className":14184},[1144],[1146,14186,14187],{"xmlns":1148},[1150,14188,14189,14193],{},[1153,14190,14191],{},[1159,14192,14144],{},[1167,14194,14195],{"encoding":1169},"\\delta"," střední doba do události, do R se dosazuje ",[3087,14198,14199],{},"1\u002Fdelta",[3087,14201,14202],{},"delta",[1110,14204,14205,14206,14238,14239,14257],{},"V R (pravděpodobnostní a distribuční funkce diskrétní náhodné veličiny ",[1115,14207,14209],{"className":14208},[1144],[1146,14210,14211],{"xmlns":1148},[1150,14212,14213,14235],{},[1153,14214,14215,14217,14219,14221,14223,14225,14228,14230,14233],{},[1159,14216,11031],{},[1289,14218,13484],{},[1159,14220,1432],{},[1159,14222,1487],{},[1289,14224,1484],{"stretchy":1483},[1163,14226,14227],{},"5",[1289,14229,11193],{"separator":1121},[1163,14231,14232],{},"0,95",[1289,14234,1495],{"stretchy":1483},[1167,14236,14237],{"encoding":1169},"X \\sim Bi(5; 0{,}95)",", a pravděpodobnost, že u exponenciálního rozdělení se střední hodnotou ",[1115,14240,14242],{"className":14241},[1144],[1146,14243,14244],{"xmlns":1148},[1150,14245,14246,14254],{},[1153,14247,14248,14250,14252],{},[1159,14249,14144],{},[1289,14251,1591],{},[1163,14253,14227],{},[1167,14255,14256],{"encoding":1169},"\\delta = 5"," nastane událost do 3 jednotek času):",[3311,14259,14261],{"className":3313,"code":14260,"language":71,"meta":3315,"style":3315},"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",[3087,14262,14263,14277,14309,14338,14343,14352],{"__ignoreMap":3315},[1115,14264,14265,14267,14269,14272,14274],{"class":3320,"line":10},[1115,14266,11019],{"class":3323},[1115,14268,3328],{"class":3327},[1115,14270,14271],{"class":3343}," 0",[1115,14273,1567],{"class":3327},[1115,14275,14276],{"class":3343},"5\n",[1115,14278,14279,14282,14284,14287,14289,14291,14293,14296,14298,14301,14303,14305,14307],{"class":3320,"line":27},[1115,14280,14281],{"class":3331},"round",[1115,14283,1484],{"class":3335},[1115,14285,14286],{"class":3331},"dbinom",[1115,14288,1484],{"class":3335},[1115,14290,11019],{"class":3323},[1115,14292,1405],{"class":3327},[1115,14294,14295],{"class":3343}," 5",[1115,14297,1405],{"class":3327},[1115,14299,14300],{"class":3343}," 0.95",[1115,14302,1495],{"class":3335},[1115,14304,1405],{"class":3327},[1115,14306,3419],{"class":3343},[1115,14308,3520],{"class":3335},[1115,14310,14311,14313,14315,14318,14320,14322,14324,14326,14328,14330,14332,14334,14336],{"class":3320,"line":148},[1115,14312,14281],{"class":3331},[1115,14314,1484],{"class":3335},[1115,14316,14317],{"class":3331},"pbinom",[1115,14319,1484],{"class":3335},[1115,14321,11019],{"class":3323},[1115,14323,1405],{"class":3327},[1115,14325,14295],{"class":3343},[1115,14327,1405],{"class":3327},[1115,14329,14300],{"class":3343},[1115,14331,1495],{"class":3335},[1115,14333,1405],{"class":3327},[1115,14335,3419],{"class":3343},[1115,14337,3520],{"class":3335},[1115,14339,14340],{"class":3320,"line":111},[1115,14341,14342],{"emptyLinePlaceholder":6298},"\n",[1115,14344,14345,14347,14349],{"class":3320,"line":96},[1115,14346,14202],{"class":3323},[1115,14348,3328],{"class":3327},[1115,14350,14351],{"class":3343}," 5\n",[1115,14353,14354,14356,14358,14361,14363,14365,14367,14370,14372,14374,14377,14380,14382,14384,14386],{"class":3320,"line":89},[1115,14355,14281],{"class":3331},[1115,14357,1484],{"class":3335},[1115,14359,14360],{"class":3331},"pexp",[1115,14362,1484],{"class":3335},[1115,14364,3209],{"class":3343},[1115,14366,1405],{"class":3327},[1115,14368,14369],{"class":3323}," rate",[1115,14371,3416],{"class":3327},[1115,14373,4260],{"class":3343},[1115,14375,14376],{"class":3327}," \u002F",[1115,14378,14379],{"class":3323}," delta",[1115,14381,1495],{"class":3335},[1115,14383,1405],{"class":3327},[1115,14385,3419],{"class":3343},[1115,14387,3520],{"class":3335},[3311,14389,14392],{"className":14390,"code":14391,"language":3542,"meta":3315},[3540],"[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",[3087,14393,14391],{"__ignoreMap":3315},[1310,14395,14397],{"id":14396},"studentovo-pearsonovo-a-fisherovo-snedecorovo-rozdělení","Studentovo, Pearsonovo a Fisherovo-Snedecorovo rozdělení",[1110,14399,14400,14401,14404],{},"Tato tři rozdělení mají statistiky, které se dále používají při konstrukci intervalů spolehlivosti a testování hypotéz (viz ",[1318,14402,141],{"className":14403,"dataFsResolvedFilePath":1329,"href":1330},[1321],") — na rozdíl od normálního rozdělení se v příkladech této kapitoly samostatně nepočítají, jsou to nástroje pro další kapitoly.",[1110,14406,14407,3571,14410,14423],{},[1131,14408,14409],{},"Studentovo rozdělení",[1115,14411,14413],{"className":14412},[1144],[1146,14414,14415],{"xmlns":1148},[1150,14416,14417,14421],{},[1153,14418,14419],{},[1159,14420,11559],{},[1167,14422,11559],{"encoding":1169}," stupni volnosti má hustotu pravděpodobnosti",[1115,14425,14427],{"className":14426},[1144],[1146,14428,14429],{"xmlns":1148,"display":1573},[1150,14430,14431,14527],{},[1153,14432,14433,14435,14437,14439,14441,14443,14475,14513,14515,14517,14519,14521,14525],{},[1159,14434,11070],{},[1289,14436,1484],{"stretchy":1483},[1159,14438,11019],{},[1289,14440,1495],{"stretchy":1483},[1289,14442,1591],{},[2355,14444,14445,14447],{},[1163,14446,1402],{},[1153,14448,14449,14451,14471],{},[1159,14450,1432],{},[1153,14452,14453,14455,14461,14463,14469],{},[1289,14454,1484],{"fence":1121},[2355,14456,14457,14459],{},[1163,14458,1402],{},[1163,14460,1189],{},[1289,14462,1405],{"separator":1121},[2355,14464,14465,14467],{},[1159,14466,11559],{},[1163,14468,1189],{},[1289,14470,1495],{"fence":1121},[4072,14472,14473],{},[1159,14474,11559],{},[1182,14476,14477,14497],{},[1153,14478,14479,14481,14483,14485,14495],{},[1289,14480,1484],{"fence":1121},[1163,14482,1402],{},[1289,14484,5096],{},[2355,14486,14487,14493],{},[1182,14488,14489,14491],{},[1159,14490,11019],{},[1163,14492,1189],{},[1159,14494,11559],{},[1289,14496,1495],{"fence":1121},[1153,14498,14499,14501],{},[1289,14500,2681],{},[2355,14502,14503,14511],{},[1153,14504,14505,14507,14509],{},[1159,14506,11559],{},[1289,14508,5096],{},[1163,14510,1402],{},[1163,14512,1189],{},[1289,14514,1405],{"separator":1121},[1621,14516],{"width":1623},[1159,14518,11019],{},[1289,14520,11318],{},[1159,14522,14524],{"mathvariant":14523},"double-struck","R",[1289,14526,1405],{"separator":1121},[1167,14528,14529],{"encoding":1169},"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},",[1110,14531,4126,14532,14545,14546,14559,14560,14573],{},[1115,14533,14535],{"className":14534},[1144],[1146,14536,14537],{"xmlns":1148},[1150,14538,14539,14543],{},[1153,14540,14541],{},[1159,14542,1432],{},[1167,14544,1432],{"encoding":1169}," je funkce beta. Je symetrické kolem nuly; číslo ",[1115,14547,14549],{"className":14548},[1144],[1146,14550,14551],{"xmlns":1148},[1150,14552,14553,14557],{},[1153,14554,14555],{},[1159,14556,11559],{},[1167,14558,11559],{"encoding":1169}," určuje tvar křivky — s rostoucím ",[1115,14561,14563],{"className":14562},[1144],[1146,14564,14565],{"xmlns":1148},[1150,14566,14567,14571],{},[1153,14568,14569],{},[1159,14570,11559],{},[1167,14572,11559],{"encoding":1169}," se rozdělení blíží normálnímu.",[1110,14575,14576,3571,14579,14592],{},[1131,14577,14578],{},"Pearsonovo (chí-kvadrát) rozdělení",[1115,14580,14582],{"className":14581},[1144],[1146,14583,14584],{"xmlns":1148},[1150,14585,14586,14590],{},[1153,14587,14588],{},[1159,14589,11559],{},[1167,14591,11559],{"encoding":1169}," stupni volnosti:",[1115,14594,14596],{"className":14595},[1144],[1146,14597,14598],{"xmlns":1148,"display":1573},[1150,14599,14600,14685],{},[1153,14601,14602,14604,14606,14608,14610,14612,14643,14659,14673,14675,14677,14679,14681,14683],{},[1159,14603,11070],{},[1289,14605,1484],{"stretchy":1483},[1159,14607,11019],{},[1289,14609,1495],{"stretchy":1483},[1289,14611,1591],{},[2355,14613,14614,14616],{},[1163,14615,1402],{},[1153,14617,14618,14630,14633,14635,14637,14639,14641],{},[1182,14619,14620,14622],{},[1163,14621,1189],{},[1153,14623,14624,14626,14628],{},[1159,14625,11559],{},[1159,14627,4223],{"mathvariant":1734},[1163,14629,1189],{},[1159,14631,14632],{"mathvariant":1734},"Γ",[1289,14634,1484],{"stretchy":1483},[1159,14636,11559],{},[1159,14638,4223],{"mathvariant":1734},[1163,14640,1189],{},[1289,14642,1495],{"stretchy":1483},[1182,14644,14645,14647],{},[1159,14646,11019],{},[1153,14648,14649,14651,14653,14655,14657],{},[1159,14650,11559],{},[1159,14652,4223],{"mathvariant":1734},[1163,14654,1189],{},[1289,14656,2681],{},[1163,14658,1402],{},[1182,14660,14661,14663],{},[1159,14662,12893],{},[1153,14664,14665,14667,14669,14671],{},[1289,14666,2681],{},[1159,14668,11019],{},[1159,14670,4223],{"mathvariant":1734},[1163,14672,1189],{},[1289,14674,1405],{"separator":1121},[1621,14676],{"width":1623},[1159,14678,11019],{},[1289,14680,1291],{},[1163,14682,1165],{},[1289,14684,1405],{"separator":1121},[1167,14686,14687],{"encoding":1169},"f(x) = \\frac{1}{2^{k\u002F2}\\Gamma(k\u002F2)} x^{k\u002F2-1} e^{-x\u002F2}, \\qquad x > 0,",[1110,14689,4126,14690,14704],{},[1115,14691,14693],{"className":14692},[1144],[1146,14694,14695],{"xmlns":1148},[1150,14696,14697,14701],{},[1153,14698,14699],{},[1159,14700,14632],{"mathvariant":1734},[1167,14702,14703],{"encoding":1169},"\\Gamma"," je funkce gama.",[1110,14706,14707,14710,14711,5360,14729,1567],{},[1131,14708,14709],{},"Fisherovo-Snedecorovo rozdělení"," se stupni volnosti ",[1115,14712,14714],{"className":14713},[1144],[1146,14715,14716],{"xmlns":1148},[1150,14717,14718,14726],{},[1153,14719,14720],{},[1156,14721,14722,14724],{},[1159,14723,11559],{},[1163,14725,1402],{},[1167,14727,14728],{"encoding":1169},"k_1",[1115,14730,14732],{"className":14731},[1144],[1146,14733,14734],{"xmlns":1148},[1150,14735,14736,14744],{},[1153,14737,14738],{},[1156,14739,14740,14742],{},[1159,14741,11559],{},[1163,14743,1189],{},[1167,14745,14746],{"encoding":1169},"k_2",[1115,14748,14750],{"className":14749},[1144],[1146,14751,14752],{"xmlns":1148,"display":1573},[1150,14753,14754,14919],{},[1153,14755,14756,14758,14760,14762,14764,14766,14802,14836,14856,14908,14910,14912,14914,14916],{},[1159,14757,11070],{},[1289,14759,1484],{"stretchy":1483},[1159,14761,11019],{},[1289,14763,1495],{"stretchy":1483},[1289,14765,1591],{},[2355,14767,14768,14770],{},[1163,14769,1402],{},[1153,14771,14772,14774],{},[1159,14773,1432],{},[1153,14775,14776,14778,14788,14790,14800],{},[1289,14777,1484],{"fence":1121},[2355,14779,14780,14786],{},[1156,14781,14782,14784],{},[1159,14783,11559],{},[1163,14785,1402],{},[1163,14787,1189],{},[1289,14789,1405],{"separator":1121},[2355,14791,14792,14798],{},[1156,14793,14794,14796],{},[1159,14795,11559],{},[1163,14797,1189],{},[1163,14799,1189],{},[1289,14801,1495],{"fence":1121},[1182,14803,14804,14824],{},[1153,14805,14806,14808,14822],{},[1289,14807,1484],{"fence":1121},[2355,14809,14810,14816],{},[1156,14811,14812,14814],{},[1159,14813,11559],{},[1163,14815,1402],{},[1156,14817,14818,14820],{},[1159,14819,11559],{},[1163,14821,1189],{},[1289,14823,1495],{"fence":1121},[1153,14825,14826,14832,14834],{},[1156,14827,14828,14830],{},[1159,14829,11559],{},[1163,14831,1402],{},[1159,14833,4223],{"mathvariant":1734},[1163,14835,1189],{},[1182,14837,14838,14840],{},[1159,14839,11019],{},[1153,14841,14842,14848,14850,14852,14854],{},[1156,14843,14844,14846],{},[1159,14845,11559],{},[1163,14847,1402],{},[1159,14849,4223],{"mathvariant":1734},[1163,14851,1189],{},[1289,14853,2681],{},[1163,14855,1402],{},[1182,14857,14858,14884],{},[1153,14859,14860,14862,14864,14866,14880,14882],{},[1289,14861,1484],{"fence":1121},[1163,14863,1402],{},[1289,14865,5096],{},[2355,14867,14868,14874],{},[1156,14869,14870,14872],{},[1159,14871,11559],{},[1163,14873,1402],{},[1156,14875,14876,14878],{},[1159,14877,11559],{},[1163,14879,1189],{},[1159,14881,11019],{},[1289,14883,1495],{"fence":1121},[1153,14885,14886,14888],{},[1289,14887,2681],{},[2355,14889,14890,14906],{},[1153,14891,14892,14898,14900],{},[1156,14893,14894,14896],{},[1159,14895,11559],{},[1163,14897,1402],{},[1289,14899,5096],{},[1156,14901,14902,14904],{},[1159,14903,11559],{},[1163,14905,1189],{},[1163,14907,1189],{},[1289,14909,1405],{"separator":1121},[1621,14911],{"width":1623},[1159,14913,11019],{},[1289,14915,1291],{},[1163,14917,14918],{},"0.",[1167,14920,14921],{"encoding":1169},"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.",[1110,14923,14924],{},[4002,14925],{"alt":14926,"className":14927,"src":14928},"mask-nv-specialni-rozdeleni",[1321,4006],"\u002Fwiki-assets\u002Fmask-nv-specialni-rozdeleni.png",[13247,14930],{"spec":14931},"{\"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\":[]}",[1110,14933,14934],{},"R funkce pro tato tři rozdělení:",[1710,14936,14937,14951],{},[1713,14938,14939],{},[1716,14940,14941,14943,14946,14948],{},[1719,14942,13842],{},[1719,14944,14945],{},"hustota",[1719,14947,11002],{},[1719,14949,14950],{},"kvantil",[1828,14952,14953,14993,15037],{},[1716,14954,14955,14978,14983,14988],{},[1833,14956,14957,14958],{},"Studentovo ",[1115,14959,14961],{"className":14960},[1144],[1146,14962,14963],{"xmlns":1148},[1150,14964,14965,14975],{},[1153,14966,14967,14969,14971,14973],{},[1159,14968,11443],{},[1289,14970,1484],{"stretchy":1483},[1159,14972,11559],{},[1289,14974,1495],{"stretchy":1483},[1167,14976,14977],{"encoding":1169},"t(k)",[1833,14979,14980],{},[3087,14981,14982],{},"dt(x, df = k)",[1833,14984,14985],{},[3087,14986,14987],{},"pt(x, df = k)",[1833,14989,14990],{},[3087,14991,14992],{},"qt(p, df = k)",[1716,14994,14995,15022,15027,15032],{},[1833,14996,14997,14998],{},"Pearsonovo ",[1115,14999,15001],{"className":15000},[1144],[1146,15002,15003],{"xmlns":1148},[1150,15004,15005,15019],{},[1153,15006,15007,15013,15015,15017],{},[1182,15008,15009,15011],{},[1159,15010,1186],{},[1163,15012,1189],{},[1289,15014,1484],{"stretchy":1483},[1159,15016,11559],{},[1289,15018,1495],{"stretchy":1483},[1167,15020,15021],{"encoding":1169},"\\chi^2(k)",[1833,15023,15024],{},[3087,15025,15026],{},"dchisq(x, df = k)",[1833,15028,15029],{},[3087,15030,15031],{},"pchisq(x, df = k)",[1833,15033,15034],{},[3087,15035,15036],{},"qchisq(p, df = k)",[1716,15038,15039,15074,15079,15084],{},[1833,15040,15041,15042],{},"Fisherovo-Snedecorovo ",[1115,15043,15045],{"className":15044},[1144],[1146,15046,15047],{"xmlns":1148},[1150,15048,15049,15071],{},[1153,15050,15051,15053,15055,15061,15063,15069],{},[1159,15052,11014],{},[1289,15054,1484],{"stretchy":1483},[1156,15056,15057,15059],{},[1159,15058,11559],{},[1163,15060,1402],{},[1289,15062,1405],{"separator":1121},[1156,15064,15065,15067],{},[1159,15066,11559],{},[1163,15068,1189],{},[1289,15070,1495],{"stretchy":1483},[1167,15072,15073],{"encoding":1169},"F(k_1, k_2)",[1833,15075,15076],{},[3087,15077,15078],{},"df(x, df1 = k1, df2 = k2)",[1833,15080,15081],{},[3087,15082,15083],{},"pf(x, df1 = k1, df2 = k2)",[1833,15085,15086],{},[3087,15087,15088],{},"qf(p, df1 = k1, df2 = k2)",[1110,15090,15091],{},"V R (97,5%-ní kvantil Studentova rozdělení s 9 stupni volnosti, 95%-ní kvantily Pearsonova a Fisherova-Snedecorova rozdělení):",[3311,15093,15095],{"className":3313,"code":15094,"language":71,"meta":3315,"style":3315},"qt(0.975, df = 9)\nqchisq(0.95, df = 9)\nqf(0.95, df1 = 3, df2 = 10)\n",[3087,15096,15097,15118,15138],{"__ignoreMap":3315},[1115,15098,15099,15102,15104,15106,15108,15111,15113,15116],{"class":3320,"line":10},[1115,15100,15101],{"class":3331},"qt",[1115,15103,1484],{"class":3335},[1115,15105,13390],{"class":3343},[1115,15107,1405],{"class":3327},[1115,15109,15110],{"class":3323}," df",[1115,15112,3416],{"class":3327},[1115,15114,15115],{"class":3343}," 9",[1115,15117,3520],{"class":3335},[1115,15119,15120,15123,15125,15128,15130,15132,15134,15136],{"class":3320,"line":27},[1115,15121,15122],{"class":3331},"qchisq",[1115,15124,1484],{"class":3335},[1115,15126,15127],{"class":3343},"0.95",[1115,15129,1405],{"class":3327},[1115,15131,15110],{"class":3323},[1115,15133,3416],{"class":3327},[1115,15135,15115],{"class":3343},[1115,15137,3520],{"class":3335},[1115,15139,15140,15143,15145,15147,15149,15152,15154,15157,15159,15162,15164,15166],{"class":3320,"line":148},[1115,15141,15142],{"class":3331},"qf",[1115,15144,1484],{"class":3335},[1115,15146,15127],{"class":3343},[1115,15148,1405],{"class":3327},[1115,15150,15151],{"class":3323}," df1",[1115,15153,3416],{"class":3327},[1115,15155,15156],{"class":3343}," 3",[1115,15158,1405],{"class":3327},[1115,15160,15161],{"class":3323}," df2",[1115,15163,3416],{"class":3327},[1115,15165,13778],{"class":3343},[1115,15167,3520],{"class":3335},[3311,15169,15172],{"className":15170,"code":15171,"language":3542,"meta":3315},[3540],"[1] 2.262157\n[1] 16.91898\n[1] 3.708265\n",[3087,15173,15171],{"__ignoreMap":3315},[1310,15175,6027],{"id":6026},[1124,15177,15178,15264,15314],{},[1127,15179,15180,15183,15184,15211,15212,4223,15214,4223,15216,15218,15219,15239,15240,15263],{},[1131,15181,15182],{},"Rozptyl vs. směrodatná odchylka v R."," Zápis ",[1115,15185,15187],{"className":15186},[1144],[1146,15188,15189],{"xmlns":1148},[1150,15190,15191,15209],{},[1153,15192,15193,15195,15197,15199,15201,15207],{},[1159,15194,11185],{},[1289,15196,1484],{"stretchy":1483},[1159,15198,11190],{},[1289,15200,11193],{"separator":1121},[1182,15202,15203,15205],{},[1159,15204,11198],{},[1163,15206,1189],{},[1289,15208,1495],{"stretchy":1483},[1167,15210,11205],{"encoding":1169}," používá rozptyl, ale ",[3087,15213,11209],{},[3087,15215,11212],{},[3087,15217,11215],{}," očekávají směrodatnou odchylku. Dosazení rozptylu místo ",[1115,15220,15222],{"className":15221},[1144],[1146,15223,15224],{"xmlns":1148},[1150,15225,15226,15236],{},[1153,15227,15228],{},[4072,15229,15230],{},[1182,15231,15232,15234],{},[1159,15233,11198],{},[1163,15235,1189],{},[1167,15237,15238],{"encoding":1169},"\\sqrt{\\sigma^2}"," dává jiný — a pro ",[1115,15241,15243],{"className":15242},[1144],[1146,15244,15245],{"xmlns":1148},[1150,15246,15247,15260],{},[1153,15248,15249,15255,15258],{},[1182,15250,15251,15253],{},[1159,15252,11198],{},[1163,15254,1189],{},[1289,15256,15257],{"mathvariant":1734},"≠",[1163,15259,1402],{},[1167,15261,15262],{"encoding":1169},"\\sigma^2 \\ne 1"," výrazně odlišný — výsledek (viz příklad s ampulkou).",[1127,15265,15266,15293,15294,15313],{},[1131,15267,15268,15292],{},[1115,15269,15271],{"className":15270},[1144],[1146,15272,15273],{"xmlns":1148},[1150,15274,15275,15289],{},[1153,15276,15277,15279,15281,15283,15285,15287],{},[1159,15278,11026],{},[1289,15280,1484],{"stretchy":1483},[1159,15282,11031],{},[1289,15284,1591],{},[1159,15286,11019],{},[1289,15288,1495],{"stretchy":1483},[1167,15290,15291],{"encoding":1169},"P(X=x)"," u spojité veličiny je vždy 0."," Hustota ",[1115,15295,15297],{"className":15296},[1144],[1146,15298,15299],{"xmlns":1148},[1150,15300,15301,15311],{},[1153,15302,15303,15305,15307,15309],{},[1159,15304,11070],{},[1289,15306,1484],{"stretchy":1483},[1159,15308,11019],{},[1289,15310,1495],{"stretchy":1483},[1167,15312,11100],{"encoding":1169}," sama o sobě pravděpodobnost neudává — pravděpodobnost dává až plocha pod křivkou na intervalu.",[1127,15315,15316,1254,15319,15336,15337,15354,15355,15358,15359,1269],{},[1131,15317,15318],{},"Záměna stupňů volnosti u Fisherova-Snedecorova rozdělení.",[1115,15320,15322],{"className":15321},[1144],[1146,15323,15324],{"xmlns":1148},[1150,15325,15326,15334],{},[1153,15327,15328],{},[1156,15329,15330,15332],{},[1159,15331,11559],{},[1163,15333,1402],{},[1167,15335,14728],{"encoding":1169}," (čitatel) a ",[1115,15338,15340],{"className":15339},[1144],[1146,15341,15342],{"xmlns":1148},[1150,15343,15344,15352],{},[1153,15345,15346],{},[1156,15347,15348,15350],{},[1159,15349,11559],{},[1163,15351,1189],{},[1167,15353,14746],{"encoding":1169}," (jmenovatel) nejsou zaměnitelné — ",[3087,15356,15357],{},"qf(p, df1, df2)"," dá jiný výsledek než ",[3087,15360,15361],{},"qf(p, df2, df1)",[1310,15363,6215],{"id":6214},[1124,15365,15366,15371,15376,15381,15387,15394,15400],{},[1127,15367,15368],{},[1318,15369,1324],{"className":15370,"dataFsResolvedFilePath":1322,"href":1323},[1321],[1127,15372,15373],{},[1318,15374,886],{"className":15375,"dataFsResolvedFilePath":6234,"href":6235},[1321],[1127,15377,15378],{},[1318,15379,141],{"className":15380,"dataFsResolvedFilePath":1329,"href":1330},[1321],[1127,15382,15383],{},[1318,15384,15386],{"className":15385,"dataFsResolvedFilePath":6250,"href":6251},[1321],"regresni-a-korelacni-analyza",[1127,15388,15389],{},[1318,15390,716],{"className":15391,"dataFsResolvedFilePath":15392,"href":15393},[1321],"topics\u002Fkontingencni-tabulky.md","\u002Fwiki\u002Fkontingencni-tabulky",[1127,15395,15396],{},[1318,15397,15399],{"className":15398,"dataFsResolvedFilePath":6258,"href":6259},[1321],"regulacni-diagramy-a-indexy-zpusobilosti",[1127,15401,15402],{},[1318,15403,6268],{"className":15404,"dataFsResolvedFilePath":6266,"href":6267},[1321],[1310,15406,6271],{"id":934},[1110,15408,6274,15409,6279],{},[6276,15410,6278],{},[6281,15412,15413],{},"html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: 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.sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}",{"title":3315,"searchDepth":27,"depth":27,"links":15415},[15416,15417,15418,15419,15420,15421,15422,15423,15424,15425],{"id":11264,"depth":27,"text":11265},{"id":11572,"depth":27,"text":11573},{"id":12258,"depth":27,"text":12259},{"id":12367,"depth":27,"text":12368},{"id":12804,"depth":27,"text":11173},{"id":13806,"depth":27,"text":13807},{"id":14396,"depth":27,"text":14397},{"id":6026,"depth":27,"text":6027},{"id":6214,"depth":27,"text":6215},{"id":934,"depth":27,"text":6271},{},"\u002Ftopics\u002Fnahodne-veliciny-a-rozdeleni",{"title":6244,"description":3315},[15430,15431,15432],"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":15437,"title":6236,"body":15438,"course":23,"courses":6294,"created":6295,"description":3315,"extension":6296,"meta":20189,"navigation":6298,"path":20190,"seo":20191,"sources":20192,"stem":20199,"tags":20200,"type":6306,"updated":6295,"__hash__":20201},"topics\u002Ftopics\u002Fpopisna-statistika.md",{"type":1096,"value":15439,"toc":20180},[15440,15443,15537,15541,15551,15677,15684,15695,15699,15742,15747,15849,15859,15864,16003,16079,16083,16184,16265,16272,16343,16362,16364,16580,16586,16596,16603,16606,16660,16666,16676,16689,16835,16838,16851,17170,17176,17179,17183,17262,17296,17325,17327,17405,17411,17472,17479,17492,17569,17685,17735,17748,17903,17909,17936,17940,17965,17968,18181,18249,18350,18357,18370,18873,18879,18911,19171,19324,19435,19464,19470,19477,19483,19496,19926,19932,19935,19937,20132,20134,20171,20173,20177],[1099,15441,6236],{"id":15442},"popisná-statistika-a-datové-soubory",[1103,15444,15446,15452],{"className":15445,"dataCallout":1108},[1106,1107],[1110,15447,15449,1122],{"className":15448},[1113],[1115,15450],{"className":15451,"ariaHidden":1121},[1118,1119,1120],[1124,15453,15454,15457,15460,15487,15534],{},[1127,15455,15456],{},"Rozlišit základní a výběrový soubor, typ statistického znaku (kvantitativní\u002Fkvalitativní, diskrétní\u002Fspojitý) a požadavek reprezentativity a nezávislého výběru.",[1127,15458,15459],{},"Spočítat výběrový průměr, rozptyl, směrodatnou odchylku a variační rozpětí; interpretovat je jako bodové odhady charakteristik náhodné veličiny.",[1127,15461,15462,15463,1269],{},"Určit medián a kvartily a číst empirickou distribuční funkci ",[1115,15464,15466],{"className":15465},[1144],[1146,15467,15468],{"xmlns":1148},[1150,15469,15470,15484],{},[1153,15471,15472,15478,15480,15482],{},[1156,15473,15474,15476],{},[1159,15475,11014],{},[1159,15477,1287],{},[1289,15479,1484],{"stretchy":1483},[1159,15481,11019],{},[1289,15483,1495],{"stretchy":1483},[1167,15485,15486],{"encoding":1169},"F_n(x)",[1127,15488,15489,15490,15533],{},"Roztřídit velký datový soubor do tříd (intervalové rozdělení četností), sestavit tabulku ",[1115,15491,15493],{"className":15492},[1144],[1146,15494,15495],{"xmlns":1148},[1150,15496,15497,15530],{},[1153,15498,15499,15506,15508,15514,15516,15522,15524],{},[1156,15500,15501,15504],{},[1159,15502,15503],{},"I",[1159,15505,1492],{},[1289,15507,1405],{"separator":1121},[1156,15509,15510,15512],{},[1159,15511,13226],{},[1159,15513,1492],{},[1289,15515,1405],{"separator":1121},[1156,15517,15518,15520],{},[1159,15519,11070],{},[1159,15521,1492],{},[1289,15523,1405],{"separator":1121},[1156,15525,15526,15528],{},[1159,15527,1110],{},[1159,15529,1492],{},[1167,15531,15532],{"encoding":1169},"I_j, Z_j, f_j, p_j"," a nakreslit histogram.",[1127,15535,15536],{},"Z histogramu odhadnout zákon rozdělení dat; formální test shody patří do testování hypotéz.",[1310,15538,15540],{"id":15539},"základní-pojmy","Základní pojmy",[1110,15542,15543,15546,15547,15550],{},[1318,15544,1324],{"className":15545,"dataFsResolvedFilePath":1322,"href":1323},[1321]," pracuje s ",[1131,15548,15549],{},"datovými soubory"," — konkrétními hodnotami, které popisují vlastnost zkoumaných prvků.",[1124,15552,15553,15559,15583,15589,15664],{},[1127,15554,15555,15558],{},[1131,15556,15557],{},"Základní soubor"," — množina prvků, na nichž provádíme šetření (např. všichni výdělečně činní obyvatelé ČR).",[1127,15560,15561,15564,15565],{},[1131,15562,15563],{},"Statistický znak"," — funkce, která vyjadřuje určitou vlastnost prvku (např. velikost platu). Znaky dělíme na:\n",[1124,15566,15567,15578],{},[1127,15568,15569,15571,15572,15574,15575,15577],{},[1131,15570,1342],{}," (vyjádřitelné číslem) — dále ",[1131,15573,10991],{}," (spočetně mnoho hodnot) nebo ",[1131,15576,10995],{}," (libovolná hodnota v intervalu);",[1127,15579,15580,15582],{},[1131,15581,1335],{}," (vyjádřitelné slovně).",[1127,15584,15585,15588],{},[1131,15586,15587],{},"Výběrový soubor"," — podmnožina prvků základního souboru, na níž znak skutečně zjišťujeme (např. 5 náhodně vybraných obyvatel).",[1127,15590,15591,15594,15595,1269],{},[1131,15592,15593],{},"Datový soubor"," — n-tice naměřených hodnot zkoumaného znaku, např. ",[1115,15596,15598],{"className":15597},[1144],[1146,15599,15600],{"xmlns":1148},[1150,15601,15602,15661],{},[1153,15603,15604,15606,15608,15610,15613,15615,15618,15621,15623,15626,15628,15630,15633,15635,15638,15640,15642,15644,15646,15648,15650,15652,15654,15656,15659],{},[1289,15605,1484],{"stretchy":1483},[1163,15607,3167],{},[2525,15609,2527],{},[1163,15611,15612],{},"500",[1289,15614,1405],{"separator":1121},[2525,15616,15617],{}," ",[1163,15619,15620],{},"38",[2525,15622,2527],{},[1163,15624,15625],{},"000",[1289,15627,1405],{"separator":1121},[2525,15629,15617],{},[1163,15631,15632],{},"37",[2525,15634,2527],{},[1163,15636,15637],{},"800",[1289,15639,1405],{"separator":1121},[2525,15641,15617],{},[1163,15643,13657],{},[2525,15645,2527],{},[1163,15647,15625],{},[1289,15649,1405],{"separator":1121},[2525,15651,15617],{},[1163,15653,3175],{},[2525,15655,2527],{},[1163,15657,15658],{},"200",[1289,15660,1495],{"stretchy":1483},[1167,15662,15663],{"encoding":1169},"(29\\,500,\\ 38\\,000,\\ 37\\,800,\\ 41\\,000,\\ 31\\,200)",[1127,15665,15666,15667,2568,15670,5360,15673,15676],{},"Podle počtu sledovaných znaků rozlišujeme ",[1131,15668,15669],{},"jednorozměrné",[1131,15671,15672],{},"dvourozměrné",[1131,15674,15675],{},"vícerozměrné"," datové soubory.",[1110,15678,15679],{},[4002,15680],{"alt":15681,"className":15682,"src":15683},"mask-ilu-zakladni-soubor-vyber",[1321,4006],"\u002Fwiki-assets\u002Fmask-ilu-zakladni-soubor-vyber.png",[1110,15685,15686,15687,15690,15691,15694],{},"Aby výběrový soubor dobře vypovídal o základním souboru, měl by být ",[1131,15688,15689],{},"reprezentativní"," (podobný základnímu souboru svým složením). Není-li to možné zajistit přímo, volí se prvky do výběru náhodně — ",[1131,15692,15693],{},"nezávislý výběr",". Bez náhodnosti výběru nelze vlastnosti základního souboru správně vystihnout.",[1310,15696,15698],{"id":15697},"empirické-charakteristiky","Empirické charakteristiky",[1110,15700,15701,15702,15705,15706,15709,15710,15723,15724,15727,15728,15741],{},"Zpracováním datového souboru získáme ",[1131,15703,15704],{},"empirické charakteristiky"," a odhad ",[1131,15707,15708],{},"zákona rozdělení"," zkoumané náhodné veličiny ",[1115,15711,15713],{"className":15712},[1144],[1146,15714,15715],{"xmlns":1148},[1150,15716,15717,15721],{},[1153,15718,15719],{},[1159,15720,11031],{},[1167,15722,11031],{"encoding":1169},". Jde o ",[1131,15725,15726],{},"bodové odhady"," charakteristik ",[1115,15729,15731],{"className":15730},[1144],[1146,15732,15733],{"xmlns":1148},[1150,15734,15735,15739],{},[1153,15736,15737],{},[1159,15738,11031],{},[1167,15740,11031],{"encoding":1169},"; ruční výpočet podle vzorců níže je potřeba jen bez dostupného softwaru.",[1110,15743,15744],{},[1131,15745,15746],{},"Míry polohy",[1115,15748,15750],{"className":15749},[1144],[1146,15751,15752],{"xmlns":1148,"display":1573},[1150,15753,15754,15846],{},[1153,15755,15756,15763,15765,15771,15785,15791,15793],{},[2339,15757,15758,15760],{"accent":1121},[1159,15759,11019],{},[1289,15761,15762],{},"ˉ",[1289,15764,1591],{},[2355,15766,15767,15769],{},[1163,15768,1402],{},[1159,15770,1287],{},[1593,15772,15773,15775,15783],{},[1289,15774,1597],{},[1153,15776,15777,15779,15781],{},[1159,15778,1487],{},[1289,15780,1591],{},[1163,15782,1402],{},[1159,15784,1287],{},[1156,15786,15787,15789],{},[1159,15788,11019],{},[1159,15790,1487],{},[1621,15792],{"width":1623},[1153,15794,15795,15798,15805,15808,15815,15818,15824,15827,15835,15837,15843],{},[2525,15796,15797],{},"(v",[2339,15799,15800,15802],{"accent":1121},[2525,15801,11429],{},[1289,15803,15804],{},"ˊ",[2525,15806,15807],{},"b",[2339,15809,15810,15812],{"accent":1121},[2525,15811,12893],{},[1289,15813,15814],{},"ˇ",[2525,15816,15817],{},"rov",[2339,15819,15820,15822],{"accent":1121},[2525,15821,11429],{},[1289,15823,15804],{},[2525,15825,15826],{}," pr",[2339,15828,15829,15832],{"accent":1121},[2525,15830,15831],{},"u",[1289,15833,15834],{},"˚",[2525,15836,4090],{},[2339,15838,15839,15841],{"accent":1121},[2525,15840,12893],{},[1289,15842,15814],{},[2525,15844,15845],{},"r)",[1167,15847,15848],{"encoding":1169},"\\bar{x} = \\frac{1}{n}\\sum_{i=1}^{n} x_i \\qquad \\text{(výběrový průměr)}",[1110,15850,15851,15852,5360,15855,15858],{},"Dalšími mírami polohy jsou ",[1131,15853,15854],{},"medián",[1131,15856,15857],{},"modus"," (nejčetnější hodnota výběru).",[1110,15860,15861],{},[1131,15862,15863],{},"Míry variability",[1115,15865,15867],{"className":15866},[1144],[1146,15868,15869],{"xmlns":1148,"display":1573},[1150,15870,15871,16000],{},[1153,15872,15873,15879,15881,15893,15935,15937,15939,15941,15943,15951,15953],{},[1182,15874,15875,15877],{},[1159,15876,1463],{},[1163,15878,1189],{},[1289,15880,1591],{},[2355,15882,15883,15885],{},[1163,15884,1402],{},[1153,15886,15887,15889,15891],{},[1159,15888,1287],{},[1289,15890,2681],{},[1163,15892,1402],{},[1153,15894,15895,15897,15911,15919,15921,15923,15933],{},[1289,15896,1484],{"fence":1121},[1593,15898,15899,15901,15909],{},[1289,15900,1597],{},[1153,15902,15903,15905,15907],{},[1159,15904,1487],{},[1289,15906,1591],{},[1163,15908,1402],{},[1159,15910,1287],{},[2970,15912,15913,15915,15917],{},[1159,15914,11019],{},[1159,15916,1487],{},[1163,15918,1189],{},[1289,15920,2681],{},[1159,15922,1287],{},[1182,15924,15925,15931],{},[2339,15926,15927,15929],{"accent":1121},[1159,15928,11019],{},[1289,15930,15762],{},[1163,15932,1189],{},[1289,15934,1495],{"fence":1121},[1289,15936,1405],{"separator":1121},[1621,15938],{"width":1623},[1159,15940,1463],{},[1289,15942,1591],{},[4072,15944,15945],{},[1182,15946,15947,15949],{},[1159,15948,1463],{},[1163,15950,1189],{},[1621,15952],{"width":1623},[1153,15954,15955,15957,15963,15965,15971,15973,15979,15982,15988,15991,15997],{},[2525,15956,15797],{},[2339,15958,15959,15961],{"accent":1121},[2525,15960,11429],{},[1289,15962,15804],{},[2525,15964,15807],{},[2339,15966,15967,15969],{"accent":1121},[2525,15968,12893],{},[1289,15970,15814],{},[2525,15972,15817],{},[2339,15974,15975,15977],{"accent":1121},[2525,15976,11429],{},[1289,15978,15804],{},[2525,15980,15981],{}," rozptyl, sm",[2339,15983,15984,15986],{"accent":1121},[2525,15985,12893],{},[1289,15987,15814],{},[2525,15989,15990],{},"rodatn",[2339,15992,15993,15995],{"accent":1121},[2525,15994,1318],{},[1289,15996,15804],{},[2525,15998,15999],{}," odchylka)",[1167,16001,16002],{"encoding":1169},"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)}",[1115,16004,16006],{"className":16005},[1144],[1146,16007,16008],{"xmlns":1148,"display":1573},[1150,16009,16010,16076],{},[1153,16011,16012,16014,16016,16025,16027,16035,16037],{},[1159,16013,14524],{},[1289,16015,1591],{},[1156,16017,16018,16020,16023],{},[1159,16019,11019],{},[1159,16021,16022],{},"max",[1289,16024,4110],{},[1289,16026,2681],{},[1156,16028,16029,16031,16033],{},[1159,16030,11019],{},[1159,16032,4107],{},[1289,16034,4110],{},[1621,16036],{"width":1623},[1153,16038,16039,16042,16048,16050,16057,16060,16066,16068,16074],{},[2525,16040,16041],{},"(varia",[2339,16043,16044,16046],{"accent":1121},[2525,16045,3338],{},[1289,16047,15814],{},[2525,16049,1287],{},[2339,16051,16052,16055],{"accent":1121},[2525,16053,16054],{},"ı",[1289,16056,15804],{},[2525,16058,16059],{}," rozp",[2339,16061,16062,16064],{"accent":1121},[2525,16063,12893],{},[1289,16065,15814],{},[2525,16067,11443],{},[2339,16069,16070,16072],{"accent":1121},[2525,16071,16054],{},[1289,16073,15804],{},[2525,16075,1495],{},[1167,16077,16078],{"encoding":1169},"R = x_{\\max} - x_{\\min} \\qquad \\text{(variační rozpětí)}",[1110,16080,16081],{},[1131,16082,12604],{},[1110,16084,16085,16086,16109,16110,16132,16133,16154,16155,16183],{},"Kvantil ",[1115,16087,16089],{"className":16088},[1144],[1146,16090,16091],{"xmlns":1148},[1150,16092,16093,16106],{},[1153,16094,16095],{},[1156,16096,16097,16104],{},[2339,16098,16099,16101],{"accent":1121},[1159,16100,11019],{},[1289,16102,16103],{},"~",[1159,16105,1110],{},[1167,16107,16108],{"encoding":1169},"\\tilde{x}_p"," dělí hodnoty datového souboru na dvě části: ",[1115,16111,16113],{"className":16112},[1144],[1146,16114,16115],{"xmlns":1148},[1150,16116,16117,16129],{},[1153,16118,16119,16122,16124,16126],{},[1163,16120,16121],{},"100",[1159,16123,1110],{},[2525,16125,2527],{},[1159,16127,16128],{"mathvariant":1734},"%",[1167,16130,16131],{"encoding":1169},"100p\\,\\%"," hodnot je menších nebo rovných ",[1115,16134,16136],{"className":16135},[1144],[1146,16137,16138],{"xmlns":1148},[1150,16139,16140,16152],{},[1153,16141,16142],{},[1156,16143,16144,16150],{},[2339,16145,16146,16148],{"accent":1121},[1159,16147,11019],{},[1289,16149,16103],{},[1159,16151,1110],{},[1167,16153,16108],{"encoding":1169},", zbylých ",[1115,16156,16158],{"className":16157},[1144],[1146,16159,16160],{"xmlns":1148},[1150,16161,16162,16180],{},[1153,16163,16164,16166,16168,16170,16172,16174,16176,16178],{},[1163,16165,16121],{},[1289,16167,1484],{"stretchy":1483},[1163,16169,1402],{},[1289,16171,2681],{},[1159,16173,1110],{},[1289,16175,1495],{"stretchy":1483},[2525,16177,2527],{},[1159,16179,16128],{"mathvariant":1734},[1167,16181,16182],{"encoding":1169},"100(1-p)\\,\\%"," je větších. Nejdůležitější kvantily:",[1124,16185,16186,16213],{},[1127,16187,16188,1254,16190,16212],{},[1131,16189,15854],{},[1115,16191,16193],{"className":16192},[1144],[1146,16194,16195],{"xmlns":1148},[1150,16196,16197,16209],{},[1153,16198,16199],{},[1156,16200,16201,16207],{},[2339,16202,16203,16205],{"accent":1121},[1159,16204,11019],{},[1289,16206,16103],{},[1163,16208,12758],{},[1167,16210,16211],{"encoding":1169},"\\tilde{x}_{0{,}5}"," — pro lichý počet prvků uspořádaného souboru prostřední prvek, pro sudý počet průměr dvou prostředních prvků;",[1127,16214,16215,1254,16218,5360,16240,1254,16243,1269],{},[1131,16216,16217],{},"dolní kvartil",[1115,16219,16221],{"className":16220},[1144],[1146,16222,16223],{"xmlns":1148},[1150,16224,16225,16237],{},[1153,16226,16227],{},[1156,16228,16229,16235],{},[2339,16230,16231,16233],{"accent":1121},[1159,16232,11019],{},[1289,16234,16103],{},[1163,16236,12778],{},[1167,16238,16239],{"encoding":1169},"\\tilde{x}_{0{,}25}",[1131,16241,16242],{},"horní kvartil",[1115,16244,16246],{"className":16245},[1144],[1146,16247,16248],{"xmlns":1148},[1150,16249,16250,16262],{},[1153,16251,16252],{},[1156,16253,16254,16260],{},[2339,16255,16256,16258],{"accent":1121},[1159,16257,11019],{},[1289,16259,16103],{},[1163,16261,12798],{},[1167,16263,16264],{"encoding":1169},"\\tilde{x}_{0{,}75}",[1110,16266,16267,16268,16271],{},"Datový soubor se do R zadává buď přímo (",[3087,16269,16270],{},"x \u003C- c(...)","), nebo načtením ze souboru:",[3311,16273,16275],{"className":3313,"code":16274,"language":71,"meta":3315,"style":3315},"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",[3087,16276,16277,16338],{"__ignoreMap":3315},[1115,16278,16279,16281,16283,16285,16287,16290,16292,16295,16297,16300,16302,16305,16307,16309,16311,16313,16315,16318,16320,16323,16325,16327,16329,16331,16334],{"class":3320,"line":10},[1115,16280,11019],{"class":3323},[1115,16282,3328],{"class":3327},[1115,16284,3454],{"class":3331},[1115,16286,1484],{"class":3335},[1115,16288,16289],{"class":3343},"4.1",[1115,16291,1405],{"class":3327},[1115,16293,16294],{"class":3343}," 4.0",[1115,16296,1405],{"class":3327},[1115,16298,16299],{"class":3343}," 3.8",[1115,16301,1405],{"class":3327},[1115,16303,16304],{"class":3343}," 3.9",[1115,16306,1405],{"class":3327},[1115,16308,16299],{"class":3343},[1115,16310,1405],{"class":3327},[1115,16312,16299],{"class":3343},[1115,16314,1405],{"class":3327},[1115,16316,16317],{"class":3343}," 3.5",[1115,16319,1405],{"class":3327},[1115,16321,16322],{"class":3343}," 3.7",[1115,16324,1405],{"class":3327},[1115,16326,16294],{"class":3343},[1115,16328,1405],{"class":3327},[1115,16330,16294],{"class":3343},[1115,16332,16333],{"class":3335},")   ",[1115,16335,16337],{"class":16336},"sCsY4","# přímé zadání hodnot\n",[1115,16339,16340],{"class":3320,"line":27},[1115,16341,16342],{"class":16336},"# x \u003C- read.table(\"data.txt\")[, 1]                       # načtení prvního sloupce ze souboru\n",[1110,16344,16345,16346,16349,16350,16353,16354,16357,16358,16361],{},"Řádek s načtením ze souboru je zakomentovaný znakem ",[3087,16347,16348],{},"#",": soubor musí ležet v pracovním adresáři R. ",[3087,16351,16352],{},"read.table()"," vrací datovou tabulku (",[3087,16355,16356],{},"data.frame","), proto ",[3087,16359,16360],{},"[, 1]"," vybere její první sloupec jako vektor.",[1110,16363,13355],{},[3311,16365,16367],{"className":3313,"code":16366,"language":71,"meta":3315,"style":3315},"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",[3087,16368,16369,16426,16437,16448,16459,16470,16508,16534,16557],{"__ignoreMap":3315},[1115,16370,16371,16373,16375,16377,16379,16382,16384,16387,16389,16392,16394,16397,16399,16401,16403,16406,16408,16410,16412,16415,16417,16420,16422,16424],{"class":3320,"line":10},[1115,16372,11019],{"class":3323},[1115,16374,3328],{"class":3327},[1115,16376,3454],{"class":3331},[1115,16378,1484],{"class":3335},[1115,16380,16381],{"class":3343},"11.1",[1115,16383,1405],{"class":3327},[1115,16385,16386],{"class":3343}," 12.7",[1115,16388,1405],{"class":3327},[1115,16390,16391],{"class":3343}," 10.8",[1115,16393,1405],{"class":3327},[1115,16395,16396],{"class":3343}," 13.2",[1115,16398,1405],{"class":3327},[1115,16400,16386],{"class":3343},[1115,16402,1405],{"class":3327},[1115,16404,16405],{"class":3343}," 13.4",[1115,16407,1405],{"class":3327},[1115,16409,16386],{"class":3343},[1115,16411,1405],{"class":3327},[1115,16413,16414],{"class":3343}," 14.4",[1115,16416,1405],{"class":3327},[1115,16418,16419],{"class":3343}," 14.7",[1115,16421,1405],{"class":3327},[1115,16423,16414],{"class":3343},[1115,16425,3520],{"class":3335},[1115,16427,16428,16431,16433,16435],{"class":3320,"line":27},[1115,16429,16430],{"class":3331},"length",[1115,16432,1484],{"class":3335},[1115,16434,11019],{"class":3323},[1115,16436,3520],{"class":3335},[1115,16438,16439,16442,16444,16446],{"class":3320,"line":148},[1115,16440,16441],{"class":3331},"mean",[1115,16443,1484],{"class":3335},[1115,16445,11019],{"class":3323},[1115,16447,3520],{"class":3335},[1115,16449,16450,16453,16455,16457],{"class":3320,"line":111},[1115,16451,16452],{"class":3331},"var",[1115,16454,1484],{"class":3335},[1115,16456,11019],{"class":3323},[1115,16458,3520],{"class":3335},[1115,16460,16461,16464,16466,16468],{"class":3320,"line":96},[1115,16462,16463],{"class":3331},"sd",[1115,16465,1484],{"class":3335},[1115,16467,11019],{"class":3323},[1115,16469,3520],{"class":3335},[1115,16471,16472,16474,16476,16478,16481,16483,16485,16487,16489,16491,16493,16495,16497,16499,16502,16504,16506],{"class":3320,"line":89},[1115,16473,4107],{"class":3331},[1115,16475,1484],{"class":3335},[1115,16477,11019],{"class":3323},[1115,16479,16480],{"class":3335},"); ",[1115,16482,16022],{"class":3331},[1115,16484,1484],{"class":3335},[1115,16486,11019],{"class":3323},[1115,16488,16480],{"class":3335},[1115,16490,16022],{"class":3331},[1115,16492,1484],{"class":3335},[1115,16494,11019],{"class":3323},[1115,16496,4220],{"class":3335},[1115,16498,4257],{"class":3327},[1115,16500,16501],{"class":3331}," min",[1115,16503,1484],{"class":3335},[1115,16505,11019],{"class":3323},[1115,16507,3520],{"class":3335},[1115,16509,16510,16513,16515,16517,16519,16522,16524,16527,16529,16532],{"class":3320,"line":82},[1115,16511,16512],{"class":3331},"quantile",[1115,16514,1484],{"class":3335},[1115,16516,11019],{"class":3323},[1115,16518,1405],{"class":3327},[1115,16520,16521],{"class":3343}," 0.5",[1115,16523,1405],{"class":3327},[1115,16525,16526],{"class":3323}," type",[1115,16528,3416],{"class":3327},[1115,16530,16531],{"class":3343}," 6",[1115,16533,3520],{"class":3335},[1115,16535,16536,16538,16540,16542,16544,16547,16549,16551,16553,16555],{"class":3320,"line":75},[1115,16537,16512],{"class":3331},[1115,16539,1484],{"class":3335},[1115,16541,11019],{"class":3323},[1115,16543,1405],{"class":3327},[1115,16545,16546],{"class":3343}," 0.25",[1115,16548,1405],{"class":3327},[1115,16550,16526],{"class":3323},[1115,16552,3416],{"class":3327},[1115,16554,16531],{"class":3343},[1115,16556,3520],{"class":3335},[1115,16558,16559,16561,16563,16565,16567,16570,16572,16574,16576,16578],{"class":3320,"line":3510},[1115,16560,16512],{"class":3331},[1115,16562,1484],{"class":3335},[1115,16564,11019],{"class":3323},[1115,16566,1405],{"class":3327},[1115,16568,16569],{"class":3343}," 0.75",[1115,16571,1405],{"class":3327},[1115,16573,16526],{"class":3323},[1115,16575,3416],{"class":3327},[1115,16577,16531],{"class":3343},[1115,16579,3520],{"class":3335},[3311,16581,16584],{"className":16582,"code":16583,"language":3542,"meta":3315},[3540],"[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",[3087,16585,16583],{"__ignoreMap":3315},[1110,16587,16588,16591,16592,16595],{},[3087,16589,16590],{},"quantile(x, p, type = 6)"," je potřeba zadat explicitně — výchozí typ v R (",[3087,16593,16594],{},"type = 7",") by u některých souborů dal mírně odlišné hodnoty kvantilů než ruční výpočet použitý v této kapitole.",[1110,16597,16598],{},[4002,16599],{"alt":16600,"className":16601,"src":16602},"mask-ps-kvantily",[1321,4006],"\u002Fwiki-assets\u002Fmask-ps-kvantily.png",[1110,16604,16605],{},"Seřazení souboru a krabicový graf:",[3311,16607,16609],{"className":3313,"code":16608,"language":71,"meta":3315,"style":3315},"sort(x)                     # vzestupně\nsort(x, decreasing = TRUE)  # sestupně\nboxplot(x)\n",[3087,16610,16611,16626,16649],{"__ignoreMap":3315},[1115,16612,16613,16616,16618,16620,16623],{"class":3320,"line":10},[1115,16614,16615],{"class":3331},"sort",[1115,16617,1484],{"class":3335},[1115,16619,11019],{"class":3323},[1115,16621,16622],{"class":3335},")                     ",[1115,16624,16625],{"class":16336},"# vzestupně\n",[1115,16627,16628,16630,16632,16634,16636,16639,16641,16643,16646],{"class":3320,"line":27},[1115,16629,16615],{"class":3331},[1115,16631,1484],{"class":3335},[1115,16633,11019],{"class":3323},[1115,16635,1405],{"class":3327},[1115,16637,16638],{"class":3323}," decreasing",[1115,16640,3416],{"class":3327},[1115,16642,3429],{"class":3343},[1115,16644,16645],{"class":3335},")  ",[1115,16647,16648],{"class":16336},"# sestupně\n",[1115,16650,16651,16654,16656,16658],{"class":3320,"line":148},[1115,16652,16653],{"class":3331},"boxplot",[1115,16655,1484],{"class":3335},[1115,16657,11019],{"class":3323},[1115,16659,3520],{"class":3335},[3311,16661,16664],{"className":16662,"code":16663,"language":3542,"meta":3315},[3540]," [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",[3087,16665,16663],{"__ignoreMap":3315},[1110,16667,16668,16671,16672,16675],{},[3087,16669,16670],{},"boxplot()"," kreslí krabici mezi hodnotami ",[3087,16673,16674],{},"fivenum(x)"," (zde 12,7 a 14,4), které se od kvartilů typu 6 mohou mírně lišit.",[1103,16677,16679,16686],{"className":16678,"dataCallout":3094},[1106,3093],[1110,16680,16682,16685],{"className":16681},[1113],[1115,16683],{"className":16684,"ariaHidden":1121},[1118,3101,1120],"Příklad: Empirické charakteristiky",[1110,16687,16688],{},"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.",[1110,16690,16691,16692,2568,16715,2568,16738,2568,16757,16776,16777,12762,16804,16819,16820,1269],{},"Výstup R kódu výše dává ",[1115,16693,16695],{"className":16694},[1144],[1146,16696,16697],{"xmlns":1148},[1150,16698,16699,16712],{},[1153,16700,16701,16707,16709],{},[2339,16702,16703,16705],{"accent":1121},[1159,16704,11019],{},[1289,16706,15762],{},[1289,16708,1591],{},[1163,16710,16711],{},"13,01",[1167,16713,16714],{"encoding":1169},"\\bar{x}=13{,}01",[1115,16716,16718],{"className":16717},[1144],[1146,16719,16720],{"xmlns":1148},[1150,16721,16722,16735],{},[1153,16723,16724,16730,16732],{},[1182,16725,16726,16728],{},[1159,16727,1463],{},[1163,16729,1189],{},[1289,16731,1591],{},[1163,16733,16734],{},"1,75",[1167,16736,16737],{"encoding":1169},"s^2=1{,}75",[1115,16739,16741],{"className":16740},[1144],[1146,16742,16743],{"xmlns":1148},[1150,16744,16745,16754],{},[1153,16746,16747,16749,16751],{},[1159,16748,1463],{},[1289,16750,1591],{},[1163,16752,16753],{},"1,32",[1167,16755,16756],{"encoding":1169},"s=1{,}32",[1115,16758,16760],{"className":16759},[1144],[1146,16761,16762],{"xmlns":1148},[1150,16763,16764,16773],{},[1153,16765,16766,16768,16770],{},[1159,16767,14524],{},[1289,16769,1591],{},[1163,16771,16772],{},"3,9",[1167,16774,16775],{"encoding":1169},"R=3{,}9",", medián ",[1115,16778,16780],{"className":16779},[1144],[1146,16781,16782],{"xmlns":1148},[1150,16783,16784,16801],{},[1153,16785,16786,16796,16798],{},[1156,16787,16788,16794],{},[2339,16789,16790,16792],{"accent":1121},[1159,16791,11019],{},[1289,16793,16103],{},[1163,16795,12758],{},[1289,16797,1591],{},[1163,16799,16800],{},"12,95",[1167,16802,16803],{"encoding":1169},"\\tilde{x}_{0{,}5}=12{,}95",[1115,16805,16807],{"className":16806},[1144],[1146,16808,16809],{"xmlns":1148},[1150,16810,16811,16816],{},[1153,16812,16813],{},[1163,16814,16815],{},"12,3",[1167,16817,16818],{"encoding":1169},"12{,}3",", horní kvartil ",[1115,16821,16823],{"className":16822},[1144],[1146,16824,16825],{"xmlns":1148},[1150,16826,16827,16832],{},[1153,16828,16829],{},[1163,16830,16831],{},"14,4",[1167,16833,16834],{"encoding":1169},"14{,}4",[1110,16836,16837],{},"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.",[1103,16839,16841,16848],{"className":16840,"dataCallout":3094},[1106,3093],[1110,16842,16844,16847],{"className":16843},[1113],[1115,16845],{"className":16846,"ariaHidden":1121},[1118,3101,1120],"Příklad: Doba oprav televizorů",[1110,16849,16850],{},"Při 50 opravách určité závady televizoru byly naměřeny časy (v minutách). Určete empirické charakteristiky.",[3311,16852,16854],{"className":3313,"code":16853,"language":71,"meta":3315,"style":3315},"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",[3087,16855,16856,16916,16967,17014,17061,17109,17119,17129,17139,17159],{"__ignoreMap":3315},[1115,16857,16858,16861,16863,16865,16867,16869,16871,16874,16876,16879,16881,16884,16886,16889,16891,16894,16896,16899,16901,16904,16906,16909,16911,16914],{"class":3320,"line":10},[1115,16859,16860],{"class":3323},"x6",[1115,16862,3328],{"class":3327},[1115,16864,3454],{"class":3331},[1115,16866,1484],{"class":3335},[1115,16868,3192],{"class":3343},[1115,16870,1405],{"class":3327},[1115,16872,16873],{"class":3343}," 40.2",[1115,16875,1405],{"class":3327},[1115,16877,16878],{"class":3343}," 41.9",[1115,16880,1405],{"class":3327},[1115,16882,16883],{"class":3343}," 43.4",[1115,16885,1405],{"class":3327},[1115,16887,16888],{"class":3343}," 42.8",[1115,16890,1405],{"class":3327},[1115,16892,16893],{"class":3343}," 42.3",[1115,16895,1405],{"class":3327},[1115,16897,16898],{"class":3343}," 43.2",[1115,16900,1405],{"class":3327},[1115,16902,16903],{"class":3343}," 45",[1115,16905,1405],{"class":3327},[1115,16907,16908],{"class":3343}," 41.5",[1115,16910,1405],{"class":3327},[1115,16912,16913],{"class":3343}," 42.7",[1115,16915,3356],{"class":3327},[1115,16917,16918,16921,16923,16926,16928,16931,16933,16936,16938,16941,16943,16946,16948,16951,16953,16956,16958,16960,16962,16965],{"class":3320,"line":27},[1115,16919,16920],{"class":3343},"        43.9",[1115,16922,1405],{"class":3327},[1115,16924,16925],{"class":3343}," 40.1",[1115,16927,1405],{"class":3327},[1115,16929,16930],{"class":3343}," 43.3",[1115,16932,1405],{"class":3327},[1115,16934,16935],{"class":3343}," 41.1",[1115,16937,1405],{"class":3327},[1115,16939,16940],{"class":3343}," 42.5",[1115,16942,1405],{"class":3327},[1115,16944,16945],{"class":3343}," 42.4",[1115,16947,1405],{"class":3327},[1115,16949,16950],{"class":3343}," 41.4",[1115,16952,1405],{"class":3327},[1115,16954,16955],{"class":3343}," 40.8",[1115,16957,1405],{"class":3327},[1115,16959,13636],{"class":3343},[1115,16961,1405],{"class":3327},[1115,16963,16964],{"class":3343}," 44.7",[1115,16966,3356],{"class":3327},[1115,16968,16969,16972,16974,16976,16978,16980,16982,16985,16987,16990,16992,16995,16997,16999,17001,17004,17006,17008,17010,17012],{"class":3320,"line":148},[1115,16970,16971],{"class":3343},"        41.2",[1115,16973,1405],{"class":3327},[1115,16975,16878],{"class":3343},[1115,16977,1405],{"class":3327},[1115,16979,16945],{"class":3343},[1115,16981,1405],{"class":3327},[1115,16983,16984],{"class":3343}," 44.4",[1115,16986,1405],{"class":3327},[1115,16988,16989],{"class":3343}," 40.5",[1115,16991,1405],{"class":3327},[1115,16993,16994],{"class":3343}," 39.7",[1115,16996,1405],{"class":3327},[1115,16998,16935],{"class":3343},[1115,17000,1405],{"class":3327},[1115,17002,17003],{"class":3343}," 41",[1115,17005,1405],{"class":3327},[1115,17007,16878],{"class":3343},[1115,17009,1405],{"class":3327},[1115,17011,16955],{"class":3343},[1115,17013,3356],{"class":3327},[1115,17015,17016,17019,17021,17023,17025,17028,17030,17032,17034,17036,17038,17041,17043,17046,17048,17050,17052,17055,17057,17059],{"class":3320,"line":111},[1115,17017,17018],{"class":3343},"        43",[1115,17020,1405],{"class":3327},[1115,17022,16888],{"class":3343},[1115,17024,1405],{"class":3327},[1115,17026,17027],{"class":3343}," 42.9",[1115,17029,1405],{"class":3327},[1115,17031,16913],{"class":3343},[1115,17033,1405],{"class":3327},[1115,17035,16930],{"class":3343},[1115,17037,1405],{"class":3327},[1115,17039,17040],{"class":3343}," 42.2",[1115,17042,1405],{"class":3327},[1115,17044,17045],{"class":3343}," 39.2",[1115,17047,1405],{"class":3327},[1115,17049,16908],{"class":3343},[1115,17051,1405],{"class":3327},[1115,17053,17054],{"class":3343}," 41.6",[1115,17056,1405],{"class":3327},[1115,17058,16913],{"class":3343},[1115,17060,3356],{"class":3327},[1115,17062,17063,17066,17068,17070,17072,17075,17077,17079,17081,17084,17086,17089,17091,17094,17096,17098,17100,17103,17105,17107],{"class":3320,"line":96},[1115,17064,17065],{"class":3343},"        45",[1115,17067,1405],{"class":3327},[1115,17069,16893],{"class":3343},[1115,17071,1405],{"class":3327},[1115,17073,17074],{"class":3343}," 43.6",[1115,17076,1405],{"class":3327},[1115,17078,16898],{"class":3343},[1115,17080,1405],{"class":3327},[1115,17082,17083],{"class":3343}," 38.8",[1115,17085,1405],{"class":3327},[1115,17087,17088],{"class":3343}," 43",[1115,17090,1405],{"class":3327},[1115,17092,17093],{"class":3343}," 44.2",[1115,17095,1405],{"class":3327},[1115,17097,17088],{"class":3343},[1115,17099,1405],{"class":3327},[1115,17101,17102],{"class":3343}," 40",[1115,17104,1405],{"class":3327},[1115,17106,16984],{"class":3343},[1115,17108,3520],{"class":3335},[1115,17110,17111,17113,17115,17117],{"class":3320,"line":89},[1115,17112,16430],{"class":3331},[1115,17114,1484],{"class":3335},[1115,17116,16860],{"class":3323},[1115,17118,3520],{"class":3335},[1115,17120,17121,17123,17125,17127],{"class":3320,"line":82},[1115,17122,16441],{"class":3331},[1115,17124,1484],{"class":3335},[1115,17126,16860],{"class":3323},[1115,17128,3520],{"class":3335},[1115,17130,17131,17133,17135,17137],{"class":3320,"line":75},[1115,17132,16463],{"class":3331},[1115,17134,1484],{"class":3335},[1115,17136,16860],{"class":3323},[1115,17138,3520],{"class":3335},[1115,17140,17141,17143,17145,17147,17149,17151,17153,17155,17157],{"class":3320,"line":3510},[1115,17142,16022],{"class":3331},[1115,17144,1484],{"class":3335},[1115,17146,16860],{"class":3323},[1115,17148,4220],{"class":3335},[1115,17150,4257],{"class":3327},[1115,17152,16501],{"class":3331},[1115,17154,1484],{"class":3335},[1115,17156,16860],{"class":3323},[1115,17158,3520],{"class":3335},[1115,17160,17161,17164,17166,17168],{"class":3320,"line":72},[1115,17162,17163],{"class":3331},"median",[1115,17165,1484],{"class":3335},[1115,17167,16860],{"class":3323},[1115,17169,3520],{"class":3335},[3311,17171,17174],{"className":17172,"code":17173,"language":3542,"meta":3315},[3540],"[1] 50\n[1] 42.27\n[1] 1.48052\n[1] 6.2\n[1] 42.4\n",[3087,17175,17173],{"__ignoreMap":3315},[1110,17177,17178],{},"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.",[1310,17180,17182],{"id":17181},"empirická-distribuční-funkce","Empirická distribuční funkce",[1110,17184,17185,17186,17199,17200,1254,17203,17226,17227,17261],{},"Pro libovolný rozsah datového souboru, diskrétní i spojitou náhodnou veličinu ",[1115,17187,17189],{"className":17188},[1144],[1146,17190,17191],{"xmlns":1148},[1150,17192,17193,17197],{},[1153,17194,17195],{},[1159,17196,11031],{},[1167,17198,11031],{"encoding":1169},", lze sestrojit ",[1131,17201,17202],{},"empirickou distribuční funkci",[1115,17204,17206],{"className":17205},[1144],[1146,17207,17208],{"xmlns":1148},[1150,17209,17210,17224],{},[1153,17211,17212,17218,17220,17222],{},[1156,17213,17214,17216],{},[1159,17215,11014],{},[1159,17217,1287],{},[1289,17219,1484],{"stretchy":1483},[1159,17221,11019],{},[1289,17223,1495],{"stretchy":1483},[1167,17225,15486],{"encoding":1169},". Pro datový soubor ",[1115,17228,17230],{"className":17229},[1144],[1146,17231,17232],{"xmlns":1148},[1150,17233,17234,17258],{},[1153,17235,17236,17238,17244,17246,17248,17250,17256],{},[1289,17237,1484],{"stretchy":1483},[1156,17239,17240,17242],{},[1159,17241,11019],{},[1163,17243,1402],{},[1289,17245,1405],{"separator":1121},[1289,17247,1408],{},[1289,17249,1405],{"separator":1121},[1156,17251,17252,17254],{},[1159,17253,11019],{},[1159,17255,1287],{},[1289,17257,1495],{"stretchy":1483},[1167,17259,17260],{"encoding":1169},"(x_1,\\dots,x_n)"," je",[1115,17263,17265],{"className":17264},[1144],[1146,17266,17267],{"xmlns":1148,"display":1573},[1150,17268,17269,17293],{},[1153,17270,17271,17277,17279,17281,17283,17285,17291],{},[1156,17272,17273,17275],{},[1159,17274,11014],{},[1159,17276,1287],{},[1289,17278,1484],{"stretchy":1483},[1159,17280,11019],{},[1289,17282,1495],{"stretchy":1483},[1289,17284,1591],{},[2355,17286,17287,17289],{},[1159,17288,11559],{},[1159,17290,1287],{},[1289,17292,1405],{"separator":1121},[1167,17294,17295],{"encoding":1169},"F_n(x) = \\frac{k}{n},",[1110,17297,4126,17298,17311,17312,1269],{},[1115,17299,17301],{"className":17300},[1144],[1146,17302,17303],{"xmlns":1148},[1150,17304,17305,17309],{},[1153,17306,17307],{},[1159,17308,11559],{},[1167,17310,11559],{"encoding":1169}," je počet prvků datového souboru menších nebo rovných číslu ",[1115,17313,17315],{"className":17314},[1144],[1146,17316,17317],{"xmlns":1148},[1150,17318,17319,17323],{},[1153,17320,17321],{},[1159,17322,11019],{},[1167,17324,11019],{"encoding":1169},[1110,17326,13355],{},[3311,17328,17330],{"className":3313,"code":17329,"language":71,"meta":3315,"style":3315},"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",[3087,17331,17332,17347,17362,17380,17394],{"__ignoreMap":3315},[1115,17333,17334,17336,17338,17341,17343,17345],{"class":3320,"line":10},[1115,17335,11070],{"class":3323},[1115,17337,3328],{"class":3327},[1115,17339,17340],{"class":3331}," ecdf",[1115,17342,1484],{"class":3335},[1115,17344,11019],{"class":3323},[1115,17346,3520],{"class":3335},[1115,17348,17349,17352,17354,17356,17359],{"class":3320,"line":27},[1115,17350,17351],{"class":3331},"knots",[1115,17353,1484],{"class":3335},[1115,17355,11070],{"class":3323},[1115,17357,17358],{"class":3335},")        ",[1115,17360,17361],{"class":16336},"# vzestupně seřazené různé hodnoty datového souboru\n",[1115,17363,17364,17366,17368,17370,17372,17374,17377],{"class":3320,"line":148},[1115,17365,11070],{"class":3331},[1115,17367,1484],{"class":3335},[1115,17369,17351],{"class":3331},[1115,17371,1484],{"class":3335},[1115,17373,11070],{"class":3323},[1115,17375,17376],{"class":3335},"))      ",[1115,17378,17379],{"class":16336},"# hodnoty Fn(x) v těchto bodech\n",[1115,17381,17382,17384,17386,17388,17391],{"class":3320,"line":111},[1115,17383,11070],{"class":3331},[1115,17385,1484],{"class":3335},[1115,17387,3162],{"class":3343},[1115,17389,17390],{"class":3335},")            ",[1115,17392,17393],{"class":16336},"# Fn v libovolném bodě\n",[1115,17395,17396,17399,17401,17403],{"class":3320,"line":96},[1115,17397,17398],{"class":3331},"plot",[1115,17400,1484],{"class":3335},[1115,17402,11070],{"class":3323},[1115,17404,3520],{"class":3335},[3311,17406,17409],{"className":17407,"code":17408,"language":3542,"meta":3315},[3540],"[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",[3087,17410,17408],{"__ignoreMap":3315},[1110,17412,17413,17416,17417,17435,17436,17439,17440,17453,17454,1269],{},[3087,17414,17415],{},"knots()"," vrací jen různé hodnoty (opakující se hodnota 12,7 je ve výpočtu ",[1115,17418,17420],{"className":17419},[1144],[1146,17421,17422],{"xmlns":1148},[1150,17423,17424,17432],{},[1153,17425,17426],{},[1156,17427,17428,17430],{},[1159,17429,11014],{},[1159,17431,1287],{},[1167,17433,17434],{"encoding":1169},"F_n"," započtena třikrát, v seznamu uzlů je ale jen jednou); ",[3087,17437,17438],{},"plot(f)"," nakreslí schodovitý graf, který v každém uzlu skáče o ",[1115,17441,17443],{"className":17442},[1144],[1146,17444,17445],{"xmlns":1148},[1150,17446,17447,17451],{},[1153,17448,17449],{},[1159,17450,11559],{},[1167,17452,11559],{"encoding":1169},"-násobek ",[1115,17455,17457],{"className":17456},[1144],[1146,17458,17459],{"xmlns":1148},[1150,17460,17461,17469],{},[1153,17462,17463,17465,17467],{},[1163,17464,1402],{},[1159,17466,4223],{"mathvariant":1734},[1159,17468,1287],{},[1167,17470,17471],{"encoding":1169},"1\u002Fn",[1110,17473,17474],{},[4002,17475],{"alt":17476,"className":17477,"src":17478},"mask-ps-ecdf",[1321,4006],"\u002Fwiki-assets\u002Fmask-ps-ecdf.png",[1103,17480,17482,17489],{"className":17481,"dataCallout":3094},[1106,3093],[1110,17483,17485,17488],{"className":17484},[1113],[1115,17486],{"className":17487,"ariaHidden":1121},[1118,3101,1120],"Příklad: Empirická distribuční funkce",[1110,17490,17491],{},"Pro předchozí datový soubor (doba opravy součástky) určete empirickou distribuční funkci.",[1110,17493,17494,17495,1269],{},"Uspořádaný soubor je ",[1115,17496,17498],{"className":17497},[1144],[1146,17499,17500],{"xmlns":1148},[1150,17501,17502,17566],{},[1153,17503,17504,17507,17509,17511,17514,17516,17518,17521,17523,17525,17527,17529,17531,17533,17535,17537,17540,17542,17544,17547,17549,17551,17553,17555,17557,17559,17561,17563],{},[1163,17505,17506],{},"10,8",[1289,17508,11193],{"separator":1121},[2525,17510,15617],{},[1163,17512,17513],{},"11,1",[1289,17515,11193],{"separator":1121},[2525,17517,15617],{},[1163,17519,17520],{},"12,7",[1289,17522,11193],{"separator":1121},[2525,17524,15617],{},[1163,17526,17520],{},[1289,17528,11193],{"separator":1121},[2525,17530,15617],{},[1163,17532,17520],{},[1289,17534,11193],{"separator":1121},[2525,17536,15617],{},[1163,17538,17539],{},"13,2",[1289,17541,11193],{"separator":1121},[2525,17543,15617],{},[1163,17545,17546],{},"13,4",[1289,17548,11193],{"separator":1121},[2525,17550,15617],{},[1163,17552,16831],{},[1289,17554,11193],{"separator":1121},[2525,17556,15617],{},[1163,17558,16831],{},[1289,17560,11193],{"separator":1121},[2525,17562,15617],{},[1163,17564,17565],{},"14,7",[1167,17567,17568],{"encoding":1169},"10{,}8;\\ 11{,}1;\\ 12{,}7;\\ 12{,}7;\\ 12{,}7;\\ 13{,}2;\\ 13{,}4;\\ 14{,}4;\\ 14{,}4;\\ 14{,}7",[1710,17570,17571,17604],{},[1713,17572,17573],{},[1716,17574,17575,17590,17592,17594,17596,17598,17600,17602],{},[1719,17576,17577],{},[1115,17578,17580],{"className":17579},[1144],[1146,17581,17582],{"xmlns":1148},[1150,17583,17584,17588],{},[1153,17585,17586],{},[1159,17587,11019],{},[1167,17589,11019],{"encoding":1169},[1719,17591,17506],{},[1719,17593,17513],{},[1719,17595,17520],{},[1719,17597,17539],{},[1719,17599,17546],{},[1719,17601,16831],{},[1719,17603,17565],{},[1828,17605,17606,17638],{},[1716,17607,17608,17623,17625,17627,17629,17631,17634,17636],{},[1833,17609,17610],{},[1115,17611,17613],{"className":17612},[1144],[1146,17614,17615],{"xmlns":1148},[1150,17616,17617,17621],{},[1153,17618,17619],{},[1159,17620,11559],{},[1167,17622,11559],{"encoding":1169},[1833,17624,1402],{},[1833,17626,1189],{},[1833,17628,14227],{},[1833,17630,3583],{},[1833,17632,17633],{},"7",[1833,17635,3212],{},[1833,17637,13334],{},[1716,17639,17640,17665,17668,17671,17673,17676,17679,17682],{},[1833,17641,17642],{},[1115,17643,17645],{"className":17644},[1144],[1146,17646,17647],{"xmlns":1148},[1150,17648,17649,17663],{},[1153,17650,17651,17657,17659,17661],{},[1156,17652,17653,17655],{},[1159,17654,11014],{},[1159,17656,1287],{},[1289,17658,1484],{"stretchy":1483},[1159,17660,11019],{},[1289,17662,1495],{"stretchy":1483},[1167,17664,15486],{"encoding":1169},[1833,17666,17667],{},"0,1",[1833,17669,17670],{},"0,2",[1833,17672,12758],{},[1833,17674,17675],{},"0,6",[1833,17677,17678],{},"0,7",[1833,17680,17681],{},"0,9",[1833,17683,17684],{},"1,0",[1110,17686,17687,17688,17710,17711,17734],{},"Graf (levý panel výše) odpovídá tabulce: funkce je nulová pod 10,8, skáče o ",[1115,17689,17691],{"className":17690},[1144],[1146,17692,17693],{"xmlns":1148},[1150,17694,17695,17707],{},[1153,17696,17697,17699,17701,17703,17705],{},[1163,17698,1402],{},[1159,17700,4223],{"mathvariant":1734},[1159,17702,1287],{},[1289,17704,1591],{},[1163,17706,17667],{},[1167,17708,17709],{"encoding":1169},"1\u002Fn = 0{,}1"," v každé jednoduché hodnotě a o ",[1115,17712,17714],{"className":17713},[1144],[1146,17715,17716],{"xmlns":1148},[1150,17717,17718,17731],{},[1153,17719,17720,17722,17724,17726,17728],{},[1163,17721,3209],{},[1159,17723,4223],{"mathvariant":1734},[1159,17725,1287],{},[1289,17727,1591],{},[1163,17729,17730],{},"0,3",[1167,17732,17733],{"encoding":1169},"3\u002Fn = 0{,}3"," v bodě 12,7, kde se hodnota opakuje třikrát.",[1103,17736,17738,17745],{"className":17737,"dataCallout":3094},[1106,3093],[1110,17739,17741,17744],{"className":17740},[1113],[1115,17742],{"className":17743,"ariaHidden":1121},[1118,3101,1120],"Příklad: Odpad materiálu",[1110,17746,17747],{},"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.",[3311,17749,17751],{"className":3313,"code":17750,"language":71,"meta":3315,"style":3315},"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",[3087,17752,17753,17804,17814,17824,17834,17854,17864,17879,17889],{"__ignoreMap":3315},[1115,17754,17755,17758,17760,17762,17764,17766,17768,17770,17772,17774,17776,17778,17780,17782,17784,17786,17788,17790,17792,17794,17796,17798,17800,17802],{"class":3320,"line":10},[1115,17756,17757],{"class":3323},"x4",[1115,17759,3328],{"class":3327},[1115,17761,3454],{"class":3331},[1115,17763,1484],{"class":3335},[1115,17765,16289],{"class":3343},[1115,17767,1405],{"class":3327},[1115,17769,16294],{"class":3343},[1115,17771,1405],{"class":3327},[1115,17773,16299],{"class":3343},[1115,17775,1405],{"class":3327},[1115,17777,16304],{"class":3343},[1115,17779,1405],{"class":3327},[1115,17781,16299],{"class":3343},[1115,17783,1405],{"class":3327},[1115,17785,16299],{"class":3343},[1115,17787,1405],{"class":3327},[1115,17789,16317],{"class":3343},[1115,17791,1405],{"class":3327},[1115,17793,16322],{"class":3343},[1115,17795,1405],{"class":3327},[1115,17797,16294],{"class":3343},[1115,17799,1405],{"class":3327},[1115,17801,16294],{"class":3343},[1115,17803,3520],{"class":3335},[1115,17805,17806,17808,17810,17812],{"class":3320,"line":27},[1115,17807,16430],{"class":3331},[1115,17809,1484],{"class":3335},[1115,17811,17757],{"class":3323},[1115,17813,3520],{"class":3335},[1115,17815,17816,17818,17820,17822],{"class":3320,"line":148},[1115,17817,16441],{"class":3331},[1115,17819,1484],{"class":3335},[1115,17821,17757],{"class":3323},[1115,17823,3520],{"class":3335},[1115,17825,17826,17828,17830,17832],{"class":3320,"line":111},[1115,17827,16463],{"class":3331},[1115,17829,1484],{"class":3335},[1115,17831,17757],{"class":3323},[1115,17833,3520],{"class":3335},[1115,17835,17836,17838,17840,17842,17844,17846,17848,17850,17852],{"class":3320,"line":96},[1115,17837,16022],{"class":3331},[1115,17839,1484],{"class":3335},[1115,17841,17757],{"class":3323},[1115,17843,4220],{"class":3335},[1115,17845,4257],{"class":3327},[1115,17847,16501],{"class":3331},[1115,17849,1484],{"class":3335},[1115,17851,17757],{"class":3323},[1115,17853,3520],{"class":3335},[1115,17855,17856,17858,17860,17862],{"class":3320,"line":89},[1115,17857,17163],{"class":3331},[1115,17859,1484],{"class":3335},[1115,17861,17757],{"class":3323},[1115,17863,3520],{"class":3335},[1115,17865,17866,17869,17871,17873,17875,17877],{"class":3320,"line":82},[1115,17867,17868],{"class":3323},"f4",[1115,17870,3328],{"class":3327},[1115,17872,17340],{"class":3331},[1115,17874,1484],{"class":3335},[1115,17876,17757],{"class":3323},[1115,17878,3520],{"class":3335},[1115,17880,17881,17883,17885,17887],{"class":3320,"line":75},[1115,17882,17351],{"class":3331},[1115,17884,1484],{"class":3335},[1115,17886,17868],{"class":3323},[1115,17888,3520],{"class":3335},[1115,17890,17891,17893,17895,17897,17899,17901],{"class":3320,"line":3510},[1115,17892,17868],{"class":3331},[1115,17894,1484],{"class":3335},[1115,17896,17351],{"class":3331},[1115,17898,1484],{"class":3335},[1115,17900,17868],{"class":3323},[1115,17902,13794],{"class":3335},[3311,17904,17907],{"className":17905,"code":17906,"language":3542,"meta":3315},[3540],"[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",[3087,17908,17906],{"__ignoreMap":3315},[1110,17910,17911,17912,17935],{},"Průměrný odpad je 3,86 % se směrodatnou odchylkou 0,18 % a mediánem 3,85 %. Pravý panel obrázku výše ukazuje tvar ",[1115,17913,17915],{"className":17914},[1144],[1146,17916,17917],{"xmlns":1148},[1150,17918,17919,17933],{},[1153,17920,17921,17927,17929,17931],{},[1156,17922,17923,17925],{},[1159,17924,11014],{},[1159,17926,1287],{},[1289,17928,1484],{"stretchy":1483},[1159,17930,11019],{},[1289,17932,1495],{"stretchy":1483},[1167,17934,15486],{"encoding":1169},": hodnota 3,8 se v souboru opakuje třikrát, proto zde funkce skáče o 0,3 najednou, stejně jako hodnota 4,0.",[1310,17937,17939],{"id":17938},"třídění-datového-souboru-do-tříd","Třídění datového souboru do tříd",[1110,17941,17942,17943,17946,17947,17960,17961,17964],{},"Je-li rozsah datového souboru velký (řádově přes 30 až 50 pozorování), hodnoty se před dalším zpracováním ",[1131,17944,17945],{},"roztřídí",": variační rozpětí ",[1115,17948,17950],{"className":17949},[1144],[1146,17951,17952],{"xmlns":1148},[1150,17953,17954,17958],{},[1153,17955,17956],{},[1159,17957,14524],{},[1167,17959,14524],{"encoding":1169}," se rozdělí na určitý počet ",[1131,17962,17963],{},"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.",[1110,17966,17967],{},"Výsledkem je tabulka četností se sloupci:",[1124,17969,17970,18050,18071,18092],{},[1127,17971,17972,17990,17991,18004,18005,18049],{},[1115,17973,17975],{"className":17974},[1144],[1146,17976,17977],{"xmlns":1148},[1150,17978,17979,17987],{},[1153,17980,17981],{},[1156,17982,17983,17985],{},[1159,17984,15503],{},[1159,17986,1492],{},[1167,17988,17989],{"encoding":1169},"I_j"," — ",[1115,17992,17994],{"className":17993},[1144],[1146,17995,17996],{"xmlns":1148},[1150,17997,17998,18002],{},[1153,17999,18000],{},[1159,18001,1492],{},[1167,18003,1492],{"encoding":1169},"-tý interval (v této kapitole vždy zleva uzavřený a zprava otevřený, ",[1115,18006,18008],{"className":18007},[1144],[1146,18009,18010],{"xmlns":1148},[1150,18011,18012,18046],{},[1153,18013,18014,18020,18022,18024,18030,18032,18044],{},[1156,18015,18016,18018],{},[1159,18017,15503],{},[1159,18019,1492],{},[1289,18021,1591],{},[1289,18023,12726],{"stretchy":1483},[1156,18025,18026,18028],{},[1159,18027,3338],{},[1159,18029,1492],{},[1289,18031,11193],{"separator":1121},[1156,18033,18034,18036],{},[1159,18035,3338],{},[1153,18037,18038,18040,18042],{},[1159,18039,1492],{},[1289,18041,5096],{},[1163,18043,1402],{},[1289,18045,1495],{"stretchy":1483},[1167,18047,18048],{"encoding":1169},"I_j = \\langle c_j; c_{j+1})","),",[1127,18051,18052,18070],{},[1115,18053,18055],{"className":18054},[1144],[1146,18056,18057],{"xmlns":1148},[1150,18058,18059,18067],{},[1153,18060,18061],{},[1156,18062,18063,18065],{},[1159,18064,13226],{},[1159,18066,1492],{},[1167,18068,18069],{"encoding":1169},"Z_j"," — střed (reprezentant) intervalu,",[1127,18072,18073,18091],{},[1115,18074,18076],{"className":18075},[1144],[1146,18077,18078],{"xmlns":1148},[1150,18079,18080,18088],{},[1153,18081,18082],{},[1156,18083,18084,18086],{},[1159,18085,11070],{},[1159,18087,1492],{},[1167,18089,18090],{"encoding":1169},"f_j"," — četnost, počet hodnot v intervalu,",[1127,18093,18094,18124,18125,5360,18153,1269],{},[1115,18095,18097],{"className":18096},[1144],[1146,18098,18099],{"xmlns":1148},[1150,18100,18101,18121],{},[1153,18102,18103,18109,18111,18117,18119],{},[1156,18104,18105,18107],{},[1159,18106,1110],{},[1159,18108,1492],{},[1289,18110,1591],{},[1156,18112,18113,18115],{},[1159,18114,11070],{},[1159,18116,1492],{},[1159,18118,4223],{"mathvariant":1734},[1159,18120,1287],{},[1167,18122,18123],{"encoding":1169},"p_j = f_j\u002Fn"," — relativní četnost, přičemž ",[1115,18126,18128],{"className":18127},[1144],[1146,18129,18130],{"xmlns":1148},[1150,18131,18132,18150],{},[1153,18133,18134,18140,18146,18148],{},[1156,18135,18136,18138],{},[1289,18137,1597],{},[1159,18139,1492],{},[1156,18141,18142,18144],{},[1159,18143,11070],{},[1159,18145,1492],{},[1289,18147,1591],{},[1159,18149,1287],{},[1167,18151,18152],{"encoding":1169},"\\sum_j f_j = n",[1115,18154,18156],{"className":18155},[1144],[1146,18157,18158],{"xmlns":1148},[1150,18159,18160,18178],{},[1153,18161,18162,18168,18174,18176],{},[1156,18163,18164,18166],{},[1289,18165,1597],{},[1159,18167,1492],{},[1156,18169,18170,18172],{},[1159,18171,1110],{},[1159,18173,1492],{},[1289,18175,1591],{},[1163,18177,1402],{},[1167,18179,18180],{"encoding":1169},"\\sum_j p_j = 1",[1110,18182,18183,18184,18187,18188,18191,18192,18195,18196,18199,18200,4226,18203,18220,18221,18224,18225,4226,18228,1420,18245,18248],{},"V R se třídění provádí příkazem ",[3087,18185,18186],{},"hist()"," — buď necháme R zvolit třídy samo (",[3087,18189,18190],{},"hist(x)","), nebo zadáme hranice přímo (",[3087,18193,18194],{},"hist(x, br = seq(0, 550, by = 50))","). Uložením výsledku do proměnné (",[3087,18197,18198],{},"y \u003C- hist(...)",") získáme jednotlivé sloupce tabulky: ",[3087,18201,18202],{},"y$counts",[1115,18204,18206],{"className":18205},[1144],[1146,18207,18208],{"xmlns":1148},[1150,18209,18210,18218],{},[1153,18211,18212],{},[1156,18213,18214,18216],{},[1159,18215,11070],{},[1159,18217,1492],{},[1167,18219,18090],{"encoding":1169},"), ",[3087,18222,18223],{},"y$breaks"," (hranice tříd), ",[3087,18226,18227],{},"y$mids",[1115,18229,18231],{"className":18230},[1144],[1146,18232,18233],{"xmlns":1148},[1150,18234,18235,18243],{},[1153,18236,18237],{},[1156,18238,18239,18241],{},[1159,18240,13226],{},[1159,18242,1492],{},[1167,18244,18069],{"encoding":1169},[3087,18246,18247],{},"y$density"," (relativní četnosti na škále hustoty).",[1110,18250,18251,18252,18269,18270,18272,18273,18309,18310,18313,18314,1269],{},"Interval ",[1115,18253,18255],{"className":18254},[1144],[1146,18256,18257],{"xmlns":1148},[1150,18258,18259,18267],{},[1153,18260,18261],{},[1156,18262,18263,18265],{},[1159,18264,15503],{},[1159,18266,1492],{},[1167,18268,17989],{"encoding":1169}," je ve výchozím nastavení ",[3087,18271,18186],{}," zleva otevřený a zprava uzavřený, ",[1115,18274,18276],{"className":18275},[1144],[1146,18277,18278],{"xmlns":1148},[1150,18279,18280,18306],{},[1153,18281,18282,18284,18290,18292,18304],{},[1289,18283,1484],{"stretchy":1483},[1156,18285,18286,18288],{},[1159,18287,3338],{},[1159,18289,1492],{},[1289,18291,11193],{"separator":1121},[1156,18293,18294,18296],{},[1159,18295,3338],{},[1153,18297,18298,18300,18302],{},[1159,18299,1492],{},[1289,18301,5096],{},[1163,18303,1402],{},[1289,18305,11743],{"stretchy":1483},[1167,18307,18308],{"encoding":1169},"(c_j; c_{j+1}\\rangle"," — opačně, než jak třídy zapisujeme v této kapitole. Parametr ",[3087,18311,18312],{},"right = FALSE"," třídy obrátí na ",[1115,18315,18317],{"className":18316},[1144],[1146,18318,18319],{"xmlns":1148},[1150,18320,18321,18347],{},[1153,18322,18323,18325,18331,18333,18345],{},[1289,18324,12726],{"stretchy":1483},[1156,18326,18327,18329],{},[1159,18328,3338],{},[1159,18330,1492],{},[1289,18332,11193],{"separator":1121},[1156,18334,18335,18337],{},[1159,18336,3338],{},[1153,18338,18339,18341,18343],{},[1159,18340,1492],{},[1289,18342,5096],{},[1163,18344,1402],{},[1289,18346,1495],{"stretchy":1483},[1167,18348,18349],{"encoding":1169},"\\langle c_j; c_{j+1})",[1110,18351,18352],{},[4002,18353],{"alt":18354,"className":18355,"src":18356},"mask-ps-histogram-trideni",[1321,4006],"\u002Fwiki-assets\u002Fmask-ps-histogram-trideni.png",[1103,18358,18360,18367],{"className":18359,"dataCallout":3094},[1106,3093],[1110,18361,18363,18366],{"className":18362},[1113],[1115,18364],{"className":18365,"ariaHidden":1121},[1118,3101,1120],"Příklad: Třídění datového souboru",[1110,18368,18369],{},"Byly provedeny zkoušky životnosti nového výrobku. Datový soubor obsahuje 68 hodnot doby do poruchy (v minutách). Určete odhady charakteristik a zákona rozdělení.",[3311,18371,18373],{"className":3313,"code":18372,"language":71,"meta":3315,"style":3315},"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",[3087,18374,18375,18432,18483,18533,18584,18634,18682,18722,18732,18752,18816,18825,18855],{"__ignoreMap":3315},[1115,18376,18377,18380,18382,18384,18386,18389,18391,18394,18396,18399,18401,18404,18406,18408,18410,18412,18414,18416,18418,18421,18423,18425,18427,18430],{"class":3320,"line":10},[1115,18378,18379],{"class":3323},"x9",[1115,18381,3328],{"class":3327},[1115,18383,3454],{"class":3331},[1115,18385,1484],{"class":3335},[1115,18387,18388],{"class":3343},"101",[1115,18390,1405],{"class":3327},[1115,18392,18393],{"class":3343}," 338",[1115,18395,1405],{"class":3327},[1115,18397,18398],{"class":3343}," 150",[1115,18400,1405],{"class":3327},[1115,18402,18403],{"class":3343}," 47",[1115,18405,1405],{"class":3327},[1115,18407,13778],{"class":3343},[1115,18409,1405],{"class":3327},[1115,18411,3799],{"class":3343},[1115,18413,1405],{"class":3327},[1115,18415,3353],{"class":3343},[1115,18417,1405],{"class":3327},[1115,18419,18420],{"class":3343}," 392",[1115,18422,1405],{"class":3327},[1115,18424,14295],{"class":3343},[1115,18426,1405],{"class":3327},[1115,18428,18429],{"class":3343}," 73",[1115,18431,3356],{"class":3327},[1115,18433,18434,18437,18439,18442,18444,18447,18449,18452,18454,18456,18458,18461,18463,18466,18468,18471,18473,18476,18478,18481],{"class":3320,"line":27},[1115,18435,18436],{"class":3343},"        367",[1115,18438,1405],{"class":3327},[1115,18440,18441],{"class":3343}," 54",[1115,18443,1405],{"class":3327},[1115,18445,18446],{"class":3343}," 114",[1115,18448,1405],{"class":3327},[1115,18450,18451],{"class":3343}," 213",[1115,18453,1405],{"class":3327},[1115,18455,3371],{"class":3343},[1115,18457,1405],{"class":3327},[1115,18459,18460],{"class":3343}," 341",[1115,18462,1405],{"class":3327},[1115,18464,18465],{"class":3343}," 313",[1115,18467,1405],{"class":3327},[1115,18469,18470],{"class":3343}," 112",[1115,18472,1405],{"class":3327},[1115,18474,18475],{"class":3343}," 343",[1115,18477,1405],{"class":3327},[1115,18479,18480],{"class":3343}," 151",[1115,18482,3356],{"class":3327},[1115,18484,18485,18488,18490,18493,18495,18498,18500,18503,18505,18508,18510,18512,18514,18517,18519,18521,18523,18526,18528,18531],{"class":3320,"line":148},[1115,18486,18487],{"class":3343},"        9",[1115,18489,1405],{"class":3327},[1115,18491,18492],{"class":3343}," 160",[1115,18494,1405],{"class":3327},[1115,18496,18497],{"class":3343}," 18",[1115,18499,1405],{"class":3327},[1115,18501,18502],{"class":3343}," 113",[1115,18504,1405],{"class":3327},[1115,18506,18507],{"class":3343}," 77",[1115,18509,1405],{"class":3327},[1115,18511,3371],{"class":3343},[1115,18513,1405],{"class":3327},[1115,18515,18516],{"class":3343}," 159",[1115,18518,1405],{"class":3327},[1115,18520,3353],{"class":3343},[1115,18522,1405],{"class":3327},[1115,18524,18525],{"class":3343}," 119",[1115,18527,1405],{"class":3327},[1115,18529,18530],{"class":3343}," 130",[1115,18532,3356],{"class":3327},[1115,18534,18535,18538,18540,18543,18545,18548,18550,18552,18554,18557,18559,18562,18564,18567,18569,18572,18574,18577,18579,18582],{"class":3320,"line":111},[1115,18536,18537],{"class":3343},"        140",[1115,18539,1405],{"class":3327},[1115,18541,18542],{"class":3343}," 161",[1115,18544,1405],{"class":3327},[1115,18546,18547],{"class":3343}," 379",[1115,18549,1405],{"class":3327},[1115,18551,18441],{"class":3343},[1115,18553,1405],{"class":3327},[1115,18555,18556],{"class":3343}," 373",[1115,18558,1405],{"class":3327},[1115,18560,18561],{"class":3343}," 168",[1115,18563,1405],{"class":3327},[1115,18565,18566],{"class":3343}," 365",[1115,18568,1405],{"class":3327},[1115,18570,18571],{"class":3343}," 110",[1115,18573,1405],{"class":3327},[1115,18575,18576],{"class":3343}," 145",[1115,18578,1405],{"class":3327},[1115,18580,18581],{"class":3343}," 88",[1115,18583,3356],{"class":3327},[1115,18585,18586,18589,18591,18594,18596,18599,18601,18604,18606,18609,18611,18613,18615,18618,18620,18622,18624,18627,18629,18632],{"class":3320,"line":96},[1115,18587,18588],{"class":3343},"        74",[1115,18590,1405],{"class":3327},[1115,18592,18593],{"class":3343}," 46",[1115,18595,1405],{"class":3327},[1115,18597,18598],{"class":3343}," 246",[1115,18600,1405],{"class":3327},[1115,18602,18603],{"class":3343}," 259",[1115,18605,1405],{"class":3327},[1115,18607,18608],{"class":3343}," 19",[1115,18610,1405],{"class":3327},[1115,18612,18525],{"class":3343},[1115,18614,1405],{"class":3327},[1115,18616,18617],{"class":3343}," 48",[1115,18619,1405],{"class":3327},[1115,18621,15156],{"class":3343},[1115,18623,1405],{"class":3327},[1115,18625,18626],{"class":3343}," 163",[1115,18628,1405],{"class":3327},[1115,18630,18631],{"class":3343}," 179",[1115,18633,3356],{"class":3327},[1115,18635,18636,18639,18641,18643,18645,18648,18650,18653,18655,18658,18660,18662,18664,18666,18668,18670,18672,18675,18677,18680],{"class":3320,"line":89},[1115,18637,18638],{"class":3343},"        194",[1115,18640,1405],{"class":3327},[1115,18642,3764],{"class":3343},[1115,18644,1405],{"class":3327},[1115,18646,18647],{"class":3343}," 49",[1115,18649,1405],{"class":3327},[1115,18651,18652],{"class":3343}," 501",[1115,18654,1405],{"class":3327},[1115,18656,18657],{"class":3343}," 193",[1115,18659,1405],{"class":3327},[1115,18661,18608],{"class":3343},[1115,18663,1405],{"class":3327},[1115,18665,14295],{"class":3343},[1115,18667,1405],{"class":3327},[1115,18669,3799],{"class":3343},[1115,18671,1405],{"class":3327},[1115,18673,18674],{"class":3343}," 221",[1115,18676,1405],{"class":3327},[1115,18678,18679],{"class":3343}," 300",[1115,18681,3356],{"class":3327},[1115,18683,18684,18687,18689,18691,18693,18696,18698,18701,18703,18706,18708,18711,18713,18715,18717,18720],{"class":3320,"line":82},[1115,18685,18686],{"class":3343},"        88",[1115,18688,1405],{"class":3327},[1115,18690,3348],{"class":3343},[1115,18692,1405],{"class":3327},[1115,18694,18695],{"class":3343}," 428",[1115,18697,1405],{"class":3327},[1115,18699,18700],{"class":3343}," 249",[1115,18702,1405],{"class":3327},[1115,18704,18705],{"class":3343}," 25",[1115,18707,1405],{"class":3327},[1115,18709,18710],{"class":3343}," 209",[1115,18712,1405],{"class":3327},[1115,18714,18441],{"class":3343},[1115,18716,1405],{"class":3327},[1115,18718,18719],{"class":3343}," 91",[1115,18721,3520],{"class":3335},[1115,18723,18724,18726,18728,18730],{"class":3320,"line":75},[1115,18725,16430],{"class":3331},[1115,18727,1484],{"class":3335},[1115,18729,18379],{"class":3323},[1115,18731,3520],{"class":3335},[1115,18733,18734,18736,18738,18740,18742,18744,18746,18748,18750],{"class":3320,"line":3510},[1115,18735,16022],{"class":3331},[1115,18737,1484],{"class":3335},[1115,18739,18379],{"class":3323},[1115,18741,4220],{"class":3335},[1115,18743,4257],{"class":3327},[1115,18745,16501],{"class":3331},[1115,18747,1484],{"class":3335},[1115,18749,18379],{"class":3323},[1115,18751,3520],{"class":3335},[1115,18753,18754,18757,18759,18762,18764,18766,18768,18771,18773,18776,18778,18780,18782,18785,18787,18790,18792,18794,18796,18798,18801,18803,18805,18807,18810,18812,18814],{"class":3320,"line":72},[1115,18755,18756],{"class":3323},"y9",[1115,18758,3328],{"class":3327},[1115,18760,18761],{"class":3331}," hist",[1115,18763,1484],{"class":3335},[1115,18765,18379],{"class":3323},[1115,18767,1405],{"class":3327},[1115,18769,18770],{"class":3323}," br",[1115,18772,3416],{"class":3327},[1115,18774,18775],{"class":3331}," seq",[1115,18777,1484],{"class":3335},[1115,18779,1165],{"class":3343},[1115,18781,1405],{"class":3327},[1115,18783,18784],{"class":3343}," 550",[1115,18786,1405],{"class":3327},[1115,18788,18789],{"class":3323}," by",[1115,18791,3416],{"class":3327},[1115,18793,5864],{"class":3343},[1115,18795,1495],{"class":3335},[1115,18797,1405],{"class":3327},[1115,18799,18800],{"class":3323}," right",[1115,18802,3416],{"class":3327},[1115,18804,5957],{"class":3343},[1115,18806,1405],{"class":3327},[1115,18808,18809],{"class":3323}," plot",[1115,18811,3416],{"class":3327},[1115,18813,5957],{"class":3343},[1115,18815,3520],{"class":3335},[1115,18817,18818,18820,18822],{"class":3320,"line":25},[1115,18819,18756],{"class":3323},[1115,18821,3533],{"class":3327},[1115,18823,18824],{"class":3323},"counts\n",[1115,18826,18827,18829,18831,18833,18835,18838,18840,18843,18845,18847,18849,18851,18853],{"class":3320,"line":65},[1115,18828,14281],{"class":3331},[1115,18830,1484],{"class":3335},[1115,18832,18756],{"class":3323},[1115,18834,3533],{"class":3327},[1115,18836,18837],{"class":3323},"counts",[1115,18839,14376],{"class":3327},[1115,18841,18842],{"class":3331}," length",[1115,18844,1484],{"class":3335},[1115,18846,18379],{"class":3323},[1115,18848,1495],{"class":3335},[1115,18850,1405],{"class":3327},[1115,18852,15156],{"class":3343},[1115,18854,3520],{"class":3335},[1115,18856,18857,18859,18861,18863,18865,18867,18869,18871],{"class":3320,"line":63},[1115,18858,16441],{"class":3331},[1115,18860,1484],{"class":3335},[1115,18862,18379],{"class":3323},[1115,18864,16480],{"class":3335},[1115,18866,16463],{"class":3331},[1115,18868,1484],{"class":3335},[1115,18870,18379],{"class":3323},[1115,18872,3520],{"class":3335},[3311,18874,18877],{"className":18875,"code":18876,"language":3542,"meta":3315},[3540],"[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",[3087,18878,18876],{"__ignoreMap":3315},[1110,18880,18881,18882,18910],{},"Variační rozpětí je ",[1115,18883,18885],{"className":18884},[1144],[1146,18886,18887],{"xmlns":1148},[1150,18888,18889,18907],{},[1153,18890,18891,18893,18895,18898,18900,18902,18904],{},[1159,18892,14524],{},[1289,18894,1591],{},[1163,18896,18897],{},"501",[1289,18899,2681],{},[1163,18901,1189],{},[1289,18903,1591],{},[1163,18905,18906],{},"499",[1167,18908,18909],{"encoding":1169},"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:",[1710,18912,18913,19009],{},[1713,18914,18915],{},[1716,18916,18917,18932,18951,18970,18989],{},[1719,18918,18919],{},[1115,18920,18922],{"className":18921},[1144],[1146,18923,18924],{"xmlns":1148},[1150,18925,18926,18930],{},[1153,18927,18928],{},[1159,18929,1492],{},[1167,18931,1492],{"encoding":1169},[1719,18933,18934],{},[1115,18935,18937],{"className":18936},[1144],[1146,18938,18939],{"xmlns":1148},[1150,18940,18941,18949],{},[1153,18942,18943],{},[1156,18944,18945,18947],{},[1159,18946,15503],{},[1159,18948,1492],{},[1167,18950,17989],{"encoding":1169},[1719,18952,18953],{},[1115,18954,18956],{"className":18955},[1144],[1146,18957,18958],{"xmlns":1148},[1150,18959,18960,18968],{},[1153,18961,18962],{},[1156,18963,18964,18966],{},[1159,18965,13226],{},[1159,18967,1492],{},[1167,18969,18069],{"encoding":1169},[1719,18971,18972],{},[1115,18973,18975],{"className":18974},[1144],[1146,18976,18977],{"xmlns":1148},[1150,18978,18979,18987],{},[1153,18980,18981],{},[1156,18982,18983,18985],{},[1159,18984,11070],{},[1159,18986,1492],{},[1167,18988,18090],{"encoding":1169},[1719,18990,18991],{},[1115,18992,18994],{"className":18993},[1144],[1146,18995,18996],{"xmlns":1148},[1150,18997,18998,19006],{},[1153,18999,19000],{},[1156,19001,19002,19004],{},[1159,19003,1110],{},[1159,19005,1492],{},[1167,19007,19008],{"encoding":1169},"p_j",[1828,19010,19011,19026,19041,19056,19069,19084,19099,19113,19128,19142,19157],{},[1716,19012,19013,19015,19018,19020,19023],{},[1833,19014,1402],{},[1833,19016,19017],{},"⟨0; 50)",[1833,19019,3677],{},[1833,19021,19022],{},"19",[1833,19024,19025],{},"0,279",[1716,19027,19028,19030,19033,19036,19038],{},[1833,19029,1189],{},[1833,19031,19032],{},"⟨50; 100)",[1833,19034,19035],{},"75",[1833,19037,1870],{},[1833,19039,19040],{},"0,162",[1716,19042,19043,19045,19048,19051,19053],{},[1833,19044,3209],{},[1833,19046,19047],{},"⟨100; 150)",[1833,19049,19050],{},"125",[1833,19052,13334],{},[1833,19054,19055],{},"0,147",[1716,19057,19058,19060,19063,19065,19067],{},[1833,19059,3159],{},[1833,19061,19062],{},"⟨150; 200)",[1833,19064,11779],{},[1833,19066,13334],{},[1833,19068,19055],{},[1716,19070,19071,19073,19076,19079,19081],{},[1833,19072,14227],{},[1833,19074,19075],{},"⟨200; 250)",[1833,19077,19078],{},"225",[1833,19080,14227],{},[1833,19082,19083],{},"0,074",[1716,19085,19086,19088,19091,19094,19096],{},[1833,19087,3583],{},[1833,19089,19090],{},"⟨250; 300)",[1833,19092,19093],{},"275",[1833,19095,1402],{},[1833,19097,19098],{},"0,015",[1716,19100,19101,19103,19106,19109,19111],{},[1833,19102,17633],{},[1833,19104,19105],{},"⟨300; 350)",[1833,19107,19108],{},"325",[1833,19110,14227],{},[1833,19112,19083],{},[1716,19114,19115,19118,19121,19124,19126],{},[1833,19116,19117],{},"8",[1833,19119,19120],{},"⟨350; 400)",[1833,19122,19123],{},"375",[1833,19125,14227],{},[1833,19127,19083],{},[1716,19129,19130,19132,19135,19138,19140],{},[1833,19131,3212],{},[1833,19133,19134],{},"⟨400; 450)",[1833,19136,19137],{},"425",[1833,19139,1402],{},[1833,19141,19098],{},[1716,19143,19144,19146,19149,19152,19154],{},[1833,19145,13334],{},[1833,19147,19148],{},"⟨450; 500)",[1833,19150,19151],{},"475",[1833,19153,1165],{},[1833,19155,19156],{},"0,000",[1716,19158,19159,19161,19164,19167,19169],{},[1833,19160,1870],{},[1833,19162,19163],{},"⟨500; ∞)",[1833,19165,19166],{},"525",[1833,19168,1402],{},[1833,19170,19098],{},[1110,19172,19173,19174,19191,19192,19209,19210,2568,19233,2568,19261,19280,19281,2568,19304,19323],{},"Asi 27,9 % výrobků vydrželo méně než 50 minut, jen asi 1,5 % mezi 250 a 300 minutami. Charakteristiky spočtené ze středů tříd ",[1115,19175,19177],{"className":19176},[1144],[1146,19178,19179],{"xmlns":1148},[1150,19180,19181,19189],{},[1153,19182,19183],{},[1156,19184,19185,19187],{},[1159,19186,13226],{},[1159,19188,1492],{},[1167,19190,18069],{"encoding":1169}," (vážený průměr a rozptyl se střední hodnotou nahrazenou ",[1115,19193,19195],{"className":19194},[1144],[1146,19196,19197],{"xmlns":1148},[1150,19198,19199,19207],{},[1153,19200,19201],{},[1156,19202,19203,19205],{},[1159,19204,13226],{},[1159,19206,1492],{},[1167,19208,18069],{"encoding":1169},") vycházejí ",[1115,19211,19213],{"className":19212},[1144],[1146,19214,19215],{"xmlns":1148},[1150,19216,19217,19230],{},[1153,19218,19219,19225,19227],{},[2339,19220,19221,19223],{"accent":1121},[1159,19222,11019],{},[1289,19224,15762],{},[1289,19226,13741],{},[1163,19228,19229],{},"149,26",[1167,19231,19232],{"encoding":1169},"\\bar{x} \\approx 149{,}26",[1115,19234,19236],{"className":19235},[1144],[1146,19237,19238],{"xmlns":1148},[1150,19239,19240,19258],{},[1153,19241,19242,19248,19250,19253,19255],{},[1182,19243,19244,19246],{},[1159,19245,1463],{},[1163,19247,1189],{},[1289,19249,13741],{},[1163,19251,19252],{},"15",[2525,19254,2527],{},[1163,19256,19257],{},"484,5",[1167,19259,19260],{"encoding":1169},"s^2 \\approx 15\\,484{,}5",[1115,19262,19264],{"className":19263},[1144],[1146,19265,19266],{"xmlns":1148},[1150,19267,19268,19277],{},[1153,19269,19270,19272,19274],{},[1159,19271,1463],{},[1289,19273,13741],{},[1163,19275,19276],{},"124,44",[1167,19278,19279],{"encoding":1169},"s \\approx 124{,}44"," — blízko hodnotám ",[1115,19282,19284],{"className":19283},[1144],[1146,19285,19286],{"xmlns":1148},[1150,19287,19288,19301],{},[1153,19289,19290,19296,19298],{},[2339,19291,19292,19294],{"accent":1121},[1159,19293,11019],{},[1289,19295,15762],{},[1289,19297,1591],{},[1163,19299,19300],{},"145,44",[1167,19302,19303],{"encoding":1169},"\\bar{x}=145{,}44",[1115,19305,19307],{"className":19306},[1144],[1146,19308,19309],{"xmlns":1148},[1150,19310,19311,19320],{},[1153,19312,19313,19315,19317],{},[1159,19314,1463],{},[1289,19316,1591],{},[1163,19318,19319],{},"126,13",[1167,19321,19322],{"encoding":1169},"s=126{,}13"," spočteným přímo z nerozdělených dat; malý rozdíl vzniká tím, že třídění nahrazuje skutečné hodnoty středy tříd.",[1110,19325,19326,19327,19330,19331,19367,19368,19386,19387,19401,19402,19428,19429,19431,19432,4485],{},"Tvar histogramu — vysoká četnost u krátkých dob, rychlý pokles — odpovídá ",[1131,19328,19329],{},"exponenciálnímu rozdělení",", které se pro dobu do poruchy používá nejčastěji. Jeho hustota je ",[1115,19332,19334],{"className":19333},[1144],[1146,19335,19336],{"xmlns":1148},[1150,19337,19338,19364],{},[1153,19339,19340,19342,19344,19346,19348,19350,19352],{},[1159,19341,11070],{},[1289,19343,1484],{"stretchy":1483},[1159,19345,11019],{},[1289,19347,1495],{"stretchy":1483},[1289,19349,1591],{},[1159,19351,14013],{},[1182,19353,19354,19356],{},[1159,19355,12893],{},[1153,19357,19358,19360,19362],{},[1289,19359,2681],{},[1159,19361,14013],{},[1159,19363,11019],{},[1167,19365,19366],{"encoding":1169},"f(x) = \\lambda e^{-\\lambda x}"," pro ",[1115,19369,19371],{"className":19370},[1144],[1146,19372,19373],{"xmlns":1148},[1150,19374,19375,19383],{},[1153,19376,19377,19379,19381],{},[1159,19378,11019],{},[1289,19380,2968],{},[1163,19382,1165],{},[1167,19384,19385],{"encoding":1169},"x \\ge 0",", s parametrem ",[1115,19388,19390],{"className":19389},[1144],[1146,19391,19392],{"xmlns":1148},[1150,19393,19394,19398],{},[1153,19395,19396],{},[1159,19397,14013],{},[1167,19399,19400],{"encoding":1169},"\\lambda"," odhadnutým jako ",[1115,19403,19405],{"className":19404},[1144],[1146,19406,19407],{"xmlns":1148},[1150,19408,19409,19425],{},[1153,19410,19411,19413,19415,19417,19419],{},[1159,19412,14013],{},[1289,19414,1591],{},[1163,19416,1402],{},[1159,19418,4223],{"mathvariant":1734},[2339,19420,19421,19423],{"accent":1121},[1159,19422,11019],{},[1289,19424,15762],{},[1167,19426,19427],{"encoding":1169},"\\lambda = 1\u002F\\bar{x}"," (v R je ",[3087,19430,14180],{}," parametrem ",[3087,19433,19434],{},"dexp()",[3311,19436,19438],{"className":3313,"code":19437,"language":71,"meta":3315,"style":3315},"rate9 \u003C- 1 \u002F mean(x9)\nrate9\n",[3087,19439,19440,19459],{"__ignoreMap":3315},[1115,19441,19442,19445,19447,19449,19451,19453,19455,19457],{"class":3320,"line":10},[1115,19443,19444],{"class":3323},"rate9",[1115,19446,3328],{"class":3327},[1115,19448,4260],{"class":3343},[1115,19450,14376],{"class":3327},[1115,19452,13532],{"class":3331},[1115,19454,1484],{"class":3335},[1115,19456,18379],{"class":3323},[1115,19458,3520],{"class":3335},[1115,19460,19461],{"class":3320,"line":27},[1115,19462,19463],{"class":3323},"rate9\n",[3311,19465,19468],{"className":19466,"code":19467,"language":3542,"meta":3315},[3540],"[1] 0.006875632\n",[3087,19469,19467],{"__ignoreMap":3315},[1110,19471,19472],{},[4002,19473],{"alt":19474,"className":19475,"src":19476},"mask-ps-hustota-fit",[1321,4006],"\u002Fwiki-assets\u002Fmask-ps-hustota-fit.png",[1110,19478,19479,19480,1269],{},"Proložená křivka dobře sleduje tvar sloupců. Zda data odpovídají exponenciálnímu rozdělení formálně, posuzuje test dobré shody popsaný v ",[1318,19481,6228],{"className":19482,"dataFsResolvedFilePath":1329,"href":1330},[1321],[1103,19484,19486,19493],{"className":19485,"dataCallout":3094},[1106,3093],[1110,19487,19489,19492],{"className":19488},[1113],[1115,19490],{"className":19491,"ariaHidden":1121},[1118,3101,1120],"Příklad: Doba života výrobku",[1110,19494,19495],{},"Sledováním doby života výrobku bylo naměřeno 50 hodnot (v minutách). Určete empirické charakteristiky, roztřiďte datový soubor a nakreslete histogram četností.",[3311,19497,19499],{"className":3313,"code":19498,"language":71,"meta":3315,"style":3315},"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",[3087,19500,19501,19562,19613,19664,19715,19767,19777,19803,19823,19881,19890,19898],{"__ignoreMap":3315},[1115,19502,19503,19506,19508,19510,19512,19515,19517,19520,19522,19525,19527,19530,19532,19535,19537,19540,19542,19545,19547,19550,19552,19555,19557,19560],{"class":3320,"line":10},[1115,19504,19505],{"class":3323},"x5",[1115,19507,3328],{"class":3327},[1115,19509,3454],{"class":3331},[1115,19511,1484],{"class":3335},[1115,19513,19514],{"class":3343},"63",[1115,19516,1405],{"class":3327},[1115,19518,19519],{"class":3343}," 156",[1115,19521,1405],{"class":3327},[1115,19523,19524],{"class":3343}," 184",[1115,19526,1405],{"class":3327},[1115,19528,19529],{"class":3343}," 786",[1115,19531,1405],{"class":3327},[1115,19533,19534],{"class":3343}," 822",[1115,19536,1405],{"class":3327},[1115,19538,19539],{"class":3343}," 278",[1115,19541,1405],{"class":3327},[1115,19543,19544],{"class":3343}," 15",[1115,19546,1405],{"class":3327},[1115,19548,19549],{"class":3343}," 561",[1115,19551,1405],{"class":3327},[1115,19553,19554],{"class":3343}," 229",[1115,19556,1405],{"class":3327},[1115,19558,19559],{"class":3343}," 8",[1115,19561,3356],{"class":3327},[1115,19563,19564,19567,19569,19572,19574,19576,19578,19581,19583,19586,19588,19591,19593,19596,19598,19601,19603,19606,19608,19611],{"class":3320,"line":27},[1115,19565,19566],{"class":3343},"        4",[1115,19568,1405],{"class":3327},[1115,19570,19571],{"class":3343}," 35",[1115,19573,1405],{"class":3327},[1115,19575,18429],{"class":3343},[1115,19577,1405],{"class":3327},[1115,19579,19580],{"class":3343}," 203",[1115,19582,1405],{"class":3327},[1115,19584,19585],{"class":3343}," 178",[1115,19587,1405],{"class":3327},[1115,19589,19590],{"class":3343}," 323",[1115,19592,1405],{"class":3327},[1115,19594,19595],{"class":3343}," 275",[1115,19597,1405],{"class":3327},[1115,19599,19600],{"class":3343}," 176",[1115,19602,1405],{"class":3327},[1115,19604,19605],{"class":3343}," 427",[1115,19607,1405],{"class":3327},[1115,19609,19610],{"class":3343}," 196",[1115,19612,3356],{"class":3327},[1115,19614,19615,19618,19620,19623,19625,19628,19630,19633,19635,19638,19640,19643,19645,19648,19650,19652,19654,19657,19659,19662],{"class":3320,"line":148},[1115,19616,19617],{"class":3343},"        415",[1115,19619,1405],{"class":3327},[1115,19621,19622],{"class":3343}," 140",[1115,19624,1405],{"class":3327},[1115,19626,19627],{"class":3343}," 17",[1115,19629,1405],{"class":3327},[1115,19631,19632],{"class":3343}," 293",[1115,19634,1405],{"class":3327},[1115,19636,19637],{"class":3343}," 991",[1115,19639,1405],{"class":3327},[1115,19641,19642],{"class":3343}," 100",[1115,19644,1405],{"class":3327},[1115,19646,19647],{"class":3343}," 189",[1115,19649,1405],{"class":3327},[1115,19651,19600],{"class":3343},[1115,19653,1405],{"class":3327},[1115,19655,19656],{"class":3343}," 672",[1115,19658,1405],{"class":3327},[1115,19660,19661],{"class":3343}," 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1050",[1115,19854,1405],{"class":3327},[1115,19856,18789],{"class":3323},[1115,19858,3416],{"class":3327},[1115,19860,18398],{"class":3343},[1115,19862,1495],{"class":3335},[1115,19864,1405],{"class":3327},[1115,19866,18800],{"class":3323},[1115,19868,3416],{"class":3327},[1115,19870,5957],{"class":3343},[1115,19872,1405],{"class":3327},[1115,19874,18809],{"class":3323},[1115,19876,3416],{"class":3327},[1115,19878,5957],{"class":3343},[1115,19880,3520],{"class":3335},[1115,19882,19883,19885,19887],{"class":3320,"line":72},[1115,19884,19827],{"class":3323},[1115,19886,3533],{"class":3327},[1115,19888,19889],{"class":3323},"mids\n",[1115,19891,19892,19894,19896],{"class":3320,"line":25},[1115,19893,19827],{"class":3323},[1115,19895,3533],{"class":3327},[1115,19897,18824],{"class":3323},[1115,19899,19900,19902,19904,19906,19908,19910,19912,19914,19916,19918,19920,19922,19924],{"class":3320,"line":65},[1115,19901,14281],{"class":3331},[1115,19903,1484],{"class":3335},[1115,19905,19827],{"class":3323},[1115,19907,3533],{"class":3327},[1115,19909,18837],{"class":3323},[1115,19911,14376],{"class":3327},[1115,19913,18842],{"class":3331},[1115,19915,1484],{"class":3335},[1115,19917,19505],{"class":3323},[1115,19919,1495],{"class":3335},[1115,19921,1405],{"class":3327},[1115,19923,15156],{"class":3343},[1115,19925,3520],{"class":3335},[3311,19927,19930],{"className":19928,"code":19929,"language":3542,"meta":3315},[3540],"[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",[3087,19931,19929],{"__ignoreMap":3315},[1110,19933,19934],{},"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.",[1310,19936,6027],{"id":6026},[1124,19938,19939,19957,20058,20126],{},[1127,19940,19941,1254,19944,19947,19948,19951,19952,19954,19955,1269],{},[1131,19942,19943],{},"Výchozí typ kvantilu v R.",[3087,19945,19946],{},"quantile()"," bez argumentu ",[3087,19949,19950],{},"type"," používá jiný výpočetní vzorec (",[3087,19953,16594],{},") než ruční postup v této kapitole — u některých souborů se hodnoty liší. Pro shodu s ručním výpočtem zadávejte ",[3087,19956,16590],{},[1127,19958,19959,19964,19965,19967,19968,20003,20004,20039,20040,20057],{},[1131,19960,19961,19962,1269],{},"Výchozí ohraničení tříd v ",[3087,19963,18186],{}," Bez ",[3087,19966,18312],{}," jsou třídy zprava uzavřené, ",[1115,19969,19971],{"className":19970},[1144],[1146,19972,19973],{"xmlns":1148},[1150,19974,19975,20001],{},[1153,19976,19977,19979,19985,19987,19999],{},[1289,19978,1484],{"stretchy":1483},[1156,19980,19981,19983],{},[1159,19982,3338],{},[1159,19984,1492],{},[1289,19986,11193],{"separator":1121},[1156,19988,19989,19991],{},[1159,19990,3338],{},[1153,19992,19993,19995,19997],{},[1159,19994,1492],{},[1289,19996,5096],{},[1163,19998,1402],{},[1289,20000,11743],{"stretchy":1483},[1167,20002,18308],{"encoding":1169}," — opačně než konvence ",[1115,20005,20007],{"className":20006},[1144],[1146,20008,20009],{"xmlns":1148},[1150,20010,20011,20037],{},[1153,20012,20013,20015,20021,20023,20035],{},[1289,20014,12726],{"stretchy":1483},[1156,20016,20017,20019],{},[1159,20018,3338],{},[1159,20020,1492],{},[1289,20022,11193],{"separator":1121},[1156,20024,20025,20027],{},[1159,20026,3338],{},[1153,20028,20029,20031,20033],{},[1159,20030,1492],{},[1289,20032,5096],{},[1163,20034,1402],{},[1289,20036,1495],{"stretchy":1483},[1167,20038,18349],{"encoding":1169}," použitá v tabulkách výše. Hodnota ležící přesně na hranici pak spadne do jiné třídy a četnosti ",[1115,20041,20043],{"className":20042},[1144],[1146,20044,20045],{"xmlns":1148},[1150,20046,20047,20055],{},[1153,20048,20049],{},[1156,20050,20051,20053],{},[1159,20052,11070],{},[1159,20054,1492],{},[1167,20056,18090],{"encoding":1169}," vyjdou jinak.",[1127,20059,20060,1254,20063,20081,20082,20095,20096,13349,20109,1269],{},[1131,20061,20062],{},"Rozptyl vs. směrodatná odchylka.",[1115,20064,20066],{"className":20065},[1144],[1146,20067,20068],{"xmlns":1148},[1150,20069,20070,20078],{},[1153,20071,20072],{},[1182,20073,20074,20076],{},[1159,20075,1463],{},[1163,20077,1189],{},[1167,20079,20080],{"encoding":1169},"s^2"," se udává v jednotkách znaku na druhou, ",[1115,20083,20085],{"className":20084},[1144],[1146,20086,20087],{"xmlns":1148},[1150,20088,20089,20093],{},[1153,20090,20091],{},[1159,20092,1463],{},[1167,20094,1463],{"encoding":1169}," ve stejných jednotkách jako data — pro interpretaci (např. „kolísání kolem průměru\") patří vždy ",[1115,20097,20099],{"className":20098},[1144],[1146,20100,20101],{"xmlns":1148},[1150,20102,20103,20107],{},[1153,20104,20105],{},[1159,20106,1463],{},[1167,20108,1463],{"encoding":1169},[1115,20110,20112],{"className":20111},[1144],[1146,20113,20114],{"xmlns":1148},[1150,20115,20116,20124],{},[1153,20117,20118],{},[1182,20119,20120,20122],{},[1159,20121,1463],{},[1163,20123,1189],{},[1167,20125,20080],{"encoding":1169},[1127,20127,20128,20131],{},[1131,20129,20130],{},"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.",[1310,20133,6215],{"id":6214},[1124,20135,20136,20141,20146,20151,20156,20161,20166],{},[1127,20137,20138],{},[1318,20139,1324],{"className":20140,"dataFsResolvedFilePath":1322,"href":1323},[1321],[1127,20142,20143],{},[1318,20144,6244],{"className":20145,"dataFsResolvedFilePath":6242,"href":6243},[1321],[1127,20147,20148],{},[1318,20149,6228],{"className":20150,"dataFsResolvedFilePath":1329,"href":1330},[1321],[1127,20152,20153],{},[1318,20154,6252],{"className":20155,"dataFsResolvedFilePath":6250,"href":6251},[1321],[1127,20157,20158],{},[1318,20159,1094],{"className":20160,"dataFsResolvedFilePath":15392,"href":15393},[1321],[1127,20162,20163],{},[1318,20164,6260],{"className":20165,"dataFsResolvedFilePath":6258,"href":6259},[1321],[1127,20167,20168],{},[1318,20169,6268],{"className":20170,"dataFsResolvedFilePath":6266,"href":6267},[1321],[1310,20172,6271],{"id":934},[1110,20174,6274,20175,6279],{},[6276,20176,6278],{},[6281,20178,20179],{},"html pre.shiki code .sP4rz, 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příkladům\u002F9.txt","topics\u002Fpopisna-statistika",[23,67,886,624,732,71],"S7Mr0W_asypsa_HGrO-Qlzv4HzQm_pC2nyjSomTKbnk",{"id":20203,"title":6252,"body":20204,"course":23,"courses":6294,"created":6295,"description":3315,"extension":6296,"meta":24896,"navigation":6298,"path":24897,"seo":24898,"sources":24899,"stem":24902,"tags":24903,"type":6306,"updated":6295,"__hash__":24904},"topics\u002Ftopics\u002Fregresni-a-korelacni-analyza.md",{"type":1096,"value":20205,"toc":24869},[20206,20209,20437,20439,20507,20513,20516,20594,20605,20609,20828,20835,20895,20898,20905,20927,20931,20937,20999,21049,21054,21065,21178,21184,21314,21317,21355,21361,21480,21497,21624,21630,21674,21678,21691,21719,21725,21782,21809,21815,21871,21891,21897,21918,21925,21928,22167,22171,22283,22603,22660,22702,22709,22713,22719,22843,22849,22898,22902,22908,22969,22975,23014,23058,23064,23157,23161,23167,23209,23215,23275,23386,23492,23496,23501,23579,23614,23645,23705,23742,23749,23812,23815,23836,23842,23872,23915,23919,23936,24056,24060,24082,24086,24097,24198,24202,24274,24281,24284,24287,24298,24365,24368,24372,24396,24399,24402,24606,24615,24645,24647,24782,24795,24808,24821,24823,24860,24862,24866],[1099,20207,6252],{"id":20208},"regresní-a-korelační-analýza",[1103,20210,20212,20218],{"className":20211,"dataCallout":1108},[1106,1107],[1110,20213,20215,1122],{"className":20214},[1113],[1115,20216],{"className":20217,"ariaHidden":1121},[1118,1119,1120],[1124,20219,20220,20258,20305,20383,20398,20404],{},[1127,20221,20222,20225,20226,20239,20240,20253,20254,20257],{},[1131,20223,20224],{},"Regresní analýza"," zkoumá jednostrannou závislost vysvětlované proměnné ",[1115,20227,20229],{"className":20228},[1144],[1146,20230,20231],{"xmlns":1148},[1150,20232,20233,20237],{},[1153,20234,20235],{},[1159,20236,11429],{},[1167,20238,11429],{"encoding":1169}," na vysvětlujících proměnných ",[1115,20241,20243],{"className":20242},[1144],[1146,20244,20245],{"xmlns":1148},[1150,20246,20247,20251],{},[1153,20248,20249],{},[1159,20250,11019],{},[1167,20252,11019],{"encoding":1169}," (příčina → následek); ",[1131,20255,20256],{},"korelační analýza"," měří intenzitu (těsnost) vzájemné závislosti.",[1127,20259,20260,20261,20264,20265,1269],{},"Parametry regresní funkce se odhadují ",[1131,20262,20263],{},"metodou nejmenších čtverců"," — minimalizací součtu čtverců reziduí ",[1115,20266,20268],{"className":20267},[1144],[1146,20269,20270],{"xmlns":1148},[1150,20271,20272,20302],{},[1153,20273,20274,20276,20278,20284,20286,20296],{},[1289,20275,1597],{},[1289,20277,1484],{"stretchy":1483},[1156,20279,20280,20282],{},[1159,20281,11429],{},[1159,20283,1487],{},[1289,20285,2681],{},[1156,20287,20288,20294],{},[2339,20289,20290,20292],{"accent":1121},[1159,20291,11429],{},[1289,20293,2345],{},[1159,20295,1487],{},[1182,20297,20298,20300],{},[1289,20299,1495],{"stretchy":1483},[1163,20301,1189],{},[1167,20303,20304],{"encoding":1169},"\\sum(y_i-\\hat y_i)^2",[1127,20306,20307,20308,1254,20311,20329,20330,1254,20333,20357,20358,1254,20361,1269],{},"Kvalitu fitu měří ",[1131,20309,20310],{},"index determinace",[1115,20312,20314],{"className":20313},[1144],[1146,20315,20316],{"xmlns":1148},[1150,20317,20318,20326],{},[1153,20319,20320],{},[1182,20321,20322,20324],{},[1159,20323,14524],{},[1163,20325,1189],{},[1167,20327,20328],{"encoding":1169},"R^2","; obecnou těsnost závislosti ",[1131,20331,20332],{},"index korelace",[1115,20334,20336],{"className":20335},[1144],[1146,20337,20338],{"xmlns":1148},[1150,20339,20340,20354],{},[1153,20341,20342,20344,20346],{},[1159,20343,15503],{},[1289,20345,1591],{},[4072,20347,20348],{},[1182,20349,20350,20352],{},[1159,20351,14524],{},[1163,20353,1189],{},[1167,20355,20356],{"encoding":1169},"I=\\sqrt{R^2}",", který je pro regresní přímku roven ",[1131,20359,20360],{},"koeficientu korelace",[1115,20362,20364],{"className":20363},[1144],[1146,20365,20366],{"xmlns":1148},[1150,20367,20368,20380],{},[1153,20369,20370],{},[1156,20371,20372,20374],{},[1159,20373,71],{},[1153,20375,20376,20378],{},[1159,20377,11019],{},[1159,20379,11429],{},[1167,20381,20382],{"encoding":1169},"r_{xy}",[1127,20384,20385,20386,20389,20390,20393,20394,20397],{},"Když přímka nestačí, volí se ",[1131,20387,20388],{},"parabolická, polynomická, hyperbolická nebo logaritmická"," regrese (stále lineární v parametrech, odhad metodou nejmenších čtverců) nebo ",[1131,20391,20392],{},"exponenciální"," regrese (nelineární v parametrech, odhad přes ",[3087,20395,20396],{},"nls2",").",[1127,20399,20400,20403],{},[1131,20401,20402],{},"Vícenásobná regrese"," rozšiřuje model o více regresorů; vyžaduje výběr proměnných (ENTER\u002Fstepwise), ověření šesti předpokladů modelu a kontrolu multikolinearity přes VIF.",[1127,20405,20406,20407,2568,20410,2568,20413,2568,20416,2568,20419,2568,20422,2568,20425,2568,20428,2568,20431,2568,20434,1269],{},"V R: ",[3087,20408,20409],{},"lm()",[3087,20411,20412],{},"nls2()",[3087,20414,20415],{},"summary()",[3087,20417,20418],{},"confint()",[3087,20420,20421],{},"predict()",[3087,20423,20424],{},"step()",[3087,20426,20427],{},"car::vif()",[3087,20429,20430],{},"lmtest::dwtest()",[3087,20432,20433],{},"whitestrap::white_test()",[3087,20435,20436],{},"shapiro.test()",[1310,20438,15540],{"id":15539},[1110,20440,20441,20444,20445,5360,20458,20471,20472,20474,20475,20488,20489,20502,20503,20506],{},[1318,20442,1324],{"className":20443,"dataFsResolvedFilePath":1322,"href":1323},[1321]," pracuje se dvěma znaky ",[1115,20446,20448],{"className":20447},[1144],[1146,20449,20450],{"xmlns":1148},[1150,20451,20452,20456],{},[1153,20453,20454],{},[1159,20455,11019],{},[1167,20457,11019],{"encoding":1169},[1115,20459,20461],{"className":20460},[1144],[1146,20462,20463],{"xmlns":1148},[1150,20464,20465,20469],{},[1153,20466,20467],{},[1159,20468,11429],{},[1167,20470,11429],{"encoding":1169}," zjištěnými na stejných jednotkách. ",[1131,20473,20224],{}," se zabývá jednostrannými závislostmi, kdy proti sobě stojí vysvětlující (nezávisle) proměnná ",[1115,20476,20478],{"className":20477},[1144],[1146,20479,20480],{"xmlns":1148},[1150,20481,20482,20486],{},[1153,20483,20484],{},[1159,20485,11019],{},[1167,20487,11019],{"encoding":1169}," v úloze příčiny a vysvětlovaná (závisle) proměnná ",[1115,20490,20492],{"className":20491},[1144],[1146,20493,20494],{"xmlns":1148},[1150,20495,20496,20500],{},[1153,20497,20498],{},[1159,20499,11429],{},[1167,20501,11429],{"encoding":1169}," v úloze následku. ",[1131,20504,20505],{},"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.",[1110,20508,20509,20510,20397],{},"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 (",[1131,20511,20512],{},"regresní funkce",[1110,20514,20515],{},"Druh regresní analýzy určuje struktura datového souboru:",[1124,20517,20518,20555],{},[1127,20519,20520,20523,20524,20537,20538,20551,20552,1405],{},[1131,20521,20522],{},"dvourozměrný datový soubor"," (jedna ",[1115,20525,20527],{"className":20526},[1144],[1146,20528,20529],{"xmlns":1148},[1150,20530,20531,20535],{},[1153,20532,20533],{},[1159,20534,11019],{},[1167,20536,11019],{"encoding":1169},", jedna ",[1115,20539,20541],{"className":20540},[1144],[1146,20542,20543],{"xmlns":1148},[1150,20544,20545,20549],{},[1153,20546,20547],{},[1159,20548,11429],{},[1167,20550,11429],{"encoding":1169},") → ",[1131,20553,20554],{},"regresní analýza dvou proměnných",[1127,20556,20557,20560,20561,20551,20591,1269],{},[1131,20558,20559],{},"vícerozměrný datový soubor"," (více ",[1115,20562,20564],{"className":20563},[1144],[1146,20565,20566],{"xmlns":1148},[1150,20567,20568,20588],{},[1153,20569,20570,20576,20578,20580,20582],{},[1156,20571,20572,20574],{},[1159,20573,11019],{},[1163,20575,1402],{},[1289,20577,1405],{"separator":1121},[1289,20579,1408],{},[1289,20581,1405],{"separator":1121},[1156,20583,20584,20586],{},[1159,20585,11019],{},[1159,20587,1110],{},[1167,20589,20590],{"encoding":1169},"x_1,\\dots,x_p",[1131,20592,20593],{},"vícenásobná regresní analýza",[1110,20595,20596,20597,20600,20601,20604],{},"Volba konkrétní regresní funkce by měla vycházet jak z ",[1131,20598,20599],{},"ekonomické teorie"," (ta napovídá, zda závislost roste, nebo klesá, zda je přímková, nebo zakřivená), tak z ",[1131,20602,20603],{},"grafické a matematicko-statistické analýzy"," dat — oba přístupy je vhodné kombinovat.",[1310,20606,20608],{"id":20607},"metoda-nejmenších-čtverců","Metoda nejmenších čtverců",[1110,20610,20611,20612,1254,20615,20669,20670,20688,20689,1254,20692,20748,20749,20767,20768,20785,20786,20824,20825,1269],{},"Rozlišují se ",[1131,20613,20614],{},"teoretická regresní funkce",[1115,20616,20618],{"className":20617},[1144],[1146,20619,20620],{"xmlns":1148},[1150,20621,20622,20666],{},[1153,20623,20624,20627,20629,20631,20633,20635,20637,20644,20646,20652,20654,20656,20658,20664],{},[1159,20625,20626],{},"η",[1289,20628,1591],{},[1159,20630,11070],{},[1289,20632,1484],{"stretchy":1483},[1159,20634,11019],{},[1289,20636,11193],{"separator":1121},[1156,20638,20639,20642],{},[1159,20640,20641],{},"β",[1163,20643,1165],{},[1289,20645,1405],{"separator":1121},[1156,20647,20648,20650],{},[1159,20649,20641],{},[1163,20651,1402],{},[1289,20653,1405],{"separator":1121},[1289,20655,1408],{},[1289,20657,1405],{"separator":1121},[1156,20659,20660,20662],{},[1159,20661,20641],{},[1159,20663,1110],{},[1289,20665,1495],{"stretchy":1483},[1167,20667,20668],{"encoding":1169},"\\eta = f(x;\\beta_0,\\beta_1,\\dots,\\beta_p)"," — neznámá, populační, daná neznámými parametry ",[1115,20671,20673],{"className":20672},[1144],[1146,20674,20675],{"xmlns":1148},[1150,20676,20677,20685],{},[1153,20678,20679],{},[1156,20680,20681,20683],{},[1159,20682,20641],{},[1159,20684,1487],{},[1167,20686,20687],{"encoding":1169},"\\beta_i"," — a ",[1131,20690,20691],{},"empirická regresní funkce",[1115,20693,20695],{"className":20694},[1144],[1146,20696,20697],{"xmlns":1148},[1150,20698,20699,20745],{},[1153,20700,20701,20707,20709,20711,20713,20715,20717,20723,20725,20731,20733,20735,20737,20743],{},[2339,20702,20703,20705],{"accent":1121},[1159,20704,11429],{},[1289,20706,2345],{},[1289,20708,1591],{},[1159,20710,11070],{},[1289,20712,1484],{"stretchy":1483},[1159,20714,11019],{},[1289,20716,11193],{"separator":1121},[1156,20718,20719,20721],{},[1159,20720,15807],{},[1163,20722,1165],{},[1289,20724,1405],{"separator":1121},[1156,20726,20727,20729],{},[1159,20728,15807],{},[1163,20730,1402],{},[1289,20732,1405],{"separator":1121},[1289,20734,1408],{},[1289,20736,1405],{"separator":1121},[1156,20738,20739,20741],{},[1159,20740,15807],{},[1159,20742,1110],{},[1289,20744,1495],{"stretchy":1483},[1167,20746,20747],{"encoding":1169},"\\hat y = f(x; b_0,b_1,\\dots,b_p)",", jejíž odhadnuté parametry ",[1115,20750,20752],{"className":20751},[1144],[1146,20753,20754],{"xmlns":1148},[1150,20755,20756,20764],{},[1153,20757,20758],{},[1156,20759,20760,20762],{},[1159,20761,15807],{},[1159,20763,1487],{},[1167,20765,20766],{"encoding":1169},"b_i"," jsou odhadem ",[1115,20769,20771],{"className":20770},[1144],[1146,20772,20773],{"xmlns":1148},[1150,20774,20775,20783],{},[1153,20776,20777],{},[1156,20778,20779,20781],{},[1159,20780,20641],{},[1159,20782,1487],{},[1167,20784,20687],{"encoding":1169}," vypočteným z konkrétních dat. Odchylky skutečných hodnot od empirické funkce, ",[1115,20787,20789],{"className":20788},[1144],[1146,20790,20791],{"xmlns":1148},[1150,20792,20793,20821],{},[1153,20794,20795,20801,20803,20809,20811],{},[1156,20796,20797,20799],{},[1159,20798,12893],{},[1159,20800,1487],{},[1289,20802,1591],{},[1156,20804,20805,20807],{},[1159,20806,11429],{},[1159,20808,1487],{},[1289,20810,2681],{},[1156,20812,20813,20819],{},[2339,20814,20815,20817],{"accent":1121},[1159,20816,11429],{},[1289,20818,2345],{},[1159,20820,1487],{},[1167,20822,20823],{"encoding":1169},"e_i=y_i-\\hat y_i",", se nazývají ",[1131,20826,20827],{},"rezidua",[1110,20829,20830,20831,20834],{},"Nejpoužívanější metodou odhadu parametrů je ",[1131,20832,20833],{},"metoda nejmenších čtverců (OLS)",": hledají se takové parametry, pro které je součet čtverců reziduí minimální,",[1115,20836,20838],{"className":20837},[1144],[1146,20839,20840],{"xmlns":1148,"display":1573},[1150,20841,20842,20892],{},[1153,20843,20844,20858,20860,20866,20868,20878,20884,20886,20888,20890],{},[1593,20845,20846,20848,20856],{},[1289,20847,1597],{},[1153,20849,20850,20852,20854],{},[1159,20851,1487],{},[1289,20853,1591],{},[1163,20855,1402],{},[1159,20857,1287],{},[1289,20859,1484],{"stretchy":1483},[1156,20861,20862,20864],{},[1159,20863,11429],{},[1159,20865,1487],{},[1289,20867,2681],{},[1156,20869,20870,20876],{},[2339,20871,20872,20874],{"accent":1121},[1159,20873,11429],{},[1289,20875,2345],{},[1159,20877,1487],{},[1182,20879,20880,20882],{},[1289,20881,1495],{"stretchy":1483},[1163,20883,1189],{},[1289,20885,11907],{},[1159,20887,4107],{},[1289,20889,4110],{},[1159,20891,1269],{"mathvariant":1734},[1167,20893,20894],{"encoding":1169},"\\sum_{i=1}^n (y_i - \\hat y_i)^2 \\to \\min.",[1110,20896,20897],{},"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.",[1110,20899,20900],{},[4002,20901],{"alt":20902,"className":20903,"src":20904},"mask-ra-primka-rezidua",[1321,4006],"\u002Fwiki-assets\u002Fmask-ra-primka-rezidua.png",[1110,20906,20907,20908,20926],{},"Obrázek ukazuje přesně to, co metoda minimalizuje: délky červených úseček jsou rezidua ",[1115,20909,20911],{"className":20910},[1144],[1146,20912,20913],{"xmlns":1148},[1150,20914,20915,20923],{},[1153,20916,20917],{},[1156,20918,20919,20921],{},[1159,20920,12893],{},[1159,20922,1487],{},[1167,20924,20925],{"encoding":1169},"e_i",", metoda nejmenších čtverců volí přímku tak, aby součet jejich čtverců byl nejmenší možný.",[1310,20928,20930],{"id":20929},"regresní-přímka","Regresní přímka",[1110,20932,20933,20934,1567],{},"Nejjednodušší regresní funkcí je ",[1131,20935,20936],{},"regresní přímka",[1115,20938,20940],{"className":20939},[1144],[1146,20941,20942],{"xmlns":1148,"display":1573},[1150,20943,20944,20996],{},[1153,20945,20946,20948,20950,20956,20958,20964,20966,20968,20970,20976,20978,20984,20986,20992,20994],{},[1159,20947,20626],{},[1289,20949,1591],{},[1156,20951,20952,20954],{},[1159,20953,20641],{},[1163,20955,1165],{},[1289,20957,5096],{},[1156,20959,20960,20962],{},[1159,20961,20641],{},[1163,20963,1402],{},[1159,20965,11019],{},[1289,20967,1405],{"separator":1121},[1621,20969],{"width":1623},[2339,20971,20972,20974],{"accent":1121},[1159,20973,11429],{},[1289,20975,2345],{},[1289,20977,1591],{},[1156,20979,20980,20982],{},[1159,20981,15807],{},[1163,20983,1165],{},[1289,20985,5096],{},[1156,20987,20988,20990],{},[1159,20989,15807],{},[1163,20991,1402],{},[1159,20993,11019],{},[1159,20995,1269],{"mathvariant":1734},[1167,20997,20998],{"encoding":1169},"\\eta = \\beta_0 + \\beta_1 x, \\qquad \\hat y = b_0 + b_1 x.",[1110,21000,21001,21002,21020,21021,21034,21035,21048],{},"Koeficient ",[1115,21003,21005],{"className":21004},[1144],[1146,21006,21007],{"xmlns":1148},[1150,21008,21009,21017],{},[1153,21010,21011],{},[1156,21012,21013,21015],{},[1159,21014,15807],{},[1163,21016,1402],{},[1167,21018,21019],{"encoding":1169},"b_1"," udává změnu průměru ",[1115,21022,21024],{"className":21023},[1144],[1146,21025,21026],{"xmlns":1148},[1150,21027,21028,21032],{},[1153,21029,21030],{},[1159,21031,11429],{},[1167,21033,11429],{"encoding":1169}," při jednotkové změně ",[1115,21036,21038],{"className":21037},[1144],[1146,21039,21040],{"xmlns":1148},[1150,21041,21042,21046],{},[1153,21043,21044],{},[1159,21045,11019],{},[1167,21047,11019],{"encoding":1169},"; jeho znaménko určuje, zda je závislost přímá, nebo nepřímá.",[21050,21051,21053],"h3",{"id":21052},"v-r","V R",[1110,21055,21056,21057,21060,21061,21064],{},"Vstupní data se nahrají buď ze souboru (",[3087,21058,21059],{},"d \u003C- read.table(\"data.txt\")",", případně ",[3087,21062,21063],{},"d \u003C- read.table(file.choose())","), nebo zapíší přímo jako vektory. Na šesti domácnostech sledujeme počet členů domácnosti a jejich týdenní výdaje:",[3311,21066,21068],{"className":3313,"code":21067,"language":71,"meta":3315,"style":3315},"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",[3087,21069,21070,21105,21146,21167],{"__ignoreMap":3315},[1115,21071,21072,21075,21077,21079,21081,21083,21085,21087,21089,21091,21093,21095,21097,21099,21101,21103],{"class":3320,"line":10},[1115,21073,21074],{"class":3323},"pocet_clenu",[1115,21076,3328],{"class":3327},[1115,21078,3454],{"class":3331},[1115,21080,1484],{"class":3335},[1115,21082,1402],{"class":3343},[1115,21084,1405],{"class":3327},[1115,21086,3799],{"class":3343},[1115,21088,1405],{"class":3327},[1115,21090,15156],{"class":3343},[1115,21092,1405],{"class":3327},[1115,21094,3419],{"class":3343},[1115,21096,1405],{"class":3327},[1115,21098,14295],{"class":3343},[1115,21100,1405],{"class":3327},[1115,21102,16531],{"class":3343},[1115,21104,3520],{"class":3335},[1115,21106,21107,21110,21112,21114,21116,21119,21121,21124,21126,21129,21131,21134,21136,21139,21141,21144],{"class":3320,"line":27},[1115,21108,21109],{"class":3323},"tydenni_vydaje",[1115,21111,3328],{"class":3327},[1115,21113,3454],{"class":3331},[1115,21115,1484],{"class":3335},[1115,21117,21118],{"class":3343},"490",[1115,21120,1405],{"class":3327},[1115,21122,21123],{"class":3343}," 820",[1115,21125,1405],{"class":3327},[1115,21127,21128],{"class":3343}," 1230",[1115,21130,1405],{"class":3327},[1115,21132,21133],{"class":3343}," 1570",[1115,21135,1405],{"class":3327},[1115,21137,21138],{"class":3343}," 1950",[1115,21140,1405],{"class":3327},[1115,21142,21143],{"class":3343}," 2320",[1115,21145,3520],{"class":3335},[1115,21147,21148,21150,21152,21155,21157,21159,21162,21165],{"class":3320,"line":148},[1115,21149,786],{"class":3323},[1115,21151,3328],{"class":3327},[1115,21153,21154],{"class":3331}," lm",[1115,21156,1484],{"class":3335},[1115,21158,21109],{"class":3323},[1115,21160,21161],{"class":3327}," ~",[1115,21163,21164],{"class":3323}," pocet_clenu",[1115,21166,3520],{"class":3335},[1115,21168,21169,21172,21174,21176],{"class":3320,"line":111},[1115,21170,21171],{"class":3331},"summary",[1115,21173,1484],{"class":3335},[1115,21175,786],{"class":3323},[1115,21177,3520],{"class":3335},[3311,21179,21182],{"className":21180,"code":21181,"language":3542,"meta":3315},[3540],"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",[3087,21183,21181],{"__ignoreMap":3315},[1110,21185,21186,21187,21219,21220,21223,21224,21254,21255,21285,21286,21289,21290,21313],{},"Odhadnutý model je ",[1115,21188,21190],{"className":21189},[1144],[1146,21191,21192],{"xmlns":1148},[1150,21193,21194,21216],{},[1153,21195,21196,21202,21204,21207,21209,21212,21214],{},[2339,21197,21198,21200],{"accent":1121},[1159,21199,11429],{},[1289,21201,2345],{},[1289,21203,1591],{},[1163,21205,21206],{},"108,7",[1289,21208,5096],{},[1163,21210,21211],{},"368,0",[2525,21213,2527],{},[1159,21215,11019],{},[1167,21217,21218],{"encoding":1169},"\\hat y = 108{,}7 + 368{,}0\\,x",". Sloupec ",[3087,21221,21222],{},"Pr(>|t|)"," je p-hodnota t-testu ",[1115,21225,21227],{"className":21226},[1144],[1146,21228,21229],{"xmlns":1148},[1150,21230,21231,21251],{},[1153,21232,21233,21239,21241,21247,21249],{},[1156,21234,21235,21237],{},[1159,21236,1161],{},[1163,21238,1165],{},[1289,21240,1567],{},[1156,21242,21243,21245],{},[1159,21244,20641],{},[1159,21246,1487],{},[1289,21248,1591],{},[1163,21250,1165],{},[1167,21252,21253],{"encoding":1169},"H_0:\\beta_i=0"," proti ",[1115,21256,21258],{"className":21257},[1144],[1146,21259,21260],{"xmlns":1148},[1150,21261,21262,21282],{},[1153,21263,21264,21270,21272,21278,21280],{},[1156,21265,21266,21268],{},[1159,21267,1161],{},[1163,21269,1402],{},[1289,21271,1567],{},[1156,21273,21274,21276],{},[1159,21275,20641],{},[1159,21277,1487],{},[1289,21279,15257],{"mathvariant":1734},[1163,21281,1165],{},[1167,21283,21284],{"encoding":1169},"H_1:\\beta_i\\neq0"," pro každý parametr — obě p-hodnoty jsou hluboko pod 0,05, oba parametry jsou tedy statisticky významné. ",[3087,21287,21288],{},"Multiple R-squared"," je index determinace ",[1115,21291,21293],{"className":21292},[1144],[1146,21294,21295],{"xmlns":1148},[1150,21296,21297,21310],{},[1153,21298,21299,21305,21307],{},[1182,21300,21301,21303],{},[1159,21302,14524],{},[1163,21304,1189],{},[1289,21306,1591],{},[1163,21308,21309],{},"0,9995",[1167,21311,21312],{"encoding":1169},"R^2=0{,}9995",": model vysvětluje 99,95 % rozptylu výdajů.",[1110,21315,21316],{},"Pro doplňkový přehled slouží přímé přístupové funkce:",[3311,21318,21320],{"className":3313,"code":21319,"language":71,"meta":3315,"style":3315},"coef(model)\nfitted(model)\nresiduals(model)\n",[3087,21321,21322,21333,21344],{"__ignoreMap":3315},[1115,21323,21324,21327,21329,21331],{"class":3320,"line":10},[1115,21325,21326],{"class":3331},"coef",[1115,21328,1484],{"class":3335},[1115,21330,786],{"class":3323},[1115,21332,3520],{"class":3335},[1115,21334,21335,21338,21340,21342],{"class":3320,"line":27},[1115,21336,21337],{"class":3331},"fitted",[1115,21339,1484],{"class":3335},[1115,21341,786],{"class":3323},[1115,21343,3520],{"class":3335},[1115,21345,21346,21349,21351,21353],{"class":3320,"line":148},[1115,21347,21348],{"class":3331},"residuals",[1115,21350,1484],{"class":3335},[1115,21352,786],{"class":3323},[1115,21354,3520],{"class":3335},[3311,21356,21359],{"className":21357,"code":21358,"language":3542,"meta":3315},[3540],"(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",[3087,21360,21358],{"__ignoreMap":3315},[1110,21362,21363,21366,21367,2568,21393,21396,21397,21419,21420,2568,21438,21441,21442,21479],{},[3087,21364,21365],{},"coef()"," vrací odhadnuté parametry ",[1115,21368,21370],{"className":21369},[1144],[1146,21371,21372],{"xmlns":1148},[1150,21373,21374,21390],{},[1153,21375,21376,21382,21384],{},[1156,21377,21378,21380],{},[1159,21379,15807],{},[1163,21381,1165],{},[1289,21383,1405],{"separator":1121},[1156,21385,21386,21388],{},[1159,21387,15807],{},[1163,21389,1402],{},[1167,21391,21392],{"encoding":1169},"b_0,b_1",[3087,21394,21395],{},"fitted()"," predikce ",[1115,21398,21400],{"className":21399},[1144],[1146,21401,21402],{"xmlns":1148},[1150,21403,21404,21416],{},[1153,21405,21406],{},[1156,21407,21408,21414],{},[2339,21409,21410,21412],{"accent":1121},[1159,21411,11429],{},[1289,21413,2345],{},[1159,21415,1487],{},[1167,21417,21418],{"encoding":1169},"\\hat y_i"," pro pozorované ",[1115,21421,21423],{"className":21422},[1144],[1146,21424,21425],{"xmlns":1148},[1150,21426,21427,21435],{},[1153,21428,21429],{},[1156,21430,21431,21433],{},[1159,21432,11019],{},[1159,21434,1487],{},[1167,21436,21437],{"encoding":1169},"x_i",[3087,21439,21440],{},"residuals()"," rezidua ",[1115,21443,21445],{"className":21444},[1144],[1146,21446,21447],{"xmlns":1148},[1150,21448,21449,21477],{},[1153,21450,21451,21457,21459,21465,21467],{},[1156,21452,21453,21455],{},[1159,21454,12893],{},[1159,21456,1487],{},[1289,21458,1591],{},[1156,21460,21461,21463],{},[1159,21462,11429],{},[1159,21464,1487],{},[1289,21466,2681],{},[1156,21468,21469,21475],{},[2339,21470,21471,21473],{"accent":1121},[1159,21472,11429],{},[1289,21474,2345],{},[1159,21476,1487],{},[1167,21478,20823],{"encoding":1169}," — stejná čísla, která na obrázku výše tvoří délky červených úseček.",[1110,21481,21482,21483,21496],{},"Intervaly spolehlivosti pro parametry a pro predikci v nových bodech ",[1115,21484,21486],{"className":21485},[1144],[1146,21487,21488],{"xmlns":1148},[1150,21489,21490,21494],{},[1153,21491,21492],{},[1159,21493,11019],{},[1167,21495,11019],{"encoding":1169}," (zde 7 a 8 členů domácnosti):",[3311,21498,21500],{"className":3313,"code":21499,"language":71,"meta":3315,"style":3315},"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",[3087,21501,21502,21522,21550,21589],{"__ignoreMap":3315},[1115,21503,21504,21507,21509,21511,21513,21516,21518,21520],{"class":3320,"line":10},[1115,21505,21506],{"class":3331},"confint",[1115,21508,1484],{"class":3335},[1115,21510,786],{"class":3323},[1115,21512,1405],{"class":3327},[1115,21514,21515],{"class":3323}," level",[1115,21517,3416],{"class":3327},[1115,21519,14300],{"class":3343},[1115,21521,3520],{"class":3335},[1115,21523,21524,21527,21529,21532,21534,21536,21538,21540,21542,21544,21546,21548],{"class":3320,"line":27},[1115,21525,21526],{"class":3323},"nove",[1115,21528,3328],{"class":3327},[1115,21530,21531],{"class":3331}," data.frame",[1115,21533,1484],{"class":3335},[1115,21535,21074],{"class":3323},[1115,21537,3416],{"class":3327},[1115,21539,3454],{"class":3331},[1115,21541,1484],{"class":3335},[1115,21543,17633],{"class":3343},[1115,21545,1405],{"class":3327},[1115,21547,19559],{"class":3343},[1115,21549,13794],{"class":3335},[1115,21551,21552,21555,21557,21559,21561,21564,21566,21569,21571,21574,21576,21579,21581,21583,21585,21587],{"class":3320,"line":148},[1115,21553,21554],{"class":3331},"predict",[1115,21556,1484],{"class":3335},[1115,21558,786],{"class":3323},[1115,21560,1405],{"class":3327},[1115,21562,21563],{"class":3323}," newdata",[1115,21565,3416],{"class":3327},[1115,21567,21568],{"class":3323}," nove",[1115,21570,1405],{"class":3327},[1115,21572,21573],{"class":3323}," interval",[1115,21575,3416],{"class":3327},[1115,21577,21578],{"class":3459}," \"confidence\"",[1115,21580,1405],{"class":3327},[1115,21582,21515],{"class":3323},[1115,21584,3416],{"class":3327},[1115,21586,14300],{"class":3343},[1115,21588,3520],{"class":3335},[1115,21590,21591,21593,21595,21597,21599,21601,21603,21605,21607,21609,21611,21614,21616,21618,21620,21622],{"class":3320,"line":111},[1115,21592,21554],{"class":3331},[1115,21594,1484],{"class":3335},[1115,21596,786],{"class":3323},[1115,21598,1405],{"class":3327},[1115,21600,21563],{"class":3323},[1115,21602,3416],{"class":3327},[1115,21604,21568],{"class":3323},[1115,21606,1405],{"class":3327},[1115,21608,21573],{"class":3323},[1115,21610,3416],{"class":3327},[1115,21612,21613],{"class":3459}," \"prediction\"",[1115,21615,1405],{"class":3327},[1115,21617,21515],{"class":3323},[1115,21619,3416],{"class":3327},[1115,21621,14300],{"class":3343},[1115,21623,3520],{"class":3335},[3311,21625,21628],{"className":21626,"code":21627,"language":3542,"meta":3315},[3540],"                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",[3087,21629,21627],{"__ignoreMap":3315},[1110,21631,21632,21635,21636,1254,21639,21652,21653,2568,21666,21669,21670,21673],{},[3087,21633,21634],{},"interval = \"confidence\""," dává interval spolehlivosti pro ",[1131,21637,21638],{},"střední hodnotu",[1115,21640,21642],{"className":21641},[1144],[1146,21643,21644],{"xmlns":1148},[1150,21645,21646,21650],{},[1153,21647,21648],{},[1159,21649,11429],{},[1167,21651,11429],{"encoding":1169}," při daném ",[1115,21654,21656],{"className":21655},[1144],[1146,21657,21658],{"xmlns":1148},[1150,21659,21660,21664],{},[1153,21661,21662],{},[1159,21663,11019],{},[1167,21665,11019],{"encoding":1169},[3087,21667,21668],{},"interval = \"prediction\""," širší interval pro ",[1131,21671,21672],{},"jednotlivé budoucí pozorování"," — ten musí zahrnout i rozptyl kolem regresní přímky, proto je vždy širší.",[21050,21675,21677],{"id":21676},"diagnostika-modelu","Diagnostika modelu",[1110,21679,21680,21681,2568,21684,5360,21687,21690],{},"Platnost závěrů z regresní přímky stojí na předpokladech o reziduích: ",[1131,21682,21683],{},"absenci autokorelace",[1131,21685,21686],{},"stálosti rozptylu (homoskedasticitě)",[1131,21688,21689],{},"normalitě",". V R se ověřují takto:",[3311,21692,21694],{"className":3313,"code":21693,"language":71,"meta":3315,"style":3315},"library(lmtest)\ndwtest(model)\n",[3087,21695,21696,21708],{"__ignoreMap":3315},[1115,21697,21698,21701,21703,21706],{"class":3320,"line":10},[1115,21699,21700],{"class":3327},"library",[1115,21702,1484],{"class":3335},[1115,21704,21705],{"class":3323},"lmtest",[1115,21707,3520],{"class":3335},[1115,21709,21710,21713,21715,21717],{"class":3320,"line":27},[1115,21711,21712],{"class":3331},"dwtest",[1115,21714,1484],{"class":3335},[1115,21716,786],{"class":3323},[1115,21718,3520],{"class":3335},[3311,21720,21723],{"className":21721,"code":21722,"language":3542,"meta":3315},[3540],"    Durbin-Watson test\n\ndata:  model\nDW = 3.4121, p-value = 0.9555\nalternative hypothesis: true autocorrelation is greater than 0\n",[3087,21724,21722],{"__ignoreMap":3315},[1110,21726,21727,21728,21745,21746,21763,21764,21781],{},"Durbinův–Watsonův test má ",[1115,21729,21731],{"className":21730},[1144],[1146,21732,21733],{"xmlns":1148},[1150,21734,21735,21743],{},[1153,21736,21737],{},[1156,21738,21739,21741],{},[1159,21740,1161],{},[1163,21742,1165],{},[1167,21744,1170],{"encoding":1169},": v modelu není problém s autokorelací, proti ",[1115,21747,21749],{"className":21748},[1144],[1146,21750,21751],{"xmlns":1148},[1150,21752,21753,21761],{},[1153,21754,21755],{},[1156,21756,21757,21759],{},[1159,21758,1161],{},[1163,21760,1402],{},[1167,21762,2613],{"encoding":1169},": 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, ",[1115,21765,21767],{"className":21766},[1144],[1146,21768,21769],{"xmlns":1148},[1150,21770,21771,21779],{},[1153,21772,21773],{},[1156,21774,21775,21777],{},[1159,21776,1161],{},[1163,21778,1165],{},[1167,21780,1170],{"encoding":1169}," se nezamítá.",[3311,21783,21785],{"className":3313,"code":21784,"language":71,"meta":3315,"style":3315},"library(whitestrap)\nwhite_test(model)\n",[3087,21786,21787,21798],{"__ignoreMap":3315},[1115,21788,21789,21791,21793,21796],{"class":3320,"line":10},[1115,21790,21700],{"class":3327},[1115,21792,1484],{"class":3335},[1115,21794,21795],{"class":3323},"whitestrap",[1115,21797,3520],{"class":3335},[1115,21799,21800,21803,21805,21807],{"class":3320,"line":27},[1115,21801,21802],{"class":3331},"white_test",[1115,21804,1484],{"class":3335},[1115,21806,786],{"class":3323},[1115,21808,3520],{"class":3335},[3311,21810,21813],{"className":21811,"code":21812,"language":3542,"meta":3315},[3540],"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",[3087,21814,21812],{"__ignoreMap":3315},[1110,21816,21817,21818,21835,21836,21853,21854,21781],{},"Whiteův test má ",[1115,21819,21821],{"className":21820},[1144],[1146,21822,21823],{"xmlns":1148},[1150,21824,21825,21833],{},[1153,21826,21827],{},[1156,21828,21829,21831],{},[1159,21830,1161],{},[1163,21832,1165],{},[1167,21834,1170],{"encoding":1169},": rozptyl reziduí je stálý (homoskedasticita), proti ",[1115,21837,21839],{"className":21838},[1144],[1146,21840,21841],{"xmlns":1148},[1150,21842,21843,21851],{},[1153,21844,21845],{},[1156,21846,21847,21849],{},[1159,21848,1161],{},[1163,21850,1402],{},[1167,21852,2613],{"encoding":1169},": rozptyl není stálý (heteroskedasticita). P-hodnota 0,21 je nad 0,05, ",[1115,21855,21857],{"className":21856},[1144],[1146,21858,21859],{"xmlns":1148},[1150,21860,21861,21869],{},[1153,21862,21863],{},[1156,21864,21865,21867],{},[1159,21866,1161],{},[1163,21868,1165],{},[1167,21870,1170],{"encoding":1169},[3311,21872,21874],{"className":3313,"code":21873,"language":71,"meta":3315,"style":3315},"shapiro.test(residuals(model))\n",[3087,21875,21876],{"__ignoreMap":3315},[1115,21877,21878,21881,21883,21885,21887,21889],{"class":3320,"line":10},[1115,21879,21880],{"class":3331},"shapiro.test",[1115,21882,1484],{"class":3335},[1115,21884,21348],{"class":3331},[1115,21886,1484],{"class":3335},[1115,21888,786],{"class":3323},[1115,21890,13794],{"class":3335},[3311,21892,21895],{"className":21893,"code":21894,"language":3542,"meta":3315},[3540],"    Shapiro-Wilk normality test\n\ndata:  residuals(model)\nW = 0.94818, p-value = 0.7255\n",[3087,21896,21894],{"__ignoreMap":3315},[1110,21898,21899,21900,21917],{},"Shapiro–Wilkův test má ",[1115,21901,21903],{"className":21902},[1144],[1146,21904,21905],{"xmlns":1148},[1150,21906,21907,21915],{},[1153,21908,21909],{},[1156,21910,21911,21913],{},[1159,21912,1161],{},[1163,21914,1165],{},[1167,21916,1170],{"encoding":1169},": rezidua pocházejí z normálního rozdělení. P-hodnota 0,73 opět nevede k zamítnutí — všechny tři předpoklady model splňuje.",[1110,21919,21920],{},[4002,21921],{"alt":21922,"className":21923,"src":21924},"mask-ra-diagnostika-rezidui",[1321,4006],"\u002Fwiki-assets\u002Fmask-ra-diagnostika-rezidui.png",[1110,21926,21927],{},"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.",[1103,21929,21931,21938,21969,22004,22069],{"className":21930,"dataCallout":3094},[1106,3093],[1110,21932,21934,21937],{"className":21933},[1113],[1115,21935],{"className":21936,"ariaHidden":1121},[1118,3101,1120],"Příklad: Regresní přímka",[1110,21939,21940,21941,21954,21955,21968],{},"V souboru s údaji o hodnotě produkce (v milionech Kč, proměnná ",[1115,21942,21944],{"className":21943},[1144],[1146,21945,21946],{"xmlns":1148},[1150,21947,21948,21952],{},[1153,21949,21950],{},[1159,21951,11429],{},[1167,21953,11429],{"encoding":1169},") a výši investic (ve stovkách tisíc Kč, proměnná ",[1115,21956,21958],{"className":21957},[1144],[1146,21959,21960],{"xmlns":1148},[1150,21961,21962,21966],{},[1153,21963,21964],{},[1159,21965,11019],{},[1167,21967,11019],{"encoding":1169},") 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.",[1110,21970,21971,21972,1269],{},"Výsledek: ",[1115,21973,21975],{"className":21974},[1144],[1146,21976,21977],{"xmlns":1148},[1150,21978,21979,22001],{},[1153,21980,21981,21987,21989,21992,21994,21997,21999],{},[2339,21982,21983,21985],{"accent":1121},[1159,21984,11429],{},[1289,21986,2345],{},[1289,21988,1591],{},[1163,21990,21991],{},"32,74",[1289,21993,5096],{},[1163,21995,21996],{},"2,15",[2525,21998,2527],{},[1159,22000,11019],{},[1167,22002,22003],{"encoding":1169},"\\hat y = 32{,}74 + 2{,}15\\,x",[1110,22005,21001,22006,22028,22029,22068],{},[1115,22007,22009],{"className":22008},[1144],[1146,22010,22011],{"xmlns":1148},[1150,22012,22013,22025],{},[1153,22014,22015,22021,22023],{},[1156,22016,22017,22019],{},[1159,22018,15807],{},[1163,22020,1402],{},[1289,22022,1591],{},[1163,22024,21996],{},[1167,22026,22027],{"encoding":1169},"b_1=2{,}15"," říká, že se zvýšením investic o 100 000 Kč vzroste produkce v průměru o ",[1115,22030,22032],{"className":22031},[1144],[1146,22033,22034],{"xmlns":1148},[1150,22035,22036,22065],{},[1153,22037,22038,22040,22042,22044,22046,22048,22050,22052,22054,22056,22058,22061,22063],{},[1163,22039,21996],{},[1289,22041,12411],{},[1163,22043,1402],{},[2525,22045,2527],{},[1163,22047,15625],{},[2525,22049,2527],{},[1163,22051,15625],{},[1289,22053,1591],{},[1163,22055,1189],{},[2525,22057,2527],{},[1163,22059,22060],{},"150",[2525,22062,2527],{},[1163,22064,15625],{},[1167,22066,22067],{"encoding":1169},"2{,}15\\cdot 1\\,000\\,000=2\\,150\\,000"," Kč.",[1110,22070,22071,22072,3607,22091,22139,22140,20397],{},"Dosazením libovolné hodnoty investic do empirické regresní funkce dostaneme predikci produkce, například pro třináctou firmu s investicemi ",[1115,22073,22075],{"className":22074},[1144],[1146,22076,22077],{"xmlns":1148},[1150,22078,22079,22088],{},[1153,22080,22081,22083,22085],{},[1159,22082,11019],{},[1289,22084,1591],{},[1163,22086,22087],{},"34",[1167,22089,22090],{"encoding":1169},"x=34",[1115,22092,22094],{"className":22093},[1144],[1146,22095,22096],{"xmlns":1148},[1150,22097,22098,22136],{},[1153,22099,22100,22110,22112,22118,22120,22126,22128,22130,22133],{},[1156,22101,22102,22108],{},[2339,22103,22104,22106],{"accent":1121},[1159,22105,11429],{},[1289,22107,2345],{},[1163,22109,3162],{},[1289,22111,1591],{},[1156,22113,22114,22116],{},[1159,22115,15807],{},[1163,22117,1165],{},[1289,22119,5096],{},[1156,22121,22122,22124],{},[1159,22123,15807],{},[1163,22125,1402],{},[1289,22127,12411],{},[1163,22129,22087],{},[1289,22131,22132],{},"≐",[1163,22134,22135],{},"105,81",[1167,22137,22138],{"encoding":1169},"\\hat y_{13} = b_0 + b_1\\cdot 34 \\doteq 105{,}81"," milionu Kč (se zaokrouhlenými koeficienty ",[1115,22141,22143],{"className":22142},[1144],[1146,22144,22145],{"xmlns":1148},[1150,22146,22147,22164],{},[1153,22148,22149,22151,22153,22155,22157,22159,22161],{},[1163,22150,21991],{},[1289,22152,5096],{},[1163,22154,21996],{},[1289,22156,12411],{},[1163,22158,22087],{},[1289,22160,22132],{},[1163,22162,22163],{},"105,8",[1167,22165,22166],{"encoding":1169},"32{,}74 + 2{,}15\\cdot 34 \\doteq 105{,}8",[1310,22168,22170],{"id":22169},"nelineární-a-vyšší-řády-regresních-funkcí","Nelineární a vyšší řády regresních funkcí",[1110,22172,22173,22174,22177,22178,22245,22246,22264,22265,22282],{},"Když přímka závislost nevystihuje, nabízí se další ",[1131,22175,22176],{},"lineární funkce"," — tedy funkce lineární ve svých parametrech, zapsatelné ve tvaru ",[1115,22179,22181],{"className":22180},[1144],[1146,22182,22183],{"xmlns":1148},[1150,22184,22185,22242],{},[1153,22186,22187,22189,22191,22197,22199,22205,22211,22213,22215,22217,22219,22222,22224,22230,22236,22238,22240],{},[1159,22188,20626],{},[1289,22190,1591],{},[1156,22192,22193,22195],{},[1159,22194,20641],{},[1163,22196,1165],{},[1289,22198,5096],{},[1156,22200,22201,22203],{},[1159,22202,20641],{},[1163,22204,1402],{},[1156,22206,22207,22209],{},[1159,22208,11070],{},[1163,22210,1402],{},[1289,22212,1484],{"stretchy":1483},[1159,22214,11019],{},[1289,22216,1495],{"stretchy":1483},[1289,22218,5096],{},[1289,22220,22221],{},"⋯",[1289,22223,5096],{},[1156,22225,22226,22228],{},[1159,22227,20641],{},[1159,22229,1110],{},[1156,22231,22232,22234],{},[1159,22233,11070],{},[1159,22235,1110],{},[1289,22237,1484],{"stretchy":1483},[1159,22239,11019],{},[1289,22241,1495],{"stretchy":1483},[1167,22243,22244],{"encoding":1169},"\\eta=\\beta_0+\\beta_1 f_1(x)+\\dots+\\beta_p f_p(x)"," se známými funkcemi ",[1115,22247,22249],{"className":22248},[1144],[1146,22250,22251],{"xmlns":1148},[1150,22252,22253,22261],{},[1153,22254,22255],{},[1156,22256,22257,22259],{},[1159,22258,11070],{},[1159,22260,1487],{},[1167,22262,22263],{"encoding":1169},"f_i"," a neznámými parametry ",[1115,22266,22268],{"className":22267},[1144],[1146,22269,22270],{"xmlns":1148},[1150,22271,22272,22280],{},[1153,22273,22274],{},[1156,22275,22276,22278],{},[1159,22277,20641],{},[1159,22279,1487],{},[1167,22281,20687],{"encoding":1169},". I tyto parametry se odhadují metodou nejmenších čtverců, stejně jako u přímky:",[1115,22284,22286],{"className":22285},[1144],[1146,22287,22288],{"xmlns":1148,"display":1573},[1150,22289,22290,22600],{},[22291,22292,22295,22368,22481,22540],"mtable",{"rowspacing":22293,"columnalign":22294,"columnspacing":11058},"0.25em","right left",[22296,22297,22298,22322],"mtr",{},[22299,22300,22301],"mtd",{},[2858,22302,22303],{"scriptlevel":1165,"displaystyle":1121},[1153,22304,22305,22319],{},[1153,22306,22307,22310,22316],{},[2525,22308,22309],{},"parabolick",[2339,22311,22312,22314],{"accent":1121},[2525,22313,1318],{},[1289,22315,15804],{},[2525,22317,22318],{}," regrese: ",[1621,22320],{"width":22321},"1em",[22299,22323,22324],{},[2858,22325,22326],{"scriptlevel":1165,"displaystyle":1121},[1153,22327,22328,22330,22336,22338,22344,22346,22352,22354,22356,22362],{},[1153,22329],{},[2339,22331,22332,22334],{"accent":1121},[1159,22333,11429],{},[1289,22335,2345],{},[1289,22337,1591],{},[1156,22339,22340,22342],{},[1159,22341,15807],{},[1163,22343,1165],{},[1289,22345,5096],{},[1156,22347,22348,22350],{},[1159,22349,15807],{},[1163,22351,1402],{},[1159,22353,11019],{},[1289,22355,5096],{},[1156,22357,22358,22360],{},[1159,22359,15807],{},[1163,22361,1189],{},[1182,22363,22364,22366],{},[1159,22365,11019],{},[1163,22367,1189],{},[22296,22369,22370,22417],{},[22299,22371,22372],{},[2858,22373,22374],{"scriptlevel":1165,"displaystyle":1121},[1153,22375,22376,22415],{},[1153,22377,22378,22381,22387,22390,22394,22397,22403,22406,22412],{},[2525,22379,22380],{},"polynomick",[2339,22382,22383,22385],{"accent":1121},[2525,22384,1318],{},[1289,22386,15804],{},[2525,22388,22389],{}," regrese ",[2858,22391,22392],{"scriptlevel":1165,"displaystyle":1483},[1159,22393,1110],{},[2525,22395,22396],{},"-t",[2339,22398,22399,22401],{"accent":1121},[2525,22400,12893],{},[1289,22402,15804],{},[2525,22404,22405],{},"ho stupn",[2339,22407,22408,22410],{"accent":1121},[2525,22409,12893],{},[1289,22411,15814],{},[2525,22413,22414],{},": ",[1621,22416],{"width":22321},[22299,22418,22419],{},[2858,22420,22421],{"scriptlevel":1165,"displaystyle":1121},[1153,22422,22423,22425,22431,22433,22439,22441,22447,22449,22451,22457,22463,22465,22467,22469,22475],{},[1153,22424],{},[2339,22426,22427,22429],{"accent":1121},[1159,22428,11429],{},[1289,22430,2345],{},[1289,22432,1591],{},[1156,22434,22435,22437],{},[1159,22436,15807],{},[1163,22438,1165],{},[1289,22440,5096],{},[1156,22442,22443,22445],{},[1159,22444,15807],{},[1163,22446,1402],{},[1159,22448,11019],{},[1289,22450,5096],{},[1156,22452,22453,22455],{},[1159,22454,15807],{},[1163,22456,1189],{},[1182,22458,22459,22461],{},[1159,22460,11019],{},[1163,22462,1189],{},[1289,22464,5096],{},[1289,22466,22221],{},[1289,22468,5096],{},[1156,22470,22471,22473],{},[1159,22472,15807],{},[1159,22474,1110],{},[1182,22476,22477,22479],{},[1159,22478,11019],{},[1159,22480,1110],{},[22296,22482,22483,22504],{},[22299,22484,22485],{},[2858,22486,22487],{"scriptlevel":1165,"displaystyle":1121},[1153,22488,22489,22502],{},[1153,22490,22491,22494,22500],{},[2525,22492,22493],{},"hyperbolick",[2339,22495,22496,22498],{"accent":1121},[2525,22497,1318],{},[1289,22499,15804],{},[2525,22501,22318],{},[1621,22503],{"width":22321},[22299,22505,22506],{},[2858,22507,22508],{"scriptlevel":1165,"displaystyle":1121},[1153,22509,22510,22512,22518,22520,22526,22528,22534],{},[1153,22511],{},[2339,22513,22514,22516],{"accent":1121},[1159,22515,11429],{},[1289,22517,2345],{},[1289,22519,1591],{},[1156,22521,22522,22524],{},[1159,22523,15807],{},[1163,22525,1165],{},[1289,22527,5096],{},[1156,22529,22530,22532],{},[1159,22531,15807],{},[1163,22533,1402],{},[2355,22535,22536,22538],{},[1163,22537,1402],{},[1159,22539,11019],{},[22296,22541,22542,22563],{},[22299,22543,22544],{},[2858,22545,22546],{"scriptlevel":1165,"displaystyle":1121},[1153,22547,22548,22561],{},[1153,22549,22550,22553,22559],{},[2525,22551,22552],{},"logaritmick",[2339,22554,22555,22557],{"accent":1121},[2525,22556,1318],{},[1289,22558,15804],{},[2525,22560,22318],{},[1621,22562],{"width":22321},[22299,22564,22565],{},[2858,22566,22567],{"scriptlevel":1165,"displaystyle":1121},[1153,22568,22569,22571,22577,22579,22585,22587,22593,22596,22598],{},[1153,22570],{},[2339,22572,22573,22575],{"accent":1121},[1159,22574,11429],{},[1289,22576,2345],{},[1289,22578,1591],{},[1156,22580,22581,22583],{},[1159,22582,15807],{},[1163,22584,1165],{},[1289,22586,5096],{},[1156,22588,22589,22591],{},[1159,22590,15807],{},[1163,22592,1402],{},[1159,22594,22595],{},"ln",[1289,22597,4110],{},[1159,22599,11019],{},[1167,22601,22602],{"encoding":1169},"\\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}",[1110,22604,22605,22606,22609,22610,22656,22657,1567],{},"Naproti tomu ",[1131,22607,22608],{},"nelineární funkce"," nelze do tvaru ",[1115,22611,22613],{"className":22612},[1144],[1146,22614,22615],{"xmlns":1148},[1150,22616,22617,22653],{},[1153,22618,22619,22621,22623,22629,22631,22637,22643,22645,22647,22649,22651],{},[1159,22620,20626],{},[1289,22622,1591],{},[1156,22624,22625,22627],{},[1159,22626,20641],{},[1163,22628,1165],{},[1289,22630,5096],{},[1156,22632,22633,22635],{},[1159,22634,20641],{},[1163,22636,1402],{},[1156,22638,22639,22641],{},[1159,22640,11070],{},[1163,22642,1402],{},[1289,22644,1484],{"stretchy":1483},[1159,22646,11019],{},[1289,22648,1495],{"stretchy":1483},[1289,22650,5096],{},[1289,22652,1408],{},[1167,22654,22655],{"encoding":1169},"\\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 ",[1131,22658,22659],{},"exponenciální regrese",[1115,22661,22663],{"className":22662},[1144],[1146,22664,22665],{"xmlns":1148,"display":1573},[1150,22666,22667,22699],{},[1153,22668,22669,22675,22677,22683,22685,22697],{},[2339,22670,22671,22673],{"accent":1121},[1159,22672,11429],{},[1289,22674,2345],{},[1289,22676,1591],{},[1156,22678,22679,22681],{},[1159,22680,15807],{},[1163,22682,1165],{},[1289,22684,12411],{},[2970,22686,22687,22689,22691],{},[1159,22688,15807],{},[1163,22690,1402],{},[1153,22692,22693,22695],{},[2525,22694,2527],{},[1159,22696,11019],{},[1159,22698,1269],{"mathvariant":1734},[1167,22700,22701],{"encoding":1169},"\\hat y = b_0 \\cdot b_1^{\\,x}.",[1110,22703,22704],{},[4002,22705],{"alt":22706,"className":22707,"src":22708},"mask-ra-nelinearni-krivky",[1321,4006],"\u002Fwiki-assets\u002Fmask-ra-nelinearni-krivky.png",[21050,22710,22712],{"id":22711},"v-r-parabolická-regrese","V R — parabolická regrese",[1110,22714,22715,22716,1567],{},"Na ročních ziscích firmy (šest let) se parabolická regrese odhadne přidáním kvadratického členu ",[3087,22717,22718],{},"I(x^2)",[3311,22720,22722],{"className":3313,"code":22721,"language":71,"meta":3315,"style":3315},"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",[3087,22723,22724,22759,22799,22833],{"__ignoreMap":3315},[1115,22725,22726,22729,22731,22733,22735,22737,22739,22741,22743,22745,22747,22749,22751,22753,22755,22757],{"class":3320,"line":10},[1115,22727,22728],{"class":3323},"rok",[1115,22730,3328],{"class":3327},[1115,22732,3454],{"class":3331},[1115,22734,1484],{"class":3335},[1115,22736,1402],{"class":3343},[1115,22738,1405],{"class":3327},[1115,22740,3799],{"class":3343},[1115,22742,1405],{"class":3327},[1115,22744,15156],{"class":3343},[1115,22746,1405],{"class":3327},[1115,22748,3419],{"class":3343},[1115,22750,1405],{"class":3327},[1115,22752,14295],{"class":3343},[1115,22754,1405],{"class":3327},[1115,22756,16531],{"class":3343},[1115,22758,3520],{"class":3335},[1115,22760,22761,22763,22765,22767,22769,22772,22774,22777,22779,22782,22784,22787,22789,22792,22794,22797],{"class":3320,"line":27},[1115,22762,1088],{"class":3323},[1115,22764,3328],{"class":3327},[1115,22766,3454],{"class":3331},[1115,22768,1484],{"class":3335},[1115,22770,22771],{"class":3343},"112",[1115,22773,1405],{"class":3327},[1115,22775,22776],{"class":3343}," 149",[1115,22778,1405],{"class":3327},[1115,22780,22781],{"class":3343}," 238",[1115,22783,1405],{"class":3327},[1115,22785,22786],{"class":3343}," 354",[1115,22788,1405],{"class":3327},[1115,22790,22791],{"class":3343}," 580",[1115,22793,1405],{"class":3327},[1115,22795,22796],{"class":3343}," 867",[1115,22798,3520],{"class":3335},[1115,22800,22801,22804,22806,22808,22810,22812,22814,22817,22820,22823,22825,22827,22829,22831],{"class":3320,"line":148},[1115,22802,22803],{"class":3323},"model_parabola",[1115,22805,3328],{"class":3327},[1115,22807,21154],{"class":3331},[1115,22809,1484],{"class":3335},[1115,22811,1088],{"class":3323},[1115,22813,21161],{"class":3327},[1115,22815,22816],{"class":3323}," rok",[1115,22818,22819],{"class":3327}," +",[1115,22821,22822],{"class":3331}," I",[1115,22824,1484],{"class":3335},[1115,22826,22728],{"class":3323},[1115,22828,2345],{"class":3327},[1115,22830,1189],{"class":3343},[1115,22832,13794],{"class":3335},[1115,22834,22835,22837,22839,22841],{"class":3320,"line":111},[1115,22836,21171],{"class":3331},[1115,22838,1484],{"class":3335},[1115,22840,22803],{"class":3323},[1115,22842,3520],{"class":3335},[3311,22844,22847],{"className":22845,"code":22846,"language":3542,"meta":3315},[3540],"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",[3087,22848,22846],{"__ignoreMap":3315},[1110,22850,22851,22852,22897],{},"Odhadnutá parabola ",[1115,22853,22855],{"className":22854},[1144],[1146,22856,22857],{"xmlns":1148},[1150,22858,22859,22894],{},[1153,22860,22861,22867,22869,22872,22874,22877,22879,22881,22883,22886,22888],{},[2339,22862,22863,22865],{"accent":1121},[1159,22864,11429],{},[1289,22866,2345],{},[1289,22868,1591],{},[1163,22870,22871],{},"164,6",[1289,22873,2681],{},[1163,22875,22876],{},"76,6",[2525,22878,2527],{},[1159,22880,11019],{},[1289,22882,5096],{},[1163,22884,22885],{},"32,1",[2525,22887,2527],{},[1182,22889,22890,22892],{},[1159,22891,11019],{},[1163,22893,1189],{},[1167,22895,22896],{"encoding":1169},"\\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.",[21050,22899,22901],{"id":22900},"v-r-exponenciální-regrese","V R — exponenciální regrese",[1110,22903,22904,22905,22907],{},"Nelineární funkce se v R odhadují funkcí ",[3087,22906,20412],{}," ze stejnojmenného balíčku. Bez zadaných počátečních hodnot R upozorní, že parametry nastavil na 1, a odhad dopočítá iteračně:",[3311,22909,22911],{"className":3313,"code":22910,"language":71,"meta":3315,"style":3315},"library(nls2)\nmodel_exp \u003C- nls2(zisk ~ b1 * exp(b2 * rok))\nsummary(model_exp)\n",[3087,22912,22913,22923,22959],{"__ignoreMap":3315},[1115,22914,22915,22917,22919,22921],{"class":3320,"line":10},[1115,22916,21700],{"class":3327},[1115,22918,1484],{"class":3335},[1115,22920,20396],{"class":3323},[1115,22922,3520],{"class":3335},[1115,22924,22925,22928,22930,22933,22935,22937,22939,22942,22945,22948,22950,22953,22955,22957],{"class":3320,"line":27},[1115,22926,22927],{"class":3323},"model_exp",[1115,22929,3328],{"class":3327},[1115,22931,22932],{"class":3331}," nls2",[1115,22934,1484],{"class":3335},[1115,22936,1088],{"class":3323},[1115,22938,21161],{"class":3327},[1115,22940,22941],{"class":3323}," b1",[1115,22943,22944],{"class":3327}," *",[1115,22946,22947],{"class":3331}," exp",[1115,22949,1484],{"class":3335},[1115,22951,22952],{"class":3323},"b2",[1115,22954,22944],{"class":3327},[1115,22956,22816],{"class":3323},[1115,22958,13794],{"class":3335},[1115,22960,22961,22963,22965,22967],{"class":3320,"line":148},[1115,22962,21171],{"class":3331},[1115,22964,1484],{"class":3335},[1115,22966,22927],{"class":3323},[1115,22968,3520],{"class":3335},[3311,22970,22973],{"className":22971,"code":22972,"language":3542,"meta":3315},[3540],"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",[3087,22974,22972],{"__ignoreMap":3315},[1110,22976,22977,22978,1567],{},"Stejnou křivku lze zapsat i v mocninném tvaru ",[1115,22979,22981],{"className":22980},[1144],[1146,22982,22983],{"xmlns":1148},[1150,22984,22985,23011],{},[1153,22986,22987,22993,22995,23001,23003],{},[2339,22988,22989,22991],{"accent":1121},[1159,22990,11429],{},[1289,22992,2345],{},[1289,22994,1591],{},[1156,22996,22997,22999],{},[1159,22998,15807],{},[1163,23000,1402],{},[1289,23002,12411],{},[2970,23004,23005,23007,23009],{},[1159,23006,15807],{},[1163,23008,1189],{},[1159,23010,11019],{},[1167,23012,23013],{"encoding":1169},"\\hat y=b_1\\cdot b_2^{x}",[3311,23015,23017],{"className":3313,"code":23016,"language":71,"meta":3315,"style":3315},"model_pow \u003C- nls2(zisk ~ b1 * (b2^rok))\nsummary(model_pow)\n",[3087,23018,23019,23048],{"__ignoreMap":3315},[1115,23020,23021,23024,23026,23028,23030,23032,23034,23036,23038,23040,23042,23044,23046],{"class":3320,"line":10},[1115,23022,23023],{"class":3323},"model_pow",[1115,23025,3328],{"class":3327},[1115,23027,22932],{"class":3331},[1115,23029,1484],{"class":3335},[1115,23031,1088],{"class":3323},[1115,23033,21161],{"class":3327},[1115,23035,22941],{"class":3323},[1115,23037,22944],{"class":3327},[1115,23039,4226],{"class":3335},[1115,23041,22952],{"class":3323},[1115,23043,2345],{"class":3327},[1115,23045,22728],{"class":3323},[1115,23047,13794],{"class":3335},[1115,23049,23050,23052,23054,23056],{"class":3320,"line":27},[1115,23051,21171],{"class":3331},[1115,23053,1484],{"class":3335},[1115,23055,23023],{"class":3323},[1115,23057,3520],{"class":3335},[3311,23059,23062],{"className":23060,"code":23061,"language":3542,"meta":3315},[3540],"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",[3087,23063,23061],{"__ignoreMap":3315},[1110,23065,23066,23067,23131,23132,23156],{},"Obě varianty popisují stejnou křivku (",[1115,23068,23070],{"className":23069},[1144],[1146,23071,23072],{"xmlns":1148},[1150,23073,23074,23128],{},[1153,23075,23076,23093,23095],{},[2970,23077,23078,23080,23082],{},[1159,23079,15807],{},[1163,23081,1189],{},[1153,23083,23084,23087],{},[2525,23085,23086],{},"mocninn",[2339,23088,23089,23091],{"accent":1121},[2525,23090,11429],{},[1289,23092,15804],{},[1289,23094,1591],{},[1182,23096,23097,23099],{},[1159,23098,12893],{},[1153,23100,23101,23103],{},[2525,23102,2527],{},[2970,23104,23105,23107,23109],{},[1159,23106,15807],{},[1163,23108,1189],{},[1153,23110,23111,23114,23120,23122],{},[2525,23112,23113],{},"exponenci",[2339,23115,23116,23118],{"accent":1121},[2525,23117,1318],{},[1289,23119,15804],{},[2525,23121,22595],{},[2339,23123,23124,23126],{"accent":1121},[2525,23125,16054],{},[1289,23127,15804],{},[1167,23129,23130],{"encoding":1169},"b_2^{\\text{mocninný}} = e^{\\,b_2^{\\text{exponenciální}}}",", zde ",[1115,23133,23135],{"className":23134},[1144],[1146,23136,23137],{"xmlns":1148},[1150,23138,23139,23153],{},[1153,23140,23141,23148,23150],{},[1182,23142,23143,23145],{},[1159,23144,12893],{},[1163,23146,23147],{},"0,4316",[1289,23149,13741],{},[1163,23151,23152],{},"1,540",[1167,23154,23155],{"encoding":1169},"e^{0{,}4316}\\approx 1{,}540",") a mají totožnou reziduální chybu — je to jen otázka parametrizace.",[21050,23158,23160],{"id":23159},"v-r-hyperbolická-regrese","V R — hyperbolická regrese",[1110,23162,23163,23164,1567],{},"Hyperbolická regrese se odhadne jako obyčejná lineární regrese na transformované proměnné ",[3087,23165,23166],{},"I(1\u002Fx)",[3311,23168,23170],{"className":3313,"code":23169,"language":71,"meta":3315,"style":3315},"model_hyperbola \u003C- lm(tydenni_vydaje ~ I(1 \u002F pocet_clenu))\nsummary(model_hyperbola)\n",[3087,23171,23172,23199],{"__ignoreMap":3315},[1115,23173,23174,23177,23179,23181,23183,23185,23187,23189,23191,23193,23195,23197],{"class":3320,"line":10},[1115,23175,23176],{"class":3323},"model_hyperbola",[1115,23178,3328],{"class":3327},[1115,23180,21154],{"class":3331},[1115,23182,1484],{"class":3335},[1115,23184,21109],{"class":3323},[1115,23186,21161],{"class":3327},[1115,23188,22822],{"class":3331},[1115,23190,1484],{"class":3335},[1115,23192,1402],{"class":3343},[1115,23194,14376],{"class":3327},[1115,23196,21164],{"class":3323},[1115,23198,13794],{"class":3335},[1115,23200,23201,23203,23205,23207],{"class":3320,"line":27},[1115,23202,21171],{"class":3331},[1115,23204,1484],{"class":3335},[1115,23206,23176],{"class":3323},[1115,23208,3520],{"class":3335},[3311,23210,23213],{"className":23211,"code":23212,"language":3542,"meta":3315},[3540],"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",[3087,23214,23212],{"__ignoreMap":3315},[1110,23216,23217,23218,23252,23253,23274],{},"Model ",[1115,23219,23221],{"className":23220},[1144],[1146,23222,23223],{"xmlns":1148},[1150,23224,23225,23249],{},[1153,23226,23227,23233,23235,23238,23240],{},[2339,23228,23229,23231],{"accent":1121},[1159,23230,11429],{},[1289,23232,2345],{},[1289,23234,1591],{},[1163,23236,23237],{},"2180,7",[1289,23239,2681],{},[2858,23241,23242],{"scriptlevel":1165,"displaystyle":1121},[2355,23243,23244,23247],{},[1163,23245,23246],{},"1920,0",[1159,23248,11019],{},[1167,23250,23251],{"encoding":1169},"\\hat y = 2180{,}7 - \\dfrac{1920{,}0}{x}"," vysvětluje jen 76,3 % rozptylu — u těchto dat je hyperbola podstatně horší volbou než přímka (",[1115,23254,23256],{"className":23255},[1144],[1146,23257,23258],{"xmlns":1148},[1150,23259,23260,23272],{},[1153,23261,23262,23268,23270],{},[1182,23263,23264,23266],{},[1159,23265,14524],{},[1163,23267,1189],{},[1289,23269,1591],{},[1163,23271,21309],{},[1167,23273,21312],{"encoding":1169},"). Právě k takovému porovnání slouží index determinace: nízká hodnota signalizuje, že zvolený typ funkce k datům nesedí.",[1103,23276,23278,23285,23316,23364],{"className":23277,"dataCallout":3094},[1106,3093],[1110,23279,23281,23284],{"className":23280},[1113],[1115,23282],{"className":23283,"ariaHidden":1121},[1118,3101,1120],"Příklad: Parabolická regrese",[1110,23286,23287,23288,23301,23302,23315],{},"Prodejna počítačových her nechala prodavače absolvovat kurz prodejních dovedností. Při dvaceti měřeních sledovala, kolik zákazníků navštíví prodejnu během prodejní doby (proměnná ",[1115,23289,23291],{"className":23290},[1144],[1146,23292,23293],{"xmlns":1148},[1150,23294,23295,23299],{},[1153,23296,23297],{},[1159,23298,11019],{},[1167,23300,11019],{"encoding":1169},") a jaká je toho dne tržba v tisících Kč (proměnná ",[1115,23303,23305],{"className":23304},[1144],[1146,23306,23307],{"xmlns":1148},[1150,23308,23309,23313],{},[1153,23310,23311],{},[1159,23312,11429],{},[1167,23314,11429],{"encoding":1169},"). Zároveň chtěla zjistit, zda při rostoucím počtu zákazníků stačí stávající počet prodavačů.",[1110,23317,21971,23318,1269],{},[1115,23319,23321],{"className":23320},[1144],[1146,23322,23323],{"xmlns":1148},[1150,23324,23325,23361],{},[1153,23326,23327,23333,23335,23337,23340,23342,23345,23347,23349,23351,23353,23355],{},[2339,23328,23329,23331],{"accent":1121},[1159,23330,11429],{},[1289,23332,2345],{},[1289,23334,1591],{},[1289,23336,2681],{},[1163,23338,23339],{},"60,3",[1289,23341,5096],{},[1163,23343,23344],{},"4,55",[2525,23346,2527],{},[1159,23348,11019],{},[1289,23350,2681],{},[1163,23352,3603],{},[2525,23354,2527],{},[1182,23356,23357,23359],{},[1159,23358,11019],{},[1163,23360,1189],{},[1167,23362,23363],{"encoding":1169},"\\hat y = -60{,}3 + 4{,}55\\,x - 0{,}05\\,x^2",[1110,23365,23366,23367,23385],{},"Záporný koeficient ",[1115,23368,23370],{"className":23369},[1144],[1146,23371,23372],{"xmlns":1148},[1150,23373,23374,23382],{},[1153,23375,23376],{},[1156,23377,23378,23380],{},[1159,23379,15807],{},[1163,23381,1189],{},[1167,23383,23384],{"encoding":1169},"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.",[1103,23387,23389,23396,23426,23471],{"className":23388,"dataCallout":3094},[1106,3093],[1110,23390,23392,23395],{"className":23391},[1113],[1115,23393],{"className":23394,"ariaHidden":1121},[1118,3101,1120],"Příklad: Hyperbolická regrese",[1110,23397,23398,23399,23412,23413,20397],{},"V podniku se podle interního účetnictví sledovala závislost vlastních nákladů na jednotku produkce v Kč (proměnná ",[1115,23400,23402],{"className":23401},[1144],[1146,23403,23404],{"xmlns":1148},[1150,23405,23406,23410],{},[1153,23407,23408],{},[1159,23409,11429],{},[1167,23411,11429],{"encoding":1169},") na objemu produkce v tisících kusů (proměnná ",[1115,23414,23416],{"className":23415},[1144],[1146,23417,23418],{"xmlns":1148},[1150,23419,23420,23424],{},[1153,23421,23422],{},[1159,23423,11019],{},[1167,23425,11019],{"encoding":1169},[1110,23427,21971,23428,1269],{},[1115,23429,23431],{"className":23430},[1144],[1146,23432,23433],{"xmlns":1148},[1150,23434,23435,23468],{},[1153,23436,23437,23443,23445,23447,23450,23452],{},[2339,23438,23439,23441],{"accent":1121},[1159,23440,11429],{},[1289,23442,2345],{},[1289,23444,1591],{},[1289,23446,2681],{},[1163,23448,23449],{},"96,78",[1289,23451,5096],{},[2858,23453,23454],{"scriptlevel":1165,"displaystyle":1121},[2355,23455,23456,23466],{},[1153,23457,23458,23461,23463],{},[1163,23459,23460],{},"250",[2525,23462,2527],{},[1163,23464,23465],{},"528,88",[1159,23467,11019],{},[1167,23469,23470],{"encoding":1169},"\\hat y = -96{,}78 + \\dfrac{250\\,528{,}88}{x}",[1110,23472,23473,23474,23491],{},"Záporná hodnota ",[1115,23475,23477],{"className":23476},[1144],[1146,23478,23479],{"xmlns":1148},[1150,23480,23481,23489],{},[1153,23482,23483],{},[1156,23484,23485,23487],{},[1159,23486,15807],{},[1163,23488,1402],{},[1167,23490,21019],{"encoding":1169}," v čitateli ukazuje klesající náklady na jednotku s rostoucím objemem produkce — typický projev úspor z rozsahu, který hyperbola dobře zachycuje.",[1310,23493,23495],{"id":23494},"kvalita-regresní-funkce-a-korelační-analýza","Kvalita regresní funkce a korelační analýza",[1110,23497,23498,23499,1567],{},"Kvalitu odhadnuté regresní funkce vyjadřuje ",[1131,23500,20310],{},[1115,23502,23504],{"className":23503},[1144],[1146,23505,23506],{"xmlns":1148,"display":1573},[1150,23507,23508,23576],{},[1153,23509,23510,23516,23518,23540,23542,23544,23546,23574],{},[1182,23511,23512,23514],{},[1159,23513,14524],{},[1163,23515,1189],{},[1289,23517,1591],{},[2355,23519,23520,23532],{},[2970,23521,23522,23524,23530],{},[1159,23523,1463],{},[2339,23525,23526,23528],{"accent":1121},[1159,23527,11429],{},[1289,23529,2345],{},[1163,23531,1189],{},[2970,23533,23534,23536,23538],{},[1159,23535,1463],{},[1159,23537,11429],{},[1163,23539,1189],{},[1289,23541,1591],{},[1163,23543,1402],{},[1289,23545,2681],{},[2355,23547,23548,23566],{},[2970,23549,23550,23552,23564],{},[1159,23551,1463],{},[1153,23553,23554,23556,23558],{},[1159,23555,11429],{},[1289,23557,2681],{},[2339,23559,23560,23562],{"accent":1121},[1159,23561,11429],{},[1289,23563,2345],{},[1163,23565,1189],{},[2970,23567,23568,23570,23572],{},[1159,23569,1463],{},[1159,23571,11429],{},[1163,23573,1189],{},[1159,23575,1269],{"mathvariant":1734},[1167,23577,23578],{"encoding":1169},"R^2 = \\frac{s^2_{\\hat y}}{s^2_y} = 1 - \\frac{s^2_{y-\\hat y}}{s^2_y}.",[1110,23580,23581,23582,23599,23600,23613],{},"Čím blíž je ",[1115,23583,23585],{"className":23584},[1144],[1146,23586,23587],{"xmlns":1148},[1150,23588,23589,23597],{},[1153,23590,23591],{},[1182,23592,23593,23595],{},[1159,23594,14524],{},[1163,23596,1189],{},[1167,23598,20328],{"encoding":1169}," k 1, tím silnější je závislost; v procentech udává, jakou část rozptylu závisle proměnné ",[1115,23601,23603],{"className":23602},[1144],[1146,23604,23605],{"xmlns":1148},[1150,23606,23607,23611],{},[1153,23608,23609],{},[1159,23610,11429],{},[1167,23612,11429],{"encoding":1169}," se podařilo vysvětlit zvolenou regresní funkcí. Nízký index determinace může signalizovat špatně zvolený typ regresní funkce, ne nutně absenci závislosti.",[1110,23615,23616,23617,1254,23619,23642,23643,1567],{},"Obecnou mírou těsnosti závislosti — platnou pro libovolný typ regresní funkce — je ",[1131,23618,20332],{},[1115,23620,23622],{"className":23621},[1144],[1146,23623,23624],{"xmlns":1148},[1150,23625,23626,23640],{},[1153,23627,23628,23630,23632],{},[1159,23629,15503],{},[1289,23631,1591],{},[4072,23633,23634],{},[1182,23635,23636,23638],{},[1159,23637,14524],{},[1163,23639,1189],{},[1167,23641,20356],{"encoding":1169},". Je-li zvolenou funkcí regresní přímka, index korelace je roven (až na znaménko) ",[1131,23644,20360],{},[1115,23646,23648],{"className":23647},[1144],[1146,23649,23650],{"xmlns":1148,"display":1573},[1150,23651,23652,23702],{},[1153,23653,23654,23664,23666,23700],{},[1156,23655,23656,23658],{},[1159,23657,71],{},[1153,23659,23660,23662],{},[1159,23661,11019],{},[1159,23663,11429],{},[1289,23665,1591],{},[2355,23667,23668,23678],{},[1156,23669,23670,23672],{},[1159,23671,1463],{},[1153,23673,23674,23676],{},[1159,23675,11019],{},[1159,23677,11429],{},[4072,23679,23680],{},[1153,23681,23682,23690,23692],{},[2970,23683,23684,23686,23688],{},[1159,23685,1463],{},[1159,23687,11019],{},[1163,23689,1189],{},[1289,23691,12411],{},[2970,23693,23694,23696,23698],{},[1159,23695,1463],{},[1159,23697,11429],{},[1163,23699,1189],{},[1159,23701,1269],{"mathvariant":1734},[1167,23703,23704],{"encoding":1169},"r_{xy} = \\frac{s_{xy}}{\\sqrt{s^2_x\\cdot s^2_y}}.",[1110,23706,23707,23708,23724,23725,23741],{},"Koeficient korelace nabývá hodnot od ",[1115,23709,23711],{"className":23710},[1144],[1146,23712,23713],{"xmlns":1148},[1150,23714,23715,23721],{},[1153,23716,23717,23719],{},[1289,23718,2681],{},[1163,23720,1402],{},[1167,23722,23723],{"encoding":1169},"-1"," do ",[1115,23726,23728],{"className":23727},[1144],[1146,23729,23730],{"xmlns":1148},[1150,23731,23732,23738],{},[1153,23733,23734,23736],{},[1289,23735,5096],{},[1163,23737,1402],{},[1167,23739,23740],{"encoding":1169},"+1",": znaménko určuje typ závislosti (pozitivní, nebo negativní), absolutní hodnota její sílu — čím blíž k 0, tím je závislost slabší.",[1110,23743,23744],{},[4002,23745],{"alt":23746,"className":23747,"src":23748},"mask-ra-korelace-sila",[1321,4006],"\u002Fwiki-assets\u002Fmask-ra-korelace-sila.png",[1110,23750,23751,23752,23765,23766,23784,23785,5360,23798,23811],{},"S rostoucí absolutní hodnotou ",[1115,23753,23755],{"className":23754},[1144],[1146,23756,23757],{"xmlns":1148},[1150,23758,23759,23763],{},[1153,23760,23761],{},[1159,23762,71],{},[1167,23764,71],{"encoding":1169}," se body v rozptylovém grafu víc blíží přímce; kolem ",[1115,23767,23769],{"className":23768},[1144],[1146,23770,23771],{"xmlns":1148},[1150,23772,23773,23781],{},[1153,23774,23775,23777,23779],{},[1159,23776,71],{},[1289,23778,13741],{},[1163,23780,1165],{},[1167,23782,23783],{"encoding":1169},"r\\approx 0"," je mezi ",[1115,23786,23788],{"className":23787},[1144],[1146,23789,23790],{"xmlns":1148},[1150,23791,23792,23796],{},[1153,23793,23794],{},[1159,23795,11019],{},[1167,23797,11019],{"encoding":1169},[1115,23799,23801],{"className":23800},[1144],[1146,23802,23803],{"xmlns":1148},[1150,23804,23805,23809],{},[1153,23806,23807],{},[1159,23808,11429],{},[1167,23810,11429],{"encoding":1169}," patrná jen náhodná rozptýlenost bez lineárního trendu.",[21050,23813,21053],{"id":23814},"v-r-1",[3311,23816,23818],{"className":3313,"code":23817,"language":71,"meta":3315,"style":3315},"cor(pocet_clenu, tydenni_vydaje)\n",[3087,23819,23820],{"__ignoreMap":3315},[1115,23821,23822,23825,23827,23829,23831,23834],{"class":3320,"line":10},[1115,23823,23824],{"class":3331},"cor",[1115,23826,1484],{"class":3335},[1115,23828,21074],{"class":3323},[1115,23830,1405],{"class":3327},[1115,23832,23833],{"class":3323}," tydenni_vydaje",[1115,23835,3520],{"class":3335},[3311,23837,23840],{"className":23838,"code":23839,"language":3542,"meta":3315},[3540],"[1] 0.9997441\n",[3087,23841,23839],{"__ignoreMap":3315},[1110,23843,23844,23845,23871],{},"Hodnota 0,9997 odpovídá ",[1115,23846,23848],{"className":23847},[1144],[1146,23849,23850],{"xmlns":1148},[1150,23851,23852,23868],{},[1153,23853,23854,23862,23864],{},[4072,23855,23856],{},[1182,23857,23858,23860],{},[1159,23859,14524],{},[1163,23861,1189],{},[1289,23863,1591],{},[4072,23865,23866],{},[1163,23867,21309],{},[1167,23869,23870],{"encoding":1169},"\\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.",[1103,23873,23875,23882,23885],{"className":23874,"dataCallout":3094},[1106,3093],[1110,23876,23878,23881],{"className":23877},[1113],[1115,23879],{"className":23880,"ariaHidden":1121},[1118,3101,1120],"Příklad: Koeficient korelace",[1110,23883,23884],{},"Pro stejná data o hodnotě produkce a výši investic dvanácti firem jako u regresní přímky byl spočten koeficient korelace mezi oběma proměnnými.",[1110,23886,21971,23887,23914],{},[1115,23888,23890],{"className":23889},[1144],[1146,23891,23892],{"xmlns":1148},[1150,23893,23894,23911],{},[1153,23895,23896,23906,23908],{},[1156,23897,23898,23900],{},[1159,23899,71],{},[1153,23901,23902,23904],{},[1159,23903,11019],{},[1159,23905,11429],{},[1289,23907,1591],{},[1163,23909,23910],{},"0,739",[1167,23912,23913],{"encoding":1169},"r_{xy} = 0{,}739"," — silná kladná závislost hodnoty produkce na výši investic.",[1310,23916,23918],{"id":23917},"vícenásobná-regrese-a-korelace","Vícenásobná regrese a korelace",[1110,23920,23921,23922,23935],{},"Pokud na závisle proměnnou ",[1115,23923,23925],{"className":23924},[1144],[1146,23926,23927],{"xmlns":1148},[1150,23928,23929,23933],{},[1153,23930,23931],{},[1159,23932,11429],{},[1167,23934,11429],{"encoding":1169}," působí víc vysvětlujících proměnných současně, analyzuje se zvlášť vliv každé z nich a výsledná regresní funkce se konstruuje jako součet jednoduchých regresních funkcí:",[1115,23937,23939],{"className":23938},[1144],[1146,23940,23941],{"xmlns":1148,"display":1573},[1150,23942,23943,24053],{},[1153,23944,23945,23947,23949,23955,23957,23963,23969,23971,23977,23983,23985,23987,23989,23995,24001,24003,24005,24011,24013,24019,24021,24027,24033,24035,24037,24039,24045,24051],{},[1159,23946,20626],{},[1289,23948,1591],{},[1156,23950,23951,23953],{},[1159,23952,20641],{},[1163,23954,1165],{},[1289,23956,5096],{},[1156,23958,23959,23961],{},[1159,23960,20641],{},[1163,23962,1402],{},[1156,23964,23965,23967],{},[1159,23966,11019],{},[1163,23968,1402],{},[1289,23970,5096],{},[1156,23972,23973,23975],{},[1159,23974,20641],{},[1163,23976,1189],{},[1156,23978,23979,23981],{},[1159,23980,11019],{},[1163,23982,1189],{},[1289,23984,5096],{},[1289,23986,22221],{},[1289,23988,5096],{},[1156,23990,23991,23993],{},[1159,23992,20641],{},[1159,23994,1110],{},[1156,23996,23997,23999],{},[1159,23998,11019],{},[1159,24000,1110],{},[1289,24002,1405],{"separator":1121},[1621,24004],{"width":1623},[2339,24006,24007,24009],{"accent":1121},[1159,24008,11429],{},[1289,24010,2345],{},[1289,24012,1591],{},[1156,24014,24015,24017],{},[1159,24016,15807],{},[1163,24018,1165],{},[1289,24020,5096],{},[1156,24022,24023,24025],{},[1159,24024,15807],{},[1163,24026,1402],{},[1156,24028,24029,24031],{},[1159,24030,11019],{},[1163,24032,1402],{},[1289,24034,5096],{},[1289,24036,22221],{},[1289,24038,5096],{},[1156,24040,24041,24043],{},[1159,24042,15807],{},[1159,24044,1110],{},[1156,24046,24047,24049],{},[1159,24048,11019],{},[1159,24050,1110],{},[1159,24052,1269],{"mathvariant":1734},[1167,24054,24055],{"encoding":1169},"\\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.",[21050,24057,24059],{"id":24058},"výběr-proměnných","Výběr proměnných",[1124,24061,24062,24068],{},[1127,24063,24064,24067],{},[1131,24065,24066],{},"Metoda ENTER"," — vloží do modelu všechny proměnné najednou. Použije se, když jde o index determinace celého modelu, o vliv každé nezávislé proměnné při kontrole vlivu ostatních, nebo o relativní důležitost proměnných. Vyžaduje poměrně vysoký počet pozorování — aspoň 20 na každou proměnnou.",[1127,24069,24070,24073,24074,24077,24078,24081],{},[1131,24071,24072],{},"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 ",[1131,24075,24076],{},"forward"," proměnné postupně přidává, varianta ",[1131,24079,24080],{},"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.",[21050,24083,24085],{"id":24084},"postup-odhadu","Postup odhadu",[2481,24087,24088,24091,24094],{},[1127,24089,24090],{},"ověření předpokladů regresního modelu,",[1127,24092,24093],{},"samotný odhad parametrů,",[1127,24095,24096],{},"reziduální analýza výsledného modelu.",[1110,24098,24099,24100,24117,24118,3607,24120,24149,24150,24179,24180,24197],{},"Důležitost každého parametru ",[1115,24101,24103],{"className":24102},[1144],[1146,24104,24105],{"xmlns":1148},[1150,24106,24107,24115],{},[1153,24108,24109],{},[1156,24110,24111,24113],{},[1159,24112,15807],{},[1159,24114,1487],{},[1167,24116,20766],{"encoding":1169}," v modelu ověřuje ",[1131,24119,992],{},[1115,24121,24123],{"className":24122},[1144],[1146,24124,24125],{"xmlns":1148},[1150,24126,24127,24147],{},[1153,24128,24129,24135,24137,24143,24145],{},[1156,24130,24131,24133],{},[1159,24132,1161],{},[1163,24134,1165],{},[1289,24136,1567],{},[1156,24138,24139,24141],{},[1159,24140,20641],{},[1159,24142,1487],{},[1289,24144,1591],{},[1163,24146,1165],{},[1167,24148,21253],{"encoding":1169}," (proměnná je v modelu nevýznamná) proti ",[1115,24151,24153],{"className":24152},[1144],[1146,24154,24155],{"xmlns":1148},[1150,24156,24157,24177],{},[1153,24158,24159,24165,24167,24173,24175],{},[1156,24160,24161,24163],{},[1159,24162,1161],{},[1163,24164,1402],{},[1289,24166,1567],{},[1156,24168,24169,24171],{},[1159,24170,20641],{},[1159,24172,1487],{},[1289,24174,15257],{"mathvariant":1734},[1163,24176,1165],{},[1167,24178,21284],{"encoding":1169}," (proměnná je významná). Při nezamítnutí ",[1115,24181,24183],{"className":24182},[1144],[1146,24184,24185],{"xmlns":1148},[1150,24186,24187,24195],{},[1153,24188,24189],{},[1156,24190,24191,24193],{},[1159,24192,1161],{},[1163,24194,1165],{},[1167,24196,1170],{"encoding":1169}," by proměnná — a s ní spojený regresor — v modelu neměla zůstat.",[21050,24199,24201],{"id":24200},"předpoklady-modelu","Předpoklady modelu",[2481,24203,24204,24221,24254,24260,24263,24266],{},[1127,24205,24206,24207,24220],{},"Závisle proměnná ",[1115,24208,24210],{"className":24209},[1144],[1146,24211,24212],{"xmlns":1148},[1150,24213,24214,24218],{},[1153,24215,24216],{},[1159,24217,11429],{},[1167,24219,11429],{"encoding":1169}," musí být aspoň intervalového typu (ne binární, diskrétní s málo hodnotami apod.) — jinak je na místě logistická regrese.",[1127,24222,24223,24224,24253],{},"Nezávislé proměnné ",[1115,24225,24227],{"className":24226},[1144],[1146,24228,24229],{"xmlns":1148},[1150,24230,24231,24251],{},[1153,24232,24233,24239,24241,24243,24245],{},[1156,24234,24235,24237],{},[1159,24236,11019],{},[1163,24238,1402],{},[1289,24240,1405],{"separator":1121},[1289,24242,1408],{},[1289,24244,1405],{"separator":1121},[1156,24246,24247,24249],{},[1159,24248,11019],{},[1159,24250,1110],{},[1167,24252,20590],{"encoding":1169}," jsou rovněž aspoň intervalového typu, mohou být i alternativní.",[1127,24255,24256,24257,1269],{},"Nezávislé proměnné by mezi sebou neměly být příliš vysoce korelované — ",[1131,24258,24259],{},"multikolinearita",[1127,24261,24262],{},"V datech nesmí být odlehlé či extrémní hodnoty; regresní analýza je na ně citlivá a mohou vážně narušit kvalitu odhadů.",[1127,24264,24265],{},"Proměnné musí být ve vzájemně lineárním vztahu — vícenásobná lineární regrese je založená na Pearsonově koeficientu korelace, takže nelineární vztahy mezi proměnnými zůstanou neodhalené.",[1127,24267,24268,24269,24273],{},"Proměnné mají mít ",[1318,24270,24272],{"className":24271,"dataFsResolvedFilePath":6242,"href":6243},[1321],"normální rozložení","; význam tohoto předpokladu ustupuje do pozadí u dostatečně velkého datového souboru díky centrální limitní větě.",[1110,24275,24276,24277,24280],{},"Normalita se u menšího počtu pozorování ověřuje stejnými testy jako u jiných znaků (viz ",[1318,24278,1331],{"className":24279,"dataFsResolvedFilePath":1329,"href":1330},[1321],") — 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.",[21050,24282,24283],{"id":24259},"Multikolinearita",[1110,24285,24286],{},"Multikolinearita vzniká, když vysvětlující proměnné silně závisejí jedna na druhé. Je nežádoucí, protože:",[1124,24288,24289,24292,24295],{},[1127,24290,24291],{},"výsledky regrese jsou pak nespolehlivé,",[1127,24293,24294],{},"zvyšuje pravděpodobnost, že se důležitá proměnná jeví jako statisticky nevýznamná a bude z modelu vyřazena,",[1127,24296,24297],{},"směrodatné odchylky odhadnutých parametrů jsou vysoké, testová kritéria t-testů nízká, p-hodnoty vysoké.",[1110,24299,24300,24301,24304,24305,24328,24329,24347,24348,24364],{},"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 ",[1131,24302,24303],{},"VIF (Variance Inflation Factor)",": hodnoty ",[1115,24306,24308],{"className":24307},[1144],[1146,24309,24310],{"xmlns":1148},[1150,24311,24312,24325],{},[1153,24313,24314,24316,24318,24321,24323],{},[1163,24315,1402],{},[1289,24317,3951],{},[2525,24319,24320],{},"VIF",[1289,24322,3951],{},[1163,24324,14227],{},[1167,24326,24327],{"encoding":1169},"1\u003C\\text{VIF}\u003C5"," jsou varující, ",[1115,24330,24332],{"className":24331},[1144],[1146,24333,24334],{"xmlns":1148},[1150,24335,24336,24344],{},[1153,24337,24338,24340,24342],{},[2525,24339,24320],{},[1289,24341,1291],{},[1163,24343,14227],{},[1167,24345,24346],{"encoding":1169},"\\text{VIF}>5"," (přísněji ",[1115,24349,24351],{"className":24350},[1144],[1146,24352,24353],{"xmlns":1148},[1150,24354,24355,24361],{},[1153,24356,24357,24359],{},[1289,24358,1291],{},[1163,24360,13334],{},[1167,24362,24363],{"encoding":1169},">10",") značí vysokou multikolinearitu.",[1110,24366,24367],{},"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.",[21050,24369,24371],{"id":24370},"další-ukazatele-kvality-modelu","Další ukazatele kvality modelu",[1124,24373,24374,24380,24386],{},[1127,24375,24376,24379],{},[1131,24377,24378],{},"F-test"," — testuje hypotézu, že všechny regresní koeficienty jsou rovny nule, proti alternativě, že aspoň jeden v modelu být má (celková významnost modelu).",[1127,24381,24382,24385],{},[1131,24383,24384],{},"RMSE"," (odmocnina z reziduálního rozptylu) — absolutní měřítko vhodnosti funkce (na rozdíl od indexu determinace, který je relativní); nižší hodnota znamená lepší fit.",[1127,24387,24388,24391,24392,24395],{},[1131,24389,24390],{},"AIC"," (Akaikeho informační kritérium) a ",[1131,24393,24394],{},"BIC"," (Bayesovo informační kritérium) — čím nižší hodnoty obou kritérií, tím lepší model; používají se hlavně při stepwise výběru proměnných.",[21050,24397,21053],{"id":24398},"v-r-2",[1110,24400,24401],{},"Pro vícenásobnou regresi je postup v R rozšířením postupu pro regresní přímku — přibývá výběr proměnných a kontrola multikolinearity:",[3311,24403,24405],{"className":3313,"code":24404,"language":71,"meta":3315,"style":3315},"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",[3087,24406,24407,24433,24477,24503,24513,24517,24528,24539,24543,24553,24563,24567,24577,24587,24592],{"__ignoreMap":3315},[1115,24408,24409,24412,24414,24417,24419,24422,24424,24427,24429,24431],{"class":3320,"line":10},[1115,24410,24411],{"class":3323},"data",[1115,24413,3328],{"class":3327},[1115,24415,24416],{"class":3331}," read.table",[1115,24418,1484],{"class":3335},[1115,24420,24421],{"class":3459},"\"4_4.txt\"",[1115,24423,1405],{"class":3327},[1115,24425,24426],{"class":3323}," header",[1115,24428,3416],{"class":3327},[1115,24430,3429],{"class":3343},[1115,24432,3520],{"class":3335},[1115,24434,24435,24438,24440,24442,24444,24446,24448,24451,24453,24456,24458,24461,24463,24466,24468,24471,24473,24475],{"class":3320,"line":27},[1115,24436,24437],{"class":3323},"model_plny",[1115,24439,3328],{"class":3327},[1115,24441,21154],{"class":3331},[1115,24443,1484],{"class":3335},[1115,24445,11429],{"class":3323},[1115,24447,21161],{"class":3327},[1115,24449,24450],{"class":3323}," x1",[1115,24452,22819],{"class":3327},[1115,24454,24455],{"class":3323}," x2",[1115,24457,22819],{"class":3327},[1115,24459,24460],{"class":3323}," x3",[1115,24462,22819],{"class":3327},[1115,24464,24465],{"class":3323}," x4",[1115,24467,1405],{"class":3327},[1115,24469,24470],{"class":3323}," data",[1115,24472,3416],{"class":3327},[1115,24474,24470],{"class":3323},[1115,24476,3520],{"class":3335},[1115,24478,24479,24482,24484,24487,24489,24491,24493,24496,24498,24501],{"class":3320,"line":148},[1115,24480,24481],{"class":3323},"model_krok",[1115,24483,3328],{"class":3327},[1115,24485,24486],{"class":3331}," step",[1115,24488,1484],{"class":3335},[1115,24490,24437],{"class":3323},[1115,24492,1405],{"class":3327},[1115,24494,24495],{"class":3323}," direction",[1115,24497,3416],{"class":3327},[1115,24499,24500],{"class":3459}," \"both\"",[1115,24502,3520],{"class":3335},[1115,24504,24505,24507,24509,24511],{"class":3320,"line":111},[1115,24506,21171],{"class":3331},[1115,24508,1484],{"class":3335},[1115,24510,24481],{"class":3323},[1115,24512,3520],{"class":3335},[1115,24514,24515],{"class":3320,"line":96},[1115,24516,14342],{"emptyLinePlaceholder":6298},[1115,24518,24519,24521,24523,24526],{"class":3320,"line":89},[1115,24520,21700],{"class":3327},[1115,24522,1484],{"class":3335},[1115,24524,24525],{"class":3323},"car",[1115,24527,3520],{"class":3335},[1115,24529,24530,24533,24535,24537],{"class":3320,"line":82},[1115,24531,24532],{"class":3331},"vif",[1115,24534,1484],{"class":3335},[1115,24536,24481],{"class":3323},[1115,24538,3520],{"class":3335},[1115,24540,24541],{"class":3320,"line":75},[1115,24542,14342],{"emptyLinePlaceholder":6298},[1115,24544,24545,24547,24549,24551],{"class":3320,"line":3510},[1115,24546,21700],{"class":3327},[1115,24548,1484],{"class":3335},[1115,24550,21705],{"class":3323},[1115,24552,3520],{"class":3335},[1115,24554,24555,24557,24559,24561],{"class":3320,"line":72},[1115,24556,21712],{"class":3331},[1115,24558,1484],{"class":3335},[1115,24560,24481],{"class":3323},[1115,24562,3520],{"class":3335},[1115,24564,24565],{"class":3320,"line":25},[1115,24566,14342],{"emptyLinePlaceholder":6298},[1115,24568,24569,24571,24573,24575],{"class":3320,"line":65},[1115,24570,21700],{"class":3327},[1115,24572,1484],{"class":3335},[1115,24574,21795],{"class":3323},[1115,24576,3520],{"class":3335},[1115,24578,24579,24581,24583,24585],{"class":3320,"line":63},[1115,24580,21802],{"class":3331},[1115,24582,1484],{"class":3335},[1115,24584,24481],{"class":3323},[1115,24586,3520],{"class":3335},[1115,24588,24590],{"class":3320,"line":24589},14,[1115,24591,14342],{"emptyLinePlaceholder":6298},[1115,24593,24594,24596,24598,24600,24602,24604],{"class":3320,"line":60},[1115,24595,21880],{"class":3331},[1115,24597,1484],{"class":3335},[1115,24599,21348],{"class":3331},[1115,24601,1484],{"class":3335},[1115,24603,24481],{"class":3323},[1115,24605,13794],{"class":3335},[1110,24607,24608,24610,24611,24614],{},[3087,24609,20424],{}," provádí stepwise výběr podle AIC, ",[3087,24612,24613],{},"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.",[1103,24616,24618,24625,24628,24631],{"className":24617,"dataCallout":3094},[1106,3093],[1110,24619,24621,24624],{"className":24620},[1113],[1115,24622],{"className":24623,"ariaHidden":1121},[1118,3101,1120],"Příklad: Vícenásobná regrese",[1110,24626,24627],{},"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.",[1110,24629,24630],{},"Postup: odhad plného modelu → stepwise analýza podle AIC → ověření předpokladů.",[1110,24632,24633,24634,24637,24638,24640,24641,24644],{},"Diagnostika odhaleného modelu ukázala tři problémy: (1) ",[1131,24635,24636],{},"nelinearita"," — mezi některými vysvětlujícími proměnnými a cenou je zjevně jiný než lineární vztah, řešením je zkusit u nich druhou mocninu; (2) ",[1131,24639,24259],{}," mezi dvojicí proměnných popisujících vzdálenost (k silnici a ke spalovně) — doporučeno jednu z nich vynechat; (3) ",[1131,24642,24643],{},"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.",[1310,24646,6027],{"id":6026},[1103,24648,24650,24657],{"className":24649,"dataCallout":6032},[1106,6031],[1110,24651,24653,24656],{"className":24652},[1113],[1115,24654],{"className":24655,"ariaHidden":1121},[1118,6039,1120],"Koeficient korelace jen pro přímku",[1110,24658,24659,24660,24716,24717,24734,24735,24755,24756,5360,24769,1269],{},"Vzorec ",[1115,24661,24663],{"className":24662},[1144],[1146,24664,24665],{"xmlns":1148},[1150,24666,24667,24713],{},[1153,24668,24669,24679,24681,24691,24693],{},[1156,24670,24671,24673],{},[1159,24672,71],{},[1153,24674,24675,24677],{},[1159,24676,11019],{},[1159,24678,11429],{},[1289,24680,1591],{},[1156,24682,24683,24685],{},[1159,24684,1463],{},[1153,24686,24687,24689],{},[1159,24688,11019],{},[1159,24690,11429],{},[1159,24692,4223],{"mathvariant":1734},[4072,24694,24695],{},[1153,24696,24697,24705],{},[2970,24698,24699,24701,24703],{},[1159,24700,1463],{},[1159,24702,11019],{},[1163,24704,1189],{},[2970,24706,24707,24709,24711],{},[1159,24708,1463],{},[1159,24710,11429],{},[1163,24712,1189],{},[1167,24714,24715],{"encoding":1169},"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 ",[1115,24718,24720],{"className":24719},[1144],[1146,24721,24722],{"xmlns":1148},[1150,24723,24724,24732],{},[1153,24725,24726],{},[1182,24727,24728,24730],{},[1159,24729,14524],{},[1163,24731,1189],{},[1167,24733,20328],{"encoding":1169},", případně obecným indexem korelace ",[1115,24736,24738],{"className":24737},[1144],[1146,24739,24740],{"xmlns":1148},[1150,24741,24742,24752],{},[1153,24743,24744],{},[4072,24745,24746],{},[1182,24747,24748,24750],{},[1159,24749,14524],{},[1163,24751,1189],{},[1167,24753,24754],{"encoding":1169},"\\sqrt{R^2}"," — ne koeficientem korelace mezi ",[1115,24757,24759],{"className":24758},[1144],[1146,24760,24761],{"xmlns":1148},[1150,24762,24763,24767],{},[1153,24764,24765],{},[1159,24766,11019],{},[1167,24768,11019],{"encoding":1169},[1115,24770,24772],{"className":24771},[1144],[1146,24773,24774],{"xmlns":1148},[1150,24775,24776,24780],{},[1153,24777,24778],{},[1159,24779,11429],{},[1167,24781,11429],{"encoding":1169},[1103,24783,24785,24792],{"className":24784,"dataCallout":6032},[1106,6031],[1110,24786,24788,24791],{"className":24787},[1113],[1115,24789],{"className":24790,"ariaHidden":1121},[1118,6039,1120],"Významný F-test, nevýznamné t-testy",[1110,24793,24794],{},"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.",[1103,24796,24798,24805],{"className":24797,"dataCallout":6032},[1106,6031],[1110,24799,24801,24804],{"className":24800},[1113],[1115,24802],{"className":24803,"ariaHidden":1121},[1118,6039,1120],"Durbin-Watsonova statistika mimo okolí 2",[1110,24806,24807],{},"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.",[1103,24809,24811,24818],{"className":24810,"dataCallout":6032},[1106,6031],[1110,24812,24814,24817],{"className":24813},[1113],[1115,24815],{"className":24816,"ariaHidden":1121},[1118,6039,1120],"Nízký počet pozorování při stepwise výběru",[1110,24819,24820],{},"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.",[1310,24822,6215],{"id":6214},[1124,24824,24825,24830,24835,24840,24845,24850,24855],{},[1127,24826,24827],{},[1318,24828,1324],{"className":24829,"dataFsResolvedFilePath":1322,"href":1323},[1321],[1127,24831,24832],{},[1318,24833,6244],{"className":24834,"dataFsResolvedFilePath":6242,"href":6243},[1321],[1127,24836,24837],{},[1318,24838,6236],{"className":24839,"dataFsResolvedFilePath":6234,"href":6235},[1321],[1127,24841,24842],{},[1318,24843,6228],{"className":24844,"dataFsResolvedFilePath":1329,"href":1330},[1321],[1127,24846,24847],{},[1318,24848,1094],{"className":24849,"dataFsResolvedFilePath":15392,"href":15393},[1321],[1127,24851,24852],{},[1318,24853,6260],{"className":24854,"dataFsResolvedFilePath":6258,"href":6259},[1321],[1127,24856,24857],{},[1318,24858,6268],{"className":24859,"dataFsResolvedFilePath":6266,"href":6267},[1321],[1310,24861,6271],{"id":934},[1110,24863,6274,24864,6279],{},[6276,24865,6278],{},[6281,24867,24868],{},"html pre.shiki code .sP4rz, html 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diagram zobrazuje vývoj variability procesu v čase a dává signál, že na proces začala působit vymezitelná příčina: bod mimo akční meze UCL a LCL.",[1127,24927,24928,24929,2568,24955,5360,24981,1269],{},"Regulace měřením (spojitá veličina s normálním rozdělením): diagramy ",[1115,24930,24932],{"className":24931},[1144],[1146,24933,24934],{"xmlns":1148},[1150,24935,24936,24952],{},[1153,24937,24938,24940,24946,24948,24950],{},[1289,24939,1484],{"stretchy":1483},[2339,24941,24942,24944],{"accent":1121},[1159,24943,11019],{},[1289,24945,15762],{},[1289,24947,1405],{"separator":1121},[1159,24949,14524],{},[1289,24951,1495],{"stretchy":1483},[1167,24953,24954],{"encoding":1169},"(\\bar{x}, R)",[1115,24956,24958],{"className":24957},[1144],[1146,24959,24960],{"xmlns":1148},[1150,24961,24962,24978],{},[1153,24963,24964,24966,24972,24974,24976],{},[1289,24965,1484],{"stretchy":1483},[2339,24967,24968,24970],{"accent":1121},[1159,24969,11019],{},[1289,24971,15762],{},[1289,24973,1405],{"separator":1121},[1159,24975,1463],{},[1289,24977,1495],{"stretchy":1483},[1167,24979,24980],{"encoding":1169},"(\\bar{x}, s)",[1115,24982,24984],{"className":24983},[1144],[1146,24985,24986],{"xmlns":1148},[1150,24987,24988,25017],{},[1153,24989,24990,24992,24998,25000,25015],{},[1289,24991,1484],{"stretchy":1483},[1156,24993,24994,24996],{},[1159,24995,11019],{},[1159,24997,1487],{},[1289,24999,1405],{"separator":1121},[1156,25001,25002,25004],{},[1159,25003,14524],{},[1153,25005,25006,25008,25011,25013],{},[1159,25007,11559],{},[1159,25009,25010],{},"l",[1289,25012,1405],{"separator":1121},[1159,25014,1487],{},[1289,25016,1495],{"stretchy":1483},[1167,25018,25019],{"encoding":1169},"(x_i, R_{kl,i})",[1127,25021,25022,25023,25036,25037,25050,25051,25067,25068,25081],{},"Regulace srovnáváním (diskrétní veličina): počet neshod ",[1115,25024,25026],{"className":25025},[1144],[1146,25027,25028],{"xmlns":1148},[1150,25029,25030,25034],{},[1153,25031,25032],{},[1159,25033,3338],{},[1167,25035,3338],{"encoding":1169}," (konstantní rozsah) a ",[1115,25038,25040],{"className":25039},[1144],[1146,25041,25042],{"xmlns":1148},[1150,25043,25044,25048],{},[1153,25045,25046],{},[1159,25047,15831],{},[1167,25049,15831],{"encoding":1169}," (nekonstantní rozsah), počet neshodných produktů ",[1115,25052,25054],{"className":25053},[1144],[1146,25055,25056],{"xmlns":1148},[1150,25057,25058,25064],{},[1153,25059,25060,25062],{},[1159,25061,1287],{},[1159,25063,1110],{},[1167,25065,25066],{"encoding":1169},"np"," (konstantní rozsah) a jejich podíl ",[1115,25069,25071],{"className":25070},[1144],[1146,25072,25073],{"xmlns":1148},[1150,25074,25075,25079],{},[1153,25076,25077],{},[1159,25078,1110],{},[1167,25080,1110],{"encoding":1169}," (nekonstantní rozsah).",[1127,25083,25084],{},"Podskupiny s vymezitelnou příčinou se po jejím odstranění z výpočtu vyřadí a meze se přepočítají, dokud jsou všechny body uvnitř mezí.",[1127,25086,25087,25088,2568,25107,2568,25129,2568,25151,25175,25176,25197],{},"Indexy způsobilosti ",[1115,25089,25091],{"className":25090},[1144],[1146,25092,25093],{"xmlns":1148},[1150,25094,25095,25104],{},[1153,25096,25097],{},[1156,25098,25099,25102],{},[1159,25100,25101],{},"C",[1159,25103,1110],{},[1167,25105,25106],{"encoding":1169},"C_p",[1115,25108,25110],{"className":25109},[1144],[1146,25111,25112],{"xmlns":1148},[1150,25113,25114,25126],{},[1153,25115,25116],{},[1156,25117,25118,25120],{},[1159,25119,25101],{},[1153,25121,25122,25124],{},[1159,25123,1110],{},[1159,25125,11559],{},[1167,25127,25128],{"encoding":1169},"C_{pk}",[1115,25130,25132],{"className":25131},[1144],[1146,25133,25134],{"xmlns":1148},[1150,25135,25136,25148],{},[1153,25137,25138],{},[1156,25139,25140,25142],{},[1159,25141,25101],{},[1153,25143,25144,25146],{},[1159,25145,1110],{},[1159,25147,4090],{},[1167,25149,25150],{"encoding":1169},"C_{pm}",[1115,25152,25154],{"className":25153},[1144],[1146,25155,25156],{"xmlns":1148},[1150,25157,25158,25172],{},[1153,25159,25160],{},[1156,25161,25162,25164],{},[1159,25163,25101],{},[1153,25165,25166,25168,25170],{},[1159,25167,1110],{},[1159,25169,4090],{},[1159,25171,11559],{},[1167,25173,25174],{"encoding":1169},"C_{pmk}"," posuzují, zda statisticky zvládnutý proces vyhovuje tolerančním mezím; ",[1115,25177,25179],{"className":25178},[1144],[1146,25180,25181],{"xmlns":1148},[1150,25182,25183,25195],{},[1153,25184,25185],{},[1156,25186,25187,25189],{},[1159,25188,25101],{},[1153,25190,25191,25193],{},[1159,25192,1110],{},[1159,25194,11559],{},[1167,25196,25128],{"encoding":1169}," navíc zohledňuje vychýlení střední hodnoty.",[1127,25199,25200,25201,1269],{},"V R diagramy i indexy počítá balíček ",[3087,25202,360],{},[1310,25204,25206],{"id":25205},"statistická-regulace-procesu","Statistická regulace procesu",[1110,25208,25209,25210,25212,25213,1269],{},"Tradiční zabezpečování jakosti kontroluje výrobky až po jejich vyrobení, což je neekonomické. ",[1131,25211,25206],{}," 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 ",[1131,25214,25215],{},"statisticky zvládnutém stavu",[1110,25217,25218,25219,25222],{},"Teorie regulace vychází z ",[1131,25220,25221],{},"variability"," procesu, kterou způsobují dva druhy příčin:",[1710,25224,25225,25237],{},[1713,25226,25227],{},[1716,25228,25229,25231,25234],{},[1719,25230],{},[1719,25232,25233],{},"Náhodné příčiny",[1719,25235,25236],{},"Vymezitelné příčiny",[1828,25238,25239,25250,25261],{},[1716,25240,25241,25244,25247],{},[1833,25242,25243],{},"Povaha",[1833,25245,25246],{},"široká skupina neidentifikovatelných vlivů, každý přispívá k variabilitě malou měrou",[1833,25248,25249],{},"vlivy, které za běžných podmínek na proces nepůsobí; vyvolají nepřirozené kolísání údajů",[1716,25251,25252,25255,25258],{},[1833,25253,25254],{},"Stav procesu",[1833,25256,25257],{},"ustálený, jakost výstupů je předvídatelná, není nutné zasahovat — statisticky zvládnutý",[1833,25259,25260],{},"jakost výstupů není předvídatelná, je nutné zasáhnout — proces není statisticky zvládnutý",[1716,25262,25263,25266,25269],{},[1833,25264,25265],{},"Příklady",[1833,25267,25268],{},"psychický stav pracovníka, chvění stroje, teplota ovzduší",[1833,25270,25271],{},"změna materiálu, nezaškolená obsluha",[1110,25273,25274,25275,25278,25279,25282],{},"Vymezitelné příčiny jsou ",[1131,25276,25277],{},"sporadické"," (vznikají náhle, změny trvají krátce) nebo ",[1131,25280,25281],{},"přetrvávající"," (trvají stále nebo se mění).",[1110,25284,25285],{},[4002,25286],{"alt":25287,"className":25288,"src":25289},"mask-ilu-pricin-variability",[1321,4006],"\u002Fwiki-assets\u002Fmask-ilu-pricin-variability.png",[1110,25291,25292],{},"Regulace probíhá ve třech fázích:",[2481,25294,25295,25305,25311],{},[1127,25296,25297,25300,25301,25304],{},[1131,25298,25299],{},"Fáze přípravná"," — stanoví se sledované znaky jakosti (rozměr, hmotnost, počet vad…), délka časového intervalu mezi měřeními, ",[1131,25302,25303],{},"logická podskupina"," (skupina měření, v níž se předpokládá působení pouze náhodných příčin), typ regulačního diagramu a místa kontroly v procesu.",[1127,25306,25307,25310],{},[1131,25308,25309],{},"Fáze zabezpečování statistické zvládnutosti"," — pomocí regulačních diagramů se identifikují vymezitelné příčiny a odstraní se jejich působení.",[1127,25312,25313,25316],{},[1131,25314,25315],{},"Fáze analýzy a zabezpečení způsobilosti"," — zkoumá se, zda statisticky zvládnutý proces vyhovuje požadavkům zákazníka; k tomu slouží indexy způsobilosti (níže).",[1310,25318,25320],{"id":25319},"princip-regulačního-diagramu","Princip regulačního diagramu",[1110,25322,25323,25326],{},[1131,25324,25325],{},"Regulační diagram"," je grafický prostředek pro zobrazení vývoje variability procesu v čase. Popisuje statistickou zvládnutelnost procesu a dává signál, že na proces začala působit vymezitelná příčina; na jeho základě se do procesu zasáhne s cílem příčinu odstranit.",[1124,25328,25329,25335,25341],{},[1127,25330,25331,25334],{},[1131,25332,25333],{},"CL"," — střední přímka, odpovídá požadované (referenční) hodnotě použité charakteristiky,",[1127,25336,25337,25340],{},[1131,25338,25339],{},"UCL"," — horní akční regulační mez,",[1127,25342,25343,25346],{},[1131,25344,25345],{},"LCL"," — dolní akční regulační mez.",[1110,25348,25349],{},"Akční meze vymezují pásmo působení pouze náhodných příčin variability.",[1110,25351,25352],{},[4002,25353],{"alt":25354,"className":25355,"src":25356},"mask-rd-schema",[1321,4006],"\u002Fwiki-assets\u002Fmask-rd-schema.png",[1110,25358,25359,25362],{},[1131,25360,25361],{},"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.",[1110,25364,25365,25366,25369,25370,25373],{},"Podle charakteru regulované veličiny se diagramy dělí na diagramy pro ",[1131,25367,25368],{},"regulaci měřením"," (regulovaná veličina je spojitá náhodná veličina) a pro ",[1131,25371,25372],{},"regulaci srovnáváním"," (diskrétní náhodná veličina).",[1110,25375,25376],{},"Postup při konstrukci regulačního diagramu:",[2481,25378,25379,25382,25385,25388,25391,25394,25397,25400,25403],{},[1127,25380,25381],{},"volba regulované veličiny,",[1127,25383,25384],{},"sběr a záznam dat,",[1127,25386,25387],{},"ověření požadovaných předpokladů o datech,",[1127,25389,25390],{},"volba rozsahu logických podskupin,",[1127,25392,25393],{},"volba vhodného regulačního diagramu,",[1127,25395,25396],{},"výpočet hodnot zvoleného testového kritéria pro jednotlivé výběry,",[1127,25398,25399],{},"ověření a zajištění statistické zvládnutosti procesu,",[1127,25401,25402],{},"ověření způsobilosti procesu,",[1127,25404,25405],{},"vlastní regulace procesu.",[1310,25407,25409],{"id":25408},"regulace-měřením","Regulace měřením",[1110,25411,25412],{},"Diagramy pro regulaci měřením se používají, když je regulovaná veličina měřitelná. Požaduje se, aby:",[1124,25414,25415,25418],{},[1127,25416,25417],{},"jednotlivá měření byla vzájemně nezávislá,",[1127,25419,25420,25421,25434,25435,25448,25449,25462,25463,25476],{},"regulovaná veličina byla spojitá náhodná veličina s normálním rozdělením se střední hodnotou ",[1115,25422,25424],{"className":25423},[1144],[1146,25425,25426],{"xmlns":1148},[1150,25427,25428,25432],{},[1153,25429,25430],{},[1159,25431,11190],{},[1167,25433,13097],{"encoding":1169}," a směrodatnou odchylkou ",[1115,25436,25438],{"className":25437},[1144],[1146,25439,25440],{"xmlns":1148},[1150,25441,25442,25446],{},[1153,25443,25444],{},[1159,25445,11198],{},[1167,25447,11230],{"encoding":1169}," — tyto dva parametry charakterizují statistickou stabilitu procesu; ",[1115,25450,25452],{"className":25451},[1144],[1146,25453,25454],{"xmlns":1148},[1150,25455,25456,25460],{},[1153,25457,25458],{},[1159,25459,11190],{},[1167,25461,13097],{"encoding":1169}," je hodnota, na niž je proces nastaven, ",[1115,25464,25466],{"className":25465},[1144],[1146,25467,25468],{"xmlns":1148},[1150,25469,25470,25474],{},[1153,25471,25472],{},[1159,25473,11198],{},[1167,25475,11230],{"encoding":1169}," charakterizuje jeho přesnost.",[1110,25478,25479,25480,2568,25505,5360,25530,25567],{},"Jsou-li předpoklady splněny, volí se diagramy, které současně sledují stabilitu polohy i stabilitu rozptylu: ",[1115,25481,25483],{"className":25482},[1144],[1146,25484,25485],{"xmlns":1148},[1150,25486,25487,25503],{},[1153,25488,25489,25491,25497,25499,25501],{},[1289,25490,1484],{"stretchy":1483},[2339,25492,25493,25495],{"accent":1121},[1159,25494,11019],{},[1289,25496,15762],{},[1289,25498,1405],{"separator":1121},[1159,25500,14524],{},[1289,25502,1495],{"stretchy":1483},[1167,25504,24954],{"encoding":1169},[1115,25506,25508],{"className":25507},[1144],[1146,25509,25510],{"xmlns":1148},[1150,25511,25512,25528],{},[1153,25513,25514,25516,25522,25524,25526],{},[1289,25515,1484],{"stretchy":1483},[2339,25517,25518,25520],{"accent":1121},[1159,25519,11019],{},[1289,25521,15762],{},[1289,25523,1405],{"separator":1121},[1159,25525,1463],{},[1289,25527,1495],{"stretchy":1483},[1167,25529,24980],{"encoding":1169},[1115,25531,25533],{"className":25532},[1144],[1146,25534,25535],{"xmlns":1148},[1150,25536,25537,25565],{},[1153,25538,25539,25541,25547,25549,25563],{},[1289,25540,1484],{"stretchy":1483},[1156,25542,25543,25545],{},[1159,25544,11019],{},[1159,25546,1487],{},[1289,25548,1405],{"separator":1121},[1156,25550,25551,25553],{},[1159,25552,14524],{},[1153,25554,25555,25557,25559,25561],{},[1159,25556,11559],{},[1159,25558,25010],{},[1289,25560,1405],{"separator":1121},[1159,25562,1487],{},[1289,25564,1495],{"stretchy":1483},[1167,25566,25019],{"encoding":1169},". Výsledkem jsou vždy dva diagramy.",[21050,25569,25571,25572],{"id":25570},"diagram-xˉrbarx-r","Diagram ",[1115,25573,25575],{"className":25574},[1144],[1146,25576,25577],{"xmlns":1148},[1150,25578,25579,25595],{},[1153,25580,25581,25583,25589,25591,25593],{},[1289,25582,1484],{"stretchy":1483},[2339,25584,25585,25587],{"accent":1121},[1159,25586,11019],{},[1289,25588,15762],{},[1289,25590,1405],{"separator":1121},[1159,25592,14524],{},[1289,25594,1495],{"stretchy":1483},[1167,25596,24954],{"encoding":1169},[1110,25598,25599,25600,25622,25623,25641],{},"Regulované veličiny jsou výběrové průměry ",[1115,25601,25603],{"className":25602},[1144],[1146,25604,25605],{"xmlns":1148},[1150,25606,25607,25619],{},[1153,25608,25609],{},[1156,25610,25611,25617],{},[2339,25612,25613,25615],{"accent":1121},[1159,25614,11019],{},[1289,25616,15762],{},[1159,25618,1487],{},[1167,25620,25621],{"encoding":1169},"\\bar{x}_i"," a výběrová rozpětí ",[1115,25624,25626],{"className":25625},[1144],[1146,25627,25628],{"xmlns":1148},[1150,25629,25630,25638],{},[1153,25631,25632],{},[1156,25633,25634,25636],{},[1159,25635,14524],{},[1159,25637,1487],{},[1167,25639,25640],{"encoding":1169},"R_i"," v logických podskupinách:",[1115,25643,25645],{"className":25644},[1144],[1146,25646,25647],{"xmlns":1148,"display":1573},[1150,25648,25649,25750],{},[1153,25650,25651,25661,25663,25669,25683,25693,25695,25697,25703,25705,25716,25726,25728,25738,25748],{},[1156,25652,25653,25659],{},[2339,25654,25655,25657],{"accent":1121},[1159,25656,11019],{},[1289,25658,15762],{},[1159,25660,1487],{},[1289,25662,1591],{},[2355,25664,25665,25667],{},[1163,25666,1402],{},[1159,25668,1287],{},[1593,25670,25671,25673,25681],{},[1289,25672,1597],{},[1153,25674,25675,25677,25679],{},[1159,25676,1492],{},[1289,25678,1591],{},[1163,25680,1402],{},[1159,25682,1287],{},[1156,25684,25685,25687],{},[1159,25686,11019],{},[1153,25688,25689,25691],{},[1159,25690,1487],{},[1159,25692,1492],{},[1289,25694,1405],{"separator":1121},[1621,25696],{"width":1623},[1156,25698,25699,25701],{},[1159,25700,14524],{},[1159,25702,1487],{},[1289,25704,1591],{},[25706,25707,25708,25714],"munder",{},[1153,25709,25710,25712],{},[1159,25711,16022],{},[1289,25713,4110],{},[1159,25715,1492],{},[1156,25717,25718,25720],{},[1159,25719,11019],{},[1153,25721,25722,25724],{},[1159,25723,1487],{},[1159,25725,1492],{},[1289,25727,2681],{},[25706,25729,25730,25736],{},[1153,25731,25732,25734],{},[1159,25733,4107],{},[1289,25735,4110],{},[1159,25737,1492],{},[1156,25739,25740,25742],{},[1159,25741,11019],{},[1153,25743,25744,25746],{},[1159,25745,1487],{},[1159,25747,1492],{},[1159,25749,1269],{"mathvariant":1734},[1167,25751,25752],{"encoding":1169},"\\bar{x}_i = \\frac{1}{n}\\sum_{j=1}^n x_{ij}, \\qquad R_i = \\max_j x_{ij} - \\min_j x_{ij}.",[1110,25754,25755],{},"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.",[1110,25757,25758,25759,25785,25786,25799,25800,5360,25821,25838,25839,25852,25853,25871,25872,1269],{},"Data se zapisují do tabulky: řádek ",[1115,25760,25762],{"className":25761},[1144],[1146,25763,25764],{"xmlns":1148},[1150,25765,25766,25782],{},[1153,25767,25768,25770,25772,25774,25776,25778,25780],{},[1159,25769,1487],{},[1289,25771,1591],{},[1163,25773,1402],{},[1289,25775,1405],{"separator":1121},[1289,25777,1408],{},[1289,25779,1405],{"separator":1121},[1159,25781,11559],{},[1167,25783,25784],{"encoding":1169},"i = 1, \\dots, k"," je logická podskupina v pořadí, v jakém byla získána, sloupce obsahují ",[1115,25787,25789],{"className":25788},[1144],[1146,25790,25791],{"xmlns":1148},[1150,25792,25793,25797],{},[1153,25794,25795],{},[1159,25796,1287],{},[1167,25798,1287],{"encoding":1169}," naměřených hodnot a poslední dva sloupce ",[1115,25801,25803],{"className":25802},[1144],[1146,25804,25805],{"xmlns":1148},[1150,25806,25807,25819],{},[1153,25808,25809],{},[1156,25810,25811,25817],{},[2339,25812,25813,25815],{"accent":1121},[1159,25814,11019],{},[1289,25816,15762],{},[1159,25818,1487],{},[1167,25820,25621],{"encoding":1169},[1115,25822,25824],{"className":25823},[1144],[1146,25825,25826],{"xmlns":1148},[1150,25827,25828,25836],{},[1153,25829,25830],{},[1156,25831,25832,25834],{},[1159,25833,14524],{},[1159,25835,1487],{},[1167,25837,25640],{"encoding":1169},". Pro sestrojení diagramu je potřeba aspoň 20 podskupin. Nejprve se určí diagram ",[1115,25840,25842],{"className":25841},[1144],[1146,25843,25844],{"xmlns":1148},[1150,25845,25846,25850],{},[1153,25847,25848],{},[1159,25849,14524],{},[1167,25851,14524],{"encoding":1169},", potom diagram ",[1115,25854,25856],{"className":25855},[1144],[1146,25857,25858],{"xmlns":1148},[1150,25859,25860,25868],{},[1153,25861,25862],{},[2339,25863,25864,25866],{"accent":1121},[1159,25865,11019],{},[1289,25867,15762],{},[1167,25869,25870],{"encoding":1169},"\\bar{x}"," — u obou střední přímka a akční meze. V R se diagramy konstruují funkcí ",[3087,25873,25874],{},"qcc()",[1103,25876,25878,25885],{"className":25877,"dataCallout":3094},[1106,3093],[1110,25879,25881,25884],{"className":25880},[1113],[1115,25882],{"className":25883,"ariaHidden":1121},[1118,3101,1120],"Příklad: kontrola rozměru dílu ve 20 logických podskupinách",[1110,25886,25887,25888,25901,25902,2568,25920,25938,25939,1269],{},"Naměřená data znaku jakosti ",[1115,25889,25891],{"className":25890},[1144],[1146,25892,25893],{"xmlns":1148},[1150,25894,25895,25899],{},[1153,25896,25897],{},[1159,25898,11031],{},[1167,25900,11031],{"encoding":1169}," byla získána ve 20 logických podskupinách po 4 měřeních (",[1115,25903,25905],{"className":25904},[1144],[1146,25906,25907],{"xmlns":1148},[1150,25908,25909,25917],{},[1153,25910,25911,25913,25915],{},[1159,25912,11559],{},[1289,25914,1591],{},[1163,25916,3664],{},[1167,25918,25919],{"encoding":1169},"k=20",[1115,25921,25923],{"className":25922},[1144],[1146,25924,25925],{"xmlns":1148},[1150,25926,25927,25935],{},[1153,25928,25929,25931,25933],{},[1159,25930,1287],{},[1289,25932,1591],{},[1163,25934,3159],{},[1167,25936,25937],{"encoding":1169},"n=4","); znak je měřitelný a má normální rozdělení. Sestrojte regulační diagram ",[1115,25940,25942],{"className":25941},[1144],[1146,25943,25944],{"xmlns":1148},[1150,25945,25946,25962],{},[1153,25947,25948,25950,25956,25958,25960],{},[1289,25949,1484],{"stretchy":1483},[2339,25951,25952,25954],{"accent":1121},[1159,25953,11019],{},[1289,25955,15762],{},[1289,25957,1405],{"separator":1121},[1159,25959,14524],{},[1289,25961,1495],{"stretchy":1483},[1167,25963,24954],{"encoding":1169},[1710,25965,25966,26081],{},[1713,25967,25968],{},[1716,25969,25970,25985,26009,26033,26057],{},[1719,25971,25972],{},[1115,25973,25975],{"className":25974},[1144],[1146,25976,25977],{"xmlns":1148},[1150,25978,25979,25983],{},[1153,25980,25981],{},[1159,25982,1487],{},[1167,25984,1487],{"encoding":1169},[1719,25986,25987],{},[1115,25988,25990],{"className":25989},[1144],[1146,25991,25992],{"xmlns":1148},[1150,25993,25994,26006],{},[1153,25995,25996],{},[1156,25997,25998,26000],{},[1159,25999,11019],{},[1153,26001,26002,26004],{},[1159,26003,1487],{},[1163,26005,1402],{},[1167,26007,26008],{"encoding":1169},"x_{i1}",[1719,26010,26011],{},[1115,26012,26014],{"className":26013},[1144],[1146,26015,26016],{"xmlns":1148},[1150,26017,26018,26030],{},[1153,26019,26020],{},[1156,26021,26022,26024],{},[1159,26023,11019],{},[1153,26025,26026,26028],{},[1159,26027,1487],{},[1163,26029,1189],{},[1167,26031,26032],{"encoding":1169},"x_{i2}",[1719,26034,26035],{},[1115,26036,26038],{"className":26037},[1144],[1146,26039,26040],{"xmlns":1148},[1150,26041,26042,26054],{},[1153,26043,26044],{},[1156,26045,26046,26048],{},[1159,26047,11019],{},[1153,26049,26050,26052],{},[1159,26051,1487],{},[1163,26053,3209],{},[1167,26055,26056],{"encoding":1169},"x_{i3}",[1719,26058,26059],{},[1115,26060,26062],{"className":26061},[1144],[1146,26063,26064],{"xmlns":1148},[1150,26065,26066,26078],{},[1153,26067,26068],{},[1156,26069,26070,26072],{},[1159,26071,11019],{},[1153,26073,26074,26076],{},[1159,26075,1487],{},[1163,26077,3159],{},[1167,26079,26080],{"encoding":1169},"x_{i4}",[1828,26082,26083,26097,26112,26128,26143,26155,26169,26181,26194],{},[1716,26084,26085,26087,26090,26093,26095],{},[1833,26086,1402],{},[1833,26088,26089],{},"106",[1833,26091,26092],{},"98",[1833,26094,18388],{},[1833,26096,18388],{},[1716,26098,26099,26101,26104,26107,26110],{},[1833,26100,1189],{},[1833,26102,26103],{},"95",[1833,26105,26106],{},"94",[1833,26108,26109],{},"108",[1833,26111,5743],{},[1716,26113,26114,26116,26119,26122,26125],{},[1833,26115,3209],{},[1833,26117,26118],{},"122",[1833,26120,26121],{},"105",[1833,26123,26124],{},"103",[1833,26126,26127],{},"133",[1716,26129,26130,26132,26135,26137,26140],{},[1833,26131,3159],{},[1833,26133,26134],{},"113",[1833,26136,3181],{},[1833,26138,26139],{},"128",[1833,26141,26142],{},"135",[1716,26144,26145,26147,26149,26151,26153],{},[1833,26146,14227],{},[1833,26148,18388],{},[1833,26150,5743],{},[1833,26152,26124],{},[1833,26154,5743],{},[1716,26156,26157,26159,26161,26163,26166],{},[1833,26158,3583],{},[1833,26160,26092],{},[1833,26162,26124],{},[1833,26164,26165],{},"97",[1833,26167,26168],{},"99",[1716,26170,26171,26173,26175,26177,26179],{},[1833,26172,1408],{},[1833,26174,1408],{},[1833,26176,1408],{},[1833,26178,1408],{},[1833,26180,1408],{},[1716,26182,26183,26185,26187,26189,26192],{},[1833,26184,19022],{},[1833,26186,26139],{},[1833,26188,26127],{},[1833,26190,26191],{},"120",[1833,26193,19050],{},[1716,26195,26196,26198,26200,26202,26204],{},[1833,26197,3664],{},[1833,26199,26092],{},[1833,26201,26124],{},[1833,26203,26165],{},[1833,26205,26168],{},[1110,26207,26208,26209,26230,26231,1567],{},"Pro každou podskupinu se dopočítá výběrový průměr ",[1115,26210,26212],{"className":26211},[1144],[1146,26213,26214],{"xmlns":1148},[1150,26215,26216,26228],{},[1153,26217,26218],{},[1156,26219,26220,26226],{},[2339,26221,26222,26224],{"accent":1121},[1159,26223,11019],{},[1289,26225,15762],{},[1159,26227,1487],{},[1167,26229,25621],{"encoding":1169}," a rozpětí ",[1115,26232,26234],{"className":26233},[1144],[1146,26235,26236],{"xmlns":1148},[1150,26237,26238,26246],{},[1153,26239,26240],{},[1156,26241,26242,26244],{},[1159,26243,14524],{},[1159,26245,1487],{},[1167,26247,25640],{"encoding":1169},[1710,26249,26250,26311],{},[1713,26251,26252],{},[1716,26253,26254,26269,26292],{},[1719,26255,26256],{},[1115,26257,26259],{"className":26258},[1144],[1146,26260,26261],{"xmlns":1148},[1150,26262,26263,26267],{},[1153,26264,26265],{},[1159,26266,1487],{},[1167,26268,1487],{"encoding":1169},[1719,26270,26271],{},[1115,26272,26274],{"className":26273},[1144],[1146,26275,26276],{"xmlns":1148},[1150,26277,26278,26290],{},[1153,26279,26280],{},[1156,26281,26282,26288],{},[2339,26283,26284,26286],{"accent":1121},[1159,26285,11019],{},[1289,26287,15762],{},[1159,26289,1487],{},[1167,26291,25621],{"encoding":1169},[1719,26293,26294],{},[1115,26295,26297],{"className":26296},[1144],[1146,26298,26299],{"xmlns":1148},[1150,26300,26301,26309],{},[1153,26302,26303],{},[1156,26304,26305,26307],{},[1159,26306,14524],{},[1159,26308,1487],{},[1167,26310,25640],{"encoding":1169},[1828,26312,26313,26322,26332,26342,26352,26361,26370,26378,26387],{},[1716,26314,26315,26317,26320],{},[1833,26316,1402],{},[1833,26318,26319],{},"101,50",[1833,26321,19117],{},[1716,26323,26324,26326,26329],{},[1833,26325,1189],{},[1833,26327,26328],{},"97,25",[1833,26330,26331],{},"16",[1716,26333,26334,26336,26339],{},[1833,26335,3209],{},[1833,26337,26338],{},"115,75",[1833,26340,26341],{},"30",[1716,26343,26344,26346,26349],{},[1833,26345,3159],{},[1833,26347,26348],{},"111,75",[1833,26350,26351],{},"64",[1716,26353,26354,26356,26359],{},[1833,26355,14227],{},[1833,26357,26358],{},"97,00",[1833,26360,1870],{},[1716,26362,26363,26365,26368],{},[1833,26364,3583],{},[1833,26366,26367],{},"99,25",[1833,26369,3583],{},[1716,26371,26372,26374,26376],{},[1833,26373,1408],{},[1833,26375,1408],{},[1833,26377,1408],{},[1716,26379,26380,26382,26385],{},[1833,26381,19022],{},[1833,26383,26384],{},"126,50",[1833,26386,3162],{},[1716,26388,26389,26391,26393],{},[1833,26390,3664],{},[1833,26392,26367],{},[1833,26394,3583],{},[1110,26396,26397,26398,26411,26412,2568,26440,2568,26470,26498,26499,26521,26522,2568,26549,2568,26578,26605,26606,1269],{},"Nejprve se posoudí diagram ",[1115,26399,26401],{"className":26400},[1144],[1146,26402,26403],{"xmlns":1148},[1150,26404,26405,26409],{},[1153,26406,26407],{},[1159,26408,14524],{},[1167,26410,14524],{"encoding":1169}," na všech 20 podskupinách: ",[1115,26413,26415],{"className":26414},[1144],[1146,26416,26417],{"xmlns":1148},[1150,26418,26419,26437],{},[1153,26420,26421,26423,26426,26428,26430,26432,26434],{},[1159,26422,25101],{},[1159,26424,26425],{},"L",[1289,26427,1484],{"stretchy":1483},[1159,26429,14524],{},[1289,26431,1495],{"stretchy":1483},[1289,26433,1591],{},[1163,26435,26436],{},"15,8",[1167,26438,26439],{"encoding":1169},"CL(R)=15{,}8",[1115,26441,26443],{"className":26442},[1144],[1146,26444,26445],{"xmlns":1148},[1150,26446,26447,26467],{},[1153,26448,26449,26452,26454,26456,26458,26460,26462,26464],{},[1159,26450,26451],{},"U",[1159,26453,25101],{},[1159,26455,26425],{},[1289,26457,1484],{"stretchy":1483},[1159,26459,14524],{},[1289,26461,1495],{"stretchy":1483},[1289,26463,1591],{},[1163,26465,26466],{},"36,06",[1167,26468,26469],{"encoding":1169},"UCL(R)=36{,}06",[1115,26471,26473],{"className":26472},[1144],[1146,26474,26475],{"xmlns":1148},[1150,26476,26477,26495],{},[1153,26478,26479,26481,26483,26485,26487,26489,26491,26493],{},[1159,26480,26425],{},[1159,26482,25101],{},[1159,26484,26425],{},[1289,26486,1484],{"stretchy":1483},[1159,26488,14524],{},[1289,26490,1495],{"stretchy":1483},[1289,26492,1591],{},[1163,26494,1165],{},[1167,26496,26497],{"encoding":1169},"LCL(R)=0",". Rozpětí čtvrté podskupiny (",[1115,26500,26502],{"className":26501},[1144],[1146,26503,26504],{"xmlns":1148},[1150,26505,26506,26518],{},[1153,26507,26508,26514,26516],{},[1156,26509,26510,26512],{},[1159,26511,14524],{},[1163,26513,3159],{},[1289,26515,1591],{},[1163,26517,26351],{},[1167,26519,26520],{"encoding":1169},"R_4=64",") mez překračuje; po potvrzení vymezitelné příčiny se podskupina 4 z výpočtu vyřadí a meze se přepočítají — ",[1115,26523,26525],{"className":26524},[1144],[1146,26526,26527],{"xmlns":1148},[1150,26528,26529,26546],{},[1153,26530,26531,26533,26535,26537,26539,26541,26543],{},[1159,26532,25101],{},[1159,26534,26425],{},[1289,26536,1484],{"stretchy":1483},[1159,26538,14524],{},[1289,26540,1495],{"stretchy":1483},[1289,26542,1591],{},[1163,26544,26545],{},"13,26",[1167,26547,26548],{"encoding":1169},"CL(R)=13{,}26",[1115,26550,26552],{"className":26551},[1144],[1146,26553,26554],{"xmlns":1148},[1150,26555,26556,26575],{},[1153,26557,26558,26560,26562,26564,26566,26568,26570,26572],{},[1159,26559,26451],{},[1159,26561,25101],{},[1159,26563,26425],{},[1289,26565,1484],{"stretchy":1483},[1159,26567,14524],{},[1289,26569,1495],{"stretchy":1483},[1289,26571,1591],{},[1163,26573,26574],{},"30,27",[1167,26576,26577],{"encoding":1169},"UCL(R)=30{,}27",[1115,26579,26581],{"className":26580},[1144],[1146,26582,26583],{"xmlns":1148},[1150,26584,26585,26603],{},[1153,26586,26587,26589,26591,26593,26595,26597,26599,26601],{},[1159,26588,26425],{},[1159,26590,25101],{},[1159,26592,26425],{},[1289,26594,1484],{"stretchy":1483},[1159,26596,14524],{},[1289,26598,1495],{"stretchy":1483},[1289,26600,1591],{},[1163,26602,1165],{},[1167,26604,26497],{"encoding":1169},". Diagram rozpětí je teď zvládnutý, lze tedy posoudit diagram ",[1115,26607,26609],{"className":26608},[1144],[1146,26610,26611],{"xmlns":1148},[1150,26612,26613,26621],{},[1153,26614,26615],{},[2339,26616,26617,26619],{"accent":1121},[1159,26618,11019],{},[1289,26620,15762],{},[1167,26622,25870],{"encoding":1169},[1110,26624,25571,26625,26642,26643,2568,26674,2568,26707,26740,26741,26754,26755,2568,26782,2568,26811,26838],{},[1115,26626,26628],{"className":26627},[1144],[1146,26629,26630],{"xmlns":1148},[1150,26631,26632,26640],{},[1153,26633,26634],{},[2339,26635,26636,26638],{"accent":1121},[1159,26637,11019],{},[1289,26639,15762],{},[1167,26641,25870],{"encoding":1169}," bez čtvrté podskupiny dává ",[1115,26644,26646],{"className":26645},[1144],[1146,26647,26648],{"xmlns":1148},[1150,26649,26650,26671],{},[1153,26651,26652,26654,26656,26658,26664,26666,26668],{},[1159,26653,25101],{},[1159,26655,26425],{},[1289,26657,1484],{"stretchy":1483},[2339,26659,26660,26662],{"accent":1121},[1159,26661,11019],{},[1289,26663,15762],{},[1289,26665,1495],{"stretchy":1483},[1289,26667,1591],{},[1163,26669,26670],{},"102,01",[1167,26672,26673],{"encoding":1169},"CL(\\bar{x})=102{,}01",[1115,26675,26677],{"className":26676},[1144],[1146,26678,26679],{"xmlns":1148},[1150,26680,26681,26704],{},[1153,26682,26683,26685,26687,26689,26691,26697,26699,26701],{},[1159,26684,26451],{},[1159,26686,25101],{},[1159,26688,26425],{},[1289,26690,1484],{"stretchy":1483},[2339,26692,26693,26695],{"accent":1121},[1159,26694,11019],{},[1289,26696,15762],{},[1289,26698,1495],{"stretchy":1483},[1289,26700,1591],{},[1163,26702,26703],{},"111,68",[1167,26705,26706],{"encoding":1169},"UCL(\\bar{x})=111{,}68",[1115,26708,26710],{"className":26709},[1144],[1146,26711,26712],{"xmlns":1148},[1150,26713,26714,26737],{},[1153,26715,26716,26718,26720,26722,26724,26730,26732,26734],{},[1159,26717,26425],{},[1159,26719,25101],{},[1159,26721,26425],{},[1289,26723,1484],{"stretchy":1483},[2339,26725,26726,26728],{"accent":1121},[1159,26727,11019],{},[1289,26729,15762],{},[1289,26731,1495],{"stretchy":1483},[1289,26733,1591],{},[1163,26735,26736],{},"92,34",[1167,26738,26739],{"encoding":1169},"LCL(\\bar{x})=92{,}34",". Mez teď překračují průměry podskupin 3 a 19. Po potvrzení vymezitelné příčiny se vyřadí obě najednou a meze diagramu ",[1115,26742,26744],{"className":26743},[1144],[1146,26745,26746],{"xmlns":1148},[1150,26747,26748,26752],{},[1153,26749,26750],{},[1159,26751,14524],{},[1167,26753,14524],{"encoding":1169}," se přepočítají bez podskupin 3, 4 a 19: ",[1115,26756,26758],{"className":26757},[1144],[1146,26759,26760],{"xmlns":1148},[1150,26761,26762,26779],{},[1153,26763,26764,26766,26768,26770,26772,26774,26776],{},[1159,26765,25101],{},[1159,26767,26425],{},[1289,26769,1484],{"stretchy":1483},[1159,26771,14524],{},[1289,26773,1495],{"stretchy":1483},[1289,26775,1591],{},[1163,26777,26778],{},"12,29",[1167,26780,26781],{"encoding":1169},"CL(R)=12{,}29",[1115,26783,26785],{"className":26784},[1144],[1146,26786,26787],{"xmlns":1148},[1150,26788,26789,26808],{},[1153,26790,26791,26793,26795,26797,26799,26801,26803,26805],{},[1159,26792,26451],{},[1159,26794,25101],{},[1159,26796,26425],{},[1289,26798,1484],{"stretchy":1483},[1159,26800,14524],{},[1289,26802,1495],{"stretchy":1483},[1289,26804,1591],{},[1163,26806,26807],{},"28,06",[1167,26809,26810],{"encoding":1169},"UCL(R)=28{,}06",[1115,26812,26814],{"className":26813},[1144],[1146,26815,26816],{"xmlns":1148},[1150,26817,26818,26836],{},[1153,26819,26820,26822,26824,26826,26828,26830,26832,26834],{},[1159,26821,26425],{},[1159,26823,25101],{},[1159,26825,26425],{},[1289,26827,1484],{"stretchy":1483},[1159,26829,14524],{},[1289,26831,1495],{"stretchy":1483},[1289,26833,1591],{},[1163,26835,1165],{},[1167,26837,26497],{"encoding":1169}," — žádná z 17 zbývajících podskupin mez nepřekračuje.",[1110,26840,26841,26842,26859,26860,2568,26891,2568,26924,26957],{},"Konečný diagram ",[1115,26843,26845],{"className":26844},[1144],[1146,26846,26847],{"xmlns":1148},[1150,26848,26849,26857],{},[1153,26850,26851],{},[2339,26852,26853,26855],{"accent":1121},[1159,26854,11019],{},[1289,26856,15762],{},[1167,26858,25870],{"encoding":1169}," na stejných 17 podskupinách má ",[1115,26861,26863],{"className":26862},[1144],[1146,26864,26865],{"xmlns":1148},[1150,26866,26867,26888],{},[1153,26868,26869,26871,26873,26875,26881,26883,26885],{},[1159,26870,25101],{},[1159,26872,26425],{},[1289,26874,1484],{"stretchy":1483},[2339,26876,26877,26879],{"accent":1121},[1159,26878,11019],{},[1289,26880,15762],{},[1289,26882,1495],{"stretchy":1483},[1289,26884,1591],{},[1163,26886,26887],{},"99,76",[1167,26889,26890],{"encoding":1169},"CL(\\bar{x})=99{,}76",[1115,26892,26894],{"className":26893},[1144],[1146,26895,26896],{"xmlns":1148},[1150,26897,26898,26921],{},[1153,26899,26900,26902,26904,26906,26908,26914,26916,26918],{},[1159,26901,26451],{},[1159,26903,25101],{},[1159,26905,26425],{},[1289,26907,1484],{"stretchy":1483},[2339,26909,26910,26912],{"accent":1121},[1159,26911,11019],{},[1289,26913,15762],{},[1289,26915,1495],{"stretchy":1483},[1289,26917,1591],{},[1163,26919,26920],{},"108,73",[1167,26922,26923],{"encoding":1169},"UCL(\\bar{x})=108{,}73",[1115,26925,26927],{"className":26926},[1144],[1146,26928,26929],{"xmlns":1148},[1150,26930,26931,26954],{},[1153,26932,26933,26935,26937,26939,26941,26947,26949,26951],{},[1159,26934,26425],{},[1159,26936,25101],{},[1159,26938,26425],{},[1289,26940,1484],{"stretchy":1483},[2339,26942,26943,26945],{"accent":1121},[1159,26944,11019],{},[1289,26946,15762],{},[1289,26948,1495],{"stretchy":1483},[1289,26950,1591],{},[1163,26952,26953],{},"90,80",[1167,26955,26956],{"encoding":1169},"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.",[1110,26959,26960],{},[4002,26961],{"alt":26962,"className":26963,"src":26964},"mask-rd-priklad1-meze",[1321,4006],"\u002Fwiki-assets\u002Fmask-rd-priklad1-meze.png",[1110,26966,26967,26968,26970,26971,26973],{},"V R se diagramy sestrojí funkcí ",[3087,26969,25874],{}," z balíčku ",[3087,26972,360],{},". Data jsou tabulka, v níž řádek odpovídá logické podskupině a sloupce jednotlivým měřením:",[3311,26975,26977],{"className":3313,"code":26976,"language":71,"meta":3315,"style":3315},"library(qcc)\ndata \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"R\")      # diagram R\nqcc(data, type = \"xbar\")   # diagram x̄\n",[3087,26978,26979,26989,27012,27035],{"__ignoreMap":3315},[1115,26980,26981,26983,26985,26987],{"class":3320,"line":10},[1115,26982,21700],{"class":3327},[1115,26984,1484],{"class":3335},[1115,26986,360],{"class":3323},[1115,26988,3520],{"class":3335},[1115,26990,26991,26993,26995,26997,26999,27002,27004,27006,27008,27010],{"class":3320,"line":27},[1115,26992,24411],{"class":3323},[1115,26994,3328],{"class":3327},[1115,26996,24416],{"class":3331},[1115,26998,1484],{"class":3335},[1115,27000,27001],{"class":3459},"\"3_2.txt\"",[1115,27003,1405],{"class":3327},[1115,27005,24426],{"class":3323},[1115,27007,3416],{"class":3327},[1115,27009,3429],{"class":3343},[1115,27011,3520],{"class":3335},[1115,27013,27014,27016,27018,27020,27022,27024,27026,27029,27032],{"class":3320,"line":148},[1115,27015,360],{"class":3331},[1115,27017,1484],{"class":3335},[1115,27019,24411],{"class":3323},[1115,27021,1405],{"class":3327},[1115,27023,16526],{"class":3323},[1115,27025,3416],{"class":3327},[1115,27027,27028],{"class":3459}," \"R\"",[1115,27030,27031],{"class":3335},")      ",[1115,27033,27034],{"class":16336},"# diagram R\n",[1115,27036,27037,27039,27041,27043,27045,27047,27049,27052,27054],{"class":3320,"line":111},[1115,27038,360],{"class":3331},[1115,27040,1484],{"class":3335},[1115,27042,24411],{"class":3323},[1115,27044,1405],{"class":3327},[1115,27046,16526],{"class":3323},[1115,27048,3416],{"class":3327},[1115,27050,27051],{"class":3459}," \"xbar\"",[1115,27053,16333],{"class":3335},[1115,27055,27056],{"class":16336},"# diagram x̄\n",[1110,27058,27059,27060,27063],{},"Funkce vykreslí diagram se střední přímkou a akčními mezemi a body mimo meze zvýrazní. Podskupina s potvrzenou vymezitelnou příčinou se vyřadí z dat (například ",[3087,27061,27062],{},"data[-4, ]",") a diagram se sestrojí znovu.",[21050,27065,25571,27067],{"id":27066},"diagram-xˉsbarx-s",[1115,27068,27070],{"className":27069},[1144],[1146,27071,27072],{"xmlns":1148},[1150,27073,27074,27090],{},[1153,27075,27076,27078,27084,27086,27088],{},[1289,27077,1484],{"stretchy":1483},[2339,27079,27080,27082],{"accent":1121},[1159,27081,11019],{},[1289,27083,15762],{},[1289,27085,1405],{"separator":1121},[1159,27087,1463],{},[1289,27089,1495],{"stretchy":1483},[1167,27091,24980],{"encoding":1169},[1110,27093,25599,27094,27115,27116,27134,27135,27160],{},[1115,27095,27097],{"className":27096},[1144],[1146,27098,27099],{"xmlns":1148},[1150,27100,27101,27113],{},[1153,27102,27103],{},[1156,27104,27105,27111],{},[2339,27106,27107,27109],{"accent":1121},[1159,27108,11019],{},[1289,27110,15762],{},[1159,27112,1487],{},[1167,27114,25621],{"encoding":1169}," a výběrové směrodatné odchylky ",[1115,27117,27119],{"className":27118},[1144],[1146,27120,27121],{"xmlns":1148},[1150,27122,27123,27131],{},[1153,27124,27125],{},[1156,27126,27127,27129],{},[1159,27128,1463],{},[1159,27130,1487],{},[1167,27132,27133],{"encoding":1169},"s_i"," v logických podskupinách. Podmínky použití jsou stejné jako u ",[1115,27136,27138],{"className":27137},[1144],[1146,27139,27140],{"xmlns":1148},[1150,27141,27142,27158],{},[1153,27143,27144,27146,27152,27154,27156],{},[1289,27145,1484],{"stretchy":1483},[2339,27147,27148,27150],{"accent":1121},[1159,27149,11019],{},[1289,27151,15762],{},[1289,27153,1405],{"separator":1121},[1159,27155,14524],{},[1289,27157,1495],{"stretchy":1483},[1167,27159,24954],{"encoding":1169},", logické podskupiny ale sestávají z většího počtu měření. Data se zapisují do obdobné tabulky.",[3311,27162,27164],{"className":3313,"code":27163,"language":71,"meta":3315,"style":3315},"data \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"S\")      # diagram s\nqcc(data, type = \"xbar\")   # diagram x̄\n",[3087,27165,27166,27188,27210],{"__ignoreMap":3315},[1115,27167,27168,27170,27172,27174,27176,27178,27180,27182,27184,27186],{"class":3320,"line":10},[1115,27169,24411],{"class":3323},[1115,27171,3328],{"class":3327},[1115,27173,24416],{"class":3331},[1115,27175,1484],{"class":3335},[1115,27177,27001],{"class":3459},[1115,27179,1405],{"class":3327},[1115,27181,24426],{"class":3323},[1115,27183,3416],{"class":3327},[1115,27185,3429],{"class":3343},[1115,27187,3520],{"class":3335},[1115,27189,27190,27192,27194,27196,27198,27200,27202,27205,27207],{"class":3320,"line":27},[1115,27191,360],{"class":3331},[1115,27193,1484],{"class":3335},[1115,27195,24411],{"class":3323},[1115,27197,1405],{"class":3327},[1115,27199,16526],{"class":3323},[1115,27201,3416],{"class":3327},[1115,27203,27204],{"class":3459}," \"S\"",[1115,27206,27031],{"class":3335},[1115,27208,27209],{"class":16336},"# diagram s\n",[1115,27211,27212,27214,27216,27218,27220,27222,27224,27226,27228],{"class":3320,"line":148},[1115,27213,360],{"class":3331},[1115,27215,1484],{"class":3335},[1115,27217,24411],{"class":3323},[1115,27219,1405],{"class":3327},[1115,27221,16526],{"class":3323},[1115,27223,3416],{"class":3327},[1115,27225,27051],{"class":3459},[1115,27227,16333],{"class":3335},[1115,27229,27056],{"class":16336},[21050,27231,25571,27233],{"id":27232},"diagram-xirklix_i-r_kli",[1115,27234,27236],{"className":27235},[1144],[1146,27237,27238],{"xmlns":1148},[1150,27239,27240,27268],{},[1153,27241,27242,27244,27250,27252,27266],{},[1289,27243,1484],{"stretchy":1483},[1156,27245,27246,27248],{},[1159,27247,11019],{},[1159,27249,1487],{},[1289,27251,1405],{"separator":1121},[1156,27253,27254,27256],{},[1159,27255,14524],{},[1153,27257,27258,27260,27262,27264],{},[1159,27259,11559],{},[1159,27261,25010],{},[1289,27263,1405],{"separator":1121},[1159,27265,1487],{},[1289,27267,1495],{"stretchy":1483},[1167,27269,25019],{"encoding":1169},[1110,27271,27272,27273,27298,27299,1567],{},"Používá se za stejných podmínek jako ",[1115,27274,27276],{"className":27275},[1144],[1146,27277,27278],{"xmlns":1148},[1150,27279,27280,27296],{},[1153,27281,27282,27284,27290,27292,27294],{},[1289,27283,1484],{"stretchy":1483},[2339,27285,27286,27288],{"accent":1121},[1159,27287,11019],{},[1289,27289,15762],{},[1289,27291,1405],{"separator":1121},[1159,27293,14524],{},[1289,27295,1495],{"stretchy":1483},[1167,27297,24954],{"encoding":1169},", 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 ",[1131,27300,27301],{},"klouzavé rozpětí",[1115,27303,27305],{"className":27304},[1144],[1146,27306,27307],{"xmlns":1148,"display":1573},[1150,27308,27309,27436],{},[1153,27310,27311,27325,27327,27330,27336,27338,27350,27352,27354,27356,27358,27360,27362,27364,27366,27368,27370,27372,27374,27376,27378,27392,27394,27406,27420,27434],{},[1156,27312,27313,27315],{},[1159,27314,14524],{},[1153,27316,27317,27319,27321,27323],{},[1159,27318,11559],{},[1159,27320,25010],{},[1289,27322,1405],{"separator":1121},[1159,27324,1487],{},[1289,27326,1591],{},[1159,27328,27329],{"mathvariant":1734},"∣",[1156,27331,27332,27334],{},[1159,27333,11019],{},[1159,27335,1487],{},[1289,27337,2681],{},[1156,27339,27340,27342],{},[1159,27341,11019],{},[1153,27343,27344,27346,27348],{},[1159,27345,1487],{},[1289,27347,2681],{},[1163,27349,1402],{},[1159,27351,27329],{"mathvariant":1734},[1289,27353,1405],{"separator":1121},[1621,27355],{"width":22321},[1159,27357,1487],{},[1289,27359,1591],{},[1163,27361,1189],{},[1289,27363,1405],{"separator":1121},[1163,27365,3209],{},[1289,27367,1405],{"separator":1121},[1289,27369,1408],{},[1289,27371,1405],{"separator":1121},[1159,27373,11559],{},[1289,27375,1405],{"separator":1121},[1621,27377],{"width":1623},[1156,27379,27380,27386],{},[2339,27381,27382,27384],{"accent":1121},[1159,27383,14524],{},[1289,27385,15762],{},[1153,27387,27388,27390],{},[1159,27389,11559],{},[1159,27391,25010],{},[1289,27393,1591],{},[2355,27395,27396,27398],{},[1163,27397,1402],{},[1153,27399,27400,27402,27404],{},[1159,27401,11559],{},[1289,27403,2681],{},[1163,27405,1402],{},[1593,27407,27408,27410,27418],{},[1289,27409,1597],{},[1153,27411,27412,27414,27416],{},[1159,27413,1487],{},[1289,27415,1591],{},[1163,27417,1189],{},[1159,27419,11559],{},[1156,27421,27422,27424],{},[1159,27423,14524],{},[1153,27425,27426,27428,27430,27432],{},[1159,27427,11559],{},[1159,27429,25010],{},[1289,27431,1405],{"separator":1121},[1159,27433,1487],{},[1159,27435,1269],{"mathvariant":1734},[1167,27437,27438],{"encoding":1169},"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}.",[1110,27440,27441,27442,5360,27459,27485,27486,27511,27512,27529],{},"Regulované veličiny jsou hodnoty ",[1115,27443,27445],{"className":27444},[1144],[1146,27446,27447],{"xmlns":1148},[1150,27448,27449,27457],{},[1153,27450,27451],{},[1156,27452,27453,27455],{},[1159,27454,11019],{},[1159,27456,1487],{},[1167,27458,21437],{"encoding":1169},[1115,27460,27462],{"className":27461},[1144],[1146,27463,27464],{"xmlns":1148},[1150,27465,27466,27482],{},[1153,27467,27468],{},[1156,27469,27470,27472],{},[1159,27471,14524],{},[1153,27473,27474,27476,27478,27480],{},[1159,27475,11559],{},[1159,27477,25010],{},[1289,27479,1405],{"separator":1121},[1159,27481,1487],{},[1167,27483,27484],{"encoding":1169},"R_{kl,i}","; nejdříve se určí střední přímka a meze diagramu ",[1115,27487,27489],{"className":27488},[1144],[1146,27490,27491],{"xmlns":1148},[1150,27492,27493,27509],{},[1153,27494,27495],{},[1156,27496,27497,27499],{},[1159,27498,14524],{},[1153,27500,27501,27503,27505,27507],{},[1159,27502,11559],{},[1159,27504,25010],{},[1289,27506,1405],{"separator":1121},[1159,27508,1487],{},[1167,27510,27484],{"encoding":1169},", potom diagramu ",[1115,27513,27515],{"className":27514},[1144],[1146,27516,27517],{"xmlns":1148},[1150,27518,27519,27527],{},[1153,27520,27521],{},[1156,27522,27523,27525],{},[1159,27524,11019],{},[1159,27526,1487],{},[1167,27528,21437],{"encoding":1169},". Data jsou jeden vektor naměřených hodnot:",[3311,27531,27533],{"className":3313,"code":27532,"language":71,"meta":3315,"style":3315},"data \u003C- read.table(\"3_3.txt\", header = TRUE)\nqcc(data[, 1], type = \"xbar.one\")\n",[3087,27534,27535,27558],{"__ignoreMap":3315},[1115,27536,27537,27539,27541,27543,27545,27548,27550,27552,27554,27556],{"class":3320,"line":10},[1115,27538,24411],{"class":3323},[1115,27540,3328],{"class":3327},[1115,27542,24416],{"class":3331},[1115,27544,1484],{"class":3335},[1115,27546,27547],{"class":3459},"\"3_3.txt\"",[1115,27549,1405],{"class":3327},[1115,27551,24426],{"class":3323},[1115,27553,3416],{"class":3327},[1115,27555,3429],{"class":3343},[1115,27557,3520],{"class":3335},[1115,27559,27560,27562,27564,27566,27568,27570,27572,27574,27576,27578,27580,27583],{"class":3320,"line":27},[1115,27561,360],{"class":3331},[1115,27563,1484],{"class":3335},[1115,27565,24411],{"class":3323},[1115,27567,12476],{"class":3335},[1115,27569,1405],{"class":3327},[1115,27571,4260],{"class":3343},[1115,27573,12493],{"class":3335},[1115,27575,1405],{"class":3327},[1115,27577,16526],{"class":3323},[1115,27579,3416],{"class":3327},[1115,27581,27582],{"class":3459}," \"xbar.one\"",[1115,27584,3520],{"class":3335},[1310,27586,27588],{"id":27587},"regulace-srovnáváním","Regulace srovnáváním",[1110,27590,27591],{},"Diagramy pro regulaci srovnáváním se používají, sledují-li se počty neshodných produktů nebo počty neshod na produktech — regulovaná veličina je diskrétní náhodná veličina.",[1710,27593,27594,27607],{},[1713,27595,27596],{},[1716,27597,27598,27601,27604],{},[1719,27599,27600],{},"Sleduje se",[1719,27602,27603],{},"Konstantní rozsah podskupin",[1719,27605,27606],{},"Nekonstantní rozsah podskupin",[1828,27608,27609,27644],{},[1716,27610,27611,27614,27629],{},[1833,27612,27613],{},"počet neshod na produktech (např. vady na stejných tabulích skla)",[1833,27615,27616],{},[1115,27617,27619],{"className":27618},[1144],[1146,27620,27621],{"xmlns":1148},[1150,27622,27623,27627],{},[1153,27624,27625],{},[1159,27626,3338],{},[1167,27628,3338],{"encoding":1169},[1833,27630,27631],{},[1115,27632,27634],{"className":27633},[1144],[1146,27635,27636],{"xmlns":1148},[1150,27637,27638,27642],{},[1153,27639,27640],{},[1159,27641,15831],{},[1167,27643,15831],{"encoding":1169},[1716,27645,27646,27649,27666],{},[1833,27647,27648],{},"počet neshodných produktů ve výběru (např. neshodné kusy ze série na výrobní lince)",[1833,27650,27651],{},[1115,27652,27654],{"className":27653},[1144],[1146,27655,27656],{"xmlns":1148},[1150,27657,27658,27664],{},[1153,27659,27660,27662],{},[1159,27661,1287],{},[1159,27663,1110],{},[1167,27665,25066],{"encoding":1169},[1833,27667,27668],{},[1115,27669,27671],{"className":27670},[1144],[1146,27672,27673],{"xmlns":1148},[1150,27674,27675,27679],{},[1153,27676,27677],{},[1159,27678,1110],{},[1167,27680,1110],{"encoding":1169},[21050,27682,25571,27684],{"id":27683},"diagram-cc",[1115,27685,27687],{"className":27686},[1144],[1146,27688,27689],{"xmlns":1148},[1150,27690,27691,27695],{},[1153,27692,27693],{},[1159,27694,3338],{},[1167,27696,3338],{"encoding":1169},[1110,27698,27699,27700,27718,27719,27732,27733,27758,27759,27772],{},"Regulovanou veličinou ",[1115,27701,27703],{"className":27702},[1144],[1146,27704,27705],{"xmlns":1148},[1150,27706,27707,27715],{},[1153,27708,27709],{},[1156,27710,27711,27713],{},[1159,27712,3338],{},[1159,27714,1487],{},[1167,27716,27717],{"encoding":1169},"c_i"," je počet neshod na produktech v ",[1115,27720,27722],{"className":27721},[1144],[1146,27723,27724],{"xmlns":1148},[1150,27725,27726,27730],{},[1153,27727,27728],{},[1159,27729,1487],{},[1167,27731,1487],{"encoding":1169},"-té logické podskupině, ",[1115,27734,27736],{"className":27735},[1144],[1146,27737,27738],{"xmlns":1148},[1150,27739,27740,27756],{},[1153,27741,27742,27744,27746,27748,27750,27752,27754],{},[1159,27743,1487],{},[1289,27745,1591],{},[1163,27747,1402],{},[1289,27749,1405],{"separator":1121},[1289,27751,1408],{},[1289,27753,1405],{"separator":1121},[1159,27755,11559],{},[1167,27757,25784],{"encoding":1169},"; v každé podskupině je stejný počet ",[1115,27760,27762],{"className":27761},[1144],[1146,27763,27764],{"xmlns":1148},[1150,27765,27766,27770],{},[1153,27767,27768],{},[1159,27769,1287],{},[1167,27771,1287],{"encoding":1169}," 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.",[1103,27774,27776,27783],{"className":27775,"dataCallout":3094},[1106,3093],[1110,27777,27779,27782],{"className":27778},[1113],[1115,27780],{"className":27781,"ariaHidden":1121},[1118,3101,1120],"Příklad: bodové vady na pásech látky",[1110,27784,27785,27786,27803,27804,1269],{},"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 ",[1115,27787,27789],{"className":27788},[1144],[1146,27790,27791],{"xmlns":1148},[1150,27792,27793,27801],{},[1153,27794,27795],{},[1156,27796,27797,27799],{},[1159,27798,3338],{},[1159,27800,1487],{},[1167,27802,27717],{"encoding":1169},". Sestrojte regulační diagram ",[1115,27805,27807],{"className":27806},[1144],[1146,27808,27809],{"xmlns":1148},[1150,27810,27811,27815],{},[1153,27812,27813],{},[1159,27814,3338],{},[1167,27816,3338],{"encoding":1169},[3311,27818,27820],{"className":3313,"code":27819,"language":71,"meta":3315,"style":3315},"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",[3087,27821,27822,27912,27916,27941],{"__ignoreMap":3315},[1115,27823,27824,27826,27828,27830,27832,27834,27836,27838,27840,27842,27844,27846,27848,27850,27852,27854,27856,27858,27860,27862,27864,27866,27868,27870,27872,27874,27876,27878,27880,27882,27884,27886,27888,27890,27892,27894,27896,27898,27900,27902,27904,27906,27908,27910],{"class":3320,"line":10},[1115,27825,27717],{"class":3323},[1115,27827,3328],{"class":3327},[1115,27829,3454],{"class":3331},[1115,27831,1484],{"class":3335},[1115,27833,17633],{"class":3343},[1115,27835,1405],{"class":3327},[1115,27837,4260],{"class":3343},[1115,27839,1405],{"class":3327},[1115,27841,3799],{"class":3343},[1115,27843,1405],{"class":3327},[1115,27845,14295],{"class":3343},[1115,27847,1405],{"class":3327},[1115,27849,14271],{"class":3343},[1115,27851,1405],{"class":3327},[1115,27853,16531],{"class":3343},[1115,27855,1405],{"class":3327},[1115,27857,3799],{"class":3343},[1115,27859,1405],{"class":3327},[1115,27861,14271],{"class":3343},[1115,27863,1405],{"class":3327},[1115,27865,3419],{"class":3343},[1115,27867,1405],{"class":3327},[1115,27869,3419],{"class":3343},[1115,27871,1405],{"class":3327},[1115,27873,16531],{"class":3343},[1115,27875,1405],{"class":3327},[1115,27877,15156],{"class":3343},[1115,27879,1405],{"class":3327},[1115,27881,15156],{"class":3343},[1115,27883,1405],{"class":3327},[1115,27885,15156],{"class":3343},[1115,27887,1405],{"class":3327},[1115,27889,4260],{"class":3343},[1115,27891,1405],{"class":3327},[1115,27893,16531],{"class":3343},[1115,27895,1405],{"class":3327},[1115,27897,15156],{"class":3343},[1115,27899,1405],{"class":3327},[1115,27901,4260],{"class":3343},[1115,27903,1405],{"class":3327},[1115,27905,14295],{"class":3343},[1115,27907,1405],{"class":3327},[1115,27909,16531],{"class":3343},[1115,27911,3520],{"class":3335},[1115,27913,27914],{"class":3320,"line":27},[1115,27915,14342],{"emptyLinePlaceholder":6298},[1115,27917,27918,27921,27923,27926,27928,27930,27932,27934,27936,27939],{"class":3320,"line":148},[1115,27919,27920],{"class":3323},"q_c",[1115,27922,3328],{"class":3327},[1115,27924,27925],{"class":3331}," qcc",[1115,27927,1484],{"class":3335},[1115,27929,27717],{"class":3323},[1115,27931,1405],{"class":3327},[1115,27933,16526],{"class":3323},[1115,27935,3416],{"class":3327},[1115,27937,27938],{"class":3459}," \"c\"",[1115,27940,3520],{"class":3335},[1115,27942,27943,27945,27947,27949],{"class":3320,"line":111},[1115,27944,21171],{"class":3331},[1115,27946,1484],{"class":3335},[1115,27948,27920],{"class":3323},[1115,27950,3520],{"class":3335},[3311,27952,27955],{"className":27953,"code":27954,"language":3542,"meta":3315},[3540],"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",[3087,27956,27954],{"__ignoreMap":3315},[1110,27958,27959,27960,27989,27990,28013,28014,28036],{},"Průměrný počet vad na pás je ",[1115,27961,27963],{"className":27962},[1144],[1146,27964,27965],{"xmlns":1148},[1150,27966,27967,27986],{},[1153,27968,27969,27971,27973,27975,27981,27983],{},[1159,27970,25101],{},[1159,27972,26425],{},[1289,27974,1591],{},[2339,27976,27977,27979],{"accent":1121},[1159,27978,3338],{},[1289,27980,15762],{},[1289,27982,1591],{},[1163,27984,27985],{},"3,4",[1167,27987,27988],{"encoding":1169},"CL = \\bar{c} = 3{,}4",", horní mez ",[1115,27991,27993],{"className":27992},[1144],[1146,27994,27995],{"xmlns":1148},[1150,27996,27997,28010],{},[1153,27998,27999,28001,28003,28005,28007],{},[1159,28000,26451],{},[1159,28002,25101],{},[1159,28004,26425],{},[1289,28006,1591],{},[1163,28008,28009],{},"8,93",[1167,28011,28012],{"encoding":1169},"UCL = 8{,}93"," a dolní mez ",[1115,28015,28017],{"className":28016},[1144],[1146,28018,28019],{"xmlns":1148},[1150,28020,28021,28033],{},[1153,28022,28023,28025,28027,28029,28031],{},[1159,28024,26425],{},[1159,28026,25101],{},[1159,28028,26425],{},[1289,28030,1591],{},[1163,28032,1165],{},[1167,28034,28035],{"encoding":1169},"LCL = 0",". Žádný pás meze nepřekračuje — proces je zvládnutý.",[1110,28038,28039],{},[4002,28040],{"alt":28041,"className":28042,"src":28043},"mask-rd-priklad2-c",[1321,4006],"\u002Fwiki-assets\u002Fmask-rd-priklad2-c.png",[21050,28045,25571,28047],{"id":28046},"diagram-uu",[1115,28048,28050],{"className":28049},[1144],[1146,28051,28052],{"xmlns":1148},[1150,28053,28054,28058],{},[1153,28055,28056],{},[1159,28057,15831],{},[1167,28059,15831],{"encoding":1169},[1110,28061,27699,28062,28096,28097,28115],{},[1115,28063,28065],{"className":28064},[1144],[1146,28066,28067],{"xmlns":1148},[1150,28068,28069,28093],{},[1153,28070,28071,28077,28079,28085,28087],{},[1156,28072,28073,28075],{},[1159,28074,15831],{},[1159,28076,1487],{},[1289,28078,1591],{},[1156,28080,28081,28083],{},[1159,28082,3338],{},[1159,28084,1487],{},[1159,28086,4223],{"mathvariant":1734},[1156,28088,28089,28091],{},[1159,28090,1287],{},[1159,28092,1487],{},[1167,28094,28095],{"encoding":1169},"u_i = c_i\u002Fn_i"," je průměrný počet neshod přepočítaný na jeden produkt z logické podskupiny; rozsah podskupin ",[1115,28098,28100],{"className":28099},[1144],[1146,28101,28102],{"xmlns":1148},[1150,28103,28104,28112],{},[1153,28105,28106],{},[1156,28107,28108,28110],{},[1159,28109,1287],{},[1159,28111,1487],{},[1167,28113,28114],{"encoding":1169},"n_i"," není konstantní, a proto se bod od bodu mění i meze.",[1110,28117,28118,28119,28122],{},"Za ",[3087,28120,28121],{},"sizes"," se dosadí vektor rozsahů jednotlivých logických podskupin, resp. rozměr jejich jednotek:",[3311,28124,28126],{"className":3313,"code":28125,"language":71,"meta":3315,"style":3315},"data \u003C- read.table(\"3_4.txt\", header = TRUE)   # počty suků a rozměry prken\nqcc(data[, 1], type = \"u\", sizes = data[, 2])\n",[3087,28127,28128,28154],{"__ignoreMap":3315},[1115,28129,28130,28132,28134,28136,28138,28141,28143,28145,28147,28149,28151],{"class":3320,"line":10},[1115,28131,24411],{"class":3323},[1115,28133,3328],{"class":3327},[1115,28135,24416],{"class":3331},[1115,28137,1484],{"class":3335},[1115,28139,28140],{"class":3459},"\"3_4.txt\"",[1115,28142,1405],{"class":3327},[1115,28144,24426],{"class":3323},[1115,28146,3416],{"class":3327},[1115,28148,3429],{"class":3343},[1115,28150,16333],{"class":3335},[1115,28152,28153],{"class":16336},"# počty suků a rozměry prken\n",[1115,28155,28156,28158,28160,28162,28164,28166,28168,28170,28172,28174,28176,28179,28181,28184,28186,28188,28190,28192,28194],{"class":3320,"line":27},[1115,28157,360],{"class":3331},[1115,28159,1484],{"class":3335},[1115,28161,24411],{"class":3323},[1115,28163,12476],{"class":3335},[1115,28165,1405],{"class":3327},[1115,28167,4260],{"class":3343},[1115,28169,12493],{"class":3335},[1115,28171,1405],{"class":3327},[1115,28173,16526],{"class":3323},[1115,28175,3416],{"class":3327},[1115,28177,28178],{"class":3459}," \"u\"",[1115,28180,1405],{"class":3327},[1115,28182,28183],{"class":3323}," sizes",[1115,28185,3416],{"class":3327},[1115,28187,24470],{"class":3323},[1115,28189,12476],{"class":3335},[1115,28191,1405],{"class":3327},[1115,28193,3799],{"class":3343},[1115,28195,28196],{"class":3335},"])\n",[21050,28198,25571,28200],{"id":28199},"diagram-npnp",[1115,28201,28203],{"className":28202},[1144],[1146,28204,28205],{"xmlns":1148},[1150,28206,28207,28213],{},[1153,28208,28209,28211],{},[1159,28210,1287],{},[1159,28212,1110],{},[1167,28214,25066],{"encoding":1169},[1110,28216,28217,28218,11080,28233,28246],{},"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 ",[1115,28219,28221],{"className":28220},[1144],[1146,28222,28223],{"xmlns":1148},[1150,28224,28225,28231],{},[1153,28226,28227,28229],{},[1159,28228,1287],{},[1159,28230,1110],{},[1167,28232,25066],{"encoding":1169},[1115,28234,28236],{"className":28235},[1144],[1146,28237,28238],{"xmlns":1148},[1150,28239,28240,28244],{},[1153,28241,28242],{},[1159,28243,1110],{},[1167,28245,1110],{"encoding":1169}," je pravděpodobnost, že vyrobený produkt je neshodný.",[1110,28248,28249,28250,1567],{},"Pro konstantní rozsah ",[1115,28251,28253],{"className":28252},[1144],[1146,28254,28255],{"xmlns":1148},[1150,28256,28257,28261],{},[1153,28258,28259],{},[1159,28260,1287],{},[1167,28262,1287],{"encoding":1169},[3311,28264,28266],{"className":3313,"code":28265,"language":71,"meta":3315,"style":3315},"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",[3087,28267,28268,28294],{"__ignoreMap":3315},[1115,28269,28270,28272,28274,28276,28278,28281,28283,28285,28287,28289,28291],{"class":3320,"line":10},[1115,28271,24411],{"class":3323},[1115,28273,3328],{"class":3327},[1115,28275,24416],{"class":3331},[1115,28277,1484],{"class":3335},[1115,28279,28280],{"class":3459},"\"3_7.txt\"",[1115,28282,1405],{"class":3327},[1115,28284,24426],{"class":3323},[1115,28286,3416],{"class":3327},[1115,28288,3429],{"class":3343},[1115,28290,16333],{"class":3335},[1115,28292,28293],{"class":16336},"# počty vadných tabletů v sériích po 100 kusech\n",[1115,28295,28296,28298,28300,28302,28304,28306,28308,28310,28312,28314,28316,28319,28321,28323,28325,28327],{"class":3320,"line":27},[1115,28297,360],{"class":3331},[1115,28299,1484],{"class":3335},[1115,28301,24411],{"class":3323},[1115,28303,12476],{"class":3335},[1115,28305,1405],{"class":3327},[1115,28307,4260],{"class":3343},[1115,28309,12493],{"class":3335},[1115,28311,1405],{"class":3327},[1115,28313,16526],{"class":3323},[1115,28315,3416],{"class":3327},[1115,28317,28318],{"class":3459}," \"np\"",[1115,28320,1405],{"class":3327},[1115,28322,28183],{"class":3323},[1115,28324,3416],{"class":3327},[1115,28326,19642],{"class":3343},[1115,28328,3520],{"class":3335},[21050,28330,25571,28332],{"id":28331},"diagram-pp",[1115,28333,28335],{"className":28334},[1144],[1146,28336,28337],{"xmlns":1148},[1150,28338,28339,28343],{},[1153,28340,28341],{},[1159,28342,1110],{},[1167,28344,1110],{"encoding":1169},[1110,28346,28347,28348,28384],{},"Regulovanou veličinou je počet neshodných produktů v logické podskupině přepočtený na jednotku, ",[1115,28349,28351],{"className":28350},[1144],[1146,28352,28353],{"xmlns":1148},[1150,28354,28355,28381],{},[1153,28356,28357,28363,28365,28367,28373,28375],{},[1156,28358,28359,28361],{},[1159,28360,1110],{},[1159,28362,1487],{},[1289,28364,1591],{},[1159,28366,1287],{},[1156,28368,28369,28371],{},[1159,28370,1110],{},[1159,28372,1487],{},[1159,28374,4223],{"mathvariant":1734},[1156,28376,28377,28379],{},[1159,28378,1287],{},[1159,28380,1487],{},[1167,28382,28383],{"encoding":1169},"p_i = np_i\u002Fn_i","; rozsahy podskupin nemusí být konstantní.",[1110,28386,28118,28387,28389],{},[3087,28388,28121],{}," se dosadí vektor rozsahů logických podskupin:",[3311,28391,28393],{"className":3313,"code":28392,"language":71,"meta":3315,"style":3315},"data \u003C- read.table(\"3_6.txt\", header = TRUE)   # počty vadných tabletů a rozsahy sérií\nqcc(data[, 1], type = \"p\", sizes = data[, 2])\n",[3087,28394,28395,28421],{"__ignoreMap":3315},[1115,28396,28397,28399,28401,28403,28405,28408,28410,28412,28414,28416,28418],{"class":3320,"line":10},[1115,28398,24411],{"class":3323},[1115,28400,3328],{"class":3327},[1115,28402,24416],{"class":3331},[1115,28404,1484],{"class":3335},[1115,28406,28407],{"class":3459},"\"3_6.txt\"",[1115,28409,1405],{"class":3327},[1115,28411,24426],{"class":3323},[1115,28413,3416],{"class":3327},[1115,28415,3429],{"class":3343},[1115,28417,16333],{"class":3335},[1115,28419,28420],{"class":16336},"# počty vadných tabletů a rozsahy sérií\n",[1115,28422,28423,28425,28427,28429,28431,28433,28435,28437,28439,28441,28443,28446,28448,28450,28452,28454,28456,28458,28460],{"class":3320,"line":27},[1115,28424,360],{"class":3331},[1115,28426,1484],{"class":3335},[1115,28428,24411],{"class":3323},[1115,28430,12476],{"class":3335},[1115,28432,1405],{"class":3327},[1115,28434,4260],{"class":3343},[1115,28436,12493],{"class":3335},[1115,28438,1405],{"class":3327},[1115,28440,16526],{"class":3323},[1115,28442,3416],{"class":3327},[1115,28444,28445],{"class":3459}," \"p\"",[1115,28447,1405],{"class":3327},[1115,28449,28183],{"class":3323},[1115,28451,3416],{"class":3327},[1115,28453,24470],{"class":3323},[1115,28455,12476],{"class":3335},[1115,28457,1405],{"class":3327},[1115,28459,3799],{"class":3343},[1115,28461,28196],{"class":3335},[1310,28463,28465],{"id":28464},"indexy-způsobilosti","Indexy způsobilosti",[1110,28467,28468,28469,28488,28489,28507],{},"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 ",[1115,28470,28472],{"className":28471},[1144],[1146,28473,28474],{"xmlns":1148},[1150,28475,28476,28485],{},[1153,28477,28478,28480,28483],{},[1159,28479,26425],{},[1159,28481,28482],{},"S",[1159,28484,26425],{},[1167,28486,28487],{"encoding":1169},"LSL"," a horní meze ",[1115,28490,28492],{"className":28491},[1144],[1146,28493,28494],{"xmlns":1148},[1150,28495,28496,28504],{},[1153,28497,28498,28500,28502],{},[1159,28499,26451],{},[1159,28501,28482],{},[1159,28503,26425],{},[1167,28505,28506],{"encoding":1169},"USL",". Způsobilost se zkoumá až pro proces, který je podle regulačních diagramů statisticky zvládnutý (třetí fáze regulace).",[21050,28509,28511,28528],{"id":28510},"cpc_p-index-způsobilosti",[1115,28512,28514],{"className":28513},[1144],[1146,28515,28516],{"xmlns":1148},[1150,28517,28518,28526],{},[1153,28519,28520],{},[1156,28521,28522,28524],{},[1159,28523,25101],{},[1159,28525,1110],{},[1167,28527,25106],{"encoding":1169}," — index způsobilosti",[1110,28530,28531,28532,1567],{},"Podíl mezi délkou tolerančního intervalu a délkou intervalu, ve kterém by za normálního rozdělení mělo ležet skoro všech 99,73 % hodnot znaku, tedy ",[1115,28533,28535],{"className":28534},[1144],[1146,28536,28537],{"xmlns":1148},[1150,28538,28539,28545],{},[1153,28540,28541,28543],{},[1163,28542,3583],{},[1159,28544,11198],{},[1167,28546,28547],{"encoding":1169},"6\\sigma",[1115,28549,28551],{"className":28550},[1144],[1146,28552,28553],{"xmlns":1148,"display":1573},[1150,28554,28555,28591],{},[1153,28556,28557,28563,28565,28589],{},[1156,28558,28559,28561],{},[1159,28560,25101],{},[1159,28562,1110],{},[1289,28564,1591],{},[2355,28566,28567,28583],{},[1153,28568,28569,28571,28573,28575,28577,28579,28581],{},[1159,28570,26451],{},[1159,28572,28482],{},[1159,28574,26425],{},[1289,28576,2681],{},[1159,28578,26425],{},[1159,28580,28482],{},[1159,28582,26425],{},[1153,28584,28585,28587],{},[1163,28586,3583],{},[1159,28588,11198],{},[1159,28590,1269],{"mathvariant":1734},[1167,28592,28593],{"encoding":1169},"C_p = \\frac{USL - LSL}{6\\sigma}.",[1110,28595,28596,28613,28614,28627,28628,1269],{},[1115,28597,28599],{"className":28598},[1144],[1146,28600,28601],{"xmlns":1148},[1150,28602,28603,28611],{},[1153,28604,28605],{},[1156,28606,28607,28609],{},[1159,28608,25101],{},[1159,28610,1110],{},[1167,28612,25106],{"encoding":1169}," srovnává jen délky, nevšímá si, kde uprostřed tolerance proces leží — centrovaný i silně vychýlený proces se stejným ",[1115,28615,28617],{"className":28616},[1144],[1146,28618,28619],{"xmlns":1148},[1150,28620,28621,28625],{},[1153,28622,28623],{},[1159,28624,11198],{},[1167,28626,11230],{"encoding":1169}," mají stejné ",[1115,28629,28631],{"className":28630},[1144],[1146,28632,28633],{"xmlns":1148},[1150,28634,28635,28643],{},[1153,28636,28637],{},[1156,28638,28639,28641],{},[1159,28640,25101],{},[1159,28642,1110],{},[1167,28644,25106],{"encoding":1169},[1110,28646,28647],{},"Doplňkové charakteristiky využití tolerančního intervalu:",[1124,28649,28650,28684,28772],{},[1127,28651,28652,3607,28655,28683],{},[1131,28653,28654],{},"míra využití tolerančního intervalu",[1115,28656,28658],{"className":28657},[1144],[1146,28659,28660],{"xmlns":1148},[1150,28661,28662,28680],{},[1153,28663,28664,28676,28678],{},[2858,28665,28666],{"scriptlevel":1165,"displaystyle":1121},[2355,28667,28668,28670],{},[1163,28669,16121],{},[1156,28671,28672,28674],{},[1159,28673,25101],{},[1159,28675,1110],{},[2525,28677,2527],{},[1159,28679,16128],{"mathvariant":1734},[1167,28681,28682],{"encoding":1169},"\\dfrac{100}{C_p}\\,\\%"," — na kolik procent je toleranční interval využíván sledovaným znakem,",[1127,28685,28686,28689,28690,28707,28708,5360,28740,1405],{},[1131,28687,28688],{},"robustnost procesu",": rezerva, kterou máme v tolerančních mezích, než index ",[1115,28691,28693],{"className":28692},[1144],[1146,28694,28695],{"xmlns":1148},[1150,28696,28697,28705],{},[1153,28698,28699],{},[1156,28700,28701,28703],{},[1159,28702,25101],{},[1159,28704,1110],{},[1167,28706,25106],{"encoding":1169}," nabyde hodnotu 1 — rovná se menší hodnotě z výrazů ",[1115,28709,28711],{"className":28710},[1144],[1146,28712,28713],{"xmlns":1148},[1150,28714,28715,28737],{},[1153,28716,28717,28719,28721,28723,28725,28727,28729,28731,28733,28735],{},[1159,28718,26451],{},[1159,28720,28482],{},[1159,28722,26425],{},[1289,28724,2681],{},[1289,28726,1484],{"stretchy":1483},[1159,28728,11190],{},[1289,28730,5096],{},[1163,28732,3209],{},[1159,28734,11198],{},[1289,28736,1495],{"stretchy":1483},[1167,28738,28739],{"encoding":1169},"USL-(\\mu+3\\sigma)",[1115,28741,28743],{"className":28742},[1144],[1146,28744,28745],{"xmlns":1148},[1150,28746,28747,28769],{},[1153,28748,28749,28751,28753,28755,28757,28759,28761,28763,28765,28767],{},[1289,28750,1484],{"stretchy":1483},[1159,28752,11190],{},[1289,28754,2681],{},[1163,28756,3209],{},[1159,28758,11198],{},[1289,28760,1495],{"stretchy":1483},[1289,28762,2681],{},[1159,28764,26425],{},[1159,28766,28482],{},[1159,28768,26425],{},[1167,28770,28771],{"encoding":1169},"(\\mu-3\\sigma)-LSL",[1127,28773,28774,3607,28777,11080,28817,28831],{},[1131,28775,28776],{},"podíl zmetků",[1115,28778,28780],{"className":28779},[1144],[1146,28781,28782],{"xmlns":1148},[1150,28783,28784,28814],{},[1153,28785,28786,28793,28795,28797,28800,28802,28804,28806,28812],{},[1156,28787,28788,28790],{},[1159,28789,11026],{},[1159,28791,28792],{},"z",[1289,28794,1591],{},[1163,28796,1189],{},[1159,28798,28799],{"mathvariant":1734},"Φ",[1289,28801,1484],{"stretchy":1483},[1289,28803,2681],{},[1163,28805,3209],{},[1156,28807,28808,28810],{},[1159,28809,25101],{},[1159,28811,1110],{},[1289,28813,1495],{"stretchy":1483},[1167,28815,28816],{"encoding":1169},"P_z = 2\\Phi(-3C_p)",[1115,28818,28820],{"className":28819},[1144],[1146,28821,28822],{"xmlns":1148},[1150,28823,28824,28828],{},[1153,28825,28826],{},[1159,28827,28799],{"mathvariant":1734},[1167,28829,28830],{"encoding":1169},"\\Phi"," je distribuční funkce normovaného normálního rozdělení.",[21050,28833,28835,28856],{"id":28834},"cpkc_pk-index-způsobilosti-s-ohledem-na-vychýlení",[1115,28836,28838],{"className":28837},[1144],[1146,28839,28840],{"xmlns":1148},[1150,28841,28842,28854],{},[1153,28843,28844],{},[1156,28845,28846,28848],{},[1159,28847,25101],{},[1153,28849,28850,28852],{},[1159,28851,1110],{},[1159,28853,11559],{},[1167,28855,25128],{"encoding":1169}," — index způsobilosti s ohledem na vychýlení",[1110,28858,28859],{},"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:",[1115,28861,28863],{"className":28862},[1144],[1146,28864,28865],{"xmlns":1148,"display":1573},[1150,28866,28867,28937],{},[1153,28868,28869,28879,28881,28883,28885,28935],{},[1156,28870,28871,28873],{},[1159,28872,25101],{},[1153,28874,28875,28877],{},[1159,28876,1110],{},[1159,28878,11559],{},[1289,28880,1591],{},[1159,28882,4107],{},[1289,28884,4110],{},[1153,28886,28887,28889,28909,28911,28913,28933],{},[1289,28888,1484],{"fence":1121},[2355,28890,28891,28903],{},[1153,28892,28893,28895,28897,28899,28901],{},[1159,28894,26451],{},[1159,28896,28482],{},[1159,28898,26425],{},[1289,28900,2681],{},[1159,28902,11190],{},[1153,28904,28905,28907],{},[1163,28906,3209],{},[1159,28908,11198],{},[1289,28910,1405],{"separator":1121},[2525,28912,15617],{},[2355,28914,28915,28927],{},[1153,28916,28917,28919,28921,28923,28925],{},[1159,28918,11190],{},[1289,28920,2681],{},[1159,28922,26425],{},[1159,28924,28482],{},[1159,28926,26425],{},[1153,28928,28929,28931],{},[1163,28930,3209],{},[1159,28932,11198],{},[1289,28934,1495],{"fence":1121},[1159,28936,1269],{"mathvariant":1734},[1167,28938,28939],{"encoding":1169},"C_{pk} = \\min\\left(\\frac{USL-\\mu}{3\\sigma},\\ \\frac{\\mu-LSL}{3\\sigma}\\right).",[1110,28941,28942,28943,28956,28957,28987,28988,29009,29010,1269],{},"Vyjde-li některý z obou podílů záporný, položí se roven nule; to nastane, když střední hodnota ",[1115,28944,28946],{"className":28945},[1144],[1146,28947,28948],{"xmlns":1148},[1150,28949,28950,28954],{},[1153,28951,28952],{},[1159,28953,11190],{},[1167,28955,13097],{"encoding":1169}," leží mimo toleranční interval, a proces pak není pod statistickou kontrolou. U centrovaného procesu jsou oba podíly stejné a ",[1115,28958,28960],{"className":28959},[1144],[1146,28961,28962],{"xmlns":1148},[1150,28963,28964,28984],{},[1153,28965,28966,28976,28978],{},[1156,28967,28968,28970],{},[1159,28969,25101],{},[1153,28971,28972,28974],{},[1159,28973,1110],{},[1159,28975,11559],{},[1289,28977,1591],{},[1156,28979,28980,28982],{},[1159,28981,25101],{},[1159,28983,1110],{},[1167,28985,28986],{"encoding":1169},"C_{pk} = C_p","; čím víc je proces vychýlený, tím víc je ",[1115,28989,28991],{"className":28990},[1144],[1146,28992,28993],{"xmlns":1148},[1150,28994,28995,29007],{},[1153,28996,28997],{},[1156,28998,28999,29001],{},[1159,29000,25101],{},[1153,29002,29003,29005],{},[1159,29004,1110],{},[1159,29006,11559],{},[1167,29008,25128],{"encoding":1169}," menší než ",[1115,29011,29013],{"className":29012},[1144],[1146,29014,29015],{"xmlns":1148},[1150,29016,29017,29025],{},[1153,29018,29019],{},[1156,29020,29021,29023],{},[1159,29022,25101],{},[1159,29024,1110],{},[1167,29026,25106],{"encoding":1169},[21050,29028,29030,5360,29051,29074],{"id":29029},"cpmc_pm-a-cpmkc_pmk-indexy-vztažené-k-cíli",[1115,29031,29033],{"className":29032},[1144],[1146,29034,29035],{"xmlns":1148},[1150,29036,29037,29049],{},[1153,29038,29039],{},[1156,29040,29041,29043],{},[1159,29042,25101],{},[1153,29044,29045,29047],{},[1159,29046,1110],{},[1159,29048,4090],{},[1167,29050,25150],{"encoding":1169},[1115,29052,29054],{"className":29053},[1144],[1146,29055,29056],{"xmlns":1148},[1150,29057,29058,29072],{},[1153,29059,29060],{},[1156,29061,29062,29064],{},[1159,29063,25101],{},[1153,29065,29066,29068,29070],{},[1159,29067,1110],{},[1159,29069,4090],{},[1159,29071,11559],{},[1167,29073,25174],{"encoding":1169}," — indexy vztažené k cíli",[1110,29076,29077,29078,29091,29092,29105,29106,29149,29150,1567],{},"Pokud má proces zadaný cílový střed ",[1115,29079,29081],{"className":29080},[1144],[1146,29082,29083],{"xmlns":1148},[1150,29084,29085,29089],{},[1153,29086,29087],{},[1159,29088,11401],{},[1167,29090,11401],{"encoding":1169}," (ne nutně střed tolerance), nahradí se ",[1115,29093,29095],{"className":29094},[1144],[1146,29096,29097],{"xmlns":1148},[1150,29098,29099,29103],{},[1153,29100,29101],{},[1159,29102,11198],{},[1167,29104,11230],{"encoding":1169}," odmocninou ze střední čtvercové odchylky od cíle ",[1115,29107,29109],{"className":29108},[1144],[1146,29110,29111],{"xmlns":1148},[1150,29112,29113,29146],{},[1153,29114,29115,29118,29120],{},[1159,29116,29117],{},"τ",[1289,29119,1591],{},[4072,29121,29122],{},[1153,29123,29124,29130,29132,29134,29136,29138,29140],{},[1182,29125,29126,29128],{},[1159,29127,11198],{},[1163,29129,1189],{},[1289,29131,5096],{},[1289,29133,1484],{"stretchy":1483},[1159,29135,11190],{},[1289,29137,2681],{},[1159,29139,11401],{},[1182,29141,29142,29144],{},[1289,29143,1495],{"stretchy":1483},[1163,29145,1189],{},[1167,29147,29148],{"encoding":1169},"\\tau = \\sqrt{\\sigma^2+(\\mu-T)^2}",", která trestá i vychýlení od ",[1115,29151,29153],{"className":29152},[1144],[1146,29154,29155],{"xmlns":1148},[1150,29156,29157,29161],{},[1153,29158,29159],{},[1159,29160,11401],{},[1167,29162,11401],{"encoding":1169},[1115,29164,29166],{"className":29165},[1144],[1146,29167,29168],{"xmlns":1148,"display":1573},[1150,29169,29170,29282],{},[1153,29171,29172,29182,29184,29208,29210,29212,29224,29226,29228,29230,29280],{},[1156,29173,29174,29176],{},[1159,29175,25101],{},[1153,29177,29178,29180],{},[1159,29179,1110],{},[1159,29181,4090],{},[1289,29183,1591],{},[2355,29185,29186,29202],{},[1153,29187,29188,29190,29192,29194,29196,29198,29200],{},[1159,29189,26451],{},[1159,29191,28482],{},[1159,29193,26425],{},[1289,29195,2681],{},[1159,29197,26425],{},[1159,29199,28482],{},[1159,29201,26425],{},[1153,29203,29204,29206],{},[1163,29205,3583],{},[1159,29207,29117],{},[1289,29209,1405],{"separator":1121},[1621,29211],{"width":1623},[1156,29213,29214,29216],{},[1159,29215,25101],{},[1153,29217,29218,29220,29222],{},[1159,29219,1110],{},[1159,29221,4090],{},[1159,29223,11559],{},[1289,29225,1591],{},[1159,29227,4107],{},[1289,29229,4110],{},[1153,29231,29232,29234,29254,29256,29258,29278],{},[1289,29233,1484],{"fence":1121},[2355,29235,29236,29248],{},[1153,29237,29238,29240,29242,29244,29246],{},[1159,29239,26451],{},[1159,29241,28482],{},[1159,29243,26425],{},[1289,29245,2681],{},[1159,29247,11190],{},[1153,29249,29250,29252],{},[1163,29251,3209],{},[1159,29253,29117],{},[1289,29255,1405],{"separator":1121},[2525,29257,15617],{},[2355,29259,29260,29272],{},[1153,29261,29262,29264,29266,29268,29270],{},[1159,29263,11190],{},[1289,29265,2681],{},[1159,29267,26425],{},[1159,29269,28482],{},[1159,29271,26425],{},[1153,29273,29274,29276],{},[1163,29275,3209],{},[1159,29277,29117],{},[1289,29279,1495],{"fence":1121},[1159,29281,1269],{"mathvariant":1734},[1167,29283,29284],{"encoding":1169},"C_{pm} = \\frac{USL-LSL}{6\\tau}, \\qquad C_{pmk} = \\min\\left(\\frac{USL-\\mu}{3\\tau},\\ \\frac{\\mu-LSL}{3\\tau}\\right).",[21050,29286,29288],{"id":29287},"interpretace","Interpretace",[1710,29290,29291,29318],{},[1713,29292,29293],{},[1716,29294,29295,29315],{},[1719,29296,29297,29298],{},"Hodnota ",[1115,29299,29301],{"className":29300},[1144],[1146,29302,29303],{"xmlns":1148},[1150,29304,29305,29313],{},[1153,29306,29307],{},[1156,29308,29309,29311],{},[1159,29310,25101],{},[1159,29312,1110],{},[1167,29314,25106],{"encoding":1169},[1719,29316,29317],{},"Způsobilost procesu",[1828,29319,29320,29349,29392],{},[1716,29321,29322,29346],{},[1833,29323,29324],{},[1115,29325,29327],{"className":29326},[1144],[1146,29328,29329],{"xmlns":1148},[1150,29330,29331,29343],{},[1153,29332,29333,29339,29341],{},[1156,29334,29335,29337],{},[1159,29336,25101],{},[1159,29338,1110],{},[1289,29340,3951],{},[1163,29342,1402],{},[1167,29344,29345],{"encoding":1169},"C_p \u003C 1",[1833,29347,29348],{},"dosahovaná přesnost je menší než předepsaná — proces je nezpůsobilý",[1716,29350,29351,29375],{},[1833,29352,29353],{},[1115,29354,29356],{"className":29355},[1144],[1146,29357,29358],{"xmlns":1148},[1150,29359,29360,29372],{},[1153,29361,29362,29368,29370],{},[1156,29363,29364,29366],{},[1159,29365,25101],{},[1159,29367,1110],{},[1289,29369,1591],{},[1163,29371,1402],{},[1167,29373,29374],{"encoding":1169},"C_p = 1",[1833,29376,29377,29378,29391],{},"dosahovaná přesnost je rovna předepsané — proces je způsobilý, ale sebemenší zvětšení ",[1115,29379,29381],{"className":29380},[1144],[1146,29382,29383],{"xmlns":1148},[1150,29384,29385,29389],{},[1153,29386,29387],{},[1159,29388,11198],{},[1167,29390,11230],{"encoding":1169}," jej posune na nezpůsobilý",[1716,29393,29394,29418],{},[1833,29395,29396],{},[1115,29397,29399],{"className":29398},[1144],[1146,29400,29401],{"xmlns":1148},[1150,29402,29403,29415],{},[1153,29404,29405,29411,29413],{},[1156,29406,29407,29409],{},[1159,29408,25101],{},[1159,29410,1110],{},[1289,29412,1291],{},[1163,29414,1402],{},[1167,29416,29417],{"encoding":1169},"C_p > 1",[1833,29419,29420],{},"dosahovaná přesnost je větší než předepsaná — proces je způsobilý",[1110,29422,29423,29424,29445,29446,1269],{},"U indexu ",[1115,29425,29427],{"className":29426},[1144],[1146,29428,29429],{"xmlns":1148},[1150,29430,29431,29443],{},[1153,29432,29433],{},[1156,29434,29435,29437],{},[1159,29436,25101],{},[1153,29438,29439,29441],{},[1159,29440,1110],{},[1159,29442,11559],{},[1167,29444,25128],{"encoding":1169}," se v praxi požaduje víc než jen hodnota nad 1: s rozvojem technologií roste nárok na rezervu, a běžně se dnes vyžaduje hodnota alespoň ",[1115,29447,29449],{"className":29448},[1144],[1146,29450,29451],{"xmlns":1148},[1150,29452,29453,29458],{},[1153,29454,29455],{},[1163,29456,29457],{},"1,5",[1167,29459,29460],{"encoding":1169},"1{,}5",[1110,29462,29463],{},[4002,29464],{"alt":29465,"className":29466,"src":29467},"mask-rd-cp-panely",[1321,4006],"\u002Fwiki-assets\u002Fmask-rd-cp-panely.png",[1110,29469,29470],{},[4002,29471],{"alt":29472,"className":29473,"src":29474},"mask-rd-cpk-off-centre",[1321,4006],"\u002Fwiki-assets\u002Fmask-rd-cpk-off-centre.png",[21050,29476,29478],{"id":29477},"výpočet-v-r","Výpočet v R",[1110,29480,29481,29482,29485,29486,29489,29490,29493,29494,5360,29511,2568,29528,29531,29532,29545],{},"Indexy způsobilosti počítá ",[3087,29483,29484],{},"process.capability()"," z výstupu regulačního diagramu ",[3087,29487,29488],{},"q","; ",[3087,29491,29492],{},"spec.limits"," jsou toleranční meze ",[1115,29495,29497],{"className":29496},[1144],[1146,29498,29499],{"xmlns":1148},[1150,29500,29501,29509],{},[1153,29502,29503,29505,29507],{},[1159,29504,26425],{},[1159,29506,28482],{},[1159,29508,26425],{},[1167,29510,28487],{"encoding":1169},[1115,29512,29514],{"className":29513},[1144],[1146,29515,29516],{"xmlns":1148},[1150,29517,29518,29526],{},[1153,29519,29520,29522,29524],{},[1159,29521,26451],{},[1159,29523,28482],{},[1159,29525,26425],{},[1167,29527,28506],{"encoding":1169},[3087,29529,29530],{},"target"," cílová hodnota ",[1115,29533,29535],{"className":29534},[1144],[1146,29536,29537],{"xmlns":1148},[1150,29538,29539,29543],{},[1153,29540,29541],{},[1159,29542,11401],{},[1167,29544,11401],{"encoding":1169},". Pro velikost výrobku v mm s tolerančními mezemi 100 a 110 mm a cílovou hodnotou 105 mm:",[3311,29547,29549],{"className":3313,"code":29548,"language":71,"meta":3315,"style":3315},"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",[3087,29550,29551,29561,29584,29599,29621],{"__ignoreMap":3315},[1115,29552,29553,29555,29557,29559],{"class":3320,"line":10},[1115,29554,21700],{"class":3327},[1115,29556,1484],{"class":3335},[1115,29558,360],{"class":3323},[1115,29560,3520],{"class":3335},[1115,29562,29563,29565,29567,29569,29571,29574,29576,29578,29580,29582],{"class":3320,"line":27},[1115,29564,24411],{"class":3323},[1115,29566,3328],{"class":3327},[1115,29568,24416],{"class":3331},[1115,29570,1484],{"class":3335},[1115,29572,29573],{"class":3459},"\"3_8.txt\"",[1115,29575,1405],{"class":3327},[1115,29577,24426],{"class":3323},[1115,29579,3416],{"class":3327},[1115,29581,3429],{"class":3343},[1115,29583,3520],{"class":3335},[1115,29585,29586,29588,29590,29593,29595,29597],{"class":3320,"line":148},[1115,29587,11019],{"class":3323},[1115,29589,3328],{"class":3327},[1115,29591,29592],{"class":3331}," as.matrix",[1115,29594,1484],{"class":3335},[1115,29596,24411],{"class":3323},[1115,29598,3520],{"class":3335},[1115,29600,29601,29603,29605,29607,29609,29611,29613,29615,29617,29619],{"class":3320,"line":111},[1115,29602,29488],{"class":3323},[1115,29604,3328],{"class":3327},[1115,29606,27925],{"class":3331},[1115,29608,1484],{"class":3335},[1115,29610,11019],{"class":3323},[1115,29612,1405],{"class":3327},[1115,29614,16526],{"class":3323},[1115,29616,3416],{"class":3327},[1115,29618,27051],{"class":3459},[1115,29620,3520],{"class":3335},[1115,29622,29623,29626,29628,29630,29632,29635,29637,29639,29641,29643,29645,29647,29649,29651,29654,29656,29659,29661,29664,29666,29668,29670,29672],{"class":3320,"line":96},[1115,29624,29625],{"class":3331},"process.capability",[1115,29627,1484],{"class":3335},[1115,29629,29488],{"class":3323},[1115,29631,1405],{"class":3327},[1115,29633,29634],{"class":3323}," spec.limits",[1115,29636,3416],{"class":3327},[1115,29638,3454],{"class":3331},[1115,29640,1484],{"class":3335},[1115,29642,16121],{"class":3343},[1115,29644,1405],{"class":3327},[1115,29646,18571],{"class":3343},[1115,29648,1495],{"class":3335},[1115,29650,1405],{"class":3327},[1115,29652,29653],{"class":3323}," target",[1115,29655,3416],{"class":3327},[1115,29657,29658],{"class":3343}," 105",[1115,29660,1405],{"class":3327},[1115,29662,29663],{"class":3323}," std.dev",[1115,29665,3416],{"class":3327},[1115,29667,13542],{"class":3331},[1115,29669,1484],{"class":3335},[1115,29671,11019],{"class":3323},[1115,29673,13794],{"class":3335},[1110,29675,29676,29677,2568,29680,2568,29683,2568,29686,5360,29689,29692,29693,5360,29695,29697,29698,29719,29720,29743],{},"Výpis obsahuje řádky ",[3087,29678,29679],{},"Cp",[3087,29681,29682],{},"Cp_l",[3087,29684,29685],{},"Cp_u",[3087,29687,29688],{},"Cp_k",[3087,29690,29691],{},"Cpm"," s hodnotou indexu a 95% intervalem spolehlivosti. ",[3087,29694,29682],{},[3087,29696,29685],{}," jsou dílčí poměry k dolní a horní mezi, jejich minimum je ",[1115,29699,29701],{"className":29700},[1144],[1146,29702,29703],{"xmlns":1148},[1150,29704,29705,29717],{},[1153,29706,29707],{},[1156,29708,29709,29711],{},[1159,29710,25101],{},[1153,29712,29713,29715],{},[1159,29714,1110],{},[1159,29716,11559],{},[1167,29718,25128],{"encoding":1169},". Index ",[1115,29721,29723],{"className":29722},[1144],[1146,29724,29725],{"xmlns":1148},[1150,29726,29727,29741],{},[1153,29728,29729],{},[1156,29730,29731,29733],{},[1159,29732,25101],{},[1153,29734,29735,29737,29739],{},[1159,29736,1110],{},[1159,29738,4090],{},[1159,29740,11559],{},[1167,29742,25174],{"encoding":1169}," a doplňkové charakteristiky se dopočítají ze vzorců výše:",[3311,29745,29747],{"className":3313,"code":29746,"language":71,"meta":3315,"style":3315},"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",[3087,29748,29749,29776,29801,29838,29868,29926,29940,29991],{"__ignoreMap":3315},[1115,29750,29751,29754,29756,29758,29760,29762,29764,29766,29768,29770,29772,29774],{"class":3320,"line":10},[1115,29752,29753],{"class":3323},"mu",[1115,29755,3328],{"class":3327},[1115,29757,13532],{"class":3331},[1115,29759,1484],{"class":3335},[1115,29761,11019],{"class":3323},[1115,29763,16480],{"class":3335},[1115,29765,380],{"class":3323},[1115,29767,3328],{"class":3327},[1115,29769,13542],{"class":3331},[1115,29771,1484],{"class":3335},[1115,29773,11019],{"class":3323},[1115,29775,3520],{"class":3335},[1115,29777,29778,29780,29782,29784,29786,29788,29790,29792,29794,29796,29798],{"class":3320,"line":27},[1115,29779,28487],{"class":3323},[1115,29781,3328],{"class":3327},[1115,29783,19642],{"class":3343},[1115,29785,29489],{"class":3335},[1115,29787,28506],{"class":3323},[1115,29789,3328],{"class":3327},[1115,29791,18571],{"class":3343},[1115,29793,29489],{"class":3335},[1115,29795,11401],{"class":3323},[1115,29797,3328],{"class":3327},[1115,29799,29800],{"class":3343}," 105\n",[1115,29802,29803,29806,29808,29810,29812,29814,29816,29818,29820,29822,29824,29827,29830,29832,29834,29836],{"class":3320,"line":148},[1115,29804,29805],{"class":3323},"tau",[1115,29807,3328],{"class":3327},[1115,29809,4197],{"class":3331},[1115,29811,1484],{"class":3335},[1115,29813,380],{"class":3323},[1115,29815,2345],{"class":3327},[1115,29817,1189],{"class":3343},[1115,29819,22819],{"class":3327},[1115,29821,4226],{"class":3335},[1115,29823,29753],{"class":3323},[1115,29825,29826],{"class":3327}," -",[1115,29828,29829],{"class":3323}," T",[1115,29831,1495],{"class":3335},[1115,29833,2345],{"class":3327},[1115,29835,1189],{"class":3343},[1115,29837,3520],{"class":3335},[1115,29839,29840,29842,29844,29846,29848,29850,29853,29855,29857,29859,29861,29863,29866],{"class":3320,"line":111},[1115,29841,29679],{"class":3323},[1115,29843,3328],{"class":3327},[1115,29845,4226],{"class":3335},[1115,29847,28506],{"class":3323},[1115,29849,29826],{"class":3327},[1115,29851,29852],{"class":3323}," LSL",[1115,29854,4220],{"class":3335},[1115,29856,4223],{"class":3327},[1115,29858,4226],{"class":3335},[1115,29860,3583],{"class":3343},[1115,29862,22944],{"class":3327},[1115,29864,29865],{"class":3323}," sigma",[1115,29867,3520],{"class":3335},[1115,29869,29870,29873,29875,29877,29880,29882,29884,29887,29889,29891,29893,29895,29897,29900,29902,29904,29906,29908,29910,29912,29914,29916,29918,29920,29922,29924],{"class":3320,"line":96},[1115,29871,29872],{"class":3323},"Cpmk",[1115,29874,3328],{"class":3327},[1115,29876,16501],{"class":3331},[1115,29878,29879],{"class":3335},"((",[1115,29881,28506],{"class":3323},[1115,29883,29826],{"class":3327},[1115,29885,29886],{"class":3323}," mu",[1115,29888,4220],{"class":3335},[1115,29890,4223],{"class":3327},[1115,29892,4226],{"class":3335},[1115,29894,3209],{"class":3343},[1115,29896,22944],{"class":3327},[1115,29898,29899],{"class":3323}," tau",[1115,29901,1495],{"class":3335},[1115,29903,1405],{"class":3327},[1115,29905,4226],{"class":3335},[1115,29907,29753],{"class":3323},[1115,29909,29826],{"class":3327},[1115,29911,29852],{"class":3323},[1115,29913,4220],{"class":3335},[1115,29915,4223],{"class":3327},[1115,29917,4226],{"class":3335},[1115,29919,3209],{"class":3343},[1115,29921,22944],{"class":3327},[1115,29923,29899],{"class":3323},[1115,29925,13794],{"class":3335},[1115,29927,29928,29931,29933,29935,29937],{"class":3320,"line":89},[1115,29929,29930],{"class":3323},"miravyuziti",[1115,29932,3328],{"class":3327},[1115,29934,19642],{"class":3343},[1115,29936,14376],{"class":3327},[1115,29938,29939],{"class":3323}," Cp\n",[1115,29941,29942,29945,29947,29949,29951,29953,29955,29957,29959,29961,29963,29965,29967,29969,29971,29973,29975,29977,29979,29981,29983,29985,29987,29989],{"class":3320,"line":82},[1115,29943,29944],{"class":3323},"robustnost",[1115,29946,3328],{"class":3327},[1115,29948,16501],{"class":3331},[1115,29950,1484],{"class":3335},[1115,29952,28506],{"class":3323},[1115,29954,29826],{"class":3327},[1115,29956,4226],{"class":3335},[1115,29958,29753],{"class":3323},[1115,29960,22819],{"class":3327},[1115,29962,15156],{"class":3343},[1115,29964,22944],{"class":3327},[1115,29966,29865],{"class":3323},[1115,29968,1495],{"class":3335},[1115,29970,1405],{"class":3327},[1115,29972,4226],{"class":3335},[1115,29974,29753],{"class":3323},[1115,29976,29826],{"class":3327},[1115,29978,15156],{"class":3343},[1115,29980,22944],{"class":3327},[1115,29982,29865],{"class":3323},[1115,29984,4220],{"class":3335},[1115,29986,4257],{"class":3327},[1115,29988,29852],{"class":3323},[1115,29990,3520],{"class":3335},[1115,29992,29993,29996,29998,30000,30002,30004,30006,30008,30010,30012,30015],{"class":3320,"line":75},[1115,29994,29995],{"class":3323},"Pz",[1115,29997,3328],{"class":3327},[1115,29999,3799],{"class":3343},[1115,30001,22944],{"class":3327},[1115,30003,13652],{"class":3331},[1115,30005,1484],{"class":3335},[1115,30007,4257],{"class":3327},[1115,30009,3209],{"class":3343},[1115,30011,22944],{"class":3327},[1115,30013,30014],{"class":3323}," Cp",[1115,30016,3520],{"class":3335},[1310,30018,6027],{"id":6026},[1124,30020,30021,30024,30084,30175,30241],{},[1127,30022,30023],{},"Počítat indexy způsobilosti pro proces, který není statisticky zvládnutý — způsobilost se zkoumá až ve třetí fázi regulace.",[1127,30025,30026,30027,30044,30045,30062,30063,1269],{},"Posuzovat jen ",[1115,30028,30030],{"className":30029},[1144],[1146,30031,30032],{"xmlns":1148},[1150,30033,30034,30042],{},[1153,30035,30036],{},[1156,30037,30038,30040],{},[1159,30039,25101],{},[1159,30041,1110],{},[1167,30043,25106],{"encoding":1169}," u vychýleného procesu — ",[1115,30046,30048],{"className":30047},[1144],[1146,30049,30050],{"xmlns":1148},[1150,30051,30052,30060],{},[1153,30053,30054],{},[1156,30055,30056,30058],{},[1159,30057,25101],{},[1159,30059,1110],{},[1167,30061,25106],{"encoding":1169}," polohu střední hodnoty nezohledňuje, vychýlení zachytí až ",[1115,30064,30066],{"className":30065},[1144],[1146,30067,30068],{"xmlns":1148},[1150,30069,30070,30082],{},[1153,30071,30072],{},[1156,30073,30074,30076],{},[1159,30075,25101],{},[1153,30077,30078,30080],{},[1159,30079,1110],{},[1159,30081,11559],{},[1167,30083,25128],{"encoding":1169},[1127,30085,30086,30087,30100,30101,30114,30115,30100,30130,30143,30144,30157,30158,30171,30172,30174],{},"Zaměnit diagram ",[1115,30088,30090],{"className":30089},[1144],[1146,30091,30092],{"xmlns":1148},[1150,30093,30094,30098],{},[1153,30095,30096],{},[1159,30097,3338],{},[1167,30099,3338],{"encoding":1169}," s diagramem ",[1115,30102,30104],{"className":30103},[1144],[1146,30105,30106],{"xmlns":1148},[1150,30107,30108,30112],{},[1153,30109,30110],{},[1159,30111,15831],{},[1167,30113,15831],{"encoding":1169}," nebo diagram ",[1115,30116,30118],{"className":30117},[1144],[1146,30119,30120],{"xmlns":1148},[1150,30121,30122,30128],{},[1153,30123,30124,30126],{},[1159,30125,1287],{},[1159,30127,1110],{},[1167,30129,25066],{"encoding":1169},[1115,30131,30133],{"className":30132},[1144],[1146,30134,30135],{"xmlns":1148},[1150,30136,30137,30141],{},[1153,30138,30139],{},[1159,30140,1110],{},[1167,30142,1110],{"encoding":1169}," — při nekonstantním rozsahu podskupin se volí ",[1115,30145,30147],{"className":30146},[1144],[1146,30148,30149],{"xmlns":1148},[1150,30150,30151,30155],{},[1153,30152,30153],{},[1159,30154,15831],{},[1167,30156,15831],{"encoding":1169},", resp. ",[1115,30159,30161],{"className":30160},[1144],[1146,30162,30163],{"xmlns":1148},[1150,30164,30165,30169],{},[1153,30166,30167],{},[1159,30168,1110],{},[1167,30170,1110],{"encoding":1169},", a do ",[3087,30173,28121],{}," se zadává vektor rozsahů.",[1127,30176,30177,30178,30195,30196,30209,30210,30223,30224,1269],{},"Posuzovat diagram ",[1115,30179,30181],{"className":30180},[1144],[1146,30182,30183],{"xmlns":1148},[1150,30184,30185,30193],{},[1153,30186,30187],{},[2339,30188,30189,30191],{"accent":1121},[1159,30190,11019],{},[1289,30192,15762],{},[1167,30194,25870],{"encoding":1169}," dřív než diagram rozpětí — nejprve se určí a stabilizuje diagram ",[1115,30197,30199],{"className":30198},[1144],[1146,30200,30201],{"xmlns":1148},[1150,30202,30203,30207],{},[1153,30204,30205],{},[1159,30206,14524],{},[1167,30208,14524],{"encoding":1169}," (resp. ",[1115,30211,30213],{"className":30212},[1144],[1146,30214,30215],{"xmlns":1148},[1150,30216,30217,30221],{},[1153,30218,30219],{},[1159,30220,1463],{},[1167,30222,1463],{"encoding":1169},"), potom diagram ",[1115,30225,30227],{"className":30226},[1144],[1146,30228,30229],{"xmlns":1148},[1150,30230,30231,30239],{},[1153,30232,30233],{},[2339,30234,30235,30237],{"accent":1121},[1159,30236,11019],{},[1289,30238,15762],{},[1167,30240,25870],{"encoding":1169},[1127,30242,30243],{},"Vyřadit podskupinu jen podle polohy bodu — vyřazuje se až po zjištění a odstranění vymezitelné příčiny.",[1310,30245,6215],{"id":6214},[1124,30247,30248,30253,30258,30264,30269,30274,30279],{},[1127,30249,30250],{},[1318,30251,1324],{"className":30252,"dataFsResolvedFilePath":1322,"href":1323},[1321],[1127,30254,30255],{},[1318,30256,886],{"className":30257,"dataFsResolvedFilePath":6234,"href":6235},[1321],[1127,30259,30260],{},[1318,30261,30263],{"className":30262,"dataFsResolvedFilePath":6242,"href":6243},[1321],"nahodne-veliciny-a-rozdeleni",[1127,30265,30266],{},[1318,30267,141],{"className":30268,"dataFsResolvedFilePath":1329,"href":1330},[1321],[1127,30270,30271],{},[1318,30272,15386],{"className":30273,"dataFsResolvedFilePath":6250,"href":6251},[1321],[1127,30275,30276],{},[1318,30277,716],{"className":30278,"dataFsResolvedFilePath":15392,"href":15393},[1321],[1127,30280,30281],{},[1318,30282,6268],{"className":30283,"dataFsResolvedFilePath":6266,"href":6267},[1321],[1310,30285,6271],{"id":934},[1110,30287,6274,30288,6279],{},[6276,30289,6278],{},[1110,30291,30292,30293,30296],{},"MONTGOMERY, D. C. ",[6276,30294,30295],{},"Introduction to Statistical Quality Control",". 6. vyd. John Wiley & Sons, 2005.",[1110,30298,30299,30300,30303],{},"ČSN ISO 8258. ",[6276,30301,30302],{},"Shewhartovy regulační diagramy",". Praha: Český normalizační institut, 1994.",[1110,30305,30306,30307,30310],{},"KUPKA, K. ",[6276,30308,30309],{},"Statistické řízení jakosti",". Pardubice: TriloByte, 1997.",[6281,30312,30313],{},"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":28464,"depth":27,"text":28465,"children":30337},[30338,30340,30342,30344,30345],{"id":28510,"depth":148,"text":30339},"CpC_p — index způsobilosti",{"id":28834,"depth":148,"text":30341},"CpkC_{pk} — index způsobilosti s ohledem na vychýlení",{"id":29029,"depth":148,"text":30343},"CpmC_{pm} a CpmkC_{pmk} — indexy vztažené k cíli",{"id":29287,"depth":148,"text":29288},{"id":29477,"depth":148,"text":29478},{"id":6026,"depth":27,"text":6027},{"id":6214,"depth":27,"text":6215},{"id":934,"depth":27,"text":6271},{},"\u002Ftopics\u002Fregulacni-diagramy-a-indexy-zpusobilosti",{"title":6260,"description":3315},[30353,30354,30355,30356],"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":30361,"title":6228,"body":30362,"course":23,"courses":6294,"created":6295,"description":3315,"extension":6296,"meta":40173,"navigation":6298,"path":40174,"seo":40175,"sources":40176,"stem":40182,"tags":40183,"type":6306,"updated":6295,"__hash__":40184},"topics\u002Ftopics\u002Ftestovani-hypotez.md",{"type":1096,"value":30363,"toc":40146},[30364,30367,30566,30610,30614,30624,30627,30693,30743,30896,30900,30903,30997,31147,31166,31173,31262,31266,31301,31338,31376,31411,31415,31422,31640,31759,31763,31895,31949,31971,32313,32320,32408,32414,32455,32740,32749,32864,32870,32877,32882,32888,32982,32988,33014,33020,33112,33118,33168,33172,33368,33428,33790,34129,34228,34234,34462,34466,34732,34736,34739,34805,34852,35308,35312,35315,35502,35535,35757,36076,36115,36122,36779,36918,36924,37080,37086,37093,37146,37152,37325,37331,37395,37400,37585,37591,37636,37640,37643,37647,37694,37922,37938,38027,38033,38059,38063,38066,38138,38231,38300,38306,38329,38776,38783,38787,38817,38821,39071,39090,39151,39160,39316,39322,39348,39523,39527,39548,39579,39583,39607,39637,39641,39701,39759,39763,39770,39943,39945,40098,40100,40137,40139,40143],[1099,30365,6228],{"id":30366},"testování-statistických-hypotéz",[1103,30368,30370,30376],{"className":30369,"dataCallout":1108},[1106,1107],[1110,30371,30373,1122],{"className":30372},[1113],[1115,30374],{"className":30375,"ariaHidden":1121},[1118,1119,1120],[1124,30377,30378,30448,30530,30533,30536],{},[1127,30379,30380,30381,30398,30399,30416,30417,2568,30430,30447],{},"Test porovnává tvrzení ",[1115,30382,30384],{"className":30383},[1144],[1146,30385,30386],{"xmlns":1148},[1150,30387,30388,30396],{},[1153,30389,30390],{},[1156,30391,30392,30394],{},[1159,30393,1161],{},[1163,30395,1165],{},[1167,30397,1170],{"encoding":1169}," s alternativou ",[1115,30400,30402],{"className":30401},[1144],[1146,30403,30404],{"xmlns":1148},[1150,30405,30406,30414],{},[1153,30407,30408],{},[1156,30409,30410,30412],{},[1159,30411,1161],{},[1163,30413,1402],{},[1167,30415,2613],{"encoding":1169}," pomocí testového kritéria spočteného z výběru; padne-li kritérium do kritického oboru ",[1115,30418,30420],{"className":30419},[1144],[1146,30421,30422],{"xmlns":1148},[1150,30423,30424,30428],{},[1153,30425,30426],{},[1159,30427,1205],{},[1167,30429,1205],{"encoding":1169},[1115,30431,30433],{"className":30432},[1144],[1146,30434,30435],{"xmlns":1148},[1150,30436,30437,30445],{},[1153,30438,30439],{},[1156,30440,30441,30443],{},[1159,30442,1161],{},[1163,30444,1165],{},[1167,30446,1170],{"encoding":1169}," zamítáme.",[1127,30449,30450,30451,30464,30465,30482,30483,30497,30498,30515,30516,30529],{},"Rozhodnutí nese dva typy chyb: chybu I. druhu (",[1115,30452,30454],{"className":30453},[1144],[1146,30455,30456],{"xmlns":1148},[1150,30457,30458,30462],{},[1153,30459,30460],{},[1159,30461,2982],{},[1167,30463,3045],{"encoding":1169},", zamítnutí platné ",[1115,30466,30468],{"className":30467},[1144],[1146,30469,30470],{"xmlns":1148},[1150,30471,30472,30480],{},[1153,30473,30474],{},[1156,30475,30476,30478],{},[1159,30477,1161],{},[1163,30479,1165],{},[1167,30481,1170],{"encoding":1169},") a chybu II. druhu (",[1115,30484,30486],{"className":30485},[1144],[1146,30487,30488],{"xmlns":1148},[1150,30489,30490,30494],{},[1153,30491,30492],{},[1159,30493,20641],{},[1167,30495,30496],{"encoding":1169},"\\beta",", přijetí neplatné ",[1115,30499,30501],{"className":30500},[1144],[1146,30502,30503],{"xmlns":1148},[1150,30504,30505,30513],{},[1153,30506,30507],{},[1156,30508,30509,30511],{},[1159,30510,1161],{},[1163,30512,1165],{},[1167,30514,1170],{"encoding":1169},"). Hladina významnosti ",[1115,30517,30519],{"className":30518},[1144],[1146,30520,30521],{"xmlns":1148},[1150,30522,30523,30527],{},[1153,30524,30525],{},[1159,30526,2982],{},[1167,30528,3045],{"encoding":1169}," se volí předem, obvykle 0,05.",[1127,30531,30532],{},"Pro střední hodnotu normálního rozdělení slouží jednovýběrový a párový t-test; pro srovnání dvou souborů F-test (rozptyly) a dvouvýběrový t-test (střední hodnoty).",[1127,30534,30535],{},"Normalitu ověřuje Shapiro-Wilkův test, shodu s libovolným rozdělením Kolmogorov-Smirnovův test; při porušené normalitě nastupují neparametrické testy (Wilcoxonovy, Kruskalův-Wallisův, mediánový, Friedmanův).",[1127,30537,30538,30539,30552,30553,1269],{},"Rozhodnutí lze číst dvěma rovnocennými způsoby — podle polohy kritéria vůči ",[1115,30540,30542],{"className":30541},[1144],[1146,30543,30544],{"xmlns":1148},[1150,30545,30546,30550],{},[1153,30547,30548],{},[1159,30549,1205],{},[1167,30551,1205],{"encoding":1169},", nebo podle p-hodnoty vůči ",[1115,30554,30556],{"className":30555},[1144],[1146,30557,30558],{"xmlns":1148},[1150,30559,30560,30564],{},[1153,30561,30562],{},[1159,30563,2982],{},[1167,30565,3045],{"encoding":1169},[1110,30567,30568,30569,30573,30574,30578,30579,30583,30584,2568,30597,20397],{},"Testy statistických hypotéz jsou nástroj ",[1318,30570,30572],{"className":30571,"dataFsResolvedFilePath":1322,"href":1323},[1321],"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 ",[1318,30575,30577],{"className":30576,"dataFsResolvedFilePath":6234,"href":6235},[1321],"popisnou statistiku"," výběru, a z rozdělení uvedených u ",[1318,30580,30582],{"className":30581,"dataFsResolvedFilePath":6242,"href":6243},[1321],"náhodných veličin"," (normální, ",[1115,30585,30587],{"className":30586},[1144],[1146,30588,30589],{"xmlns":1148},[1150,30590,30591,30595],{},[1153,30592,30593],{},[1159,30594,11443],{},[1167,30596,11443],{"encoding":1169},[1115,30598,30600],{"className":30599},[1144],[1146,30601,30602],{"xmlns":1148},[1150,30603,30604,30608],{},[1153,30605,30606],{},[1159,30607,11014],{},[1167,30609,11014],{"encoding":1169},[1310,30611,30613],{"id":30612},"statistická-hypotéza-a-její-test","Statistická hypotéza a její test",[1110,30615,30616,30619,30620,30623],{},[1131,30617,30618],{},"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. ",[1131,30621,30622],{},"Testování hypotéz"," je proces ověření správnosti nebo nesprávnosti hypotézy pomocí výsledků získaných náhodným výběrem.",[1110,30625,30626],{},"Proti sobě stojí dvě hypotézy:",[1124,30628,30629,30652],{},[1127,30630,30631,30651],{},[1131,30632,30633,30634],{},"Nulová hypotéza ",[1115,30635,30637],{"className":30636},[1144],[1146,30638,30639],{"xmlns":1148},[1150,30640,30641,30649],{},[1153,30642,30643],{},[1156,30644,30645,30647],{},[1159,30646,1161],{},[1163,30648,1165],{},[1167,30650,1170],{"encoding":1169}," — tvrzení o parametru nebo rozdělení, které chceme ověřit.",[1127,30653,30654,30674,30675,30692],{},[1131,30655,30656,30657],{},"Alternativní hypotéza ",[1115,30658,30660],{"className":30659},[1144],[1146,30661,30662],{"xmlns":1148},[1150,30663,30664,30672],{},[1153,30665,30666],{},[1156,30667,30668,30670],{},[1159,30669,1161],{},[1163,30671,1402],{},[1167,30673,2613],{"encoding":1169}," — staví se proti ",[1115,30676,30678],{"className":30677},[1144],[1146,30679,30680],{"xmlns":1148},[1150,30681,30682,30690],{},[1153,30683,30684],{},[1156,30685,30686,30688],{},[1159,30687,1161],{},[1163,30689,1165],{},[1167,30691,1170],{"encoding":1169}," a určitým způsobem popírá její tvrzení.",[1110,30694,1300,30695,30725,30726,1567],{},[1115,30696,30698],{"className":30697},[1144],[1146,30699,30700],{"xmlns":1148},[1150,30701,30702,30722],{},[1153,30703,30704,30710,30712,30714,30716],{},[1156,30705,30706,30708],{},[1159,30707,1161],{},[1163,30709,1165],{},[1289,30711,1567],{},[1159,30713,11190],{},[1289,30715,1591],{},[1156,30717,30718,30720],{},[1159,30719,11190],{},[1163,30721,1165],{},[1167,30723,30724],{"encoding":1169},"H_0: \\mu = \\mu_0"," existují tři varianty ",[1115,30727,30729],{"className":30728},[1144],[1146,30730,30731],{"xmlns":1148},[1150,30732,30733,30741],{},[1153,30734,30735],{},[1156,30736,30737,30739],{},[1159,30738,1161],{},[1163,30740,1402],{},[1167,30742,2613],{"encoding":1169},[1710,30744,30745,30775],{},[1713,30746,30747],{},[1716,30748,30749,30769,30772],{},[1719,30750,30751,30752],{},"Tvar ",[1115,30753,30755],{"className":30754},[1144],[1146,30756,30757],{"xmlns":1148},[1150,30758,30759,30767],{},[1153,30760,30761],{},[1156,30762,30763,30765],{},[1159,30764,1161],{},[1163,30766,1402],{},[1167,30768,2613],{"encoding":1169},[1719,30770,30771],{},"Zápis",[1719,30773,30774],{},"Typ",[1828,30776,30777,30817,30857],{},[1716,30778,30779,30782,30814],{},[1833,30780,30781],{},"nerovnost",[1833,30783,30784],{},[1115,30785,30787],{"className":30786},[1144],[1146,30788,30789],{"xmlns":1148},[1150,30790,30791,30811],{},[1153,30792,30793,30799,30801,30803,30805],{},[1156,30794,30795,30797],{},[1159,30796,1161],{},[1163,30798,1402],{},[1289,30800,1567],{},[1159,30802,11190],{},[1289,30804,15257],{"mathvariant":1734},[1156,30806,30807,30809],{},[1159,30808,11190],{},[1163,30810,1165],{},[1167,30812,30813],{"encoding":1169},"H_1: \\mu \\neq \\mu_0",[1833,30815,30816],{},"dvoustranná",[1716,30818,30819,30822,30854],{},[1833,30820,30821],{},"větší",[1833,30823,30824],{},[1115,30825,30827],{"className":30826},[1144],[1146,30828,30829],{"xmlns":1148},[1150,30830,30831,30851],{},[1153,30832,30833,30839,30841,30843,30845],{},[1156,30834,30835,30837],{},[1159,30836,1161],{},[1163,30838,1402],{},[1289,30840,1567],{},[1159,30842,11190],{},[1289,30844,1291],{},[1156,30846,30847,30849],{},[1159,30848,11190],{},[1163,30850,1165],{},[1167,30852,30853],{"encoding":1169},"H_1: \\mu > \\mu_0",[1833,30855,30856],{},"jednostranná",[1716,30858,30859,30862,30894],{},[1833,30860,30861],{},"menší",[1833,30863,30864],{},[1115,30865,30867],{"className":30866},[1144],[1146,30868,30869],{"xmlns":1148},[1150,30870,30871,30891],{},[1153,30872,30873,30879,30881,30883,30885],{},[1156,30874,30875,30877],{},[1159,30876,1161],{},[1163,30878,1402],{},[1289,30880,1567],{},[1159,30882,11190],{},[1289,30884,3951],{},[1156,30886,30887,30889],{},[1159,30888,11190],{},[1163,30890,1165],{},[1167,30892,30893],{"encoding":1169},"H_1: \\mu \u003C \\mu_0",[1833,30895,30856],{},[21050,30897,30899],{"id":30898},"chyba-i-a-ii-druhu","Chyba I. a II. druhu",[1110,30901,30902],{},"Protože je úsudek odvozen z náhodného výběru, může vést ke dvěma typům chybného rozhodnutí:",[1124,30904,30905,30942],{},[1127,30906,30907,30910,30911,30928,30929,1269],{},[1131,30908,30909],{},"Chyba I. druhu"," — zamítnutí ",[1115,30912,30914],{"className":30913},[1144],[1146,30915,30916],{"xmlns":1148},[1150,30917,30918,30926],{},[1153,30919,30920],{},[1156,30921,30922,30924],{},[1159,30923,1161],{},[1163,30925,1165],{},[1167,30927,1170],{"encoding":1169},", ačkoliv ve skutečnosti platí. Pravděpodobnost ",[1115,30930,30932],{"className":30931},[1144],[1146,30933,30934],{"xmlns":1148},[1150,30935,30936,30940],{},[1153,30937,30938],{},[1159,30939,2982],{},[1167,30941,3045],{"encoding":1169},[1127,30943,30944,30947,30948,30965,30966,30983,30984,1269],{},[1131,30945,30946],{},"Chyba II. druhu"," — přijetí ",[1115,30949,30951],{"className":30950},[1144],[1146,30952,30953],{"xmlns":1148},[1150,30954,30955,30963],{},[1153,30956,30957],{},[1156,30958,30959,30961],{},[1159,30960,1161],{},[1163,30962,1165],{},[1167,30964,1170],{"encoding":1169},", ačkoliv platí ",[1115,30967,30969],{"className":30968},[1144],[1146,30970,30971],{"xmlns":1148},[1150,30972,30973,30981],{},[1153,30974,30975],{},[1156,30976,30977,30979],{},[1159,30978,1161],{},[1163,30980,1402],{},[1167,30982,2613],{"encoding":1169},". Pravděpodobnost ",[1115,30985,30987],{"className":30986},[1144],[1146,30988,30989],{"xmlns":1148},[1150,30990,30991,30995],{},[1153,30992,30993],{},[1159,30994,20641],{},[1167,30996,30496],{"encoding":1169},[1710,30998,30999,31062],{},[1713,31000,31001],{},[1716,31002,31003,31023,31042],{},[1719,31004,31005,31006],{},"Úsudek o ",[1115,31007,31009],{"className":31008},[1144],[1146,31010,31011],{"xmlns":1148},[1150,31012,31013,31021],{},[1153,31014,31015],{},[1156,31016,31017,31019],{},[1159,31018,1161],{},[1163,31020,1165],{},[1167,31022,1170],{"encoding":1169},[1719,31024,31025,12652],{},[1115,31026,31028],{"className":31027},[1144],[1146,31029,31030],{"xmlns":1148},[1150,31031,31032,31040],{},[1153,31033,31034],{},[1156,31035,31036,31038],{},[1159,31037,1161],{},[1163,31039,1165],{},[1167,31041,1170],{"encoding":1169},[1719,31043,31044,31061],{},[1115,31045,31047],{"className":31046},[1144],[1146,31048,31049],{"xmlns":1148},[1150,31050,31051,31059],{},[1153,31052,31053],{},[1156,31054,31055,31057],{},[1159,31056,1161],{},[1163,31058,1165],{},[1167,31060,1170],{"encoding":1169}," neplatí",[1828,31063,31064,31106],{},[1716,31065,31066,31069,31090],{},[1833,31067,31068],{},"Nezamítá se",[1833,31070,31071,31072],{},"správné rozhodnutí, ",[1115,31073,31075],{"className":31074},[1144],[1146,31076,31077],{"xmlns":1148},[1150,31078,31079,31087],{},[1153,31080,31081,31083,31085],{},[1163,31082,1402],{},[1289,31084,2681],{},[1159,31086,2982],{},[1167,31088,31089],{"encoding":1169},"1-\\alpha",[1833,31091,31092,31093],{},"chyba II. druhu, ",[1115,31094,31096],{"className":31095},[1144],[1146,31097,31098],{"xmlns":1148},[1150,31099,31100,31104],{},[1153,31101,31102],{},[1159,31103,20641],{},[1167,31105,30496],{"encoding":1169},[1716,31107,31108,31111,31127],{},[1833,31109,31110],{},"Zamítá se",[1833,31112,31113,31114],{},"chyba I. druhu, ",[1115,31115,31117],{"className":31116},[1144],[1146,31118,31119],{"xmlns":1148},[1150,31120,31121,31125],{},[1153,31122,31123],{},[1159,31124,2982],{},[1167,31126,3045],{"encoding":1169},[1833,31128,31071,31129],{},[1115,31130,31132],{"className":31131},[1144],[1146,31133,31134],{"xmlns":1148},[1150,31135,31136,31144],{},[1153,31137,31138,31140,31142],{},[1163,31139,1402],{},[1289,31141,2681],{},[1159,31143,20641],{},[1167,31145,31146],{"encoding":1169},"1-\\beta",[1110,31148,31149,1254,31152,31165],{},[1131,31150,31151],{},"Hladina významnosti",[1115,31153,31155],{"className":31154},[1144],[1146,31156,31157],{"xmlns":1148},[1150,31158,31159,31163],{},[1153,31160,31161],{},[1159,31162,2982],{},[1167,31164,3045],{"encoding":1169}," 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.",[1110,31167,31168],{},[4002,31169],{"alt":31170,"className":31171,"src":31172},"mask-th-chyba-i-ii",[1321,4006],"\u002Fwiki-assets\u002Fmask-th-chyba-i-ii.png",[1110,31174,31175,31176,31189,31190,31203,31204,31217,31218,1499,31231,31244,31245,1269],{},"Obrázek ukazuje, proč jde o kompromis: posunutí kritické hodnoty ",[1115,31177,31179],{"className":31178},[1144],[1146,31180,31181],{"xmlns":1148},[1150,31182,31183,31187],{},[1153,31184,31185],{},[1159,31186,3338],{},[1167,31188,3338],{"encoding":1169}," doleva zmenší ",[1115,31191,31193],{"className":31192},[1144],[1146,31194,31195],{"xmlns":1148},[1150,31196,31197,31201],{},[1153,31198,31199],{},[1159,31200,20641],{},[1167,31202,30496],{"encoding":1169},", ale zvětší ",[1115,31205,31207],{"className":31206},[1144],[1146,31208,31209],{"xmlns":1148},[1150,31210,31211,31215],{},[1153,31212,31213],{},[1159,31214,2982],{},[1167,31216,3045],{"encoding":1169},", a naopak. Pro danou hladinu ",[1115,31219,31221],{"className":31220},[1144],[1146,31222,31223],{"xmlns":1148},[1150,31224,31225,31229],{},[1153,31226,31227],{},[1159,31228,2982],{},[1167,31230,3045],{"encoding":1169},[1115,31232,31234],{"className":31233},[1144],[1146,31235,31236],{"xmlns":1148},[1150,31237,31238,31242],{},[1153,31239,31240],{},[1159,31241,3338],{},[1167,31243,3338],{"encoding":1169}," jednoznačně určena rozdělením kritéria za platnosti ",[1115,31246,31248],{"className":31247},[1144],[1146,31249,31250],{"xmlns":1148},[1150,31251,31252,31260],{},[1153,31253,31254],{},[1156,31255,31256,31258],{},[1159,31257,1161],{},[1163,31259,1165],{},[1167,31261,1170],{"encoding":1169},[21050,31263,31265],{"id":31264},"testové-kritérium-a-kritický-obor","Testové kritérium a kritický obor",[1110,31267,31268,1254,31270,31283,31284,1269],{},[1131,31269,2617],{},[1115,31271,31273],{"className":31272},[1144],[1146,31274,31275],{"xmlns":1148},[1150,31276,31277,31281],{},[1153,31278,31279],{},[1159,31280,11401],{},[1167,31282,11401],{"encoding":1169}," je statistika spočtená z výběru; aby bylo možné test provést, musí být známo jeho rozdělení za platnosti ",[1115,31285,31287],{"className":31286},[1144],[1146,31288,31289],{"xmlns":1148},[1150,31290,31291,31299],{},[1153,31292,31293],{},[1156,31294,31295,31297],{},[1159,31296,1161],{},[1163,31298,1165],{},[1167,31300,1170],{"encoding":1169},[1110,31302,31303,1254,31306,31319,31320,31337],{},[1131,31304,31305],{},"Kritický obor",[1115,31307,31309],{"className":31308},[1144],[1146,31310,31311],{"xmlns":1148},[1150,31312,31313,31317],{},[1153,31314,31315],{},[1159,31316,1205],{},[1167,31318,1205],{"encoding":1169}," je množina hodnot svědčících pro ",[1115,31321,31323],{"className":31322},[1144],[1146,31324,31325],{"xmlns":1148},[1150,31326,31327,31335],{},[1153,31328,31329],{},[1156,31330,31331,31333],{},[1159,31332,1161],{},[1163,31334,1402],{},[1167,31336,2613],{"encoding":1169},". Je zkonstruován tak, aby",[1115,31339,31341],{"className":31340},[1144],[1146,31342,31343],{"xmlns":1148,"display":1573},[1150,31344,31345,31373],{},[1153,31346,31347,31349,31351,31353,31355,31357,31359,31365,31367,31369,31371],{},[1159,31348,11026],{},[1289,31350,1484],{"stretchy":1483},[1159,31352,11401],{},[1289,31354,11318],{},[1159,31356,1205],{},[1289,31358,27329],{},[1156,31360,31361,31363],{},[1159,31362,1161],{},[1163,31364,1165],{},[1289,31366,1495],{"stretchy":1483},[1289,31368,1591],{},[1159,31370,2982],{},[1289,31372,1405],{"separator":1121},[1167,31374,31375],{"encoding":1169},"P(T \\in W \\mid H_0) = \\alpha,",[1110,31377,31378,31379,31392,31393,31410],{},"tedy aby pravděpodobnost, že výběr dá hodnotu kritéria v ",[1115,31380,31382],{"className":31381},[1144],[1146,31383,31384],{"xmlns":1148},[1150,31385,31386,31390],{},[1153,31387,31388],{},[1159,31389,1205],{},[1167,31391,1205],{"encoding":1169}," i při platné ",[1115,31394,31396],{"className":31395},[1144],[1146,31397,31398],{"xmlns":1148},[1150,31399,31400,31408],{},[1153,31401,31402],{},[1156,31403,31404,31406],{},[1159,31405,1161],{},[1163,31407,1165],{},[1167,31409,1170],{"encoding":1169},", byla rovna zvolené hladině významnosti.",[21050,31412,31414],{"id":31413},"postup-testování-hypotézy","Postup testování hypotézy",[1110,31416,31417],{},[4002,31418],{"alt":31419,"className":31420,"src":31421},"mask-ilu-postup-testovani",[1321,4006],"\u002Fwiki-assets\u002Fmask-ilu-postup-testovani.png",[2481,31423,31424,31461,31464,31480],{},[1127,31425,31426,31427,5360,31444,1269],{},"Formulace hypotéz ",[1115,31428,31430],{"className":31429},[1144],[1146,31431,31432],{"xmlns":1148},[1150,31433,31434,31442],{},[1153,31435,31436],{},[1156,31437,31438,31440],{},[1159,31439,1161],{},[1163,31441,1165],{},[1167,31443,1170],{"encoding":1169},[1115,31445,31447],{"className":31446},[1144],[1146,31448,31449],{"xmlns":1148},[1150,31450,31451,31459],{},[1153,31452,31453],{},[1156,31454,31455,31457],{},[1159,31456,1161],{},[1163,31458,1402],{},[1167,31460,2613],{"encoding":1169},[1127,31462,31463],{},"Volba testového kritéria a výpočet jeho hodnoty.",[1127,31465,31466,31467,1269],{},"Volba hladiny významnosti a sestrojení příslušného kritického oboru ",[1115,31468,31470],{"className":31469},[1144],[1146,31471,31472],{"xmlns":1148},[1150,31473,31474,31478],{},[1153,31475,31476],{},[1159,31477,1205],{},[1167,31479,1205],{"encoding":1169},[1127,31481,31482,31483],{},"Formulace závěru:\n",[1124,31484,31485,31563],{},[1127,31486,31487,31488,3607,31506,31523,31524,31544,31545,31562],{},"pokud ",[1115,31489,31491],{"className":31490},[1144],[1146,31492,31493],{"xmlns":1148},[1150,31494,31495,31503],{},[1153,31496,31497,31499,31501],{},[1159,31498,11401],{},[1289,31500,11318],{},[1159,31502,1205],{},[1167,31504,31505],{"encoding":1169},"T \\in W",[1115,31507,31509],{"className":31508},[1144],[1146,31510,31511],{"xmlns":1148},[1150,31512,31513,31521],{},[1153,31514,31515],{},[1156,31516,31517,31519],{},[1159,31518,1161],{},[1163,31520,1402],{},[1167,31522,2613],{"encoding":1169}," je testem prokázána na hladině významnosti ",[1115,31525,31527],{"className":31526},[1144],[1146,31528,31529],{"xmlns":1148},[1150,31530,31531,31541],{},[1153,31532,31533,31535,31537,31539],{},[1163,31534,16121],{},[1159,31536,2982],{},[2525,31538,2527],{},[1159,31540,16128],{"mathvariant":1734},[1167,31542,31543],{"encoding":1169},"100\\alpha\\,\\%"," (zamítáme ",[1115,31546,31548],{"className":31547},[1144],[1146,31549,31550],{"xmlns":1148},[1150,31551,31552,31560],{},[1153,31553,31554],{},[1156,31555,31556,31558],{},[1159,31557,1161],{},[1163,31559,1165],{},[1167,31561,1170],{"encoding":1169},");",[1127,31564,31487,31565,3607,31584,31601,31602,31621,31622,31639],{},[1115,31566,31568],{"className":31567},[1144],[1146,31569,31570],{"xmlns":1148},[1150,31571,31572,31581],{},[1153,31573,31574,31576,31579],{},[1159,31575,11401],{},[1289,31577,31578],{"mathvariant":1734},"∉",[1159,31580,1205],{},[1167,31582,31583],{"encoding":1169},"T \\notin W",[1115,31585,31587],{"className":31586},[1144],[1146,31588,31589],{"xmlns":1148},[1150,31590,31591,31599],{},[1153,31592,31593],{},[1156,31594,31595,31597],{},[1159,31596,1161],{},[1163,31598,1402],{},[1167,31600,2613],{"encoding":1169}," není testem prokázána na hladině významnosti ",[1115,31603,31605],{"className":31604},[1144],[1146,31606,31607],{"xmlns":1148},[1150,31608,31609,31619],{},[1153,31610,31611,31613,31615,31617],{},[1163,31612,16121],{},[1159,31614,2982],{},[2525,31616,2527],{},[1159,31618,16128],{"mathvariant":1734},[1167,31620,31543],{"encoding":1169}," ; ",[1115,31623,31625],{"className":31624},[1144],[1146,31626,31627],{"xmlns":1148},[1150,31628,31629,31637],{},[1153,31630,31631],{},[1156,31632,31633,31635],{},[1159,31634,1161],{},[1163,31636,1165],{},[1167,31638,1170],{"encoding":1169}," nezamítáme.",[1110,31641,31642,31643,31646,31647,31664,31665,31682,31683,31703,31704,29489,31721,1254,31741,31758],{},"Rovnocennou alternativou je ",[1131,31644,31645],{},"p-hodnota",": udává, nakolik jsou data slučitelná s ",[1115,31648,31650],{"className":31649},[1144],[1146,31651,31652],{"xmlns":1148},[1150,31653,31654,31662],{},[1153,31655,31656],{},[1156,31657,31658,31660],{},[1159,31659,1161],{},[1163,31661,1165],{},[1167,31663,1170],{"encoding":1169},". Čím menší p-hodnota, tím více data svědčí proti ",[1115,31666,31668],{"className":31667},[1144],[1146,31669,31670],{"xmlns":1148},[1150,31671,31672,31680],{},[1153,31673,31674],{},[1156,31675,31676,31678],{},[1159,31677,1161],{},[1163,31679,1165],{},[1167,31681,1170],{"encoding":1169},". Rozhodovací pravidlo: ",[1115,31684,31686],{"className":31685},[1144],[1146,31687,31688],{"xmlns":1148},[1150,31689,31690,31700],{},[1153,31691,31692,31694,31696,31698],{},[1159,31693,1110],{},[1289,31695,11034],{},[1159,31697,2982],{},[1289,31699,11849],{},[1167,31701,31702],{"encoding":1169},"p \\le \\alpha \\Rightarrow"," zamítáme ",[1115,31705,31707],{"className":31706},[1144],[1146,31708,31709],{"xmlns":1148},[1150,31710,31711,31719],{},[1153,31712,31713],{},[1156,31714,31715,31717],{},[1159,31716,1161],{},[1163,31718,1165],{},[1167,31720,1170],{"encoding":1169},[1115,31722,31724],{"className":31723},[1144],[1146,31725,31726],{"xmlns":1148},[1150,31727,31728,31738],{},[1153,31729,31730,31732,31734,31736],{},[1159,31731,1110],{},[1289,31733,1291],{},[1159,31735,2982],{},[1289,31737,11849],{},[1167,31739,31740],{"encoding":1169},"p > \\alpha \\Rightarrow",[1115,31742,31744],{"className":31743},[1144],[1146,31745,31746],{"xmlns":1148},[1150,31747,31748,31756],{},[1153,31749,31750],{},[1156,31751,31752,31754],{},[1159,31753,1161],{},[1163,31755,1165],{},[1167,31757,1170],{"encoding":1169}," nezamítáme. Obě cesty — kritický obor i p-hodnota — vedou vždy ke stejnému závěru; R u všech testů vrací p-hodnotu přímo.",[1310,31760,31762],{"id":31761},"jednovýběrový-t-test","Jednovýběrový t-test",[1110,31764,31765,31766,31779,31780,31812,31813,31826,31827,5360,31844,31861,31862,31880,31881,31894],{},"Test o střední hodnotě ",[1115,31767,31769],{"className":31768},[1144],[1146,31770,31771],{"xmlns":1148},[1150,31772,31773,31777],{},[1153,31774,31775],{},[1159,31776,11190],{},[1167,31778,13097],{"encoding":1169}," rozdělení ",[1115,31781,31783],{"className":31782},[1144],[1146,31784,31785],{"xmlns":1148},[1150,31786,31787,31809],{},[1153,31788,31789,31791,31793,31795,31797,31799,31801,31807],{},[1159,31790,11031],{},[1289,31792,13484],{},[1159,31794,11185],{},[1289,31796,1484],{"stretchy":1483},[1159,31798,11190],{},[1289,31800,1405],{"separator":1121},[1182,31802,31803,31805],{},[1159,31804,11198],{},[1163,31806,1189],{},[1289,31808,1495],{"stretchy":1483},[1167,31810,31811],{"encoding":1169},"X \\sim N(\\mu, \\sigma^2)",". Z výběru o rozsahu ",[1115,31814,31816],{"className":31815},[1144],[1146,31817,31818],{"xmlns":1148},[1150,31819,31820,31824],{},[1153,31821,31822],{},[1159,31823,1287],{},[1167,31825,1287],{"encoding":1169}," se určí charakteristiky ",[1115,31828,31830],{"className":31829},[1144],[1146,31831,31832],{"xmlns":1148},[1150,31833,31834,31842],{},[1153,31835,31836],{},[2339,31837,31838,31840],{"accent":1121},[1159,31839,11019],{},[1289,31841,15762],{},[1167,31843,25870],{"encoding":1169},[1115,31845,31847],{"className":31846},[1144],[1146,31848,31849],{"xmlns":1148},[1150,31850,31851,31859],{},[1153,31852,31853],{},[1182,31854,31855,31857],{},[1159,31856,1463],{},[1163,31858,1189],{},[1167,31860,20080],{"encoding":1169},"; testem se posuzuje vztah mezi zvoleným číslem ",[1115,31863,31865],{"className":31864},[1144],[1146,31866,31867],{"xmlns":1148},[1150,31868,31869,31877],{},[1153,31870,31871],{},[1156,31872,31873,31875],{},[1159,31874,11190],{},[1163,31876,1165],{},[1167,31878,31879],{"encoding":1169},"\\mu_0"," a neznámou hodnotou ",[1115,31882,31884],{"className":31883},[1144],[1146,31885,31886],{"xmlns":1148},[1150,31887,31888,31892],{},[1153,31889,31890],{},[1159,31891,11190],{},[1167,31893,13097],{"encoding":1169},". Testové kritérium",[1115,31896,31898],{"className":31897},[1144],[1146,31899,31900],{"xmlns":1148,"display":1573},[1150,31901,31902,31946],{},[1153,31903,31904,31906,31908,31928,31932,31934],{},[1159,31905,11401],{},[1289,31907,1591],{},[2355,31909,31910,31926],{},[1153,31911,31912,31918,31920],{},[2339,31913,31914,31916],{"accent":1121},[1159,31915,11019],{},[1289,31917,15762],{},[1289,31919,2681],{},[1156,31921,31922,31924],{},[1159,31923,11190],{},[1163,31925,1165],{},[1159,31927,1463],{},[4072,31929,31930],{},[1159,31931,1287],{},[1289,31933,13484],{},[1156,31935,31936,31938],{},[1159,31937,11443],{},[1153,31939,31940,31942,31944],{},[1159,31941,1287],{},[1289,31943,2681],{},[1163,31945,1402],{},[1167,31947,31948],{"encoding":1169},"T = \\frac{\\bar{x} - \\mu_0}{s}\\sqrt{n} \\sim t_{n-1}",[1110,31950,31951,31952,31970],{},"má Studentovo rozdělení o ",[1115,31953,31955],{"className":31954},[1144],[1146,31956,31957],{"xmlns":1148},[1150,31958,31959,31967],{},[1153,31960,31961,31963,31965],{},[1159,31962,1287],{},[1289,31964,2681],{},[1163,31966,1402],{},[1167,31968,31969],{"encoding":1169},"n-1"," stupních volnosti.",[1710,31972,31973,32031],{},[1713,31974,31975],{},[1716,31976,31977,31996,32015],{},[1719,31978,31979],{},[1115,31980,31982],{"className":31981},[1144],[1146,31983,31984],{"xmlns":1148},[1150,31985,31986,31994],{},[1153,31987,31988],{},[1156,31989,31990,31992],{},[1159,31991,1161],{},[1163,31993,1165],{},[1167,31995,1170],{"encoding":1169},[1719,31997,31998],{},[1115,31999,32001],{"className":32000},[1144],[1146,32002,32003],{"xmlns":1148},[1150,32004,32005,32013],{},[1153,32006,32007],{},[1156,32008,32009,32011],{},[1159,32010,1161],{},[1163,32012,1402],{},[1167,32014,2613],{"encoding":1169},[1719,32016,32017,32018],{},"Kritický obor ",[1115,32019,32021],{"className":32020},[1144],[1146,32022,32023],{"xmlns":1148},[1150,32024,32025,32029],{},[1153,32026,32027],{},[1159,32028,1205],{},[1167,32030,1205],{"encoding":1169},[1828,32032,32033,32123,32221],{},[1716,32034,32035,32059,32083],{},[1833,32036,32037],{},[1115,32038,32040],{"className":32039},[1144],[1146,32041,32042],{"xmlns":1148},[1150,32043,32044,32056],{},[1153,32045,32046,32048,32050],{},[1159,32047,11190],{},[1289,32049,11034],{},[1156,32051,32052,32054],{},[1159,32053,11190],{},[1163,32055,1165],{},[1167,32057,32058],{"encoding":1169},"\\mu \\le \\mu_0",[1833,32060,32061],{},[1115,32062,32064],{"className":32063},[1144],[1146,32065,32066],{"xmlns":1148},[1150,32067,32068,32080],{},[1153,32069,32070,32072,32074],{},[1159,32071,11190],{},[1289,32073,1291],{},[1156,32075,32076,32078],{},[1159,32077,11190],{},[1163,32079,1165],{},[1167,32081,32082],{"encoding":1169},"\\mu > \\mu_0",[1833,32084,32085],{},[1115,32086,32088],{"className":32087},[1144],[1146,32089,32090],{"xmlns":1148},[1150,32091,32092,32120],{},[1153,32093,32094,32096,32098,32110,32112,32114,32116,32118],{},[1159,32095,11443],{},[1289,32097,2968],{},[1156,32099,32100,32102],{},[1159,32101,11443],{},[1153,32103,32104,32106,32108],{},[1163,32105,1402],{},[1289,32107,2681],{},[1159,32109,2982],{},[1289,32111,1484],{"stretchy":1483},[1159,32113,1287],{},[1289,32115,2681],{},[1163,32117,1402],{},[1289,32119,1495],{"stretchy":1483},[1167,32121,32122],{"encoding":1169},"t \\ge t_{1-\\alpha}(n-1)",[1716,32124,32125,32149,32173],{},[1833,32126,32127],{},[1115,32128,32130],{"className":32129},[1144],[1146,32131,32132],{"xmlns":1148},[1150,32133,32134,32146],{},[1153,32135,32136,32138,32140],{},[1159,32137,11190],{},[1289,32139,1591],{},[1156,32141,32142,32144],{},[1159,32143,11190],{},[1163,32145,1165],{},[1167,32147,32148],{"encoding":1169},"\\mu = \\mu_0",[1833,32150,32151],{},[1115,32152,32154],{"className":32153},[1144],[1146,32155,32156],{"xmlns":1148},[1150,32157,32158,32170],{},[1153,32159,32160,32162,32164],{},[1159,32161,11190],{},[1289,32163,15257],{"mathvariant":1734},[1156,32165,32166,32168],{},[1159,32167,11190],{},[1163,32169,1165],{},[1167,32171,32172],{"encoding":1169},"\\mu \\neq \\mu_0",[1833,32174,32175],{},[1115,32176,32178],{"className":32177},[1144],[1146,32179,32180],{"xmlns":1148},[1150,32181,32182,32218],{},[1153,32183,32184,32186,32188,32190,32192,32208,32210,32212,32214,32216],{},[1289,32185,27329],{"stretchy":1483},[1159,32187,11443],{},[1289,32189,27329],{"stretchy":1483},[1289,32191,2968],{},[1156,32193,32194,32196],{},[1159,32195,11443],{},[1153,32197,32198,32200,32202,32204,32206],{},[1163,32199,1402],{},[1289,32201,2681],{},[1159,32203,2982],{},[1159,32205,4223],{"mathvariant":1734},[1163,32207,1189],{},[1289,32209,1484],{"stretchy":1483},[1159,32211,1287],{},[1289,32213,2681],{},[1163,32215,1402],{},[1289,32217,1495],{"stretchy":1483},[1167,32219,32220],{"encoding":1169},"\\lvert t \\rvert \\ge t_{1-\\alpha\u002F2}(n-1)",[1716,32222,32223,32247,32271],{},[1833,32224,32225],{},[1115,32226,32228],{"className":32227},[1144],[1146,32229,32230],{"xmlns":1148},[1150,32231,32232,32244],{},[1153,32233,32234,32236,32238],{},[1159,32235,11190],{},[1289,32237,2968],{},[1156,32239,32240,32242],{},[1159,32241,11190],{},[1163,32243,1165],{},[1167,32245,32246],{"encoding":1169},"\\mu \\ge \\mu_0",[1833,32248,32249],{},[1115,32250,32252],{"className":32251},[1144],[1146,32253,32254],{"xmlns":1148},[1150,32255,32256,32268],{},[1153,32257,32258,32260,32262],{},[1159,32259,11190],{},[1289,32261,3951],{},[1156,32263,32264,32266],{},[1159,32265,11190],{},[1163,32267,1165],{},[1167,32269,32270],{"encoding":1169},"\\mu \u003C \\mu_0",[1833,32272,32273],{},[1115,32274,32276],{"className":32275},[1144],[1146,32277,32278],{"xmlns":1148},[1150,32279,32280,32310],{},[1153,32281,32282,32284,32286,32288,32300,32302,32304,32306,32308],{},[1159,32283,11443],{},[1289,32285,11034],{},[1289,32287,2681],{},[1156,32289,32290,32292],{},[1159,32291,11443],{},[1153,32293,32294,32296,32298],{},[1163,32295,1402],{},[1289,32297,2681],{},[1159,32299,2982],{},[1289,32301,1484],{"stretchy":1483},[1159,32303,1287],{},[1289,32305,2681],{},[1163,32307,1402],{},[1289,32309,1495],{"stretchy":1483},[1167,32311,32312],{"encoding":1169},"t \\le -t_{1-\\alpha}(n-1)",[1110,32314,32315,32316,32319],{},"V R test provádí ",[3087,32317,32318],{},"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?",[3311,32321,32323],{"className":3313,"code":32322,"language":71,"meta":3315,"style":3315},"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",[3087,32324,32325,32379],{"__ignoreMap":3315},[1115,32326,32327,32329,32331,32333,32335,32338,32340,32343,32345,32348,32350,32353,32355,32358,32360,32363,32365,32367,32369,32372,32374,32377],{"class":3320,"line":10},[1115,32328,11019],{"class":3323},[1115,32330,3328],{"class":3327},[1115,32332,3454],{"class":3331},[1115,32334,1484],{"class":3335},[1115,32336,32337],{"class":3343},"12.5",[1115,32339,1405],{"class":3327},[1115,32341,32342],{"class":3343}," 13.5",[1115,32344,1405],{"class":3327},[1115,32346,32347],{"class":3343}," 11.9",[1115,32349,1405],{"class":3327},[1115,32351,32352],{"class":3343}," 12.2",[1115,32354,1405],{"class":3327},[1115,32356,32357],{"class":3343}," 13.0",[1115,32359,1405],{"class":3327},[1115,32361,32362],{"class":3343}," 14.3",[1115,32364,1405],{"class":3327},[1115,32366,32352],{"class":3343},[1115,32368,1405],{"class":3327},[1115,32370,32371],{"class":3343}," 11.8",[1115,32373,1405],{"class":3327},[1115,32375,32376],{"class":3343}," 14.0",[1115,32378,3520],{"class":3335},[1115,32380,32381,32384,32386,32388,32390,32392,32394,32396,32398,32401,32403,32406],{"class":3320,"line":27},[1115,32382,32383],{"class":3331},"t.test",[1115,32385,1484],{"class":3335},[1115,32387,11019],{"class":3323},[1115,32389,1405],{"class":3327},[1115,32391,29886],{"class":3323},[1115,32393,3416],{"class":3327},[1115,32395,3353],{"class":3343},[1115,32397,1405],{"class":3327},[1115,32399,32400],{"class":3323}," alternative",[1115,32402,3416],{"class":3327},[1115,32404,32405],{"class":3459}," \"two.sided\"",[1115,32407,3520],{"class":3335},[3311,32409,32412],{"className":32410,"code":32411,"language":3542,"meta":3315},[3540],"    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",[3087,32413,32411],{"__ignoreMap":3315},[1110,32415,32416,32418,32419,32422,32423,32426,32427,32430,32431,32454],{},[3087,32417,11443],{}," je testové kritérium, ",[3087,32420,32421],{},"df"," stupně volnosti, ",[3087,32424,32425],{},"p-value"," p-hodnota pro zvolenou alternativu a ",[3087,32428,32429],{},"mean of x"," výběrový průměr. Zde ",[1115,32432,32434],{"className":32433},[1144],[1146,32435,32436],{"xmlns":1148},[1150,32437,32438,32451],{},[1153,32439,32440,32442,32444,32447,32449],{},[1159,32441,1110],{},[1289,32443,1591],{},[1163,32445,32446],{},"0,02843",[1289,32448,3951],{},[1163,32450,3603],{},[1167,32452,32453],{"encoding":1169},"p = 0{,}02843 \u003C 0{,}05",": úprava trasy průměrnou dobu jízdy (původně 12 minut) statisticky významně změnila.",[1103,32456,32458,32465,32553,32609,32701],{"className":32457,"dataCallout":3094},[1106,3093],[1110,32459,32461,32464],{"className":32460},[1113],[1115,32462],{"className":32463,"ariaHidden":1121},[1118,3101,1120],"Příklad: Kontrola objemu lahví",[1110,32466,32467,32468,32490,32491,32509,32510,32533,32534,32552],{},"Pivovar plní lahve, deklarovaný objem je ",[1115,32469,32471],{"className":32470},[1144],[1146,32472,32473],{"xmlns":1148},[1150,32474,32475,32487],{},[1153,32476,32477,32483,32485],{},[1156,32478,32479,32481],{},[1159,32480,11190],{},[1163,32482,1165],{},[1289,32484,1591],{},[1163,32486,12758],{},[1167,32488,32489],{"encoding":1169},"\\mu_0 = 0{,}5"," l. Náhodný výběr ",[1115,32492,32494],{"className":32493},[1144],[1146,32495,32496],{"xmlns":1148},[1150,32497,32498,32506],{},[1153,32499,32500,32502,32504],{},[1159,32501,1287],{},[1289,32503,1591],{},[1163,32505,3664],{},[1167,32507,32508],{"encoding":1169},"n = 20"," lahví dal ",[1115,32511,32513],{"className":32512},[1144],[1146,32514,32515],{"xmlns":1148},[1150,32516,32517,32530],{},[1153,32518,32519,32525,32527],{},[2339,32520,32521,32523],{"accent":1121},[1159,32522,11019],{},[1289,32524,15762],{},[1289,32526,1591],{},[1163,32528,32529],{},"0,492",[1167,32531,32532],{"encoding":1169},"\\bar{x} = 0{,}492"," l, ",[1115,32535,32537],{"className":32536},[1144],[1146,32538,32539],{"xmlns":1148},[1150,32540,32541,32549],{},[1153,32542,32543,32545,32547],{},[1159,32544,1463],{},[1289,32546,1591],{},[1163,32548,19098],{},[1167,32550,32551],{"encoding":1169},"s = 0{,}015"," l. Na hladině významnosti 5 % ověřte podezření, že pivovar lahve nedoplňuje.",[1110,32554,32555,32581,32582,32608],{},[1115,32556,32558],{"className":32557},[1144],[1146,32559,32560],{"xmlns":1148},[1150,32561,32562,32578],{},[1153,32563,32564,32570,32572,32574,32576],{},[1156,32565,32566,32568],{},[1159,32567,1161],{},[1163,32569,1165],{},[1289,32571,1567],{},[1159,32573,11190],{},[1289,32575,2968],{},[1163,32577,12758],{},[1167,32579,32580],{"encoding":1169},"H_0: \\mu \\ge 0{,}5"," l (objem je v pořádku nebo větší), ",[1115,32583,32585],{"className":32584},[1144],[1146,32586,32587],{"xmlns":1148},[1150,32588,32589,32605],{},[1153,32590,32591,32597,32599,32601,32603],{},[1156,32592,32593,32595],{},[1159,32594,1161],{},[1163,32596,1402],{},[1289,32598,1567],{},[1159,32600,11190],{},[1289,32602,3951],{},[1163,32604,12758],{},[1167,32606,32607],{"encoding":1169},"H_1: \\mu \u003C 0{,}5"," l (lahve jsou nedoplněné).",[1110,32610,32611],{},[1115,32612,32614],{"className":32613},[1144],[1146,32615,32616],{"xmlns":1148},[1150,32617,32618,32698],{},[1153,32619,32620,32622,32624,32636,32640,32642,32644,32647,32649,32651,32653,32655,32657,32659,32661,32663,32675,32677,32679,32681,32683,32685,32687,32689,32691,32693,32696],{},[1159,32621,11443],{},[1289,32623,1591],{},[2355,32625,32626,32634],{},[1153,32627,32628,32630,32632],{},[1163,32629,32529],{},[1289,32631,2681],{},[1163,32633,12758],{},[1163,32635,19098],{},[4072,32637,32638],{},[1163,32639,3664],{},[1289,32641,1591],{},[1289,32643,2681],{},[1163,32645,32646],{},"2,385",[1289,32648,1405],{"separator":1121},[1621,32650],{"width":1623},[1159,32652,1205],{},[1289,32654,1591],{},[1289,32656,2951],{"stretchy":1483},[1159,32658,11443],{},[1289,32660,11034],{},[1289,32662,2681],{},[1156,32664,32665,32667],{},[1159,32666,11443],{},[1153,32668,32669,32671,32673],{},[1163,32670,1165],{},[1289,32672,1405],{"separator":1121},[1163,32674,26103],{},[1289,32676,1484],{"stretchy":1483},[1163,32678,19022],{},[1289,32680,1495],{"stretchy":1483},[1289,32682,3011],{"stretchy":1483},[1289,32684,1591],{},[1289,32686,2951],{"stretchy":1483},[1159,32688,11443],{},[1289,32690,11034],{},[1289,32692,2681],{},[1163,32694,32695],{},"1,729",[1289,32697,3011],{"stretchy":1483},[1167,32699,32700],{"encoding":1169},"t = \\frac{0{,}492 - 0{,}5}{0{,}015}\\sqrt{20} = -2{,}385, \\qquad W = \\{t \\le -t_{0,95}(19)\\} = \\{t \\le -1{,}729\\}",[1110,32702,32703,32704,5626,32722,32739],{},"Protože ",[1115,32705,32707],{"className":32706},[1144],[1146,32708,32709],{"xmlns":1148},[1150,32710,32711,32719],{},[1153,32712,32713,32715,32717],{},[1159,32714,11443],{},[1289,32716,11318],{},[1159,32718,1205],{},[1167,32720,32721],{"encoding":1169},"t \\in W",[1115,32723,32725],{"className":32724},[1144],[1146,32726,32727],{"xmlns":1148},[1150,32728,32729,32737],{},[1153,32730,32731],{},[1156,32732,32733,32735],{},[1159,32734,1161],{},[1163,32736,1165],{},[1167,32738,1170],{"encoding":1169},": na hladině významnosti 5 % se potvrdilo, že pivovar plní lahve pod deklarovaný objem.",[1110,32741,32742,32743,32745,32746,1567],{},"Ze souhrnných charakteristik bez surových dat ",[3087,32744,32318],{}," spustit nelze — kritérium a kritická hodnota se dopočítají přímo z definice pomocí ",[3087,32747,32748],{},"qt()",[3311,32750,32752],{"className":3313,"code":32751,"language":71,"meta":3315,"style":3315},"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",[3087,32753,32754,32792,32824,32854,32859],{"__ignoreMap":3315},[1115,32755,32756,32759,32761,32764,32766,32768,32770,32773,32775,32777,32779,32782,32784,32787,32789],{"class":3320,"line":10},[1115,32757,32758],{"class":3323},"xbar",[1115,32760,3328],{"class":3327},[1115,32762,32763],{"class":3343}," 0.492",[1115,32765,29489],{"class":3335},[1115,32767,1463],{"class":3323},[1115,32769,3328],{"class":3327},[1115,32771,32772],{"class":3343}," 0.015",[1115,32774,29489],{"class":3335},[1115,32776,1287],{"class":3323},[1115,32778,3328],{"class":3327},[1115,32780,32781],{"class":3343}," 20",[1115,32783,29489],{"class":3335},[1115,32785,32786],{"class":3323},"mu0",[1115,32788,3328],{"class":3327},[1115,32790,32791],{"class":3343}," 0.5\n",[1115,32793,32794,32796,32798,32800,32802,32804,32807,32809,32811,32814,32816,32818,32820,32822],{"class":3320,"line":27},[1115,32795,11443],{"class":3323},[1115,32797,3328],{"class":3327},[1115,32799,4226],{"class":3335},[1115,32801,32758],{"class":3323},[1115,32803,29826],{"class":3327},[1115,32805,32806],{"class":3323}," mu0",[1115,32808,4220],{"class":3335},[1115,32810,4223],{"class":3327},[1115,32812,32813],{"class":3323}," s",[1115,32815,22944],{"class":3327},[1115,32817,4197],{"class":3331},[1115,32819,1484],{"class":3335},[1115,32821,1287],{"class":3323},[1115,32823,3520],{"class":3335},[1115,32825,32826,32829,32831,32834,32836,32839,32841,32843,32845,32848,32850,32852],{"class":3320,"line":148},[1115,32827,32828],{"class":3323},"t_krit",[1115,32830,3328],{"class":3327},[1115,32832,32833],{"class":3331}," qt",[1115,32835,1484],{"class":3335},[1115,32837,32838],{"class":3343},"0.05",[1115,32840,1405],{"class":3327},[1115,32842,15110],{"class":3323},[1115,32844,3416],{"class":3327},[1115,32846,32847],{"class":3323}," n",[1115,32849,29826],{"class":3327},[1115,32851,4260],{"class":3343},[1115,32853,3520],{"class":3335},[1115,32855,32856],{"class":3320,"line":111},[1115,32857,32858],{"class":3323},"t\n",[1115,32860,32861],{"class":3320,"line":96},[1115,32862,32863],{"class":3323},"t_krit\n",[3311,32865,32868],{"className":32866,"code":32867,"language":3542,"meta":3315},[3540],"[1] -2.385139\n[1] -1.729133\n",[3087,32869,32867],{"__ignoreMap":3315},[1110,32871,32872],{},[4002,32873],{"alt":32874,"className":32875,"src":32876},"mask-th-t-jednostranny",[1321,4006],"\u002Fwiki-assets\u002Fmask-th-t-jednostranny.png",[1110,32878,32879,32880,1567],{},"Další dva příklady mají k dispozici surová data, takže je lze otestovat přímo ",[3087,32881,32318],{},[1110,32883,32884,32887],{},[1131,32885,32886],{},"Životnost baterií."," Výrobce udává průměrnou životnost 10 hodin, na 11 bateriích byly naměřeny hodnoty v hodinách.",[3311,32889,32891],{"className":3313,"code":32890,"language":71,"meta":3315,"style":3315},"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",[3087,32892,32893,32956],{"__ignoreMap":3315},[1115,32894,32895,32898,32900,32902,32904,32907,32909,32912,32914,32917,32919,32922,32924,32927,32929,32932,32934,32936,32938,32941,32943,32945,32947,32950,32952,32954],{"class":3320,"line":10},[1115,32896,32897],{"class":3323},"x2",[1115,32899,3328],{"class":3327},[1115,32901,3454],{"class":3331},[1115,32903,1484],{"class":3335},[1115,32905,32906],{"class":3343},"9.5",[1115,32908,1405],{"class":3327},[1115,32910,32911],{"class":3343}," 10.5",[1115,32913,1405],{"class":3327},[1115,32915,32916],{"class":3343}," 8.9",[1115,32918,1405],{"class":3327},[1115,32920,32921],{"class":3343}," 9.2",[1115,32923,1405],{"class":3327},[1115,32925,32926],{"class":3343}," 10.0",[1115,32928,1405],{"class":3327},[1115,32930,32931],{"class":3343}," 8.5",[1115,32933,1405],{"class":3327},[1115,32935,32921],{"class":3343},[1115,32937,1405],{"class":3327},[1115,32939,32940],{"class":3343}," 8.8",[1115,32942,1405],{"class":3327},[1115,32944,32926],{"class":3343},[1115,32946,1405],{"class":3327},[1115,32948,32949],{"class":3343}," 9.5",[1115,32951,1405],{"class":3327},[1115,32953,32921],{"class":3343},[1115,32955,3520],{"class":3335},[1115,32957,32958,32960,32962,32964,32966,32968,32970,32972,32974,32976,32978,32980],{"class":3320,"line":27},[1115,32959,32383],{"class":3331},[1115,32961,1484],{"class":3335},[1115,32963,32897],{"class":3323},[1115,32965,1405],{"class":3327},[1115,32967,29886],{"class":3323},[1115,32969,3416],{"class":3327},[1115,32971,13778],{"class":3343},[1115,32973,1405],{"class":3327},[1115,32975,32400],{"class":3323},[1115,32977,3416],{"class":3327},[1115,32979,32405],{"class":3459},[1115,32981,3520],{"class":3335},[3311,32983,32986],{"className":32984,"code":32985,"language":3542,"meta":3315},[3540],"    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",[3087,32987,32985],{"__ignoreMap":3315},[1110,32989,32990,33013],{},[1115,32991,32993],{"className":32992},[1144],[1146,32994,32995],{"xmlns":1148},[1150,32996,32997,33010],{},[1153,32998,32999,33001,33003,33006,33008],{},[1159,33000,1110],{},[1289,33002,1591],{},[1163,33004,33005],{},"0,006548",[1289,33007,3951],{},[1163,33009,3603],{},[1167,33011,33012],{"encoding":1169},"p = 0{,}006548 \u003C 0{,}05",": skutečná životnost se od deklarovaných 10 hodin statisticky významně liší (baterie vydrží méně).",[1110,33015,33016,33019],{},[1131,33017,33018],{},"Odpad materiálu."," Na deseti obráběných kusech byl naměřen odpad materiálu v procentech; testuje se rozdíl proti 4 % a zároveň normalita dat.",[3311,33021,33023],{"className":3313,"code":33022,"language":71,"meta":3315,"style":3315},"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",[3087,33024,33025,33076,33102],{"__ignoreMap":3315},[1115,33026,33027,33030,33032,33034,33036,33038,33040,33042,33044,33046,33048,33050,33052,33054,33056,33058,33060,33062,33064,33066,33068,33070,33072,33074],{"class":3320,"line":10},[1115,33028,33029],{"class":3323},"x3",[1115,33031,3328],{"class":3327},[1115,33033,3454],{"class":3331},[1115,33035,1484],{"class":3335},[1115,33037,16289],{"class":3343},[1115,33039,1405],{"class":3327},[1115,33041,16294],{"class":3343},[1115,33043,1405],{"class":3327},[1115,33045,16299],{"class":3343},[1115,33047,1405],{"class":3327},[1115,33049,16304],{"class":3343},[1115,33051,1405],{"class":3327},[1115,33053,16299],{"class":3343},[1115,33055,1405],{"class":3327},[1115,33057,16299],{"class":3343},[1115,33059,1405],{"class":3327},[1115,33061,16317],{"class":3343},[1115,33063,1405],{"class":3327},[1115,33065,16322],{"class":3343},[1115,33067,1405],{"class":3327},[1115,33069,16294],{"class":3343},[1115,33071,1405],{"class":3327},[1115,33073,16294],{"class":3343},[1115,33075,3520],{"class":3335},[1115,33077,33078,33080,33082,33084,33086,33088,33090,33092,33094,33096,33098,33100],{"class":3320,"line":27},[1115,33079,32383],{"class":3331},[1115,33081,1484],{"class":3335},[1115,33083,33029],{"class":3323},[1115,33085,1405],{"class":3327},[1115,33087,29886],{"class":3323},[1115,33089,3416],{"class":3327},[1115,33091,3419],{"class":3343},[1115,33093,1405],{"class":3327},[1115,33095,32400],{"class":3323},[1115,33097,3416],{"class":3327},[1115,33099,32405],{"class":3459},[1115,33101,3520],{"class":3335},[1115,33103,33104,33106,33108,33110],{"class":3320,"line":148},[1115,33105,21880],{"class":3331},[1115,33107,1484],{"class":3335},[1115,33109,33029],{"class":3323},[1115,33111,3520],{"class":3335},[3311,33113,33116],{"className":33114,"code":33115,"language":3542,"meta":3315},[3540],"    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",[3087,33117,33115],{"__ignoreMap":3315},[1110,33119,33120,33143,33144,33167],{},[1115,33121,33123],{"className":33122},[1144],[1146,33124,33125],{"xmlns":1148},[1150,33126,33127,33140],{},[1153,33128,33129,33131,33133,33136,33138],{},[1159,33130,1110],{},[1289,33132,1591],{},[1163,33134,33135],{},"0,0343",[1289,33137,3951],{},[1163,33139,3603],{},[1167,33141,33142],{"encoding":1169},"p = 0{,}0343 \u003C 0{,}05",": průměrný odpad se od 4 % statisticky významně liší (výběrový průměr 3,86 %). Shapiro-Wilkův test dává ",[1115,33145,33147],{"className":33146},[1144],[1146,33148,33149],{"xmlns":1148},[1150,33150,33151,33164],{},[1153,33152,33153,33155,33157,33160,33162],{},[1159,33154,1110],{},[1289,33156,1591],{},[1163,33158,33159],{},"0,4634",[1289,33161,1291],{},[1163,33163,3603],{},[1167,33165,33166],{"encoding":1169},"p = 0{,}4634 > 0{,}05",", předpoklad normality pro t-test je v pořádku.",[1310,33169,33171],{"id":33170},"párový-t-test","Párový t-test",[1110,33173,33174,33175,33205,33206,11080,33240,33278,33279,33292,33293,5360,33311,33331,33332,33349,33350,31894],{},"Používá se, když jsou měření závislá — na stejných objektech se měří dvě hodnoty ",[1115,33176,33178],{"className":33177},[1144],[1146,33179,33180],{"xmlns":1148},[1150,33181,33182,33202],{},[1153,33183,33184,33186,33192,33194,33200],{},[1289,33185,1484],{"stretchy":1483},[1156,33187,33188,33190],{},[1159,33189,11031],{},[1159,33191,1487],{},[1289,33193,1405],{"separator":1121},[1156,33195,33196,33198],{},[1159,33197,11387],{},[1159,33199,1487],{},[1289,33201,1495],{"stretchy":1483},[1167,33203,33204],{"encoding":1169},"(X_i, Y_i)"," a vyhodnocují se jejich diference ",[1115,33207,33209],{"className":33208},[1144],[1146,33210,33211],{"xmlns":1148},[1150,33212,33213,33237],{},[1153,33214,33215,33221,33223,33229,33231],{},[1156,33216,33217,33219],{},[1159,33218,12453],{},[1159,33220,1487],{},[1289,33222,1591],{},[1156,33224,33225,33227],{},[1159,33226,11031],{},[1159,33228,1487],{},[1289,33230,2681],{},[1156,33232,33233,33235],{},[1159,33234,11387],{},[1159,33236,1487],{},[1167,33238,33239],{"encoding":1169},"D_i = X_i - Y_i",[1115,33241,33243],{"className":33242},[1144],[1146,33244,33245],{"xmlns":1148},[1150,33246,33247,33275],{},[1153,33248,33249,33251,33253,33255,33257,33263,33265,33273],{},[1159,33250,12453],{},[1289,33252,13484],{},[1159,33254,11185],{},[1289,33256,1484],{"stretchy":1483},[1156,33258,33259,33261],{},[1159,33260,11190],{},[1159,33262,12453],{},[1289,33264,1405],{"separator":1121},[2970,33266,33267,33269,33271],{},[1159,33268,11198],{},[1159,33270,12453],{},[1163,33272,1189],{},[1289,33274,1495],{"stretchy":1483},[1167,33276,33277],{"encoding":1169},"D \\sim N(\\mu_D, \\sigma_D^2)",". Z ",[1115,33280,33282],{"className":33281},[1144],[1146,33283,33284],{"xmlns":1148},[1150,33285,33286,33290],{},[1153,33287,33288],{},[1159,33289,1287],{},[1167,33291,1287],{"encoding":1169}," dvojic se určí ",[1115,33294,33296],{"className":33295},[1144],[1146,33297,33298],{"xmlns":1148},[1150,33299,33300,33308],{},[1153,33301,33302],{},[2339,33303,33304,33306],{"accent":1121},[1159,33305,12096],{},[1289,33307,15762],{},[1167,33309,33310],{"encoding":1169},"\\bar{d}",[1115,33312,33314],{"className":33313},[1144],[1146,33315,33316],{"xmlns":1148},[1150,33317,33318,33328],{},[1153,33319,33320],{},[2970,33321,33322,33324,33326],{},[1159,33323,1463],{},[1159,33325,12096],{},[1163,33327,1189],{},[1167,33329,33330],{"encoding":1169},"s_d^2","; testuje se vztah mezi zvoleným číslem ",[1115,33333,33335],{"className":33334},[1144],[1146,33336,33337],{"xmlns":1148},[1150,33338,33339,33347],{},[1153,33340,33341],{},[1156,33342,33343,33345],{},[1159,33344,11190],{},[1163,33346,1165],{},[1167,33348,31879],{"encoding":1169}," (obvykle 0) a ",[1115,33351,33353],{"className":33352},[1144],[1146,33354,33355],{"xmlns":1148},[1150,33356,33357,33365],{},[1153,33358,33359],{},[1156,33360,33361,33363],{},[1159,33362,11190],{},[1159,33364,12453],{},[1167,33366,33367],{"encoding":1169},"\\mu_D",[1115,33369,33371],{"className":33370},[1144],[1146,33372,33373],{"xmlns":1148,"display":1573},[1150,33374,33375,33425],{},[1153,33376,33377,33379,33381,33405,33409,33411,33423],{},[1159,33378,11401],{},[1289,33380,1591],{},[2355,33382,33383,33399],{},[1153,33384,33385,33391,33393],{},[2339,33386,33387,33389],{"accent":1121},[1159,33388,12096],{},[1289,33390,15762],{},[1289,33392,2681],{},[1156,33394,33395,33397],{},[1159,33396,11190],{},[1163,33398,1165],{},[1156,33400,33401,33403],{},[1159,33402,1463],{},[1159,33404,12096],{},[4072,33406,33407],{},[1159,33408,1287],{},[1289,33410,13484],{},[1156,33412,33413,33415],{},[1159,33414,11443],{},[1153,33416,33417,33419,33421],{},[1159,33418,1287],{},[1289,33420,2681],{},[1163,33422,1402],{},[1159,33424,1269],{"mathvariant":1734},[1167,33426,33427],{"encoding":1169},"T = \\frac{\\bar{d} - \\mu_0}{s_d}\\sqrt{n} \\sim t_{n-1}.",[1710,33429,33430,33487],{},[1713,33431,33432],{},[1716,33433,33434,33453,33472],{},[1719,33435,33436],{},[1115,33437,33439],{"className":33438},[1144],[1146,33440,33441],{"xmlns":1148},[1150,33442,33443,33451],{},[1153,33444,33445],{},[1156,33446,33447,33449],{},[1159,33448,1161],{},[1163,33450,1165],{},[1167,33452,1170],{"encoding":1169},[1719,33454,33455],{},[1115,33456,33458],{"className":33457},[1144],[1146,33459,33460],{"xmlns":1148},[1150,33461,33462,33470],{},[1153,33463,33464],{},[1156,33465,33466,33468],{},[1159,33467,1161],{},[1163,33469,1402],{},[1167,33471,2613],{"encoding":1169},[1719,33473,32017,33474],{},[1115,33475,33477],{"className":33476},[1144],[1146,33478,33479],{"xmlns":1148},[1150,33480,33481,33485],{},[1153,33482,33483],{},[1159,33484,1205],{},[1167,33486,1205],{"encoding":1169},[1828,33488,33489,33586,33691],{},[1716,33490,33491,33519,33547],{},[1833,33492,33493],{},[1115,33494,33496],{"className":33495},[1144],[1146,33497,33498],{"xmlns":1148},[1150,33499,33500,33516],{},[1153,33501,33502,33508,33510],{},[1156,33503,33504,33506],{},[1159,33505,11190],{},[1159,33507,12453],{},[1289,33509,11034],{},[1156,33511,33512,33514],{},[1159,33513,11190],{},[1163,33515,1165],{},[1167,33517,33518],{"encoding":1169},"\\mu_D \\le \\mu_0",[1833,33520,33521],{},[1115,33522,33524],{"className":33523},[1144],[1146,33525,33526],{"xmlns":1148},[1150,33527,33528,33544],{},[1153,33529,33530,33536,33538],{},[1156,33531,33532,33534],{},[1159,33533,11190],{},[1159,33535,12453],{},[1289,33537,1291],{},[1156,33539,33540,33542],{},[1159,33541,11190],{},[1163,33543,1165],{},[1167,33545,33546],{"encoding":1169},"\\mu_D > \\mu_0",[1833,33548,33549],{},[1115,33550,33552],{"className":33551},[1144],[1146,33553,33554],{"xmlns":1148},[1150,33555,33556,33584],{},[1153,33557,33558,33560,33562,33574,33576,33578,33580,33582],{},[1159,33559,11443],{},[1289,33561,2968],{},[1156,33563,33564,33566],{},[1159,33565,11443],{},[1153,33567,33568,33570,33572],{},[1163,33569,1402],{},[1289,33571,2681],{},[1159,33573,2982],{},[1289,33575,1484],{"stretchy":1483},[1159,33577,1287],{},[1289,33579,2681],{},[1163,33581,1402],{},[1289,33583,1495],{"stretchy":1483},[1167,33585,32122],{"encoding":1169},[1716,33587,33588,33616,33644],{},[1833,33589,33590],{},[1115,33591,33593],{"className":33592},[1144],[1146,33594,33595],{"xmlns":1148},[1150,33596,33597,33613],{},[1153,33598,33599,33605,33607],{},[1156,33600,33601,33603],{},[1159,33602,11190],{},[1159,33604,12453],{},[1289,33606,1591],{},[1156,33608,33609,33611],{},[1159,33610,11190],{},[1163,33612,1165],{},[1167,33614,33615],{"encoding":1169},"\\mu_D = \\mu_0",[1833,33617,33618],{},[1115,33619,33621],{"className":33620},[1144],[1146,33622,33623],{"xmlns":1148},[1150,33624,33625,33641],{},[1153,33626,33627,33633,33635],{},[1156,33628,33629,33631],{},[1159,33630,11190],{},[1159,33632,12453],{},[1289,33634,15257],{"mathvariant":1734},[1156,33636,33637,33639],{},[1159,33638,11190],{},[1163,33640,1165],{},[1167,33642,33643],{"encoding":1169},"\\mu_D \\neq \\mu_0",[1833,33645,33646],{},[1115,33647,33649],{"className":33648},[1144],[1146,33650,33651],{"xmlns":1148},[1150,33652,33653,33689],{},[1153,33654,33655,33657,33659,33661,33663,33679,33681,33683,33685,33687],{},[1289,33656,27329],{"stretchy":1483},[1159,33658,11443],{},[1289,33660,27329],{"stretchy":1483},[1289,33662,2968],{},[1156,33664,33665,33667],{},[1159,33666,11443],{},[1153,33668,33669,33671,33673,33675,33677],{},[1163,33670,1402],{},[1289,33672,2681],{},[1159,33674,2982],{},[1159,33676,4223],{"mathvariant":1734},[1163,33678,1189],{},[1289,33680,1484],{"stretchy":1483},[1159,33682,1287],{},[1289,33684,2681],{},[1163,33686,1402],{},[1289,33688,1495],{"stretchy":1483},[1167,33690,32220],{"encoding":1169},[1716,33692,33693,33721,33749],{},[1833,33694,33695],{},[1115,33696,33698],{"className":33697},[1144],[1146,33699,33700],{"xmlns":1148},[1150,33701,33702,33718],{},[1153,33703,33704,33710,33712],{},[1156,33705,33706,33708],{},[1159,33707,11190],{},[1159,33709,12453],{},[1289,33711,2968],{},[1156,33713,33714,33716],{},[1159,33715,11190],{},[1163,33717,1165],{},[1167,33719,33720],{"encoding":1169},"\\mu_D \\ge \\mu_0",[1833,33722,33723],{},[1115,33724,33726],{"className":33725},[1144],[1146,33727,33728],{"xmlns":1148},[1150,33729,33730,33746],{},[1153,33731,33732,33738,33740],{},[1156,33733,33734,33736],{},[1159,33735,11190],{},[1159,33737,12453],{},[1289,33739,3951],{},[1156,33741,33742,33744],{},[1159,33743,11190],{},[1163,33745,1165],{},[1167,33747,33748],{"encoding":1169},"\\mu_D \u003C \\mu_0",[1833,33750,33751],{},[1115,33752,33754],{"className":33753},[1144],[1146,33755,33756],{"xmlns":1148},[1150,33757,33758,33788],{},[1153,33759,33760,33762,33764,33766,33778,33780,33782,33784,33786],{},[1159,33761,11443],{},[1289,33763,11034],{},[1289,33765,2681],{},[1156,33767,33768,33770],{},[1159,33769,11443],{},[1153,33771,33772,33774,33776],{},[1163,33773,1402],{},[1289,33775,2681],{},[1159,33777,2982],{},[1289,33779,1484],{"stretchy":1483},[1159,33781,1287],{},[1289,33783,2681],{},[1163,33785,1402],{},[1289,33787,1495],{"stretchy":1483},[1167,33789,32312],{"encoding":1169},[1103,33791,33793,33800,33942,34006,34092],{"className":33792,"dataCallout":3094},[1106,3093],[1110,33794,33796,33799],{"className":33795},[1113],[1115,33797],{"className":33798,"ariaHidden":1121},[1118,3101,1120],"Příklad: Snížení spotřeby paliva aditivem",[1110,33801,33802,33803,33821,33822,33840,33841,33859,33860,33893,33894,33917,33918,33941],{},"U ",[1115,33804,33806],{"className":33805},[1144],[1146,33807,33808],{"xmlns":1148},[1150,33809,33810,33818],{},[1153,33811,33812,33814,33816],{},[1159,33813,1287],{},[1289,33815,1591],{},[1163,33817,13334],{},[1167,33819,33820],{"encoding":1169},"n = 10"," vozů se změřila spotřeba před přidáním aditiva (",[1115,33823,33825],{"className":33824},[1144],[1146,33826,33827],{"xmlns":1148},[1150,33828,33829,33837],{},[1153,33830,33831],{},[1156,33832,33833,33835],{},[1159,33834,11031],{},[1159,33836,1487],{},[1167,33838,33839],{"encoding":1169},"X_i",") a po něm (",[1115,33842,33844],{"className":33843},[1144],[1146,33845,33846],{"xmlns":1148},[1150,33847,33848,33856],{},[1153,33849,33850],{},[1156,33851,33852,33854],{},[1159,33853,11387],{},[1159,33855,1487],{},[1167,33857,33858],{"encoding":1169},"Y_i","), diference ",[1115,33861,33863],{"className":33862},[1144],[1146,33864,33865],{"xmlns":1148},[1150,33866,33867,33891],{},[1153,33868,33869,33875,33877,33883,33885],{},[1156,33870,33871,33873],{},[1159,33872,12453],{},[1159,33874,1487],{},[1289,33876,1591],{},[1156,33878,33879,33881],{},[1159,33880,11031],{},[1159,33882,1487],{},[1289,33884,2681],{},[1156,33886,33887,33889],{},[1159,33888,11387],{},[1159,33890,1487],{},[1167,33892,33239],{"encoding":1169}," představují úsporu paliva. Z dat vyšla průměrná úspora ",[1115,33895,33897],{"className":33896},[1144],[1146,33898,33899],{"xmlns":1148},[1150,33900,33901,33914],{},[1153,33902,33903,33909,33911],{},[2339,33904,33905,33907],{"accent":1121},[1159,33906,12096],{},[1289,33908,15762],{},[1289,33910,1591],{},[1163,33912,33913],{},"0,4",[1167,33915,33916],{"encoding":1169},"\\bar{d} = 0{,}4"," l\u002F100 km, ",[1115,33919,33921],{"className":33920},[1144],[1146,33922,33923],{"xmlns":1148},[1150,33924,33925,33938],{},[1153,33926,33927,33933,33935],{},[1156,33928,33929,33931],{},[1159,33930,1463],{},[1159,33932,12096],{},[1289,33934,1591],{},[1163,33936,33937],{},"0,35",[1167,33939,33940],{"encoding":1169},"s_d = 0{,}35"," l\u002F100 km. Ověřte, že aditivum spotřebu statisticky významně snižuje.",[1110,33943,33944,33974,33975,34005],{},[1115,33945,33947],{"className":33946},[1144],[1146,33948,33949],{"xmlns":1148},[1150,33950,33951,33971],{},[1153,33952,33953,33959,33961,33967,33969],{},[1156,33954,33955,33957],{},[1159,33956,1161],{},[1163,33958,1165],{},[1289,33960,1567],{},[1156,33962,33963,33965],{},[1159,33964,11190],{},[1159,33966,12453],{},[1289,33968,11034],{},[1163,33970,1165],{},[1167,33972,33973],{"encoding":1169},"H_0: \\mu_D \\le 0"," (aditivum nemá vliv nebo spotřebu zvyšuje), ",[1115,33976,33978],{"className":33977},[1144],[1146,33979,33980],{"xmlns":1148},[1150,33981,33982,34002],{},[1153,33983,33984,33990,33992,33998,34000],{},[1156,33985,33986,33988],{},[1159,33987,1161],{},[1163,33989,1402],{},[1289,33991,1567],{},[1156,33993,33994,33996],{},[1159,33995,11190],{},[1159,33997,12453],{},[1289,33999,1291],{},[1163,34001,1165],{},[1167,34003,34004],{"encoding":1169},"H_1: \\mu_D > 0"," (aditivum spotřebu snižuje).",[1110,34007,34008],{},[1115,34009,34011],{"className":34010},[1144],[1146,34012,34013],{"xmlns":1148},[1150,34014,34015,34089],{},[1153,34016,34017,34019,34021,34033,34037,34039,34042,34044,34046,34048,34050,34052,34054,34056,34068,34070,34072,34074,34076,34078,34080,34082,34084,34087],{},[1159,34018,11443],{},[1289,34020,1591],{},[2355,34022,34023,34031],{},[1153,34024,34025,34027,34029],{},[1163,34026,33913],{},[1289,34028,2681],{},[1163,34030,1165],{},[1163,34032,33937],{},[4072,34034,34035],{},[1163,34036,13334],{},[1289,34038,1591],{},[1163,34040,34041],{},"3,614",[1289,34043,1405],{"separator":1121},[1621,34045],{"width":1623},[1159,34047,1205],{},[1289,34049,1591],{},[1289,34051,2951],{"stretchy":1483},[1159,34053,11443],{},[1289,34055,2968],{},[1156,34057,34058,34060],{},[1159,34059,11443],{},[1153,34061,34062,34064,34066],{},[1163,34063,1165],{},[1289,34065,1405],{"separator":1121},[1163,34067,26103],{},[1289,34069,1484],{"stretchy":1483},[1163,34071,3212],{},[1289,34073,1495],{"stretchy":1483},[1289,34075,3011],{"stretchy":1483},[1289,34077,1591],{},[1289,34079,2951],{"stretchy":1483},[1159,34081,11443],{},[1289,34083,2968],{},[1163,34085,34086],{},"1,833",[1289,34088,3011],{"stretchy":1483},[1167,34090,34091],{"encoding":1169},"t = \\frac{0{,}4 - 0}{0{,}35}\\sqrt{10} = 3{,}614, \\qquad W = \\{t \\ge t_{0,95}(9)\\} = \\{t \\ge 1{,}833\\}",[1110,34093,32703,34094,5626,34111,34128],{},[1115,34095,34097],{"className":34096},[1144],[1146,34098,34099],{"xmlns":1148},[1150,34100,34101,34109],{},[1153,34102,34103,34105,34107],{},[1159,34104,11443],{},[1289,34106,11318],{},[1159,34108,1205],{},[1167,34110,32721],{"encoding":1169},[1115,34112,34114],{"className":34113},[1144],[1146,34115,34116],{"xmlns":1148},[1150,34117,34118,34126],{},[1153,34119,34120],{},[1156,34121,34122,34124],{},[1159,34123,1161],{},[1163,34125,1165],{},[1167,34127,1170],{"encoding":1169},": aditivum prokazatelně snižuje průměrnou spotřebu paliva.",[3311,34130,34132],{"className":3313,"code":34131,"language":71,"meta":3315,"style":3315},"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",[3087,34133,34134,34163,34194,34220,34224],{"__ignoreMap":3315},[1115,34135,34136,34139,34141,34144,34146,34149,34151,34154,34156,34158,34160],{"class":3320,"line":10},[1115,34137,34138],{"class":3323},"dbar",[1115,34140,3328],{"class":3327},[1115,34142,34143],{"class":3343}," 0.4",[1115,34145,29489],{"class":3335},[1115,34147,34148],{"class":3323},"sd_d",[1115,34150,3328],{"class":3327},[1115,34152,34153],{"class":3343}," 0.35",[1115,34155,29489],{"class":3335},[1115,34157,1287],{"class":3323},[1115,34159,3328],{"class":3327},[1115,34161,34162],{"class":3343}," 10\n",[1115,34164,34165,34167,34169,34171,34173,34175,34177,34179,34181,34184,34186,34188,34190,34192],{"class":3320,"line":27},[1115,34166,11443],{"class":3323},[1115,34168,3328],{"class":3327},[1115,34170,4226],{"class":3335},[1115,34172,34138],{"class":3323},[1115,34174,29826],{"class":3327},[1115,34176,14271],{"class":3343},[1115,34178,4220],{"class":3335},[1115,34180,4223],{"class":3327},[1115,34182,34183],{"class":3323}," sd_d",[1115,34185,22944],{"class":3327},[1115,34187,4197],{"class":3331},[1115,34189,1484],{"class":3335},[1115,34191,1287],{"class":3323},[1115,34193,3520],{"class":3335},[1115,34195,34196,34198,34200,34202,34204,34206,34208,34210,34212,34214,34216,34218],{"class":3320,"line":148},[1115,34197,32828],{"class":3323},[1115,34199,3328],{"class":3327},[1115,34201,32833],{"class":3331},[1115,34203,1484],{"class":3335},[1115,34205,15127],{"class":3343},[1115,34207,1405],{"class":3327},[1115,34209,15110],{"class":3323},[1115,34211,3416],{"class":3327},[1115,34213,32847],{"class":3323},[1115,34215,29826],{"class":3327},[1115,34217,4260],{"class":3343},[1115,34219,3520],{"class":3335},[1115,34221,34222],{"class":3320,"line":111},[1115,34223,32858],{"class":3323},[1115,34225,34226],{"class":3320,"line":96},[1115,34227,32863],{"class":3323},[3311,34229,34232],{"className":34230,"code":34231,"language":3542,"meta":3315},[3540],"[1] 3.614032\n[1] 1.833113\n",[3087,34233,34231],{"__ignoreMap":3315},[1103,34235,34237,34244,34247,34392,34398],{"className":34236,"dataCallout":6032},[1106,6031],[1110,34238,34240,34243],{"className":34239},[1113],[1115,34241],{"className":34242,"ariaHidden":1121},[1118,6039,1120],"Ověřte normalitu diferencí, ne jen výsledek testu",[1110,34245,34246],{},"Realitní kancelář nechala dva odhadce ocenit osm nemovitostí (tisíce Kč):",[3311,34248,34250],{"className":3313,"code":34249,"language":71,"meta":3315,"style":3315},"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",[3087,34251,34252,34303,34354,34378],{"__ignoreMap":3315},[1115,34253,34254,34257,34259,34261,34263,34266,34268,34271,34273,34276,34278,34281,34283,34286,34288,34291,34293,34296,34298,34301],{"class":3320,"line":10},[1115,34255,34256],{"class":3323},"estA",[1115,34258,3328],{"class":3327},[1115,34260,3454],{"class":3331},[1115,34262,1484],{"class":3335},[1115,34264,34265],{"class":3343},"3282",[1115,34267,1405],{"class":3327},[1115,34269,34270],{"class":3343}," 2506",[1115,34272,1405],{"class":3327},[1115,34274,34275],{"class":3343}," 2812",[1115,34277,1405],{"class":3327},[1115,34279,34280],{"class":3343}," 5453",[1115,34282,1405],{"class":3327},[1115,34284,34285],{"class":3343}," 3263",[1115,34287,1405],{"class":3327},[1115,34289,34290],{"class":3343}," 4571",[1115,34292,1405],{"class":3327},[1115,34294,34295],{"class":3343}," 3121",[1115,34297,1405],{"class":3327},[1115,34299,34300],{"class":3343}," 2963",[1115,34302,3520],{"class":3335},[1115,34304,34305,34308,34310,34312,34314,34317,34319,34322,34324,34327,34329,34332,34334,34337,34339,34342,34344,34347,34349,34352],{"class":3320,"line":27},[1115,34306,34307],{"class":3323},"estB",[1115,34309,3328],{"class":3327},[1115,34311,3454],{"class":3331},[1115,34313,1484],{"class":3335},[1115,34315,34316],{"class":3343},"3271",[1115,34318,1405],{"class":3327},[1115,34320,34321],{"class":3343}," 2531",[1115,34323,1405],{"class":3327},[1115,34325,34326],{"class":3343}," 2799",[1115,34328,1405],{"class":3327},[1115,34330,34331],{"class":3343}," 5471",[1115,34333,1405],{"class":3327},[1115,34335,34336],{"class":3343}," 3285",[1115,34338,1405],{"class":3327},[1115,34340,34341],{"class":3343}," 4557",[1115,34343,1405],{"class":3327},[1115,34345,34346],{"class":3343}," 3139",[1115,34348,1405],{"class":3327},[1115,34350,34351],{"class":3343}," 2976",[1115,34353,3520],{"class":3335},[1115,34355,34356,34358,34360,34362,34364,34367,34369,34372,34374,34376],{"class":3320,"line":148},[1115,34357,32383],{"class":3331},[1115,34359,1484],{"class":3335},[1115,34361,34256],{"class":3323},[1115,34363,1405],{"class":3327},[1115,34365,34366],{"class":3323}," estB",[1115,34368,1405],{"class":3327},[1115,34370,34371],{"class":3323}," paired",[1115,34373,3416],{"class":3327},[1115,34375,3429],{"class":3343},[1115,34377,3520],{"class":3335},[1115,34379,34380,34382,34384,34386,34388,34390],{"class":3320,"line":111},[1115,34381,21880],{"class":3331},[1115,34383,1484],{"class":3335},[1115,34385,34256],{"class":3323},[1115,34387,29826],{"class":3327},[1115,34389,34366],{"class":3323},[1115,34391,3520],{"class":3335},[3311,34393,34396],{"className":34394,"code":34395,"language":3542,"meta":3315},[3540],"    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",[3087,34397,34395],{"__ignoreMap":3315},[1110,34399,34400,34401,4226,34418,34437,34438,34461],{},"Párový t-test sám nezamítá ",[1115,34402,34404],{"className":34403},[1144],[1146,34405,34406],{"xmlns":1148},[1150,34407,34408,34416],{},[1153,34409,34410],{},[1156,34411,34412,34414],{},[1159,34413,1161],{},[1163,34415,1165],{},[1167,34417,1170],{"encoding":1169},[1115,34419,34421],{"className":34420},[1144],[1146,34422,34423],{"xmlns":1148},[1150,34424,34425,34434],{},[1153,34426,34427,34429,34431],{},[1159,34428,1110],{},[1289,34430,1591],{},[1163,34432,34433],{},"0,2635",[1167,34435,34436],{"encoding":1169},"p = 0{,}2635","): odhadci se podle něj neliší. Shapiro-Wilkův test na diferencích ale dává ",[1115,34439,34441],{"className":34440},[1144],[1146,34442,34443],{"xmlns":1148},[1150,34444,34445,34458],{},[1153,34446,34447,34449,34451,34454,34456],{},[1159,34448,1110],{},[1289,34450,1591],{},[1163,34452,34453],{},"0,03203",[1289,34455,3951],{},[1163,34457,3603],{},[1167,34459,34460],{"encoding":1169},"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).",[1310,34463,34465],{"id":34464},"testy-o-dvou-základních-souborech","Testy o dvou základních souborech",[1110,34467,34468,34469,34495,34496,34534,34535,5360,34553,34534,34591,34609,34610,5360,34642,34674,34675,34701,34702,1269],{},"Uvažují se dva nezávislé základní soubory ",[1115,34470,34472],{"className":34471},[1144],[1146,34473,34474],{"xmlns":1148},[1150,34475,34476,34492],{},[1153,34477,34478,34484,34486],{},[1156,34479,34480,34482],{},[1159,34481,13226],{},[1163,34483,1402],{},[1289,34485,1405],{"separator":1121},[1156,34487,34488,34490],{},[1159,34489,13226],{},[1163,34491,1189],{},[1167,34493,34494],{"encoding":1169},"Z_1, Z_2"," se znakem ",[1115,34497,34499],{"className":34498},[1144],[1146,34500,34501],{"xmlns":1148},[1150,34502,34503,34531],{},[1153,34504,34505,34507,34509,34511,34513,34519,34521,34529],{},[1159,34506,11031],{},[1289,34508,13484],{},[1159,34510,11185],{},[1289,34512,1484],{"stretchy":1483},[1156,34514,34515,34517],{},[1159,34516,11190],{},[1163,34518,1402],{},[1289,34520,1405],{"separator":1121},[2970,34522,34523,34525,34527],{},[1159,34524,11198],{},[1163,34526,1402],{},[1163,34528,1189],{},[1289,34530,1495],{"stretchy":1483},[1167,34532,34533],{"encoding":1169},"X \\sim N(\\mu_1, \\sigma_1^2)"," v ",[1115,34536,34538],{"className":34537},[1144],[1146,34539,34540],{"xmlns":1148},[1150,34541,34542,34550],{},[1153,34543,34544],{},[1156,34545,34546,34548],{},[1159,34547,13226],{},[1163,34549,1402],{},[1167,34551,34552],{"encoding":1169},"Z_1",[1115,34554,34556],{"className":34555},[1144],[1146,34557,34558],{"xmlns":1148},[1150,34559,34560,34588],{},[1153,34561,34562,34564,34566,34568,34570,34576,34578,34586],{},[1159,34563,11031],{},[1289,34565,13484],{},[1159,34567,11185],{},[1289,34569,1484],{"stretchy":1483},[1156,34571,34572,34574],{},[1159,34573,11190],{},[1163,34575,1189],{},[1289,34577,1405],{"separator":1121},[2970,34579,34580,34582,34584],{},[1159,34581,11198],{},[1163,34583,1189],{},[1163,34585,1189],{},[1289,34587,1495],{"stretchy":1483},[1167,34589,34590],{"encoding":1169},"X \\sim N(\\mu_2, \\sigma_2^2)",[1115,34592,34594],{"className":34593},[1144],[1146,34595,34596],{"xmlns":1148},[1150,34597,34598,34606],{},[1153,34599,34600],{},[1156,34601,34602,34604],{},[1159,34603,13226],{},[1163,34605,1189],{},[1167,34607,34608],{"encoding":1169},"Z_2",". Z výběrů se určí ",[1115,34611,34613],{"className":34612},[1144],[1146,34614,34615],{"xmlns":1148},[1150,34616,34617,34639],{},[1153,34618,34619,34629,34631],{},[1156,34620,34621,34627],{},[2339,34622,34623,34625],{"accent":1121},[1159,34624,11019],{},[1289,34626,15762],{},[1163,34628,1402],{},[1289,34630,1405],{"separator":1121},[2970,34632,34633,34635,34637],{},[1159,34634,1463],{},[1163,34636,1402],{},[1163,34638,1189],{},[1167,34640,34641],{"encoding":1169},"\\bar{x}_1, s_1^2",[1115,34643,34645],{"className":34644},[1144],[1146,34646,34647],{"xmlns":1148},[1150,34648,34649,34671],{},[1153,34650,34651,34661,34663],{},[1156,34652,34653,34659],{},[2339,34654,34655,34657],{"accent":1121},[1159,34656,11019],{},[1289,34658,15762],{},[1163,34660,1189],{},[1289,34662,1405],{"separator":1121},[2970,34664,34665,34667,34669],{},[1159,34666,1463],{},[1163,34668,1189],{},[1163,34670,1189],{},[1167,34672,34673],{"encoding":1169},"\\bar{x}_2, s_2^2",". Testují se varianty vztahů mezi ",[1115,34676,34678],{"className":34677},[1144],[1146,34679,34680],{"xmlns":1148},[1150,34681,34682,34698],{},[1153,34683,34684,34690,34692],{},[1156,34685,34686,34688],{},[1159,34687,11190],{},[1163,34689,1402],{},[1289,34691,1405],{"separator":1121},[1156,34693,34694,34696],{},[1159,34695,11190],{},[1163,34697,1189],{},[1167,34699,34700],{"encoding":1169},"\\mu_1, \\mu_2",", resp. mezi ",[1115,34703,34705],{"className":34704},[1144],[1146,34706,34707],{"xmlns":1148},[1150,34708,34709,34729],{},[1153,34710,34711,34719,34721],{},[2970,34712,34713,34715,34717],{},[1159,34714,11198],{},[1163,34716,1402],{},[1163,34718,1189],{},[1289,34720,1405],{"separator":1121},[2970,34722,34723,34725,34727],{},[1159,34724,11198],{},[1163,34726,1189],{},[1163,34728,1189],{},[1167,34730,34731],{"encoding":1169},"\\sigma_1^2, \\sigma_2^2",[21050,34733,34735],{"id":34734},"f-test-o-rozptylech","F-test o rozptylech",[1110,34737,34738],{},"Statistika",[1115,34740,34742],{"className":34741},[1144],[1146,34743,34744],{"xmlns":1148,"display":1573},[1150,34745,34746,34802],{},[1153,34747,34748,34750,34752,34770,34772],{},[1159,34749,11014],{},[1289,34751,1591],{},[2355,34753,34754,34762],{},[2970,34755,34756,34758,34760],{},[1159,34757,1463],{},[1163,34759,1402],{},[1163,34761,1189],{},[2970,34763,34764,34766,34768],{},[1159,34765,1463],{},[1163,34767,1189],{},[1163,34769,1189],{},[1289,34771,13484],{},[1156,34773,34774,34776],{},[1159,34775,11014],{},[1153,34777,34778,34784,34786,34788,34790,34792,34798,34800],{},[1156,34779,34780,34782],{},[1159,34781,1287],{},[1163,34783,1402],{},[1289,34785,2681],{},[1163,34787,1402],{},[1289,34789,1405],{"separator":1121},[2525,34791,2527],{},[1156,34793,34794,34796],{},[1159,34795,1287],{},[1163,34797,1189],{},[1289,34799,2681],{},[1163,34801,1402],{},[1167,34803,34804],{"encoding":1169},"F = \\frac{s_1^2}{s_2^2} \\sim F_{n_1-1,\\,n_2-1}",[1110,34806,34807,34808,5360,34830,31970],{},"má Fisherovo-Snedecorovo rozdělení o ",[1115,34809,34811],{"className":34810},[1144],[1146,34812,34813],{"xmlns":1148},[1150,34814,34815,34827],{},[1153,34816,34817,34823,34825],{},[1156,34818,34819,34821],{},[1159,34820,1287],{},[1163,34822,1402],{},[1289,34824,2681],{},[1163,34826,1402],{},[1167,34828,34829],{"encoding":1169},"n_1-1",[1115,34831,34833],{"className":34832},[1144],[1146,34834,34835],{"xmlns":1148},[1150,34836,34837,34849],{},[1153,34838,34839,34845,34847],{},[1156,34840,34841,34843],{},[1159,34842,1287],{},[1163,34844,1189],{},[1289,34846,2681],{},[1163,34848,1402],{},[1167,34850,34851],{"encoding":1169},"n_2-1",[1710,34853,34854,34911],{},[1713,34855,34856],{},[1716,34857,34858,34877,34896],{},[1719,34859,34860],{},[1115,34861,34863],{"className":34862},[1144],[1146,34864,34865],{"xmlns":1148},[1150,34866,34867,34875],{},[1153,34868,34869],{},[1156,34870,34871,34873],{},[1159,34872,1161],{},[1163,34874,1165],{},[1167,34876,1170],{"encoding":1169},[1719,34878,34879],{},[1115,34880,34882],{"className":34881},[1144],[1146,34883,34884],{"xmlns":1148},[1150,34885,34886,34894],{},[1153,34887,34888],{},[1156,34889,34890,34892],{},[1159,34891,1161],{},[1163,34893,1402],{},[1167,34895,2613],{"encoding":1169},[1719,34897,32017,34898],{},[1115,34899,34901],{"className":34900},[1144],[1146,34902,34903],{"xmlns":1148},[1150,34904,34905,34909],{},[1153,34906,34907],{},[1159,34908,1205],{},[1167,34910,1205],{"encoding":1169},[1828,34912,34913,35027,35200],{},[1716,34914,34915,34943,34971],{},[1833,34916,34917],{},[1115,34918,34920],{"className":34919},[1144],[1146,34921,34922],{"xmlns":1148},[1150,34923,34924,34940],{},[1153,34925,34926,34932,34934],{},[1156,34927,34928,34930],{},[1159,34929,11198],{},[1163,34931,1402],{},[1289,34933,11034],{},[1156,34935,34936,34938],{},[1159,34937,11198],{},[1163,34939,1189],{},[1167,34941,34942],{"encoding":1169},"\\sigma_1 \\le \\sigma_2",[1833,34944,34945],{},[1115,34946,34948],{"className":34947},[1144],[1146,34949,34950],{"xmlns":1148},[1150,34951,34952,34968],{},[1153,34953,34954,34960,34962],{},[1156,34955,34956,34958],{},[1159,34957,11198],{},[1163,34959,1402],{},[1289,34961,1291],{},[1156,34963,34964,34966],{},[1159,34965,11198],{},[1163,34967,1189],{},[1167,34969,34970],{"encoding":1169},"\\sigma_1 > \\sigma_2",[1833,34972,34973],{},[1115,34974,34976],{"className":34975},[1144],[1146,34977,34978],{"xmlns":1148},[1150,34979,34980,35024],{},[1153,34981,34982,34984,34986,34998,35000,35006,35008,35010,35012,35018,35020,35022],{},[1159,34983,11014],{},[1289,34985,2968],{},[1156,34987,34988,34990],{},[1159,34989,11014],{},[1153,34991,34992,34994,34996],{},[1163,34993,1402],{},[1289,34995,2681],{},[1159,34997,2982],{},[1289,34999,1484],{"stretchy":1483},[1156,35001,35002,35004],{},[1159,35003,1287],{},[1163,35005,1402],{},[1289,35007,2681],{},[1163,35009,1402],{},[1289,35011,1405],{"separator":1121},[1156,35013,35014,35016],{},[1159,35015,1287],{},[1163,35017,1189],{},[1289,35019,2681],{},[1163,35021,1402],{},[1289,35023,1495],{"stretchy":1483},[1167,35025,35026],{"encoding":1169},"F \\ge F_{1-\\alpha}(n_1-1, n_2-1)",[1716,35028,35029,35057,35085],{},[1833,35030,35031],{},[1115,35032,35034],{"className":35033},[1144],[1146,35035,35036],{"xmlns":1148},[1150,35037,35038,35054],{},[1153,35039,35040,35046,35048],{},[1156,35041,35042,35044],{},[1159,35043,11198],{},[1163,35045,1402],{},[1289,35047,1591],{},[1156,35049,35050,35052],{},[1159,35051,11198],{},[1163,35053,1189],{},[1167,35055,35056],{"encoding":1169},"\\sigma_1 = \\sigma_2",[1833,35058,35059],{},[1115,35060,35062],{"className":35061},[1144],[1146,35063,35064],{"xmlns":1148},[1150,35065,35066,35082],{},[1153,35067,35068,35074,35076],{},[1156,35069,35070,35072],{},[1159,35071,11198],{},[1163,35073,1402],{},[1289,35075,15257],{"mathvariant":1734},[1156,35077,35078,35080],{},[1159,35079,11198],{},[1163,35081,1189],{},[1167,35083,35084],{"encoding":1169},"\\sigma_1 \\neq \\sigma_2",[1833,35086,35087,35141,35142],{},[1115,35088,35090],{"className":35089},[1144],[1146,35091,35092],{"xmlns":1148},[1150,35093,35094,35138],{},[1153,35095,35096,35098,35100,35112,35114,35120,35122,35124,35126,35132,35134,35136],{},[1159,35097,11014],{},[1289,35099,11034],{},[1156,35101,35102,35104],{},[1159,35103,11014],{},[1153,35105,35106,35108,35110],{},[1159,35107,2982],{},[1159,35109,4223],{"mathvariant":1734},[1163,35111,1189],{},[1289,35113,1484],{"stretchy":1483},[1156,35115,35116,35118],{},[1159,35117,1287],{},[1163,35119,1402],{},[1289,35121,2681],{},[1163,35123,1402],{},[1289,35125,1405],{"separator":1121},[1156,35127,35128,35130],{},[1159,35129,1287],{},[1163,35131,1189],{},[1289,35133,2681],{},[1163,35135,1402],{},[1289,35137,1495],{"stretchy":1483},[1167,35139,35140],{"encoding":1169},"F \\le F_{\\alpha\u002F2}(n_1-1, n_2-1)"," nebo ",[1115,35143,35145],{"className":35144},[1144],[1146,35146,35147],{"xmlns":1148},[1150,35148,35149,35197],{},[1153,35150,35151,35153,35155,35171,35173,35179,35181,35183,35185,35191,35193,35195],{},[1159,35152,11014],{},[1289,35154,2968],{},[1156,35156,35157,35159],{},[1159,35158,11014],{},[1153,35160,35161,35163,35165,35167,35169],{},[1163,35162,1402],{},[1289,35164,2681],{},[1159,35166,2982],{},[1159,35168,4223],{"mathvariant":1734},[1163,35170,1189],{},[1289,35172,1484],{"stretchy":1483},[1156,35174,35175,35177],{},[1159,35176,1287],{},[1163,35178,1402],{},[1289,35180,2681],{},[1163,35182,1402],{},[1289,35184,1405],{"separator":1121},[1156,35186,35187,35189],{},[1159,35188,1287],{},[1163,35190,1189],{},[1289,35192,2681],{},[1163,35194,1402],{},[1289,35196,1495],{"stretchy":1483},[1167,35198,35199],{"encoding":1169},"F \\ge F_{1-\\alpha\u002F2}(n_1-1, n_2-1)",[1716,35201,35202,35230,35258],{},[1833,35203,35204],{},[1115,35205,35207],{"className":35206},[1144],[1146,35208,35209],{"xmlns":1148},[1150,35210,35211,35227],{},[1153,35212,35213,35219,35221],{},[1156,35214,35215,35217],{},[1159,35216,11198],{},[1163,35218,1402],{},[1289,35220,2968],{},[1156,35222,35223,35225],{},[1159,35224,11198],{},[1163,35226,1189],{},[1167,35228,35229],{"encoding":1169},"\\sigma_1 \\ge \\sigma_2",[1833,35231,35232],{},[1115,35233,35235],{"className":35234},[1144],[1146,35236,35237],{"xmlns":1148},[1150,35238,35239,35255],{},[1153,35240,35241,35247,35249],{},[1156,35242,35243,35245],{},[1159,35244,11198],{},[1163,35246,1402],{},[1289,35248,3951],{},[1156,35250,35251,35253],{},[1159,35252,11198],{},[1163,35254,1189],{},[1167,35256,35257],{"encoding":1169},"\\sigma_1 \u003C \\sigma_2",[1833,35259,35260],{},[1115,35261,35263],{"className":35262},[1144],[1146,35264,35265],{"xmlns":1148},[1150,35266,35267,35305],{},[1153,35268,35269,35271,35273,35279,35281,35287,35289,35291,35293,35299,35301,35303],{},[1159,35270,11014],{},[1289,35272,11034],{},[1156,35274,35275,35277],{},[1159,35276,11014],{},[1159,35278,2982],{},[1289,35280,1484],{"stretchy":1483},[1156,35282,35283,35285],{},[1159,35284,1287],{},[1163,35286,1402],{},[1289,35288,2681],{},[1163,35290,1402],{},[1289,35292,1405],{"separator":1121},[1156,35294,35295,35297],{},[1159,35296,1287],{},[1163,35298,1189],{},[1289,35300,2681],{},[1163,35302,1402],{},[1289,35304,1495],{"stretchy":1483},[1167,35306,35307],{"encoding":1169},"F \\le F_{\\alpha}(n_1-1, n_2-1)",[21050,35309,35311],{"id":35310},"dvouvýběrový-t-test-o-středních-hodnotách","Dvouvýběrový t-test o středních hodnotách",[1110,35313,35314],{},"Volba statistiky závisí na tom, zda jsou rozptyly považovány za shodné:",[1115,35316,35318],{"className":35317},[1144],[1146,35319,35320],{"xmlns":1148,"display":1573},[1150,35321,35322,35499],{},[1153,35323,35324,35330,35332,35408,35456,35458,35460,35469,35471,35477,35479,35485,35487,35493,35495,35497],{},[1156,35325,35326,35328],{},[1159,35327,11401],{},[1163,35329,1402],{},[1289,35331,1591],{},[2355,35333,35334,35358],{},[1153,35335,35336,35346,35348],{},[1156,35337,35338,35344],{},[2339,35339,35340,35342],{"accent":1121},[1159,35341,11019],{},[1289,35343,15762],{},[1163,35345,1402],{},[1289,35347,2681],{},[1156,35349,35350,35356],{},[2339,35351,35352,35354],{"accent":1121},[1159,35353,11019],{},[1289,35355,15762],{},[1163,35357,1189],{},[4072,35359,35360],{},[1153,35361,35362,35364,35370,35372,35374,35376,35384,35386,35388,35394,35396,35398,35400],{},[1289,35363,1484],{"stretchy":1483},[1156,35365,35366,35368],{},[1159,35367,1287],{},[1163,35369,1402],{},[1289,35371,2681],{},[1163,35373,1402],{},[1289,35375,1495],{"stretchy":1483},[2970,35377,35378,35380,35382],{},[1159,35379,1463],{},[1163,35381,1402],{},[1163,35383,1189],{},[1289,35385,5096],{},[1289,35387,1484],{"stretchy":1483},[1156,35389,35390,35392],{},[1159,35391,1287],{},[1163,35393,1189],{},[1289,35395,2681],{},[1163,35397,1402],{},[1289,35399,1495],{"stretchy":1483},[2970,35401,35402,35404,35406],{},[1159,35403,1463],{},[1163,35405,1189],{},[1163,35407,1189],{},[4072,35409,35410],{},[2355,35411,35412,35432],{},[1153,35413,35414,35420,35422,35428,35430],{},[1156,35415,35416,35418],{},[1159,35417,1287],{},[1163,35419,1402],{},[1289,35421,5096],{},[1156,35423,35424,35426],{},[1159,35425,1287],{},[1163,35427,1189],{},[1289,35429,2681],{},[1163,35431,1189],{},[1153,35433,35434,35444,35446],{},[2355,35435,35436,35438],{},[1163,35437,1402],{},[1156,35439,35440,35442],{},[1159,35441,1287],{},[1163,35443,1402],{},[1289,35445,5096],{},[2355,35447,35448,35450],{},[1163,35449,1402],{},[1156,35451,35452,35454],{},[1159,35453,1287],{},[1163,35455,1189],{},[1289,35457,1405],{"separator":1121},[1621,35459],{"width":1623},[2970,35461,35462,35464,35466],{},[1159,35463,11443],{},[1159,35465,1110],{},[1289,35467,35468],{},"∗",[1289,35470,1591],{},[1156,35472,35473,35475],{},[1159,35474,11443],{},[1159,35476,1110],{},[1289,35478,1484],{"stretchy":1483},[1156,35480,35481,35483],{},[1159,35482,1287],{},[1163,35484,1402],{},[1289,35486,5096],{},[1156,35488,35489,35491],{},[1159,35490,1287],{},[1163,35492,1189],{},[1289,35494,2681],{},[1163,35496,1189],{},[1289,35498,1495],{"stretchy":1483},[1167,35500,35501],{"encoding":1169},"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)",[1110,35503,35504,35505,35534],{},"se použije, pokud jsou rozptyly ",[1115,35506,35508],{"className":35507},[1144],[1146,35509,35510],{"xmlns":1148},[1150,35511,35512,35532],{},[1153,35513,35514,35522,35524],{},[2970,35515,35516,35518,35520],{},[1159,35517,11198],{},[1163,35519,1402],{},[1163,35521,1189],{},[1289,35523,1405],{"separator":1121},[2970,35525,35526,35528,35530],{},[1159,35527,11198],{},[1163,35529,1189],{},[1163,35531,1189],{},[1167,35533,34731],{"encoding":1169}," alespoň přibližně shodné; při rozdílných rozptylech",[1115,35536,35538],{"className":35537},[1144],[1146,35539,35540],{"xmlns":1148,"display":1573},[1150,35541,35542,35754],{},[1153,35543,35544,35550,35552,35616,35618,35620,35628,35630,35752],{},[1156,35545,35546,35548],{},[1159,35547,11401],{},[1163,35549,1189],{},[1289,35551,1591],{},[2355,35553,35554,35578],{},[1153,35555,35556,35566,35568],{},[1156,35557,35558,35564],{},[2339,35559,35560,35562],{"accent":1121},[1159,35561,11019],{},[1289,35563,15762],{},[1163,35565,1402],{},[1289,35567,2681],{},[1156,35569,35570,35576],{},[2339,35571,35572,35574],{"accent":1121},[1159,35573,11019],{},[1289,35575,15762],{},[1163,35577,1189],{},[4072,35579,35580],{},[1153,35581,35582,35590,35592,35598,35600,35608,35610],{},[2970,35583,35584,35586,35588],{},[1159,35585,1463],{},[1163,35587,1402],{},[1163,35589,1189],{},[1159,35591,4223],{"mathvariant":1734},[1156,35593,35594,35596],{},[1159,35595,1287],{},[1163,35597,1402],{},[1289,35599,5096],{},[2970,35601,35602,35604,35606],{},[1159,35603,1463],{},[1163,35605,1189],{},[1163,35607,1189],{},[1159,35609,4223],{"mathvariant":1734},[1156,35611,35612,35614],{},[1159,35613,1287],{},[1163,35615,1189],{},[1289,35617,1405],{"separator":1121},[1621,35619],{"width":1623},[2970,35621,35622,35624,35626],{},[1159,35623,11443],{},[1159,35625,1110],{},[1289,35627,35468],{},[1289,35629,1591],{},[2355,35631,35632,35712],{},[1153,35633,35634,35652,35658,35660,35666,35668,35670,35672,35674,35692,35698,35700,35706,35708,35710],{},[2858,35635,35636],{"scriptlevel":1165,"displaystyle":1121},[2355,35637,35638,35646],{},[2970,35639,35640,35642,35644],{},[1159,35641,1463],{},[1163,35643,1402],{},[1163,35645,1189],{},[1156,35647,35648,35650],{},[1159,35649,1287],{},[1163,35651,1402],{},[1156,35653,35654,35656],{},[1159,35655,11443],{},[1159,35657,1110],{},[1289,35659,1484],{"stretchy":1483},[1156,35661,35662,35664],{},[1159,35663,1287],{},[1163,35665,1402],{},[1289,35667,2681],{},[1163,35669,1402],{},[1289,35671,1495],{"stretchy":1483},[1289,35673,5096],{},[2858,35675,35676],{"scriptlevel":1165,"displaystyle":1121},[2355,35677,35678,35686],{},[2970,35679,35680,35682,35684],{},[1159,35681,1463],{},[1163,35683,1189],{},[1163,35685,1189],{},[1156,35687,35688,35690],{},[1159,35689,1287],{},[1163,35691,1189],{},[1156,35693,35694,35696],{},[1159,35695,11443],{},[1159,35697,1110],{},[1289,35699,1484],{"stretchy":1483},[1156,35701,35702,35704],{},[1159,35703,1287],{},[1163,35705,1189],{},[1289,35707,2681],{},[1163,35709,1402],{},[1289,35711,1495],{"stretchy":1483},[1153,35713,35714,35732,35734],{},[2858,35715,35716],{"scriptlevel":1165,"displaystyle":1121},[2355,35717,35718,35726],{},[2970,35719,35720,35722,35724],{},[1159,35721,1463],{},[1163,35723,1402],{},[1163,35725,1189],{},[1156,35727,35728,35730],{},[1159,35729,1287],{},[1163,35731,1402],{},[1289,35733,5096],{},[2858,35735,35736],{"scriptlevel":1165,"displaystyle":1121},[2355,35737,35738,35746],{},[2970,35739,35740,35742,35744],{},[1159,35741,1463],{},[1163,35743,1189],{},[1163,35745,1189],{},[1156,35747,35748,35750],{},[1159,35749,1287],{},[1163,35751,1189],{},[1159,35753,1269],{"mathvariant":1734},[1167,35755,35756],{"encoding":1169},"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}}.",[1710,35758,35759,35816],{},[1713,35760,35761],{},[1716,35762,35763,35782,35801],{},[1719,35764,35765],{},[1115,35766,35768],{"className":35767},[1144],[1146,35769,35770],{"xmlns":1148},[1150,35771,35772,35780],{},[1153,35773,35774],{},[1156,35775,35776,35778],{},[1159,35777,1161],{},[1163,35779,1165],{},[1167,35781,1170],{"encoding":1169},[1719,35783,35784],{},[1115,35785,35787],{"className":35786},[1144],[1146,35788,35789],{"xmlns":1148},[1150,35790,35791,35799],{},[1153,35792,35793],{},[1156,35794,35795,35797],{},[1159,35796,1161],{},[1163,35798,1402],{},[1167,35800,2613],{"encoding":1169},[1719,35802,32017,35803],{},[1115,35804,35806],{"className":35805},[1144],[1146,35807,35808],{"xmlns":1148},[1150,35809,35810,35814],{},[1153,35811,35812],{},[1159,35813,1205],{},[1167,35815,1205],{"encoding":1169},[1828,35817,35818,35902,35990],{},[1716,35819,35820,35848,35876],{},[1833,35821,35822],{},[1115,35823,35825],{"className":35824},[1144],[1146,35826,35827],{"xmlns":1148},[1150,35828,35829,35845],{},[1153,35830,35831,35837,35839],{},[1156,35832,35833,35835],{},[1159,35834,11190],{},[1163,35836,1402],{},[1289,35838,11034],{},[1156,35840,35841,35843],{},[1159,35842,11190],{},[1163,35844,1189],{},[1167,35846,35847],{"encoding":1169},"\\mu_1 \\le \\mu_2",[1833,35849,35850],{},[1115,35851,35853],{"className":35852},[1144],[1146,35854,35855],{"xmlns":1148},[1150,35856,35857,35873],{},[1153,35858,35859,35865,35867],{},[1156,35860,35861,35863],{},[1159,35862,11190],{},[1163,35864,1402],{},[1289,35866,1291],{},[1156,35868,35869,35871],{},[1159,35870,11190],{},[1163,35872,1189],{},[1167,35874,35875],{"encoding":1169},"\\mu_1 > \\mu_2",[1833,35877,35878],{},[1115,35879,35881],{"className":35880},[1144],[1146,35882,35883],{"xmlns":1148},[1150,35884,35885,35899],{},[1153,35886,35887,35889,35891],{},[1159,35888,11443],{},[1289,35890,2968],{},[2970,35892,35893,35895,35897],{},[1159,35894,11443],{},[1159,35896,1110],{},[1289,35898,35468],{},[1167,35900,35901],{"encoding":1169},"t \\ge t_p^*",[1716,35903,35904,35932,35960],{},[1833,35905,35906],{},[1115,35907,35909],{"className":35908},[1144],[1146,35910,35911],{"xmlns":1148},[1150,35912,35913,35929],{},[1153,35914,35915,35921,35923],{},[1156,35916,35917,35919],{},[1159,35918,11190],{},[1163,35920,1402],{},[1289,35922,1591],{},[1156,35924,35925,35927],{},[1159,35926,11190],{},[1163,35928,1189],{},[1167,35930,35931],{"encoding":1169},"\\mu_1 = \\mu_2",[1833,35933,35934],{},[1115,35935,35937],{"className":35936},[1144],[1146,35938,35939],{"xmlns":1148},[1150,35940,35941,35957],{},[1153,35942,35943,35949,35951],{},[1156,35944,35945,35947],{},[1159,35946,11190],{},[1163,35948,1402],{},[1289,35950,15257],{"mathvariant":1734},[1156,35952,35953,35955],{},[1159,35954,11190],{},[1163,35956,1189],{},[1167,35958,35959],{"encoding":1169},"\\mu_1 \\neq \\mu_2",[1833,35961,35962],{},[1115,35963,35965],{"className":35964},[1144],[1146,35966,35967],{"xmlns":1148},[1150,35968,35969,35987],{},[1153,35970,35971,35973,35975,35977,35979],{},[1289,35972,27329],{"stretchy":1483},[1159,35974,11443],{},[1289,35976,27329],{"stretchy":1483},[1289,35978,2968],{},[2970,35980,35981,35983,35985],{},[1159,35982,11443],{},[1159,35984,1110],{},[1289,35986,35468],{},[1167,35988,35989],{"encoding":1169},"\\lvert t \\rvert \\ge t_p^*",[1716,35991,35992,36020,36048],{},[1833,35993,35994],{},[1115,35995,35997],{"className":35996},[1144],[1146,35998,35999],{"xmlns":1148},[1150,36000,36001,36017],{},[1153,36002,36003,36009,36011],{},[1156,36004,36005,36007],{},[1159,36006,11190],{},[1163,36008,1402],{},[1289,36010,2968],{},[1156,36012,36013,36015],{},[1159,36014,11190],{},[1163,36016,1189],{},[1167,36018,36019],{"encoding":1169},"\\mu_1 \\ge \\mu_2",[1833,36021,36022],{},[1115,36023,36025],{"className":36024},[1144],[1146,36026,36027],{"xmlns":1148},[1150,36028,36029,36045],{},[1153,36030,36031,36037,36039],{},[1156,36032,36033,36035],{},[1159,36034,11190],{},[1163,36036,1402],{},[1289,36038,3951],{},[1156,36040,36041,36043],{},[1159,36042,11190],{},[1163,36044,1189],{},[1167,36046,36047],{"encoding":1169},"\\mu_1 \u003C \\mu_2",[1833,36049,36050],{},[1115,36051,36053],{"className":36052},[1144],[1146,36054,36055],{"xmlns":1148},[1150,36056,36057,36073],{},[1153,36058,36059,36061,36063,36065],{},[1159,36060,11443],{},[1289,36062,11034],{},[1289,36064,2681],{},[2970,36066,36067,36069,36071],{},[1159,36068,11443],{},[1159,36070,1110],{},[1289,36072,35468],{},[1167,36074,36075],{"encoding":1169},"t \\le -t_p^*",[1110,36077,36078,36079,35141,36097,1269],{},"Postup je dvoukrokový: nejprve F-test rozhodne o shodě rozptylů, pak se podle výsledku zvolí ",[1115,36080,36082],{"className":36081},[1144],[1146,36083,36084],{"xmlns":1148},[1150,36085,36086,36094],{},[1153,36087,36088],{},[1156,36089,36090,36092],{},[1159,36091,11401],{},[1163,36093,1402],{},[1167,36095,36096],{"encoding":1169},"T_1",[1115,36098,36100],{"className":36099},[1144],[1146,36101,36102],{"xmlns":1148},[1150,36103,36104,36112],{},[1153,36105,36106],{},[1156,36107,36108,36110],{},[1159,36109,11401],{},[1163,36111,1189],{},[1167,36113,36114],{"encoding":1169},"T_2",[1110,36116,36117],{},[4002,36118],{"alt":36119,"className":36120,"src":36121},"mask-th-f-kriticky-obor",[1321,4006],"\u002Fwiki-assets\u002Fmask-th-f-kriticky-obor.png",[1103,36123,36125,36132,36282,36363,36492,36530,36603,36742],{"className":36124,"dataCallout":3094},[1106,3093],[1110,36126,36128,36131],{"className":36127},[1113],[1115,36129],{"className":36130,"ariaHidden":1121},[1118,3101,1120],"Příklad: Porovnání dvou dodavatelů součástek",[1110,36133,36134,36135,2568,36157,36183,36184,36208,36209,2568,36231,36183,36257,36281],{},"Pevnost plastových dílů: dodavatel A (",[1115,36136,36138],{"className":36137},[1144],[1146,36139,36140],{"xmlns":1148},[1150,36141,36142,36154],{},[1153,36143,36144,36150,36152],{},[1156,36145,36146,36148],{},[1159,36147,1287],{},[1163,36149,1402],{},[1289,36151,1591],{},[1163,36153,13334],{},[1167,36155,36156],{"encoding":1169},"n_1 = 10",[1115,36158,36160],{"className":36159},[1144],[1146,36161,36162],{"xmlns":1148},[1150,36163,36164,36180],{},[1153,36165,36166,36176,36178],{},[1156,36167,36168,36174],{},[2339,36169,36170,36172],{"accent":1121},[1159,36171,11019],{},[1289,36173,15762],{},[1163,36175,1402],{},[1289,36177,1591],{},[1163,36179,3245],{},[1167,36181,36182],{"encoding":1169},"\\bar{x}_1 = 82"," MPa, ",[1115,36185,36187],{"className":36186},[1144],[1146,36188,36189],{"xmlns":1148},[1150,36190,36191,36205],{},[1153,36192,36193,36201,36203],{},[2970,36194,36195,36197,36199],{},[1159,36196,1463],{},[1163,36198,1402],{},[1163,36200,1189],{},[1289,36202,1591],{},[1163,36204,3677],{},[1167,36206,36207],{"encoding":1169},"s_1^2 = 25","), dodavatel B (",[1115,36210,36212],{"className":36211},[1144],[1146,36213,36214],{"xmlns":1148},[1150,36215,36216,36228],{},[1153,36217,36218,36224,36226],{},[1156,36219,36220,36222],{},[1159,36221,1287],{},[1163,36223,1189],{},[1289,36225,1591],{},[1163,36227,1891],{},[1167,36229,36230],{"encoding":1169},"n_2 = 12",[1115,36232,36234],{"className":36233},[1144],[1146,36235,36236],{"xmlns":1148},[1150,36237,36238,36254],{},[1153,36239,36240,36250,36252],{},[1156,36241,36242,36248],{},[2339,36243,36244,36246],{"accent":1121},[1159,36245,11019],{},[1289,36247,15762],{},[1163,36249,1189],{},[1289,36251,1591],{},[1163,36253,19035],{},[1167,36255,36256],{"encoding":1169},"\\bar{x}_2 = 75",[1115,36258,36260],{"className":36259},[1144],[1146,36261,36262],{"xmlns":1148},[1150,36263,36264,36278],{},[1153,36265,36266,36274,36276],{},[2970,36267,36268,36270,36272],{},[1159,36269,1463],{},[1163,36271,1189],{},[1163,36273,1189],{},[1289,36275,1591],{},[1163,36277,26331],{},[1167,36279,36280],{"encoding":1169},"s_2^2 = 16","). Předpokládá se normalita obou rozdělení.",[1110,36283,36284,1254,36287,2568,36325,1269],{},[1131,36285,36286],{},"Krok 1 — F-test rozptylů.",[1115,36288,36290],{"className":36289},[1144],[1146,36291,36292],{"xmlns":1148},[1150,36293,36294,36322],{},[1153,36295,36296,36302,36304,36312,36314],{},[1156,36297,36298,36300],{},[1159,36299,1161],{},[1163,36301,1165],{},[1289,36303,1567],{},[2970,36305,36306,36308,36310],{},[1159,36307,11198],{},[1163,36309,1402],{},[1163,36311,1189],{},[1289,36313,1591],{},[2970,36315,36316,36318,36320],{},[1159,36317,11198],{},[1163,36319,1189],{},[1163,36321,1189],{},[1167,36323,36324],{"encoding":1169},"H_0: \\sigma_1^2 = \\sigma_2^2",[1115,36326,36328],{"className":36327},[1144],[1146,36329,36330],{"xmlns":1148},[1150,36331,36332,36360],{},[1153,36333,36334,36340,36342,36350,36352],{},[1156,36335,36336,36338],{},[1159,36337,1161],{},[1163,36339,1402],{},[1289,36341,1567],{},[2970,36343,36344,36346,36348],{},[1159,36345,11198],{},[1163,36347,1402],{},[1163,36349,1189],{},[1289,36351,15257],{"mathvariant":1734},[2970,36353,36354,36356,36358],{},[1159,36355,11198],{},[1163,36357,1189],{},[1163,36359,1189],{},[1167,36361,36362],{"encoding":1169},"H_1: \\sigma_1^2 \\neq \\sigma_2^2",[1110,36364,36365],{},[1115,36366,36368],{"className":36367},[1144],[1146,36369,36370],{"xmlns":1148},[1150,36371,36372,36489],{},[1153,36373,36374,36376,36378,36384,36386,36389,36391,36393,36395,36397,36399,36401,36403,36416,36418,36420,36422,36424,36426,36429,36432,36434,36436,36438,36451,36453,36455,36457,36459,36461,36463,36465,36467,36469,36471,36474,36476,36478,36480,36482,36484,36487],{},[1159,36375,11014],{},[1289,36377,1591],{},[2355,36379,36380,36382],{},[1163,36381,3677],{},[1163,36383,26331],{},[1289,36385,1591],{},[1163,36387,36388],{},"1,5625",[1289,36390,1405],{"separator":1121},[1621,36392],{"width":1623},[1159,36394,1205],{},[1289,36396,1591],{},[1289,36398,2951],{"stretchy":1483},[1159,36400,11014],{},[1289,36402,11034],{},[1156,36404,36405,36407],{},[1159,36406,11014],{},[1153,36408,36409,36411,36413],{},[1163,36410,1165],{},[1289,36412,1405],{"separator":1121},[1163,36414,36415],{},"025",[1289,36417,1484],{"stretchy":1483},[1163,36419,3212],{},[1289,36421,1405],{"separator":1121},[1163,36423,1870],{},[1289,36425,1495],{"stretchy":1483},[2525,36427,36428],{},"  ",[2525,36430,36431],{},"nebo",[2525,36433,36428],{},[1159,36435,11014],{},[1289,36437,2968],{},[1156,36439,36440,36442],{},[1159,36441,11014],{},[1153,36443,36444,36446,36448],{},[1163,36445,1165],{},[1289,36447,1405],{"separator":1121},[1163,36449,36450],{},"975",[1289,36452,1484],{"stretchy":1483},[1163,36454,3212],{},[1289,36456,1405],{"separator":1121},[1163,36458,1870],{},[1289,36460,1495],{"stretchy":1483},[1289,36462,3011],{"stretchy":1483},[1289,36464,1591],{},[1289,36466,2951],{"stretchy":1483},[1159,36468,11014],{},[1289,36470,11034],{},[1163,36472,36473],{},"0,256",[2525,36475,36428],{},[2525,36477,36431],{},[2525,36479,36428],{},[1159,36481,11014],{},[1289,36483,2968],{},[1163,36485,36486],{},"3,588",[1289,36488,3011],{"stretchy":1483},[1167,36490,36491],{"encoding":1169},"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\\}",[1110,36493,36494,36512,36513,1269],{},[1115,36495,36497],{"className":36496},[1144],[1146,36498,36499],{"xmlns":1148},[1150,36500,36501,36509],{},[1153,36502,36503,36505,36507],{},[1159,36504,11014],{},[1289,36506,31578],{"mathvariant":1734},[1159,36508,1205],{},[1167,36510,36511],{"encoding":1169},"F \\notin W",", rozptyly nezamítáme jako shodné — pro t-test se použije ",[1115,36514,36516],{"className":36515},[1144],[1146,36517,36518],{"xmlns":1148},[1150,36519,36520,36528],{},[1153,36521,36522],{},[1156,36523,36524,36526],{},[1159,36525,11401],{},[1163,36527,1402],{},[1167,36529,36096],{"encoding":1169},[1110,36531,36532,1254,36535,2568,36569,1269],{},[1131,36533,36534],{},"Krok 2 — dvouvýběrový t-test středních hodnot.",[1115,36536,36538],{"className":36537},[1144],[1146,36539,36540],{"xmlns":1148},[1150,36541,36542,36566],{},[1153,36543,36544,36550,36552,36558,36560],{},[1156,36545,36546,36548],{},[1159,36547,1161],{},[1163,36549,1165],{},[1289,36551,1567],{},[1156,36553,36554,36556],{},[1159,36555,11190],{},[1163,36557,1402],{},[1289,36559,1591],{},[1156,36561,36562,36564],{},[1159,36563,11190],{},[1163,36565,1189],{},[1167,36567,36568],{"encoding":1169},"H_0: \\mu_1 = \\mu_2",[1115,36570,36572],{"className":36571},[1144],[1146,36573,36574],{"xmlns":1148},[1150,36575,36576,36600],{},[1153,36577,36578,36584,36586,36592,36594],{},[1156,36579,36580,36582],{},[1159,36581,1161],{},[1163,36583,1402],{},[1289,36585,1567],{},[1156,36587,36588,36590],{},[1159,36589,11190],{},[1163,36591,1402],{},[1289,36593,15257],{"mathvariant":1734},[1156,36595,36596,36598],{},[1159,36597,11190],{},[1163,36599,1189],{},[1167,36601,36602],{"encoding":1169},"H_1: \\mu_1 \\neq \\mu_2",[1110,36604,36605],{},[1115,36606,36608],{"className":36607},[1144],[1146,36609,36610],{"xmlns":1148},[1150,36611,36612,36739],{},[1153,36613,36614,36622,36624,36644,36646,36649,36651,36653,36655,36657,36671,36679,36681,36684,36686,36688,36690,36692,36694,36696,36698,36700,36702,36714,36716,36718,36720,36722,36724,36726,36728,36730,36732,36734,36737],{},[2970,36615,36616,36618,36620],{},[1159,36617,1463],{},[1159,36619,1110],{},[1163,36621,1189],{},[1289,36623,1591],{},[2355,36625,36626,36642],{},[1153,36627,36628,36630,36632,36634,36636,36638,36640],{},[1163,36629,3212],{},[1289,36631,12411],{},[1163,36633,3677],{},[1289,36635,5096],{},[1163,36637,1870],{},[1289,36639,12411],{},[1163,36641,26331],{},[1163,36643,3664],{},[1289,36645,1591],{},[1163,36647,36648],{},"20,05",[1289,36650,1405],{"separator":1121},[1621,36652],{"width":1623},[1159,36654,11443],{},[1289,36656,1591],{},[2355,36658,36659,36667],{},[1153,36660,36661,36663,36665],{},[1163,36662,3245],{},[1289,36664,2681],{},[1163,36666,19035],{},[4072,36668,36669],{},[1163,36670,36648],{},[4072,36672,36673],{},[2355,36674,36675,36677],{},[1163,36676,26191],{},[1163,36678,2005],{},[1289,36680,13741],{},[1163,36682,36683],{},"3,651",[1289,36685,1405],{"separator":1121},[1621,36687],{"width":1623},[1159,36689,1205],{},[1289,36691,1591],{},[1289,36693,2951],{"stretchy":1483},[1289,36695,27329],{"stretchy":1483},[1159,36697,11443],{},[1289,36699,27329],{"stretchy":1483},[1289,36701,2968],{},[1156,36703,36704,36706],{},[1159,36705,11443],{},[1153,36707,36708,36710,36712],{},[1163,36709,1165],{},[1289,36711,1405],{"separator":1121},[1163,36713,36450],{},[1289,36715,1484],{"stretchy":1483},[1163,36717,3664],{},[1289,36719,1495],{"stretchy":1483},[1289,36721,3011],{"stretchy":1483},[1289,36723,1591],{},[1289,36725,2951],{"stretchy":1483},[1289,36727,27329],{"stretchy":1483},[1159,36729,11443],{},[1289,36731,27329],{"stretchy":1483},[1289,36733,2968],{},[1163,36735,36736],{},"2,086",[1289,36738,3011],{"stretchy":1483},[1167,36740,36741],{"encoding":1169},"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\\}",[1110,36743,36744,5626,36761,36778],{},[1115,36745,36747],{"className":36746},[1144],[1146,36748,36749],{"xmlns":1148},[1150,36750,36751,36759],{},[1153,36752,36753,36755,36757],{},[1159,36754,11443],{},[1289,36756,11318],{},[1159,36758,1205],{},[1167,36760,32721],{"encoding":1169},[1115,36762,36764],{"className":36763},[1144],[1146,36765,36766],{"xmlns":1148},[1150,36767,36768,36776],{},[1153,36769,36770],{},[1156,36771,36772,36774],{},[1159,36773,1161],{},[1163,36775,1165],{},[1167,36777,1170],{"encoding":1169},": pevnost součástek od obou dodavatelů se statisticky významně liší.",[3311,36780,36782],{"className":3313,"code":36781,"language":71,"meta":3315,"style":3315},"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",[3087,36783,36784,36802,36822,36837,36872,36903,36908,36913],{"__ignoreMap":3315},[1115,36785,36786,36789,36791,36793,36795,36798,36800],{"class":3320,"line":10},[1115,36787,36788],{"class":3323},"s1",[1115,36790,3328],{"class":3327},[1115,36792,18705],{"class":3343},[1115,36794,29489],{"class":3335},[1115,36796,36797],{"class":3323},"n1",[1115,36799,3328],{"class":3327},[1115,36801,34162],{"class":3343},[1115,36803,36804,36807,36809,36812,36814,36817,36819],{"class":3320,"line":27},[1115,36805,36806],{"class":3323},"s2",[1115,36808,3328],{"class":3327},[1115,36810,36811],{"class":3343}," 16",[1115,36813,29489],{"class":3335},[1115,36815,36816],{"class":3323},"n2",[1115,36818,3328],{"class":3327},[1115,36820,36821],{"class":3343}," 12\n",[1115,36823,36824,36827,36829,36832,36834],{"class":3320,"line":148},[1115,36825,36826],{"class":3323},"Fstat",[1115,36828,3328],{"class":3327},[1115,36830,36831],{"class":3323}," s1",[1115,36833,14376],{"class":3327},[1115,36835,36836],{"class":3323}," s2\n",[1115,36838,36839,36842,36844,36847,36849,36852,36854,36857,36859,36861,36863,36866,36868,36870],{"class":3320,"line":111},[1115,36840,36841],{"class":3323},"F_dolni",[1115,36843,3328],{"class":3327},[1115,36845,36846],{"class":3331}," qf",[1115,36848,1484],{"class":3335},[1115,36850,36851],{"class":3343},"0.025",[1115,36853,1405],{"class":3327},[1115,36855,36856],{"class":3323}," n1",[1115,36858,29826],{"class":3327},[1115,36860,4260],{"class":3343},[1115,36862,1405],{"class":3327},[1115,36864,36865],{"class":3323}," n2",[1115,36867,29826],{"class":3327},[1115,36869,4260],{"class":3343},[1115,36871,3520],{"class":3335},[1115,36873,36874,36877,36879,36881,36883,36885,36887,36889,36891,36893,36895,36897,36899,36901],{"class":3320,"line":96},[1115,36875,36876],{"class":3323},"F_horni",[1115,36878,3328],{"class":3327},[1115,36880,36846],{"class":3331},[1115,36882,1484],{"class":3335},[1115,36884,13390],{"class":3343},[1115,36886,1405],{"class":3327},[1115,36888,36856],{"class":3323},[1115,36890,29826],{"class":3327},[1115,36892,4260],{"class":3343},[1115,36894,1405],{"class":3327},[1115,36896,36865],{"class":3323},[1115,36898,29826],{"class":3327},[1115,36900,4260],{"class":3343},[1115,36902,3520],{"class":3335},[1115,36904,36905],{"class":3320,"line":89},[1115,36906,36907],{"class":3323},"Fstat\n",[1115,36909,36910],{"class":3320,"line":82},[1115,36911,36912],{"class":3323},"F_dolni\n",[1115,36914,36915],{"class":3320,"line":75},[1115,36916,36917],{"class":3323},"F_horni\n",[3311,36919,36922],{"className":36920,"code":36921,"language":3542,"meta":3315},[3540],"[1] 1.5625\n[1] 0.2556189\n[1] 3.587899\n",[3087,36923,36921],{"__ignoreMap":3315},[3311,36925,36927],{"className":3313,"code":36926,"language":71,"meta":3315,"style":3315},"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",[3087,36928,36929,36986,37037,37067,37072,37076],{"__ignoreMap":3315},[1115,36930,36931,36934,36936,36939,36941,36943,36945,36947,36949,36951,36953,36955,36957,36959,36961,36963,36965,36968,36970,36972,36974,36976,36978,36980,36982,36984],{"class":3320,"line":10},[1115,36932,36933],{"class":3323},"sp2",[1115,36935,3328],{"class":3327},[1115,36937,36938],{"class":3335}," ((",[1115,36940,36797],{"class":3323},[1115,36942,29826],{"class":3327},[1115,36944,4260],{"class":3343},[1115,36946,4220],{"class":3335},[1115,36948,4238],{"class":3327},[1115,36950,36831],{"class":3323},[1115,36952,22819],{"class":3327},[1115,36954,4226],{"class":3335},[1115,36956,36816],{"class":3323},[1115,36958,29826],{"class":3327},[1115,36960,4260],{"class":3343},[1115,36962,4220],{"class":3335},[1115,36964,4238],{"class":3327},[1115,36966,36967],{"class":3323}," s2",[1115,36969,4220],{"class":3335},[1115,36971,4223],{"class":3327},[1115,36973,4226],{"class":3335},[1115,36975,36797],{"class":3323},[1115,36977,22819],{"class":3327},[1115,36979,36865],{"class":3323},[1115,36981,29826],{"class":3327},[1115,36983,3799],{"class":3343},[1115,36985,3520],{"class":3335},[1115,36987,36988,36990,36992,36994,36996,36998,37001,37003,37005,37007,37009,37011,37013,37015,37017,37019,37021,37023,37025,37027,37029,37031,37033,37035],{"class":3320,"line":27},[1115,36989,11443],{"class":3323},[1115,36991,3328],{"class":3327},[1115,36993,4226],{"class":3335},[1115,36995,3245],{"class":3343},[1115,36997,29826],{"class":3327},[1115,36999,37000],{"class":3343}," 75",[1115,37002,4220],{"class":3335},[1115,37004,4223],{"class":3327},[1115,37006,4197],{"class":3331},[1115,37008,1484],{"class":3335},[1115,37010,36933],{"class":3323},[1115,37012,4220],{"class":3335},[1115,37014,4238],{"class":3327},[1115,37016,4197],{"class":3331},[1115,37018,1484],{"class":3335},[1115,37020,36797],{"class":3323},[1115,37022,22944],{"class":3327},[1115,37024,36865],{"class":3323},[1115,37026,14376],{"class":3327},[1115,37028,4226],{"class":3335},[1115,37030,36797],{"class":3323},[1115,37032,22819],{"class":3327},[1115,37034,36865],{"class":3323},[1115,37036,13794],{"class":3335},[1115,37038,37039,37041,37043,37045,37047,37049,37051,37053,37055,37057,37059,37061,37063,37065],{"class":3320,"line":148},[1115,37040,32828],{"class":3323},[1115,37042,3328],{"class":3327},[1115,37044,32833],{"class":3331},[1115,37046,1484],{"class":3335},[1115,37048,13390],{"class":3343},[1115,37050,1405],{"class":3327},[1115,37052,15110],{"class":3323},[1115,37054,3416],{"class":3327},[1115,37056,36856],{"class":3323},[1115,37058,22819],{"class":3327},[1115,37060,36865],{"class":3323},[1115,37062,29826],{"class":3327},[1115,37064,3799],{"class":3343},[1115,37066,3520],{"class":3335},[1115,37068,37069],{"class":3320,"line":111},[1115,37070,37071],{"class":3323},"sp2\n",[1115,37073,37074],{"class":3320,"line":96},[1115,37075,32858],{"class":3323},[1115,37077,37078],{"class":3320,"line":89},[1115,37079,32863],{"class":3323},[3311,37081,37084],{"className":37082,"code":37083,"language":3542,"meta":3315},[3540],"[1] 20.05\n[1] 3.65107\n[1] 2.085963\n",[3087,37085,37083],{"__ignoreMap":3315},[1110,37087,37088],{},[4002,37089],{"alt":37090,"className":37091,"src":37092},"mask-th-t-dvoustranny",[1321,4006],"\u002Fwiki-assets\u002Fmask-th-t-dvoustranny.png",[1110,37094,37095,37096,5360,37099,37101,37102,37105,37106,5360,37123,3607,37140,37142,37143,37145],{},"V R provede obě kroky ",[3087,37097,37098],{},"var.test()",[3087,37100,32318],{},". Parametr ",[3087,37103,37104],{},"var.equal"," nastavuje volbu mezi ",[1115,37107,37109],{"className":37108},[1144],[1146,37110,37111],{"xmlns":1148},[1150,37112,37113,37121],{},[1153,37114,37115],{},[1156,37116,37117,37119],{},[1159,37118,11401],{},[1163,37120,1402],{},[1167,37122,36096],{"encoding":1169},[1115,37124,37126],{"className":37125},[1144],[1146,37127,37128],{"xmlns":1148},[1150,37129,37130,37138],{},[1153,37131,37132],{},[1156,37133,37134,37136],{},[1159,37135,11401],{},[1163,37137,1189],{},[1167,37139,36114],{"encoding":1169},[3087,37141,13825],{}," znamená předpoklad shodných rozptylů (podle výsledku F-testu), ",[3087,37144,13828],{}," předpoklad rozdílných rozptylů.",[1110,37147,37148,37151],{},[1131,37149,37150],{},"Kabely A\u002FB."," Pevnost v tahu dvou výrobců (MPa, 12 kabelů od každého):",[3311,37153,37155],{"className":3313,"code":37154,"language":71,"meta":3315,"style":3315},"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",[3087,37156,37157,37223,37286,37302],{"__ignoreMap":3315},[1115,37158,37159,37161,37163,37165,37167,37170,37172,37175,37177,37180,37182,37185,37187,37189,37191,37194,37196,37199,37201,37203,37205,37208,37210,37212,37214,37217,37219,37221],{"class":3320,"line":10},[1115,37160,1383],{"class":3323},[1115,37162,3328],{"class":3327},[1115,37164,3454],{"class":3331},[1115,37166,1484],{"class":3335},[1115,37168,37169],{"class":3343},"313",[1115,37171,1405],{"class":3327},[1115,37173,37174],{"class":3343}," 299",[1115,37176,1405],{"class":3327},[1115,37178,37179],{"class":3343}," 315",[1115,37181,1405],{"class":3327},[1115,37183,37184],{"class":3343}," 312",[1115,37186,1405],{"class":3327},[1115,37188,19673],{"class":3343},[1115,37190,1405],{"class":3327},[1115,37192,37193],{"class":3343}," 308",[1115,37195,1405],{"class":3327},[1115,37197,37198],{"class":3343}," 314",[1115,37200,1405],{"class":3327},[1115,37202,18465],{"class":3343},[1115,37204,1405],{"class":3327},[1115,37206,37207],{"class":3343}," 305",[1115,37209,1405],{"class":3327},[1115,37211,19673],{"class":3343},[1115,37213,1405],{"class":3327},[1115,37215,37216],{"class":3343}," 309",[1115,37218,1405],{"class":3327},[1115,37220,37198],{"class":3343},[1115,37222,3520],{"class":3335},[1115,37224,37225,37227,37229,37231,37233,37236,37238,37241,37243,37245,37247,37249,37251,37254,37256,37259,37261,37263,37265,37267,37269,37271,37273,37276,37278,37280,37282,37284],{"class":3320,"line":27},[1115,37226,1432],{"class":3323},[1115,37228,3328],{"class":3327},[1115,37230,3454],{"class":3331},[1115,37232,1484],{"class":3335},[1115,37234,37235],{"class":3343},"307",[1115,37237,1405],{"class":3327},[1115,37239,37240],{"class":3343}," 322",[1115,37242,1405],{"class":3327},[1115,37244,18465],{"class":3343},[1115,37246,1405],{"class":3327},[1115,37248,18465],{"class":3343},[1115,37250,1405],{"class":3327},[1115,37252,37253],{"class":3343}," 311",[1115,37255,1405],{"class":3327},[1115,37257,37258],{"class":3343}," 316",[1115,37260,1405],{"class":3327},[1115,37262,37179],{"class":3343},[1115,37264,1405],{"class":3327},[1115,37266,37198],{"class":3343},[1115,37268,1405],{"class":3327},[1115,37270,37193],{"class":3343},[1115,37272,1405],{"class":3327},[1115,37274,37275],{"class":3343}," 319",[1115,37277,1405],{"class":3327},[1115,37279,18465],{"class":3343},[1115,37281,1405],{"class":3327},[1115,37283,37184],{"class":3343},[1115,37285,3520],{"class":3335},[1115,37287,37288,37291,37293,37295,37297,37300],{"class":3320,"line":148},[1115,37289,37290],{"class":3331},"var.test",[1115,37292,1484],{"class":3335},[1115,37294,1383],{"class":3323},[1115,37296,1405],{"class":3327},[1115,37298,37299],{"class":3323}," B",[1115,37301,3520],{"class":3335},[1115,37303,37304,37306,37308,37310,37312,37314,37316,37319,37321,37323],{"class":3320,"line":111},[1115,37305,32383],{"class":3331},[1115,37307,1484],{"class":3335},[1115,37309,1383],{"class":3323},[1115,37311,1405],{"class":3327},[1115,37313,37299],{"class":3323},[1115,37315,1405],{"class":3327},[1115,37317,37318],{"class":3323}," var.equal",[1115,37320,3416],{"class":3327},[1115,37322,3429],{"class":3343},[1115,37324,3520],{"class":3335},[3311,37326,37329],{"className":37327,"code":37328,"language":3542,"meta":3315},[3540],"    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",[3087,37330,37328],{"__ignoreMap":3315},[1110,37332,37333,37334,16357,37353,37356,37357,37376,37377,37394],{},"F-test shodu rozptylů nezamítá (",[1115,37335,37337],{"className":37336},[1144],[1146,37338,37339],{"xmlns":1148},[1150,37340,37341,37350],{},[1153,37342,37343,37345,37347],{},[1159,37344,1110],{},[1289,37346,1591],{},[1163,37348,37349],{},"0,7776",[1167,37351,37352],{"encoding":1169},"p = 0{,}7776",[3087,37354,37355],{},"var.equal = TRUE",". Výsledný t-test dává ",[1115,37358,37360],{"className":37359},[1144],[1146,37361,37362],{"xmlns":1148},[1150,37363,37364,37373],{},[1153,37365,37366,37368,37370],{},[1159,37367,1110],{},[1289,37369,1591],{},[1163,37371,37372],{},"0,06932",[1167,37374,37375],{"encoding":1169},"p = 0{,}06932"," — na hladině 5 % se ",[1115,37378,37380],{"className":37379},[1144],[1146,37381,37382],{"xmlns":1148},[1150,37383,37384,37392],{},[1153,37385,37386],{},[1156,37387,37388,37390],{},[1159,37389,1161],{},[1163,37391,1165],{},[1167,37393,1170],{"encoding":1169}," nezamítá, ale hodnota je těsně nad hranicí.",[1110,37396,37397],{},[1131,37398,37399],{},"Výšky chlapců a dívek v páté třídě:",[3311,37401,37403],{"className":3313,"code":37402,"language":71,"meta":3315,"style":3315},"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",[3087,37404,37405,37485,37548,37563],{"__ignoreMap":3315},[1115,37406,37407,37410,37412,37414,37416,37419,37421,37423,37425,37428,37430,37433,37435,37438,37440,37443,37445,37447,37449,37451,37453,37455,37457,37459,37461,37464,37466,37469,37471,37474,37476,37478,37480,37483],{"class":3320,"line":10},[1115,37408,37409],{"class":3323},"boys",[1115,37411,3328],{"class":3327},[1115,37413,3454],{"class":3331},[1115,37415,1484],{"class":3335},[1115,37417,37418],{"class":3343},"130",[1115,37420,1405],{"class":3327},[1115,37422,19622],{"class":3343},[1115,37424,1405],{"class":3327},[1115,37426,37427],{"class":3343}," 136",[1115,37429,1405],{"class":3327},[1115,37431,37432],{"class":3343}," 141",[1115,37434,1405],{"class":3327},[1115,37436,37437],{"class":3343}," 139",[1115,37439,1405],{"class":3327},[1115,37441,37442],{"class":3343}," 133",[1115,37444,1405],{"class":3327},[1115,37446,22776],{"class":3343},[1115,37448,1405],{"class":3327},[1115,37450,18480],{"class":3343},[1115,37452,1405],{"class":3327},[1115,37454,37437],{"class":3343},[1115,37456,1405],{"class":3327},[1115,37458,37427],{"class":3343},[1115,37460,1405],{"class":3327},[1115,37462,37463],{"class":3343}," 138",[1115,37465,1405],{"class":3327},[1115,37467,37468],{"class":3343}," 142",[1115,37470,1405],{"class":3327},[1115,37472,37473],{"class":3343}," 127",[1115,37475,1405],{"class":3327},[1115,37477,37437],{"class":3343},[1115,37479,1405],{"class":3327},[1115,37481,37482],{"class":3343}," 147",[1115,37484,3520],{"class":3335},[1115,37486,37487,37490,37492,37494,37496,37498,37500,37502,37504,37507,37509,37512,37514,37517,37519,37521,37523,37525,37527,37529,37531,37533,37535,37538,37540,37542,37544,37546],{"class":3320,"line":27},[1115,37488,37489],{"class":3323},"girls",[1115,37491,3328],{"class":3327},[1115,37493,3454],{"class":3331},[1115,37495,1484],{"class":3335},[1115,37497,26142],{"class":3343},[1115,37499,1405],{"class":3327},[1115,37501,37432],{"class":3343},[1115,37503,1405],{"class":3327},[1115,37505,37506],{"class":3343}," 143",[1115,37508,1405],{"class":3327},[1115,37510,37511],{"class":3343}," 132",[1115,37513,1405],{"class":3327},[1115,37515,37516],{"class":3343}," 146",[1115,37518,1405],{"class":3327},[1115,37520,37516],{"class":3343},[1115,37522,1405],{"class":3327},[1115,37524,18480],{"class":3343},[1115,37526,1405],{"class":3327},[1115,37528,37432],{"class":3343},[1115,37530,1405],{"class":3327},[1115,37532,37432],{"class":3343},[1115,37534,1405],{"class":3327},[1115,37536,37537],{"class":3343}," 131",[1115,37539,1405],{"class":3327},[1115,37541,37468],{"class":3343},[1115,37543,1405],{"class":3327},[1115,37545,37432],{"class":3343},[1115,37547,3520],{"class":3335},[1115,37549,37550,37552,37554,37556,37558,37561],{"class":3320,"line":148},[1115,37551,37290],{"class":3331},[1115,37553,1484],{"class":3335},[1115,37555,37409],{"class":3323},[1115,37557,1405],{"class":3327},[1115,37559,37560],{"class":3323}," girls",[1115,37562,3520],{"class":3335},[1115,37564,37565,37567,37569,37571,37573,37575,37577,37579,37581,37583],{"class":3320,"line":111},[1115,37566,32383],{"class":3331},[1115,37568,1484],{"class":3335},[1115,37570,37409],{"class":3323},[1115,37572,1405],{"class":3327},[1115,37574,37560],{"class":3323},[1115,37576,1405],{"class":3327},[1115,37578,37318],{"class":3323},[1115,37580,3416],{"class":3327},[1115,37582,3429],{"class":3343},[1115,37584,3520],{"class":3335},[3311,37586,37589],{"className":37587,"code":37588,"language":3542,"meta":3315},[3540],"    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",[3087,37590,37588],{"__ignoreMap":3315},[1110,37592,37333,37593,37612,37613,37615,37616,37635],{},[1115,37594,37596],{"className":37595},[1144],[1146,37597,37598],{"xmlns":1148},[1150,37599,37600,37609],{},[1153,37601,37602,37604,37606],{},[1159,37603,1110],{},[1289,37605,1591],{},[1163,37607,37608],{},"0,6977",[1167,37610,37611],{"encoding":1169},"p = 0{,}6977","), t-test s ",[3087,37614,37355],{}," dává ",[1115,37617,37619],{"className":37618},[1144],[1146,37620,37621],{"xmlns":1148},[1150,37622,37623,37632],{},[1153,37624,37625,37627,37629],{},[1159,37626,1110],{},[1289,37628,1591],{},[1163,37630,37631],{},"0,4883",[1167,37633,37634],{"encoding":1169},"p = 0{,}4883",": na hladině 5 % se rozdíl průměrných výšek chlapců a dívek neprokázal.",[1310,37637,37639],{"id":37638},"testy-dobré-shody-a-normalita","Testy dobré shody a normalita",[1110,37641,37642],{},"Testy dobré shody ověřují, zda datový soubor pochází ze základního souboru s určitým typem rozdělení (normální, exponenciální apod.).",[21050,37644,37646],{"id":37645},"kolmogorovův-smirnovův-test","Kolmogorovův-Smirnovův test",[1110,37648,37649,37650,37673,37674,37693],{},"Univerzální test pro spojitá rozdělení. Porovnává empirickou distribuční funkci ",[1115,37651,37653],{"className":37652},[1144],[1146,37654,37655],{"xmlns":1148},[1150,37656,37657,37671],{},[1153,37658,37659,37665,37667,37669],{},[1156,37660,37661,37663],{},[1159,37662,11014],{},[1159,37664,1287],{},[1289,37666,1484],{"stretchy":1483},[1159,37668,11019],{},[1289,37670,1495],{"stretchy":1483},[1167,37672,15486],{"encoding":1169}," s teoretickou distribuční funkcí ",[1115,37675,37677],{"className":37676},[1144],[1146,37678,37679],{"xmlns":1148},[1150,37680,37681,37691],{},[1153,37682,37683,37685,37687,37689],{},[1159,37684,11014],{},[1289,37686,1484],{"stretchy":1483},[1159,37688,11019],{},[1289,37690,1495],{"stretchy":1483},[1167,37692,11635],{"encoding":1169}," testovaného rozdělení.",[1124,37695,37696,37759,37779,37835],{},[1127,37697,37698,37715,37716,5360,37739,37758],{},[1115,37699,37701],{"className":37700},[1144],[1146,37702,37703],{"xmlns":1148},[1150,37704,37705,37713],{},[1153,37706,37707],{},[1156,37708,37709,37711],{},[1159,37710,1161],{},[1163,37712,1165],{},[1167,37714,1170],{"encoding":1169},": odchylky mezi ",[1115,37717,37719],{"className":37718},[1144],[1146,37720,37721],{"xmlns":1148},[1150,37722,37723,37737],{},[1153,37724,37725,37731,37733,37735],{},[1156,37726,37727,37729],{},[1159,37728,11014],{},[1159,37730,1287],{},[1289,37732,1484],{"stretchy":1483},[1159,37734,11019],{},[1289,37736,1495],{"stretchy":1483},[1167,37738,15486],{"encoding":1169},[1115,37740,37742],{"className":37741},[1144],[1146,37743,37744],{"xmlns":1148},[1150,37745,37746,37756],{},[1153,37747,37748,37750,37752,37754],{},[1159,37749,11014],{},[1289,37751,1484],{"stretchy":1483},[1159,37753,11019],{},[1289,37755,1495],{"stretchy":1483},[1167,37757,11635],{"encoding":1169}," jsou náhodné (data mají dané rozdělení).",[1127,37760,37761,37778],{},[1115,37762,37764],{"className":37763},[1144],[1146,37765,37766],{"xmlns":1148},[1150,37767,37768,37776],{},[1153,37769,37770],{},[1156,37771,37772,37774],{},[1159,37773,1161],{},[1163,37775,1402],{},[1167,37777,2613],{"encoding":1169},": data nemají dané rozdělení.",[1127,37780,37781,37782,1269],{},"Testové kritérium: ",[1115,37783,37785],{"className":37784},[1144],[1146,37786,37787],{"xmlns":1148},[1150,37788,37789,37832],{},[1153,37790,37791,37793,37795,37806,37808,37814,37816,37818,37820,37822,37824,37826,37828,37830],{},[1159,37792,12453],{},[1289,37794,1591],{},[1156,37796,37797,37804],{},[1153,37798,37799,37802],{},[1159,37800,37801],{},"sup",[1289,37803,4110],{},[1159,37805,11019],{},[1289,37807,27329],{"stretchy":1483},[1156,37809,37810,37812],{},[1159,37811,11014],{},[1159,37813,1287],{},[1289,37815,1484],{"stretchy":1483},[1159,37817,11019],{},[1289,37819,1495],{"stretchy":1483},[1289,37821,2681],{},[1159,37823,11014],{},[1289,37825,1484],{"stretchy":1483},[1159,37827,11019],{},[1289,37829,1495],{"stretchy":1483},[1289,37831,27329],{"stretchy":1483},[1167,37833,37834],{"encoding":1169},"D = \\sup_x \\lvert F_n(x) - F(x) \\rvert",[1127,37836,2935,37837,37881,37882,37900,37901,1269],{},[1115,37838,37840],{"className":37839},[1144],[1146,37841,37842],{"xmlns":1148},[1150,37843,37844,37878],{},[1153,37845,37846,37852,37854,37856,37858,37860,37862,37864,37870,37872,37874,37876],{},[1156,37847,37848,37850],{},[1159,37849,1205],{},[1159,37851,2982],{},[1289,37853,1591],{},[1289,37855,2951],{"stretchy":1483},[1159,37857,12096],{},[1289,37859,1567],{},[1159,37861,12096],{},[1289,37863,1291],{},[1156,37865,37866,37868],{},[1159,37867,12453],{},[1159,37869,2982],{},[1289,37871,1484],{"stretchy":1483},[1159,37873,1287],{},[1289,37875,1495],{"stretchy":1483},[1289,37877,3011],{"stretchy":1483},[1167,37879,37880],{"encoding":1169},"W_\\alpha = \\{d : d > D_\\alpha(n)\\}","; pro ",[1115,37883,37885],{"className":37884},[1144],[1146,37886,37887],{"xmlns":1148},[1150,37888,37889,37897],{},[1153,37890,37891,37893,37895],{},[1159,37892,1287],{},[1289,37894,1291],{},[1163,37896,26341],{},[1167,37898,37899],{"encoding":1169},"n>30"," se kritická hodnota aproximuje zlomkem ",[1115,37902,37904],{"className":37903},[1144],[1146,37905,37906],{"xmlns":1148},[1150,37907,37908,37919],{},[1153,37909,37910,37913,37915],{},[1163,37911,37912],{},"1,36",[1159,37914,4223],{"mathvariant":1734},[4072,37916,37917],{},[1159,37918,1287],{},[1167,37920,37921],{"encoding":1169},"1{,}36\u002F\\sqrt{n}",[1110,37923,32315,37924,37927,37928,37930,37931,2568,37934,37937],{},[3087,37925,37926],{},"ks.test()",", kde se za ",[3087,37929,11635],{}," dosadí příslušná distribuční funkce (",[3087,37932,37933],{},"\"pnorm\"",[3087,37935,37936],{},"\"pexp\"",", …) s jejími parametry:",[3311,37939,37941],{"className":3313,"code":37940,"language":71,"meta":3315,"style":3315},"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",[3087,37942,37943,37993],{"__ignoreMap":3315},[1115,37944,37945,37947,37949,37951,37953,37955,37957,37959,37961,37963,37965,37967,37969,37971,37973,37975,37977,37979,37981,37983,37985,37987,37989,37991],{"class":3320,"line":10},[1115,37946,33029],{"class":3323},[1115,37948,3328],{"class":3327},[1115,37950,3454],{"class":3331},[1115,37952,1484],{"class":3335},[1115,37954,16289],{"class":3343},[1115,37956,1405],{"class":3327},[1115,37958,16294],{"class":3343},[1115,37960,1405],{"class":3327},[1115,37962,16299],{"class":3343},[1115,37964,1405],{"class":3327},[1115,37966,16304],{"class":3343},[1115,37968,1405],{"class":3327},[1115,37970,16299],{"class":3343},[1115,37972,1405],{"class":3327},[1115,37974,16299],{"class":3343},[1115,37976,1405],{"class":3327},[1115,37978,16317],{"class":3343},[1115,37980,1405],{"class":3327},[1115,37982,16322],{"class":3343},[1115,37984,1405],{"class":3327},[1115,37986,16294],{"class":3343},[1115,37988,1405],{"class":3327},[1115,37990,16294],{"class":3343},[1115,37992,3520],{"class":3335},[1115,37994,37995,37998,38000,38002,38004,38007,38009,38011,38013,38015,38017,38019,38021,38023,38025],{"class":3320,"line":27},[1115,37996,37997],{"class":3331},"ks.test",[1115,37999,1484],{"class":3335},[1115,38001,33029],{"class":3323},[1115,38003,1405],{"class":3327},[1115,38005,38006],{"class":3459}," \"pnorm\"",[1115,38008,1405],{"class":3327},[1115,38010,13532],{"class":3331},[1115,38012,1484],{"class":3335},[1115,38014,33029],{"class":3323},[1115,38016,1495],{"class":3335},[1115,38018,1405],{"class":3327},[1115,38020,13542],{"class":3331},[1115,38022,1484],{"class":3335},[1115,38024,33029],{"class":3323},[1115,38026,13794],{"class":3335},[3311,38028,38031],{"className":38029,"code":38030,"language":3542,"meta":3315},[3540],"    Asymptotic one-sample Kolmogorov-Smirnov test\n\ndata:  x3\nD = 0.18469, p-value = 0.8847\nalternative hypothesis: two-sided\n",[3087,38032,38030],{"__ignoreMap":3315},[1110,38034,38035,38058],{},[1115,38036,38038],{"className":38037},[1144],[1146,38039,38040],{"xmlns":1148},[1150,38041,38042,38055],{},[1153,38043,38044,38046,38048,38051,38053],{},[1159,38045,1110],{},[1289,38047,1591],{},[1163,38049,38050],{},"0,8847",[1289,38052,1291],{},[1163,38054,3603],{},[1167,38056,38057],{"encoding":1169},"p = 0{,}8847 > 0{,}05",": odpad materiálu je slučitelný s normálním rozdělením se stejným průměrem a směrodatnou odchylkou.",[21050,38060,38062],{"id":38061},"shapiro-wilkův-test","Shapiro-Wilkův test",[1110,38064,38065],{},"Nejpoužívanější a nejsilnější obecný test normality, citlivý na odchylky v šikmosti i špičatosti. Využívá korelaci mezi uspořádanými hodnotami výběru a jejich očekávanými hodnotami v normálním rozdělení.",[1124,38067,38068,38088,38108],{},[1127,38069,38070,38087],{},[1115,38071,38073],{"className":38072},[1144],[1146,38074,38075],{"xmlns":1148},[1150,38076,38077,38085],{},[1153,38078,38079],{},[1156,38080,38081,38083],{},[1159,38082,1161],{},[1163,38084,1165],{},[1167,38086,1170],{"encoding":1169},": data mají normální rozdělení.",[1127,38089,38090,38107],{},[1115,38091,38093],{"className":38092},[1144],[1146,38094,38095],{"xmlns":1148},[1150,38096,38097,38105],{},[1153,38098,38099],{},[1156,38100,38101,38103],{},[1159,38102,1161],{},[1163,38104,1402],{},[1167,38106,2613],{"encoding":1169},": data nemají normální rozdělení.",[1127,38109,38110,38111,38137],{},"Testová statistika ",[1115,38112,38114],{"className":38113},[1144],[1146,38115,38116],{"xmlns":1148},[1150,38117,38118,38134],{},[1153,38119,38120,38122,38124,38126,38128,38130,38132],{},[1159,38121,1205],{},[1289,38123,11318],{},[1289,38125,12726],{"stretchy":1483},[1163,38127,1165],{},[1289,38129,1405],{"separator":1121},[1163,38131,1402],{},[1289,38133,11743],{"stretchy":1483},[1167,38135,38136],{"encoding":1169},"W \\in \\langle 0,1 \\rangle","; hodnoty blízké 1 indikují shodu s normalitou.",[1110,38139,38140,38141,38154,38155,1254,38175,38192,38193,1254,38213,38230],{},"Na rozdíl od ostatních testů v této kapitole se Shapiro-Wilkův test v praxi vyhodnocuje pouze přes p-hodnotu (tabulka kritických hodnot pro ",[1115,38142,38144],{"className":38143},[1144],[1146,38145,38146],{"xmlns":1148},[1150,38147,38148,38152],{},[1153,38149,38150],{},[1159,38151,1205],{},[1167,38153,1205],{"encoding":1169}," se běžně neudává): ",[1115,38156,38158],{"className":38157},[1144],[1146,38159,38160],{"xmlns":1148},[1150,38161,38162,38172],{},[1153,38163,38164,38166,38168,38170],{},[1159,38165,1110],{},[1289,38167,2968],{},[1159,38169,2982],{},[1289,38171,11849],{},[1167,38173,38174],{"encoding":1169},"p \\ge \\alpha \\Rightarrow",[1115,38176,38178],{"className":38177},[1144],[1146,38179,38180],{"xmlns":1148},[1150,38181,38182,38190],{},[1153,38183,38184],{},[1156,38185,38186,38188],{},[1159,38187,1161],{},[1163,38189,1165],{},[1167,38191,1170],{"encoding":1169}," nezamítáme (normalitu lze předpokládat); ",[1115,38194,38196],{"className":38195},[1144],[1146,38197,38198],{"xmlns":1148},[1150,38199,38200,38210],{},[1153,38201,38202,38204,38206,38208],{},[1159,38203,1110],{},[1289,38205,3951],{},[1159,38207,2982],{},[1289,38209,11849],{},[1167,38211,38212],{"encoding":1169},"p \u003C \\alpha \\Rightarrow",[1115,38214,38216],{"className":38215},[1144],[1146,38217,38218],{"xmlns":1148},[1150,38219,38220,38228],{},[1153,38221,38222],{},[1156,38223,38224,38226],{},[1159,38225,1161],{},[1163,38227,1165],{},[1167,38229,1170],{"encoding":1169}," zamítáme (předpoklad normality je porušen).",[3311,38232,38234],{"className":3313,"code":38233,"language":71,"meta":3315,"style":3315},"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",[3087,38235,38236,38290],{"__ignoreMap":3315},[1115,38237,38238,38240,38242,38244,38246,38248,38250,38252,38254,38256,38258,38260,38262,38264,38266,38268,38270,38272,38274,38276,38278,38280,38282,38284,38286,38288],{"class":3320,"line":10},[1115,38239,32897],{"class":3323},[1115,38241,3328],{"class":3327},[1115,38243,3454],{"class":3331},[1115,38245,1484],{"class":3335},[1115,38247,32906],{"class":3343},[1115,38249,1405],{"class":3327},[1115,38251,32911],{"class":3343},[1115,38253,1405],{"class":3327},[1115,38255,32916],{"class":3343},[1115,38257,1405],{"class":3327},[1115,38259,32921],{"class":3343},[1115,38261,1405],{"class":3327},[1115,38263,32926],{"class":3343},[1115,38265,1405],{"class":3327},[1115,38267,32931],{"class":3343},[1115,38269,1405],{"class":3327},[1115,38271,32921],{"class":3343},[1115,38273,1405],{"class":3327},[1115,38275,32940],{"class":3343},[1115,38277,1405],{"class":3327},[1115,38279,32926],{"class":3343},[1115,38281,1405],{"class":3327},[1115,38283,32949],{"class":3343},[1115,38285,1405],{"class":3327},[1115,38287,32921],{"class":3343},[1115,38289,3520],{"class":3335},[1115,38291,38292,38294,38296,38298],{"class":3320,"line":27},[1115,38293,21880],{"class":3331},[1115,38295,1484],{"class":3335},[1115,38297,32897],{"class":3323},[1115,38299,3520],{"class":3335},[3311,38301,38304],{"className":38302,"code":38303,"language":3542,"meta":3315},[3540],"    Shapiro-Wilk normality test\n\ndata:  x2\nW = 0.96022, p-value = 0.7744\n",[3087,38305,38303],{"__ignoreMap":3315},[1110,38307,38308,38309,38328],{},"U dat o životnosti baterií se normalita nezamítá (",[1115,38310,38312],{"className":38311},[1144],[1146,38313,38314],{"xmlns":1148},[1150,38315,38316,38325],{},[1153,38317,38318,38320,38322],{},[1159,38319,1110],{},[1289,38321,1591],{},[1163,38323,38324],{},"0,7744",[1167,38326,38327],{"encoding":1169},"p = 0{,}7744","), předpoklad t-testu je tedy splněn.",[1103,38330,38332,38339,38342,38709,38715],{"className":38331,"dataCallout":3094},[1106,3093],[1110,38333,38335,38338],{"className":38334},[1113],[1115,38336],{"className":38337,"ariaHidden":1121},[1118,3101,1120],"Příklad: Doba do poruchy výrobku",[1110,38340,38341],{},"Zkoušky životnosti nového výrobku daly soubor 68 hodnot doby do poruchy (v minutách). Odhadněte charakteristiky a zákon rozdělení.",[3311,38343,38345],{"className":3313,"code":38344,"language":71,"meta":3315,"style":3315},"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",[3087,38346,38347,38438,38516,38604,38638,38648,38658,38668,38678],{"__ignoreMap":3315},[1115,38348,38349,38351,38353,38355,38357,38359,38361,38363,38365,38367,38369,38371,38373,38375,38377,38379,38381,38383,38385,38387,38389,38391,38393,38395,38397,38400,38402,38404,38406,38408,38410,38412,38414,38416,38418,38420,38422,38424,38426,38428,38430,38432,38434,38436],{"class":3320,"line":10},[1115,38350,18379],{"class":3323},[1115,38352,3328],{"class":3327},[1115,38354,3454],{"class":3331},[1115,38356,1484],{"class":3335},[1115,38358,18388],{"class":3343},[1115,38360,1405],{"class":3327},[1115,38362,18393],{"class":3343},[1115,38364,1405],{"class":3327},[1115,38366,18398],{"class":3343},[1115,38368,1405],{"class":3327},[1115,38370,18403],{"class":3343},[1115,38372,1405],{"class":3327},[1115,38374,13778],{"class":3343},[1115,38376,1405],{"class":3327},[1115,38378,3799],{"class":3343},[1115,38380,1405],{"class":3327},[1115,38382,3353],{"class":3343},[1115,38384,1405],{"class":3327},[1115,38386,18420],{"class":3343},[1115,38388,1405],{"class":3327},[1115,38390,14295],{"class":3343},[1115,38392,1405],{"class":3327},[1115,38394,18429],{"class":3343},[1115,38396,1405],{"class":3327},[1115,38398,38399],{"class":3343}," 367",[1115,38401,1405],{"class":3327},[1115,38403,18441],{"class":3343},[1115,38405,1405],{"class":3327},[1115,38407,18446],{"class":3343},[1115,38409,1405],{"class":3327},[1115,38411,18451],{"class":3343},[1115,38413,1405],{"class":3327},[1115,38415,3371],{"class":3343},[1115,38417,1405],{"class":3327},[1115,38419,18460],{"class":3343},[1115,38421,1405],{"class":3327},[1115,38423,18465],{"class":3343},[1115,38425,1405],{"class":3327},[1115,38427,18470],{"class":3343},[1115,38429,1405],{"class":3327},[1115,38431,18475],{"class":3343},[1115,38433,1405],{"class":3327},[1115,38435,18480],{"class":3343},[1115,38437,3356],{"class":3327},[1115,38439,38440,38442,38444,38446,38448,38450,38452,38454,38456,38458,38460,38462,38464,38466,38468,38470,38472,38474,38476,38478,38480,38482,38484,38486,38488,38490,38492,38494,38496,38498,38500,38502,38504,38506,38508,38510,38512,38514],{"class":3320,"line":27},[1115,38441,18487],{"class":3343},[1115,38443,1405],{"class":3327},[1115,38445,18492],{"class":3343},[1115,38447,1405],{"class":3327},[1115,38449,18497],{"class":3343},[1115,38451,1405],{"class":3327},[1115,38453,18502],{"class":3343},[1115,38455,1405],{"class":3327},[1115,38457,18507],{"class":3343},[1115,38459,1405],{"class":3327},[1115,38461,3371],{"class":3343},[1115,38463,1405],{"class":3327},[1115,38465,18516],{"class":3343},[1115,38467,1405],{"class":3327},[1115,38469,3353],{"class":3343},[1115,38471,1405],{"class":3327},[1115,38473,18525],{"class":3343},[1115,38475,1405],{"class":3327},[1115,38477,18530],{"class":3343},[1115,38479,1405],{"class":3327},[1115,38481,19622],{"class":3343},[1115,38483,1405],{"class":3327},[1115,38485,18542],{"class":3343},[1115,38487,1405],{"class":3327},[1115,38489,18547],{"class":3343},[1115,38491,1405],{"class":3327},[1115,38493,18441],{"class":3343},[1115,38495,1405],{"class":3327},[1115,38497,18556],{"class":3343},[1115,38499,1405],{"class":3327},[1115,38501,18561],{"class":3343},[1115,38503,1405],{"class":3327},[1115,38505,18566],{"class":3343},[1115,38507,1405],{"class":3327},[1115,38509,18571],{"class":3343},[1115,38511,1405],{"class":3327},[1115,38513,18576],{"class":3343},[1115,38515,3356],{"class":3327},[1115,38517,38518,38520,38522,38525,38527,38529,38531,38533,38535,38537,38539,38541,38543,38545,38547,38549,38551,38553,38555,38557,38559,38561,38563,38566,38568,38570,38572,38574,38576,38578,38580,38582,38584,38586,38588,38590,38592,38594,38596,38598,38600,38602],{"class":3320,"line":148},[1115,38519,18686],{"class":3343},[1115,38521,1405],{"class":3327},[1115,38523,38524],{"class":3343}," 74",[1115,38526,1405],{"class":3327},[1115,38528,18593],{"class":3343},[1115,38530,1405],{"class":3327},[1115,38532,18598],{"class":3343},[1115,38534,1405],{"class":3327},[1115,38536,18603],{"class":3343},[1115,38538,1405],{"class":3327},[1115,38540,18608],{"class":3343},[1115,38542,1405],{"class":3327},[1115,38544,18525],{"class":3343},[1115,38546,1405],{"class":3327},[1115,38548,18617],{"class":3343},[1115,38550,1405],{"class":3327},[1115,38552,15156],{"class":3343},[1115,38554,1405],{"class":3327},[1115,38556,18626],{"class":3343},[1115,38558,1405],{"class":3327},[1115,38560,18631],{"class":3343},[1115,38562,1405],{"class":3327},[1115,38564,38565],{"class":3343}," 194",[1115,38567,1405],{"class":3327},[1115,38569,3764],{"class":3343},[1115,38571,1405],{"class":3327},[1115,38573,18647],{"class":3343},[1115,38575,1405],{"class":3327},[1115,38577,18652],{"class":3343},[1115,38579,1405],{"class":3327},[1115,38581,18657],{"class":3343},[1115,38583,1405],{"class":3327},[1115,38585,18608],{"class":3343},[1115,38587,1405],{"class":3327},[1115,38589,14295],{"class":3343},[1115,38591,1405],{"class":3327},[1115,38593,3799],{"class":3343},[1115,38595,1405],{"class":3327},[1115,38597,18674],{"class":3343},[1115,38599,1405],{"class":3327},[1115,38601,18679],{"class":3343},[1115,38603,3356],{"class":3327},[1115,38605,38606,38608,38610,38612,38614,38616,38618,38620,38622,38624,38626,38628,38630,38632,38634,38636],{"class":3320,"line":111},[1115,38607,18686],{"class":3343},[1115,38609,1405],{"class":3327},[1115,38611,3348],{"class":3343},[1115,38613,1405],{"class":3327},[1115,38615,18695],{"class":3343},[1115,38617,1405],{"class":3327},[1115,38619,18700],{"class":3343},[1115,38621,1405],{"class":3327},[1115,38623,18705],{"class":3343},[1115,38625,1405],{"class":3327},[1115,38627,18710],{"class":3343},[1115,38629,1405],{"class":3327},[1115,38631,18441],{"class":3343},[1115,38633,1405],{"class":3327},[1115,38635,18719],{"class":3343},[1115,38637,3520],{"class":3335},[1115,38639,38640,38642,38644,38646],{"class":3320,"line":96},[1115,38641,16441],{"class":3331},[1115,38643,1484],{"class":3335},[1115,38645,18379],{"class":3323},[1115,38647,3520],{"class":3335},[1115,38649,38650,38652,38654,38656],{"class":3320,"line":89},[1115,38651,16463],{"class":3331},[1115,38653,1484],{"class":3335},[1115,38655,18379],{"class":3323},[1115,38657,3520],{"class":3335},[1115,38659,38660,38662,38664,38666],{"class":3320,"line":82},[1115,38661,17163],{"class":3331},[1115,38663,1484],{"class":3335},[1115,38665,18379],{"class":3323},[1115,38667,3520],{"class":3335},[1115,38669,38670,38672,38674,38676],{"class":3320,"line":75},[1115,38671,21880],{"class":3331},[1115,38673,1484],{"class":3335},[1115,38675,18379],{"class":3323},[1115,38677,3520],{"class":3335},[1115,38679,38680,38682,38684,38686,38688,38691,38693,38695,38697,38699,38701,38703,38705,38707],{"class":3320,"line":3510},[1115,38681,37997],{"class":3331},[1115,38683,1484],{"class":3335},[1115,38685,18379],{"class":3323},[1115,38687,1405],{"class":3327},[1115,38689,38690],{"class":3459}," \"pexp\"",[1115,38692,1405],{"class":3327},[1115,38694,14369],{"class":3323},[1115,38696,3416],{"class":3327},[1115,38698,4260],{"class":3343},[1115,38700,14376],{"class":3327},[1115,38702,13532],{"class":3331},[1115,38704,1484],{"class":3335},[1115,38706,18379],{"class":3323},[1115,38708,13794],{"class":3335},[3311,38710,38713],{"className":38711,"code":38712,"language":3542,"meta":3315},[3540],"[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",[3087,38714,38712],{"__ignoreMap":3315},[1110,38716,38717,38718,38737,38738,38755,38756,38775],{},"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 (",[1115,38719,38721],{"className":38720},[1144],[1146,38722,38723],{"xmlns":1148},[1150,38724,38725,38734],{},[1153,38726,38727,38729,38731],{},[1159,38728,1110],{},[1289,38730,3951],{},[1163,38732,38733],{},"0,0001",[1167,38735,38736],{"encoding":1169},"p \u003C 0{,}0001","), zatímco Kolmogorov-Smirnovův test proti exponenciálnímu rozdělení se střední hodnotou ",[1115,38739,38741],{"className":38740},[1144],[1146,38742,38743],{"xmlns":1148},[1150,38744,38745,38753],{},[1153,38746,38747],{},[2339,38748,38749,38751],{"accent":1121},[1159,38750,11019],{},[1289,38752,15762],{},[1167,38754,25870],{"encoding":1169}," shodu nezamítá (",[1115,38757,38759],{"className":38758},[1144],[1146,38760,38761],{"xmlns":1148},[1150,38762,38763,38772],{},[1153,38764,38765,38767,38769],{},[1159,38766,1110],{},[1289,38768,1591],{},[1163,38770,38771],{},"0,8421",[1167,38773,38774],{"encoding":1169},"p = 0{,}8421","): data odpovídají spíše exponenciálnímu rozdělení než normálnímu.",[1110,38777,38778],{},[4002,38779],{"alt":38780,"className":38781,"src":38782},"mask-th-exponencialni-shoda",[1321,4006],"\u002Fwiki-assets\u002Fmask-th-exponencialni-shoda.png",[1310,38784,38786],{"id":38785},"neparametrické-testy","Neparametrické testy",[1110,38788,38789,38790,4226,38792,38816],{},"Když předpoklad normality neplatí, nahrazují t-testy jejich neparametrické obdoby — Wilcoxonovy testy posuzují ",[1131,38791,15854],{},[1115,38793,38795],{"className":38794},[1144],[1146,38796,38797],{"xmlns":1148},[1150,38798,38799,38813],{},[1153,38800,38801],{},[1156,38802,38803,38805],{},[1159,38804,11019],{},[1153,38806,38807,38809,38811],{},[1163,38808,1165],{},[1289,38810,1405],{"separator":1121},[1163,38812,14227],{},[1167,38814,38815],{"encoding":1169},"x_{0,5}",") místo střední hodnoty a nevyžadují normalitu dat.",[21050,38818,38820],{"id":38819},"wilcoxonovy-testy","Wilcoxonovy testy",[1710,38822,38823,38868],{},[1713,38824,38825],{},[1716,38826,38827,38846,38865],{},[1719,38828,38829],{},[1115,38830,38832],{"className":38831},[1144],[1146,38833,38834],{"xmlns":1148},[1150,38835,38836,38844],{},[1153,38837,38838],{},[1156,38839,38840,38842],{},[1159,38841,1161],{},[1163,38843,1165],{},[1167,38845,1170],{"encoding":1169},[1719,38847,38848],{},[1115,38849,38851],{"className":38850},[1144],[1146,38852,38853],{"xmlns":1148},[1150,38854,38855,38863],{},[1153,38856,38857],{},[1156,38858,38859,38861],{},[1159,38860,1161],{},[1163,38862,1402],{},[1167,38864,2613],{"encoding":1169},[1719,38866,38867],{},"Příkaz v R",[1828,38869,38870,38937,39004],{},[1716,38871,38872,38902,38932],{},[1833,38873,38874],{},[1115,38875,38877],{"className":38876},[1144],[1146,38878,38879],{"xmlns":1148},[1150,38880,38881,38899],{},[1153,38882,38883,38895,38897],{},[1156,38884,38885,38887],{},[1159,38886,11019],{},[1153,38888,38889,38891,38893],{},[1163,38890,1165],{},[1289,38892,1405],{"separator":1121},[1163,38894,14227],{},[1289,38896,11034],{},[1159,38898,3338],{},[1167,38900,38901],{"encoding":1169},"x_{0,5} \\le c",[1833,38903,38904],{},[1115,38905,38907],{"className":38906},[1144],[1146,38908,38909],{"xmlns":1148},[1150,38910,38911,38929],{},[1153,38912,38913,38925,38927],{},[1156,38914,38915,38917],{},[1159,38916,11019],{},[1153,38918,38919,38921,38923],{},[1163,38920,1165],{},[1289,38922,1405],{"separator":1121},[1163,38924,14227],{},[1289,38926,1291],{},[1159,38928,3338],{},[1167,38930,38931],{"encoding":1169},"x_{0,5} > c",[1833,38933,38934],{},[3087,38935,38936],{},"wilcox.test(x, alternative = \"greater\", mu = c)",[1716,38938,38939,38969,38999],{},[1833,38940,38941],{},[1115,38942,38944],{"className":38943},[1144],[1146,38945,38946],{"xmlns":1148},[1150,38947,38948,38966],{},[1153,38949,38950,38962,38964],{},[1156,38951,38952,38954],{},[1159,38953,11019],{},[1153,38955,38956,38958,38960],{},[1163,38957,1165],{},[1289,38959,1405],{"separator":1121},[1163,38961,14227],{},[1289,38963,1591],{},[1159,38965,3338],{},[1167,38967,38968],{"encoding":1169},"x_{0,5} = c",[1833,38970,38971],{},[1115,38972,38974],{"className":38973},[1144],[1146,38975,38976],{"xmlns":1148},[1150,38977,38978,38996],{},[1153,38979,38980,38992,38994],{},[1156,38981,38982,38984],{},[1159,38983,11019],{},[1153,38985,38986,38988,38990],{},[1163,38987,1165],{},[1289,38989,1405],{"separator":1121},[1163,38991,14227],{},[1289,38993,15257],{"mathvariant":1734},[1159,38995,3338],{},[1167,38997,38998],{"encoding":1169},"x_{0,5} \\neq c",[1833,39000,39001],{},[3087,39002,39003],{},"wilcox.test(x, alternative = \"two.sided\", mu = c)",[1716,39005,39006,39036,39066],{},[1833,39007,39008],{},[1115,39009,39011],{"className":39010},[1144],[1146,39012,39013],{"xmlns":1148},[1150,39014,39015,39033],{},[1153,39016,39017,39029,39031],{},[1156,39018,39019,39021],{},[1159,39020,11019],{},[1153,39022,39023,39025,39027],{},[1163,39024,1165],{},[1289,39026,1405],{"separator":1121},[1163,39028,14227],{},[1289,39030,2968],{},[1159,39032,3338],{},[1167,39034,39035],{"encoding":1169},"x_{0,5} \\ge c",[1833,39037,39038],{},[1115,39039,39041],{"className":39040},[1144],[1146,39042,39043],{"xmlns":1148},[1150,39044,39045,39063],{},[1153,39046,39047,39059,39061],{},[1156,39048,39049,39051],{},[1159,39050,11019],{},[1153,39052,39053,39055,39057],{},[1163,39054,1165],{},[1289,39056,1405],{"separator":1121},[1163,39058,14227],{},[1289,39060,3951],{},[1159,39062,3338],{},[1167,39064,39065],{"encoding":1169},"x_{0,5} \u003C c",[1833,39067,39068],{},[3087,39069,39070],{},"wilcox.test(x, alternative = \"less\", mu = c)",[1110,39072,39073,39076,39077,1269],{},[6276,39074,39075],{},"Jednovýběrový Wilcoxonův test"," (obdoba t-testu) posuzuje odchylku mediánu od konstanty ",[1115,39078,39080],{"className":39079},[1144],[1146,39081,39082],{"xmlns":1148},[1150,39083,39084,39088],{},[1153,39085,39086],{},[1159,39087,3338],{},[1167,39089,3338],{"encoding":1169},[1110,39091,39092,39095,39096,13135,39134,39147,39148,1269],{},[6276,39093,39094],{},"Jednovýběrový Wilcoxonův test na diferencích"," (obdoba párového t-testu) posuzuje odchylku mediánu rozdílu ",[1115,39097,39099],{"className":39098},[1144],[1146,39100,39101],{"xmlns":1148},[1150,39102,39103,39131],{},[1153,39104,39105,39117,39119],{},[1156,39106,39107,39109],{},[1159,39108,11019],{},[1153,39110,39111,39113,39115],{},[1163,39112,1165],{},[1289,39114,1405],{"separator":1121},[1163,39116,14227],{},[1289,39118,2681],{},[1156,39120,39121,39123],{},[1159,39122,11429],{},[1153,39124,39125,39127,39129],{},[1163,39126,1165],{},[1289,39128,1405],{"separator":1121},[1163,39130,14227],{},[1167,39132,39133],{"encoding":1169},"x_{0,5}-y_{0,5}",[1115,39135,39137],{"className":39136},[1144],[1146,39138,39139],{"xmlns":1148},[1150,39140,39141,39145],{},[1153,39142,39143],{},[1159,39144,3338],{},[1167,39146,3338],{"encoding":1169},"; v R se volá se stejnými argumenty jako výše a navíc ",[3087,39149,39150],{},"paired = TRUE",[1110,39152,39153,39156,39157,39159],{},[6276,39154,39155],{},"Dvouvýběrový Wilcoxonův test"," (obdoba dvouvýběrového t-testu) posuzuje odchylku mediánů dvou nezávislých výběrů; argument ",[3087,39158,29753],{}," odpadá. Pro výšky chlapců a dívek z příkladu výše:",[3311,39161,39163],{"className":3313,"code":39162,"language":71,"meta":3315,"style":3315},"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",[3087,39164,39165,39235,39293],{"__ignoreMap":3315},[1115,39166,39167,39169,39171,39173,39175,39177,39179,39181,39183,39185,39187,39189,39191,39193,39195,39197,39199,39201,39203,39205,39207,39209,39211,39213,39215,39217,39219,39221,39223,39225,39227,39229,39231,39233],{"class":3320,"line":10},[1115,39168,37409],{"class":3323},[1115,39170,3328],{"class":3327},[1115,39172,3454],{"class":3331},[1115,39174,1484],{"class":3335},[1115,39176,37418],{"class":3343},[1115,39178,1405],{"class":3327},[1115,39180,19622],{"class":3343},[1115,39182,1405],{"class":3327},[1115,39184,37427],{"class":3343},[1115,39186,1405],{"class":3327},[1115,39188,37432],{"class":3343},[1115,39190,1405],{"class":3327},[1115,39192,37437],{"class":3343},[1115,39194,1405],{"class":3327},[1115,39196,37442],{"class":3343},[1115,39198,1405],{"class":3327},[1115,39200,22776],{"class":3343},[1115,39202,1405],{"class":3327},[1115,39204,18480],{"class":3343},[1115,39206,1405],{"class":3327},[1115,39208,37437],{"class":3343},[1115,39210,1405],{"class":3327},[1115,39212,37427],{"class":3343},[1115,39214,1405],{"class":3327},[1115,39216,37463],{"class":3343},[1115,39218,1405],{"class":3327},[1115,39220,37468],{"class":3343},[1115,39222,1405],{"class":3327},[1115,39224,37473],{"class":3343},[1115,39226,1405],{"class":3327},[1115,39228,37437],{"class":3343},[1115,39230,1405],{"class":3327},[1115,39232,37482],{"class":3343},[1115,39234,3520],{"class":3335},[1115,39236,39237,39239,39241,39243,39245,39247,39249,39251,39253,39255,39257,39259,39261,39263,39265,39267,39269,39271,39273,39275,39277,39279,39281,39283,39285,39287,39289,39291],{"class":3320,"line":27},[1115,39238,37489],{"class":3323},[1115,39240,3328],{"class":3327},[1115,39242,3454],{"class":3331},[1115,39244,1484],{"class":3335},[1115,39246,26142],{"class":3343},[1115,39248,1405],{"class":3327},[1115,39250,37432],{"class":3343},[1115,39252,1405],{"class":3327},[1115,39254,37506],{"class":3343},[1115,39256,1405],{"class":3327},[1115,39258,37511],{"class":3343},[1115,39260,1405],{"class":3327},[1115,39262,37516],{"class":3343},[1115,39264,1405],{"class":3327},[1115,39266,37516],{"class":3343},[1115,39268,1405],{"class":3327},[1115,39270,18480],{"class":3343},[1115,39272,1405],{"class":3327},[1115,39274,37432],{"class":3343},[1115,39276,1405],{"class":3327},[1115,39278,37432],{"class":3343},[1115,39280,1405],{"class":3327},[1115,39282,37537],{"class":3343},[1115,39284,1405],{"class":3327},[1115,39286,37468],{"class":3343},[1115,39288,1405],{"class":3327},[1115,39290,37432],{"class":3343},[1115,39292,3520],{"class":3335},[1115,39294,39295,39298,39300,39302,39304,39306,39308,39310,39312,39314],{"class":3320,"line":148},[1115,39296,39297],{"class":3331},"wilcox.test",[1115,39299,1484],{"class":3335},[1115,39301,37409],{"class":3323},[1115,39303,1405],{"class":3327},[1115,39305,37560],{"class":3323},[1115,39307,1405],{"class":3327},[1115,39309,32400],{"class":3323},[1115,39311,3416],{"class":3327},[1115,39313,32405],{"class":3459},[1115,39315,3520],{"class":3335},[3311,39317,39320],{"className":39318,"code":39319,"language":3542,"meta":3315},[3540],"    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",[3087,39321,39319],{"__ignoreMap":3315},[1110,39323,39324,39347],{},[1115,39325,39327],{"className":39326},[1144],[1146,39328,39329],{"xmlns":1148},[1150,39330,39331,39344],{},[1153,39332,39333,39335,39337,39340,39342],{},[1159,39334,1110],{},[1289,39336,1591],{},[1163,39338,39339],{},"0,315",[1289,39341,1291],{},[1163,39343,3603],{},[1167,39345,39346],{"encoding":1169},"p = 0{,}315 > 0{,}05",": mediány výšek chlapců a dívek se statisticky významně neliší — stejný závěr jako u dvouvýběrového t-testu.",[1103,39349,39351,39358,39380,39491,39497],{"className":39350,"dataCallout":3094},[1106,3093],[1110,39352,39354,39357],{"className":39353},[1113],[1115,39355],{"className":39356,"ariaHidden":1121},[1118,3101,1120],"Příklad: Realitní odhadci — neparametrická alternativa",[1110,39359,39360,39361,39379],{},"U odhadů cen z párového t-testu výše normalita diferencí neplatí (",[1115,39362,39364],{"className":39363},[1144],[1146,39365,39366],{"xmlns":1148},[1150,39367,39368,39376],{},[1153,39369,39370,39372,39374],{},[1159,39371,1110],{},[1289,39373,1591],{},[1163,39375,34453],{},[1167,39377,39378],{"encoding":1169},"p = 0{,}03203","). Správnou volbou je párový Wilcoxonův test:",[3311,39381,39383],{"className":3313,"code":39382,"language":71,"meta":3315,"style":3315},"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",[3087,39384,39385,39427,39469],{"__ignoreMap":3315},[1115,39386,39387,39389,39391,39393,39395,39397,39399,39401,39403,39405,39407,39409,39411,39413,39415,39417,39419,39421,39423,39425],{"class":3320,"line":10},[1115,39388,34256],{"class":3323},[1115,39390,3328],{"class":3327},[1115,39392,3454],{"class":3331},[1115,39394,1484],{"class":3335},[1115,39396,34265],{"class":3343},[1115,39398,1405],{"class":3327},[1115,39400,34270],{"class":3343},[1115,39402,1405],{"class":3327},[1115,39404,34275],{"class":3343},[1115,39406,1405],{"class":3327},[1115,39408,34280],{"class":3343},[1115,39410,1405],{"class":3327},[1115,39412,34285],{"class":3343},[1115,39414,1405],{"class":3327},[1115,39416,34290],{"class":3343},[1115,39418,1405],{"class":3327},[1115,39420,34295],{"class":3343},[1115,39422,1405],{"class":3327},[1115,39424,34300],{"class":3343},[1115,39426,3520],{"class":3335},[1115,39428,39429,39431,39433,39435,39437,39439,39441,39443,39445,39447,39449,39451,39453,39455,39457,39459,39461,39463,39465,39467],{"class":3320,"line":27},[1115,39430,34307],{"class":3323},[1115,39432,3328],{"class":3327},[1115,39434,3454],{"class":3331},[1115,39436,1484],{"class":3335},[1115,39438,34316],{"class":3343},[1115,39440,1405],{"class":3327},[1115,39442,34321],{"class":3343},[1115,39444,1405],{"class":3327},[1115,39446,34326],{"class":3343},[1115,39448,1405],{"class":3327},[1115,39450,34331],{"class":3343},[1115,39452,1405],{"class":3327},[1115,39454,34336],{"class":3343},[1115,39456,1405],{"class":3327},[1115,39458,34341],{"class":3343},[1115,39460,1405],{"class":3327},[1115,39462,34346],{"class":3343},[1115,39464,1405],{"class":3327},[1115,39466,34351],{"class":3343},[1115,39468,3520],{"class":3335},[1115,39470,39471,39473,39475,39477,39479,39481,39483,39485,39487,39489],{"class":3320,"line":148},[1115,39472,39297],{"class":3331},[1115,39474,1484],{"class":3335},[1115,39476,34256],{"class":3323},[1115,39478,1405],{"class":3327},[1115,39480,34366],{"class":3323},[1115,39482,1405],{"class":3327},[1115,39484,34371],{"class":3323},[1115,39486,3416],{"class":3327},[1115,39488,3429],{"class":3343},[1115,39490,3520],{"class":3335},[3311,39492,39495],{"className":39493,"code":39494,"language":3542,"meta":3315},[3540],"    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",[3087,39496,39494],{"__ignoreMap":3315},[1110,39498,39499,39522],{},[1115,39500,39502],{"className":39501},[1144],[1146,39503,39504],{"xmlns":1148},[1150,39505,39506,39519],{},[1153,39507,39508,39510,39512,39515,39517],{},[1159,39509,1110],{},[1289,39511,1591],{},[1163,39513,39514],{},"0,1484",[1289,39516,1291],{},[1163,39518,3603],{},[1167,39520,39521],{"encoding":1169},"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.",[21050,39524,39526],{"id":39525},"kruskalův-wallisův-test","Kruskalův-Wallisův test",[1110,39528,39529,39530,39547],{},"Zobecnění dvouvýběrového Wilcoxonova testu, neparametrická obdoba analýzy rozptylu jednoduchého třídění. ",[1115,39531,39533],{"className":39532},[1144],[1146,39534,39535],{"xmlns":1148},[1150,39536,39537,39545],{},[1153,39538,39539],{},[1156,39540,39541,39543],{},[1159,39542,1161],{},[1163,39544,1165],{},[1167,39546,1170],{"encoding":1169},": všechny výběry pocházejí ze stejného rozdělení.",[3311,39549,39551],{"className":3313,"code":39550,"language":71,"meta":3315,"style":3315},"kruskal.test(kvantitativní_proměnná ~ faktor, data = soubor)\n",[3087,39552,39553],{"__ignoreMap":3315},[1115,39554,39555,39558,39560,39563,39565,39568,39570,39572,39574,39577],{"class":3320,"line":10},[1115,39556,39557],{"class":3331},"kruskal.test",[1115,39559,1484],{"class":3335},[1115,39561,39562],{"class":3323},"kvantitativní_proměnná",[1115,39564,21161],{"class":3327},[1115,39566,39567],{"class":3323}," faktor",[1115,39569,1405],{"class":3327},[1115,39571,24470],{"class":3323},[1115,39573,3416],{"class":3327},[1115,39575,39576],{"class":3323}," soubor",[1115,39578,3520],{"class":3335},[21050,39580,39582],{"id":39581},"mediánový-test","Mediánový test",[1110,39584,39585,39586,39603,39604,1567],{},"Má stejný účel jako Kruskalův-Wallisův test (obdoba analýzy rozptylu jednoduchého třídění, ",[1115,39587,39589],{"className":39588},[1144],[1146,39590,39591],{"xmlns":1148},[1150,39592,39593,39601],{},[1153,39594,39595],{},[1156,39596,39597,39599],{},[1159,39598,1161],{},[1163,39600,1165],{},[1167,39602,1170],{"encoding":1169},": všechny výběry pocházejí ze stejného rozdělení) a je součástí balíčku ",[3087,39605,39606],{},"agricolae",[3311,39608,39610],{"className":3313,"code":39609,"language":71,"meta":3315,"style":3315},"library(agricolae)\nMedian.test(kvantitativní_proměnná, faktor)\n",[3087,39611,39612,39622],{"__ignoreMap":3315},[1115,39613,39614,39616,39618,39620],{"class":3320,"line":10},[1115,39615,21700],{"class":3327},[1115,39617,1484],{"class":3335},[1115,39619,39606],{"class":3323},[1115,39621,3520],{"class":3335},[1115,39623,39624,39627,39629,39631,39633,39635],{"class":3320,"line":27},[1115,39625,39626],{"class":3331},"Median.test",[1115,39628,1484],{"class":3335},[1115,39630,39562],{"class":3323},[1115,39632,1405],{"class":3327},[1115,39634,39567],{"class":3323},[1115,39636,3520],{"class":3335},[21050,39638,39640],{"id":39639},"friedmanův-test","Friedmanův test",[1110,39642,39643,39644,39661,39662,39700],{},"Neparametrická obdoba analýzy rozptylu dvojného třídění s jedním pozorováním v každé podtřídě. ",[1115,39645,39647],{"className":39646},[1144],[1146,39648,39649],{"xmlns":1148},[1150,39650,39651,39659],{},[1153,39652,39653],{},[1156,39654,39655,39657],{},[1159,39656,1161],{},[1163,39658,1165],{},[1167,39660,1170],{"encoding":1169},": distribuční funkce veličin ",[1115,39663,39665],{"className":39664},[1144],[1146,39666,39667],{"xmlns":1148},[1150,39668,39669,39697],{},[1153,39670,39671,39681,39683,39685,39687],{},[1156,39672,39673,39675],{},[1159,39674,11031],{},[1153,39676,39677,39679],{},[1159,39678,1487],{},[1163,39680,1402],{},[1289,39682,1405],{"separator":1121},[1289,39684,1408],{},[1289,39686,1405],{"separator":1121},[1156,39688,39689,39691],{},[1159,39690,11031],{},[1153,39692,39693,39695],{},[1159,39694,1487],{},[1159,39696,11559],{},[1167,39698,39699],{"encoding":1169},"X_{i1}, \\dots, X_{ik}"," jsou totožné.",[3311,39702,39704],{"className":3313,"code":39703,"language":71,"meta":3315,"style":3315},"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",[3087,39705,39706,39736,39741],{"__ignoreMap":3315},[1115,39707,39708,39711,39713,39715,39717,39720,39723,39726,39728,39730,39732,39734],{"class":3320,"line":10},[1115,39709,39710],{"class":3331},"friedman.test",[1115,39712,1484],{"class":3335},[1115,39714,39562],{"class":3323},[1115,39716,21161],{"class":3327},[1115,39718,39719],{"class":3323}," faktor_A",[1115,39721,39722],{"class":3327}," |",[1115,39724,39725],{"class":3323}," faktor_B",[1115,39727,1405],{"class":3327},[1115,39729,24470],{"class":3323},[1115,39731,3416],{"class":3327},[1115,39733,39576],{"class":3323},[1115,39735,3520],{"class":3335},[1115,39737,39738],{"class":3320,"line":27},[1115,39739,39740],{"class":16336},"# jsou-li proměnné samostatné vektory (bez argumentu data):\n",[1115,39742,39743,39745,39747,39749,39751,39753,39755,39757],{"class":3320,"line":148},[1115,39744,39710],{"class":3331},[1115,39746,1484],{"class":3335},[1115,39748,39562],{"class":3323},[1115,39750,1405],{"class":3327},[1115,39752,39719],{"class":3323},[1115,39754,1405],{"class":3327},[1115,39756,39725],{"class":3323},[1115,39758,3520],{"class":3335},[1310,39760,39762],{"id":39761},"přehled-testů","Přehled testů",[1110,39764,39765],{},[4002,39766],{"alt":39767,"className":39768,"src":39769},"mask-ilu-volba-testu",[1321,4006],"\u002Fwiki-assets\u002Fmask-ilu-volba-testu.png",[1710,39771,39772,39785],{},[1713,39773,39774],{},[1716,39775,39776,39779,39782],{},[1719,39777,39778],{},"Situace",[1719,39780,39781],{},"Test",[1719,39783,39784],{},"R funkce",[1828,39786,39787,39800,39813,39825,39838,39853,39865,39878,39891,39904,39916,39931],{},[1716,39788,39789,39792,39795],{},[1833,39790,39791],{},"Jedna střední hodnota vs. zadané číslo, normální data",[1833,39793,39794],{},"jednovýběrový t-test",[1833,39796,39797],{},[3087,39798,39799],{},"t.test(x, mu = ..., alternative = ...)",[1716,39801,39802,39805,39808],{},[1833,39803,39804],{},"Rozdíl dvou závislých měření, diference normální",[1833,39806,39807],{},"párový t-test",[1833,39809,39810],{},[3087,39811,39812],{},"t.test(x, y, paired = TRUE)",[1716,39814,39815,39818,39820],{},[1833,39816,39817],{},"Shoda rozptylů dvou nezávislých normálních výběrů",[1833,39819,24378],{},[1833,39821,39822],{},[3087,39823,39824],{},"var.test(x, y)",[1716,39826,39827,39830,39833],{},[1833,39828,39829],{},"Shoda středních hodnot dvou nezávislých normálních výběrů",[1833,39831,39832],{},"dvouvýběrový t-test",[1833,39834,39835],{},[3087,39836,39837],{},"t.test(x, y, var.equal = TRUE\u002FFALSE)",[1716,39839,39840,39843,39845],{},[1833,39841,39842],{},"Shoda dat se zadaným typem rozdělení (normální, exponenciální, …)",[1833,39844,37646],{},[1833,39846,39847,2568,39850],{},[3087,39848,39849],{},"ks.test(x, \"pnorm\", mu, sigma)",[3087,39851,39852],{},"ks.test(x, \"pexp\", 1\u002Fdelta)",[1716,39854,39855,39858,39860],{},[1833,39856,39857],{},"Normalita dat",[1833,39859,38062],{},[1833,39861,39862],{},[3087,39863,39864],{},"shapiro.test(x)",[1716,39866,39867,39870,39873],{},[1833,39868,39869],{},"Medián jednoho výběru vs. konstanta, data nejsou normální",[1833,39871,39872],{},"jednovýběrový Wilcoxonův test",[1833,39874,39875],{},[3087,39876,39877],{},"wilcox.test(x, mu = c, alternative = ...)",[1716,39879,39880,39883,39886],{},[1833,39881,39882],{},"Medián diferencí dvou závislých měření, data nejsou normální",[1833,39884,39885],{},"párový Wilcoxonův test",[1833,39887,39888],{},[3087,39889,39890],{},"wilcox.test(x, y, paired = TRUE, mu = c)",[1716,39892,39893,39896,39899],{},[1833,39894,39895],{},"Mediány dvou nezávislých výběrů, data nejsou normální",[1833,39897,39898],{},"dvouvýběrový Wilcoxonův test",[1833,39900,39901],{},[3087,39902,39903],{},"wilcox.test(x, y)",[1716,39905,39906,39909,39911],{},[1833,39907,39908],{},"Více než dva nezávislé výběry, data nejsou normální",[1833,39910,39526],{},[1833,39912,39913],{},[3087,39914,39915],{},"kruskal.test(y ~ faktor, data)",[1716,39917,39918,39921,39924],{},[1833,39919,39920],{},"Více než dva nezávislé výběry, data nejsou normální (alternativa)",[1833,39922,39923],{},"mediánový test",[1833,39925,39926,26970,39929],{},[3087,39927,39928],{},"Median.test(y, faktor)",[3087,39930,39606],{},[1716,39932,39933,39936,39938],{},[1833,39934,39935],{},"Více než dva závislé výběry (dvojné třídění, jedno pozorování na podtřídu)",[1833,39937,39640],{},[1833,39939,39940],{},[3087,39941,39942],{},"friedman.test(y ~ A | B, data)",[1310,39944,6027],{"id":6026},[1124,39946,39947,40024,40030,40047,40078],{},[1127,39948,39949,39988,39989,37376,40006,40023],{},[1131,39950,39951,39952,39969,39970,39987],{},"Nezamítnutí ",[1115,39953,39955],{"className":39954},[1144],[1146,39956,39957],{"xmlns":1148},[1150,39958,39959,39967],{},[1153,39960,39961],{},[1156,39962,39963,39965],{},[1159,39964,1161],{},[1163,39966,1165],{},[1167,39968,1170],{"encoding":1169}," není důkaz, že ",[1115,39971,39973],{"className":39972},[1144],[1146,39974,39975],{"xmlns":1148},[1150,39976,39977,39985],{},[1153,39978,39979],{},[1156,39980,39981,39983],{},[1159,39982,1161],{},[1163,39984,1165],{},[1167,39986,1170],{"encoding":1169}," platí."," U kabelů A\u002FB vyšlo ",[1115,39990,39992],{"className":39991},[1144],[1146,39993,39994],{"xmlns":1148},[1150,39995,39996,40004],{},[1153,39997,39998,40000,40002],{},[1159,39999,1110],{},[1289,40001,1591],{},[1163,40003,37372],{},[1167,40005,37375],{"encoding":1169},[1115,40007,40009],{"className":40008},[1144],[1146,40010,40011],{"xmlns":1148},[1150,40012,40013,40021],{},[1153,40014,40015],{},[1156,40016,40017,40019],{},[1159,40018,1161],{},[1163,40020,1165],{},[1167,40022,1170],{"encoding":1169}," nezamítá, ale hodnota je blízko hranice; správná interpretace je „data rovnost průměrů nevyvracejí“, ne „rovnost je prokázána“.",[1127,40025,40026,40029],{},[1131,40027,40028],{},"Před párovým nebo dvouvýběrovým t-testem ověřte normalitu."," U realitních odhadců vycházel párový t-test bez varování, ale Shapiro-Wilkův test na diferencích normalitu zamítl — správným testem byl párový Wilcoxonův test.",[1127,40031,40032,40039,40040,40043,40044,40046],{},[1131,40033,40034,34534,40036,40038],{},[3087,40035,37104],{},[3087,40037,32318],{}," se volí podle F-testu, ne podle výchozí hodnoty."," Výchozí nastavení R je ",[3087,40041,40042],{},"var.equal = FALSE"," (Welchova varianta); pokud F-test potvrdí shodné rozptyly, je třeba explicitně napsat ",[3087,40045,37355],{},", jinak se použije jiná statistika a jiné stupně volnosti.",[1127,40048,40049,40052,40053,40056,40057,40074,40075,1269],{},[1131,40050,40051],{},"Jednostranná vs. dvoustranná alternativa mění kritický obor i závěr."," Volba ",[3087,40054,40055],{},"alternative = \"greater\"\u002F\"less\"\u002F\"two.sided\""," musí odpovídat formulaci ",[1115,40058,40060],{"className":40059},[1144],[1146,40061,40062],{"xmlns":1148},[1150,40063,40064,40072],{},[1153,40065,40066],{},[1156,40067,40068,40070],{},[1159,40069,1161],{},[1163,40071,1402],{},[1167,40073,2613],{"encoding":1169}," v zadání, ne být ponechána na výchozí hodnotě ",[3087,40076,40077],{},"\"two.sided\"",[1127,40079,40080,40083,40084,40097],{},[1131,40081,40082],{},"Shapiro-Wilkův test se vyhodnocuje jen přes p-hodnotu",", ne porovnáním ",[1115,40085,40087],{"className":40086},[1144],[1146,40088,40089],{"xmlns":1148},[1150,40090,40091,40095],{},[1153,40092,40093],{},[1159,40094,1205],{},[1167,40096,1205],{"encoding":1169}," s tabulkovou kritickou hodnotou jako u ostatních testů v této kapitole.",[1310,40099,6215],{"id":6214},[1124,40101,40102,40107,40112,40117,40122,40127,40132],{},[1127,40103,40104],{},[1318,40105,1324],{"className":40106,"dataFsResolvedFilePath":1322,"href":1323},[1321],[1127,40108,40109],{},[1318,40110,6244],{"className":40111,"dataFsResolvedFilePath":6242,"href":6243},[1321],[1127,40113,40114],{},[1318,40115,6236],{"className":40116,"dataFsResolvedFilePath":6234,"href":6235},[1321],[1127,40118,40119],{},[1318,40120,6252],{"className":40121,"dataFsResolvedFilePath":6250,"href":6251},[1321],[1127,40123,40124],{},[1318,40125,1094],{"className":40126,"dataFsResolvedFilePath":15392,"href":15393},[1321],[1127,40128,40129],{},[1318,40130,6260],{"className":40131,"dataFsResolvedFilePath":6258,"href":6259},[1321],[1127,40133,40134],{},[1318,40135,6268],{"className":40136,"dataFsResolvedFilePath":6266,"href":6267},[1321],[1310,40138,6271],{"id":934},[1110,40140,6274,40141,6279],{},[6276,40142,6278],{},[6281,40144,40145],{},"html pre.shiki code .sP4rz, 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