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kostce",[1124,1125,1126,1139,1260,1334,1417],"ul",{},[1127,1128,1129,1130,1134,1135,1138],"li",{},"Náhodná veličina je funkce, která výsledkům pokusu přiřazuje reálná čísla; rozlišujeme ",[1131,1132,1133],"strong",{},"diskrétní"," (izolované hodnoty s nenulovou pravděpodobností) a ",[1131,1136,1137],{},"spojité"," (hodnoty z intervalu, každý bod má nulovou pravděpodobnost).",[1127,1140,1141,1142,1145,1146,1198,1199,1238,1239,1259],{},"Každou náhodnou veličinu popisuje ",[1131,1143,1144],{},"distribuční funkce"," ",[1115,1147,1150],{"className":1148},[1149],"katex",[1151,1152,1154],"math",{"xmlns":1153},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1155,1156,1157,1193],"semantics",{},[1158,1159,1160,1164,1169,1172,1175,1178,1181,1183,1186,1189,1191],"mrow",{},[1161,1162,1163],"mi",{},"F",[1165,1166,1168],"mo",{"stretchy":1167},"false","(",[1161,1170,1171],{},"x",[1165,1173,1174],{"stretchy":1167},")",[1165,1176,1177],{},"=",[1161,1179,1180],{},"P",[1165,1182,1168],{"stretchy":1167},[1161,1184,1185],{},"X",[1165,1187,1188],{},"≤",[1161,1190,1171],{},[1165,1192,1174],{"stretchy":1167},[1194,1195,1197],"annotation",{"encoding":1196},"application\u002Fx-tex","F(x) = P(X \\le x)","; u spojité veličiny platí ",[1115,1200,1202],{"className":1201},[1149],[1151,1203,1204],{"xmlns":1153},[1155,1205,1206,1235],{},[1158,1207,1208,1218,1220,1222,1224,1226,1229,1231,1233],{},[1209,1210,1211,1213],"msup",{},[1161,1212,1163],{},[1165,1214,1217],{"mathvariant":1215,"lspace":1216,"rspace":1216},"normal","0em","′",[1165,1219,1168],{"stretchy":1167},[1161,1221,1171],{},[1165,1223,1174],{"stretchy":1167},[1165,1225,1177],{},[1161,1227,1228],{},"f",[1165,1230,1168],{"stretchy":1167},[1161,1232,1171],{},[1165,1234,1174],{"stretchy":1167},[1194,1236,1237],{"encoding":1196},"F'(x) = f(x)",", kde ",[1115,1240,1242],{"className":1241},[1149],[1151,1243,1244],{"xmlns":1153},[1155,1245,1246,1256],{},[1158,1247,1248,1250,1252,1254],{},[1161,1249,1228],{},[1165,1251,1168],{"stretchy":1167},[1161,1253,1171],{},[1165,1255,1174],{"stretchy":1167},[1194,1257,1258],{"encoding":1196},"f(x)"," je hustota pravděpodobnosti.",[1127,1261,1262,1263,1333],{},"Pravděpodobnost na intervalu se počítá jako ",[1115,1264,1266],{"className":1265},[1149],[1151,1267,1268],{"xmlns":1153},[1155,1269,1270,1330],{},[1158,1271,1272,1274,1276,1285,1288,1290,1292,1299,1301,1303,1305,1307,1313,1315,1318,1320,1322,1328],{},[1161,1273,1180],{},[1165,1275,1168],{"stretchy":1167},[1277,1278,1279,1281],"msub",{},[1161,1280,1171],{},[1282,1283,1284],"mn",{},"1",[1165,1286,1287],{},"\u003C",[1161,1289,1185],{},[1165,1291,1287],{},[1277,1293,1294,1296],{},[1161,1295,1171],{},[1282,1297,1298],{},"2",[1165,1300,1174],{"stretchy":1167},[1165,1302,1177],{},[1161,1304,1163],{},[1165,1306,1168],{"stretchy":1167},[1277,1308,1309,1311],{},[1161,1310,1171],{},[1282,1312,1298],{},[1165,1314,1174],{"stretchy":1167},[1165,1316,1317],{},"−",[1161,1319,1163],{},[1165,1321,1168],{"stretchy":1167},[1277,1323,1324,1326],{},[1161,1325,1171],{},[1282,1327,1284],{},[1165,1329,1174],{"stretchy":1167},[1194,1331,1332],{"encoding":1196},"P(x_1 \u003C X \u003C x_2) = F(x_2) - F(x_1)",".",[1127,1335,1336,1145,1339,1371,1372,1376,1377,1376,1380,1383,1384,1398,1399,1333],{},[1131,1337,1338],{},"Normální rozdělení",[1115,1340,1342],{"className":1341},[1149],[1151,1343,1344],{"xmlns":1153},[1155,1345,1346,1368],{},[1158,1347,1348,1351,1353,1356,1359,1366],{},[1161,1349,1350],{},"N",[1165,1352,1168],{"stretchy":1167},[1161,1354,1355],{},"μ",[1165,1357,1358],{"separator":1121},";",[1209,1360,1361,1364],{},[1161,1362,1363],{},"σ",[1282,1365,1298],{},[1165,1367,1174],{"stretchy":1167},[1194,1369,1370],{"encoding":1196},"N(\\mu; \\sigma^2)"," je nejdůležitější spojité rozdělení; v R ho počítáme funkcemi ",[1373,1374,1375],"code",{},"dnorm",", ",[1373,1378,1379],{},"pnorm",[1373,1381,1382],{},"qnorm"," — R jako parametr očekává směrodatnou odchylku ",[1115,1385,1387],{"className":1386},[1149],[1151,1388,1389],{"xmlns":1153},[1155,1390,1391,1395],{},[1158,1392,1393],{},[1161,1394,1363],{},[1194,1396,1397],{"encoding":1196},"\\sigma",", ne rozptyl ",[1115,1400,1402],{"className":1401},[1149],[1151,1403,1404],{"xmlns":1153},[1155,1405,1406,1414],{},[1158,1407,1408],{},[1209,1409,1410,1412],{},[1161,1411,1363],{},[1282,1413,1298],{},[1194,1415,1416],{"encoding":1196},"\\sigma^2",[1127,1418,1419,1376,1422,1425,1426,1429],{},[1131,1420,1421],{},"Studentovo",[1131,1423,1424],{},"Pearsonovo (χ²)"," a ",[1131,1427,1428],{},"Fisherovo-Snedecorovo"," rozdělení slouží jako nástroj pro pozdější konstrukci intervalů spolehlivosti a testování hypotéz.",[1431,1432,1434],"h2",{"id":1433},"náhodná-veličina","Náhodná veličina",[1110,1436,1437,1445,1446,1461,1462,1145,1464,1477,1478,1498,1499,1238,1512,1536,1537,1376,1550,1376,1564,1578,1579,1376,1592,1376,1606,1620,1621,1634,1635,1648,1649,1333],{},[1438,1439,1444],"a",{"className":1440,"dataFsResolvedFilePath":1442,"href":1443},[1441],"wikilink","courses\u002Fmask.md","\u002Fwiki\u002Fmask","Metody aplikované statistiky"," pracuje s veličinami, jejichž hodnota závisí na náhodě. Formálně: uvažujeme základní prostor ",[1115,1447,1449],{"className":1448},[1149],[1151,1450,1451],{"xmlns":1153},[1155,1452,1453,1458],{},[1158,1454,1455],{},[1161,1456,1457],{"mathvariant":1215},"Ω",[1194,1459,1460],{"encoding":1196},"\\Omega"," přiřazený výsledkům pokusu. ",[1131,1463,1434],{},[1115,1465,1467],{"className":1466},[1149],[1151,1468,1469],{"xmlns":1153},[1155,1470,1471,1475],{},[1158,1472,1473],{},[1161,1474,1185],{},[1194,1476,1185],{"encoding":1196}," je funkce, která prvkům ",[1115,1479,1481],{"className":1480},[1149],[1151,1482,1483],{"xmlns":1153},[1155,1484,1485,1495],{},[1158,1486,1487,1490,1493],{},[1161,1488,1489],{},"ω",[1165,1491,1492],{},"∈",[1161,1494,1457],{"mathvariant":1215},[1194,1496,1497],{"encoding":1196},"\\omega \\in \\Omega"," přiřazuje reálná čísla ",[1115,1500,1502],{"className":1501},[1149],[1151,1503,1504],{"xmlns":1153},[1155,1505,1506,1510],{},[1158,1507,1508],{},[1161,1509,1171],{},[1194,1511,1171],{"encoding":1196},[1115,1513,1515],{"className":1514},[1149],[1151,1516,1517],{"xmlns":1153},[1155,1518,1519,1533],{},[1158,1520,1521,1523,1525,1527,1529,1531],{},[1161,1522,1171],{},[1165,1524,1177],{},[1161,1526,1185],{},[1165,1528,1168],{"stretchy":1167},[1161,1530,1489],{},[1165,1532,1174],{"stretchy":1167},[1194,1534,1535],{"encoding":1196},"x = X(\\omega)",". Náhodné veličiny značíme velkými písmeny (",[1115,1538,1540],{"className":1539},[1149],[1151,1541,1542],{"xmlns":1153},[1155,1543,1544,1548],{},[1158,1545,1546],{},[1161,1547,1185],{},[1194,1549,1185],{"encoding":1196},[1115,1551,1553],{"className":1552},[1149],[1151,1554,1555],{"xmlns":1153},[1155,1556,1557,1562],{},[1158,1558,1559],{},[1161,1560,1561],{},"Y",[1194,1563,1561],{"encoding":1196},[1115,1565,1567],{"className":1566},[1149],[1151,1568,1569],{"xmlns":1153},[1155,1570,1571,1576],{},[1158,1572,1573],{},[1161,1574,1575],{},"T",[1194,1577,1575],{"encoding":1196},"), jejich konkrétní hodnoty odpovídajícími malými písmeny (",[1115,1580,1582],{"className":1581},[1149],[1151,1583,1584],{"xmlns":1153},[1155,1585,1586,1590],{},[1158,1587,1588],{},[1161,1589,1171],{},[1194,1591,1171],{"encoding":1196},[1115,1593,1595],{"className":1594},[1149],[1151,1596,1597],{"xmlns":1153},[1155,1598,1599,1604],{},[1158,1600,1601],{},[1161,1602,1603],{},"y",[1194,1605,1603],{"encoding":1196},[1115,1607,1609],{"className":1608},[1149],[1151,1610,1611],{"xmlns":1153},[1155,1612,1613,1618],{},[1158,1614,1615],{},[1161,1616,1617],{},"t",[1194,1619,1617],{"encoding":1196},"); pravděpodobnost, že ",[1115,1622,1624],{"className":1623},[1149],[1151,1625,1626],{"xmlns":1153},[1155,1627,1628,1632],{},[1158,1629,1630],{},[1161,1631,1185],{},[1194,1633,1185],{"encoding":1196}," nabyla hodnoty ",[1115,1636,1638],{"className":1637},[1149],[1151,1639,1640],{"xmlns":1153},[1155,1641,1642,1646],{},[1158,1643,1644],{},[1161,1645,1171],{},[1194,1647,1171],{"encoding":1196},", zapisujeme ",[1115,1650,1652],{"className":1651},[1149],[1151,1653,1654],{"xmlns":1153},[1155,1655,1656,1670],{},[1158,1657,1658,1660,1662,1664,1666,1668],{},[1161,1659,1180],{},[1165,1661,1168],{"stretchy":1167},[1161,1663,1185],{},[1165,1665,1177],{},[1161,1667,1171],{},[1165,1669,1174],{"stretchy":1167},[1194,1671,1672],{"encoding":1196},"P(X = x)",[1110,1674,1675],{},"Podle typu hodnot, kterých náhodná veličina nabývá, rozlišujeme dva typy:",[1124,1677,1678,1740],{},[1127,1679,1680,1683,1684,1697,1698,1739],{},[1131,1681,1682],{},"Diskrétní náhodná veličina"," — prvky ",[1115,1685,1687],{"className":1686},[1149],[1151,1688,1689],{"xmlns":1153},[1155,1690,1691,1695],{},[1158,1692,1693],{},[1161,1694,1457],{"mathvariant":1215},[1194,1696,1460],{"encoding":1196}," se zobrazí na osu reálných čísel jako izolované body ",[1115,1699,1701],{"className":1700},[1149],[1151,1702,1703],{"xmlns":1153},[1155,1704,1705,1736],{},[1158,1706,1707,1713,1716,1722,1724,1727,1729],{},[1277,1708,1709,1711],{},[1161,1710,1171],{},[1282,1712,1284],{},[1165,1714,1715],{"separator":1121},",",[1277,1717,1718,1720],{},[1161,1719,1171],{},[1282,1721,1298],{},[1165,1723,1715],{"separator":1121},[1165,1725,1726],{},"…",[1165,1728,1715],{"separator":1121},[1277,1730,1731,1733],{},[1161,1732,1171],{},[1161,1734,1735],{},"k",[1194,1737,1738],{"encoding":1196},"x_1, x_2, \\dots, x_k",", přičemž každý z nich má nenulovou pravděpodobnost. Příklad: počet bodů při hodu kostkou, počet studentů na cvičení.",[1127,1741,1742,1745],{},[1131,1743,1744],{},"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.",[1431,1747,1749],{"id":1748},"distribuční-funkce","Distribuční funkce",[1110,1751,1752,1753,1756],{},"Náhodná veličina nabývá při pokusu určité hodnoty, aniž bychom předem věděli, které. Při opakování pokusu se ale projevují zákonitosti, které popisují ",[1131,1754,1755],{},"zákony rozdělení",". Nejobecnějším z nich je distribuční funkce.",[1110,1758,1759],{},[1760,1761],"img",{"alt":1762,"className":1763,"src":1765},"mask-nv-distribucni-funkce",[1441,1764],"wikilink-broken","\u002Fwiki-assets\u002Fmask-nv-distribucni-funkce.png",[1103,1767,1770,1777],{"className":1768,"dataCallout":654},[1106,1769],"callout-info",[1110,1771,1773,1776],{"className":1772},[1113],[1115,1774],{"className":1775,"ariaHidden":1121},[1118,1119,1120],"Definice",[1110,1778,1779,1780,1793,1794,1814,1815,1828,1829,1865,1884,1885,1898,1899,1333],{},"Distribuční funkcí náhodné veličiny ",[1115,1781,1783],{"className":1782},[1149],[1151,1784,1785],{"xmlns":1153},[1155,1786,1787,1791],{},[1158,1788,1789],{},[1161,1790,1185],{},[1194,1792,1185],{"encoding":1196}," nazýváme reálnou funkci ",[1115,1795,1797],{"className":1796},[1149],[1151,1798,1799],{"xmlns":1153},[1155,1800,1801,1811],{},[1158,1802,1803,1805,1807,1809],{},[1161,1804,1163],{},[1165,1806,1168],{"stretchy":1167},[1161,1808,1171],{},[1165,1810,1174],{"stretchy":1167},[1194,1812,1813],{"encoding":1196},"F(x)"," definovanou pro každé reálné číslo ",[1115,1816,1818],{"className":1817},[1149],[1151,1819,1820],{"xmlns":1153},[1155,1821,1822,1826],{},[1158,1823,1824],{},[1161,1825,1171],{},[1194,1827,1171],{"encoding":1196}," jako\n",[1115,1830,1832],{"className":1831},[1149],[1151,1833,1834],{"xmlns":1153},[1155,1835,1836,1862],{},[1158,1837,1838,1840,1842,1844,1846,1848,1850,1852,1854,1856,1858,1860],{},[1161,1839,1163],{},[1165,1841,1168],{"stretchy":1167},[1161,1843,1171],{},[1165,1845,1174],{"stretchy":1167},[1165,1847,1177],{},[1161,1849,1180],{},[1165,1851,1168],{"stretchy":1167},[1161,1853,1185],{},[1165,1855,1188],{},[1161,1857,1171],{},[1165,1859,1174],{"stretchy":1167},[1161,1861,1333],{"mathvariant":1215},[1194,1863,1864],{"encoding":1196},"F(x) = P(X \\le x).",[1115,1866,1868],{"className":1867},[1149],[1151,1869,1870],{"xmlns":1153},[1155,1871,1872,1882],{},[1158,1873,1874,1876,1878,1880],{},[1161,1875,1163],{},[1165,1877,1168],{"stretchy":1167},[1161,1879,1171],{},[1165,1881,1174],{"stretchy":1167},[1194,1883,1813],{"encoding":1196}," tedy vyjadřuje pravděpodobnost, s jakou ",[1115,1886,1888],{"className":1887},[1149],[1151,1889,1890],{"xmlns":1153},[1155,1891,1892,1896],{},[1158,1893,1894],{},[1161,1895,1185],{},[1194,1897,1185],{"encoding":1196}," nabude hodnoty z intervalu ",[1115,1900,1902],{"className":1901},[1149],[1151,1903,1904],{"xmlns":1153},[1155,1905,1906,1922],{},[1158,1907,1908,1910,1912,1915,1917,1919],{},[1165,1909,1168],{"stretchy":1167},[1165,1911,1317],{},[1161,1913,1914],{"mathvariant":1215},"∞",[1165,1916,1715],{"separator":1121},[1161,1918,1171],{},[1165,1920,1921],{"stretchy":1167},"⟩",[1194,1923,1924],{"encoding":1196},"(-\\infty, x\\rangle",[1110,1926,1927,1928,1941,1942,1963],{},"Značí-li například ",[1115,1929,1931],{"className":1930},[1149],[1151,1932,1933],{"xmlns":1153},[1155,1934,1935,1939],{},[1158,1936,1937],{},[1161,1938,1185],{},[1194,1940,1185],{"encoding":1196}," výšku mužů v populaci, pak ",[1115,1943,1945],{"className":1944},[1149],[1151,1946,1947],{"xmlns":1153},[1155,1948,1949,1960],{},[1158,1950,1951,1953,1955,1958],{},[1161,1952,1163],{},[1165,1954,1168],{"stretchy":1167},[1282,1956,1957],{},"175",[1165,1959,1174],{"stretchy":1167},[1194,1961,1962],{"encoding":1196},"F(175)"," je pravděpodobnost, že muž měří nejvýše 175 cm.",[1110,1965,1966],{},"Pro distribuční funkci vždy platí:",[1124,1968,1969,2000,2058,2120],{},[1127,1970,1971,1715],{},[1115,1972,1974],{"className":1973},[1149],[1151,1975,1976],{"xmlns":1153},[1155,1977,1978,1997],{},[1158,1979,1980,1983,1985,1987,1989,1991,1993,1995],{},[1282,1981,1982],{},"0",[1165,1984,1188],{},[1161,1986,1163],{},[1165,1988,1168],{"stretchy":1167},[1161,1990,1171],{},[1165,1992,1174],{"stretchy":1167},[1165,1994,1188],{},[1282,1996,1284],{},[1194,1998,1999],{"encoding":1196},"0 \\le F(x) \\le 1",[1127,2001,2002,2003,1715],{},"je neklesající: ",[1115,2004,2006],{"className":2005},[1149],[1151,2007,2008],{"xmlns":1153},[1155,2009,2010,2055],{},[1158,2011,2012,2018,2020,2026,2029,2031,2033,2039,2041,2043,2045,2047,2053],{},[1277,2013,2014,2016],{},[1161,2015,1171],{},[1282,2017,1284],{},[1165,2019,1188],{},[1277,2021,2022,2024],{},[1161,2023,1171],{},[1282,2025,1298],{},[1165,2027,2028],{},"⇒",[1161,2030,1163],{},[1165,2032,1168],{"stretchy":1167},[1277,2034,2035,2037],{},[1161,2036,1171],{},[1282,2038,1284],{},[1165,2040,1174],{"stretchy":1167},[1165,2042,1188],{},[1161,2044,1163],{},[1165,2046,1168],{"stretchy":1167},[1277,2048,2049,2051],{},[1161,2050,1171],{},[1282,2052,1298],{},[1165,2054,1174],{"stretchy":1167},[1194,2056,2057],{"encoding":1196},"x_1 \\le x_2 \\Rightarrow F(x_1) \\le F(x_2)",[1127,2059,2060,2061,1715],{},"je spojitá zprava: ",[1115,2062,2064],{"className":2063},[1149],[1151,2065,2066],{"xmlns":1153},[1155,2067,2068,2117],{},[1158,2069,2070,2095,2097,2099,2101,2103,2105,2107,2109,2111,2113,2115],{},[1277,2071,2072,2080],{},[1158,2073,2074,2077],{},[1161,2075,2076],{},"lim",[1165,2078,2079],{},"⁡",[1158,2081,2082,2085,2088],{},[1161,2083,2084],{},"h",[1165,2086,2087],{},"→",[1209,2089,2090,2092],{},[1282,2091,1982],{},[1165,2093,2094],{},"+",[1161,2096,1163],{},[1165,2098,1168],{"stretchy":1167},[1161,2100,1171],{},[1165,2102,2094],{},[1161,2104,2084],{},[1165,2106,1174],{"stretchy":1167},[1165,2108,1177],{},[1161,2110,1163],{},[1165,2112,1168],{"stretchy":1167},[1161,2114,1171],{},[1165,2116,1174],{"stretchy":1167},[1194,2118,2119],{"encoding":1196},"\\lim_{h \\to 0^+} F(x+h) = F(x)",[1127,2121,2122,1376,2164,1333],{},[1115,2123,2125],{"className":2124},[1149],[1151,2126,2127],{"xmlns":1153},[1155,2128,2129,2161],{},[1158,2130,2131,2149,2151,2153,2155,2157,2159],{},[1277,2132,2133,2139],{},[1158,2134,2135,2137],{},[1161,2136,2076],{},[1165,2138,2079],{},[1158,2140,2141,2143,2145,2147],{},[1161,2142,1171],{},[1165,2144,2087],{},[1165,2146,1317],{},[1161,2148,1914],{"mathvariant":1215},[1161,2150,1163],{},[1165,2152,1168],{"stretchy":1167},[1161,2154,1171],{},[1165,2156,1174],{"stretchy":1167},[1165,2158,1177],{},[1282,2160,1982],{},[1194,2162,2163],{"encoding":1196},"\\lim_{x \\to -\\infty} F(x) = 0",[1115,2165,2167],{"className":2166},[1149],[1151,2168,2169],{"xmlns":1153},[1155,2170,2171,2201],{},[1158,2172,2173,2189,2191,2193,2195,2197,2199],{},[1277,2174,2175,2181],{},[1158,2176,2177,2179],{},[1161,2178,2076],{},[1165,2180,2079],{},[1158,2182,2183,2185,2187],{},[1161,2184,1171],{},[1165,2186,2087],{},[1161,2188,1914],{"mathvariant":1215},[1161,2190,1163],{},[1165,2192,1168],{"stretchy":1167},[1161,2194,1171],{},[1165,2196,1174],{"stretchy":1167},[1165,2198,1177],{},[1282,2200,1284],{},[1194,2202,2203],{"encoding":1196},"\\lim_{x \\to \\infty} F(x) = 1",[1110,2205,2206],{},"U spojité náhodné veličiny je distribuční funkce svázaná s hustotou pravděpodobnosti vztahem",[1115,2208,2210],{"className":2209},[1149],[1151,2211,2213],{"xmlns":1153,"display":2212},"block",[1155,2214,2215,2288],{},[1158,2216,2217,2223,2225,2227,2229,2231,2233,2235,2237,2239,2241,2245,2247,2249,2251,2253,2255,2269,2271,2273,2275,2277,2281,2284,2286],{},[1209,2218,2219,2221],{},[1161,2220,1163],{},[1165,2222,1217],{"mathvariant":1215,"lspace":1216,"rspace":1216},[1165,2224,1168],{"stretchy":1167},[1161,2226,1171],{},[1165,2228,1174],{"stretchy":1167},[1165,2230,1177],{},[1161,2232,1228],{},[1165,2234,1168],{"stretchy":1167},[1161,2236,1171],{},[1165,2238,1174],{"stretchy":1167},[1165,2240,1715],{"separator":1121},[2242,2243],"mspace",{"width":2244},"2em",[1161,2246,1163],{},[1165,2248,1168],{"stretchy":1167},[1161,2250,1171],{},[1165,2252,1174],{"stretchy":1167},[1165,2254,1177],{},[2256,2257,2258,2261,2267],"msubsup",{},[1165,2259,2260],{},"∫",[1158,2262,2263,2265],{},[1165,2264,1317],{},[1161,2266,1914],{"mathvariant":1215},[1161,2268,1171],{},[1161,2270,1228],{},[1165,2272,1168],{"stretchy":1167},[1161,2274,1617],{},[1165,2276,1174],{"stretchy":1167},[2278,2279,2280],"mtext",{}," ",[1161,2282,2283],{},"d",[1161,2285,1617],{},[1161,2287,1333],{"mathvariant":1215},[1194,2289,2290],{"encoding":1196},"F'(x) = f(x), \\qquad F(x) = \\int_{-\\infty}^{x} f(t)\\,dt.",[1110,2292,2293,2294,2307,2308,1425,2326,2344],{},"Pravděpodobnost, že ",[1115,2295,2297],{"className":2296},[1149],[1151,2298,2299],{"xmlns":1153},[1155,2300,2301,2305],{},[1158,2302,2303],{},[1161,2304,1185],{},[1194,2306,1185],{"encoding":1196}," padne mezi body ",[1115,2309,2311],{"className":2310},[1149],[1151,2312,2313],{"xmlns":1153},[1155,2314,2315,2323],{},[1158,2316,2317],{},[1277,2318,2319,2321],{},[1161,2320,1171],{},[1282,2322,1284],{},[1194,2324,2325],{"encoding":1196},"x_1",[1115,2327,2329],{"className":2328},[1149],[1151,2330,2331],{"xmlns":1153},[1155,2332,2333,2341],{},[1158,2334,2335],{},[1277,2336,2337,2339],{},[1161,2338,1171],{},[1282,2340,1298],{},[1194,2342,2343],{"encoding":1196},"x_2",", se pak počítá jako",[1115,2346,2348],{"className":2347},[1149],[1151,2349,2350],{"xmlns":1153,"display":2212},[1155,2351,2352,2440],{},[1158,2353,2354,2356,2358,2364,2366,2368,2370,2376,2378,2380,2396,2398,2400,2402,2404,2406,2408,2410,2412,2414,2416,2422,2424,2426,2428,2430,2436,2438],{},[1161,2355,1180],{},[1165,2357,1168],{"stretchy":1167},[1277,2359,2360,2362],{},[1161,2361,1171],{},[1282,2363,1284],{},[1165,2365,1287],{},[1161,2367,1185],{},[1165,2369,1287],{},[1277,2371,2372,2374],{},[1161,2373,1171],{},[1282,2375,1298],{},[1165,2377,1174],{"stretchy":1167},[1165,2379,1177],{},[2256,2381,2382,2384,2390],{},[1165,2383,2260],{},[1277,2385,2386,2388],{},[1161,2387,1171],{},[1282,2389,1284],{},[1277,2391,2392,2394],{},[1161,2393,1171],{},[1282,2395,1298],{},[1161,2397,1228],{},[1165,2399,1168],{"stretchy":1167},[1161,2401,1617],{},[1165,2403,1174],{"stretchy":1167},[2278,2405,2280],{},[1161,2407,2283],{},[1161,2409,1617],{},[1165,2411,1177],{},[1161,2413,1163],{},[1165,2415,1168],{"stretchy":1167},[1277,2417,2418,2420],{},[1161,2419,1171],{},[1282,2421,1298],{},[1165,2423,1174],{"stretchy":1167},[1165,2425,1317],{},[1161,2427,1163],{},[1165,2429,1168],{"stretchy":1167},[1277,2431,2432,2434],{},[1161,2433,1171],{},[1282,2435,1284],{},[1165,2437,1174],{"stretchy":1167},[1161,2439,1333],{"mathvariant":1215},[1194,2441,2442],{"encoding":1196},"P(x_1 \u003C X \u003C x_2) = \\int_{x_1}^{x_2} f(t)\\,dt = F(x_2) - F(x_1).",[1431,2444,2446],{"id":2445},"hustota-pravděpodobnosti","Hustota pravděpodobnosti",[1103,2448,2450,2456],{"className":2449,"dataCallout":654},[1106,1769],[1110,2451,2453,1776],{"className":2452},[1113],[1115,2454],{"className":2455,"ariaHidden":1121},[1118,1119,1120],[1110,2457,2458,2459,2478,2479,2492,2493,2506,2507,1333],{},"Hustota pravděpodobnosti ",[1115,2460,2462],{"className":2461},[1149],[1151,2463,2464],{"xmlns":1153},[1155,2465,2466,2476],{},[1158,2467,2468,2470,2472,2474],{},[1161,2469,1228],{},[1165,2471,1168],{"stretchy":1167},[1161,2473,1171],{},[1165,2475,1174],{"stretchy":1167},[1194,2477,1258],{"encoding":1196}," určuje, jak jsou hodnoty spojité náhodné veličiny ",[1115,2480,2482],{"className":2481},[1149],[1151,2483,2484],{"xmlns":1153},[1155,2485,2486,2490],{},[1158,2487,2488],{},[1161,2489,1185],{},[1194,2491,1185],{"encoding":1196}," nahuštěny v okolí bodu ",[1115,2494,2496],{"className":2495},[1149],[1151,2497,2498],{"xmlns":1153},[1155,2499,2500,2504],{},[1158,2501,2502],{},[1161,2503,1171],{},[1194,2505,1171],{"encoding":1196},". Je vždy nezáporná a platí pro ni ",[1115,2508,2510],{"className":2509},[1149],[1151,2511,2512],{"xmlns":1153},[1155,2513,2514,2546],{},[1158,2515,2516,2528,2530,2532,2534,2536,2538,2540,2542,2544],{},[2256,2517,2518,2520,2526],{},[1165,2519,2260],{},[1158,2521,2522,2524],{},[1165,2523,1317],{},[1161,2525,1914],{"mathvariant":1215},[1161,2527,1914],{"mathvariant":1215},[1161,2529,1228],{},[1165,2531,1168],{"stretchy":1167},[1161,2533,1171],{},[1165,2535,1174],{"stretchy":1167},[2278,2537,2280],{},[1161,2539,2283],{},[1161,2541,1171],{},[1165,2543,1177],{},[1282,2545,1284],{},[1194,2547,2548],{"encoding":1196},"\\int_{-\\infty}^{\\infty} f(x)\\,dx = 1",[1110,2550,2551],{},"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.",[1431,2553,2555],{"id":2554},"charakteristiky-spojité-náhodné-veličiny","Charakteristiky spojité náhodné veličiny",[1110,2557,2558,2561],{},[1131,2559,2560],{},"Střední hodnota"," je nejdůležitější charakteristika náhodné veličiny:",[1115,2563,2565],{"className":2564},[1149],[1151,2566,2567],{"xmlns":1153,"display":2212},[1155,2568,2569,2615],{},[1158,2570,2571,2574,2576,2578,2580,2582,2594,2596,2599,2601,2603,2605,2607,2609,2611,2613],{},[1161,2572,2573],{},"E",[1165,2575,1168],{"stretchy":1167},[1161,2577,1185],{},[1165,2579,1174],{"stretchy":1167},[1165,2581,1177],{},[2256,2583,2584,2586,2592],{},[1165,2585,2260],{},[1158,2587,2588,2590],{},[1165,2589,1317],{},[1161,2591,1914],{"mathvariant":1215},[1161,2593,1914],{"mathvariant":1215},[1161,2595,1171],{},[1165,2597,2598],{},"⋅",[1161,2600,1228],{},[1165,2602,1168],{"stretchy":1167},[1161,2604,1171],{},[1165,2606,1174],{"stretchy":1167},[2278,2608,2280],{},[1161,2610,2283],{},[1161,2612,1171],{},[1161,2614,1333],{"mathvariant":1215},[1194,2616,2617],{"encoding":1196},"E(X) = \\int_{-\\infty}^{\\infty} x \\cdot f(x)\\,dx.",[1110,2619,2620],{},"Je to číslo, kolem něhož kolísají výběrové průměry vypočtené ze sérií pozorovaných hodnot náhodné veličiny.",[1110,2622,2623,1425,2626,2629],{},[1131,2624,2625],{},"Rozptyl",[1131,2627,2628],{},"směrodatná odchylka",":",[1115,2631,2633],{"className":2632},[1149],[1151,2634,2635],{"xmlns":1153,"display":2212},[1155,2636,2637,2779],{},[1158,2638,2639,2642,2644,2646,2648,2650,2662,2665,2667,2669,2671,2673,2675,2677,2684,2686,2688,2690,2692,2694,2696,2698,2700,2712,2718,2720,2722,2724,2726,2728,2730,2732,2734,2736,2738,2740,2742,2744,2750,2752,2754,2756,2758,2760,2762,2764,2777],{},[1161,2640,2641],{},"D",[1165,2643,1168],{"stretchy":1167},[1161,2645,1185],{},[1165,2647,1174],{"stretchy":1167},[1165,2649,1177],{},[2256,2651,2652,2654,2660],{},[1165,2653,2260],{},[1158,2655,2656,2658],{},[1165,2657,1317],{},[1161,2659,1914],{"mathvariant":1215},[1161,2661,1914],{"mathvariant":1215},[1165,2663,2664],{"stretchy":1167},"[",[1161,2666,1171],{},[1165,2668,1317],{},[1161,2670,2573],{},[1165,2672,1168],{"stretchy":1167},[1161,2674,1185],{},[1165,2676,1174],{"stretchy":1167},[1209,2678,2679,2682],{},[1165,2680,2681],{"stretchy":1167},"]",[1282,2683,1298],{},[1161,2685,1228],{},[1165,2687,1168],{"stretchy":1167},[1161,2689,1171],{},[1165,2691,1174],{"stretchy":1167},[2278,2693,2280],{},[1161,2695,2283],{},[1161,2697,1171],{},[1165,2699,1177],{},[2256,2701,2702,2704,2710],{},[1165,2703,2260],{},[1158,2705,2706,2708],{},[1165,2707,1317],{},[1161,2709,1914],{"mathvariant":1215},[1161,2711,1914],{"mathvariant":1215},[1209,2713,2714,2716],{},[1161,2715,1171],{},[1282,2717,1298],{},[1161,2719,1228],{},[1165,2721,1168],{"stretchy":1167},[1161,2723,1171],{},[1165,2725,1174],{"stretchy":1167},[2278,2727,2280],{},[1161,2729,2283],{},[1161,2731,1171],{},[1165,2733,1317],{},[1165,2735,2664],{"stretchy":1167},[1161,2737,2573],{},[1165,2739,1168],{"stretchy":1167},[1161,2741,1185],{},[1165,2743,1174],{"stretchy":1167},[1209,2745,2746,2748],{},[1165,2747,2681],{"stretchy":1167},[1282,2749,1298],{},[1165,2751,1715],{"separator":1121},[2242,2753],{"width":2244},[1161,2755,1363],{},[1165,2757,1168],{"stretchy":1167},[1161,2759,1185],{},[1165,2761,1174],{"stretchy":1167},[1165,2763,1177],{},[2765,2766,2767],"msqrt",{},[1158,2768,2769,2771,2773,2775],{},[1161,2770,2641],{},[1165,2772,1168],{"stretchy":1167},[1161,2774,1185],{},[1165,2776,1174],{"stretchy":1167},[1161,2778,1333],{"mathvariant":1215},[1194,2780,2781],{"encoding":1196},"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)}.",[1110,2783,2784,2785,2790],{},"Směrodatná odchylka udává, jak moc jsou hodnoty náhodné veličiny rozptýlené kolem střední hodnoty. (Pro odhad těchto charakteristik z naměřených dat viz empirické protějšky v ",[1438,2786,886],{"className":2787,"dataFsResolvedFilePath":2788,"href":2789},[1441],"topics\u002Fpopisna-statistika.md","\u002Fwiki\u002Fpopisna-statistika",".)",[1110,2792,2793,2796,2797,2810,2811,2829,2830,2843],{},[1131,2794,2795],{},"Kvantily"," udávají, jak jsou hodnoty náhodné veličiny ",[1115,2798,2800],{"className":2799},[1149],[1151,2801,2802],{"xmlns":1153},[1155,2803,2804,2808],{},[1158,2805,2806],{},[1161,2807,1185],{},[1194,2809,1185],{"encoding":1196}," rozděleny na ose reálných čísel v určitém pravděpodobnostním poměru. 100p%-ní kvantil ",[1115,2812,2814],{"className":2813},[1149],[1151,2815,2816],{"xmlns":1153},[1155,2817,2818,2826],{},[1158,2819,2820],{},[1277,2821,2822,2824],{},[1161,2823,1171],{},[1161,2825,1110],{},[1194,2827,2828],{"encoding":1196},"x_p"," je číslo, pro které při zvolené pravděpodobnosti ",[1115,2831,2833],{"className":2832},[1149],[1151,2834,2835],{"xmlns":1153},[1155,2836,2837,2841],{},[1158,2838,2839],{},[1161,2840,1110],{},[1194,2842,1110],{"encoding":1196}," platí",[1115,2845,2847],{"className":2846},[1149],[1151,2848,2849],{"xmlns":1153,"display":2212},[1155,2850,2851,2871],{},[1158,2852,2853,2855,2857,2863,2865,2867,2869],{},[1161,2854,1163],{},[1165,2856,1168],{"stretchy":1167},[1277,2858,2859,2861],{},[1161,2860,1171],{},[1161,2862,1110],{},[1165,2864,1174],{"stretchy":1167},[1165,2866,1177],{},[1161,2868,1110],{},[1161,2870,1333],{"mathvariant":1215},[1194,2872,2873],{"encoding":1196},"F(x_p) = p.",[1110,2875,2876,2877,2905,2906,2933,2934,2953,2954,2973,2974,1333],{},"V intervalu ",[1115,2878,2880],{"className":2879},[1149],[1151,2881,2882],{"xmlns":1153},[1155,2883,2884,2902],{},[1158,2885,2886,2888,2890,2892,2894,2900],{},[1165,2887,1168],{"stretchy":1167},[1165,2889,1317],{},[1161,2891,1914],{"mathvariant":1215},[1165,2893,1358],{"separator":1121},[1277,2895,2896,2898],{},[1161,2897,1171],{},[1161,2899,1110],{},[1165,2901,1174],{"stretchy":1167},[1194,2903,2904],{"encoding":1196},"(-\\infty; x_p)"," leží 100p % hodnot, v intervalu ",[1115,2907,2909],{"className":2908},[1149],[1151,2910,2911],{"xmlns":1153},[1155,2912,2913,2930],{},[1158,2914,2915,2918,2924,2926,2928],{},[1165,2916,2917],{"stretchy":1167},"⟨",[1277,2919,2920,2922],{},[1161,2921,1171],{},[1161,2923,1110],{},[1165,2925,1358],{"separator":1121},[1161,2927,1914],{"mathvariant":1215},[1165,2929,1174],{"stretchy":1167},[1194,2931,2932],{"encoding":1196},"\\langle x_p; \\infty)"," leží 100(1-p) % hodnot. Nejdůležitější kvantily jsou medián ",[1115,2935,2937],{"className":2936},[1149],[1151,2938,2939],{"xmlns":1153},[1155,2940,2941,2950],{},[1158,2942,2943],{},[1277,2944,2945,2947],{},[1161,2946,1171],{},[1282,2948,2949],{},"0,5",[1194,2951,2952],{"encoding":1196},"x_{0{,}5}",", dolní kvartil ",[1115,2955,2957],{"className":2956},[1149],[1151,2958,2959],{"xmlns":1153},[1155,2960,2961,2970],{},[1158,2962,2963],{},[1277,2964,2965,2967],{},[1161,2966,1171],{},[1282,2968,2969],{},"0,25",[1194,2971,2972],{"encoding":1196},"x_{0{,}25}"," a horní kvartil ",[1115,2975,2977],{"className":2976},[1149],[1151,2978,2979],{"xmlns":1153},[1155,2980,2981,2990],{},[1158,2982,2983],{},[1277,2984,2985,2987],{},[1161,2986,1171],{},[1282,2988,2989],{},"0,75",[1194,2991,2992],{"encoding":1196},"x_{0{,}75}",[1431,2994,1338],{"id":2995},"normální-rozdělení",[1110,2997,2998,2999,3012,3013,1145,3016,3043],{},"Spojitá náhodná veličina ",[1115,3000,3002],{"className":3001},[1149],[1151,3003,3004],{"xmlns":1153},[1155,3005,3006,3010],{},[1158,3007,3008],{},[1161,3009,1185],{},[1194,3011,1185],{"encoding":1196}," má ",[1131,3014,3015],{},"normální rozdělení",[1115,3017,3019],{"className":3018},[1149],[1151,3020,3021],{"xmlns":1153},[1155,3022,3023,3041],{},[1158,3024,3025,3027,3029,3031,3033,3039],{},[1161,3026,1350],{},[1165,3028,1168],{"stretchy":1167},[1161,3030,1355],{},[1165,3032,1358],{"separator":1121},[1209,3034,3035,3037],{},[1161,3036,1363],{},[1282,3038,1298],{},[1165,3040,1174],{"stretchy":1167},[1194,3042,1370],{"encoding":1196},", jestliže její hustota pravděpodobnosti a distribuční funkce jsou dány předpisy",[1115,3045,3047],{"className":3046},[1149],[1151,3048,3049],{"xmlns":1153,"display":2212},[1155,3050,3051,3204],{},[1158,3052,3053,3055,3057,3059,3061,3063,3081,3118,3120,3122,3124,3126,3128,3130,3132,3148,3160,3196,3198,3200,3202],{},[1161,3054,1228],{},[1165,3056,1168],{"stretchy":1167},[1161,3058,1171],{},[1165,3060,1174],{"stretchy":1167},[1165,3062,1177],{},[3064,3065,3066,3068],"mfrac",{},[1282,3067,1284],{},[1158,3069,3070,3072],{},[1161,3071,1363],{},[2765,3073,3074],{},[1158,3075,3076,3078],{},[1282,3077,1298],{},[1161,3079,3080],{},"π",[1209,3082,3083,3086],{},[1161,3084,3085],{},"e",[1158,3087,3088,3090],{},[1165,3089,1317],{},[3064,3091,3092,3108],{},[1158,3093,3094,3096,3098,3100,3102],{},[1165,3095,1168],{"stretchy":1167},[1161,3097,1171],{},[1165,3099,1317],{},[1161,3101,1355],{},[1209,3103,3104,3106],{},[1165,3105,1174],{"stretchy":1167},[1282,3107,1298],{},[1158,3109,3110,3112],{},[1282,3111,1298],{},[1209,3113,3114,3116],{},[1161,3115,1363],{},[1282,3117,1298],{},[1165,3119,1715],{"separator":1121},[2242,3121],{"width":2244},[1161,3123,1163],{},[1165,3125,1168],{"stretchy":1167},[1161,3127,1171],{},[1165,3129,1174],{"stretchy":1167},[1165,3131,1177],{},[3064,3133,3134,3136],{},[1282,3135,1284],{},[1158,3137,3138,3140],{},[1161,3139,1363],{},[2765,3141,3142],{},[1158,3143,3144,3146],{},[1282,3145,1298],{},[1161,3147,3080],{},[2256,3149,3150,3152,3158],{},[1165,3151,2260],{},[1158,3153,3154,3156],{},[1165,3155,1317],{},[1161,3157,1914],{"mathvariant":1215},[1161,3159,1171],{},[1209,3161,3162,3164],{},[1161,3163,3085],{},[1158,3165,3166,3168],{},[1165,3167,1317],{},[3064,3169,3170,3186],{},[1158,3171,3172,3174,3176,3178,3180],{},[1165,3173,1168],{"stretchy":1167},[1161,3175,1617],{},[1165,3177,1317],{},[1161,3179,1355],{},[1209,3181,3182,3184],{},[1165,3183,1174],{"stretchy":1167},[1282,3185,1298],{},[1158,3187,3188,3190],{},[1282,3189,1298],{},[1209,3191,3192,3194],{},[1161,3193,1363],{},[1282,3195,1298],{},[2278,3197,2280],{},[1161,3199,2283],{},[1161,3201,1617],{},[1165,3203,1715],{"separator":1121},[1194,3205,3206],{"encoding":1196},"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,",[1110,3208,3209,3210,1376,3234,1333],{},"přičemž ",[1115,3211,3213],{"className":3212},[1149],[1151,3214,3215],{"xmlns":1153},[1155,3216,3217,3231],{},[1158,3218,3219,3221,3223,3225,3227,3229],{},[1161,3220,2573],{},[1165,3222,1168],{"stretchy":1167},[1161,3224,1185],{},[1165,3226,1174],{"stretchy":1167},[1165,3228,1177],{},[1161,3230,1355],{},[1194,3232,3233],{"encoding":1196},"E(X) = \\mu",[1115,3235,3237],{"className":3236},[1149],[1151,3238,3239],{"xmlns":1153},[1155,3240,3241,3259],{},[1158,3242,3243,3245,3247,3249,3251,3253],{},[1161,3244,2641],{},[1165,3246,1168],{"stretchy":1167},[1161,3248,1185],{},[1165,3250,1174],{"stretchy":1167},[1165,3252,1177],{},[1209,3254,3255,3257],{},[1161,3256,1363],{},[1282,3258,1298],{},[1194,3260,3261],{"encoding":1196},"D(X) = \\sigma^2",[1110,3263,3264],{},[1760,3265],{"alt":3266,"className":3267,"src":3268},"mask-nv-normalni",[1441,1764],"\u002Fwiki-assets\u002Fmask-nv-normalni.png",[1110,3270,3271,3272,3275,3276,3290,3291,3310,3311,3328,3329,3342,3343,1333],{},"Křivka hustoty se nazývá ",[1131,3273,3274],{},"Gaussova křivka",": je symetrická kolem svislé přímky procházející ",[1115,3277,3279],{"className":3278},[1149],[1151,3280,3281],{"xmlns":1153},[1155,3282,3283,3287],{},[1158,3284,3285],{},[1161,3286,1355],{},[1194,3288,3289],{"encoding":1196},"\\mu",", kde má ",[1115,3292,3294],{"className":3293},[1149],[1151,3295,3296],{"xmlns":1153},[1155,3297,3298,3308],{},[1158,3299,3300,3302,3304,3306],{},[1161,3301,1228],{},[1165,3303,1168],{"stretchy":1167},[1161,3305,1171],{},[1165,3307,1174],{"stretchy":1167},[1194,3309,1258],{"encoding":1196}," globální maximum, a ve vzdálenosti ",[1115,3312,3314],{"className":3313},[1149],[1151,3315,3316],{"xmlns":1153},[1155,3317,3318,3325],{},[1158,3319,3320,3323],{},[1282,3321,3322],{},"3",[1161,3324,1363],{},[1194,3326,3327],{"encoding":1196},"3\\sigma"," od ",[1115,3330,3332],{"className":3331},[1149],[1151,3333,3334],{"xmlns":1153},[1155,3335,3336,3340],{},[1158,3337,3338],{},[1161,3339,1355],{},[1194,3341,3289],{"encoding":1196}," se téměř dotýká osy x — zhruba 99,73 % hodnot leží v intervalu ",[1115,3344,3346],{"className":3345},[1149],[1151,3347,3348],{"xmlns":1153},[1155,3349,3350,3374],{},[1158,3351,3352,3354,3356,3358,3360,3362,3364,3366,3368,3370,3372],{},[1165,3353,1168],{"stretchy":1167},[1161,3355,1355],{},[1165,3357,1317],{},[1282,3359,3322],{},[1161,3361,1363],{},[1165,3363,1358],{"separator":1121},[1161,3365,1355],{},[1165,3367,2094],{},[1282,3369,3322],{},[1161,3371,1363],{},[1165,3373,1174],{"stretchy":1167},[1194,3375,3376],{"encoding":1196},"(\\mu - 3\\sigma; \\mu + 3\\sigma)",[1110,3378,3379,3380,1145,3383,3407,3408,1333],{},"Zvláštní postavení má ",[1131,3381,3382],{},"normované normální rozdělení",[1115,3384,3386],{"className":3385},[1149],[1151,3387,3388],{"xmlns":1153},[1155,3389,3390,3404],{},[1158,3391,3392,3394,3396,3398,3400,3402],{},[1161,3393,1350],{},[1165,3395,1168],{"stretchy":1167},[1282,3397,1982],{},[1165,3399,1358],{"separator":1121},[1282,3401,1284],{},[1165,3403,1174],{"stretchy":1167},[1194,3405,3406],{"encoding":1196},"N(0; 1)",", na které se dá libovolné normální rozdělení převést standardizací ",[1115,3409,3411],{"className":3410},[1149],[1151,3412,3413],{"xmlns":1153},[1155,3414,3415,3437],{},[1158,3416,3417,3420,3422,3424,3426,3428,3430,3432,3435],{},[1161,3418,3419],{},"Z",[1165,3421,1177],{},[1165,3423,1168],{"stretchy":1167},[1161,3425,1185],{},[1165,3427,1317],{},[1161,3429,1355],{},[1165,3431,1174],{"stretchy":1167},[1161,3433,3434],{"mathvariant":1215},"\u002F",[1161,3436,1363],{},[1194,3438,3439],{"encoding":1196},"Z = (X-\\mu)\u002F\\sigma",[3441,3442],"graph-mount",{"spec":3443},"{\"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\"}]}",[1103,3445,3449,3457],{"className":3446,"dataCallout":3448},[1106,3447],"callout-warning","warning",[1110,3450,3452,3456],{"className":3451},[1113],[1115,3453],{"className":3454,"ariaHidden":1121},[1118,3455,1120],"i-lucide:triangle-alert","R očekává směrodatnou odchylku, ne rozptyl",[1110,3458,3459,3460,3487,3488,3491,3492,1376,3494,1425,3496,3498,3499,1145,3502,3515,3516,3542,3543,3546,3547,1333],{},"Zápis ",[1115,3461,3463],{"className":3462},[1149],[1151,3464,3465],{"xmlns":1153},[1155,3466,3467,3485],{},[1158,3468,3469,3471,3473,3475,3477,3483],{},[1161,3470,1350],{},[1165,3472,1168],{"stretchy":1167},[1161,3474,1355],{},[1165,3476,1358],{"separator":1121},[1209,3478,3479,3481],{},[1161,3480,1363],{},[1282,3482,1298],{},[1165,3484,1174],{"stretchy":1167},[1194,3486,1370],{"encoding":1196}," v definici používá ",[1131,3489,3490],{},"rozptyl",". Funkce ",[1373,3493,1375],{},[1373,3495,1379],{},[1373,3497,1382],{}," v R ale jako třetí argument berou ",[1131,3500,3501],{},"směrodatnou odchylku",[1115,3503,3505],{"className":3504},[1149],[1151,3506,3507],{"xmlns":1153},[1155,3508,3509,3513],{},[1158,3510,3511],{},[1161,3512,1363],{},[1194,3514,1397],{"encoding":1196},". Má-li náhodná veličina rozdělení ",[1115,3517,3519],{"className":3518},[1149],[1151,3520,3521],{"xmlns":1153},[1155,3522,3523,3539],{},[1158,3524,3525,3527,3529,3532,3534,3537],{},[1161,3526,1350],{},[1165,3528,1168],{"stretchy":1167},[1282,3530,3531],{},"10",[1165,3533,1358],{"separator":1121},[1282,3535,3536],{},"0,12",[1165,3538,1174],{"stretchy":1167},[1194,3540,3541],{"encoding":1196},"N(10; 0{,}12)",", je ",[1373,3544,3545],{},"sd = sqrt(0.12)",", ne ",[1373,3548,3549],{},"sd = 0.12",[1110,3551,3552],{},"V R:",[3554,3555,3559],"pre",{"className":3556,"code":3557,"language":71,"meta":3558,"style":3558},"language-r shiki shiki-themes github-light github-light github-dark","dnorm(0)\npnorm(1.96)\nqnorm(0.975)\n","",[1373,3560,3561,3576,3587],{"__ignoreMap":3558},[1115,3562,3564,3567,3570,3573],{"class":3563,"line":10},"line",[1115,3565,1375],{"class":3566},"snPdu",[1115,3568,1168],{"class":3569},"sxrX7",[1115,3571,1982],{"class":3572},"sBjJW",[1115,3574,3575],{"class":3569},")\n",[1115,3577,3578,3580,3582,3585],{"class":3563,"line":27},[1115,3579,1379],{"class":3566},[1115,3581,1168],{"class":3569},[1115,3583,3584],{"class":3572},"1.96",[1115,3586,3575],{"class":3569},[1115,3588,3589,3591,3593,3596],{"class":3563,"line":148},[1115,3590,1382],{"class":3566},[1115,3592,1168],{"class":3569},[1115,3594,3595],{"class":3572},"0.975",[1115,3597,3575],{"class":3569},[3554,3599,3604],{"className":3600,"code":3602,"language":3603,"meta":3558},[3601],"language-text","[1] 0.3989423\n[1] 0.9750021\n[1] 1.959964\n","text",[1373,3605,3602],{"__ignoreMap":3558},[1110,3607,3608,3611,3612,3636,3637,3640,3641,1425,3662,3665],{},[1373,3609,3610],{},"dnorm(0)"," je hodnota hustoty ",[1115,3613,3615],{"className":3614},[1149],[1151,3616,3617],{"xmlns":1153},[1155,3618,3619,3633],{},[1158,3620,3621,3623,3625,3627,3629,3631],{},[1161,3622,1350],{},[1165,3624,1168],{"stretchy":1167},[1282,3626,1982],{},[1165,3628,1358],{"separator":1121},[1282,3630,1284],{},[1165,3632,1174],{"stretchy":1167},[1194,3634,3635],{"encoding":1196},"N(0;1)"," v bodě 0, ",[1373,3638,3639],{},"pnorm(1.96)"," je ",[1115,3642,3644],{"className":3643},[1149],[1151,3645,3646],{"xmlns":1153},[1155,3647,3648,3659],{},[1158,3649,3650,3652,3654,3657],{},[1161,3651,1163],{},[1165,3653,1168],{"stretchy":1167},[1282,3655,3656],{},"1,96",[1165,3658,1174],{"stretchy":1167},[1194,3660,3661],{"encoding":1196},"F(1{,}96)",[1373,3663,3664],{},"qnorm(0.975)"," je 97,5%-ní kvantil — hodnota, pod kterou leží 97,5 % pravděpodobnosti.",[1103,3667,3671,3679],{"className":3668,"dataCallout":3670},[1106,3669],"callout-example","example",[1110,3672,3674,3678],{"className":3673},[1113],[1115,3675],{"className":3676,"ariaHidden":1121},[1118,3677,1120],"i-lucide:flask-conical","Příklad: Návštěvnost zábavního parku",[1110,3680,3681,3682,3717],{},"Denní návštěvnost zábavního parku je náhodná veličina s normálním rozdělením, průměrnou hodnotou 230 a směrodatnou odchylkou 27,5 návštěvníků: ",[1115,3683,3685],{"className":3684},[1149],[1151,3686,3687],{"xmlns":1153},[1155,3688,3689,3714],{},[1158,3690,3691,3693,3696,3698,3700,3703,3705,3712],{},[1161,3692,1185],{},[1165,3694,3695],{},"∼",[1161,3697,1350],{},[1165,3699,1168],{"stretchy":1167},[1282,3701,3702],{},"230",[1165,3704,1358],{"separator":1121},[1209,3706,3707,3710],{},[1282,3708,3709],{},"27,5",[1282,3711,1298],{},[1165,3713,1174],{"stretchy":1167},[1194,3715,3716],{"encoding":1196},"X \\sim N(230; 27{,}5^2)",". Přijde-li za den méně než 180 návštěvníků, je park ztrátový. Kolik procent dní je ztrátových?",[1110,3719,3720],{},[1760,3721],{"alt":3722,"className":3723,"src":3724},"mask-nv-priklad-park",[1441,1764],"\u002Fwiki-assets\u002Fmask-nv-priklad-park.png",[3554,3726,3728],{"className":3556,"code":3727,"language":71,"meta":3558,"style":3558},"pnorm(180, mean = 230, sd = 27.5)\n",[1373,3729,3730],{"__ignoreMap":3558},[1115,3731,3732,3734,3736,3739,3742,3746,3749,3752,3754,3757,3759,3762],{"class":3563,"line":10},[1115,3733,1379],{"class":3566},[1115,3735,1168],{"class":3569},[1115,3737,3738],{"class":3572},"180",[1115,3740,1715],{"class":3741},"s8jYJ",[1115,3743,3745],{"class":3744},"sP4rz"," mean",[1115,3747,3748],{"class":3741}," =",[1115,3750,3751],{"class":3572}," 230",[1115,3753,1715],{"class":3741},[1115,3755,3756],{"class":3744}," sd",[1115,3758,3748],{"class":3741},[1115,3760,3761],{"class":3572}," 27.5",[1115,3763,3575],{"class":3569},[3554,3765,3768],{"className":3766,"code":3767,"language":3603,"meta":3558},[3601],"[1] 0.03451817\n",[1373,3769,3767],{"__ignoreMap":3558},[1110,3771,3772],{},"Park je ztrátový přibližně v 3,45 % dní.",[1103,3774,3776,3783],{"className":3775,"dataCallout":3670},[1106,3669],[1110,3777,3779,3782],{"className":3778},[1113],[1115,3780],{"className":3781,"ariaHidden":1121},[1118,3677,1120],"Příklad: Délka výrobku",[1110,3784,3785,3786,3820],{},"Automat je seřízen tak, aby střední hodnota délky výrobku byla 42 mm, s přesností charakterizovanou směrodatnou odchylkou 1,2 mm: ",[1115,3787,3789],{"className":3788},[1149],[1151,3790,3791],{"xmlns":1153},[1155,3792,3793,3817],{},[1158,3794,3795,3797,3799,3801,3803,3806,3808,3815],{},[1161,3796,1185],{},[1165,3798,3695],{},[1161,3800,1350],{},[1165,3802,1168],{"stretchy":1167},[1282,3804,3805],{},"42",[1165,3807,1358],{"separator":1121},[1209,3809,3810,3813],{},[1282,3811,3812],{},"1,2",[1282,3814,1298],{},[1165,3816,1174],{"stretchy":1167},[1194,3818,3819],{"encoding":1196},"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?",[1110,3822,3823],{},[1760,3824],{"alt":3825,"className":3826,"src":3827},"mask-nv-priklad-delka",[1441,1764],"\u002Fwiki-assets\u002Fmask-nv-priklad-delka.png",[3554,3829,3831],{"className":3556,"code":3830,"language":71,"meta":3558,"style":3558},"pnorm(43, mean = 42, sd = 1.2) - pnorm(41, mean = 42, sd = 1.2)\n",[1373,3832,3833],{"__ignoreMap":3558},[1115,3834,3835,3837,3839,3842,3844,3846,3848,3851,3853,3855,3857,3860,3863,3866,3869,3871,3874,3876,3878,3880,3882,3884,3886,3888,3890],{"class":3563,"line":10},[1115,3836,1379],{"class":3566},[1115,3838,1168],{"class":3569},[1115,3840,3841],{"class":3572},"43",[1115,3843,1715],{"class":3741},[1115,3845,3745],{"class":3744},[1115,3847,3748],{"class":3741},[1115,3849,3850],{"class":3572}," 42",[1115,3852,1715],{"class":3741},[1115,3854,3756],{"class":3744},[1115,3856,3748],{"class":3741},[1115,3858,3859],{"class":3572}," 1.2",[1115,3861,3862],{"class":3569},") ",[1115,3864,3865],{"class":3741},"-",[1115,3867,3868],{"class":3566}," pnorm",[1115,3870,1168],{"class":3569},[1115,3872,3873],{"class":3572},"41",[1115,3875,1715],{"class":3741},[1115,3877,3745],{"class":3744},[1115,3879,3748],{"class":3741},[1115,3881,3850],{"class":3572},[1115,3883,1715],{"class":3741},[1115,3885,3756],{"class":3744},[1115,3887,3748],{"class":3741},[1115,3889,3859],{"class":3572},[1115,3891,3575],{"class":3569},[3554,3893,3896],{"className":3894,"code":3895,"language":3603,"meta":3558},[3601],"[1] 0.5953432\n",[1373,3897,3895],{"__ignoreMap":3558},[1110,3899,3900],{},"Do 1. jakostní třídy spadá přibližně 59,53 % výrobků.",[1103,3902,3904,3911],{"className":3903,"dataCallout":3670},[1106,3669],[1110,3905,3907,3910],{"className":3906},[1113],[1115,3908],{"className":3909,"ariaHidden":1121},[1118,3677,1120],"Příklad: Obsah ampulky",[1110,3912,3913,3914,3937,3938,3964],{},"Obsah ampulky s lékem (v cm³) má rozdělení ",[1115,3915,3917],{"className":3916},[1149],[1151,3918,3919],{"xmlns":1153},[1155,3920,3921,3935],{},[1158,3922,3923,3925,3927,3929,3931,3933],{},[1161,3924,1350],{},[1165,3926,1168],{"stretchy":1167},[1282,3928,3531],{},[1165,3930,1358],{"separator":1121},[1282,3932,3536],{},[1165,3934,1174],{"stretchy":1167},[1194,3936,3541],{"encoding":1196},", tedy střední hodnota 10 a rozptyl 0,12 (",[1115,3939,3941],{"className":3940},[1149],[1151,3942,3943],{"xmlns":1153},[1155,3944,3945,3961],{},[1158,3946,3947,3949,3951,3955,3958],{},[1161,3948,1363],{},[1165,3950,1177],{},[2765,3952,3953],{},[1282,3954,3536],{},[1165,3956,3957],{},"≈",[1282,3959,3960],{},"0,346",[1194,3962,3963],{"encoding":1196},"\\sigma = \\sqrt{0{,}12} \\approx 0{,}346","). Kolik procent ampulek má obsah menší než 9,8 cm³?",[1110,3966,3967],{},[1760,3968],{"alt":3969,"className":3970,"src":3971},"mask-nv-priklad-ampulka",[1441,1764],"\u002Fwiki-assets\u002Fmask-nv-priklad-ampulka.png",[3554,3973,3975],{"className":3556,"code":3974,"language":71,"meta":3558,"style":3558},"pnorm(9.8, mean = 10, sd = sqrt(0.12))\n",[1373,3976,3977],{"__ignoreMap":3558},[1115,3978,3979,3981,3983,3986,3988,3990,3992,3995,3997,3999,4001,4004,4006,4009],{"class":3563,"line":10},[1115,3980,1379],{"class":3566},[1115,3982,1168],{"class":3569},[1115,3984,3985],{"class":3572},"9.8",[1115,3987,1715],{"class":3741},[1115,3989,3745],{"class":3744},[1115,3991,3748],{"class":3741},[1115,3993,3994],{"class":3572}," 10",[1115,3996,1715],{"class":3741},[1115,3998,3756],{"class":3744},[1115,4000,3748],{"class":3741},[1115,4002,4003],{"class":3566}," sqrt",[1115,4005,1168],{"class":3569},[1115,4007,4008],{"class":3572},"0.12",[1115,4010,4011],{"class":3569},"))\n",[3554,4013,4016],{"className":4014,"code":4015,"language":3603,"meta":3558},[3601],"[1] 0.2818514\n",[1373,4017,4015],{"__ignoreMap":3558},[1110,4019,4020],{},"Obsah menší než 9,8 cm³ má přibližně 28,19 % ampulek.",[1431,4022,4024],{"id":4023},"další-rozdělení-dostupná-v-r","Další rozdělení dostupná v R",[1110,4026,4027,4028,4031,4032,4035,4036,4039,4040,3434,4043,4046,4047,4050],{},"Vedle normálního rozdělení R přímo nabízí hustotu, distribuční funkci a kvantilovou funkci i pro další běžná rozdělení. Pojmenování funkcí je jednotné: ",[1373,4029,4030],{},"d*"," je hustota\u002Fpravděpodobnostní funkce, ",[1373,4033,4034],{},"p*"," distribuční funkce (s ",[1373,4037,4038],{},"lower.tail = FALSE",", případně čtvrtým argumentem ",[1373,4041,4042],{},"TRUE",[1373,4044,4045],{},"FALSE",", pro horní chvost) a ",[1373,4048,4049],{},"q*"," kvantilová funkce.",[4052,4053,4054,4164],"table",{},[4055,4056,4057],"thead",{},[4058,4059,4060,4064,4110,4136],"tr",{},[4061,4062,4063],"th",{},"Rozdělení",[4061,4065,4066,4090,4091],{},[1115,4067,4069],{"className":4068},[1149],[1151,4070,4071],{"xmlns":1153},[1155,4072,4073,4087],{},[1158,4074,4075,4077,4079,4081,4083,4085],{},[1161,4076,1180],{},[1165,4078,1168],{"stretchy":1167},[1161,4080,1185],{},[1165,4082,1177],{},[1161,4084,1735],{},[1165,4086,1174],{"stretchy":1167},[1194,4088,4089],{"encoding":1196},"P(X=k)"," \u002F ",[1115,4092,4094],{"className":4093},[1149],[1151,4095,4096],{"xmlns":1153},[1155,4097,4098,4108],{},[1158,4099,4100,4102,4104,4106],{},[1161,4101,1228],{},[1165,4103,1168],{"stretchy":1167},[1161,4105,1171],{},[1165,4107,1174],{"stretchy":1167},[1194,4109,1258],{"encoding":1196},[4061,4111,4112],{},[1115,4113,4115],{"className":4114},[1149],[1151,4116,4117],{"xmlns":1153},[1155,4118,4119,4133],{},[1158,4120,4121,4123,4125,4127,4129,4131],{},[1161,4122,1180],{},[1165,4124,1168],{"stretchy":1167},[1161,4126,1185],{},[1165,4128,1188],{},[1161,4130,1735],{},[1165,4132,1174],{"stretchy":1167},[1194,4134,4135],{"encoding":1196},"P(X \\le k)",[4061,4137,4138,4139],{},"horní chvost ",[1115,4140,4142],{"className":4141},[1149],[1151,4143,4144],{"xmlns":1153},[1155,4145,4146,4161],{},[1158,4147,4148,4150,4152,4154,4157,4159],{},[1161,4149,1180],{},[1165,4151,1168],{"stretchy":1167},[1161,4153,1185],{},[1165,4155,4156],{},">",[1161,4158,1735],{},[1165,4160,1174],{"stretchy":1167},[1194,4162,4163],{"encoding":1196},"P(X>k)",[4165,4166,4167,4217,4261,4302,4352],"tbody",{},[4058,4168,4169,4202,4207,4212],{},[4170,4171,4172,4173],"td",{},"Binomické ",[1115,4174,4176],{"className":4175},[1149],[1151,4177,4178],{"xmlns":1153},[1155,4179,4180,4199],{},[1158,4181,4182,4185,4188,4190,4193,4195,4197],{},[1161,4183,4184],{},"B",[1161,4186,4187],{},"i",[1165,4189,1168],{"stretchy":1167},[1161,4191,4192],{},"n",[1165,4194,1715],{"separator":1121},[1161,4196,1110],{},[1165,4198,1174],{"stretchy":1167},[1194,4200,4201],{"encoding":1196},"Bi(n,p)",[4170,4203,4204],{},[1373,4205,4206],{},"dbinom(k, n, p)",[4170,4208,4209],{},[1373,4210,4211],{},"pbinom(k, n, p)",[4170,4213,4214],{},[1373,4215,4216],{},"pbinom(k, n, p, FALSE)",[4058,4218,4219,4246,4251,4256],{},[4170,4220,4221,4222],{},"Poissonovo ",[1115,4223,4225],{"className":4224},[1149],[1151,4226,4227],{"xmlns":1153},[1155,4228,4229,4243],{},[1158,4230,4231,4233,4236,4238,4241],{},[1161,4232,1180],{},[1161,4234,4235],{},"o",[1165,4237,1168],{"stretchy":1167},[1161,4239,4240],{},"λ",[1165,4242,1174],{"stretchy":1167},[1194,4244,4245],{"encoding":1196},"Po(\\lambda)",[4170,4247,4248],{},[1373,4249,4250],{},"dpois(k, lambda)",[4170,4252,4253],{},[1373,4254,4255],{},"ppois(k, lambda)",[4170,4257,4258],{},[1373,4259,4260],{},"ppois(k, lambda, FALSE)",[4058,4262,4263,4287,4292,4297],{},[4170,4264,4265,4266],{},"Geometrické ",[1115,4267,4269],{"className":4268},[1149],[1151,4270,4271],{"xmlns":1153},[1155,4272,4273,4284],{},[1158,4274,4275,4278,4280,4282],{},[1161,4276,4277],{},"G",[1165,4279,1168],{"stretchy":1167},[1161,4281,1110],{},[1165,4283,1174],{"stretchy":1167},[1194,4285,4286],{"encoding":1196},"G(p)",[4170,4288,4289],{},[1373,4290,4291],{},"dgeom(k, p)",[4170,4293,4294],{},[1373,4295,4296],{},"pgeom(k, p)",[4170,4298,4299],{},[1373,4300,4301],{},"pgeom(k, p, FALSE)",[4058,4303,4304,4337,4342,4347],{},[4170,4305,4306,4307],{},"Hypergeometrické ",[1115,4308,4310],{"className":4309},[1149],[1151,4311,4312],{"xmlns":1153},[1155,4313,4314,4334],{},[1158,4315,4316,4319,4321,4323,4325,4328,4330,4332],{},[1161,4317,4318],{},"H",[1165,4320,1168],{"stretchy":1167},[1161,4322,1350],{},[1165,4324,1715],{"separator":1121},[1161,4326,4327],{},"M",[1165,4329,1715],{"separator":1121},[1161,4331,4192],{},[1165,4333,1174],{"stretchy":1167},[1194,4335,4336],{"encoding":1196},"H(N,M,n)",[4170,4338,4339],{},[1373,4340,4341],{},"dhyper(k, M, N-M, n)",[4170,4343,4344],{},[1373,4345,4346],{},"phyper(k, M, N-M, n)",[4170,4348,4349],{},[1373,4350,4351],{},"phyper(k, M, N-M, n, FALSE)",[4058,4353,4354,4378,4383,4388],{},[4170,4355,4356,4357],{},"Exponenciální ",[1115,4358,4360],{"className":4359},[1149],[1151,4361,4362],{"xmlns":1153},[1155,4363,4364,4375],{},[1158,4365,4366,4368,4370,4373],{},[1161,4367,2573],{},[1165,4369,1168],{"stretchy":1167},[1161,4371,4372],{},"δ",[1165,4374,1174],{"stretchy":1167},[1194,4376,4377],{"encoding":1196},"E(\\delta)",[4170,4379,4380],{},[1373,4381,4382],{},"dexp(k, 1\u002Fdelta)",[4170,4384,4385],{},[1373,4386,4387],{},"pexp(k, 1\u002Fdelta)",[4170,4389,4390],{},[1373,4391,4392],{},"pexp(k, 1\u002Fdelta, FALSE)",[1103,4394,4396,4403],{"className":4395,"dataCallout":3448},[1106,3447],[1110,4397,4399,4402],{"className":4398},[1113],[1115,4400],{"className":4401,"ariaHidden":1121},[1118,3455,1120],"Exponenciální rozdělení: R bere intenzitu, ne střední hodnotu",[1110,4404,4405,4406,4409,4410,4424,4425,3546,4428,1333],{},"R parametrizuje exponenciální rozdělení intenzitou (",[1373,4407,4408],{},"rate","). Je-li ",[1115,4411,4413],{"className":4412},[1149],[1151,4414,4415],{"xmlns":1153},[1155,4416,4417,4421],{},[1158,4418,4419],{},[1161,4420,4372],{},[1194,4422,4423],{"encoding":1196},"\\delta"," střední doba do události, do R se dosazuje ",[1373,4426,4427],{},"1\u002Fdelta",[1373,4429,4430],{},"delta",[1110,4432,4433,4434,4466,4467,4485],{},"V R (pravděpodobnostní a distribuční funkce diskrétní náhodné veličiny ",[1115,4435,4437],{"className":4436},[1149],[1151,4438,4439],{"xmlns":1153},[1155,4440,4441,4463],{},[1158,4442,4443,4445,4447,4449,4451,4453,4456,4458,4461],{},[1161,4444,1185],{},[1165,4446,3695],{},[1161,4448,4184],{},[1161,4450,4187],{},[1165,4452,1168],{"stretchy":1167},[1282,4454,4455],{},"5",[1165,4457,1358],{"separator":1121},[1282,4459,4460],{},"0,95",[1165,4462,1174],{"stretchy":1167},[1194,4464,4465],{"encoding":1196},"X \\sim Bi(5; 0{,}95)",", a pravděpodobnost, že u exponenciálního rozdělení se střední hodnotou ",[1115,4468,4470],{"className":4469},[1149],[1151,4471,4472],{"xmlns":1153},[1155,4473,4474,4482],{},[1158,4475,4476,4478,4480],{},[1161,4477,4372],{},[1165,4479,1177],{},[1282,4481,4455],{},[1194,4483,4484],{"encoding":1196},"\\delta = 5"," nastane událost do 3 jednotek času):",[3554,4487,4489],{"className":3556,"code":4488,"language":71,"meta":3558,"style":3558},"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",[1373,4490,4491,4506,4539,4568,4574,4583],{"__ignoreMap":3558},[1115,4492,4493,4495,4498,4501,4503],{"class":3563,"line":10},[1115,4494,1171],{"class":3744},[1115,4496,4497],{"class":3741}," \u003C-",[1115,4499,4500],{"class":3572}," 0",[1115,4502,2629],{"class":3741},[1115,4504,4505],{"class":3572},"5\n",[1115,4507,4508,4511,4513,4516,4518,4520,4522,4525,4527,4530,4532,4534,4537],{"class":3563,"line":27},[1115,4509,4510],{"class":3566},"round",[1115,4512,1168],{"class":3569},[1115,4514,4515],{"class":3566},"dbinom",[1115,4517,1168],{"class":3569},[1115,4519,1171],{"class":3744},[1115,4521,1715],{"class":3741},[1115,4523,4524],{"class":3572}," 5",[1115,4526,1715],{"class":3741},[1115,4528,4529],{"class":3572}," 0.95",[1115,4531,1174],{"class":3569},[1115,4533,1715],{"class":3741},[1115,4535,4536],{"class":3572}," 4",[1115,4538,3575],{"class":3569},[1115,4540,4541,4543,4545,4548,4550,4552,4554,4556,4558,4560,4562,4564,4566],{"class":3563,"line":148},[1115,4542,4510],{"class":3566},[1115,4544,1168],{"class":3569},[1115,4546,4547],{"class":3566},"pbinom",[1115,4549,1168],{"class":3569},[1115,4551,1171],{"class":3744},[1115,4553,1715],{"class":3741},[1115,4555,4524],{"class":3572},[1115,4557,1715],{"class":3741},[1115,4559,4529],{"class":3572},[1115,4561,1174],{"class":3569},[1115,4563,1715],{"class":3741},[1115,4565,4536],{"class":3572},[1115,4567,3575],{"class":3569},[1115,4569,4570],{"class":3563,"line":111},[1115,4571,4573],{"emptyLinePlaceholder":4572},true,"\n",[1115,4575,4576,4578,4580],{"class":3563,"line":96},[1115,4577,4430],{"class":3744},[1115,4579,4497],{"class":3741},[1115,4581,4582],{"class":3572}," 5\n",[1115,4584,4585,4587,4589,4592,4594,4596,4598,4601,4603,4606,4609,4612,4614,4616,4618],{"class":3563,"line":89},[1115,4586,4510],{"class":3566},[1115,4588,1168],{"class":3569},[1115,4590,4591],{"class":3566},"pexp",[1115,4593,1168],{"class":3569},[1115,4595,3322],{"class":3572},[1115,4597,1715],{"class":3741},[1115,4599,4600],{"class":3744}," rate",[1115,4602,3748],{"class":3741},[1115,4604,4605],{"class":3572}," 1",[1115,4607,4608],{"class":3741}," \u002F",[1115,4610,4611],{"class":3744}," delta",[1115,4613,1174],{"class":3569},[1115,4615,1715],{"class":3741},[1115,4617,4536],{"class":3572},[1115,4619,3575],{"class":3569},[3554,4621,4624],{"className":4622,"code":4623,"language":3603,"meta":3558},[3601],"[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",[1373,4625,4623],{"__ignoreMap":3558},[1431,4627,4629],{"id":4628},"studentovo-pearsonovo-a-fisherovo-snedecorovo-rozdělení","Studentovo, Pearsonovo a Fisherovo-Snedecorovo rozdělení",[1110,4631,4632,4633,4638],{},"Tato tři rozdělení mají statistiky, které se dále používají při konstrukci intervalů spolehlivosti a testování hypotéz (viz ",[1438,4634,141],{"className":4635,"dataFsResolvedFilePath":4636,"href":4637},[1441],"topics\u002Ftestovani-hypotez.md","\u002Fwiki\u002Ftestovani-hypotez",") — na rozdíl od normálního rozdělení se v příkladech této kapitoly samostatně nepočítají, jsou to nástroje pro další kapitoly.",[1110,4640,4641,4644,4645,4658],{},[1131,4642,4643],{},"Studentovo rozdělení"," s ",[1115,4646,4648],{"className":4647},[1149],[1151,4649,4650],{"xmlns":1153},[1155,4651,4652,4656],{},[1158,4653,4654],{},[1161,4655,1735],{},[1194,4657,1735],{"encoding":1196}," stupni volnosti má hustotu pravděpodobnosti",[1115,4660,4662],{"className":4661},[1149],[1151,4663,4664],{"xmlns":1153,"display":2212},[1155,4665,4666,4762],{},[1158,4667,4668,4670,4672,4674,4676,4678,4710,4748,4750,4752,4754,4756,4760],{},[1161,4669,1228],{},[1165,4671,1168],{"stretchy":1167},[1161,4673,1171],{},[1165,4675,1174],{"stretchy":1167},[1165,4677,1177],{},[3064,4679,4680,4682],{},[1282,4681,1284],{},[1158,4683,4684,4686,4706],{},[1161,4685,4184],{},[1158,4687,4688,4690,4696,4698,4704],{},[1165,4689,1168],{"fence":1121},[3064,4691,4692,4694],{},[1282,4693,1284],{},[1282,4695,1298],{},[1165,4697,1715],{"separator":1121},[3064,4699,4700,4702],{},[1161,4701,1735],{},[1282,4703,1298],{},[1165,4705,1174],{"fence":1121},[2765,4707,4708],{},[1161,4709,1735],{},[1209,4711,4712,4732],{},[1158,4713,4714,4716,4718,4720,4730],{},[1165,4715,1168],{"fence":1121},[1282,4717,1284],{},[1165,4719,2094],{},[3064,4721,4722,4728],{},[1209,4723,4724,4726],{},[1161,4725,1171],{},[1282,4727,1298],{},[1161,4729,1735],{},[1165,4731,1174],{"fence":1121},[1158,4733,4734,4736],{},[1165,4735,1317],{},[3064,4737,4738,4746],{},[1158,4739,4740,4742,4744],{},[1161,4741,1735],{},[1165,4743,2094],{},[1282,4745,1284],{},[1282,4747,1298],{},[1165,4749,1715],{"separator":1121},[2242,4751],{"width":2244},[1161,4753,1171],{},[1165,4755,1492],{},[1161,4757,4759],{"mathvariant":4758},"double-struck","R",[1165,4761,1715],{"separator":1121},[1194,4763,4764],{"encoding":1196},"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},",[1110,4766,4767,4768,4781,4782,4795,4796,4809],{},"kde ",[1115,4769,4771],{"className":4770},[1149],[1151,4772,4773],{"xmlns":1153},[1155,4774,4775,4779],{},[1158,4776,4777],{},[1161,4778,4184],{},[1194,4780,4184],{"encoding":1196}," je funkce beta. Je symetrické kolem nuly; číslo ",[1115,4783,4785],{"className":4784},[1149],[1151,4786,4787],{"xmlns":1153},[1155,4788,4789,4793],{},[1158,4790,4791],{},[1161,4792,1735],{},[1194,4794,1735],{"encoding":1196}," určuje tvar křivky — s rostoucím ",[1115,4797,4799],{"className":4798},[1149],[1151,4800,4801],{"xmlns":1153},[1155,4802,4803,4807],{},[1158,4804,4805],{},[1161,4806,1735],{},[1194,4808,1735],{"encoding":1196}," se rozdělení blíží normálnímu.",[1110,4811,4812,4644,4815,4828],{},[1131,4813,4814],{},"Pearsonovo (chí-kvadrát) rozdělení",[1115,4816,4818],{"className":4817},[1149],[1151,4819,4820],{"xmlns":1153},[1155,4821,4822,4826],{},[1158,4823,4824],{},[1161,4825,1735],{},[1194,4827,1735],{"encoding":1196}," stupni volnosti:",[1115,4830,4832],{"className":4831},[1149],[1151,4833,4834],{"xmlns":1153,"display":2212},[1155,4835,4836,4921],{},[1158,4837,4838,4840,4842,4844,4846,4848,4879,4895,4909,4911,4913,4915,4917,4919],{},[1161,4839,1228],{},[1165,4841,1168],{"stretchy":1167},[1161,4843,1171],{},[1165,4845,1174],{"stretchy":1167},[1165,4847,1177],{},[3064,4849,4850,4852],{},[1282,4851,1284],{},[1158,4853,4854,4866,4869,4871,4873,4875,4877],{},[1209,4855,4856,4858],{},[1282,4857,1298],{},[1158,4859,4860,4862,4864],{},[1161,4861,1735],{},[1161,4863,3434],{"mathvariant":1215},[1282,4865,1298],{},[1161,4867,4868],{"mathvariant":1215},"Γ",[1165,4870,1168],{"stretchy":1167},[1161,4872,1735],{},[1161,4874,3434],{"mathvariant":1215},[1282,4876,1298],{},[1165,4878,1174],{"stretchy":1167},[1209,4880,4881,4883],{},[1161,4882,1171],{},[1158,4884,4885,4887,4889,4891,4893],{},[1161,4886,1735],{},[1161,4888,3434],{"mathvariant":1215},[1282,4890,1298],{},[1165,4892,1317],{},[1282,4894,1284],{},[1209,4896,4897,4899],{},[1161,4898,3085],{},[1158,4900,4901,4903,4905,4907],{},[1165,4902,1317],{},[1161,4904,1171],{},[1161,4906,3434],{"mathvariant":1215},[1282,4908,1298],{},[1165,4910,1715],{"separator":1121},[2242,4912],{"width":2244},[1161,4914,1171],{},[1165,4916,4156],{},[1282,4918,1982],{},[1165,4920,1715],{"separator":1121},[1194,4922,4923],{"encoding":1196},"f(x) = \\frac{1}{2^{k\u002F2}\\Gamma(k\u002F2)} x^{k\u002F2-1} e^{-x\u002F2}, \\qquad x > 0,",[1110,4925,4767,4926,4940],{},[1115,4927,4929],{"className":4928},[1149],[1151,4930,4931],{"xmlns":1153},[1155,4932,4933,4937],{},[1158,4934,4935],{},[1161,4936,4868],{"mathvariant":1215},[1194,4938,4939],{"encoding":1196},"\\Gamma"," je funkce gama.",[1110,4942,4943,4946,4947,1425,4965,2629],{},[1131,4944,4945],{},"Fisherovo-Snedecorovo rozdělení"," se stupni volnosti ",[1115,4948,4950],{"className":4949},[1149],[1151,4951,4952],{"xmlns":1153},[1155,4953,4954,4962],{},[1158,4955,4956],{},[1277,4957,4958,4960],{},[1161,4959,1735],{},[1282,4961,1284],{},[1194,4963,4964],{"encoding":1196},"k_1",[1115,4966,4968],{"className":4967},[1149],[1151,4969,4970],{"xmlns":1153},[1155,4971,4972,4980],{},[1158,4973,4974],{},[1277,4975,4976,4978],{},[1161,4977,1735],{},[1282,4979,1298],{},[1194,4981,4982],{"encoding":1196},"k_2",[1115,4984,4986],{"className":4985},[1149],[1151,4987,4988],{"xmlns":1153,"display":2212},[1155,4989,4990,5155],{},[1158,4991,4992,4994,4996,4998,5000,5002,5038,5072,5092,5144,5146,5148,5150,5152],{},[1161,4993,1228],{},[1165,4995,1168],{"stretchy":1167},[1161,4997,1171],{},[1165,4999,1174],{"stretchy":1167},[1165,5001,1177],{},[3064,5003,5004,5006],{},[1282,5005,1284],{},[1158,5007,5008,5010],{},[1161,5009,4184],{},[1158,5011,5012,5014,5024,5026,5036],{},[1165,5013,1168],{"fence":1121},[3064,5015,5016,5022],{},[1277,5017,5018,5020],{},[1161,5019,1735],{},[1282,5021,1284],{},[1282,5023,1298],{},[1165,5025,1715],{"separator":1121},[3064,5027,5028,5034],{},[1277,5029,5030,5032],{},[1161,5031,1735],{},[1282,5033,1298],{},[1282,5035,1298],{},[1165,5037,1174],{"fence":1121},[1209,5039,5040,5060],{},[1158,5041,5042,5044,5058],{},[1165,5043,1168],{"fence":1121},[3064,5045,5046,5052],{},[1277,5047,5048,5050],{},[1161,5049,1735],{},[1282,5051,1284],{},[1277,5053,5054,5056],{},[1161,5055,1735],{},[1282,5057,1298],{},[1165,5059,1174],{"fence":1121},[1158,5061,5062,5068,5070],{},[1277,5063,5064,5066],{},[1161,5065,1735],{},[1282,5067,1284],{},[1161,5069,3434],{"mathvariant":1215},[1282,5071,1298],{},[1209,5073,5074,5076],{},[1161,5075,1171],{},[1158,5077,5078,5084,5086,5088,5090],{},[1277,5079,5080,5082],{},[1161,5081,1735],{},[1282,5083,1284],{},[1161,5085,3434],{"mathvariant":1215},[1282,5087,1298],{},[1165,5089,1317],{},[1282,5091,1284],{},[1209,5093,5094,5120],{},[1158,5095,5096,5098,5100,5102,5116,5118],{},[1165,5097,1168],{"fence":1121},[1282,5099,1284],{},[1165,5101,2094],{},[3064,5103,5104,5110],{},[1277,5105,5106,5108],{},[1161,5107,1735],{},[1282,5109,1284],{},[1277,5111,5112,5114],{},[1161,5113,1735],{},[1282,5115,1298],{},[1161,5117,1171],{},[1165,5119,1174],{"fence":1121},[1158,5121,5122,5124],{},[1165,5123,1317],{},[3064,5125,5126,5142],{},[1158,5127,5128,5134,5136],{},[1277,5129,5130,5132],{},[1161,5131,1735],{},[1282,5133,1284],{},[1165,5135,2094],{},[1277,5137,5138,5140],{},[1161,5139,1735],{},[1282,5141,1298],{},[1282,5143,1298],{},[1165,5145,1715],{"separator":1121},[2242,5147],{"width":2244},[1161,5149,1171],{},[1165,5151,4156],{},[1282,5153,5154],{},"0.",[1194,5156,5157],{"encoding":1196},"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.",[1110,5159,5160],{},[1760,5161],{"alt":5162,"className":5163,"src":5164},"mask-nv-specialni-rozdeleni",[1441,1764],"\u002Fwiki-assets\u002Fmask-nv-specialni-rozdeleni.png",[3441,5166],{"spec":5167},"{\"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\":[]}",[1110,5169,5170],{},"R funkce pro tato tři rozdělení:",[4052,5172,5173,5187],{},[4055,5174,5175],{},[4058,5176,5177,5179,5182,5184],{},[4061,5178,4063],{},[4061,5180,5181],{},"hustota",[4061,5183,1144],{},[4061,5185,5186],{},"kvantil",[4165,5188,5189,5229,5274],{},[4058,5190,5191,5214,5219,5224],{},[4170,5192,5193,5194],{},"Studentovo ",[1115,5195,5197],{"className":5196},[1149],[1151,5198,5199],{"xmlns":1153},[1155,5200,5201,5211],{},[1158,5202,5203,5205,5207,5209],{},[1161,5204,1617],{},[1165,5206,1168],{"stretchy":1167},[1161,5208,1735],{},[1165,5210,1174],{"stretchy":1167},[1194,5212,5213],{"encoding":1196},"t(k)",[4170,5215,5216],{},[1373,5217,5218],{},"dt(x, df = k)",[4170,5220,5221],{},[1373,5222,5223],{},"pt(x, df = k)",[4170,5225,5226],{},[1373,5227,5228],{},"qt(p, df = k)",[4058,5230,5231,5259,5264,5269],{},[4170,5232,5233,5234],{},"Pearsonovo ",[1115,5235,5237],{"className":5236},[1149],[1151,5238,5239],{"xmlns":1153},[1155,5240,5241,5256],{},[1158,5242,5243,5250,5252,5254],{},[1209,5244,5245,5248],{},[1161,5246,5247],{},"χ",[1282,5249,1298],{},[1165,5251,1168],{"stretchy":1167},[1161,5253,1735],{},[1165,5255,1174],{"stretchy":1167},[1194,5257,5258],{"encoding":1196},"\\chi^2(k)",[4170,5260,5261],{},[1373,5262,5263],{},"dchisq(x, df = k)",[4170,5265,5266],{},[1373,5267,5268],{},"pchisq(x, df = k)",[4170,5270,5271],{},[1373,5272,5273],{},"qchisq(p, df = k)",[4058,5275,5276,5311,5316,5321],{},[4170,5277,5278,5279],{},"Fisherovo-Snedecorovo ",[1115,5280,5282],{"className":5281},[1149],[1151,5283,5284],{"xmlns":1153},[1155,5285,5286,5308],{},[1158,5287,5288,5290,5292,5298,5300,5306],{},[1161,5289,1163],{},[1165,5291,1168],{"stretchy":1167},[1277,5293,5294,5296],{},[1161,5295,1735],{},[1282,5297,1284],{},[1165,5299,1715],{"separator":1121},[1277,5301,5302,5304],{},[1161,5303,1735],{},[1282,5305,1298],{},[1165,5307,1174],{"stretchy":1167},[1194,5309,5310],{"encoding":1196},"F(k_1, k_2)",[4170,5312,5313],{},[1373,5314,5315],{},"df(x, df1 = k1, df2 = k2)",[4170,5317,5318],{},[1373,5319,5320],{},"pf(x, df1 = k1, df2 = k2)",[4170,5322,5323],{},[1373,5324,5325],{},"qf(p, df1 = k1, df2 = k2)",[1110,5327,5328],{},"V R (97,5%-ní kvantil Studentova rozdělení s 9 stupni volnosti, 95%-ní kvantily Pearsonova a Fisherova-Snedecorova rozdělení):",[3554,5330,5332],{"className":3556,"code":5331,"language":71,"meta":3558,"style":3558},"qt(0.975, df = 9)\nqchisq(0.95, df = 9)\nqf(0.95, df1 = 3, df2 = 10)\n",[1373,5333,5334,5355,5375],{"__ignoreMap":3558},[1115,5335,5336,5339,5341,5343,5345,5348,5350,5353],{"class":3563,"line":10},[1115,5337,5338],{"class":3566},"qt",[1115,5340,1168],{"class":3569},[1115,5342,3595],{"class":3572},[1115,5344,1715],{"class":3741},[1115,5346,5347],{"class":3744}," df",[1115,5349,3748],{"class":3741},[1115,5351,5352],{"class":3572}," 9",[1115,5354,3575],{"class":3569},[1115,5356,5357,5360,5362,5365,5367,5369,5371,5373],{"class":3563,"line":27},[1115,5358,5359],{"class":3566},"qchisq",[1115,5361,1168],{"class":3569},[1115,5363,5364],{"class":3572},"0.95",[1115,5366,1715],{"class":3741},[1115,5368,5347],{"class":3744},[1115,5370,3748],{"class":3741},[1115,5372,5352],{"class":3572},[1115,5374,3575],{"class":3569},[1115,5376,5377,5380,5382,5384,5386,5389,5391,5394,5396,5399,5401,5403],{"class":3563,"line":148},[1115,5378,5379],{"class":3566},"qf",[1115,5381,1168],{"class":3569},[1115,5383,5364],{"class":3572},[1115,5385,1715],{"class":3741},[1115,5387,5388],{"class":3744}," df1",[1115,5390,3748],{"class":3741},[1115,5392,5393],{"class":3572}," 3",[1115,5395,1715],{"class":3741},[1115,5397,5398],{"class":3744}," df2",[1115,5400,3748],{"class":3741},[1115,5402,3994],{"class":3572},[1115,5404,3575],{"class":3569},[3554,5406,5409],{"className":5407,"code":5408,"language":3603,"meta":3558},[3601],"[1] 2.262157\n[1] 16.91898\n[1] 3.708265\n",[1373,5410,5408],{"__ignoreMap":3558},[1431,5412,5414],{"id":5413},"časté-chyby","Časté chyby",[1124,5416,5417,5503,5553],{},[1127,5418,5419,5422,5423,5450,5451,3434,5453,3434,5455,5457,5458,5478,5479,5502],{},[1131,5420,5421],{},"Rozptyl vs. směrodatná odchylka v R."," Zápis ",[1115,5424,5426],{"className":5425},[1149],[1151,5427,5428],{"xmlns":1153},[1155,5429,5430,5448],{},[1158,5431,5432,5434,5436,5438,5440,5446],{},[1161,5433,1350],{},[1165,5435,1168],{"stretchy":1167},[1161,5437,1355],{},[1165,5439,1358],{"separator":1121},[1209,5441,5442,5444],{},[1161,5443,1363],{},[1282,5445,1298],{},[1165,5447,1174],{"stretchy":1167},[1194,5449,1370],{"encoding":1196}," používá rozptyl, ale ",[1373,5452,1375],{},[1373,5454,1379],{},[1373,5456,1382],{}," očekávají směrodatnou odchylku. Dosazení rozptylu místo ",[1115,5459,5461],{"className":5460},[1149],[1151,5462,5463],{"xmlns":1153},[1155,5464,5465,5475],{},[1158,5466,5467],{},[2765,5468,5469],{},[1209,5470,5471,5473],{},[1161,5472,1363],{},[1282,5474,1298],{},[1194,5476,5477],{"encoding":1196},"\\sqrt{\\sigma^2}"," dává jiný — a pro ",[1115,5480,5482],{"className":5481},[1149],[1151,5483,5484],{"xmlns":1153},[1155,5485,5486,5499],{},[1158,5487,5488,5494,5497],{},[1209,5489,5490,5492],{},[1161,5491,1363],{},[1282,5493,1298],{},[1165,5495,5496],{"mathvariant":1215},"≠",[1282,5498,1284],{},[1194,5500,5501],{"encoding":1196},"\\sigma^2 \\ne 1"," výrazně odlišný — výsledek (viz příklad s ampulkou).",[1127,5504,5505,5532,5533,5552],{},[1131,5506,5507,5531],{},[1115,5508,5510],{"className":5509},[1149],[1151,5511,5512],{"xmlns":1153},[1155,5513,5514,5528],{},[1158,5515,5516,5518,5520,5522,5524,5526],{},[1161,5517,1180],{},[1165,5519,1168],{"stretchy":1167},[1161,5521,1185],{},[1165,5523,1177],{},[1161,5525,1171],{},[1165,5527,1174],{"stretchy":1167},[1194,5529,5530],{"encoding":1196},"P(X=x)"," u spojité veličiny je vždy 0."," Hustota ",[1115,5534,5536],{"className":5535},[1149],[1151,5537,5538],{"xmlns":1153},[1155,5539,5540,5550],{},[1158,5541,5542,5544,5546,5548],{},[1161,5543,1228],{},[1165,5545,1168],{"stretchy":1167},[1161,5547,1171],{},[1165,5549,1174],{"stretchy":1167},[1194,5551,1258],{"encoding":1196}," sama o sobě pravděpodobnost neudává — pravděpodobnost dává až plocha pod křivkou na intervalu.",[1127,5554,5555,1145,5558,5575,5576,5593,5594,5597,5598,1333],{},[1131,5556,5557],{},"Záměna stupňů volnosti u Fisherova-Snedecorova rozdělení.",[1115,5559,5561],{"className":5560},[1149],[1151,5562,5563],{"xmlns":1153},[1155,5564,5565,5573],{},[1158,5566,5567],{},[1277,5568,5569,5571],{},[1161,5570,1735],{},[1282,5572,1284],{},[1194,5574,4964],{"encoding":1196}," (čitatel) a ",[1115,5577,5579],{"className":5578},[1149],[1151,5580,5581],{"xmlns":1153},[1155,5582,5583,5591],{},[1158,5584,5585],{},[1277,5586,5587,5589],{},[1161,5588,1735],{},[1282,5590,1298],{},[1194,5592,4982],{"encoding":1196}," (jmenovatel) nejsou zaměnitelné — ",[1373,5595,5596],{},"qf(p, df1, df2)"," dá jiný výsledek než ",[1373,5599,5600],{},"qf(p, df2, df1)",[1431,5602,5604],{"id":5603},"související-stránky","Související stránky",[1124,5606,5607,5612,5617,5622,5630,5637,5645],{},[1127,5608,5609],{},[1438,5610,1444],{"className":5611,"dataFsResolvedFilePath":1442,"href":1443},[1441],[1127,5613,5614],{},[1438,5615,886],{"className":5616,"dataFsResolvedFilePath":2788,"href":2789},[1441],[1127,5618,5619],{},[1438,5620,141],{"className":5621,"dataFsResolvedFilePath":4636,"href":4637},[1441],[1127,5623,5624],{},[1438,5625,5629],{"className":5626,"dataFsResolvedFilePath":5627,"href":5628},[1441],"topics\u002Fregresni-a-korelacni-analyza.md","\u002Fwiki\u002Fregresni-a-korelacni-analyza","regresni-a-korelacni-analyza",[1127,5631,5632],{},[1438,5633,716],{"className":5634,"dataFsResolvedFilePath":5635,"href":5636},[1441],"topics\u002Fkontingencni-tabulky.md","\u002Fwiki\u002Fkontingencni-tabulky",[1127,5638,5639],{},[1438,5640,5644],{"className":5641,"dataFsResolvedFilePath":5642,"href":5643},[1441],"topics\u002Fregulacni-diagramy-a-indexy-zpusobilosti.md","\u002Fwiki\u002Fregulacni-diagramy-a-indexy-zpusobilosti","regulacni-diagramy-a-indexy-zpusobilosti",[1127,5646,5647],{},[1438,5648,5652],{"className":5649,"dataFsResolvedFilePath":5650,"href":5651},[1441],"outputs\u002Fmask-r-tahak.md","\u002Fwiki\u002Fmask-r-tahak","Tahák pro R",[1431,5654,5655],{"id":934},"Reference",[1110,5657,5658,5659,5663],{},"KROPÁČ, J. ",[5660,5661,5662],"em",{},"Statistika A",". 4. vyd. Brno: Fakulta podnikatelská VUT, 2011.",[5665,5666,5667],"style",{},"html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .sP4rz, html code.shiki .sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}",{"title":3558,"searchDepth":27,"depth":27,"links":5669},[5670,5671,5672,5673,5674,5675,5676,5677,5678,5679],{"id":1433,"depth":27,"text":1434},{"id":1748,"depth":27,"text":1749},{"id":2445,"depth":27,"text":2446},{"id":2554,"depth":27,"text":2555},{"id":2995,"depth":27,"text":1338},{"id":4023,"depth":27,"text":4024},{"id":4628,"depth":27,"text":4629},{"id":5413,"depth":27,"text":5414},{"id":5603,"depth":27,"text":5604},{"id":934,"depth":27,"text":5655},null,"2026-10-02","md",{},"\u002Ftopics\u002Fnahodne-veliciny-a-rozdeleni",{"title":1094,"description":3558},[5687,5688,5689],"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],"topic","y7MCWBwmskoGgsMoqVPhRRaL6YYTo3Cf-R4Yf-89eMs","topics",[5696,10778,14804,19570,24273,29728],{"id":5697,"title":5698,"body":5699,"course":23,"courses":5680,"created":5681,"description":3558,"extension":5682,"meta":10769,"navigation":4572,"path":10770,"seo":10771,"sources":10772,"stem":10775,"tags":10776,"type":5692,"updated":5681,"__hash__":10777},"topics\u002Ftopics\u002Fkontingencni-tabulky.md","Kontingenční tabulky",{"type":1096,"value":5700,"toc":10759},[5701,5704,5876,5880,5896,5914,6117,6254,6848,6865,6977,6981,7012,7017,7615,7621,7837,8051,8057,8137,8249,8402,8408,8488,8509,8516,8550,8557,8560,8566,8630,8688,8836,8842,8849,8927,8930,8986,9324,9345,9449,9558,9561,9582,9585,9839,9920,9927,9931,10161,10175,10324,10458,10464,10522,10524,10540,10555,10561,10606,10625,10640,10646,10705,10707,10750,10752,10756],[1099,5702,5698],{"id":5703},"kontingenční-tabulky",[1103,5705,5707,5713],{"className":5706,"dataCallout":1108},[1106,1107],[1110,5708,5710,1122],{"className":5709},[1113],[1115,5711],{"className":5712,"ariaHidden":1121},[1118,1119,1120],[1124,5714,5715,5722,5781,5802,5840,5865],{},[1127,5716,5717,5718,5721],{},"Kontingenční tabulka zaznamenává ",[1131,5719,5720],{},"simultánní četnosti"," dvou kvalitativních znaků naměřených na stejném souboru.",[1127,5723,5724,5727,5728,5746,5747,5765,5766,5780],{},[1131,5725,5726],{},"Test nezávislosti"," srovnává pozorované četnosti s očekávanými za platnosti ",[1115,5729,5731],{"className":5730},[1149],[1151,5732,5733],{"xmlns":1153},[1155,5734,5735,5743],{},[1158,5736,5737],{},[1277,5738,5739,5741],{},[1161,5740,4318],{},[1282,5742,1982],{},[1194,5744,5745],{"encoding":1196},"H_0"," pomocí statistiky ",[1115,5748,5750],{"className":5749},[1149],[1151,5751,5752],{"xmlns":1153},[1155,5753,5754,5762],{},[1158,5755,5756],{},[1209,5757,5758,5760],{},[1161,5759,5247],{},[1282,5761,1298],{},[1194,5763,5764],{"encoding":1196},"\\chi^2","; rozhoduje kritický obor ",[1115,5767,5769],{"className":5768},[1149],[1151,5770,5771],{"xmlns":1153},[1155,5772,5773,5778],{},[1158,5774,5775],{},[1161,5776,5777],{},"W",[1194,5779,5777],{"encoding":1196},", prakticky p-hodnota.",[1127,5782,5783,5784,5801],{},"Aproximace ",[1115,5785,5787],{"className":5786},[1149],[1151,5788,5789],{"xmlns":1153},[1155,5790,5791,5799],{},[1158,5792,5793],{},[1209,5794,5795,5797],{},[1161,5796,5247],{},[1282,5798,1298],{},[1194,5800,5764],{"encoding":1196}," rozdělením platí jen tehdy, když jsou očekávané četnosti dostatečně velké — proto se vždy kontrolují.",[1127,5803,5804,5805,5822,5823,1145,5826,1333],{},"Zamítnutí ",[1115,5806,5808],{"className":5807},[1149],[1151,5809,5810],{"xmlns":1153},[1155,5811,5812,5820],{},[1158,5813,5814],{},[1277,5815,5816,5818],{},[1161,5817,4318],{},[1282,5819,1982],{},[1194,5821,5745],{"encoding":1196}," samo o sobě neříká, jak silná závislost je — na to slouží ",[1131,5824,5825],{},"Cramérův koeficient kontingence",[1115,5827,5829],{"className":5828},[1149],[1151,5830,5831],{"xmlns":1153},[1155,5832,5833,5838],{},[1158,5834,5835],{},[1161,5836,5837],{},"V",[1194,5839,5837],{"encoding":1196},[1127,5841,5842,5845,5846,1333],{},[1131,5843,5844],{},"Čtyřpolní tabulka"," (2×2) je speciální případ s vlastním zjednodušeným vzorcem pro ",[1115,5847,5849],{"className":5848},[1149],[1151,5850,5851],{"xmlns":1153},[1155,5852,5853,5862],{},[1158,5854,5855,5857,5859],{},[1161,5856,4192],{},[1165,5858,4156],{},[1282,5860,5861],{},"40",[1194,5863,5864],{"encoding":1196},"n>40",[1127,5866,5867,5868,5871,5872,5875],{},"Pro ",[1131,5869,5870],{},"párová data"," (stejné prvky měřené dvakrát, např. před\u002Fpo zásahu) se používá ",[1131,5873,5874],{},"McNemarův test",", ne obyčejný test nezávislosti.",[1431,5877,5879],{"id":5878},"kontingenční-tabulka","Kontingenční tabulka",[1110,5881,5882,5883,5886,5887,5891,5892,5895],{},"V rámci ",[1438,5884,1444],{"className":5885,"dataFsResolvedFilePath":1442,"href":1443},[1441]," navazují kontingenční tabulky na\n",[1438,5888,5890],{"className":5889,"dataFsResolvedFilePath":4636,"href":4637},[1441],"testování statistických hypotéz",": místo jedné náhodné veličiny teď sledujeme dva\n",[1131,5893,5894],{},"kvalitativní"," (kategoriální) znaky současně a ptáme se, zda spolu souvisí.",[1110,5897,5898,5899,5902,5903,5905,5906,5909,5910,5913],{},"Znak je ",[1131,5900,5901],{},"kvantitativní",", pokud nabývá číselných hodnot (stáří, stav tachometru), a ",[1131,5904,5894],{},"\n(kategoriální), pokud nabývá slovních variant (vzdělání, kuřák\u002Fnekuřák). Kvalitativní znaky dále dělíme na\n",[1131,5907,5908],{},"alternativní"," (dvě varianty, např. vada ano\u002Fne) a ",[1131,5911,5912],{},"množné"," (více než dvě varianty, např. svobodný\u002Frozvedený\u002Fženatý).",[1110,5915,5916,5917,5930,5931,5945,5946,5976,5977,5990,5991,6022,6023,6026,6027,3640,6050,1145,6053,6075,6076,6094,6095,6113,6114,2629],{},"Mějme ",[1115,5918,5920],{"className":5919},[1149],[1151,5921,5922],{"xmlns":1153},[1155,5923,5924,5928],{},[1158,5925,5926],{},[1161,5927,4192],{},[1194,5929,4192],{"encoding":1196}," opakování pokusu, při nichž sledujeme dva kvalitativní znaky ",[1115,5932,5934],{"className":5933},[1149],[1151,5935,5936],{"xmlns":1153},[1155,5937,5938,5943],{},[1158,5939,5940],{},[1161,5941,5942],{},"A",[1194,5944,5942],{"encoding":1196}," (varianty ",[1115,5947,5949],{"className":5948},[1149],[1151,5950,5951],{"xmlns":1153},[1155,5952,5953,5973],{},[1158,5954,5955,5961,5963,5965,5967],{},[1277,5956,5957,5959],{},[1161,5958,5942],{},[1282,5960,1284],{},[1165,5962,1715],{"separator":1121},[1165,5964,1726],{},[1165,5966,1715],{"separator":1121},[1277,5968,5969,5971],{},[1161,5970,5942],{},[1161,5972,71],{},[1194,5974,5975],{"encoding":1196},"A_1,\\dots,A_r",") a ",[1115,5978,5980],{"className":5979},[1149],[1151,5981,5982],{"xmlns":1153},[1155,5983,5984,5988],{},[1158,5985,5986],{},[1161,5987,4184],{},[1194,5989,4184],{"encoding":1196},"\n(varianty ",[1115,5992,5994],{"className":5993},[1149],[1151,5995,5996],{"xmlns":1153},[1155,5997,5998,6019],{},[1158,5999,6000,6006,6008,6010,6012],{},[1277,6001,6002,6004],{},[1161,6003,4184],{},[1282,6005,1284],{},[1165,6007,1715],{"separator":1121},[1165,6009,1726],{},[1165,6011,1715],{"separator":1121},[1277,6013,6014,6016],{},[1161,6015,4184],{},[1161,6017,6018],{},"s",[1194,6020,6021],{"encoding":1196},"B_1,\\dots,B_s","). Výsledky zapíšeme do ",[1131,6024,6025],{},"kontingenční tabulky",": v políčku ",[1115,6028,6030],{"className":6029},[1149],[1151,6031,6032],{"xmlns":1153},[1155,6033,6034,6047],{},[1158,6035,6036,6038,6040,6042,6045],{},[1165,6037,1168],{"stretchy":1167},[1161,6039,4187],{},[1165,6041,1715],{"separator":1121},[1161,6043,6044],{},"j",[1165,6046,1174],{"stretchy":1167},[1194,6048,6049],{"encoding":1196},"(i,j)",[1131,6051,6052],{},"simultánní\nčetnost",[1115,6054,6056],{"className":6055},[1149],[1151,6057,6058],{"xmlns":1153},[1155,6059,6060,6072],{},[1158,6061,6062],{},[1277,6063,6064,6066],{},[1161,6065,4192],{},[1158,6067,6068,6070],{},[1161,6069,4187],{},[1161,6071,6044],{},[1194,6073,6074],{"encoding":1196},"n_{ij}",", tedy počet pokusů s variantou ",[1115,6077,6079],{"className":6078},[1149],[1151,6080,6081],{"xmlns":1153},[1155,6082,6083,6091],{},[1158,6084,6085],{},[1277,6086,6087,6089],{},[1161,6088,5942],{},[1161,6090,4187],{},[1194,6092,6093],{"encoding":1196},"A_i"," zároveň s variantou ",[1115,6096,6098],{"className":6097},[1149],[1151,6099,6100],{"xmlns":1153},[1155,6101,6102,6110],{},[1158,6103,6104],{},[1277,6105,6106,6108],{},[1161,6107,4184],{},[1161,6109,6044],{},[1194,6111,6112],{"encoding":1196},"B_j",". Řádkové a sloupcové součty\njsou ",[1131,6115,6116],{},"marginální četnosti",[1115,6118,6120],{"className":6119},[1149],[1151,6121,6122],{"xmlns":1153,"display":2212},[1155,6123,6124,6251],{},[1158,6125,6126,6137,6139,6155,6165,6167,6169,6179,6181,6195,6205,6207,6209,6211,6213,6227,6241],{},[1277,6127,6128,6130],{},[1161,6129,4192],{},[1158,6131,6132,6134],{},[1161,6133,4187],{},[1165,6135,6136],{},"∙",[1165,6138,1177],{},[6140,6141,6142,6145,6153],"munderover",{},[1165,6143,6144],{},"∑",[1158,6146,6147,6149,6151],{},[1161,6148,6044],{},[1165,6150,1177],{},[1282,6152,1284],{},[1161,6154,6018],{},[1277,6156,6157,6159],{},[1161,6158,4192],{},[1158,6160,6161,6163],{},[1161,6162,4187],{},[1161,6164,6044],{},[1165,6166,1715],{"separator":1121},[2242,6168],{"width":2244},[1277,6170,6171,6173],{},[1161,6172,4192],{},[1158,6174,6175,6177],{},[1165,6176,6136],{},[1161,6178,6044],{},[1165,6180,1177],{},[6140,6182,6183,6185,6193],{},[1165,6184,6144],{},[1158,6186,6187,6189,6191],{},[1161,6188,4187],{},[1165,6190,1177],{},[1282,6192,1284],{},[1161,6194,71],{},[1277,6196,6197,6199],{},[1161,6198,4192],{},[1158,6200,6201,6203],{},[1161,6202,4187],{},[1161,6204,6044],{},[1165,6206,1715],{"separator":1121},[2242,6208],{"width":2244},[1161,6210,4192],{},[1165,6212,1177],{},[6140,6214,6215,6217,6225],{},[1165,6216,6144],{},[1158,6218,6219,6221,6223],{},[1161,6220,4187],{},[1165,6222,1177],{},[1282,6224,1284],{},[1161,6226,71],{},[6140,6228,6229,6231,6239],{},[1165,6230,6144],{},[1158,6232,6233,6235,6237],{},[1161,6234,6044],{},[1165,6236,1177],{},[1282,6238,1284],{},[1161,6240,6018],{},[1277,6242,6243,6245],{},[1161,6244,4192],{},[1158,6246,6247,6249],{},[1161,6248,4187],{},[1161,6250,6044],{},[1194,6252,6253],{"encoding":1196},"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}",[4052,6255,6256,6367],{},[4055,6257,6258],{},[4058,6259,6260,6281,6301,6321,6323,6343],{},[4061,6261,6262],{},[1115,6263,6265],{"className":6264},[1149],[1151,6266,6267],{"xmlns":1153},[1155,6268,6269,6278],{},[1158,6270,6271,6273,6276],{},[1161,6272,5942],{},[1161,6274,6275],{"mathvariant":1215},"\\",[1161,6277,4184],{},[1194,6279,6280],{"encoding":1196},"A \\backslash B",[4061,6282,6283],{},[1115,6284,6286],{"className":6285},[1149],[1151,6287,6288],{"xmlns":1153},[1155,6289,6290,6298],{},[1158,6291,6292],{},[1277,6293,6294,6296],{},[1161,6295,4184],{},[1282,6297,1284],{},[1194,6299,6300],{"encoding":1196},"B_1",[4061,6302,6303],{},[1115,6304,6306],{"className":6305},[1149],[1151,6307,6308],{"xmlns":1153},[1155,6309,6310,6318],{},[1158,6311,6312],{},[1277,6313,6314,6316],{},[1161,6315,4184],{},[1282,6317,1298],{},[1194,6319,6320],{"encoding":1196},"B_2",[4061,6322,1726],{},[4061,6324,6325],{},[1115,6326,6328],{"className":6327},[1149],[1151,6329,6330],{"xmlns":1153},[1155,6331,6332,6340],{},[1158,6333,6334],{},[1277,6335,6336,6338],{},[1161,6337,4184],{},[1161,6339,6018],{},[1194,6341,6342],{"encoding":1196},"B_s",[4061,6344,6345],{},[1115,6346,6348],{"className":6347},[1149],[1151,6349,6350],{"xmlns":1153},[1155,6351,6352,6364],{},[1158,6353,6354],{},[1277,6355,6356,6358],{},[1161,6357,4192],{},[1158,6359,6360,6362],{},[1161,6361,4187],{},[1165,6363,6136],{},[1194,6365,6366],{"encoding":1196},"n_{i\\bullet}",[4165,6368,6369,6483,6597,6613,6733],{},[4058,6370,6371,6391,6412,6433,6435,6459],{},[4170,6372,6373],{},[1115,6374,6376],{"className":6375},[1149],[1151,6377,6378],{"xmlns":1153},[1155,6379,6380,6388],{},[1158,6381,6382],{},[1277,6383,6384,6386],{},[1161,6385,5942],{},[1282,6387,1284],{},[1194,6389,6390],{"encoding":1196},"A_1",[4170,6392,6393],{},[1115,6394,6396],{"className":6395},[1149],[1151,6397,6398],{"xmlns":1153},[1155,6399,6400,6409],{},[1158,6401,6402],{},[1277,6403,6404,6406],{},[1161,6405,4192],{},[1282,6407,6408],{},"11",[1194,6410,6411],{"encoding":1196},"n_{11}",[4170,6413,6414],{},[1115,6415,6417],{"className":6416},[1149],[1151,6418,6419],{"xmlns":1153},[1155,6420,6421,6430],{},[1158,6422,6423],{},[1277,6424,6425,6427],{},[1161,6426,4192],{},[1282,6428,6429],{},"12",[1194,6431,6432],{"encoding":1196},"n_{12}",[4170,6434,1726],{},[4170,6436,6437],{},[1115,6438,6440],{"className":6439},[1149],[1151,6441,6442],{"xmlns":1153},[1155,6443,6444,6456],{},[1158,6445,6446],{},[1277,6447,6448,6450],{},[1161,6449,4192],{},[1158,6451,6452,6454],{},[1282,6453,1284],{},[1161,6455,6018],{},[1194,6457,6458],{"encoding":1196},"n_{1s}",[4170,6460,6461],{},[1115,6462,6464],{"className":6463},[1149],[1151,6465,6466],{"xmlns":1153},[1155,6467,6468,6480],{},[1158,6469,6470],{},[1277,6471,6472,6474],{},[1161,6473,4192],{},[1158,6475,6476,6478],{},[1282,6477,1284],{},[1165,6479,6136],{},[1194,6481,6482],{"encoding":1196},"n_{1\\bullet}",[4058,6484,6485,6505,6526,6547,6549,6573],{},[4170,6486,6487],{},[1115,6488,6490],{"className":6489},[1149],[1151,6491,6492],{"xmlns":1153},[1155,6493,6494,6502],{},[1158,6495,6496],{},[1277,6497,6498,6500],{},[1161,6499,5942],{},[1282,6501,1298],{},[1194,6503,6504],{"encoding":1196},"A_2",[4170,6506,6507],{},[1115,6508,6510],{"className":6509},[1149],[1151,6511,6512],{"xmlns":1153},[1155,6513,6514,6523],{},[1158,6515,6516],{},[1277,6517,6518,6520],{},[1161,6519,4192],{},[1282,6521,6522],{},"21",[1194,6524,6525],{"encoding":1196},"n_{21}",[4170,6527,6528],{},[1115,6529,6531],{"className":6530},[1149],[1151,6532,6533],{"xmlns":1153},[1155,6534,6535,6544],{},[1158,6536,6537],{},[1277,6538,6539,6541],{},[1161,6540,4192],{},[1282,6542,6543],{},"22",[1194,6545,6546],{"encoding":1196},"n_{22}",[4170,6548,1726],{},[4170,6550,6551],{},[1115,6552,6554],{"className":6553},[1149],[1151,6555,6556],{"xmlns":1153},[1155,6557,6558,6570],{},[1158,6559,6560],{},[1277,6561,6562,6564],{},[1161,6563,4192],{},[1158,6565,6566,6568],{},[1282,6567,1298],{},[1161,6569,6018],{},[1194,6571,6572],{"encoding":1196},"n_{2s}",[4170,6574,6575],{},[1115,6576,6578],{"className":6577},[1149],[1151,6579,6580],{"xmlns":1153},[1155,6581,6582,6594],{},[1158,6583,6584],{},[1277,6585,6586,6588],{},[1161,6587,4192],{},[1158,6589,6590,6592],{},[1282,6591,1298],{},[1165,6593,6136],{},[1194,6595,6596],{"encoding":1196},"n_{2\\bullet}",[4058,6598,6599,6602,6604,6606,6609,6611],{},[4170,6600,6601],{},"⋮",[4170,6603,6601],{},[4170,6605,6601],{},[4170,6607,6608],{},"⋱",[4170,6610,6601],{},[4170,6612,6601],{},[4058,6614,6615,6635,6659,6683,6685,6709],{},[4170,6616,6617],{},[1115,6618,6620],{"className":6619},[1149],[1151,6621,6622],{"xmlns":1153},[1155,6623,6624,6632],{},[1158,6625,6626],{},[1277,6627,6628,6630],{},[1161,6629,5942],{},[1161,6631,71],{},[1194,6633,6634],{"encoding":1196},"A_r",[4170,6636,6637],{},[1115,6638,6640],{"className":6639},[1149],[1151,6641,6642],{"xmlns":1153},[1155,6643,6644,6656],{},[1158,6645,6646],{},[1277,6647,6648,6650],{},[1161,6649,4192],{},[1158,6651,6652,6654],{},[1161,6653,71],{},[1282,6655,1284],{},[1194,6657,6658],{"encoding":1196},"n_{r1}",[4170,6660,6661],{},[1115,6662,6664],{"className":6663},[1149],[1151,6665,6666],{"xmlns":1153},[1155,6667,6668,6680],{},[1158,6669,6670],{},[1277,6671,6672,6674],{},[1161,6673,4192],{},[1158,6675,6676,6678],{},[1161,6677,71],{},[1282,6679,1298],{},[1194,6681,6682],{"encoding":1196},"n_{r2}",[4170,6684,1726],{},[4170,6686,6687],{},[1115,6688,6690],{"className":6689},[1149],[1151,6691,6692],{"xmlns":1153},[1155,6693,6694,6706],{},[1158,6695,6696],{},[1277,6697,6698,6700],{},[1161,6699,4192],{},[1158,6701,6702,6704],{},[1161,6703,71],{},[1161,6705,6018],{},[1194,6707,6708],{"encoding":1196},"n_{rs}",[4170,6710,6711],{},[1115,6712,6714],{"className":6713},[1149],[1151,6715,6716],{"xmlns":1153},[1155,6717,6718,6730],{},[1158,6719,6720],{},[1277,6721,6722,6724],{},[1161,6723,4192],{},[1158,6725,6726,6728],{},[1161,6727,71],{},[1165,6729,6136],{},[1194,6731,6732],{"encoding":1196},"n_{r\\bullet}",[4058,6734,6735,6759,6783,6807,6809,6833],{},[4170,6736,6737],{},[1115,6738,6740],{"className":6739},[1149],[1151,6741,6742],{"xmlns":1153},[1155,6743,6744,6756],{},[1158,6745,6746],{},[1277,6747,6748,6750],{},[1161,6749,4192],{},[1158,6751,6752,6754],{},[1165,6753,6136],{},[1161,6755,6044],{},[1194,6757,6758],{"encoding":1196},"n_{\\bullet j}",[4170,6760,6761],{},[1115,6762,6764],{"className":6763},[1149],[1151,6765,6766],{"xmlns":1153},[1155,6767,6768,6780],{},[1158,6769,6770],{},[1277,6771,6772,6774],{},[1161,6773,4192],{},[1158,6775,6776,6778],{},[1165,6777,6136],{},[1282,6779,1284],{},[1194,6781,6782],{"encoding":1196},"n_{\\bullet 1}",[4170,6784,6785],{},[1115,6786,6788],{"className":6787},[1149],[1151,6789,6790],{"xmlns":1153},[1155,6791,6792,6804],{},[1158,6793,6794],{},[1277,6795,6796,6798],{},[1161,6797,4192],{},[1158,6799,6800,6802],{},[1165,6801,6136],{},[1282,6803,1298],{},[1194,6805,6806],{"encoding":1196},"n_{\\bullet 2}",[4170,6808,1726],{},[4170,6810,6811],{},[1115,6812,6814],{"className":6813},[1149],[1151,6815,6816],{"xmlns":1153},[1155,6817,6818,6830],{},[1158,6819,6820],{},[1277,6821,6822,6824],{},[1161,6823,4192],{},[1158,6825,6826,6828],{},[1165,6827,6136],{},[1161,6829,6018],{},[1194,6831,6832],{"encoding":1196},"n_{\\bullet s}",[4170,6834,6835],{},[1115,6836,6838],{"className":6837},[1149],[1151,6839,6840],{"xmlns":1153},[1155,6841,6842,6846],{},[1158,6843,6844],{},[1161,6845,4192],{},[1194,6847,4192],{"encoding":1196},[1110,6849,6850,6851,6864],{},"Vydělením četností počtem opakování ",[1115,6852,6854],{"className":6853},[1149],[1151,6855,6856],{"xmlns":1153},[1155,6857,6858,6862],{},[1158,6859,6860],{},[1161,6861,4192],{},[1194,6863,4192],{"encoding":1196}," dostaneme odhady pravděpodobností:",[1115,6866,6868],{"className":6867},[1149],[1151,6869,6870],{"xmlns":1153,"display":2212},[1155,6871,6872,6974],{},[1158,6873,6874,6890,6892,6906,6908,6910,6924,6926,6940,6942,6944,6958,6960],{},[1277,6875,6876,6884],{},[6877,6878,6879,6881],"mover",{"accent":1121},[1161,6880,1110],{},[1165,6882,6883],{},"^",[1158,6885,6886,6888],{},[1161,6887,4187],{},[1161,6889,6044],{},[1165,6891,1177],{},[3064,6893,6894,6904],{},[1277,6895,6896,6898],{},[1161,6897,4192],{},[1158,6899,6900,6902],{},[1161,6901,4187],{},[1161,6903,6044],{},[1161,6905,4192],{},[1165,6907,1715],{"separator":1121},[2242,6909],{"width":2244},[1277,6911,6912,6918],{},[6877,6913,6914,6916],{"accent":1121},[1161,6915,1110],{},[1165,6917,6883],{},[1158,6919,6920,6922],{},[1161,6921,4187],{},[1165,6923,6136],{},[1165,6925,1177],{},[3064,6927,6928,6938],{},[1277,6929,6930,6932],{},[1161,6931,4192],{},[1158,6933,6934,6936],{},[1161,6935,4187],{},[1165,6937,6136],{},[1161,6939,4192],{},[1165,6941,1715],{"separator":1121},[2242,6943],{"width":2244},[1277,6945,6946,6952],{},[6877,6947,6948,6950],{"accent":1121},[1161,6949,1110],{},[1165,6951,6883],{},[1158,6953,6954,6956],{},[1165,6955,6136],{},[1161,6957,6044],{},[1165,6959,1177],{},[3064,6961,6962,6972],{},[1277,6963,6964,6966],{},[1161,6965,4192],{},[1158,6967,6968,6970],{},[1165,6969,6136],{},[1161,6971,6044],{},[1161,6973,4192],{},[1194,6975,6976],{"encoding":1196},"\\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}",[1431,6978,6980],{"id":6979},"test-nezávislosti-dvou-kvalitativních-znaků","Test nezávislosti dvou kvalitativních znaků",[1110,6982,6983,6984,6997,6998,7011],{},"Test ověřuje, zda varianty znaku ",[1115,6985,6987],{"className":6986},[1149],[1151,6988,6989],{"xmlns":1153},[1155,6990,6991,6995],{},[1158,6992,6993],{},[1161,6994,5942],{},[1194,6996,5942],{"encoding":1196}," a varianty znaku ",[1115,6999,7001],{"className":7000},[1149],[1151,7002,7003],{"xmlns":1153},[1155,7004,7005,7009],{},[1158,7006,7007],{},[1161,7008,4184],{},[1194,7010,4184],{"encoding":1196}," jsou na sobě nezávislé, tedy zda simultánní\npravděpodobnost je součinem marginálních pravděpodobností.",[1110,7013,7014],{},[1131,7015,7016],{},"Postup testu:",[7018,7019,7020,7149,7466,7547],"ol",{},[1127,7021,7022,7076,7077,1376,7103,7129,7130,7148],{},[1115,7023,7025],{"className":7024},[1149],[1151,7026,7027],{"xmlns":1153},[1155,7028,7029,7073],{},[1158,7030,7031,7037,7039,7049,7051,7061,7063],{},[1277,7032,7033,7035],{},[1161,7034,4318],{},[1282,7036,1982],{},[1165,7038,2629],{},[1277,7040,7041,7043],{},[1161,7042,1110],{},[1158,7044,7045,7047],{},[1161,7046,4187],{},[1161,7048,6044],{},[1165,7050,1177],{},[1277,7052,7053,7055],{},[1161,7054,1110],{},[1158,7056,7057,7059],{},[1161,7058,4187],{},[1165,7060,6136],{},[2278,7062,2280],{},[1277,7064,7065,7067],{},[1161,7066,1110],{},[1158,7068,7069,7071],{},[1165,7070,6136],{},[1161,7072,6044],{},[1194,7074,7075],{"encoding":1196},"H_0: p_{ij} = p_{i\\bullet}\\,p_{\\bullet j}"," pro všechna ",[1115,7078,7080],{"className":7079},[1149],[1151,7081,7082],{"xmlns":1153},[1155,7083,7084,7100],{},[1158,7085,7086,7088,7090,7092,7094,7096,7098],{},[1161,7087,4187],{},[1165,7089,1177],{},[1282,7091,1284],{},[1165,7093,1715],{"separator":1121},[1165,7095,1726],{},[1165,7097,1715],{"separator":1121},[1161,7099,71],{},[1194,7101,7102],{"encoding":1196},"i = 1,\\dots,r",[1115,7104,7106],{"className":7105},[1149],[1151,7107,7108],{"xmlns":1153},[1155,7109,7110,7126],{},[1158,7111,7112,7114,7116,7118,7120,7122,7124],{},[1161,7113,6044],{},[1165,7115,1177],{},[1282,7117,1284],{},[1165,7119,1715],{"separator":1121},[1165,7121,1726],{},[1165,7123,1715],{"separator":1121},[1161,7125,6018],{},[1194,7127,7128],{"encoding":1196},"j = 1,\\dots,s"," (znaky jsou na sobě\nnezávislé) proti ",[1115,7131,7133],{"className":7132},[1149],[1151,7134,7135],{"xmlns":1153},[1155,7136,7137,7145],{},[1158,7138,7139],{},[1277,7140,7141,7143],{},[1161,7142,4318],{},[1282,7144,1284],{},[1194,7146,7147],{"encoding":1196},"H_1",": znaky jsou závislé.",[1127,7150,7151,7152,7308,7311,7312,7329,7330,7362,7363,3640,7422,7425,7426,7447,7448,7465],{},"Testové kritérium",[1115,7153,7155],{"className":7154},[1149],[1151,7156,7157],{"xmlns":1153,"display":2212},[1155,7158,7159,7305],{},[1158,7160,7161,7167,7169,7183,7197,7255,7257,7259,7273,7275,7289,7291],{},[1209,7162,7163,7165],{},[1161,7164,5247],{},[1282,7166,1298],{},[1165,7168,1177],{},[6140,7170,7171,7173,7181],{},[1165,7172,6144],{},[1158,7174,7175,7177,7179],{},[1161,7176,4187],{},[1165,7178,1177],{},[1282,7180,1284],{},[1161,7182,71],{},[6140,7184,7185,7187,7195],{},[1165,7186,6144],{},[1158,7188,7189,7191,7193],{},[1161,7190,6044],{},[1165,7192,1177],{},[1282,7194,1284],{},[1161,7196,6018],{},[3064,7198,7199,7237],{},[1158,7200,7201,7203,7213,7215,7217,7231],{},[1165,7202,1168],{"stretchy":1167},[1277,7204,7205,7207],{},[1161,7206,4192],{},[1158,7208,7209,7211],{},[1161,7210,4187],{},[1161,7212,6044],{},[1165,7214,1317],{},[1161,7216,4192],{},[1277,7218,7219,7225],{},[6877,7220,7221,7223],{"accent":1121},[1161,7222,1110],{},[1165,7224,6883],{},[1158,7226,7227,7229],{},[1161,7228,4187],{},[1161,7230,6044],{},[1209,7232,7233,7235],{},[1165,7234,1174],{"stretchy":1167},[1282,7236,1298],{},[1158,7238,7239,7241],{},[1161,7240,4192],{},[1277,7242,7243,7249],{},[6877,7244,7245,7247],{"accent":1121},[1161,7246,1110],{},[1165,7248,6883],{},[1158,7250,7251,7253],{},[1161,7252,4187],{},[1161,7254,6044],{},[1165,7256,1715],{"separator":1121},[2242,7258],{"width":2244},[1277,7260,7261,7267],{},[6877,7262,7263,7265],{"accent":1121},[1161,7264,1110],{},[1165,7266,6883],{},[1158,7268,7269,7271],{},[1161,7270,4187],{},[1161,7272,6044],{},[1165,7274,1177],{},[1277,7276,7277,7283],{},[6877,7278,7279,7281],{"accent":1121},[1161,7280,1110],{},[1165,7282,6883],{},[1158,7284,7285,7287],{},[1161,7286,4187],{},[1165,7288,6136],{},[2278,7290,2280],{},[1277,7292,7293,7299],{},[6877,7294,7295,7297],{"accent":1121},[1161,7296,1110],{},[1165,7298,6883],{},[1158,7300,7301,7303],{},[1165,7302,6136],{},[1161,7304,6044],{},[1194,7306,7307],{"encoding":1196},"\\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}",[7309,7310],"br",{},"má asymptoticky Pearsonovo (",[1115,7313,7315],{"className":7314},[1149],[1151,7316,7317],{"xmlns":1153},[1155,7318,7319,7327],{},[1158,7320,7321],{},[1209,7322,7323,7325],{},[1161,7324,5247],{},[1282,7326,1298],{},[1194,7328,5764],{"encoding":1196},") rozdělení o ",[1115,7331,7333],{"className":7332},[1149],[1151,7334,7335],{"xmlns":1153},[1155,7336,7337,7359],{},[1158,7338,7339,7341,7343,7345,7347,7349,7351,7353,7355,7357],{},[1165,7340,1168],{"stretchy":1167},[1161,7342,71],{},[1165,7344,1317],{},[1282,7346,1284],{},[1165,7348,1174],{"stretchy":1167},[1165,7350,1168],{"stretchy":1167},[1161,7352,6018],{},[1165,7354,1317],{},[1282,7356,1284],{},[1165,7358,1174],{"stretchy":1167},[1194,7360,7361],{"encoding":1196},"(r-1)(s-1)"," stupních volnosti. Hodnota ",[1115,7364,7366],{"className":7365},[1149],[1151,7367,7368],{"xmlns":1153},[1155,7369,7370,7419],{},[1158,7371,7372,7374,7388,7390],{},[1161,7373,4192],{},[1277,7375,7376,7382],{},[6877,7377,7378,7380],{"accent":1121},[1161,7379,1110],{},[1165,7381,6883],{},[1158,7383,7384,7386],{},[1161,7385,4187],{},[1161,7387,6044],{},[1165,7389,1177],{},[7391,7392,7393],"mstyle",{"scriptlevel":1982,"displaystyle":1121},[3064,7394,7395,7417],{},[1158,7396,7397,7407],{},[1277,7398,7399,7401],{},[1161,7400,4192],{},[1158,7402,7403,7405],{},[1161,7404,4187],{},[1165,7406,6136],{},[1277,7408,7409,7411],{},[1161,7410,4192],{},[1158,7412,7413,7415],{},[1165,7414,6136],{},[1161,7416,6044],{},[1161,7418,4192],{},[1194,7420,7421],{"encoding":1196},"n\\hat p_{ij} = \\dfrac{n_{i\\bullet}n_{\\bullet j}}{n}",[1131,7423,7424],{},"očekávaná četnost"," políčka ",[1115,7427,7429],{"className":7428},[1149],[1151,7430,7431],{"xmlns":1153},[1155,7432,7433,7445],{},[1158,7434,7435,7437,7439,7441,7443],{},[1165,7436,1168],{"stretchy":1167},[1161,7438,4187],{},[1165,7440,1715],{"separator":1121},[1161,7442,6044],{},[1165,7444,1174],{"stretchy":1167},[1194,7446,6049],{"encoding":1196}," — četnost, kterou bychom čekali, kdyby ",[1115,7449,7451],{"className":7450},[1149],[1151,7452,7453],{"xmlns":1153},[1155,7454,7455,7463],{},[1158,7456,7457],{},[1277,7458,7459,7461],{},[1161,7460,4318],{},[1282,7462,1982],{},[1194,7464,5745],{"encoding":1196}," platila.",[1127,7467,7468,7469,1333],{},"Kritický obor: ",[1115,7470,7472],{"className":7471},[1149],[1151,7473,7474],{"xmlns":1153},[1155,7475,7476,7544],{},[1158,7477,7478,7480,7482,7485,7491,7493,7499,7502,7517,7519,7521,7523,7525,7527,7529,7531,7533,7535,7537,7539,7541],{},[1161,7479,5777],{},[1165,7481,1177],{},[1165,7483,7484],{"stretchy":1167},"{",[1209,7486,7487,7489],{},[1161,7488,5247],{},[1282,7490,1298],{},[1165,7492,2629],{},[1209,7494,7495,7497],{},[1161,7496,5247],{},[1282,7498,1298],{},[1165,7500,7501],{},"≥",[2256,7503,7504,7506,7515],{},[1161,7505,5247],{},[1158,7507,7508,7510,7512],{},[1282,7509,1284],{},[1165,7511,1317],{},[1161,7513,7514],{},"α",[1282,7516,1298],{},[1165,7518,1168],{"stretchy":1167},[1165,7520,1168],{"stretchy":1167},[1161,7522,71],{},[1165,7524,1317],{},[1282,7526,1284],{},[1165,7528,1174],{"stretchy":1167},[1165,7530,1168],{"stretchy":1167},[1161,7532,6018],{},[1165,7534,1317],{},[1282,7536,1284],{},[1165,7538,1174],{"stretchy":1167},[1165,7540,1174],{"stretchy":1167},[1165,7542,7543],{"stretchy":1167},"}",[1194,7545,7546],{"encoding":1196},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}((r-1)(s-1))\\}",[1127,7548,7549,7550,7563,7564,7578,7579,7596,7597,7614],{},"Padne-li testové kritérium do ",[1115,7551,7553],{"className":7552},[1149],[1151,7554,7555],{"xmlns":1153},[1155,7556,7557,7561],{},[1158,7558,7559],{},[1161,7560,5777],{},[1194,7562,5777],{"encoding":1196},", zamítáme na hladině ",[1115,7565,7567],{"className":7566},[1149],[1151,7568,7569],{"xmlns":1153},[1155,7570,7571,7575],{},[1158,7572,7573],{},[1161,7574,7514],{},[1194,7576,7577],{"encoding":1196},"\\alpha"," nulovou hypotézu o nezávislosti a přijímáme\n",[1115,7580,7582],{"className":7581},[1149],[1151,7583,7584],{"xmlns":1153},[1155,7585,7586,7594],{},[1158,7587,7588],{},[1277,7589,7590,7592],{},[1161,7591,4318],{},[1282,7593,1284],{},[1194,7595,7147],{"encoding":1196},"; jinak nemáme důvod ",[1115,7598,7600],{"className":7599},[1149],[1151,7601,7602],{"xmlns":1153},[1155,7603,7604,7612],{},[1158,7605,7606],{},[1277,7607,7608,7610],{},[1161,7609,4318],{},[1282,7611,1982],{},[1194,7613,5745],{"encoding":1196}," zamítnout.",[1110,7616,7617,7618,1333],{},"V R počítá test i očekávané četnosti funkce ",[1373,7619,7620],{},"chisq.test()",[1103,7622,7624,7631,7634,7637,7782],{"className":7623,"dataCallout":3670},[1106,3669],[1110,7625,7627,7630],{"className":7626},[1113],[1115,7628],{"className":7629,"ariaHidden":1121},[1118,3677,1120],"Příklad: nákup potravin na internetu a vzdělání",[1110,7632,7633],{},"Testujte hypotézu, zda se vzájemně ovlivňuje zkušenost s nákupem potravin na internetu a vzdělání respondenta\n(n = 385 respondentů).",[1110,7635,7636],{},"Základní soubor: respondenti; výběrový soubor: respondenti, kteří odpověděli; měřený znak A: vzdělání, měřený\nznak B: způsob nákupu.",[4052,7638,7639,7678],{},[4055,7640,7641],{},[4058,7642,7643,7646,7649,7652,7655],{},[4061,7644,7645],{},"vzdělání \\ nákup",[4061,7647,7648],{},"ano",[4061,7650,7651],{},"ne, ale plánuji",[4061,7653,7654],{},"ne, neplánuji",[4061,7656,7657],{},[1115,7658,7660],{"className":7659},[1149],[1151,7661,7662],{"xmlns":1153},[1155,7663,7664,7676],{},[1158,7665,7666],{},[1277,7667,7668,7670],{},[1161,7669,4192],{},[1158,7671,7672,7674],{},[1161,7673,4187],{},[1165,7675,6136],{},[1194,7677,6366],{"encoding":1196},[4165,7679,7680,7696,7713,7730,7745],{},[4058,7681,7682,7685,7688,7691,7693],{},[4170,7683,7684],{},"SŠ bez maturity",[4170,7686,7687],{},"4",[4170,7689,7690],{},"13",[4170,7692,6429],{},[4170,7694,7695],{},"29",[4058,7697,7698,7701,7704,7707,7710],{},[4170,7699,7700],{},"SŠ s maturitou, VOŠ",[4170,7702,7703],{},"31",[4170,7705,7706],{},"62",[4170,7708,7709],{},"71",[4170,7711,7712],{},"164",[4058,7714,7715,7718,7721,7724,7727],{},[4170,7716,7717],{},"VŠ",[4170,7719,7720],{},"44",[4170,7722,7723],{},"58",[4170,7725,7726],{},"66",[4170,7728,7729],{},"168",[4058,7731,7732,7735,7737,7740,7742],{},[4170,7733,7734],{},"ZŠ",[4170,7736,3322],{},[4170,7738,7739],{},"9",[4170,7741,6429],{},[4170,7743,7744],{},"24",[4058,7746,7747,7770,7773,7776,7779],{},[4170,7748,7749],{},[1115,7750,7752],{"className":7751},[1149],[1151,7753,7754],{"xmlns":1153},[1155,7755,7756,7768],{},[1158,7757,7758],{},[1277,7759,7760,7762],{},[1161,7761,4192],{},[1158,7763,7764,7766],{},[1165,7765,6136],{},[1161,7767,6044],{},[1194,7769,6758],{"encoding":1196},[4170,7771,7772],{},"82",[4170,7774,7775],{},"142",[4170,7777,7778],{},"161",[4170,7780,7781],{},"385",[1110,7783,7784,7836],{},[1115,7785,7787],{"className":7786},[1149],[1151,7788,7789],{"xmlns":1153},[1155,7790,7791,7833],{},[1158,7792,7793,7799,7801,7811,7813,7823],{},[1277,7794,7795,7797],{},[1161,7796,4318],{},[1282,7798,1982],{},[1165,7800,2629],{},[1277,7802,7803,7805],{},[1161,7804,1110],{},[1158,7806,7807,7809],{},[1161,7808,4187],{},[1161,7810,6044],{},[1165,7812,1177],{},[1277,7814,7815,7817],{},[1161,7816,1110],{},[1158,7818,7819,7821],{},[1161,7820,4187],{},[1165,7822,6136],{},[1277,7824,7825,7827],{},[1161,7826,1110],{},[1158,7828,7829,7831],{},[1165,7830,6136],{},[1161,7832,6044],{},[1194,7834,7835],{"encoding":1196},"H_0: p_{ij} = p_{i\\bullet}p_{\\bullet j}"," — vzdělání a způsob nákupu jsou na sobě nezávislé.",[3554,7838,7840],{"className":3556,"code":7839,"language":71,"meta":3558,"style":3558},"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",[1373,7841,7842,7874,7891,7908,7926,7947,7960,7995,8023,8035],{"__ignoreMap":3558},[1115,7843,7844,7847,7849,7852,7854,7857,7859,7861,7863,7866,7868,7871],{"class":3563,"line":10},[1115,7845,7846],{"class":3744},"tab1",[1115,7848,4497],{"class":3741},[1115,7850,7851],{"class":3566}," matrix",[1115,7853,1168],{"class":3569},[1115,7855,7856],{"class":3566},"c",[1115,7858,1168],{"class":3569},[1115,7860,7687],{"class":3572},[1115,7862,1715],{"class":3741},[1115,7864,7865],{"class":3572}," 13",[1115,7867,1715],{"class":3741},[1115,7869,7870],{"class":3572}," 12",[1115,7872,7873],{"class":3741},",\n",[1115,7875,7876,7879,7881,7884,7886,7889],{"class":3563,"line":27},[1115,7877,7878],{"class":3572},"                 31",[1115,7880,1715],{"class":3741},[1115,7882,7883],{"class":3572}," 62",[1115,7885,1715],{"class":3741},[1115,7887,7888],{"class":3572}," 71",[1115,7890,7873],{"class":3741},[1115,7892,7893,7896,7898,7901,7903,7906],{"class":3563,"line":148},[1115,7894,7895],{"class":3572},"                 44",[1115,7897,1715],{"class":3741},[1115,7899,7900],{"class":3572}," 58",[1115,7902,1715],{"class":3741},[1115,7904,7905],{"class":3572}," 66",[1115,7907,7873],{"class":3741},[1115,7909,7910,7913,7915,7918,7920,7922,7924],{"class":3563,"line":111},[1115,7911,7912],{"class":3572},"                 3",[1115,7914,1715],{"class":3741},[1115,7916,7917],{"class":3572},"  9",[1115,7919,1715],{"class":3741},[1115,7921,7870],{"class":3572},[1115,7923,1174],{"class":3569},[1115,7925,7873],{"class":3741},[1115,7927,7928,7931,7933,7935,7937,7940,7942,7945],{"class":3563,"line":96},[1115,7929,7930],{"class":3744},"               nrow",[1115,7932,3748],{"class":3741},[1115,7934,4536],{"class":3572},[1115,7936,1715],{"class":3741},[1115,7938,7939],{"class":3744}," byrow",[1115,7941,3748],{"class":3741},[1115,7943,7944],{"class":3572}," TRUE",[1115,7946,7873],{"class":3741},[1115,7948,7949,7952,7954,7957],{"class":3563,"line":89},[1115,7950,7951],{"class":3744},"               dimnames",[1115,7953,3748],{"class":3741},[1115,7955,7956],{"class":3566}," list",[1115,7958,7959],{"class":3569},"(\n",[1115,7961,7962,7965,7967,7970,7972,7976,7978,7981,7983,7986,7988,7991,7993],{"class":3563,"line":82},[1115,7963,7964],{"class":3744},"                 vzdelani",[1115,7966,3748],{"class":3741},[1115,7968,7969],{"class":3566}," c",[1115,7971,1168],{"class":3569},[1115,7973,7975],{"class":7974},"sIIMD","\"SS bez maturity\"",[1115,7977,1715],{"class":3741},[1115,7979,7980],{"class":7974}," \"SS s maturitou nebo VOS\"",[1115,7982,1715],{"class":3741},[1115,7984,7985],{"class":7974}," \"VS\"",[1115,7987,1715],{"class":3741},[1115,7989,7990],{"class":7974}," \"ZS\"",[1115,7992,1174],{"class":3569},[1115,7994,7873],{"class":3741},[1115,7996,7997,8000,8003,8005,8007,8010,8012,8015,8017,8020],{"class":3563,"line":75},[1115,7998,7999],{"class":3744},"                 nakup",[1115,8001,8002],{"class":3741},"    =",[1115,8004,7969],{"class":3566},[1115,8006,1168],{"class":3569},[1115,8008,8009],{"class":7974},"\"ano\"",[1115,8011,1715],{"class":3741},[1115,8013,8014],{"class":7974}," \"ne, ale planuji\"",[1115,8016,1715],{"class":3741},[1115,8018,8019],{"class":7974}," \"ne, neplanuji\"",[1115,8021,8022],{"class":3569},")))\n",[1115,8024,8026,8029,8031,8033],{"class":3563,"line":8025},9,[1115,8027,8028],{"class":3566},"chisq.test",[1115,8030,1168],{"class":3569},[1115,8032,7846],{"class":3744},[1115,8034,3575],{"class":3569},[1115,8036,8037,8039,8041,8043,8045,8048],{"class":3563,"line":72},[1115,8038,8028],{"class":3566},[1115,8040,1168],{"class":3569},[1115,8042,7846],{"class":3744},[1115,8044,1174],{"class":3569},[1115,8046,8047],{"class":3741},"$",[1115,8049,8050],{"class":3744},"expected\n",[3554,8052,8055],{"className":8053,"code":8054,"language":3603,"meta":3558},[3601],"    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",[1373,8056,8054],{"__ignoreMap":3558},[1110,8058,8059,8060,4644,8083,8097,8098,8118,8119,8136],{},"Všechny očekávané četnosti jsou nad 5, aproximace je v pořádku. Testové kritérium ",[1115,8061,8063],{"className":8062},[1149],[1151,8064,8065],{"xmlns":1153},[1155,8066,8067,8080],{},[1158,8068,8069,8075,8077],{},[1209,8070,8071,8073],{},[1161,8072,5247],{},[1282,8074,1298],{},[1165,8076,1177],{},[1282,8078,8079],{},"5,49",[1194,8081,8082],{"encoding":1196},"\\chi^2 = 5{,}49",[1115,8084,8086],{"className":8085},[1149],[1151,8087,8088],{"xmlns":1153},[1155,8089,8090,8095],{},[1158,8091,8092],{},[1282,8093,8094],{},"6",[1194,8096,8094],{"encoding":1196}," stupni\nvolnosti dává p-hodnotu ",[1115,8099,8101],{"className":8100},[1149],[1151,8102,8103],{"xmlns":1153},[1155,8104,8105,8115],{},[1158,8106,8107,8110,8112],{},[1282,8108,8109],{},"0,483",[1165,8111,4156],{},[1282,8113,8114],{},"0,05",[1194,8116,8117],{"encoding":1196},"0{,}483 > 0{,}05",": ",[1115,8120,8122],{"className":8121},[1149],[1151,8123,8124],{"xmlns":1153},[1155,8125,8126,8134],{},[1158,8127,8128],{},[1277,8129,8130,8132],{},[1161,8131,4318],{},[1282,8133,1982],{},[1194,8135,5745],{"encoding":1196}," nezamítáme, závislost mezi zkušeností s nákupem potravin na\ninternetu a vzděláním respondenta se neprokázala.",[1103,8138,8140,8147,8150,8195],{"className":8139,"dataCallout":3670},[1106,3669],[1110,8141,8143,8146],{"className":8142},[1113],[1115,8144],{"className":8145,"ariaHidden":1121},[1118,3677,1120],"Příklad: vzdělání a zveřejňování citlivých údajů na Facebooku",[1110,8148,8149],{},"Mezi 221 osobami bylo zaznamenáno vzdělání a zda zveřejňují na Facebooku citlivé údaje. Proveďte test\nnezávislosti.",[4052,8151,8152,8166],{},[4055,8153,8154],{},[4058,8155,8156,8159,8162,8164],{},[4061,8157,8158],{},"zveřejňuje \\ vzdělání",[4061,8160,8161],{},"SŠ",[4061,8163,7717],{},[4061,8165,7734],{},[4165,8167,8168,8182],{},[4058,8169,8170,8173,8176,8179],{},[4170,8171,8172],{},"ne",[4170,8174,8175],{},"20",[4170,8177,8178],{},"33",[4170,8180,8181],{},"39",[4058,8183,8184,8186,8189,8192],{},[4170,8185,7648],{},[4170,8187,8188],{},"25",[4170,8190,8191],{},"28",[4170,8193,8194],{},"76",[1110,8196,8197,8248],{},[1115,8198,8200],{"className":8199},[1149],[1151,8201,8202],{"xmlns":1153},[1155,8203,8204,8246],{},[1158,8205,8206,8212,8214,8224,8226,8236],{},[1277,8207,8208,8210],{},[1161,8209,4318],{},[1282,8211,1982],{},[1165,8213,2629],{},[1277,8215,8216,8218],{},[1161,8217,1110],{},[1158,8219,8220,8222],{},[1161,8221,4187],{},[1161,8223,6044],{},[1165,8225,1177],{},[1277,8227,8228,8230],{},[1161,8229,1110],{},[1158,8231,8232,8234],{},[1161,8233,4187],{},[1165,8235,6136],{},[1277,8237,8238,8240],{},[1161,8239,1110],{},[1158,8241,8242,8244],{},[1165,8243,6136],{},[1161,8245,6044],{},[1194,8247,7835],{"encoding":1196}," — vzdělání a zveřejňování citlivých údajů jsou na sobě nezávislé.",[3554,8250,8252],{"className":3556,"code":8251,"language":71,"meta":3558,"style":3558},"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",[1373,8253,8254,8283,8302,8321,8331,8354,8378,8388],{"__ignoreMap":3558},[1115,8255,8256,8259,8261,8263,8265,8267,8269,8271,8273,8276,8278,8281],{"class":3563,"line":10},[1115,8257,8258],{"class":3744},"tab2",[1115,8260,4497],{"class":3741},[1115,8262,7851],{"class":3566},[1115,8264,1168],{"class":3569},[1115,8266,7856],{"class":3566},[1115,8268,1168],{"class":3569},[1115,8270,8175],{"class":3572},[1115,8272,1715],{"class":3741},[1115,8274,8275],{"class":3572}," 33",[1115,8277,1715],{"class":3741},[1115,8279,8280],{"class":3572}," 39",[1115,8282,7873],{"class":3741},[1115,8284,8285,8288,8290,8293,8295,8298,8300],{"class":3563,"line":27},[1115,8286,8287],{"class":3572},"                 25",[1115,8289,1715],{"class":3741},[1115,8291,8292],{"class":3572}," 28",[1115,8294,1715],{"class":3741},[1115,8296,8297],{"class":3572}," 76",[1115,8299,1174],{"class":3569},[1115,8301,7873],{"class":3741},[1115,8303,8304,8306,8308,8311,8313,8315,8317,8319],{"class":3563,"line":148},[1115,8305,7930],{"class":3744},[1115,8307,3748],{"class":3741},[1115,8309,8310],{"class":3572}," 2",[1115,8312,1715],{"class":3741},[1115,8314,7939],{"class":3744},[1115,8316,3748],{"class":3741},[1115,8318,7944],{"class":3572},[1115,8320,7873],{"class":3741},[1115,8322,8323,8325,8327,8329],{"class":3563,"line":111},[1115,8324,7951],{"class":3744},[1115,8326,3748],{"class":3741},[1115,8328,7956],{"class":3566},[1115,8330,7959],{"class":3569},[1115,8332,8333,8336,8338,8340,8342,8345,8347,8350,8352],{"class":3563,"line":96},[1115,8334,8335],{"class":3744},"                 zverejnuje",[1115,8337,3748],{"class":3741},[1115,8339,7969],{"class":3566},[1115,8341,1168],{"class":3569},[1115,8343,8344],{"class":7974},"\"ne\"",[1115,8346,1715],{"class":3741},[1115,8348,8349],{"class":7974}," \"ano\"",[1115,8351,1174],{"class":3569},[1115,8353,7873],{"class":3741},[1115,8355,8356,8358,8361,8363,8365,8368,8370,8372,8374,8376],{"class":3563,"line":89},[1115,8357,7964],{"class":3744},[1115,8359,8360],{"class":3741},"   =",[1115,8362,7969],{"class":3566},[1115,8364,1168],{"class":3569},[1115,8366,8367],{"class":7974},"\"SS\"",[1115,8369,1715],{"class":3741},[1115,8371,7985],{"class":7974},[1115,8373,1715],{"class":3741},[1115,8375,7990],{"class":7974},[1115,8377,8022],{"class":3569},[1115,8379,8380,8382,8384,8386],{"class":3563,"line":82},[1115,8381,8028],{"class":3566},[1115,8383,1168],{"class":3569},[1115,8385,8258],{"class":3744},[1115,8387,3575],{"class":3569},[1115,8389,8390,8392,8394,8396,8398,8400],{"class":3563,"line":75},[1115,8391,8028],{"class":3566},[1115,8393,1168],{"class":3569},[1115,8395,8258],{"class":3744},[1115,8397,1174],{"class":3569},[1115,8399,8047],{"class":3741},[1115,8401,8050],{"class":3744},[3554,8403,8406],{"className":8404,"code":8405,"language":3603,"meta":3558},[3601],"    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",[1373,8407,8405],{"__ignoreMap":3558},[1110,8409,8410,8411,4644,8434,8447,8448,8118,8467,8484,8485,1333],{},"I zde jsou všechny očekávané četnosti nad 5. Testové kritérium ",[1115,8412,8414],{"className":8413},[1149],[1151,8415,8416],{"xmlns":1153},[1155,8417,8418,8431],{},[1158,8419,8420,8426,8428],{},[1209,8421,8422,8424],{},[1161,8423,5247],{},[1282,8425,1298],{},[1165,8427,1177],{},[1282,8429,8430],{},"6,87",[1194,8432,8433],{"encoding":1196},"\\chi^2 = 6{,}87",[1115,8435,8437],{"className":8436},[1149],[1151,8438,8439],{"xmlns":1153},[1155,8440,8441,8445],{},[1158,8442,8443],{},[1282,8444,1298],{},[1194,8446,1298],{"encoding":1196}," stupni volnosti dává\np-hodnotu ",[1115,8449,8451],{"className":8450},[1149],[1151,8452,8453],{"xmlns":1153},[1155,8454,8455,8464],{},[1158,8456,8457,8460,8462],{},[1282,8458,8459],{},"0,032",[1165,8461,1287],{},[1282,8463,8114],{},[1194,8465,8466],{"encoding":1196},"0{,}032 \u003C 0{,}05",[1115,8468,8470],{"className":8469},[1149],[1151,8471,8472],{"xmlns":1153},[1155,8473,8474,8482],{},[1158,8475,8476],{},[1277,8477,8478,8480],{},[1161,8479,4318],{},[1282,8481,1982],{},[1194,8483,5745],{"encoding":1196}," zamítáme — na rozdíl od předchozího příkladu tady vzdělání a zveřejňování\ncitlivých údajů na Facebooku na sobě ",[1131,8486,8487],{},"závisí",[1110,8489,8490,8491,8508],{},"Srovnání pozorovaných a očekávaných četností ukazuje, proč jeden příklad ",[1115,8492,8494],{"className":8493},[1149],[1151,8495,8496],{"xmlns":1153},[1155,8497,8498,8506],{},[1158,8499,8500],{},[1277,8501,8502,8504],{},[1161,8503,4318],{},[1282,8505,1982],{},[1194,8507,5745],{"encoding":1196}," nezamítá a druhý ano — ve druhém\nse pozorované sloupce (zejména u ZŠ) systematicky odchylují od očekávaných, v prvním kolísají jen náhodně kolem nich:",[1110,8510,8511],{},[1760,8512],{"alt":8513,"className":8514,"src":8515},"mask-kt-observed-expected",[1441,1764],"\u002Fwiki-assets\u002Fmask-kt-observed-expected.png",[1110,8517,8518,8519,8536,8537,2629],{},"Totéž je vidět na rozdělení testového kritéria: u prvního příkladu leží ",[1115,8520,8522],{"className":8521},[1149],[1151,8523,8524],{"xmlns":1153},[1155,8525,8526,8534],{},[1158,8527,8528],{},[1209,8529,8530,8532],{},[1161,8531,5247],{},[1282,8533,1298],{},[1194,8535,5764],{"encoding":1196}," hluboko pod kritickou hodnotou,\nu druhého uvnitř kritického oboru ",[1115,8538,8540],{"className":8539},[1149],[1151,8541,8542],{"xmlns":1153},[1155,8543,8544,8548],{},[1158,8545,8546],{},[1161,8547,5777],{},[1194,8549,5777],{"encoding":1196},[1110,8551,8552],{},[1760,8553],{"alt":8554,"className":8555,"src":8556},"mask-kt-chi2-kriticky-obor",[1441,1764],"\u002Fwiki-assets\u002Fmask-kt-chi2-kriticky-obor.png",[1431,8558,5825],{"id":8559},"cramérův-koeficient-kontingence",[1110,8561,8562,8563,2629],{},"Test nezávislosti pouze rozhodne, zda jsou znaky závislé, nebo ne. Sílu závislosti měří ",[1131,8564,8565],{},"Cramérův koeficient\nkontingence",[1115,8567,8569],{"className":8568},[1149],[1151,8570,8571],{"xmlns":1153,"display":2212},[1155,8572,8573,8627],{},[1158,8574,8575,8577,8579,8604,8606,8608,8610,8612,8615,8617,8619,8621,8623,8625],{},[1161,8576,5837],{},[1165,8578,1177],{},[2765,8580,8581],{},[3064,8582,8583,8589],{},[1209,8584,8585,8587],{},[1161,8586,5247],{},[1282,8588,1298],{},[1158,8590,8591,8593,8595,8598,8600,8602],{},[1161,8592,4192],{},[1165,8594,1168],{"stretchy":1167},[1161,8596,8597],{},"m",[1165,8599,1317],{},[1282,8601,1284],{},[1165,8603,1174],{"stretchy":1167},[1165,8605,1715],{"separator":1121},[2242,8607],{"width":2244},[1161,8609,8597],{},[1165,8611,1177],{},[1161,8613,8614],{},"min",[1165,8616,2079],{},[1165,8618,1168],{"stretchy":1167},[1161,8620,71],{},[1165,8622,1715],{"separator":1121},[1161,8624,6018],{},[1165,8626,1174],{"stretchy":1167},[1194,8628,8629],{"encoding":1196},"V = \\sqrt{\\frac{\\chi^2}{n(m-1)}}, \\qquad m = \\min(r, s)",[1110,8631,4767,8632,8649,8650,8668,8669,8687],{},[1115,8633,8635],{"className":8634},[1149],[1151,8636,8637],{"xmlns":1153},[1155,8638,8639,8647],{},[1158,8640,8641],{},[1209,8642,8643,8645],{},[1161,8644,5247],{},[1282,8646,1298],{},[1194,8648,5764],{"encoding":1196}," je hodnota testového kritéria z testu nezávislosti. ",[1115,8651,8653],{"className":8652},[1149],[1151,8654,8655],{"xmlns":1153},[1155,8656,8657,8665],{},[1158,8658,8659,8661,8663],{},[1161,8660,5837],{},[1165,8662,1177],{},[1282,8664,1982],{},[1194,8666,8667],{"encoding":1196},"V = 0"," odpovídá úplné nezávislosti znaků,\n",[1115,8670,8672],{"className":8671},[1149],[1151,8673,8674],{"xmlns":1153},[1155,8675,8676,8684],{},[1158,8677,8678,8680,8682],{},[1161,8679,5837],{},[1165,8681,1177],{},[1282,8683,1284],{},[1194,8685,8686],{"encoding":1196},"V = 1"," jejich úplné závislosti.",[3554,8689,8691],{"className":3556,"code":8690,"language":71,"meta":3558,"style":3558},"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",[1373,8692,8693,8763,8826,8831],{"__ignoreMap":3558},[1115,8694,8695,8698,8700,8702,8704,8707,8709,8711,8713,8715,8717,8719,8722,8724,8726,8729,8732,8734,8736,8738,8741,8743,8745,8747,8750,8752,8754,8757,8759,8761],{"class":3563,"line":10},[1115,8696,8697],{"class":3744},"V1",[1115,8699,4497],{"class":3741},[1115,8701,4003],{"class":3566},[1115,8703,1168],{"class":3569},[1115,8705,8706],{"class":3566},"as.numeric",[1115,8708,1168],{"class":3569},[1115,8710,8028],{"class":3566},[1115,8712,1168],{"class":3569},[1115,8714,7846],{"class":3744},[1115,8716,1174],{"class":3569},[1115,8718,8047],{"class":3741},[1115,8720,8721],{"class":3744},"statistic",[1115,8723,3862],{"class":3569},[1115,8725,3434],{"class":3741},[1115,8727,8728],{"class":3569}," (",[1115,8730,8731],{"class":3566},"sum",[1115,8733,1168],{"class":3569},[1115,8735,7846],{"class":3744},[1115,8737,3862],{"class":3569},[1115,8739,8740],{"class":3741},"*",[1115,8742,8728],{"class":3569},[1115,8744,8614],{"class":3566},[1115,8746,1168],{"class":3569},[1115,8748,8749],{"class":3566},"dim",[1115,8751,1168],{"class":3569},[1115,8753,7846],{"class":3744},[1115,8755,8756],{"class":3569},")) ",[1115,8758,3865],{"class":3741},[1115,8760,4605],{"class":3572},[1115,8762,8022],{"class":3569},[1115,8764,8765,8768,8770,8772,8774,8776,8778,8780,8782,8784,8786,8788,8790,8792,8794,8796,8798,8800,8802,8804,8806,8808,8810,8812,8814,8816,8818,8820,8822,8824],{"class":3563,"line":27},[1115,8766,8767],{"class":3744},"V2",[1115,8769,4497],{"class":3741},[1115,8771,4003],{"class":3566},[1115,8773,1168],{"class":3569},[1115,8775,8706],{"class":3566},[1115,8777,1168],{"class":3569},[1115,8779,8028],{"class":3566},[1115,8781,1168],{"class":3569},[1115,8783,8258],{"class":3744},[1115,8785,1174],{"class":3569},[1115,8787,8047],{"class":3741},[1115,8789,8721],{"class":3744},[1115,8791,3862],{"class":3569},[1115,8793,3434],{"class":3741},[1115,8795,8728],{"class":3569},[1115,8797,8731],{"class":3566},[1115,8799,1168],{"class":3569},[1115,8801,8258],{"class":3744},[1115,8803,3862],{"class":3569},[1115,8805,8740],{"class":3741},[1115,8807,8728],{"class":3569},[1115,8809,8614],{"class":3566},[1115,8811,1168],{"class":3569},[1115,8813,8749],{"class":3566},[1115,8815,1168],{"class":3569},[1115,8817,8258],{"class":3744},[1115,8819,8756],{"class":3569},[1115,8821,3865],{"class":3741},[1115,8823,4605],{"class":3572},[1115,8825,8022],{"class":3569},[1115,8827,8828],{"class":3563,"line":148},[1115,8829,8830],{"class":3744},"V1\n",[1115,8832,8833],{"class":3563,"line":111},[1115,8834,8835],{"class":3744},"V2\n",[3554,8837,8840],{"className":8838,"code":8839,"language":3603,"meta":3558},[3601],"[1] 0.08441958\n[1] 0.1762822\n",[1373,8841,8839],{"__ignoreMap":3558},[1110,8843,8844],{},[1760,8845],{"alt":8846,"className":8847,"src":8848},"mask-kt-cramerovo-v",[1441,1764],"\u002Fwiki-assets\u002Fmask-kt-cramerovo-v.png",[1110,8850,8851,8852,8871,8872,8889,8890,8118,8909,8926],{},"U nákupu potravin je ",[1115,8853,8855],{"className":8854},[1149],[1151,8856,8857],{"xmlns":1153},[1155,8858,8859,8868],{},[1158,8860,8861,8863,8865],{},[1161,8862,5837],{},[1165,8864,1177],{},[1282,8866,8867],{},"0,084",[1194,8869,8870],{"encoding":1196},"V = 0{,}084"," zanedbatelné — ostatně ",[1115,8873,8875],{"className":8874},[1149],[1151,8876,8877],{"xmlns":1153},[1155,8878,8879,8887],{},[1158,8880,8881],{},[1277,8882,8883,8885],{},[1161,8884,4318],{},[1282,8886,1982],{},[1194,8888,5745],{"encoding":1196}," jsme ani nezamítli. U zveřejňování údajů je ",[1115,8891,8893],{"className":8892},[1149],[1151,8894,8895],{"xmlns":1153},[1155,8896,8897,8906],{},[1158,8898,8899,8901,8903],{},[1161,8900,5837],{},[1165,8902,1177],{},[1282,8904,8905],{},"0,176",[1194,8907,8908],{"encoding":1196},"V = 0{,}176",[1115,8910,8912],{"className":8911},[1149],[1151,8913,8914],{"xmlns":1153},[1155,8915,8916,8924],{},[1158,8917,8918],{},[1277,8919,8920,8922],{},[1161,8921,4318],{},[1282,8923,1982],{},[1194,8925,5745],{"encoding":1196},"\njsme zamítli, ale samotná závislost je stále slabá.",[1431,8928,5844],{"id":8929},"čtyřpolní-tabulka",[1110,8931,8932,8934,8935,8948,8949,8962,8963,8985],{},[1131,8933,5844],{}," je speciální případ kontingenční tabulky, kdy oba znaky ",[1115,8936,8938],{"className":8937},[1149],[1151,8939,8940],{"xmlns":1153},[1155,8941,8942,8946],{},[1158,8943,8944],{},[1161,8945,5942],{},[1194,8947,5942],{"encoding":1196}," i ",[1115,8950,8952],{"className":8951},[1149],[1151,8953,8954],{"xmlns":1153},[1155,8955,8956,8960],{},[1158,8957,8958],{},[1161,8959,4184],{},[1194,8961,4184],{"encoding":1196}," mají jen dvě varianty\n(",[1115,8964,8966],{"className":8965},[1149],[1151,8967,8968],{"xmlns":1153},[1155,8969,8970,8982],{},[1158,8971,8972,8974,8976,8978,8980],{},[1161,8973,71],{},[1165,8975,1177],{},[1161,8977,6018],{},[1165,8979,1177],{},[1282,8981,1298],{},[1194,8983,8984],{"encoding":1196},"r = s = 2","):",[4052,8987,8988,9072],{},[4055,8989,8990],{},[4058,8991,8992,9011,9030,9049],{},[4061,8993,8994],{},[1115,8995,8997],{"className":8996},[1149],[1151,8998,8999],{"xmlns":1153},[1155,9000,9001,9009],{},[1158,9002,9003,9005,9007],{},[1161,9004,5942],{},[1161,9006,6275],{"mathvariant":1215},[1161,9008,4184],{},[1194,9010,6280],{"encoding":1196},[4061,9012,9013],{},[1115,9014,9016],{"className":9015},[1149],[1151,9017,9018],{"xmlns":1153},[1155,9019,9020,9028],{},[1158,9021,9022],{},[1277,9023,9024,9026],{},[1161,9025,4184],{},[1282,9027,1284],{},[1194,9029,6300],{"encoding":1196},[4061,9031,9032],{},[1115,9033,9035],{"className":9034},[1149],[1151,9036,9037],{"xmlns":1153},[1155,9038,9039,9047],{},[1158,9040,9041],{},[1277,9042,9043,9045],{},[1161,9044,4184],{},[1282,9046,1298],{},[1194,9048,6320],{"encoding":1196},[4061,9050,9051],{},[1115,9052,9054],{"className":9053},[1149],[1151,9055,9056],{"xmlns":1153},[1155,9057,9058,9070],{},[1158,9059,9060],{},[1277,9061,9062,9064],{},[1161,9063,4192],{},[1158,9065,9066,9068],{},[1161,9067,4187],{},[1165,9069,6136],{},[1194,9071,6366],{"encoding":1196},[4165,9073,9074,9156,9238],{},[4058,9075,9076,9095,9114,9133],{},[4170,9077,9078],{},[1115,9079,9081],{"className":9080},[1149],[1151,9082,9083],{"xmlns":1153},[1155,9084,9085,9093],{},[1158,9086,9087],{},[1277,9088,9089,9091],{},[1161,9090,5942],{},[1282,9092,1284],{},[1194,9094,6390],{"encoding":1196},[4170,9096,9097],{},[1115,9098,9100],{"className":9099},[1149],[1151,9101,9102],{"xmlns":1153},[1155,9103,9104,9112],{},[1158,9105,9106],{},[1277,9107,9108,9110],{},[1161,9109,4192],{},[1282,9111,6408],{},[1194,9113,6411],{"encoding":1196},[4170,9115,9116],{},[1115,9117,9119],{"className":9118},[1149],[1151,9120,9121],{"xmlns":1153},[1155,9122,9123,9131],{},[1158,9124,9125],{},[1277,9126,9127,9129],{},[1161,9128,4192],{},[1282,9130,6429],{},[1194,9132,6432],{"encoding":1196},[4170,9134,9135],{},[1115,9136,9138],{"className":9137},[1149],[1151,9139,9140],{"xmlns":1153},[1155,9141,9142,9154],{},[1158,9143,9144],{},[1277,9145,9146,9148],{},[1161,9147,4192],{},[1158,9149,9150,9152],{},[1282,9151,1284],{},[1165,9153,6136],{},[1194,9155,6482],{"encoding":1196},[4058,9157,9158,9177,9196,9215],{},[4170,9159,9160],{},[1115,9161,9163],{"className":9162},[1149],[1151,9164,9165],{"xmlns":1153},[1155,9166,9167,9175],{},[1158,9168,9169],{},[1277,9170,9171,9173],{},[1161,9172,5942],{},[1282,9174,1298],{},[1194,9176,6504],{"encoding":1196},[4170,9178,9179],{},[1115,9180,9182],{"className":9181},[1149],[1151,9183,9184],{"xmlns":1153},[1155,9185,9186,9194],{},[1158,9187,9188],{},[1277,9189,9190,9192],{},[1161,9191,4192],{},[1282,9193,6522],{},[1194,9195,6525],{"encoding":1196},[4170,9197,9198],{},[1115,9199,9201],{"className":9200},[1149],[1151,9202,9203],{"xmlns":1153},[1155,9204,9205,9213],{},[1158,9206,9207],{},[1277,9208,9209,9211],{},[1161,9210,4192],{},[1282,9212,6543],{},[1194,9214,6546],{"encoding":1196},[4170,9216,9217],{},[1115,9218,9220],{"className":9219},[1149],[1151,9221,9222],{"xmlns":1153},[1155,9223,9224,9236],{},[1158,9225,9226],{},[1277,9227,9228,9230],{},[1161,9229,4192],{},[1158,9231,9232,9234],{},[1282,9233,1298],{},[1165,9235,6136],{},[1194,9237,6596],{"encoding":1196},[4058,9239,9240,9263,9286,9309],{},[4170,9241,9242],{},[1115,9243,9245],{"className":9244},[1149],[1151,9246,9247],{"xmlns":1153},[1155,9248,9249,9261],{},[1158,9250,9251],{},[1277,9252,9253,9255],{},[1161,9254,4192],{},[1158,9256,9257,9259],{},[1165,9258,6136],{},[1161,9260,6044],{},[1194,9262,6758],{"encoding":1196},[4170,9264,9265],{},[1115,9266,9268],{"className":9267},[1149],[1151,9269,9270],{"xmlns":1153},[1155,9271,9272,9284],{},[1158,9273,9274],{},[1277,9275,9276,9278],{},[1161,9277,4192],{},[1158,9279,9280,9282],{},[1165,9281,6136],{},[1282,9283,1284],{},[1194,9285,6782],{"encoding":1196},[4170,9287,9288],{},[1115,9289,9291],{"className":9290},[1149],[1151,9292,9293],{"xmlns":1153},[1155,9294,9295,9307],{},[1158,9296,9297],{},[1277,9298,9299,9301],{},[1161,9300,4192],{},[1158,9302,9303,9305],{},[1165,9304,6136],{},[1282,9306,1298],{},[1194,9308,6806],{"encoding":1196},[4170,9310,9311],{},[1115,9312,9314],{"className":9313},[1149],[1151,9315,9316],{"xmlns":1153},[1155,9317,9318,9322],{},[1158,9319,9320],{},[1161,9321,4192],{},[1194,9323,4192],{"encoding":1196},[1110,9325,5867,9326,9344],{},[1115,9327,9329],{"className":9328},[1149],[1151,9330,9331],{"xmlns":1153},[1155,9332,9333,9341],{},[1158,9334,9335,9337,9339],{},[1161,9336,4192],{},[1165,9338,4156],{},[1282,9340,5861],{},[1194,9342,9343],{"encoding":1196},"n > 40"," se místo obecného vzorce používá zjednodušená varianta testového kritéria:",[1115,9346,9348],{"className":9347},[1149],[1151,9349,9350],{"xmlns":1153,"display":2212},[1155,9351,9352,9446],{},[1158,9353,9354,9360,9362,9364,9366],{},[1209,9355,9356,9358],{},[1161,9357,5247],{},[1282,9359,1298],{},[1165,9361,1177],{},[1161,9363,4192],{},[2278,9365,2280],{},[3064,9367,9368,9404],{},[1158,9369,9370,9372,9378,9384,9386,9392,9398],{},[1165,9371,1168],{"stretchy":1167},[1277,9373,9374,9376],{},[1161,9375,4192],{},[1282,9377,6408],{},[1277,9379,9380,9382],{},[1161,9381,4192],{},[1282,9383,6543],{},[1165,9385,1317],{},[1277,9387,9388,9390],{},[1161,9389,4192],{},[1282,9391,6429],{},[1277,9393,9394,9396],{},[1161,9395,4192],{},[1282,9397,6522],{},[1209,9399,9400,9402],{},[1165,9401,1174],{"stretchy":1167},[1282,9403,1298],{},[1158,9405,9406,9416,9426,9436],{},[1277,9407,9408,9410],{},[1161,9409,4192],{},[1158,9411,9412,9414],{},[1282,9413,1284],{},[1165,9415,6136],{},[1277,9417,9418,9420],{},[1161,9419,4192],{},[1158,9421,9422,9424],{},[1282,9423,1298],{},[1165,9425,6136],{},[1277,9427,9428,9430],{},[1161,9429,4192],{},[1158,9431,9432,9434],{},[1165,9433,6136],{},[1282,9435,1284],{},[1277,9437,9438,9440],{},[1161,9439,4192],{},[1158,9441,9442,9444],{},[1165,9443,6136],{},[1282,9445,1298],{},[1194,9447,9448],{"encoding":1196},"\\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}}",[1110,9450,9451,9452,9512,9513,9549,9550,9553,9554,9557],{},"s kritickým oborem ",[1115,9453,9455],{"className":9454},[1149],[1151,9456,9457],{"xmlns":1153},[1155,9458,9459,9509],{},[1158,9460,9461,9467,9469,9471,9477,9479,9485,9487,9501,9503,9505,9507],{},[1277,9462,9463,9465],{},[1161,9464,5777],{},[1161,9466,7514],{},[1165,9468,1177],{},[1165,9470,7484],{"stretchy":1167},[1209,9472,9473,9475],{},[1161,9474,5247],{},[1282,9476,1298],{},[1165,9478,2629],{},[1209,9480,9481,9483],{},[1161,9482,5247],{},[1282,9484,1298],{},[1165,9486,7501],{},[2256,9488,9489,9491,9499],{},[1161,9490,5247],{},[1158,9492,9493,9495,9497],{},[1282,9494,1284],{},[1165,9496,1317],{},[1161,9498,7514],{},[1282,9500,1298],{},[1165,9502,1168],{"stretchy":1167},[1282,9504,1284],{},[1165,9506,1174],{"stretchy":1167},[1165,9508,7543],{"stretchy":1167},[1194,9510,9511],{"encoding":1196},"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 ",[1115,9514,9516],{"className":9515},[1149],[1151,9517,9518],{"xmlns":1153},[1155,9519,9520,9546],{},[1158,9521,9522,9524,9526,9528,9530,9532,9534,9536,9538,9540,9542,9544],{},[1165,9523,1168],{"stretchy":1167},[1161,9525,71],{},[1165,9527,1317],{},[1282,9529,1284],{},[1165,9531,1174],{"stretchy":1167},[1165,9533,1168],{"stretchy":1167},[1161,9535,6018],{},[1165,9537,1317],{},[1282,9539,1284],{},[1165,9541,1174],{"stretchy":1167},[1165,9543,1177],{},[1282,9545,1284],{},[1194,9547,9548],{"encoding":1196},"(r-1)(s-1) = 1"," stupeň volnosti. V R dává tuto hodnotu ",[1373,9551,9552],{},"chisq.test(tab, correct = FALSE)",". Bez ",[1373,9555,9556],{},"correct = FALSE"," R u tabulky 2 × 2 použije Yatesovu korekci na kontinuitu a testové kritérium vyjde menší.",[1431,9559,5874],{"id":9560},"mcnemarův-test",[1110,9562,9563,9564,9567,9568,9570,9571,9574,9575,9578,9579,9581],{},"Čtyřpolní tabulka z předchozí sekce porovnává dva ",[1131,9565,9566],{},"různé"," znaky na stejném souboru. ",[1131,9569,5874],{}," řeší\njinou situaci: na prvcích základního souboru se měří ",[1131,9572,9573],{},"jeden"," alternativní znak, a to ",[1131,9576,9577],{},"dvakrát"," — před a po\nnějakém zásahu. Cílem je zjistit, zda zásah změnil pravděpodobnostní rozdělení variant tohoto znaku. Jde tedy o\n",[1131,9580,5870],{}," (stejné prvky měřené opakovaně), ne o dva nezávisle naměřené znaky.",[1110,9583,9584],{},"Kontingenční tabulka před\u002Fpo má tvar:",[4052,9586,9587,9621],{},[4055,9588,9589],{},[4058,9590,9591,9594,9596,9598],{},[4061,9592,9593],{},"před \\ po",[4061,9595,2094],{},[4061,9597,1317],{},[4061,9599,9600],{},[1115,9601,9603],{"className":9602},[1149],[1151,9604,9605],{"xmlns":1153},[1155,9606,9607,9619],{},[1158,9608,9609],{},[1277,9610,9611,9613],{},[1161,9612,4192],{},[1158,9614,9615,9617],{},[1161,9616,4187],{},[1165,9618,6136],{},[1194,9620,6366],{"encoding":1196},[4165,9622,9623,9688,9753],{},[4058,9624,9625,9627,9646,9665],{},[4170,9626,2094],{},[4170,9628,9629],{},[1115,9630,9632],{"className":9631},[1149],[1151,9633,9634],{"xmlns":1153},[1155,9635,9636,9644],{},[1158,9637,9638],{},[1277,9639,9640,9642],{},[1161,9641,4192],{},[1282,9643,6408],{},[1194,9645,6411],{"encoding":1196},[4170,9647,9648],{},[1115,9649,9651],{"className":9650},[1149],[1151,9652,9653],{"xmlns":1153},[1155,9654,9655,9663],{},[1158,9656,9657],{},[1277,9658,9659,9661],{},[1161,9660,4192],{},[1282,9662,6429],{},[1194,9664,6432],{"encoding":1196},[4170,9666,9667],{},[1115,9668,9670],{"className":9669},[1149],[1151,9671,9672],{"xmlns":1153},[1155,9673,9674,9686],{},[1158,9675,9676],{},[1277,9677,9678,9680],{},[1161,9679,4192],{},[1158,9681,9682,9684],{},[1282,9683,1284],{},[1165,9685,6136],{},[1194,9687,6482],{"encoding":1196},[4058,9689,9690,9692,9711,9730],{},[4170,9691,1317],{},[4170,9693,9694],{},[1115,9695,9697],{"className":9696},[1149],[1151,9698,9699],{"xmlns":1153},[1155,9700,9701,9709],{},[1158,9702,9703],{},[1277,9704,9705,9707],{},[1161,9706,4192],{},[1282,9708,6522],{},[1194,9710,6525],{"encoding":1196},[4170,9712,9713],{},[1115,9714,9716],{"className":9715},[1149],[1151,9717,9718],{"xmlns":1153},[1155,9719,9720,9728],{},[1158,9721,9722],{},[1277,9723,9724,9726],{},[1161,9725,4192],{},[1282,9727,6543],{},[1194,9729,6546],{"encoding":1196},[4170,9731,9732],{},[1115,9733,9735],{"className":9734},[1149],[1151,9736,9737],{"xmlns":1153},[1155,9738,9739,9751],{},[1158,9740,9741],{},[1277,9742,9743,9745],{},[1161,9744,4192],{},[1158,9746,9747,9749],{},[1282,9748,1298],{},[1165,9750,6136],{},[1194,9752,6596],{"encoding":1196},[4058,9754,9755,9778,9801,9824],{},[4170,9756,9757],{},[1115,9758,9760],{"className":9759},[1149],[1151,9761,9762],{"xmlns":1153},[1155,9763,9764,9776],{},[1158,9765,9766],{},[1277,9767,9768,9770],{},[1161,9769,4192],{},[1158,9771,9772,9774],{},[1165,9773,6136],{},[1161,9775,6044],{},[1194,9777,6758],{"encoding":1196},[4170,9779,9780],{},[1115,9781,9783],{"className":9782},[1149],[1151,9784,9785],{"xmlns":1153},[1155,9786,9787,9799],{},[1158,9788,9789],{},[1277,9790,9791,9793],{},[1161,9792,4192],{},[1158,9794,9795,9797],{},[1165,9796,6136],{},[1282,9798,1284],{},[1194,9800,6782],{"encoding":1196},[4170,9802,9803],{},[1115,9804,9806],{"className":9805},[1149],[1151,9807,9808],{"xmlns":1153},[1155,9809,9810,9822],{},[1158,9811,9812],{},[1277,9813,9814,9816],{},[1161,9815,4192],{},[1158,9817,9818,9820],{},[1165,9819,6136],{},[1282,9821,1298],{},[1194,9823,6806],{"encoding":1196},[4170,9825,9826],{},[1115,9827,9829],{"className":9828},[1149],[1151,9830,9831],{"xmlns":1153},[1155,9832,9833,9837],{},[1158,9834,9835],{},[1161,9836,4192],{},[1194,9838,4192],{"encoding":1196},[1110,9840,9841,9842,1425,9859,9876,9877,9880,9881,1425,9898,9915,9916,9919],{},"Pole ",[1115,9843,9845],{"className":9844},[1149],[1151,9846,9847],{"xmlns":1153},[1155,9848,9849,9857],{},[1158,9850,9851],{},[1277,9852,9853,9855],{},[1161,9854,4192],{},[1282,9856,6408],{},[1194,9858,6411],{"encoding":1196},[1115,9860,9862],{"className":9861},[1149],[1151,9863,9864],{"xmlns":1153},[1155,9865,9866,9874],{},[1158,9867,9868],{},[1277,9869,9870,9872],{},[1161,9871,4192],{},[1282,9873,6543],{},[1194,9875,6546],{"encoding":1196}," jsou ",[1131,9878,9879],{},"shodná"," (prvek zůstal ve stejné variantě), pole ",[1115,9882,9884],{"className":9883},[1149],[1151,9885,9886],{"xmlns":1153},[1155,9887,9888,9896],{},[1158,9889,9890],{},[1277,9891,9892,9894],{},[1161,9893,4192],{},[1282,9895,6429],{},[1194,9897,6432],{"encoding":1196},[1115,9899,9901],{"className":9900},[1149],[1151,9902,9903],{"xmlns":1153},[1155,9904,9905,9913],{},[1158,9906,9907],{},[1277,9908,9909,9911],{},[1161,9910,4192],{},[1282,9912,6522],{},[1194,9914,6525],{"encoding":1196}," jsou\n",[1131,9917,9918],{},"diskordantní"," (prvek mezi měřeními variantu změnil) — jen ta rozhodují o výsledku testu:",[1110,9921,9922],{},[1760,9923],{"alt":9924,"className":9925,"src":9926},"mask-kt-mcnemar-tabulka",[1441,1764],"\u002Fwiki-assets\u002Fmask-kt-mcnemar-tabulka.png",[1110,9928,9929],{},[1131,9930,7016],{},[7018,9932,9933,9970,10051,10109],{},[1127,9934,9935,9969],{},[1115,9936,9938],{"className":9937},[1149],[1151,9939,9940],{"xmlns":1153},[1155,9941,9942,9966],{},[1158,9943,9944,9950,9952,9958,9960],{},[1277,9945,9946,9948],{},[1161,9947,4318],{},[1282,9949,1982],{},[1165,9951,2629],{},[1277,9953,9954,9956],{},[1161,9955,1110],{},[1282,9957,6429],{},[1165,9959,1177],{},[1277,9961,9962,9964],{},[1161,9963,1110],{},[1282,9965,6522],{},[1194,9967,9968],{"encoding":1196},"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.",[1127,9971,7151,9972,10034,10036,10037,10050],{},[1115,9973,9975],{"className":9974},[1149],[1151,9976,9977],{"xmlns":1153,"display":2212},[1155,9978,9979,10031],{},[1158,9980,9981,9987,9989],{},[1209,9982,9983,9985],{},[1161,9984,5247],{},[1282,9986,1298],{},[1165,9988,1177],{},[3064,9990,9991,10015],{},[1158,9992,9993,9995,10001,10003,10009],{},[1165,9994,1168],{"stretchy":1167},[1277,9996,9997,9999],{},[1161,9998,4192],{},[1282,10000,6429],{},[1165,10002,1317],{},[1277,10004,10005,10007],{},[1161,10006,4192],{},[1282,10008,6522],{},[1209,10010,10011,10013],{},[1165,10012,1174],{"stretchy":1167},[1282,10014,1298],{},[1158,10016,10017,10023,10025],{},[1277,10018,10019,10021],{},[1161,10020,4192],{},[1282,10022,6429],{},[1165,10024,2094],{},[1277,10026,10027,10029],{},[1161,10028,4192],{},[1282,10030,6522],{},[1194,10032,10033],{"encoding":1196},"\\chi^2 = \\frac{(n_{12} - n_{21})^2}{n_{12} + n_{21}}",[7309,10035],{},"má asymptoticky Pearsonovo rozdělení o ",[1115,10038,10040],{"className":10039},[1149],[1151,10041,10042],{"xmlns":1153},[1155,10043,10044,10048],{},[1158,10045,10046],{},[1282,10047,1284],{},[1194,10049,1284],{"encoding":1196}," stupni volnosti.",[1127,10052,7468,10053,1333],{},[1115,10054,10056],{"className":10055},[1149],[1151,10057,10058],{"xmlns":1153},[1155,10059,10060,10106],{},[1158,10061,10062,10064,10066,10068,10074,10076,10082,10084,10098,10100,10102,10104],{},[1161,10063,5777],{},[1165,10065,1177],{},[1165,10067,7484],{"stretchy":1167},[1209,10069,10070,10072],{},[1161,10071,5247],{},[1282,10073,1298],{},[1165,10075,2629],{},[1209,10077,10078,10080],{},[1161,10079,5247],{},[1282,10081,1298],{},[1165,10083,7501],{},[2256,10085,10086,10088,10096],{},[1161,10087,5247],{},[1158,10089,10090,10092,10094],{},[1282,10091,1284],{},[1165,10093,1317],{},[1161,10095,7514],{},[1282,10097,1298],{},[1165,10099,1168],{"stretchy":1167},[1282,10101,1284],{},[1165,10103,1174],{"stretchy":1167},[1165,10105,7543],{"stretchy":1167},[1194,10107,10108],{"encoding":1196},"W = \\{\\chi^2 : \\chi^2 \\ge \\chi^2_{1-\\alpha}(1)\\}",[1127,10110,7549,10111,10124,10125,10142,10143,10160],{},[1115,10112,10114],{"className":10113},[1149],[1151,10115,10116],{"xmlns":1153},[1155,10117,10118,10122],{},[1158,10119,10120],{},[1161,10121,5777],{},[1194,10123,5777],{"encoding":1196},", zamítáme ",[1115,10126,10128],{"className":10127},[1149],[1151,10129,10130],{"xmlns":1153},[1155,10131,10132,10140],{},[1158,10133,10134],{},[1277,10135,10136,10138],{},[1161,10137,4318],{},[1282,10139,1982],{},[1194,10141,5745],{"encoding":1196}," a přijímáme ",[1115,10144,10146],{"className":10145},[1149],[1151,10147,10148],{"xmlns":1153},[1155,10149,10150,10158],{},[1158,10151,10152],{},[1277,10153,10154,10156],{},[1161,10155,4318],{},[1282,10157,1284],{},[1194,10159,7147],{"encoding":1196},": zásah rozdělení variant změnil.",[1110,10162,10163,10164,10167,10168,10171,10172,10174],{},"V R počítá tento test funkce ",[1373,10165,10166],{},"mcnemar.test()",". Vzorec výše ",[1131,10169,10170],{},"neobsahuje korekci na kontinuitu"," — aby R vrátilo\npřesně tuto hodnotu, musí se volat s ",[1373,10173,9556],{}," (viz Časté chyby níže).",[1103,10176,10178,10185,10188,10191,10288],{"className":10177,"dataCallout":3670},[1106,3669],[1110,10179,10181,10184],{"className":10180},[1113],[1115,10182],{"className":10183,"ariaHidden":1121},[1118,3677,1120],"Příklad: informační kampaň a zveřejňování na Facebooku",[1110,10186,10187],{},"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.",[1110,10189,10190],{},"Základní soubor: všichni studenti; výběrový soubor: vybraní studenti; měřený znak: zveřejňování (ano \u002F ne).",[4052,10192,10193,10228],{},[4055,10194,10195],{},[4058,10196,10197,10199,10202,10205],{},[4061,10198,9593],{},[4061,10200,10201],{},"nezveřejňuje",[4061,10203,10204],{},"zveřejňuje",[4061,10206,10207],{},[1115,10208,10210],{"className":10209},[1149],[1151,10211,10212],{"xmlns":1153},[1155,10213,10214,10226],{},[1158,10215,10216],{},[1277,10217,10218,10220],{},[1161,10219,4192],{},[1158,10221,10222,10224],{},[1161,10223,4187],{},[1165,10225,6136],{},[1194,10227,6366],{"encoding":1196},[4165,10229,10230,10242,10254],{},[4058,10231,10232,10234,10236,10239],{},[4170,10233,10201],{},[4170,10235,7744],{},[4170,10237,10238],{},"68",[4170,10240,10241],{},"92",[4058,10243,10244,10246,10248,10251],{},[4170,10245,10204],{},[4170,10247,8191],{},[4170,10249,10250],{},"50",[4170,10252,10253],{},"78",[4058,10255,10256,10279,10282,10285],{},[4170,10257,10258],{},[1115,10259,10261],{"className":10260},[1149],[1151,10262,10263],{"xmlns":1153},[1155,10264,10265,10277],{},[1158,10266,10267],{},[1277,10268,10269,10271],{},[1161,10270,4192],{},[1158,10272,10273,10275],{},[1165,10274,6136],{},[1161,10276,6044],{},[1194,10278,6758],{"encoding":1196},[4170,10280,10281],{},"52",[4170,10283,10284],{},"118",[4170,10286,10287],{},"170",[1110,10289,10290,10323],{},[1115,10291,10293],{"className":10292},[1149],[1151,10294,10295],{"xmlns":1153},[1155,10296,10297,10321],{},[1158,10298,10299,10305,10307,10313,10315],{},[1277,10300,10301,10303],{},[1161,10302,4318],{},[1282,10304,1982],{},[1165,10306,2629],{},[1277,10308,10309,10311],{},[1161,10310,1110],{},[1282,10312,6429],{},[1165,10314,1177],{},[1277,10316,10317,10319],{},[1161,10318,1110],{},[1282,10320,6522],{},[1194,10322,9968],{"encoding":1196}," — informační kampaň nemá na chování vliv.",[3554,10325,10327],{"className":3556,"code":10326,"language":71,"meta":3558,"style":3558},"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",[1373,10328,10329,10353,10367,10385,10395,10418,10437],{"__ignoreMap":3558},[1115,10330,10331,10334,10336,10338,10340,10342,10344,10346,10348,10351],{"class":3563,"line":10},[1115,10332,10333],{"class":3744},"tab3",[1115,10335,4497],{"class":3741},[1115,10337,7851],{"class":3566},[1115,10339,1168],{"class":3569},[1115,10341,7856],{"class":3566},[1115,10343,1168],{"class":3569},[1115,10345,7744],{"class":3572},[1115,10347,1715],{"class":3741},[1115,10349,10350],{"class":3572}," 68",[1115,10352,7873],{"class":3741},[1115,10354,10355,10358,10360,10363,10365],{"class":3563,"line":27},[1115,10356,10357],{"class":3572},"                 28",[1115,10359,1715],{"class":3741},[1115,10361,10362],{"class":3572}," 50",[1115,10364,1174],{"class":3569},[1115,10366,7873],{"class":3741},[1115,10368,10369,10371,10373,10375,10377,10379,10381,10383],{"class":3563,"line":148},[1115,10370,7930],{"class":3744},[1115,10372,3748],{"class":3741},[1115,10374,8310],{"class":3572},[1115,10376,1715],{"class":3741},[1115,10378,7939],{"class":3744},[1115,10380,3748],{"class":3741},[1115,10382,7944],{"class":3572},[1115,10384,7873],{"class":3741},[1115,10386,10387,10389,10391,10393],{"class":3563,"line":111},[1115,10388,7951],{"class":3744},[1115,10390,3748],{"class":3741},[1115,10392,7956],{"class":3566},[1115,10394,7959],{"class":3569},[1115,10396,10397,10400,10402,10404,10406,10409,10411,10414,10416],{"class":3563,"line":96},[1115,10398,10399],{"class":3744},"                 pred",[1115,10401,3748],{"class":3741},[1115,10403,7969],{"class":3566},[1115,10405,1168],{"class":3569},[1115,10407,10408],{"class":7974},"\"nezverejnuje\"",[1115,10410,1715],{"class":3741},[1115,10412,10413],{"class":7974}," \"zverejnuje\"",[1115,10415,1174],{"class":3569},[1115,10417,7873],{"class":3741},[1115,10419,10420,10423,10425,10427,10429,10431,10433,10435],{"class":3563,"line":89},[1115,10421,10422],{"class":3744},"                 po",[1115,10424,8360],{"class":3741},[1115,10426,7969],{"class":3566},[1115,10428,1168],{"class":3569},[1115,10430,10408],{"class":7974},[1115,10432,1715],{"class":3741},[1115,10434,10413],{"class":7974},[1115,10436,8022],{"class":3569},[1115,10438,10439,10442,10444,10446,10448,10451,10453,10456],{"class":3563,"line":82},[1115,10440,10441],{"class":3566},"mcnemar.test",[1115,10443,1168],{"class":3569},[1115,10445,10333],{"class":3744},[1115,10447,1715],{"class":3741},[1115,10449,10450],{"class":3744}," correct",[1115,10452,3748],{"class":3741},[1115,10454,10455],{"class":3572}," FALSE",[1115,10457,3575],{"class":3569},[3554,10459,10462],{"className":10460,"code":10461,"language":3603,"meta":3558},[3601],"    McNemar's Chi-squared test\n\ndata:  tab3\nMcNemar's chi-squared = 16.667, df = 1, p-value = 4.456e-05\n",[1373,10463,10461],{"__ignoreMap":3558},[1110,10465,10466,10467,8118,10486,10503,10504,10521],{},"P-hodnota ",[1115,10468,10470],{"className":10469},[1149],[1151,10471,10472],{"xmlns":1153},[1155,10473,10474,10483],{},[1158,10475,10476,10479,10481],{},[1282,10477,10478],{},"0,00004456",[1165,10480,1287],{},[1282,10482,8114],{},[1194,10484,10485],{"encoding":1196},"0{,}00004456 \u003C 0{,}05",[1115,10487,10489],{"className":10488},[1149],[1151,10490,10491],{"xmlns":1153},[1155,10492,10493,10501],{},[1158,10494,10495],{},[1277,10496,10497,10499],{},[1161,10498,4318],{},[1282,10500,1982],{},[1194,10502,5745],{"encoding":1196}," zamítáme, přijímáme ",[1115,10505,10507],{"className":10506},[1149],[1151,10508,10509],{"xmlns":1153},[1155,10510,10511,10519],{},[1158,10512,10513],{},[1277,10514,10515,10517],{},[1161,10516,4318],{},[1282,10518,1284],{},[1194,10520,7147],{"encoding":1196}," — informační kampaň měla vliv na změnu\nchování studentů ve zveřejňování údajů na Facebooku.",[1431,10523,5414],{"id":5413},[1103,10525,10527,10534],{"className":10526,"dataCallout":3448},[1106,3447],[1110,10528,10530,10533],{"className":10529},[1113],[1115,10531],{"className":10532,"ariaHidden":1121},[1118,3455,1120],"Test nezávislosti na párovaných datech",[1110,10535,10536,10537,10539],{},"Tabulka před\u002Fpo vypadá jako obyčejná kontingenční tabulka, ale ",[1373,10538,7620],{}," 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.",[3554,10541,10543],{"className":3556,"code":10542,"language":71,"meta":3558,"style":3558},"chisq.test(tab3)\n",[1373,10544,10545],{"__ignoreMap":3558},[1115,10546,10547,10549,10551,10553],{"class":3563,"line":10},[1115,10548,8028],{"class":3566},[1115,10550,1168],{"class":3569},[1115,10552,10333],{"class":3744},[1115,10554,3575],{"class":3569},[3554,10556,10559],{"className":10557,"code":10558,"language":3603,"meta":3558},[3601],"    Pearson's Chi-squared test with Yates' continuity correction\n\ndata:  tab3\nX-squared = 1.4793, df = 1, p-value = 0.2239\n",[1373,10560,10558],{"__ignoreMap":3558},[1110,10562,10466,10563,10582,10583,10600,10601,10603,10604,1333],{},[1115,10564,10566],{"className":10565},[1149],[1151,10567,10568],{"xmlns":1153},[1155,10569,10570,10579],{},[1158,10571,10572,10575,10577],{},[1282,10573,10574],{},"0,224",[1165,10576,4156],{},[1282,10578,8114],{},[1194,10580,10581],{"encoding":1196},"0{,}224 > 0{,}05"," by vedla k nezamítnutí ",[1115,10584,10586],{"className":10585},[1149],[1151,10587,10588],{"xmlns":1153},[1155,10589,10590,10598],{},[1158,10591,10592],{},[1277,10593,10594,10596],{},[1161,10595,4318],{},[1282,10597,1982],{},[1194,10599,5745],{"encoding":1196}," — opačný závěr než správný McNemarův test. Na\npárovaná data (stejné prvky měřené dvakrát) vždy patří ",[1373,10602,10166],{},", nikdy ",[1373,10605,7620],{},[1103,10607,10609,10618],{"className":10608,"dataCallout":3448},[1106,3447],[1110,10610,10612,10615,10616],{"className":10611},[1113],[1115,10613],{"className":10614,"ariaHidden":1121},[1118,3455,1120],"Výchozí korekce na kontinuitu v ",[1373,10617,10166],{},[1110,10619,10620,10621,10624],{},"Bez argumentu ",[1373,10622,10623],{},"correct"," R ve výchozím nastavení použije Yatesovu korekci na kontinuitu, která dá jinou\np-hodnotu než nekorigovaný vzorec uvedený výše.",[3554,10626,10628],{"className":3556,"code":10627,"language":71,"meta":3558,"style":3558},"mcnemar.test(tab3)\n",[1373,10629,10630],{"__ignoreMap":3558},[1115,10631,10632,10634,10636,10638],{"class":3563,"line":10},[1115,10633,10441],{"class":3566},[1115,10635,1168],{"class":3569},[1115,10637,10333],{"class":3744},[1115,10639,3575],{"class":3569},[3554,10641,10644],{"className":10642,"code":10643,"language":3603,"meta":3558},[3601],"    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",[1373,10645,10643],{"__ignoreMap":3558},[1110,10647,10648,10649,10667,10668,10687,10688,10701,10702,1333],{},"Oproti nekorigované hodnotě ",[1115,10650,10652],{"className":10651},[1149],[1151,10653,10654],{"xmlns":1153},[1155,10655,10656,10664],{},[1158,10657,10658,10660,10662],{},[1161,10659,1110],{},[1165,10661,1177],{},[1282,10663,10478],{},[1194,10665,10666],{"encoding":1196},"p = 0{,}00004456"," vyjde ",[1115,10669,10671],{"className":10670},[1149],[1151,10672,10673],{"xmlns":1153},[1155,10674,10675,10684],{},[1158,10676,10677,10679,10681],{},[1161,10678,1110],{},[1165,10680,1177],{},[1282,10682,10683],{},"0,00006879",[1194,10685,10686],{"encoding":1196},"p = 0{,}00006879"," — v tomto příkladu obě vedou ke\nstejnému rozhodnutí, ale u hodnot blíž hranici ",[1115,10689,10691],{"className":10690},[1149],[1151,10692,10693],{"xmlns":1153},[1155,10694,10695,10699],{},[1158,10696,10697],{},[1161,10698,7514],{},[1194,10700,7577],{"encoding":1196}," by korekce mohla rozhodnutí změnit. Aby R reprodukovalo\nnekorigovaný vzorec, je třeba vždy volat ",[1373,10703,10704],{},"mcnemar.test(x, correct = FALSE)",[1431,10706,5604],{"id":5603},[1124,10708,10709,10714,10720,10726,10733,10739,10745],{},[1127,10710,10711],{},[1438,10712,1444],{"className":10713,"dataFsResolvedFilePath":1442,"href":1443},[1441],[1127,10715,10716],{},[1438,10717,10719],{"className":10718,"dataFsResolvedFilePath":4636,"href":4637},[1441],"Testování statistických hypotéz",[1127,10721,10722],{},[1438,10723,10725],{"className":10724,"dataFsResolvedFilePath":2788,"href":2789},[1441],"Popisná statistika a datové soubory",[1127,10727,10728],{},[1438,10729,1094],{"className":10730,"dataFsResolvedFilePath":10731,"href":10732},[1441],"topics\u002Fnahodne-veliciny-a-rozdeleni.md","\u002Fwiki\u002Fnahodne-veliciny-a-rozdeleni",[1127,10734,10735],{},[1438,10736,10738],{"className":10737,"dataFsResolvedFilePath":5627,"href":5628},[1441],"Regresní a korelační analýza",[1127,10740,10741],{},[1438,10742,10744],{"className":10743,"dataFsResolvedFilePath":5642,"href":5643},[1441],"Regulační diagramy a indexy způsobilosti",[1127,10746,10747],{},[1438,10748,5652],{"className":10749,"dataFsResolvedFilePath":5650,"href":5651},[1441],[1431,10751,5655],{"id":934},[1110,10753,5658,10754,5663],{},[5660,10755,5662],{},[5665,10757,10758],{},"html pre.shiki code .sP4rz, html code.shiki .sP4rz{--shiki-light:#E36209;--shiki-default:#E36209;--shiki-dark:#FFAB70}html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .snPdu, html code.shiki .snPdu{--shiki-light:#6F42C1;--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sIIMD, html 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80,"created":5681,"description":3558,"extension":5682,"meta":19557,"navigation":4572,"path":19558,"seo":19559,"sources":19560,"stem":19567,"tags":19568,"type":5692,"updated":5681,"__hash__":19569},"topics\u002Ftopics\u002Fpopisna-statistika.md",{"type":1096,"value":14807,"toc":19548},[14808,14811,14905,14909,14919,15045,15052,15063,15067,15110,15115,15217,15227,15232,15371,15447,15451,15552,15633,15640,15711,15730,15732,15948,15954,15964,15971,15974,16028,16034,16044,16057,16203,16206,16219,16538,16544,16547,16551,16630,16664,16693,16695,16773,16779,16840,16847,16860,16937,17053,17103,17116,17271,17277,17304,17308,17333,17336,17549,17617,17718,17725,17738,18241,18247,18279,18539,18692,18803,18832,18838,18845,18851,18864,19294,19300,19303,19305,19500,19502,19539,19541,19545],[1099,14809,10725],{"id":14810},"popisná-statistika-a-datové-soubory",[1103,14812,14814,14820],{"className":14813,"dataCallout":1108},[1106,1107],[1110,14815,14817,1122],{"className":14816},[1113],[1115,14818],{"className":14819,"ariaHidden":1121},[1118,1119,1120],[1124,14821,14822,14825,14828,14855,14902],{},[1127,14823,14824],{},"Rozlišit základní a výběrový soubor, typ statistického znaku (kvantitativní\u002Fkvalitativní, diskrétní\u002Fspojitý) a požadavek reprezentativity a nezávislého výběru.",[1127,14826,14827],{},"Spočítat výběrový průměr, rozptyl, směrodatnou odchylku a variační rozpětí; interpretovat je jako bodové odhady charakteristik náhodné veličiny.",[1127,14829,14830,14831,1333],{},"Určit medián a kvartily a číst empirickou distribuční funkci ",[1115,14832,14834],{"className":14833},[1149],[1151,14835,14836],{"xmlns":1153},[1155,14837,14838,14852],{},[1158,14839,14840,14846,14848,14850],{},[1277,14841,14842,14844],{},[1161,14843,1163],{},[1161,14845,4192],{},[1165,14847,1168],{"stretchy":1167},[1161,14849,1171],{},[1165,14851,1174],{"stretchy":1167},[1194,14853,14854],{"encoding":1196},"F_n(x)",[1127,14856,14857,14858,14901],{},"Roztřídit velký datový soubor do tříd (intervalové rozdělení četností), sestavit tabulku ",[1115,14859,14861],{"className":14860},[1149],[1151,14862,14863],{"xmlns":1153},[1155,14864,14865,14898],{},[1158,14866,14867,14874,14876,14882,14884,14890,14892],{},[1277,14868,14869,14872],{},[1161,14870,14871],{},"I",[1161,14873,6044],{},[1165,14875,1715],{"separator":1121},[1277,14877,14878,14880],{},[1161,14879,3419],{},[1161,14881,6044],{},[1165,14883,1715],{"separator":1121},[1277,14885,14886,14888],{},[1161,14887,1228],{},[1161,14889,6044],{},[1165,14891,1715],{"separator":1121},[1277,14893,14894,14896],{},[1161,14895,1110],{},[1161,14897,6044],{},[1194,14899,14900],{"encoding":1196},"I_j, Z_j, f_j, p_j"," a nakreslit histogram.",[1127,14903,14904],{},"Z histogramu odhadnout zákon rozdělení dat; formální test shody patří do testování hypotéz.",[1431,14906,14908],{"id":14907},"základní-pojmy","Základní pojmy",[1110,14910,14911,14914,14915,14918],{},[1438,14912,1444],{"className":14913,"dataFsResolvedFilePath":1442,"href":1443},[1441]," pracuje s ",[1131,14916,14917],{},"datovými soubory"," — konkrétními hodnotami, které popisují vlastnost zkoumaných prvků.",[1124,14920,14921,14927,14951,14957,15032],{},[1127,14922,14923,14926],{},[1131,14924,14925],{},"Základní soubor"," — množina prvků, na nichž provádíme šetření (např. všichni výdělečně činní obyvatelé ČR).",[1127,14928,14929,14932,14933],{},[1131,14930,14931],{},"Statistický znak"," — funkce, která vyjadřuje určitou vlastnost prvku (např. velikost platu). Znaky dělíme na:\n",[1124,14934,14935,14946],{},[1127,14936,14937,14939,14940,14942,14943,14945],{},[1131,14938,5901],{}," (vyjádřitelné číslem) — dále ",[1131,14941,1133],{}," (spočetně mnoho hodnot) nebo ",[1131,14944,1137],{}," (libovolná hodnota v intervalu);",[1127,14947,14948,14950],{},[1131,14949,5894],{}," (vyjádřitelné slovně).",[1127,14952,14953,14956],{},[1131,14954,14955],{},"Výběrový soubor"," — podmnožina prvků základního souboru, na níž znak skutečně zjišťujeme (např. 5 náhodně vybraných obyvatel).",[1127,14958,14959,14962,14963,1333],{},[1131,14960,14961],{},"Datový soubor"," — n-tice naměřených hodnot zkoumaného znaku, např. ",[1115,14964,14966],{"className":14965},[1149],[1151,14967,14968],{"xmlns":1153},[1155,14969,14970,15029],{},[1158,14971,14972,14974,14976,14978,14981,14983,14986,14989,14991,14994,14996,14998,15001,15003,15006,15008,15010,15012,15014,15016,15018,15020,15022,15024,15027],{},[1165,14973,1168],{"stretchy":1167},[1282,14975,7695],{},[2278,14977,2280],{},[1282,14979,14980],{},"500",[1165,14982,1715],{"separator":1121},[2278,14984,14985],{}," ",[1282,14987,14988],{},"38",[2278,14990,2280],{},[1282,14992,14993],{},"000",[1165,14995,1715],{"separator":1121},[2278,14997,14985],{},[1282,14999,15000],{},"37",[2278,15002,2280],{},[1282,15004,15005],{},"800",[1165,15007,1715],{"separator":1121},[2278,15009,14985],{},[1282,15011,3873],{},[2278,15013,2280],{},[1282,15015,14993],{},[1165,15017,1715],{"separator":1121},[2278,15019,14985],{},[1282,15021,7703],{},[2278,15023,2280],{},[1282,15025,15026],{},"200",[1165,15028,1174],{"stretchy":1167},[1194,15030,15031],{"encoding":1196},"(29\\,500,\\ 38\\,000,\\ 37\\,800,\\ 41\\,000,\\ 31\\,200)",[1127,15033,15034,15035,1376,15038,1425,15041,15044],{},"Podle počtu sledovaných znaků rozlišujeme ",[1131,15036,15037],{},"jednorozměrné",[1131,15039,15040],{},"dvourozměrné",[1131,15042,15043],{},"vícerozměrné"," datové soubory.",[1110,15046,15047],{},[1760,15048],{"alt":15049,"className":15050,"src":15051},"mask-ilu-zakladni-soubor-vyber",[1441,1764],"\u002Fwiki-assets\u002Fmask-ilu-zakladni-soubor-vyber.png",[1110,15053,15054,15055,15058,15059,15062],{},"Aby výběrový soubor dobře vypovídal o základním souboru, měl by být ",[1131,15056,15057],{},"reprezentativní"," (podobný základnímu souboru svým složením). Není-li to možné zajistit přímo, volí se prvky do výběru náhodně — ",[1131,15060,15061],{},"nezávislý výběr",". Bez náhodnosti výběru nelze vlastnosti základního souboru správně vystihnout.",[1431,15064,15066],{"id":15065},"empirické-charakteristiky","Empirické charakteristiky",[1110,15068,15069,15070,15073,15074,15077,15078,15091,15092,15095,15096,15109],{},"Zpracováním datového souboru získáme ",[1131,15071,15072],{},"empirické charakteristiky"," a odhad ",[1131,15075,15076],{},"zákona rozdělení"," zkoumané náhodné veličiny ",[1115,15079,15081],{"className":15080},[1149],[1151,15082,15083],{"xmlns":1153},[1155,15084,15085,15089],{},[1158,15086,15087],{},[1161,15088,1185],{},[1194,15090,1185],{"encoding":1196},". Jde o ",[1131,15093,15094],{},"bodové odhady"," charakteristik ",[1115,15097,15099],{"className":15098},[1149],[1151,15100,15101],{"xmlns":1153},[1155,15102,15103,15107],{},[1158,15104,15105],{},[1161,15106,1185],{},[1194,15108,1185],{"encoding":1196},"; ruční výpočet podle vzorců níže je potřeba jen bez dostupného softwaru.",[1110,15111,15112],{},[1131,15113,15114],{},"Míry polohy",[1115,15116,15118],{"className":15117},[1149],[1151,15119,15120],{"xmlns":1153,"display":2212},[1155,15121,15122,15214],{},[1158,15123,15124,15131,15133,15139,15153,15159,15161],{},[6877,15125,15126,15128],{"accent":1121},[1161,15127,1171],{},[1165,15129,15130],{},"ˉ",[1165,15132,1177],{},[3064,15134,15135,15137],{},[1282,15136,1284],{},[1161,15138,4192],{},[6140,15140,15141,15143,15151],{},[1165,15142,6144],{},[1158,15144,15145,15147,15149],{},[1161,15146,4187],{},[1165,15148,1177],{},[1282,15150,1284],{},[1161,15152,4192],{},[1277,15154,15155,15157],{},[1161,15156,1171],{},[1161,15158,4187],{},[2242,15160],{"width":2244},[1158,15162,15163,15166,15173,15176,15183,15186,15192,15195,15203,15205,15211],{},[2278,15164,15165],{},"(v",[6877,15167,15168,15170],{"accent":1121},[2278,15169,1603],{},[1165,15171,15172],{},"ˊ",[2278,15174,15175],{},"b",[6877,15177,15178,15180],{"accent":1121},[2278,15179,3085],{},[1165,15181,15182],{},"ˇ",[2278,15184,15185],{},"rov",[6877,15187,15188,15190],{"accent":1121},[2278,15189,1603],{},[1165,15191,15172],{},[2278,15193,15194],{}," pr",[6877,15196,15197,15200],{"accent":1121},[2278,15198,15199],{},"u",[1165,15201,15202],{},"˚",[2278,15204,8597],{},[6877,15206,15207,15209],{"accent":1121},[2278,15208,3085],{},[1165,15210,15182],{},[2278,15212,15213],{},"r)",[1194,15215,15216],{"encoding":1196},"\\bar{x} = \\frac{1}{n}\\sum_{i=1}^{n} x_i \\qquad \\text{(výběrový průměr)}",[1110,15218,15219,15220,1425,15223,15226],{},"Dalšími mírami polohy jsou ",[1131,15221,15222],{},"medián",[1131,15224,15225],{},"modus"," (nejčetnější hodnota výběru).",[1110,15228,15229],{},[1131,15230,15231],{},"Míry variability",[1115,15233,15235],{"className":15234},[1149],[1151,15236,15237],{"xmlns":1153,"display":2212},[1155,15238,15239,15368],{},[1158,15240,15241,15247,15249,15261,15303,15305,15307,15309,15311,15319,15321],{},[1209,15242,15243,15245],{},[1161,15244,6018],{},[1282,15246,1298],{},[1165,15248,1177],{},[3064,15250,15251,15253],{},[1282,15252,1284],{},[1158,15254,15255,15257,15259],{},[1161,15256,4192],{},[1165,15258,1317],{},[1282,15260,1284],{},[1158,15262,15263,15265,15279,15287,15289,15291,15301],{},[1165,15264,1168],{"fence":1121},[6140,15266,15267,15269,15277],{},[1165,15268,6144],{},[1158,15270,15271,15273,15275],{},[1161,15272,4187],{},[1165,15274,1177],{},[1282,15276,1284],{},[1161,15278,4192],{},[2256,15280,15281,15283,15285],{},[1161,15282,1171],{},[1161,15284,4187],{},[1282,15286,1298],{},[1165,15288,1317],{},[1161,15290,4192],{},[1209,15292,15293,15299],{},[6877,15294,15295,15297],{"accent":1121},[1161,15296,1171],{},[1165,15298,15130],{},[1282,15300,1298],{},[1165,15302,1174],{"fence":1121},[1165,15304,1715],{"separator":1121},[2242,15306],{"width":2244},[1161,15308,6018],{},[1165,15310,1177],{},[2765,15312,15313],{},[1209,15314,15315,15317],{},[1161,15316,6018],{},[1282,15318,1298],{},[2242,15320],{"width":2244},[1158,15322,15323,15325,15331,15333,15339,15341,15347,15350,15356,15359,15365],{},[2278,15324,15165],{},[6877,15326,15327,15329],{"accent":1121},[2278,15328,1603],{},[1165,15330,15172],{},[2278,15332,15175],{},[6877,15334,15335,15337],{"accent":1121},[2278,15336,3085],{},[1165,15338,15182],{},[2278,15340,15185],{},[6877,15342,15343,15345],{"accent":1121},[2278,15344,1603],{},[1165,15346,15172],{},[2278,15348,15349],{}," rozptyl, sm",[6877,15351,15352,15354],{"accent":1121},[2278,15353,3085],{},[1165,15355,15182],{},[2278,15357,15358],{},"rodatn",[6877,15360,15361,15363],{"accent":1121},[2278,15362,1438],{},[1165,15364,15172],{},[2278,15366,15367],{}," odchylka)",[1194,15369,15370],{"encoding":1196},"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)}",[1115,15372,15374],{"className":15373},[1149],[1151,15375,15376],{"xmlns":1153,"display":2212},[1155,15377,15378,15444],{},[1158,15379,15380,15382,15384,15393,15395,15403,15405],{},[1161,15381,4759],{},[1165,15383,1177],{},[1277,15385,15386,15388,15391],{},[1161,15387,1171],{},[1161,15389,15390],{},"max",[1165,15392,2079],{},[1165,15394,1317],{},[1277,15396,15397,15399,15401],{},[1161,15398,1171],{},[1161,15400,8614],{},[1165,15402,2079],{},[2242,15404],{"width":2244},[1158,15406,15407,15410,15416,15418,15425,15428,15434,15436,15442],{},[2278,15408,15409],{},"(varia",[6877,15411,15412,15414],{"accent":1121},[2278,15413,7856],{},[1165,15415,15182],{},[2278,15417,4192],{},[6877,15419,15420,15423],{"accent":1121},[2278,15421,15422],{},"ı",[1165,15424,15172],{},[2278,15426,15427],{}," rozp",[6877,15429,15430,15432],{"accent":1121},[2278,15431,3085],{},[1165,15433,15182],{},[2278,15435,1617],{},[6877,15437,15438,15440],{"accent":1121},[2278,15439,15422],{},[1165,15441,15172],{},[2278,15443,1174],{},[1194,15445,15446],{"encoding":1196},"R = x_{\\max} - x_{\\min} \\qquad \\text{(variační rozpětí)}",[1110,15448,15449],{},[1131,15450,2795],{},[1110,15452,15453,15454,15477,15478,15500,15501,15522,15523,15551],{},"Kvantil ",[1115,15455,15457],{"className":15456},[1149],[1151,15458,15459],{"xmlns":1153},[1155,15460,15461,15474],{},[1158,15462,15463],{},[1277,15464,15465,15472],{},[6877,15466,15467,15469],{"accent":1121},[1161,15468,1171],{},[1165,15470,15471],{},"~",[1161,15473,1110],{},[1194,15475,15476],{"encoding":1196},"\\tilde{x}_p"," dělí hodnoty datového souboru na dvě části: ",[1115,15479,15481],{"className":15480},[1149],[1151,15482,15483],{"xmlns":1153},[1155,15484,15485,15497],{},[1158,15486,15487,15490,15492,15494],{},[1282,15488,15489],{},"100",[1161,15491,1110],{},[2278,15493,2280],{},[1161,15495,15496],{"mathvariant":1215},"%",[1194,15498,15499],{"encoding":1196},"100p\\,\\%"," hodnot je menších nebo rovných ",[1115,15502,15504],{"className":15503},[1149],[1151,15505,15506],{"xmlns":1153},[1155,15507,15508,15520],{},[1158,15509,15510],{},[1277,15511,15512,15518],{},[6877,15513,15514,15516],{"accent":1121},[1161,15515,1171],{},[1165,15517,15471],{},[1161,15519,1110],{},[1194,15521,15476],{"encoding":1196},", zbylých ",[1115,15524,15526],{"className":15525},[1149],[1151,15527,15528],{"xmlns":1153},[1155,15529,15530,15548],{},[1158,15531,15532,15534,15536,15538,15540,15542,15544,15546],{},[1282,15533,15489],{},[1165,15535,1168],{"stretchy":1167},[1282,15537,1284],{},[1165,15539,1317],{},[1161,15541,1110],{},[1165,15543,1174],{"stretchy":1167},[2278,15545,2280],{},[1161,15547,15496],{"mathvariant":1215},[1194,15549,15550],{"encoding":1196},"100(1-p)\\,\\%"," je větších. Nejdůležitější kvantily:",[1124,15553,15554,15581],{},[1127,15555,15556,1145,15558,15580],{},[1131,15557,15222],{},[1115,15559,15561],{"className":15560},[1149],[1151,15562,15563],{"xmlns":1153},[1155,15564,15565,15577],{},[1158,15566,15567],{},[1277,15568,15569,15575],{},[6877,15570,15571,15573],{"accent":1121},[1161,15572,1171],{},[1165,15574,15471],{},[1282,15576,2949],{},[1194,15578,15579],{"encoding":1196},"\\tilde{x}_{0{,}5}"," — pro lichý počet prvků uspořádaného souboru prostřední prvek, pro sudý počet průměr dvou prostředních prvků;",[1127,15582,15583,1145,15586,1425,15608,1145,15611,1333],{},[1131,15584,15585],{},"dolní kvartil",[1115,15587,15589],{"className":15588},[1149],[1151,15590,15591],{"xmlns":1153},[1155,15592,15593,15605],{},[1158,15594,15595],{},[1277,15596,15597,15603],{},[6877,15598,15599,15601],{"accent":1121},[1161,15600,1171],{},[1165,15602,15471],{},[1282,15604,2969],{},[1194,15606,15607],{"encoding":1196},"\\tilde{x}_{0{,}25}",[1131,15609,15610],{},"horní kvartil",[1115,15612,15614],{"className":15613},[1149],[1151,15615,15616],{"xmlns":1153},[1155,15617,15618,15630],{},[1158,15619,15620],{},[1277,15621,15622,15628],{},[6877,15623,15624,15626],{"accent":1121},[1161,15625,1171],{},[1165,15627,15471],{},[1282,15629,2989],{},[1194,15631,15632],{"encoding":1196},"\\tilde{x}_{0{,}75}",[1110,15634,15635,15636,15639],{},"Datový soubor se do R zadává buď přímo (",[1373,15637,15638],{},"x \u003C- c(...)","), nebo načtením ze souboru:",[3554,15641,15643],{"className":3556,"code":15642,"language":71,"meta":3558,"style":3558},"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",[1373,15644,15645,15706],{"__ignoreMap":3558},[1115,15646,15647,15649,15651,15653,15655,15658,15660,15663,15665,15668,15670,15673,15675,15677,15679,15681,15683,15686,15688,15691,15693,15695,15697,15699,15702],{"class":3563,"line":10},[1115,15648,1171],{"class":3744},[1115,15650,4497],{"class":3741},[1115,15652,7969],{"class":3566},[1115,15654,1168],{"class":3569},[1115,15656,15657],{"class":3572},"4.1",[1115,15659,1715],{"class":3741},[1115,15661,15662],{"class":3572}," 4.0",[1115,15664,1715],{"class":3741},[1115,15666,15667],{"class":3572}," 3.8",[1115,15669,1715],{"class":3741},[1115,15671,15672],{"class":3572}," 3.9",[1115,15674,1715],{"class":3741},[1115,15676,15667],{"class":3572},[1115,15678,1715],{"class":3741},[1115,15680,15667],{"class":3572},[1115,15682,1715],{"class":3741},[1115,15684,15685],{"class":3572}," 3.5",[1115,15687,1715],{"class":3741},[1115,15689,15690],{"class":3572}," 3.7",[1115,15692,1715],{"class":3741},[1115,15694,15662],{"class":3572},[1115,15696,1715],{"class":3741},[1115,15698,15662],{"class":3572},[1115,15700,15701],{"class":3569},")   ",[1115,15703,15705],{"class":15704},"sCsY4","# přímé zadání hodnot\n",[1115,15707,15708],{"class":3563,"line":27},[1115,15709,15710],{"class":15704},"# x \u003C- read.table(\"data.txt\")[, 1]                       # načtení prvního sloupce ze souboru\n",[1110,15712,15713,15714,15717,15718,15721,15722,15725,15726,15729],{},"Řádek s načtením ze souboru je zakomentovaný znakem ",[1373,15715,15716],{},"#",": soubor musí ležet v pracovním adresáři R. ",[1373,15719,15720],{},"read.table()"," vrací datovou tabulku (",[1373,15723,15724],{},"data.frame","), proto ",[1373,15727,15728],{},"[, 1]"," vybere její první sloupec jako vektor.",[1110,15731,3552],{},[3554,15733,15735],{"className":3556,"code":15734,"language":71,"meta":3558,"style":3558},"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",[1373,15736,15737,15794,15805,15816,15827,15838,15876,15902,15925],{"__ignoreMap":3558},[1115,15738,15739,15741,15743,15745,15747,15750,15752,15755,15757,15760,15762,15765,15767,15769,15771,15774,15776,15778,15780,15783,15785,15788,15790,15792],{"class":3563,"line":10},[1115,15740,1171],{"class":3744},[1115,15742,4497],{"class":3741},[1115,15744,7969],{"class":3566},[1115,15746,1168],{"class":3569},[1115,15748,15749],{"class":3572},"11.1",[1115,15751,1715],{"class":3741},[1115,15753,15754],{"class":3572}," 12.7",[1115,15756,1715],{"class":3741},[1115,15758,15759],{"class":3572}," 10.8",[1115,15761,1715],{"class":3741},[1115,15763,15764],{"class":3572}," 13.2",[1115,15766,1715],{"class":3741},[1115,15768,15754],{"class":3572},[1115,15770,1715],{"class":3741},[1115,15772,15773],{"class":3572}," 13.4",[1115,15775,1715],{"class":3741},[1115,15777,15754],{"class":3572},[1115,15779,1715],{"class":3741},[1115,15781,15782],{"class":3572}," 14.4",[1115,15784,1715],{"class":3741},[1115,15786,15787],{"class":3572}," 14.7",[1115,15789,1715],{"class":3741},[1115,15791,15782],{"class":3572},[1115,15793,3575],{"class":3569},[1115,15795,15796,15799,15801,15803],{"class":3563,"line":27},[1115,15797,15798],{"class":3566},"length",[1115,15800,1168],{"class":3569},[1115,15802,1171],{"class":3744},[1115,15804,3575],{"class":3569},[1115,15806,15807,15810,15812,15814],{"class":3563,"line":148},[1115,15808,15809],{"class":3566},"mean",[1115,15811,1168],{"class":3569},[1115,15813,1171],{"class":3744},[1115,15815,3575],{"class":3569},[1115,15817,15818,15821,15823,15825],{"class":3563,"line":111},[1115,15819,15820],{"class":3566},"var",[1115,15822,1168],{"class":3569},[1115,15824,1171],{"class":3744},[1115,15826,3575],{"class":3569},[1115,15828,15829,15832,15834,15836],{"class":3563,"line":96},[1115,15830,15831],{"class":3566},"sd",[1115,15833,1168],{"class":3569},[1115,15835,1171],{"class":3744},[1115,15837,3575],{"class":3569},[1115,15839,15840,15842,15844,15846,15849,15851,15853,15855,15857,15859,15861,15863,15865,15867,15870,15872,15874],{"class":3563,"line":89},[1115,15841,8614],{"class":3566},[1115,15843,1168],{"class":3569},[1115,15845,1171],{"class":3744},[1115,15847,15848],{"class":3569},"); ",[1115,15850,15390],{"class":3566},[1115,15852,1168],{"class":3569},[1115,15854,1171],{"class":3744},[1115,15856,15848],{"class":3569},[1115,15858,15390],{"class":3566},[1115,15860,1168],{"class":3569},[1115,15862,1171],{"class":3744},[1115,15864,3862],{"class":3569},[1115,15866,3865],{"class":3741},[1115,15868,15869],{"class":3566}," min",[1115,15871,1168],{"class":3569},[1115,15873,1171],{"class":3744},[1115,15875,3575],{"class":3569},[1115,15877,15878,15881,15883,15885,15887,15890,15892,15895,15897,15900],{"class":3563,"line":82},[1115,15879,15880],{"class":3566},"quantile",[1115,15882,1168],{"class":3569},[1115,15884,1171],{"class":3744},[1115,15886,1715],{"class":3741},[1115,15888,15889],{"class":3572}," 0.5",[1115,15891,1715],{"class":3741},[1115,15893,15894],{"class":3744}," type",[1115,15896,3748],{"class":3741},[1115,15898,15899],{"class":3572}," 6",[1115,15901,3575],{"class":3569},[1115,15903,15904,15906,15908,15910,15912,15915,15917,15919,15921,15923],{"class":3563,"line":75},[1115,15905,15880],{"class":3566},[1115,15907,1168],{"class":3569},[1115,15909,1171],{"class":3744},[1115,15911,1715],{"class":3741},[1115,15913,15914],{"class":3572}," 0.25",[1115,15916,1715],{"class":3741},[1115,15918,15894],{"class":3744},[1115,15920,3748],{"class":3741},[1115,15922,15899],{"class":3572},[1115,15924,3575],{"class":3569},[1115,15926,15927,15929,15931,15933,15935,15938,15940,15942,15944,15946],{"class":3563,"line":8025},[1115,15928,15880],{"class":3566},[1115,15930,1168],{"class":3569},[1115,15932,1171],{"class":3744},[1115,15934,1715],{"class":3741},[1115,15936,15937],{"class":3572}," 0.75",[1115,15939,1715],{"class":3741},[1115,15941,15894],{"class":3744},[1115,15943,3748],{"class":3741},[1115,15945,15899],{"class":3572},[1115,15947,3575],{"class":3569},[3554,15949,15952],{"className":15950,"code":15951,"language":3603,"meta":3558},[3601],"[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",[1373,15953,15951],{"__ignoreMap":3558},[1110,15955,15956,15959,15960,15963],{},[1373,15957,15958],{},"quantile(x, p, type = 6)"," je potřeba zadat explicitně — výchozí typ v R (",[1373,15961,15962],{},"type = 7",") by u některých souborů dal mírně odlišné hodnoty kvantilů než ruční výpočet použitý v této kapitole.",[1110,15965,15966],{},[1760,15967],{"alt":15968,"className":15969,"src":15970},"mask-ps-kvantily",[1441,1764],"\u002Fwiki-assets\u002Fmask-ps-kvantily.png",[1110,15972,15973],{},"Seřazení souboru a krabicový graf:",[3554,15975,15977],{"className":3556,"code":15976,"language":71,"meta":3558,"style":3558},"sort(x)                     # vzestupně\nsort(x, decreasing = TRUE)  # sestupně\nboxplot(x)\n",[1373,15978,15979,15994,16017],{"__ignoreMap":3558},[1115,15980,15981,15984,15986,15988,15991],{"class":3563,"line":10},[1115,15982,15983],{"class":3566},"sort",[1115,15985,1168],{"class":3569},[1115,15987,1171],{"class":3744},[1115,15989,15990],{"class":3569},")                     ",[1115,15992,15993],{"class":15704},"# vzestupně\n",[1115,15995,15996,15998,16000,16002,16004,16007,16009,16011,16014],{"class":3563,"line":27},[1115,15997,15983],{"class":3566},[1115,15999,1168],{"class":3569},[1115,16001,1171],{"class":3744},[1115,16003,1715],{"class":3741},[1115,16005,16006],{"class":3744}," decreasing",[1115,16008,3748],{"class":3741},[1115,16010,7944],{"class":3572},[1115,16012,16013],{"class":3569},")  ",[1115,16015,16016],{"class":15704},"# sestupně\n",[1115,16018,16019,16022,16024,16026],{"class":3563,"line":148},[1115,16020,16021],{"class":3566},"boxplot",[1115,16023,1168],{"class":3569},[1115,16025,1171],{"class":3744},[1115,16027,3575],{"class":3569},[3554,16029,16032],{"className":16030,"code":16031,"language":3603,"meta":3558},[3601]," [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",[1373,16033,16031],{"__ignoreMap":3558},[1110,16035,16036,16039,16040,16043],{},[1373,16037,16038],{},"boxplot()"," kreslí krabici mezi hodnotami ",[1373,16041,16042],{},"fivenum(x)"," (zde 12,7 a 14,4), které se od kvartilů typu 6 mohou mírně lišit.",[1103,16045,16047,16054],{"className":16046,"dataCallout":3670},[1106,3669],[1110,16048,16050,16053],{"className":16049},[1113],[1115,16051],{"className":16052,"ariaHidden":1121},[1118,3677,1120],"Příklad: Empirické charakteristiky",[1110,16055,16056],{},"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.",[1110,16058,16059,16060,1376,16083,1376,16106,1376,16125,16144,16145,2953,16172,16187,16188,1333],{},"Výstup R kódu výše dává ",[1115,16061,16063],{"className":16062},[1149],[1151,16064,16065],{"xmlns":1153},[1155,16066,16067,16080],{},[1158,16068,16069,16075,16077],{},[6877,16070,16071,16073],{"accent":1121},[1161,16072,1171],{},[1165,16074,15130],{},[1165,16076,1177],{},[1282,16078,16079],{},"13,01",[1194,16081,16082],{"encoding":1196},"\\bar{x}=13{,}01",[1115,16084,16086],{"className":16085},[1149],[1151,16087,16088],{"xmlns":1153},[1155,16089,16090,16103],{},[1158,16091,16092,16098,16100],{},[1209,16093,16094,16096],{},[1161,16095,6018],{},[1282,16097,1298],{},[1165,16099,1177],{},[1282,16101,16102],{},"1,75",[1194,16104,16105],{"encoding":1196},"s^2=1{,}75",[1115,16107,16109],{"className":16108},[1149],[1151,16110,16111],{"xmlns":1153},[1155,16112,16113,16122],{},[1158,16114,16115,16117,16119],{},[1161,16116,6018],{},[1165,16118,1177],{},[1282,16120,16121],{},"1,32",[1194,16123,16124],{"encoding":1196},"s=1{,}32",[1115,16126,16128],{"className":16127},[1149],[1151,16129,16130],{"xmlns":1153},[1155,16131,16132,16141],{},[1158,16133,16134,16136,16138],{},[1161,16135,4759],{},[1165,16137,1177],{},[1282,16139,16140],{},"3,9",[1194,16142,16143],{"encoding":1196},"R=3{,}9",", medián ",[1115,16146,16148],{"className":16147},[1149],[1151,16149,16150],{"xmlns":1153},[1155,16151,16152,16169],{},[1158,16153,16154,16164,16166],{},[1277,16155,16156,16162],{},[6877,16157,16158,16160],{"accent":1121},[1161,16159,1171],{},[1165,16161,15471],{},[1282,16163,2949],{},[1165,16165,1177],{},[1282,16167,16168],{},"12,95",[1194,16170,16171],{"encoding":1196},"\\tilde{x}_{0{,}5}=12{,}95",[1115,16173,16175],{"className":16174},[1149],[1151,16176,16177],{"xmlns":1153},[1155,16178,16179,16184],{},[1158,16180,16181],{},[1282,16182,16183],{},"12,3",[1194,16185,16186],{"encoding":1196},"12{,}3",", horní kvartil ",[1115,16189,16191],{"className":16190},[1149],[1151,16192,16193],{"xmlns":1153},[1155,16194,16195,16200],{},[1158,16196,16197],{},[1282,16198,16199],{},"14,4",[1194,16201,16202],{"encoding":1196},"14{,}4",[1110,16204,16205],{},"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.",[1103,16207,16209,16216],{"className":16208,"dataCallout":3670},[1106,3669],[1110,16210,16212,16215],{"className":16211},[1113],[1115,16213],{"className":16214,"ariaHidden":1121},[1118,3677,1120],"Příklad: Doba oprav televizorů",[1110,16217,16218],{},"Při 50 opravách určité závady televizoru byly naměřeny časy (v minutách). Určete empirické charakteristiky.",[3554,16220,16222],{"className":3556,"code":16221,"language":71,"meta":3558,"style":3558},"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",[1373,16223,16224,16284,16335,16382,16429,16477,16487,16497,16507,16527],{"__ignoreMap":3558},[1115,16225,16226,16229,16231,16233,16235,16237,16239,16242,16244,16247,16249,16252,16254,16257,16259,16262,16264,16267,16269,16272,16274,16277,16279,16282],{"class":3563,"line":10},[1115,16227,16228],{"class":3744},"x6",[1115,16230,4497],{"class":3741},[1115,16232,7969],{"class":3566},[1115,16234,1168],{"class":3569},[1115,16236,7720],{"class":3572},[1115,16238,1715],{"class":3741},[1115,16240,16241],{"class":3572}," 40.2",[1115,16243,1715],{"class":3741},[1115,16245,16246],{"class":3572}," 41.9",[1115,16248,1715],{"class":3741},[1115,16250,16251],{"class":3572}," 43.4",[1115,16253,1715],{"class":3741},[1115,16255,16256],{"class":3572}," 42.8",[1115,16258,1715],{"class":3741},[1115,16260,16261],{"class":3572}," 42.3",[1115,16263,1715],{"class":3741},[1115,16265,16266],{"class":3572}," 43.2",[1115,16268,1715],{"class":3741},[1115,16270,16271],{"class":3572}," 45",[1115,16273,1715],{"class":3741},[1115,16275,16276],{"class":3572}," 41.5",[1115,16278,1715],{"class":3741},[1115,16280,16281],{"class":3572}," 42.7",[1115,16283,7873],{"class":3741},[1115,16285,16286,16289,16291,16294,16296,16299,16301,16304,16306,16309,16311,16314,16316,16319,16321,16324,16326,16328,16330,16333],{"class":3563,"line":27},[1115,16287,16288],{"class":3572},"        43.9",[1115,16290,1715],{"class":3741},[1115,16292,16293],{"class":3572}," 40.1",[1115,16295,1715],{"class":3741},[1115,16297,16298],{"class":3572}," 43.3",[1115,16300,1715],{"class":3741},[1115,16302,16303],{"class":3572}," 41.1",[1115,16305,1715],{"class":3741},[1115,16307,16308],{"class":3572}," 42.5",[1115,16310,1715],{"class":3741},[1115,16312,16313],{"class":3572}," 42.4",[1115,16315,1715],{"class":3741},[1115,16317,16318],{"class":3572}," 41.4",[1115,16320,1715],{"class":3741},[1115,16322,16323],{"class":3572}," 40.8",[1115,16325,1715],{"class":3741},[1115,16327,3850],{"class":3572},[1115,16329,1715],{"class":3741},[1115,16331,16332],{"class":3572}," 44.7",[1115,16334,7873],{"class":3741},[1115,16336,16337,16340,16342,16344,16346,16348,16350,16353,16355,16358,16360,16363,16365,16367,16369,16372,16374,16376,16378,16380],{"class":3563,"line":148},[1115,16338,16339],{"class":3572},"        41.2",[1115,16341,1715],{"class":3741},[1115,16343,16246],{"class":3572},[1115,16345,1715],{"class":3741},[1115,16347,16313],{"class":3572},[1115,16349,1715],{"class":3741},[1115,16351,16352],{"class":3572}," 44.4",[1115,16354,1715],{"class":3741},[1115,16356,16357],{"class":3572}," 40.5",[1115,16359,1715],{"class":3741},[1115,16361,16362],{"class":3572}," 39.7",[1115,16364,1715],{"class":3741},[1115,16366,16303],{"class":3572},[1115,16368,1715],{"class":3741},[1115,16370,16371],{"class":3572}," 41",[1115,16373,1715],{"class":3741},[1115,16375,16246],{"class":3572},[1115,16377,1715],{"class":3741},[1115,16379,16323],{"class":3572},[1115,16381,7873],{"class":3741},[1115,16383,16384,16387,16389,16391,16393,16396,16398,16400,16402,16404,16406,16409,16411,16414,16416,16418,16420,16423,16425,16427],{"class":3563,"line":111},[1115,16385,16386],{"class":3572},"        43",[1115,16388,1715],{"class":3741},[1115,16390,16256],{"class":3572},[1115,16392,1715],{"class":3741},[1115,16394,16395],{"class":3572}," 42.9",[1115,16397,1715],{"class":3741},[1115,16399,16281],{"class":3572},[1115,16401,1715],{"class":3741},[1115,16403,16298],{"class":3572},[1115,16405,1715],{"class":3741},[1115,16407,16408],{"class":3572}," 42.2",[1115,16410,1715],{"class":3741},[1115,16412,16413],{"class":3572}," 39.2",[1115,16415,1715],{"class":3741},[1115,16417,16276],{"class":3572},[1115,16419,1715],{"class":3741},[1115,16421,16422],{"class":3572}," 41.6",[1115,16424,1715],{"class":3741},[1115,16426,16281],{"class":3572},[1115,16428,7873],{"class":3741},[1115,16430,16431,16434,16436,16438,16440,16443,16445,16447,16449,16452,16454,16457,16459,16462,16464,16466,16468,16471,16473,16475],{"class":3563,"line":96},[1115,16432,16433],{"class":3572},"        45",[1115,16435,1715],{"class":3741},[1115,16437,16261],{"class":3572},[1115,16439,1715],{"class":3741},[1115,16441,16442],{"class":3572}," 43.6",[1115,16444,1715],{"class":3741},[1115,16446,16266],{"class":3572},[1115,16448,1715],{"class":3741},[1115,16450,16451],{"class":3572}," 38.8",[1115,16453,1715],{"class":3741},[1115,16455,16456],{"class":3572}," 43",[1115,16458,1715],{"class":3741},[1115,16460,16461],{"class":3572}," 44.2",[1115,16463,1715],{"class":3741},[1115,16465,16456],{"class":3572},[1115,16467,1715],{"class":3741},[1115,16469,16470],{"class":3572}," 40",[1115,16472,1715],{"class":3741},[1115,16474,16352],{"class":3572},[1115,16476,3575],{"class":3569},[1115,16478,16479,16481,16483,16485],{"class":3563,"line":89},[1115,16480,15798],{"class":3566},[1115,16482,1168],{"class":3569},[1115,16484,16228],{"class":3744},[1115,16486,3575],{"class":3569},[1115,16488,16489,16491,16493,16495],{"class":3563,"line":82},[1115,16490,15809],{"class":3566},[1115,16492,1168],{"class":3569},[1115,16494,16228],{"class":3744},[1115,16496,3575],{"class":3569},[1115,16498,16499,16501,16503,16505],{"class":3563,"line":75},[1115,16500,15831],{"class":3566},[1115,16502,1168],{"class":3569},[1115,16504,16228],{"class":3744},[1115,16506,3575],{"class":3569},[1115,16508,16509,16511,16513,16515,16517,16519,16521,16523,16525],{"class":3563,"line":8025},[1115,16510,15390],{"class":3566},[1115,16512,1168],{"class":3569},[1115,16514,16228],{"class":3744},[1115,16516,3862],{"class":3569},[1115,16518,3865],{"class":3741},[1115,16520,15869],{"class":3566},[1115,16522,1168],{"class":3569},[1115,16524,16228],{"class":3744},[1115,16526,3575],{"class":3569},[1115,16528,16529,16532,16534,16536],{"class":3563,"line":72},[1115,16530,16531],{"class":3566},"median",[1115,16533,1168],{"class":3569},[1115,16535,16228],{"class":3744},[1115,16537,3575],{"class":3569},[3554,16539,16542],{"className":16540,"code":16541,"language":3603,"meta":3558},[3601],"[1] 50\n[1] 42.27\n[1] 1.48052\n[1] 6.2\n[1] 42.4\n",[1373,16543,16541],{"__ignoreMap":3558},[1110,16545,16546],{},"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.",[1431,16548,16550],{"id":16549},"empirická-distribuční-funkce","Empirická distribuční funkce",[1110,16552,16553,16554,16567,16568,1145,16571,16594,16595,16629],{},"Pro libovolný rozsah datového souboru, diskrétní i spojitou náhodnou veličinu ",[1115,16555,16557],{"className":16556},[1149],[1151,16558,16559],{"xmlns":1153},[1155,16560,16561,16565],{},[1158,16562,16563],{},[1161,16564,1185],{},[1194,16566,1185],{"encoding":1196},", lze sestrojit ",[1131,16569,16570],{},"empirickou distribuční funkci",[1115,16572,16574],{"className":16573},[1149],[1151,16575,16576],{"xmlns":1153},[1155,16577,16578,16592],{},[1158,16579,16580,16586,16588,16590],{},[1277,16581,16582,16584],{},[1161,16583,1163],{},[1161,16585,4192],{},[1165,16587,1168],{"stretchy":1167},[1161,16589,1171],{},[1165,16591,1174],{"stretchy":1167},[1194,16593,14854],{"encoding":1196},". Pro datový soubor ",[1115,16596,16598],{"className":16597},[1149],[1151,16599,16600],{"xmlns":1153},[1155,16601,16602,16626],{},[1158,16603,16604,16606,16612,16614,16616,16618,16624],{},[1165,16605,1168],{"stretchy":1167},[1277,16607,16608,16610],{},[1161,16609,1171],{},[1282,16611,1284],{},[1165,16613,1715],{"separator":1121},[1165,16615,1726],{},[1165,16617,1715],{"separator":1121},[1277,16619,16620,16622],{},[1161,16621,1171],{},[1161,16623,4192],{},[1165,16625,1174],{"stretchy":1167},[1194,16627,16628],{"encoding":1196},"(x_1,\\dots,x_n)"," je",[1115,16631,16633],{"className":16632},[1149],[1151,16634,16635],{"xmlns":1153,"display":2212},[1155,16636,16637,16661],{},[1158,16638,16639,16645,16647,16649,16651,16653,16659],{},[1277,16640,16641,16643],{},[1161,16642,1163],{},[1161,16644,4192],{},[1165,16646,1168],{"stretchy":1167},[1161,16648,1171],{},[1165,16650,1174],{"stretchy":1167},[1165,16652,1177],{},[3064,16654,16655,16657],{},[1161,16656,1735],{},[1161,16658,4192],{},[1165,16660,1715],{"separator":1121},[1194,16662,16663],{"encoding":1196},"F_n(x) = \\frac{k}{n},",[1110,16665,4767,16666,16679,16680,1333],{},[1115,16667,16669],{"className":16668},[1149],[1151,16670,16671],{"xmlns":1153},[1155,16672,16673,16677],{},[1158,16674,16675],{},[1161,16676,1735],{},[1194,16678,1735],{"encoding":1196}," je počet prvků datového souboru menších nebo rovných číslu ",[1115,16681,16683],{"className":16682},[1149],[1151,16684,16685],{"xmlns":1153},[1155,16686,16687,16691],{},[1158,16688,16689],{},[1161,16690,1171],{},[1194,16692,1171],{"encoding":1196},[1110,16694,3552],{},[3554,16696,16698],{"className":3556,"code":16697,"language":71,"meta":3558,"style":3558},"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",[1373,16699,16700,16715,16730,16748,16762],{"__ignoreMap":3558},[1115,16701,16702,16704,16706,16709,16711,16713],{"class":3563,"line":10},[1115,16703,1228],{"class":3744},[1115,16705,4497],{"class":3741},[1115,16707,16708],{"class":3566}," ecdf",[1115,16710,1168],{"class":3569},[1115,16712,1171],{"class":3744},[1115,16714,3575],{"class":3569},[1115,16716,16717,16720,16722,16724,16727],{"class":3563,"line":27},[1115,16718,16719],{"class":3566},"knots",[1115,16721,1168],{"class":3569},[1115,16723,1228],{"class":3744},[1115,16725,16726],{"class":3569},")        ",[1115,16728,16729],{"class":15704},"# vzestupně seřazené různé hodnoty datového souboru\n",[1115,16731,16732,16734,16736,16738,16740,16742,16745],{"class":3563,"line":148},[1115,16733,1228],{"class":3566},[1115,16735,1168],{"class":3569},[1115,16737,16719],{"class":3566},[1115,16739,1168],{"class":3569},[1115,16741,1228],{"class":3744},[1115,16743,16744],{"class":3569},"))      ",[1115,16746,16747],{"class":15704},"# hodnoty Fn(x) v těchto bodech\n",[1115,16749,16750,16752,16754,16756,16759],{"class":3563,"line":111},[1115,16751,1228],{"class":3566},[1115,16753,1168],{"class":3569},[1115,16755,7690],{"class":3572},[1115,16757,16758],{"class":3569},")            ",[1115,16760,16761],{"class":15704},"# Fn v libovolném bodě\n",[1115,16763,16764,16767,16769,16771],{"class":3563,"line":96},[1115,16765,16766],{"class":3566},"plot",[1115,16768,1168],{"class":3569},[1115,16770,1228],{"class":3744},[1115,16772,3575],{"class":3569},[3554,16774,16777],{"className":16775,"code":16776,"language":3603,"meta":3558},[3601],"[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",[1373,16778,16776],{"__ignoreMap":3558},[1110,16780,16781,16784,16785,16803,16804,16807,16808,16821,16822,1333],{},[1373,16782,16783],{},"knots()"," vrací jen různé hodnoty (opakující se hodnota 12,7 je ve výpočtu ",[1115,16786,16788],{"className":16787},[1149],[1151,16789,16790],{"xmlns":1153},[1155,16791,16792,16800],{},[1158,16793,16794],{},[1277,16795,16796,16798],{},[1161,16797,1163],{},[1161,16799,4192],{},[1194,16801,16802],{"encoding":1196},"F_n"," započtena třikrát, v seznamu uzlů je ale jen jednou); ",[1373,16805,16806],{},"plot(f)"," nakreslí schodovitý graf, který v každém uzlu skáče o ",[1115,16809,16811],{"className":16810},[1149],[1151,16812,16813],{"xmlns":1153},[1155,16814,16815,16819],{},[1158,16816,16817],{},[1161,16818,1735],{},[1194,16820,1735],{"encoding":1196},"-násobek ",[1115,16823,16825],{"className":16824},[1149],[1151,16826,16827],{"xmlns":1153},[1155,16828,16829,16837],{},[1158,16830,16831,16833,16835],{},[1282,16832,1284],{},[1161,16834,3434],{"mathvariant":1215},[1161,16836,4192],{},[1194,16838,16839],{"encoding":1196},"1\u002Fn",[1110,16841,16842],{},[1760,16843],{"alt":16844,"className":16845,"src":16846},"mask-ps-ecdf",[1441,1764],"\u002Fwiki-assets\u002Fmask-ps-ecdf.png",[1103,16848,16850,16857],{"className":16849,"dataCallout":3670},[1106,3669],[1110,16851,16853,16856],{"className":16852},[1113],[1115,16854],{"className":16855,"ariaHidden":1121},[1118,3677,1120],"Příklad: Empirická distribuční funkce",[1110,16858,16859],{},"Pro předchozí datový soubor (doba opravy součástky) určete empirickou distribuční funkci.",[1110,16861,16862,16863,1333],{},"Uspořádaný soubor je ",[1115,16864,16866],{"className":16865},[1149],[1151,16867,16868],{"xmlns":1153},[1155,16869,16870,16934],{},[1158,16871,16872,16875,16877,16879,16882,16884,16886,16889,16891,16893,16895,16897,16899,16901,16903,16905,16908,16910,16912,16915,16917,16919,16921,16923,16925,16927,16929,16931],{},[1282,16873,16874],{},"10,8",[1165,16876,1358],{"separator":1121},[2278,16878,14985],{},[1282,16880,16881],{},"11,1",[1165,16883,1358],{"separator":1121},[2278,16885,14985],{},[1282,16887,16888],{},"12,7",[1165,16890,1358],{"separator":1121},[2278,16892,14985],{},[1282,16894,16888],{},[1165,16896,1358],{"separator":1121},[2278,16898,14985],{},[1282,16900,16888],{},[1165,16902,1358],{"separator":1121},[2278,16904,14985],{},[1282,16906,16907],{},"13,2",[1165,16909,1358],{"separator":1121},[2278,16911,14985],{},[1282,16913,16914],{},"13,4",[1165,16916,1358],{"separator":1121},[2278,16918,14985],{},[1282,16920,16199],{},[1165,16922,1358],{"separator":1121},[2278,16924,14985],{},[1282,16926,16199],{},[1165,16928,1358],{"separator":1121},[2278,16930,14985],{},[1282,16932,16933],{},"14,7",[1194,16935,16936],{"encoding":1196},"10{,}8;\\ 11{,}1;\\ 12{,}7;\\ 12{,}7;\\ 12{,}7;\\ 13{,}2;\\ 13{,}4;\\ 14{,}4;\\ 14{,}4;\\ 14{,}7",[4052,16938,16939,16972],{},[4055,16940,16941],{},[4058,16942,16943,16958,16960,16962,16964,16966,16968,16970],{},[4061,16944,16945],{},[1115,16946,16948],{"className":16947},[1149],[1151,16949,16950],{"xmlns":1153},[1155,16951,16952,16956],{},[1158,16953,16954],{},[1161,16955,1171],{},[1194,16957,1171],{"encoding":1196},[4061,16959,16874],{},[4061,16961,16881],{},[4061,16963,16888],{},[4061,16965,16907],{},[4061,16967,16914],{},[4061,16969,16199],{},[4061,16971,16933],{},[4165,16973,16974,17006],{},[4058,16975,16976,16991,16993,16995,16997,16999,17002,17004],{},[4170,16977,16978],{},[1115,16979,16981],{"className":16980},[1149],[1151,16982,16983],{"xmlns":1153},[1155,16984,16985,16989],{},[1158,16986,16987],{},[1161,16988,1735],{},[1194,16990,1735],{"encoding":1196},[4170,16992,1284],{},[4170,16994,1298],{},[4170,16996,4455],{},[4170,16998,8094],{},[4170,17000,17001],{},"7",[4170,17003,7739],{},[4170,17005,3531],{},[4058,17007,17008,17033,17036,17039,17041,17044,17047,17050],{},[4170,17009,17010],{},[1115,17011,17013],{"className":17012},[1149],[1151,17014,17015],{"xmlns":1153},[1155,17016,17017,17031],{},[1158,17018,17019,17025,17027,17029],{},[1277,17020,17021,17023],{},[1161,17022,1163],{},[1161,17024,4192],{},[1165,17026,1168],{"stretchy":1167},[1161,17028,1171],{},[1165,17030,1174],{"stretchy":1167},[1194,17032,14854],{"encoding":1196},[4170,17034,17035],{},"0,1",[4170,17037,17038],{},"0,2",[4170,17040,2949],{},[4170,17042,17043],{},"0,6",[4170,17045,17046],{},"0,7",[4170,17048,17049],{},"0,9",[4170,17051,17052],{},"1,0",[1110,17054,17055,17056,17078,17079,17102],{},"Graf (levý panel výše) odpovídá tabulce: funkce je nulová pod 10,8, skáče o ",[1115,17057,17059],{"className":17058},[1149],[1151,17060,17061],{"xmlns":1153},[1155,17062,17063,17075],{},[1158,17064,17065,17067,17069,17071,17073],{},[1282,17066,1284],{},[1161,17068,3434],{"mathvariant":1215},[1161,17070,4192],{},[1165,17072,1177],{},[1282,17074,17035],{},[1194,17076,17077],{"encoding":1196},"1\u002Fn = 0{,}1"," v každé jednoduché hodnotě a o ",[1115,17080,17082],{"className":17081},[1149],[1151,17083,17084],{"xmlns":1153},[1155,17085,17086,17099],{},[1158,17087,17088,17090,17092,17094,17096],{},[1282,17089,3322],{},[1161,17091,3434],{"mathvariant":1215},[1161,17093,4192],{},[1165,17095,1177],{},[1282,17097,17098],{},"0,3",[1194,17100,17101],{"encoding":1196},"3\u002Fn = 0{,}3"," v bodě 12,7, kde se hodnota opakuje třikrát.",[1103,17104,17106,17113],{"className":17105,"dataCallout":3670},[1106,3669],[1110,17107,17109,17112],{"className":17108},[1113],[1115,17110],{"className":17111,"ariaHidden":1121},[1118,3677,1120],"Příklad: Odpad materiálu",[1110,17114,17115],{},"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.",[3554,17117,17119],{"className":3556,"code":17118,"language":71,"meta":3558,"style":3558},"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",[1373,17120,17121,17172,17182,17192,17202,17222,17232,17247,17257],{"__ignoreMap":3558},[1115,17122,17123,17126,17128,17130,17132,17134,17136,17138,17140,17142,17144,17146,17148,17150,17152,17154,17156,17158,17160,17162,17164,17166,17168,17170],{"class":3563,"line":10},[1115,17124,17125],{"class":3744},"x4",[1115,17127,4497],{"class":3741},[1115,17129,7969],{"class":3566},[1115,17131,1168],{"class":3569},[1115,17133,15657],{"class":3572},[1115,17135,1715],{"class":3741},[1115,17137,15662],{"class":3572},[1115,17139,1715],{"class":3741},[1115,17141,15667],{"class":3572},[1115,17143,1715],{"class":3741},[1115,17145,15672],{"class":3572},[1115,17147,1715],{"class":3741},[1115,17149,15667],{"class":3572},[1115,17151,1715],{"class":3741},[1115,17153,15667],{"class":3572},[1115,17155,1715],{"class":3741},[1115,17157,15685],{"class":3572},[1115,17159,1715],{"class":3741},[1115,17161,15690],{"class":3572},[1115,17163,1715],{"class":3741},[1115,17165,15662],{"class":3572},[1115,17167,1715],{"class":3741},[1115,17169,15662],{"class":3572},[1115,17171,3575],{"class":3569},[1115,17173,17174,17176,17178,17180],{"class":3563,"line":27},[1115,17175,15798],{"class":3566},[1115,17177,1168],{"class":3569},[1115,17179,17125],{"class":3744},[1115,17181,3575],{"class":3569},[1115,17183,17184,17186,17188,17190],{"class":3563,"line":148},[1115,17185,15809],{"class":3566},[1115,17187,1168],{"class":3569},[1115,17189,17125],{"class":3744},[1115,17191,3575],{"class":3569},[1115,17193,17194,17196,17198,17200],{"class":3563,"line":111},[1115,17195,15831],{"class":3566},[1115,17197,1168],{"class":3569},[1115,17199,17125],{"class":3744},[1115,17201,3575],{"class":3569},[1115,17203,17204,17206,17208,17210,17212,17214,17216,17218,17220],{"class":3563,"line":96},[1115,17205,15390],{"class":3566},[1115,17207,1168],{"class":3569},[1115,17209,17125],{"class":3744},[1115,17211,3862],{"class":3569},[1115,17213,3865],{"class":3741},[1115,17215,15869],{"class":3566},[1115,17217,1168],{"class":3569},[1115,17219,17125],{"class":3744},[1115,17221,3575],{"class":3569},[1115,17223,17224,17226,17228,17230],{"class":3563,"line":89},[1115,17225,16531],{"class":3566},[1115,17227,1168],{"class":3569},[1115,17229,17125],{"class":3744},[1115,17231,3575],{"class":3569},[1115,17233,17234,17237,17239,17241,17243,17245],{"class":3563,"line":82},[1115,17235,17236],{"class":3744},"f4",[1115,17238,4497],{"class":3741},[1115,17240,16708],{"class":3566},[1115,17242,1168],{"class":3569},[1115,17244,17125],{"class":3744},[1115,17246,3575],{"class":3569},[1115,17248,17249,17251,17253,17255],{"class":3563,"line":75},[1115,17250,16719],{"class":3566},[1115,17252,1168],{"class":3569},[1115,17254,17236],{"class":3744},[1115,17256,3575],{"class":3569},[1115,17258,17259,17261,17263,17265,17267,17269],{"class":3563,"line":8025},[1115,17260,17236],{"class":3566},[1115,17262,1168],{"class":3569},[1115,17264,16719],{"class":3566},[1115,17266,1168],{"class":3569},[1115,17268,17236],{"class":3744},[1115,17270,4011],{"class":3569},[3554,17272,17275],{"className":17273,"code":17274,"language":3603,"meta":3558},[3601],"[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",[1373,17276,17274],{"__ignoreMap":3558},[1110,17278,17279,17280,17303],{},"Průměrný odpad je 3,86 % se směrodatnou odchylkou 0,18 % a mediánem 3,85 %. Pravý panel obrázku výše ukazuje tvar ",[1115,17281,17283],{"className":17282},[1149],[1151,17284,17285],{"xmlns":1153},[1155,17286,17287,17301],{},[1158,17288,17289,17295,17297,17299],{},[1277,17290,17291,17293],{},[1161,17292,1163],{},[1161,17294,4192],{},[1165,17296,1168],{"stretchy":1167},[1161,17298,1171],{},[1165,17300,1174],{"stretchy":1167},[1194,17302,14854],{"encoding":1196},": hodnota 3,8 se v souboru opakuje třikrát, proto zde funkce skáče o 0,3 najednou, stejně jako hodnota 4,0.",[1431,17305,17307],{"id":17306},"třídění-datového-souboru-do-tříd","Třídění datového souboru do tříd",[1110,17309,17310,17311,17314,17315,17328,17329,17332],{},"Je-li rozsah datového souboru velký (řádově přes 30 až 50 pozorování), hodnoty se před dalším zpracováním ",[1131,17312,17313],{},"roztřídí",": variační rozpětí ",[1115,17316,17318],{"className":17317},[1149],[1151,17319,17320],{"xmlns":1153},[1155,17321,17322,17326],{},[1158,17323,17324],{},[1161,17325,4759],{},[1194,17327,4759],{"encoding":1196}," se rozdělí na určitý počet ",[1131,17330,17331],{},"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.",[1110,17334,17335],{},"Výsledkem je tabulka četností se sloupci:",[1124,17337,17338,17418,17439,17460],{},[1127,17339,17340,17358,17359,17372,17373,17417],{},[1115,17341,17343],{"className":17342},[1149],[1151,17344,17345],{"xmlns":1153},[1155,17346,17347,17355],{},[1158,17348,17349],{},[1277,17350,17351,17353],{},[1161,17352,14871],{},[1161,17354,6044],{},[1194,17356,17357],{"encoding":1196},"I_j"," — ",[1115,17360,17362],{"className":17361},[1149],[1151,17363,17364],{"xmlns":1153},[1155,17365,17366,17370],{},[1158,17367,17368],{},[1161,17369,6044],{},[1194,17371,6044],{"encoding":1196},"-tý interval (v této kapitole vždy zleva uzavřený a zprava otevřený, ",[1115,17374,17376],{"className":17375},[1149],[1151,17377,17378],{"xmlns":1153},[1155,17379,17380,17414],{},[1158,17381,17382,17388,17390,17392,17398,17400,17412],{},[1277,17383,17384,17386],{},[1161,17385,14871],{},[1161,17387,6044],{},[1165,17389,1177],{},[1165,17391,2917],{"stretchy":1167},[1277,17393,17394,17396],{},[1161,17395,7856],{},[1161,17397,6044],{},[1165,17399,1358],{"separator":1121},[1277,17401,17402,17404],{},[1161,17403,7856],{},[1158,17405,17406,17408,17410],{},[1161,17407,6044],{},[1165,17409,2094],{},[1282,17411,1284],{},[1165,17413,1174],{"stretchy":1167},[1194,17415,17416],{"encoding":1196},"I_j = \\langle c_j; c_{j+1})","),",[1127,17419,17420,17438],{},[1115,17421,17423],{"className":17422},[1149],[1151,17424,17425],{"xmlns":1153},[1155,17426,17427,17435],{},[1158,17428,17429],{},[1277,17430,17431,17433],{},[1161,17432,3419],{},[1161,17434,6044],{},[1194,17436,17437],{"encoding":1196},"Z_j"," — střed (reprezentant) intervalu,",[1127,17440,17441,17459],{},[1115,17442,17444],{"className":17443},[1149],[1151,17445,17446],{"xmlns":1153},[1155,17447,17448,17456],{},[1158,17449,17450],{},[1277,17451,17452,17454],{},[1161,17453,1228],{},[1161,17455,6044],{},[1194,17457,17458],{"encoding":1196},"f_j"," — četnost, počet hodnot v intervalu,",[1127,17461,17462,17492,17493,1425,17521,1333],{},[1115,17463,17465],{"className":17464},[1149],[1151,17466,17467],{"xmlns":1153},[1155,17468,17469,17489],{},[1158,17470,17471,17477,17479,17485,17487],{},[1277,17472,17473,17475],{},[1161,17474,1110],{},[1161,17476,6044],{},[1165,17478,1177],{},[1277,17480,17481,17483],{},[1161,17482,1228],{},[1161,17484,6044],{},[1161,17486,3434],{"mathvariant":1215},[1161,17488,4192],{},[1194,17490,17491],{"encoding":1196},"p_j = f_j\u002Fn"," — relativní četnost, přičemž ",[1115,17494,17496],{"className":17495},[1149],[1151,17497,17498],{"xmlns":1153},[1155,17499,17500,17518],{},[1158,17501,17502,17508,17514,17516],{},[1277,17503,17504,17506],{},[1165,17505,6144],{},[1161,17507,6044],{},[1277,17509,17510,17512],{},[1161,17511,1228],{},[1161,17513,6044],{},[1165,17515,1177],{},[1161,17517,4192],{},[1194,17519,17520],{"encoding":1196},"\\sum_j f_j = n",[1115,17522,17524],{"className":17523},[1149],[1151,17525,17526],{"xmlns":1153},[1155,17527,17528,17546],{},[1158,17529,17530,17536,17542,17544],{},[1277,17531,17532,17534],{},[1165,17533,6144],{},[1161,17535,6044],{},[1277,17537,17538,17540],{},[1161,17539,1110],{},[1161,17541,6044],{},[1165,17543,1177],{},[1282,17545,1284],{},[1194,17547,17548],{"encoding":1196},"\\sum_j p_j = 1",[1110,17550,17551,17552,17555,17556,17559,17560,17563,17564,17567,17568,8728,17571,17588,17589,17592,17593,8728,17596,5976,17613,17616],{},"V R se třídění provádí příkazem ",[1373,17553,17554],{},"hist()"," — buď necháme R zvolit třídy samo (",[1373,17557,17558],{},"hist(x)","), nebo zadáme hranice přímo (",[1373,17561,17562],{},"hist(x, br = seq(0, 550, by = 50))","). Uložením výsledku do proměnné (",[1373,17565,17566],{},"y \u003C- hist(...)",") získáme jednotlivé sloupce tabulky: ",[1373,17569,17570],{},"y$counts",[1115,17572,17574],{"className":17573},[1149],[1151,17575,17576],{"xmlns":1153},[1155,17577,17578,17586],{},[1158,17579,17580],{},[1277,17581,17582,17584],{},[1161,17583,1228],{},[1161,17585,6044],{},[1194,17587,17458],{"encoding":1196},"), ",[1373,17590,17591],{},"y$breaks"," (hranice tříd), ",[1373,17594,17595],{},"y$mids",[1115,17597,17599],{"className":17598},[1149],[1151,17600,17601],{"xmlns":1153},[1155,17602,17603,17611],{},[1158,17604,17605],{},[1277,17606,17607,17609],{},[1161,17608,3419],{},[1161,17610,6044],{},[1194,17612,17437],{"encoding":1196},[1373,17614,17615],{},"y$density"," (relativní četnosti na škále hustoty).",[1110,17618,17619,17620,17637,17638,17640,17641,17677,17678,17681,17682,1333],{},"Interval ",[1115,17621,17623],{"className":17622},[1149],[1151,17624,17625],{"xmlns":1153},[1155,17626,17627,17635],{},[1158,17628,17629],{},[1277,17630,17631,17633],{},[1161,17632,14871],{},[1161,17634,6044],{},[1194,17636,17357],{"encoding":1196}," je ve výchozím nastavení ",[1373,17639,17554],{}," zleva otevřený a zprava uzavřený, ",[1115,17642,17644],{"className":17643},[1149],[1151,17645,17646],{"xmlns":1153},[1155,17647,17648,17674],{},[1158,17649,17650,17652,17658,17660,17672],{},[1165,17651,1168],{"stretchy":1167},[1277,17653,17654,17656],{},[1161,17655,7856],{},[1161,17657,6044],{},[1165,17659,1358],{"separator":1121},[1277,17661,17662,17664],{},[1161,17663,7856],{},[1158,17665,17666,17668,17670],{},[1161,17667,6044],{},[1165,17669,2094],{},[1282,17671,1284],{},[1165,17673,1921],{"stretchy":1167},[1194,17675,17676],{"encoding":1196},"(c_j; c_{j+1}\\rangle"," — opačně, než jak třídy zapisujeme v této kapitole. Parametr ",[1373,17679,17680],{},"right = FALSE"," třídy obrátí na ",[1115,17683,17685],{"className":17684},[1149],[1151,17686,17687],{"xmlns":1153},[1155,17688,17689,17715],{},[1158,17690,17691,17693,17699,17701,17713],{},[1165,17692,2917],{"stretchy":1167},[1277,17694,17695,17697],{},[1161,17696,7856],{},[1161,17698,6044],{},[1165,17700,1358],{"separator":1121},[1277,17702,17703,17705],{},[1161,17704,7856],{},[1158,17706,17707,17709,17711],{},[1161,17708,6044],{},[1165,17710,2094],{},[1282,17712,1284],{},[1165,17714,1174],{"stretchy":1167},[1194,17716,17717],{"encoding":1196},"\\langle c_j; c_{j+1})",[1110,17719,17720],{},[1760,17721],{"alt":17722,"className":17723,"src":17724},"mask-ps-histogram-trideni",[1441,1764],"\u002Fwiki-assets\u002Fmask-ps-histogram-trideni.png",[1103,17726,17728,17735],{"className":17727,"dataCallout":3670},[1106,3669],[1110,17729,17731,17734],{"className":17730},[1113],[1115,17732],{"className":17733,"ariaHidden":1121},[1118,3677,1120],"Příklad: Třídění datového souboru",[1110,17736,17737],{},"Byly provedeny zkoušky životnosti nového výrobku. Datový soubor obsahuje 68 hodnot doby do poruchy (v minutách). Určete odhady charakteristik a zákona rozdělení.",[3554,17739,17741],{"className":3556,"code":17740,"language":71,"meta":3558,"style":3558},"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",[1373,17742,17743,17800,17851,17901,17952,18002,18050,18090,18100,18120,18184,18193,18223],{"__ignoreMap":3558},[1115,17744,17745,17748,17750,17752,17754,17757,17759,17762,17764,17767,17769,17772,17774,17776,17778,17780,17782,17784,17786,17789,17791,17793,17795,17798],{"class":3563,"line":10},[1115,17746,17747],{"class":3744},"x9",[1115,17749,4497],{"class":3741},[1115,17751,7969],{"class":3566},[1115,17753,1168],{"class":3569},[1115,17755,17756],{"class":3572},"101",[1115,17758,1715],{"class":3741},[1115,17760,17761],{"class":3572}," 338",[1115,17763,1715],{"class":3741},[1115,17765,17766],{"class":3572}," 150",[1115,17768,1715],{"class":3741},[1115,17770,17771],{"class":3572}," 47",[1115,17773,1715],{"class":3741},[1115,17775,3994],{"class":3572},[1115,17777,1715],{"class":3741},[1115,17779,8310],{"class":3572},[1115,17781,1715],{"class":3741},[1115,17783,7870],{"class":3572},[1115,17785,1715],{"class":3741},[1115,17787,17788],{"class":3572}," 392",[1115,17790,1715],{"class":3741},[1115,17792,4524],{"class":3572},[1115,17794,1715],{"class":3741},[1115,17796,17797],{"class":3572}," 73",[1115,17799,7873],{"class":3741},[1115,17801,17802,17805,17807,17810,17812,17815,17817,17820,17822,17824,17826,17829,17831,17834,17836,17839,17841,17844,17846,17849],{"class":3563,"line":27},[1115,17803,17804],{"class":3572},"        367",[1115,17806,1715],{"class":3741},[1115,17808,17809],{"class":3572}," 54",[1115,17811,1715],{"class":3741},[1115,17813,17814],{"class":3572}," 114",[1115,17816,1715],{"class":3741},[1115,17818,17819],{"class":3572}," 213",[1115,17821,1715],{"class":3741},[1115,17823,7888],{"class":3572},[1115,17825,1715],{"class":3741},[1115,17827,17828],{"class":3572}," 341",[1115,17830,1715],{"class":3741},[1115,17832,17833],{"class":3572}," 313",[1115,17835,1715],{"class":3741},[1115,17837,17838],{"class":3572}," 112",[1115,17840,1715],{"class":3741},[1115,17842,17843],{"class":3572}," 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88",[1115,17951,7873],{"class":3741},[1115,17953,17954,17957,17959,17962,17964,17967,17969,17972,17974,17977,17979,17981,17983,17986,17988,17990,17992,17995,17997,18000],{"class":3563,"line":96},[1115,17955,17956],{"class":3572},"        74",[1115,17958,1715],{"class":3741},[1115,17960,17961],{"class":3572}," 46",[1115,17963,1715],{"class":3741},[1115,17965,17966],{"class":3572}," 246",[1115,17968,1715],{"class":3741},[1115,17970,17971],{"class":3572}," 259",[1115,17973,1715],{"class":3741},[1115,17975,17976],{"class":3572}," 19",[1115,17978,1715],{"class":3741},[1115,17980,17893],{"class":3572},[1115,17982,1715],{"class":3741},[1115,17984,17985],{"class":3572}," 48",[1115,17987,1715],{"class":3741},[1115,17989,5393],{"class":3572},[1115,17991,1715],{"class":3741},[1115,17993,17994],{"class":3572}," 163",[1115,17996,1715],{"class":3741},[1115,17998,17999],{"class":3572}," 179",[1115,18001,7873],{"class":3741},[1115,18003,18004,18007,18009,18011,18013,18016,18018,18021,18023,18026,18028,18030,18032,18034,18036,18038,18040,18043,18045,18048],{"class":3563,"line":89},[1115,18005,18006],{"class":3572},"        194",[1115,18008,1715],{"class":3741},[1115,18010,8275],{"class":3572},[1115,18012,1715],{"class":3741},[1115,18014,18015],{"class":3572}," 49",[1115,18017,1715],{"class":3741},[1115,18019,18020],{"class":3572}," 501",[1115,18022,1715],{"class":3741},[1115,18024,18025],{"class":3572}," 193",[1115,18027,1715],{"class":3741},[1115,18029,17976],{"class":3572},[1115,18031,1715],{"class":3741},[1115,18033,4524],{"class":3572},[1115,18035,1715],{"class":3741},[1115,18037,8310],{"class":3572},[1115,18039,1715],{"class":3741},[1115,18041,18042],{"class":3572}," 221",[1115,18044,1715],{"class":3741},[1115,18046,18047],{"class":3572}," 300",[1115,18049,7873],{"class":3741},[1115,18051,18052,18055,18057,18059,18061,18064,18066,18069,18071,18074,18076,18079,18081,18083,18085,18088],{"class":3563,"line":82},[1115,18053,18054],{"class":3572},"        88",[1115,18056,1715],{"class":3741},[1115,18058,7865],{"class":3572},[1115,18060,1715],{"class":3741},[1115,18062,18063],{"class":3572}," 428",[1115,18065,1715],{"class":3741},[1115,18067,18068],{"class":3572}," 249",[1115,18070,1715],{"class":3741},[1115,18072,18073],{"class":3572}," 25",[1115,18075,1715],{"class":3741},[1115,18077,18078],{"class":3572}," 209",[1115,18080,1715],{"class":3741},[1115,18082,17809],{"class":3572},[1115,18084,1715],{"class":3741},[1115,18086,18087],{"class":3572}," 91",[1115,18089,3575],{"class":3569},[1115,18091,18092,18094,18096,18098],{"class":3563,"line":75},[1115,18093,15798],{"class":3566},[1115,18095,1168],{"class":3569},[1115,18097,17747],{"class":3744},[1115,18099,3575],{"class":3569},[1115,18101,18102,18104,18106,18108,18110,18112,18114,18116,18118],{"class":3563,"line":8025},[1115,18103,15390],{"class":3566},[1115,18105,1168],{"class":3569},[1115,18107,17747],{"class":3744},[1115,18109,3862],{"class":3569},[1115,18111,3865],{"class":3741},[1115,18113,15869],{"class":3566},[1115,18115,1168],{"class":3569},[1115,18117,17747],{"class":3744},[1115,18119,3575],{"class":3569},[1115,18121,18122,18125,18127,18130,18132,18134,18136,18139,18141,18144,18146,18148,18150,18153,18155,18158,18160,18162,18164,18166,18169,18171,18173,18175,18178,18180,18182],{"class":3563,"line":72},[1115,18123,18124],{"class":3744},"y9",[1115,18126,4497],{"class":3741},[1115,18128,18129],{"class":3566}," hist",[1115,18131,1168],{"class":3569},[1115,18133,17747],{"class":3744},[1115,18135,1715],{"class":3741},[1115,18137,18138],{"class":3744}," br",[1115,18140,3748],{"class":3741},[1115,18142,18143],{"class":3566}," seq",[1115,18145,1168],{"class":3569},[1115,18147,1982],{"class":3572},[1115,18149,1715],{"class":3741},[1115,18151,18152],{"class":3572}," 550",[1115,18154,1715],{"class":3741},[1115,18156,18157],{"class":3744}," by",[1115,18159,3748],{"class":3741},[1115,18161,10362],{"class":3572},[1115,18163,1174],{"class":3569},[1115,18165,1715],{"class":3741},[1115,18167,18168],{"class":3744}," right",[1115,18170,3748],{"class":3741},[1115,18172,10455],{"class":3572},[1115,18174,1715],{"class":3741},[1115,18176,18177],{"class":3744}," plot",[1115,18179,3748],{"class":3741},[1115,18181,10455],{"class":3572},[1115,18183,3575],{"class":3569},[1115,18185,18186,18188,18190],{"class":3563,"line":25},[1115,18187,18124],{"class":3744},[1115,18189,8047],{"class":3741},[1115,18191,18192],{"class":3744},"counts\n",[1115,18194,18195,18197,18199,18201,18203,18206,18208,18211,18213,18215,18217,18219,18221],{"class":3563,"line":65},[1115,18196,4510],{"class":3566},[1115,18198,1168],{"class":3569},[1115,18200,18124],{"class":3744},[1115,18202,8047],{"class":3741},[1115,18204,18205],{"class":3744},"counts",[1115,18207,4608],{"class":3741},[1115,18209,18210],{"class":3566}," length",[1115,18212,1168],{"class":3569},[1115,18214,17747],{"class":3744},[1115,18216,1174],{"class":3569},[1115,18218,1715],{"class":3741},[1115,18220,5393],{"class":3572},[1115,18222,3575],{"class":3569},[1115,18224,18225,18227,18229,18231,18233,18235,18237,18239],{"class":3563,"line":63},[1115,18226,15809],{"class":3566},[1115,18228,1168],{"class":3569},[1115,18230,17747],{"class":3744},[1115,18232,15848],{"class":3569},[1115,18234,15831],{"class":3566},[1115,18236,1168],{"class":3569},[1115,18238,17747],{"class":3744},[1115,18240,3575],{"class":3569},[3554,18242,18245],{"className":18243,"code":18244,"language":3603,"meta":3558},[3601],"[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",[1373,18246,18244],{"__ignoreMap":3558},[1110,18248,18249,18250,18278],{},"Variační rozpětí je ",[1115,18251,18253],{"className":18252},[1149],[1151,18254,18255],{"xmlns":1153},[1155,18256,18257,18275],{},[1158,18258,18259,18261,18263,18266,18268,18270,18272],{},[1161,18260,4759],{},[1165,18262,1177],{},[1282,18264,18265],{},"501",[1165,18267,1317],{},[1282,18269,1298],{},[1165,18271,1177],{},[1282,18273,18274],{},"499",[1194,18276,18277],{"encoding":1196},"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:",[4052,18280,18281,18377],{},[4055,18282,18283],{},[4058,18284,18285,18300,18319,18338,18357],{},[4061,18286,18287],{},[1115,18288,18290],{"className":18289},[1149],[1151,18291,18292],{"xmlns":1153},[1155,18293,18294,18298],{},[1158,18295,18296],{},[1161,18297,6044],{},[1194,18299,6044],{"encoding":1196},[4061,18301,18302],{},[1115,18303,18305],{"className":18304},[1149],[1151,18306,18307],{"xmlns":1153},[1155,18308,18309,18317],{},[1158,18310,18311],{},[1277,18312,18313,18315],{},[1161,18314,14871],{},[1161,18316,6044],{},[1194,18318,17357],{"encoding":1196},[4061,18320,18321],{},[1115,18322,18324],{"className":18323},[1149],[1151,18325,18326],{"xmlns":1153},[1155,18327,18328,18336],{},[1158,18329,18330],{},[1277,18331,18332,18334],{},[1161,18333,3419],{},[1161,18335,6044],{},[1194,18337,17437],{"encoding":1196},[4061,18339,18340],{},[1115,18341,18343],{"className":18342},[1149],[1151,18344,18345],{"xmlns":1153},[1155,18346,18347,18355],{},[1158,18348,18349],{},[1277,18350,18351,18353],{},[1161,18352,1228],{},[1161,18354,6044],{},[1194,18356,17458],{"encoding":1196},[4061,18358,18359],{},[1115,18360,18362],{"className":18361},[1149],[1151,18363,18364],{"xmlns":1153},[1155,18365,18366,18374],{},[1158,18367,18368],{},[1277,18369,18370,18372],{},[1161,18371,1110],{},[1161,18373,6044],{},[1194,18375,18376],{"encoding":1196},"p_j",[4165,18378,18379,18394,18409,18424,18437,18452,18467,18481,18496,18510,18525],{},[4058,18380,18381,18383,18386,18388,18391],{},[4170,18382,1284],{},[4170,18384,18385],{},"⟨0; 50)",[4170,18387,8188],{},[4170,18389,18390],{},"19",[4170,18392,18393],{},"0,279",[4058,18395,18396,18398,18401,18404,18406],{},[4170,18397,1298],{},[4170,18399,18400],{},"⟨50; 100)",[4170,18402,18403],{},"75",[4170,18405,6408],{},[4170,18407,18408],{},"0,162",[4058,18410,18411,18413,18416,18419,18421],{},[4170,18412,3322],{},[4170,18414,18415],{},"⟨100; 150)",[4170,18417,18418],{},"125",[4170,18420,3531],{},[4170,18422,18423],{},"0,147",[4058,18425,18426,18428,18431,18433,18435],{},[4170,18427,7687],{},[4170,18429,18430],{},"⟨150; 200)",[4170,18432,1957],{},[4170,18434,3531],{},[4170,18436,18423],{},[4058,18438,18439,18441,18444,18447,18449],{},[4170,18440,4455],{},[4170,18442,18443],{},"⟨200; 250)",[4170,18445,18446],{},"225",[4170,18448,4455],{},[4170,18450,18451],{},"0,074",[4058,18453,18454,18456,18459,18462,18464],{},[4170,18455,8094],{},[4170,18457,18458],{},"⟨250; 300)",[4170,18460,18461],{},"275",[4170,18463,1284],{},[4170,18465,18466],{},"0,015",[4058,18468,18469,18471,18474,18477,18479],{},[4170,18470,17001],{},[4170,18472,18473],{},"⟨300; 350)",[4170,18475,18476],{},"325",[4170,18478,4455],{},[4170,18480,18451],{},[4058,18482,18483,18486,18489,18492,18494],{},[4170,18484,18485],{},"8",[4170,18487,18488],{},"⟨350; 400)",[4170,18490,18491],{},"375",[4170,18493,4455],{},[4170,18495,18451],{},[4058,18497,18498,18500,18503,18506,18508],{},[4170,18499,7739],{},[4170,18501,18502],{},"⟨400; 450)",[4170,18504,18505],{},"425",[4170,18507,1284],{},[4170,18509,18466],{},[4058,18511,18512,18514,18517,18520,18522],{},[4170,18513,3531],{},[4170,18515,18516],{},"⟨450; 500)",[4170,18518,18519],{},"475",[4170,18521,1982],{},[4170,18523,18524],{},"0,000",[4058,18526,18527,18529,18532,18535,18537],{},[4170,18528,6408],{},[4170,18530,18531],{},"⟨500; ∞)",[4170,18533,18534],{},"525",[4170,18536,1284],{},[4170,18538,18466],{},[1110,18540,18541,18542,18559,18560,18577,18578,1376,18601,1376,18629,18648,18649,1376,18672,18691],{},"Asi 27,9 % výrobků vydrželo méně než 50 minut, jen asi 1,5 % mezi 250 a 300 minutami. Charakteristiky spočtené ze středů tříd ",[1115,18543,18545],{"className":18544},[1149],[1151,18546,18547],{"xmlns":1153},[1155,18548,18549,18557],{},[1158,18550,18551],{},[1277,18552,18553,18555],{},[1161,18554,3419],{},[1161,18556,6044],{},[1194,18558,17437],{"encoding":1196}," (vážený průměr a rozptyl se střední hodnotou nahrazenou ",[1115,18561,18563],{"className":18562},[1149],[1151,18564,18565],{"xmlns":1153},[1155,18566,18567,18575],{},[1158,18568,18569],{},[1277,18570,18571,18573],{},[1161,18572,3419],{},[1161,18574,6044],{},[1194,18576,17437],{"encoding":1196},") vycházejí ",[1115,18579,18581],{"className":18580},[1149],[1151,18582,18583],{"xmlns":1153},[1155,18584,18585,18598],{},[1158,18586,18587,18593,18595],{},[6877,18588,18589,18591],{"accent":1121},[1161,18590,1171],{},[1165,18592,15130],{},[1165,18594,3957],{},[1282,18596,18597],{},"149,26",[1194,18599,18600],{"encoding":1196},"\\bar{x} \\approx 149{,}26",[1115,18602,18604],{"className":18603},[1149],[1151,18605,18606],{"xmlns":1153},[1155,18607,18608,18626],{},[1158,18609,18610,18616,18618,18621,18623],{},[1209,18611,18612,18614],{},[1161,18613,6018],{},[1282,18615,1298],{},[1165,18617,3957],{},[1282,18619,18620],{},"15",[2278,18622,2280],{},[1282,18624,18625],{},"484,5",[1194,18627,18628],{"encoding":1196},"s^2 \\approx 15\\,484{,}5",[1115,18630,18632],{"className":18631},[1149],[1151,18633,18634],{"xmlns":1153},[1155,18635,18636,18645],{},[1158,18637,18638,18640,18642],{},[1161,18639,6018],{},[1165,18641,3957],{},[1282,18643,18644],{},"124,44",[1194,18646,18647],{"encoding":1196},"s \\approx 124{,}44"," — blízko hodnotám ",[1115,18650,18652],{"className":18651},[1149],[1151,18653,18654],{"xmlns":1153},[1155,18655,18656,18669],{},[1158,18657,18658,18664,18666],{},[6877,18659,18660,18662],{"accent":1121},[1161,18661,1171],{},[1165,18663,15130],{},[1165,18665,1177],{},[1282,18667,18668],{},"145,44",[1194,18670,18671],{"encoding":1196},"\\bar{x}=145{,}44",[1115,18673,18675],{"className":18674},[1149],[1151,18676,18677],{"xmlns":1153},[1155,18678,18679,18688],{},[1158,18680,18681,18683,18685],{},[1161,18682,6018],{},[1165,18684,1177],{},[1282,18686,18687],{},"126,13",[1194,18689,18690],{"encoding":1196},"s=126{,}13"," spočteným přímo z nerozdělených dat; malý rozdíl vzniká tím, že třídění nahrazuje skutečné hodnoty středy tříd.",[1110,18693,18694,18695,18698,18699,18735,18736,18754,18755,18769,18770,18796,18797,18799,18800,8985],{},"Tvar histogramu — vysoká četnost u krátkých dob, rychlý pokles — odpovídá ",[1131,18696,18697],{},"exponenciálnímu rozdělení",", které se pro dobu do poruchy používá nejčastěji. Jeho hustota je ",[1115,18700,18702],{"className":18701},[1149],[1151,18703,18704],{"xmlns":1153},[1155,18705,18706,18732],{},[1158,18707,18708,18710,18712,18714,18716,18718,18720],{},[1161,18709,1228],{},[1165,18711,1168],{"stretchy":1167},[1161,18713,1171],{},[1165,18715,1174],{"stretchy":1167},[1165,18717,1177],{},[1161,18719,4240],{},[1209,18721,18722,18724],{},[1161,18723,3085],{},[1158,18725,18726,18728,18730],{},[1165,18727,1317],{},[1161,18729,4240],{},[1161,18731,1171],{},[1194,18733,18734],{"encoding":1196},"f(x) = \\lambda e^{-\\lambda x}"," pro ",[1115,18737,18739],{"className":18738},[1149],[1151,18740,18741],{"xmlns":1153},[1155,18742,18743,18751],{},[1158,18744,18745,18747,18749],{},[1161,18746,1171],{},[1165,18748,7501],{},[1282,18750,1982],{},[1194,18752,18753],{"encoding":1196},"x \\ge 0",", s parametrem ",[1115,18756,18758],{"className":18757},[1149],[1151,18759,18760],{"xmlns":1153},[1155,18761,18762,18766],{},[1158,18763,18764],{},[1161,18765,4240],{},[1194,18767,18768],{"encoding":1196},"\\lambda"," odhadnutým jako ",[1115,18771,18773],{"className":18772},[1149],[1151,18774,18775],{"xmlns":1153},[1155,18776,18777,18793],{},[1158,18778,18779,18781,18783,18785,18787],{},[1161,18780,4240],{},[1165,18782,1177],{},[1282,18784,1284],{},[1161,18786,3434],{"mathvariant":1215},[6877,18788,18789,18791],{"accent":1121},[1161,18790,1171],{},[1165,18792,15130],{},[1194,18794,18795],{"encoding":1196},"\\lambda = 1\u002F\\bar{x}"," (v R je ",[1373,18798,4408],{}," parametrem ",[1373,18801,18802],{},"dexp()",[3554,18804,18806],{"className":3556,"code":18805,"language":71,"meta":3558,"style":3558},"rate9 \u003C- 1 \u002F mean(x9)\nrate9\n",[1373,18807,18808,18827],{"__ignoreMap":3558},[1115,18809,18810,18813,18815,18817,18819,18821,18823,18825],{"class":3563,"line":10},[1115,18811,18812],{"class":3744},"rate9",[1115,18814,4497],{"class":3741},[1115,18816,4605],{"class":3572},[1115,18818,4608],{"class":3741},[1115,18820,3745],{"class":3566},[1115,18822,1168],{"class":3569},[1115,18824,17747],{"class":3744},[1115,18826,3575],{"class":3569},[1115,18828,18829],{"class":3563,"line":27},[1115,18830,18831],{"class":3744},"rate9\n",[3554,18833,18836],{"className":18834,"code":18835,"language":3603,"meta":3558},[3601],"[1] 0.006875632\n",[1373,18837,18835],{"__ignoreMap":3558},[1110,18839,18840],{},[1760,18841],{"alt":18842,"className":18843,"src":18844},"mask-ps-hustota-fit",[1441,1764],"\u002Fwiki-assets\u002Fmask-ps-hustota-fit.png",[1110,18846,18847,18848,1333],{},"Proložená křivka dobře sleduje tvar sloupců. Zda data odpovídají exponenciálnímu rozdělení formálně, posuzuje test dobré shody popsaný v ",[1438,18849,10719],{"className":18850,"dataFsResolvedFilePath":4636,"href":4637},[1441],[1103,18852,18854,18861],{"className":18853,"dataCallout":3670},[1106,3669],[1110,18855,18857,18860],{"className":18856},[1113],[1115,18858],{"className":18859,"ariaHidden":1121},[1118,3677,1120],"Příklad: Doba života výrobku",[1110,18862,18863],{},"Sledováním doby života výrobku bylo naměřeno 50 hodnot (v minutách). Určete empirické charakteristiky, roztřiďte datový soubor a nakreslete histogram četností.",[3554,18865,18867],{"className":3556,"code":18866,"language":71,"meta":3558,"style":3558},"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",[1373,18868,18869,18930,18981,19032,19083,19135,19145,19171,19191,19249,19258,19266],{"__ignoreMap":3558},[1115,18870,18871,18874,18876,18878,18880,18883,18885,18888,18890,18893,18895,18898,18900,18903,18905,18908,18910,18913,18915,18918,18920,18923,18925,18928],{"class":3563,"line":10},[1115,18872,18873],{"class":3744},"x5",[1115,18875,4497],{"class":3741},[1115,18877,7969],{"class":3566},[1115,18879,1168],{"class":3569},[1115,18881,18882],{"class":3572},"63",[1115,18884,1715],{"class":3741},[1115,18886,18887],{"class":3572}," 156",[1115,18889,1715],{"class":3741},[1115,18891,18892],{"class":3572}," 184",[1115,18894,1715],{"class":3741},[1115,18896,18897],{"class":3572}," 786",[1115,18899,1715],{"class":3741},[1115,18901,18902],{"class":3572}," 822",[1115,18904,1715],{"class":3741},[1115,18906,18907],{"class":3572}," 278",[1115,18909,1715],{"class":3741},[1115,18911,18912],{"class":3572}," 15",[1115,18914,1715],{"class":3741},[1115,18916,18917],{"class":3572}," 561",[1115,18919,1715],{"class":3741},[1115,18921,18922],{"class":3572}," 229",[1115,18924,1715],{"class":3741},[1115,18926,18927],{"class":3572}," 8",[1115,18929,7873],{"class":3741},[1115,18931,18932,18935,18937,18940,18942,18944,18946,18949,18951,18954,18956,18959,18961,18964,18966,18969,18971,18974,18976,18979],{"class":3563,"line":27},[1115,18933,18934],{"class":3572},"        4",[1115,18936,1715],{"class":3741},[1115,18938,18939],{"class":3572}," 35",[1115,18941,1715],{"class":3741},[1115,18943,17797],{"class":3572},[1115,18945,1715],{"class":3741},[1115,18947,18948],{"class":3572}," 203",[1115,18950,1715],{"class":3741},[1115,18952,18953],{"class":3572}," 178",[1115,18955,1715],{"class":3741},[1115,18957,18958],{"class":3572}," 323",[1115,18960,1715],{"class":3741},[1115,18962,18963],{"class":3572}," 275",[1115,18965,1715],{"class":3741},[1115,18967,18968],{"class":3572}," 176",[1115,18970,1715],{"class":3741},[1115,18972,18973],{"class":3572}," 427",[1115,18975,1715],{"class":3741},[1115,18977,18978],{"class":3572}," 196",[1115,18980,7873],{"class":3741},[1115,18982,18983,18986,18988,18991,18993,18996,18998,19001,19003,19006,19008,19011,19013,19016,19018,19020,19022,19025,19027,19030],{"class":3563,"line":148},[1115,18984,18985],{"class":3572},"        415",[1115,18987,1715],{"class":3741},[1115,18989,18990],{"class":3572}," 140",[1115,18992,1715],{"class":3741},[1115,18994,18995],{"class":3572}," 17",[1115,18997,1715],{"class":3741},[1115,18999,19000],{"class":3572}," 293",[1115,19002,1715],{"class":3741},[1115,19004,19005],{"class":3572}," 991",[1115,19007,1715],{"class":3741},[1115,19009,19010],{"class":3572}," 100",[1115,19012,1715],{"class":3741},[1115,19014,19015],{"class":3572}," 189",[1115,19017,1715],{"class":3741},[1115,19019,18968],{"class":3572},[1115,19021,1715],{"class":3741},[1115,19023,19024],{"class":3572}," 672",[1115,19026,1715],{"class":3741},[1115,19028,19029],{"class":3572}," 134",[1115,19031,7873],{"class":3741},[1115,19033,19034,19037,19039,19042,19044,19047,19049,19052,19054,19056,19058,19061,19063,19066,19068,19071,19073,19076,19078,19081],{"class":3563,"line":111},[1115,19035,19036],{"class":3572},"        529",[1115,19038,1715],{"class":3741},[1115,19040,19041],{"class":3572}," 310",[1115,19043,1715],{"class":3741},[1115,19045,19046],{"class":3572}," 22",[1115,19048,1715],{"class":3741},[1115,19050,19051],{"class":3572}," 69",[1115,19053,1715],{"class":3741},[1115,19055,17898],{"class":3572},[1115,19057,1715],{"class":3741},[1115,19059,19060],{"class":3572}," 272",[1115,19062,1715],{"class":3741},[1115,19064,19065],{"class":3572}," 117",[1115,19067,1715],{"class":3741},[1115,19069,19070],{"class":3572}," 169",[1115,19072,1715],{"class":3741},[1115,19074,19075],{"class":3572}," 466",[1115,19077,1715],{"class":3741},[1115,19079,19080],{"class":3572}," 286",[1115,19082,7873],{"class":3741},[1115,19084,19085,19088,19090,19093,19095,19098,19100,19103,19105,19108,19110,19113,19115,19118,19120,19123,19125,19128,19130,19133],{"class":3563,"line":96},[1115,19086,19087],{"class":3572},"        46",[1115,19089,1715],{"class":3741},[1115,19091,19092],{"class":3572}," 236",[1115,19094,1715],{"class":3741},[1115,19096,19097],{"class":3572}," 387",[1115,19099,1715],{"class":3741},[1115,19101,19102],{"class":3572}," 92",[1115,19104,1715],{"class":3741},[1115,19106,19107],{"class":3572}," 177",[1115,19109,1715],{"class":3741},[1115,19111,19112],{"class":3572}," 188",[1115,19114,1715],{"class":3741},[1115,19116,19117],{"class":3572}," 124",[1115,19119,1715],{"class":3741},[1115,19121,19122],{"class":3572}," 385",[1115,19124,1715],{"class":3741},[1115,19126,19127],{"class":3572}," 174",[1115,19129,1715],{"class":3741},[1115,19131,19132],{"class":3572}," 23",[1115,19134,3575],{"class":3569},[1115,19136,19137,19139,19141,19143],{"class":3563,"line":89},[1115,19138,15798],{"class":3566},[1115,19140,1168],{"class":3569},[1115,19142,18873],{"class":3744},[1115,19144,3575],{"class":3569},[1115,19146,19147,19149,19151,19153,19155,19157,19159,19161,19163,19165,19167,19169],{"class":3563,"line":82},[1115,19148,15809],{"class":3566},[1115,19150,1168],{"class":3569},[1115,19152,18873],{"class":3744},[1115,19154,15848],{"class":3569},[1115,19156,15831],{"class":3566},[1115,19158,1168],{"class":3569},[1115,19160,18873],{"class":3744},[1115,19162,15848],{"class":3569},[1115,19164,16531],{"class":3566},[1115,19166,1168],{"class":3569},[1115,19168,18873],{"class":3744},[1115,19170,3575],{"class":3569},[1115,19172,19173,19175,19177,19179,19181,19183,19185,19187,19189],{"class":3563,"line":75},[1115,19174,15390],{"class":3566},[1115,19176,1168],{"class":3569},[1115,19178,18873],{"class":3744},[1115,19180,3862],{"class":3569},[1115,19182,3865],{"class":3741},[1115,19184,15869],{"class":3566},[1115,19186,1168],{"class":3569},[1115,19188,18873],{"class":3744},[1115,19190,3575],{"class":3569},[1115,19192,19193,19196,19198,19200,19202,19204,19206,19208,19210,19212,19214,19216,19218,19221,19223,19225,19227,19229,19231,19233,19235,19237,19239,19241,19243,19245,19247],{"class":3563,"line":8025},[1115,19194,19195],{"class":3744},"y5",[1115,19197,4497],{"class":3741},[1115,19199,18129],{"class":3566},[1115,19201,1168],{"class":3569},[1115,19203,18873],{"class":3744},[1115,19205,1715],{"class":3741},[1115,19207,18138],{"class":3744},[1115,19209,3748],{"class":3741},[1115,19211,18143],{"class":3566},[1115,19213,1168],{"class":3569},[1115,19215,1982],{"class":3572},[1115,19217,1715],{"class":3741},[1115,19219,19220],{"class":3572}," 1050",[1115,19222,1715],{"class":3741},[1115,19224,18157],{"class":3744},[1115,19226,3748],{"class":3741},[1115,19228,17766],{"class":3572},[1115,19230,1174],{"class":3569},[1115,19232,1715],{"class":3741},[1115,19234,18168],{"class":3744},[1115,19236,3748],{"class":3741},[1115,19238,10455],{"class":3572},[1115,19240,1715],{"class":3741},[1115,19242,18177],{"class":3744},[1115,19244,3748],{"class":3741},[1115,19246,10455],{"class":3572},[1115,19248,3575],{"class":3569},[1115,19250,19251,19253,19255],{"class":3563,"line":72},[1115,19252,19195],{"class":3744},[1115,19254,8047],{"class":3741},[1115,19256,19257],{"class":3744},"mids\n",[1115,19259,19260,19262,19264],{"class":3563,"line":25},[1115,19261,19195],{"class":3744},[1115,19263,8047],{"class":3741},[1115,19265,18192],{"class":3744},[1115,19267,19268,19270,19272,19274,19276,19278,19280,19282,19284,19286,19288,19290,19292],{"class":3563,"line":65},[1115,19269,4510],{"class":3566},[1115,19271,1168],{"class":3569},[1115,19273,19195],{"class":3744},[1115,19275,8047],{"class":3741},[1115,19277,18205],{"class":3744},[1115,19279,4608],{"class":3741},[1115,19281,18210],{"class":3566},[1115,19283,1168],{"class":3569},[1115,19285,18873],{"class":3744},[1115,19287,1174],{"class":3569},[1115,19289,1715],{"class":3741},[1115,19291,5393],{"class":3572},[1115,19293,3575],{"class":3569},[3554,19295,19298],{"className":19296,"code":19297,"language":3603,"meta":3558},[3601],"[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",[1373,19299,19297],{"__ignoreMap":3558},[1110,19301,19302],{},"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.",[1431,19304,5414],{"id":5413},[1124,19306,19307,19325,19426,19494],{},[1127,19308,19309,1145,19312,19315,19316,19319,19320,19322,19323,1333],{},[1131,19310,19311],{},"Výchozí typ kvantilu v R.",[1373,19313,19314],{},"quantile()"," bez argumentu ",[1373,19317,19318],{},"type"," používá jiný výpočetní vzorec (",[1373,19321,15962],{},") než ruční postup v této kapitole — u některých souborů se hodnoty liší. Pro shodu s ručním výpočtem zadávejte ",[1373,19324,15958],{},[1127,19326,19327,19332,19333,19335,19336,19371,19372,19407,19408,19425],{},[1131,19328,19329,19330,1333],{},"Výchozí ohraničení tříd v ",[1373,19331,17554],{}," Bez ",[1373,19334,17680],{}," jsou třídy zprava uzavřené, ",[1115,19337,19339],{"className":19338},[1149],[1151,19340,19341],{"xmlns":1153},[1155,19342,19343,19369],{},[1158,19344,19345,19347,19353,19355,19367],{},[1165,19346,1168],{"stretchy":1167},[1277,19348,19349,19351],{},[1161,19350,7856],{},[1161,19352,6044],{},[1165,19354,1358],{"separator":1121},[1277,19356,19357,19359],{},[1161,19358,7856],{},[1158,19360,19361,19363,19365],{},[1161,19362,6044],{},[1165,19364,2094],{},[1282,19366,1284],{},[1165,19368,1921],{"stretchy":1167},[1194,19370,17676],{"encoding":1196}," — opačně než konvence ",[1115,19373,19375],{"className":19374},[1149],[1151,19376,19377],{"xmlns":1153},[1155,19378,19379,19405],{},[1158,19380,19381,19383,19389,19391,19403],{},[1165,19382,2917],{"stretchy":1167},[1277,19384,19385,19387],{},[1161,19386,7856],{},[1161,19388,6044],{},[1165,19390,1358],{"separator":1121},[1277,19392,19393,19395],{},[1161,19394,7856],{},[1158,19396,19397,19399,19401],{},[1161,19398,6044],{},[1165,19400,2094],{},[1282,19402,1284],{},[1165,19404,1174],{"stretchy":1167},[1194,19406,17717],{"encoding":1196}," použitá v tabulkách výše. Hodnota ležící přesně na hranici pak spadne do jiné třídy a četnosti ",[1115,19409,19411],{"className":19410},[1149],[1151,19412,19413],{"xmlns":1153},[1155,19414,19415,19423],{},[1158,19416,19417],{},[1277,19418,19419,19421],{},[1161,19420,1228],{},[1161,19422,6044],{},[1194,19424,17458],{"encoding":1196}," vyjdou jinak.",[1127,19427,19428,1145,19431,19449,19450,19463,19464,3546,19477,1333],{},[1131,19429,19430],{},"Rozptyl vs. směrodatná odchylka.",[1115,19432,19434],{"className":19433},[1149],[1151,19435,19436],{"xmlns":1153},[1155,19437,19438,19446],{},[1158,19439,19440],{},[1209,19441,19442,19444],{},[1161,19443,6018],{},[1282,19445,1298],{},[1194,19447,19448],{"encoding":1196},"s^2"," se udává v jednotkách znaku na druhou, ",[1115,19451,19453],{"className":19452},[1149],[1151,19454,19455],{"xmlns":1153},[1155,19456,19457,19461],{},[1158,19458,19459],{},[1161,19460,6018],{},[1194,19462,6018],{"encoding":1196}," ve stejných jednotkách jako data — pro interpretaci (např. „kolísání kolem průměru\") patří vždy ",[1115,19465,19467],{"className":19466},[1149],[1151,19468,19469],{"xmlns":1153},[1155,19470,19471,19475],{},[1158,19472,19473],{},[1161,19474,6018],{},[1194,19476,6018],{"encoding":1196},[1115,19478,19480],{"className":19479},[1149],[1151,19481,19482],{"xmlns":1153},[1155,19483,19484,19492],{},[1158,19485,19486],{},[1209,19487,19488,19490],{},[1161,19489,6018],{},[1282,19491,1298],{},[1194,19493,19448],{"encoding":1196},[1127,19495,19496,19499],{},[1131,19497,19498],{},"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.",[1431,19501,5604],{"id":5603},[1124,19503,19504,19509,19514,19519,19524,19529,19534],{},[1127,19505,19506],{},[1438,19507,1444],{"className":19508,"dataFsResolvedFilePath":1442,"href":1443},[1441],[1127,19510,19511],{},[1438,19512,1094],{"className":19513,"dataFsResolvedFilePath":10731,"href":10732},[1441],[1127,19515,19516],{},[1438,19517,10719],{"className":19518,"dataFsResolvedFilePath":4636,"href":4637},[1441],[1127,19520,19521],{},[1438,19522,10738],{"className":19523,"dataFsResolvedFilePath":5627,"href":5628},[1441],[1127,19525,19526],{},[1438,19527,5698],{"className":19528,"dataFsResolvedFilePath":5635,"href":5636},[1441],[1127,19530,19531],{},[1438,19532,10744],{"className":19533,"dataFsResolvedFilePath":5642,"href":5643},[1441],[1127,19535,19536],{},[1438,19537,5652],{"className":19538,"dataFsResolvedFilePath":5650,"href":5651},[1441],[1431,19540,5655],{"id":934},[1110,19542,5658,19543,5663],{},[5660,19544,5662],{},[5665,19546,19547],{},"html pre.shiki code .sP4rz, 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analýza"," zkoumá jednostrannou závislost vysvětlované proměnné ",[1115,19595,19597],{"className":19596},[1149],[1151,19598,19599],{"xmlns":1153},[1155,19600,19601,19605],{},[1158,19602,19603],{},[1161,19604,1603],{},[1194,19606,1603],{"encoding":1196}," na vysvětlujících proměnných ",[1115,19609,19611],{"className":19610},[1149],[1151,19612,19613],{"xmlns":1153},[1155,19614,19615,19619],{},[1158,19616,19617],{},[1161,19618,1171],{},[1194,19620,1171],{"encoding":1196}," (příčina → následek); ",[1131,19623,19624],{},"korelační analýza"," měří intenzitu (těsnost) vzájemné závislosti.",[1127,19627,19628,19629,19632,19633,1333],{},"Parametry regresní funkce se odhadují ",[1131,19630,19631],{},"metodou nejmenších čtverců"," — minimalizací součtu čtverců reziduí ",[1115,19634,19636],{"className":19635},[1149],[1151,19637,19638],{"xmlns":1153},[1155,19639,19640,19670],{},[1158,19641,19642,19644,19646,19652,19654,19664],{},[1165,19643,6144],{},[1165,19645,1168],{"stretchy":1167},[1277,19647,19648,19650],{},[1161,19649,1603],{},[1161,19651,4187],{},[1165,19653,1317],{},[1277,19655,19656,19662],{},[6877,19657,19658,19660],{"accent":1121},[1161,19659,1603],{},[1165,19661,6883],{},[1161,19663,4187],{},[1209,19665,19666,19668],{},[1165,19667,1174],{"stretchy":1167},[1282,19669,1298],{},[1194,19671,19672],{"encoding":1196},"\\sum(y_i-\\hat y_i)^2",[1127,19674,19675,19676,1145,19679,19697,19698,1145,19701,19725,19726,1145,19729,1333],{},"Kvalitu fitu měří ",[1131,19677,19678],{},"index determinace",[1115,19680,19682],{"className":19681},[1149],[1151,19683,19684],{"xmlns":1153},[1155,19685,19686,19694],{},[1158,19687,19688],{},[1209,19689,19690,19692],{},[1161,19691,4759],{},[1282,19693,1298],{},[1194,19695,19696],{"encoding":1196},"R^2","; obecnou těsnost závislosti ",[1131,19699,19700],{},"index korelace",[1115,19702,19704],{"className":19703},[1149],[1151,19705,19706],{"xmlns":1153},[1155,19707,19708,19722],{},[1158,19709,19710,19712,19714],{},[1161,19711,14871],{},[1165,19713,1177],{},[2765,19715,19716],{},[1209,19717,19718,19720],{},[1161,19719,4759],{},[1282,19721,1298],{},[1194,19723,19724],{"encoding":1196},"I=\\sqrt{R^2}",", který je pro regresní přímku roven ",[1131,19727,19728],{},"koeficientu korelace",[1115,19730,19732],{"className":19731},[1149],[1151,19733,19734],{"xmlns":1153},[1155,19735,19736,19748],{},[1158,19737,19738],{},[1277,19739,19740,19742],{},[1161,19741,71],{},[1158,19743,19744,19746],{},[1161,19745,1171],{},[1161,19747,1603],{},[1194,19749,19750],{"encoding":1196},"r_{xy}",[1127,19752,19753,19754,19757,19758,19761,19762,19765],{},"Když přímka nestačí, volí se ",[1131,19755,19756],{},"parabolická, polynomická, hyperbolická nebo logaritmická"," regrese (stále lineární v parametrech, odhad metodou nejmenších čtverců) nebo ",[1131,19759,19760],{},"exponenciální"," regrese (nelineární v parametrech, odhad přes ",[1373,19763,19764],{},"nls2",").",[1127,19767,19768,19771],{},[1131,19769,19770],{},"Vícenásobná regrese"," rozšiřuje model o více regresorů; vyžaduje výběr proměnných (ENTER\u002Fstepwise), ověření šesti předpokladů modelu a kontrolu multikolinearity přes VIF.",[1127,19773,19774,19775,1376,19778,1376,19781,1376,19784,1376,19787,1376,19790,1376,19793,1376,19796,1376,19799,1376,19802,1333],{},"V R: ",[1373,19776,19777],{},"lm()",[1373,19779,19780],{},"nls2()",[1373,19782,19783],{},"summary()",[1373,19785,19786],{},"confint()",[1373,19788,19789],{},"predict()",[1373,19791,19792],{},"step()",[1373,19794,19795],{},"car::vif()",[1373,19797,19798],{},"lmtest::dwtest()",[1373,19800,19801],{},"whitestrap::white_test()",[1373,19803,19804],{},"shapiro.test()",[1431,19806,14908],{"id":14907},[1110,19808,19809,19812,19813,1425,19826,19839,19840,19842,19843,19856,19857,19870,19871,19874],{},[1438,19810,1444],{"className":19811,"dataFsResolvedFilePath":1442,"href":1443},[1441]," pracuje se dvěma znaky ",[1115,19814,19816],{"className":19815},[1149],[1151,19817,19818],{"xmlns":1153},[1155,19819,19820,19824],{},[1158,19821,19822],{},[1161,19823,1171],{},[1194,19825,1171],{"encoding":1196},[1115,19827,19829],{"className":19828},[1149],[1151,19830,19831],{"xmlns":1153},[1155,19832,19833,19837],{},[1158,19834,19835],{},[1161,19836,1603],{},[1194,19838,1603],{"encoding":1196}," zjištěnými na stejných jednotkách. ",[1131,19841,19592],{}," se zabývá jednostrannými závislostmi, kdy proti sobě stojí vysvětlující (nezávisle) proměnná ",[1115,19844,19846],{"className":19845},[1149],[1151,19847,19848],{"xmlns":1153},[1155,19849,19850,19854],{},[1158,19851,19852],{},[1161,19853,1171],{},[1194,19855,1171],{"encoding":1196}," v úloze příčiny a vysvětlovaná (závisle) proměnná ",[1115,19858,19860],{"className":19859},[1149],[1151,19861,19862],{"xmlns":1153},[1155,19863,19864,19868],{},[1158,19865,19866],{},[1161,19867,1603],{},[1194,19869,1603],{"encoding":1196}," v úloze následku. ",[1131,19872,19873],{},"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.",[1110,19876,19877,19878,19765],{},"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 (",[1131,19879,19880],{},"regresní funkce",[1110,19882,19883],{},"Druh regresní analýzy určuje struktura datového souboru:",[1124,19885,19886,19923],{},[1127,19887,19888,19891,19892,19905,19906,19919,19920,1715],{},[1131,19889,19890],{},"dvourozměrný datový soubor"," (jedna ",[1115,19893,19895],{"className":19894},[1149],[1151,19896,19897],{"xmlns":1153},[1155,19898,19899,19903],{},[1158,19900,19901],{},[1161,19902,1171],{},[1194,19904,1171],{"encoding":1196},", jedna ",[1115,19907,19909],{"className":19908},[1149],[1151,19910,19911],{"xmlns":1153},[1155,19912,19913,19917],{},[1158,19914,19915],{},[1161,19916,1603],{},[1194,19918,1603],{"encoding":1196},") → ",[1131,19921,19922],{},"regresní analýza dvou proměnných",[1127,19924,19925,19928,19929,19919,19959,1333],{},[1131,19926,19927],{},"vícerozměrný datový soubor"," (více ",[1115,19930,19932],{"className":19931},[1149],[1151,19933,19934],{"xmlns":1153},[1155,19935,19936,19956],{},[1158,19937,19938,19944,19946,19948,19950],{},[1277,19939,19940,19942],{},[1161,19941,1171],{},[1282,19943,1284],{},[1165,19945,1715],{"separator":1121},[1165,19947,1726],{},[1165,19949,1715],{"separator":1121},[1277,19951,19952,19954],{},[1161,19953,1171],{},[1161,19955,1110],{},[1194,19957,19958],{"encoding":1196},"x_1,\\dots,x_p",[1131,19960,19961],{},"vícenásobná regresní analýza",[1110,19963,19964,19965,19968,19969,19972],{},"Volba konkrétní regresní funkce by měla vycházet jak z ",[1131,19966,19967],{},"ekonomické teorie"," (ta napovídá, zda závislost roste, nebo klesá, zda je přímková, nebo zakřivená), tak z ",[1131,19970,19971],{},"grafické a matematicko-statistické analýzy"," dat — oba přístupy je vhodné kombinovat.",[1431,19974,19976],{"id":19975},"metoda-nejmenších-čtverců","Metoda nejmenších čtverců",[1110,19978,19979,19980,1145,19983,20037,20038,20056,20057,1145,20060,20116,20117,20135,20136,20153,20154,20192,20193,1333],{},"Rozlišují se ",[1131,19981,19982],{},"teoretická regresní funkce",[1115,19984,19986],{"className":19985},[1149],[1151,19987,19988],{"xmlns":1153},[1155,19989,19990,20034],{},[1158,19991,19992,19995,19997,19999,20001,20003,20005,20012,20014,20020,20022,20024,20026,20032],{},[1161,19993,19994],{},"η",[1165,19996,1177],{},[1161,19998,1228],{},[1165,20000,1168],{"stretchy":1167},[1161,20002,1171],{},[1165,20004,1358],{"separator":1121},[1277,20006,20007,20010],{},[1161,20008,20009],{},"β",[1282,20011,1982],{},[1165,20013,1715],{"separator":1121},[1277,20015,20016,20018],{},[1161,20017,20009],{},[1282,20019,1284],{},[1165,20021,1715],{"separator":1121},[1165,20023,1726],{},[1165,20025,1715],{"separator":1121},[1277,20027,20028,20030],{},[1161,20029,20009],{},[1161,20031,1110],{},[1165,20033,1174],{"stretchy":1167},[1194,20035,20036],{"encoding":1196},"\\eta = f(x;\\beta_0,\\beta_1,\\dots,\\beta_p)"," — neznámá, populační, daná neznámými parametry ",[1115,20039,20041],{"className":20040},[1149],[1151,20042,20043],{"xmlns":1153},[1155,20044,20045,20053],{},[1158,20046,20047],{},[1277,20048,20049,20051],{},[1161,20050,20009],{},[1161,20052,4187],{},[1194,20054,20055],{"encoding":1196},"\\beta_i"," — a ",[1131,20058,20059],{},"empirická regresní funkce",[1115,20061,20063],{"className":20062},[1149],[1151,20064,20065],{"xmlns":1153},[1155,20066,20067,20113],{},[1158,20068,20069,20075,20077,20079,20081,20083,20085,20091,20093,20099,20101,20103,20105,20111],{},[6877,20070,20071,20073],{"accent":1121},[1161,20072,1603],{},[1165,20074,6883],{},[1165,20076,1177],{},[1161,20078,1228],{},[1165,20080,1168],{"stretchy":1167},[1161,20082,1171],{},[1165,20084,1358],{"separator":1121},[1277,20086,20087,20089],{},[1161,20088,15175],{},[1282,20090,1982],{},[1165,20092,1715],{"separator":1121},[1277,20094,20095,20097],{},[1161,20096,15175],{},[1282,20098,1284],{},[1165,20100,1715],{"separator":1121},[1165,20102,1726],{},[1165,20104,1715],{"separator":1121},[1277,20106,20107,20109],{},[1161,20108,15175],{},[1161,20110,1110],{},[1165,20112,1174],{"stretchy":1167},[1194,20114,20115],{"encoding":1196},"\\hat y = f(x; b_0,b_1,\\dots,b_p)",", jejíž odhadnuté parametry ",[1115,20118,20120],{"className":20119},[1149],[1151,20121,20122],{"xmlns":1153},[1155,20123,20124,20132],{},[1158,20125,20126],{},[1277,20127,20128,20130],{},[1161,20129,15175],{},[1161,20131,4187],{},[1194,20133,20134],{"encoding":1196},"b_i"," jsou odhadem ",[1115,20137,20139],{"className":20138},[1149],[1151,20140,20141],{"xmlns":1153},[1155,20142,20143,20151],{},[1158,20144,20145],{},[1277,20146,20147,20149],{},[1161,20148,20009],{},[1161,20150,4187],{},[1194,20152,20055],{"encoding":1196}," vypočteným z konkrétních dat. Odchylky skutečných hodnot od empirické funkce, ",[1115,20155,20157],{"className":20156},[1149],[1151,20158,20159],{"xmlns":1153},[1155,20160,20161,20189],{},[1158,20162,20163,20169,20171,20177,20179],{},[1277,20164,20165,20167],{},[1161,20166,3085],{},[1161,20168,4187],{},[1165,20170,1177],{},[1277,20172,20173,20175],{},[1161,20174,1603],{},[1161,20176,4187],{},[1165,20178,1317],{},[1277,20180,20181,20187],{},[6877,20182,20183,20185],{"accent":1121},[1161,20184,1603],{},[1165,20186,6883],{},[1161,20188,4187],{},[1194,20190,20191],{"encoding":1196},"e_i=y_i-\\hat y_i",", se nazývají ",[1131,20194,20195],{},"rezidua",[1110,20197,20198,20199,20202],{},"Nejpoužívanější metodou odhadu parametrů je ",[1131,20200,20201],{},"metoda nejmenších čtverců (OLS)",": hledají se takové parametry, pro které je součet čtverců reziduí minimální,",[1115,20204,20206],{"className":20205},[1149],[1151,20207,20208],{"xmlns":1153,"display":2212},[1155,20209,20210,20260],{},[1158,20211,20212,20226,20228,20234,20236,20246,20252,20254,20256,20258],{},[6140,20213,20214,20216,20224],{},[1165,20215,6144],{},[1158,20217,20218,20220,20222],{},[1161,20219,4187],{},[1165,20221,1177],{},[1282,20223,1284],{},[1161,20225,4192],{},[1165,20227,1168],{"stretchy":1167},[1277,20229,20230,20232],{},[1161,20231,1603],{},[1161,20233,4187],{},[1165,20235,1317],{},[1277,20237,20238,20244],{},[6877,20239,20240,20242],{"accent":1121},[1161,20241,1603],{},[1165,20243,6883],{},[1161,20245,4187],{},[1209,20247,20248,20250],{},[1165,20249,1174],{"stretchy":1167},[1282,20251,1298],{},[1165,20253,2087],{},[1161,20255,8614],{},[1165,20257,2079],{},[1161,20259,1333],{"mathvariant":1215},[1194,20261,20262],{"encoding":1196},"\\sum_{i=1}^n (y_i - \\hat y_i)^2 \\to \\min.",[1110,20264,20265],{},"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.",[1110,20267,20268],{},[1760,20269],{"alt":20270,"className":20271,"src":20272},"mask-ra-primka-rezidua",[1441,1764],"\u002Fwiki-assets\u002Fmask-ra-primka-rezidua.png",[1110,20274,20275,20276,20294],{},"Obrázek ukazuje přesně to, co metoda minimalizuje: délky červených úseček jsou rezidua ",[1115,20277,20279],{"className":20278},[1149],[1151,20280,20281],{"xmlns":1153},[1155,20282,20283,20291],{},[1158,20284,20285],{},[1277,20286,20287,20289],{},[1161,20288,3085],{},[1161,20290,4187],{},[1194,20292,20293],{"encoding":1196},"e_i",", metoda nejmenších čtverců volí přímku tak, aby součet jejich čtverců byl nejmenší možný.",[1431,20296,20298],{"id":20297},"regresní-přímka","Regresní přímka",[1110,20300,20301,20302,2629],{},"Nejjednodušší regresní funkcí je ",[1131,20303,20304],{},"regresní přímka",[1115,20306,20308],{"className":20307},[1149],[1151,20309,20310],{"xmlns":1153,"display":2212},[1155,20311,20312,20364],{},[1158,20313,20314,20316,20318,20324,20326,20332,20334,20336,20338,20344,20346,20352,20354,20360,20362],{},[1161,20315,19994],{},[1165,20317,1177],{},[1277,20319,20320,20322],{},[1161,20321,20009],{},[1282,20323,1982],{},[1165,20325,2094],{},[1277,20327,20328,20330],{},[1161,20329,20009],{},[1282,20331,1284],{},[1161,20333,1171],{},[1165,20335,1715],{"separator":1121},[2242,20337],{"width":2244},[6877,20339,20340,20342],{"accent":1121},[1161,20341,1603],{},[1165,20343,6883],{},[1165,20345,1177],{},[1277,20347,20348,20350],{},[1161,20349,15175],{},[1282,20351,1982],{},[1165,20353,2094],{},[1277,20355,20356,20358],{},[1161,20357,15175],{},[1282,20359,1284],{},[1161,20361,1171],{},[1161,20363,1333],{"mathvariant":1215},[1194,20365,20366],{"encoding":1196},"\\eta = \\beta_0 + \\beta_1 x, \\qquad \\hat y = b_0 + b_1 x.",[1110,20368,20369,20370,20388,20389,20402,20403,20416],{},"Koeficient ",[1115,20371,20373],{"className":20372},[1149],[1151,20374,20375],{"xmlns":1153},[1155,20376,20377,20385],{},[1158,20378,20379],{},[1277,20380,20381,20383],{},[1161,20382,15175],{},[1282,20384,1284],{},[1194,20386,20387],{"encoding":1196},"b_1"," udává změnu průměru ",[1115,20390,20392],{"className":20391},[1149],[1151,20393,20394],{"xmlns":1153},[1155,20395,20396,20400],{},[1158,20397,20398],{},[1161,20399,1603],{},[1194,20401,1603],{"encoding":1196}," při jednotkové změně ",[1115,20404,20406],{"className":20405},[1149],[1151,20407,20408],{"xmlns":1153},[1155,20409,20410,20414],{},[1158,20411,20412],{},[1161,20413,1171],{},[1194,20415,1171],{"encoding":1196},"; jeho znaménko určuje, zda je závislost přímá, nebo nepřímá.",[20418,20419,20421],"h3",{"id":20420},"v-r","V R",[1110,20423,20424,20425,20428,20429,20432],{},"Vstupní data se nahrají buď ze souboru (",[1373,20426,20427],{},"d \u003C- read.table(\"data.txt\")",", případně ",[1373,20430,20431],{},"d \u003C- read.table(file.choose())","), nebo zapíší přímo jako vektory. Na šesti domácnostech sledujeme počet členů domácnosti a jejich týdenní výdaje:",[3554,20434,20436],{"className":3556,"code":20435,"language":71,"meta":3558,"style":3558},"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",[1373,20437,20438,20473,20514,20535],{"__ignoreMap":3558},[1115,20439,20440,20443,20445,20447,20449,20451,20453,20455,20457,20459,20461,20463,20465,20467,20469,20471],{"class":3563,"line":10},[1115,20441,20442],{"class":3744},"pocet_clenu",[1115,20444,4497],{"class":3741},[1115,20446,7969],{"class":3566},[1115,20448,1168],{"class":3569},[1115,20450,1284],{"class":3572},[1115,20452,1715],{"class":3741},[1115,20454,8310],{"class":3572},[1115,20456,1715],{"class":3741},[1115,20458,5393],{"class":3572},[1115,20460,1715],{"class":3741},[1115,20462,4536],{"class":3572},[1115,20464,1715],{"class":3741},[1115,20466,4524],{"class":3572},[1115,20468,1715],{"class":3741},[1115,20470,15899],{"class":3572},[1115,20472,3575],{"class":3569},[1115,20474,20475,20478,20480,20482,20484,20487,20489,20492,20494,20497,20499,20502,20504,20507,20509,20512],{"class":3563,"line":27},[1115,20476,20477],{"class":3744},"tydenni_vydaje",[1115,20479,4497],{"class":3741},[1115,20481,7969],{"class":3566},[1115,20483,1168],{"class":3569},[1115,20485,20486],{"class":3572},"490",[1115,20488,1715],{"class":3741},[1115,20490,20491],{"class":3572}," 820",[1115,20493,1715],{"class":3741},[1115,20495,20496],{"class":3572}," 1230",[1115,20498,1715],{"class":3741},[1115,20500,20501],{"class":3572}," 1570",[1115,20503,1715],{"class":3741},[1115,20505,20506],{"class":3572}," 1950",[1115,20508,1715],{"class":3741},[1115,20510,20511],{"class":3572}," 2320",[1115,20513,3575],{"class":3569},[1115,20515,20516,20518,20520,20523,20525,20527,20530,20533],{"class":3563,"line":148},[1115,20517,786],{"class":3744},[1115,20519,4497],{"class":3741},[1115,20521,20522],{"class":3566}," lm",[1115,20524,1168],{"class":3569},[1115,20526,20477],{"class":3744},[1115,20528,20529],{"class":3741}," ~",[1115,20531,20532],{"class":3744}," pocet_clenu",[1115,20534,3575],{"class":3569},[1115,20536,20537,20540,20542,20544],{"class":3563,"line":111},[1115,20538,20539],{"class":3566},"summary",[1115,20541,1168],{"class":3569},[1115,20543,786],{"class":3744},[1115,20545,3575],{"class":3569},[3554,20547,20550],{"className":20548,"code":20549,"language":3603,"meta":3558},[3601],"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",[1373,20551,20549],{"__ignoreMap":3558},[1110,20553,20554,20555,20587,20588,20591,20592,20622,20623,20653,20654,20657,20658,20681],{},"Odhadnutý model je ",[1115,20556,20558],{"className":20557},[1149],[1151,20559,20560],{"xmlns":1153},[1155,20561,20562,20584],{},[1158,20563,20564,20570,20572,20575,20577,20580,20582],{},[6877,20565,20566,20568],{"accent":1121},[1161,20567,1603],{},[1165,20569,6883],{},[1165,20571,1177],{},[1282,20573,20574],{},"108,7",[1165,20576,2094],{},[1282,20578,20579],{},"368,0",[2278,20581,2280],{},[1161,20583,1171],{},[1194,20585,20586],{"encoding":1196},"\\hat y = 108{,}7 + 368{,}0\\,x",". Sloupec ",[1373,20589,20590],{},"Pr(>|t|)"," je p-hodnota t-testu ",[1115,20593,20595],{"className":20594},[1149],[1151,20596,20597],{"xmlns":1153},[1155,20598,20599,20619],{},[1158,20600,20601,20607,20609,20615,20617],{},[1277,20602,20603,20605],{},[1161,20604,4318],{},[1282,20606,1982],{},[1165,20608,2629],{},[1277,20610,20611,20613],{},[1161,20612,20009],{},[1161,20614,4187],{},[1165,20616,1177],{},[1282,20618,1982],{},[1194,20620,20621],{"encoding":1196},"H_0:\\beta_i=0"," proti ",[1115,20624,20626],{"className":20625},[1149],[1151,20627,20628],{"xmlns":1153},[1155,20629,20630,20650],{},[1158,20631,20632,20638,20640,20646,20648],{},[1277,20633,20634,20636],{},[1161,20635,4318],{},[1282,20637,1284],{},[1165,20639,2629],{},[1277,20641,20642,20644],{},[1161,20643,20009],{},[1161,20645,4187],{},[1165,20647,5496],{"mathvariant":1215},[1282,20649,1982],{},[1194,20651,20652],{"encoding":1196},"H_1:\\beta_i\\neq0"," pro každý parametr — obě p-hodnoty jsou hluboko pod 0,05, oba parametry jsou tedy statisticky významné. ",[1373,20655,20656],{},"Multiple R-squared"," je index determinace ",[1115,20659,20661],{"className":20660},[1149],[1151,20662,20663],{"xmlns":1153},[1155,20664,20665,20678],{},[1158,20666,20667,20673,20675],{},[1209,20668,20669,20671],{},[1161,20670,4759],{},[1282,20672,1298],{},[1165,20674,1177],{},[1282,20676,20677],{},"0,9995",[1194,20679,20680],{"encoding":1196},"R^2=0{,}9995",": model vysvětluje 99,95 % rozptylu výdajů.",[1110,20683,20684],{},"Pro doplňkový přehled slouží přímé přístupové funkce:",[3554,20686,20688],{"className":3556,"code":20687,"language":71,"meta":3558,"style":3558},"coef(model)\nfitted(model)\nresiduals(model)\n",[1373,20689,20690,20701,20712],{"__ignoreMap":3558},[1115,20691,20692,20695,20697,20699],{"class":3563,"line":10},[1115,20693,20694],{"class":3566},"coef",[1115,20696,1168],{"class":3569},[1115,20698,786],{"class":3744},[1115,20700,3575],{"class":3569},[1115,20702,20703,20706,20708,20710],{"class":3563,"line":27},[1115,20704,20705],{"class":3566},"fitted",[1115,20707,1168],{"class":3569},[1115,20709,786],{"class":3744},[1115,20711,3575],{"class":3569},[1115,20713,20714,20717,20719,20721],{"class":3563,"line":148},[1115,20715,20716],{"class":3566},"residuals",[1115,20718,1168],{"class":3569},[1115,20720,786],{"class":3744},[1115,20722,3575],{"class":3569},[3554,20724,20727],{"className":20725,"code":20726,"language":3603,"meta":3558},[3601],"(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",[1373,20728,20726],{"__ignoreMap":3558},[1110,20730,20731,20734,20735,1376,20761,20764,20765,20787,20788,1376,20806,20809,20810,20847],{},[1373,20732,20733],{},"coef()"," vrací odhadnuté parametry ",[1115,20736,20738],{"className":20737},[1149],[1151,20739,20740],{"xmlns":1153},[1155,20741,20742,20758],{},[1158,20743,20744,20750,20752],{},[1277,20745,20746,20748],{},[1161,20747,15175],{},[1282,20749,1982],{},[1165,20751,1715],{"separator":1121},[1277,20753,20754,20756],{},[1161,20755,15175],{},[1282,20757,1284],{},[1194,20759,20760],{"encoding":1196},"b_0,b_1",[1373,20762,20763],{},"fitted()"," predikce ",[1115,20766,20768],{"className":20767},[1149],[1151,20769,20770],{"xmlns":1153},[1155,20771,20772,20784],{},[1158,20773,20774],{},[1277,20775,20776,20782],{},[6877,20777,20778,20780],{"accent":1121},[1161,20779,1603],{},[1165,20781,6883],{},[1161,20783,4187],{},[1194,20785,20786],{"encoding":1196},"\\hat y_i"," pro pozorované ",[1115,20789,20791],{"className":20790},[1149],[1151,20792,20793],{"xmlns":1153},[1155,20794,20795,20803],{},[1158,20796,20797],{},[1277,20798,20799,20801],{},[1161,20800,1171],{},[1161,20802,4187],{},[1194,20804,20805],{"encoding":1196},"x_i",[1373,20807,20808],{},"residuals()"," rezidua ",[1115,20811,20813],{"className":20812},[1149],[1151,20814,20815],{"xmlns":1153},[1155,20816,20817,20845],{},[1158,20818,20819,20825,20827,20833,20835],{},[1277,20820,20821,20823],{},[1161,20822,3085],{},[1161,20824,4187],{},[1165,20826,1177],{},[1277,20828,20829,20831],{},[1161,20830,1603],{},[1161,20832,4187],{},[1165,20834,1317],{},[1277,20836,20837,20843],{},[6877,20838,20839,20841],{"accent":1121},[1161,20840,1603],{},[1165,20842,6883],{},[1161,20844,4187],{},[1194,20846,20191],{"encoding":1196}," — stejná čísla, která na obrázku výše tvoří délky červených úseček.",[1110,20849,20850,20851,20864],{},"Intervaly spolehlivosti pro parametry a pro predikci v nových bodech ",[1115,20852,20854],{"className":20853},[1149],[1151,20855,20856],{"xmlns":1153},[1155,20857,20858,20862],{},[1158,20859,20860],{},[1161,20861,1171],{},[1194,20863,1171],{"encoding":1196}," (zde 7 a 8 členů domácnosti):",[3554,20866,20868],{"className":3556,"code":20867,"language":71,"meta":3558,"style":3558},"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",[1373,20869,20870,20890,20918,20957],{"__ignoreMap":3558},[1115,20871,20872,20875,20877,20879,20881,20884,20886,20888],{"class":3563,"line":10},[1115,20873,20874],{"class":3566},"confint",[1115,20876,1168],{"class":3569},[1115,20878,786],{"class":3744},[1115,20880,1715],{"class":3741},[1115,20882,20883],{"class":3744}," level",[1115,20885,3748],{"class":3741},[1115,20887,4529],{"class":3572},[1115,20889,3575],{"class":3569},[1115,20891,20892,20895,20897,20900,20902,20904,20906,20908,20910,20912,20914,20916],{"class":3563,"line":27},[1115,20893,20894],{"class":3744},"nove",[1115,20896,4497],{"class":3741},[1115,20898,20899],{"class":3566}," data.frame",[1115,20901,1168],{"class":3569},[1115,20903,20442],{"class":3744},[1115,20905,3748],{"class":3741},[1115,20907,7969],{"class":3566},[1115,20909,1168],{"class":3569},[1115,20911,17001],{"class":3572},[1115,20913,1715],{"class":3741},[1115,20915,18927],{"class":3572},[1115,20917,4011],{"class":3569},[1115,20919,20920,20923,20925,20927,20929,20932,20934,20937,20939,20942,20944,20947,20949,20951,20953,20955],{"class":3563,"line":148},[1115,20921,20922],{"class":3566},"predict",[1115,20924,1168],{"class":3569},[1115,20926,786],{"class":3744},[1115,20928,1715],{"class":3741},[1115,20930,20931],{"class":3744}," newdata",[1115,20933,3748],{"class":3741},[1115,20935,20936],{"class":3744}," nove",[1115,20938,1715],{"class":3741},[1115,20940,20941],{"class":3744}," interval",[1115,20943,3748],{"class":3741},[1115,20945,20946],{"class":7974}," \"confidence\"",[1115,20948,1715],{"class":3741},[1115,20950,20883],{"class":3744},[1115,20952,3748],{"class":3741},[1115,20954,4529],{"class":3572},[1115,20956,3575],{"class":3569},[1115,20958,20959,20961,20963,20965,20967,20969,20971,20973,20975,20977,20979,20982,20984,20986,20988,20990],{"class":3563,"line":111},[1115,20960,20922],{"class":3566},[1115,20962,1168],{"class":3569},[1115,20964,786],{"class":3744},[1115,20966,1715],{"class":3741},[1115,20968,20931],{"class":3744},[1115,20970,3748],{"class":3741},[1115,20972,20936],{"class":3744},[1115,20974,1715],{"class":3741},[1115,20976,20941],{"class":3744},[1115,20978,3748],{"class":3741},[1115,20980,20981],{"class":7974}," \"prediction\"",[1115,20983,1715],{"class":3741},[1115,20985,20883],{"class":3744},[1115,20987,3748],{"class":3741},[1115,20989,4529],{"class":3572},[1115,20991,3575],{"class":3569},[3554,20993,20996],{"className":20994,"code":20995,"language":3603,"meta":3558},[3601],"                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",[1373,20997,20995],{"__ignoreMap":3558},[1110,20999,21000,21003,21004,1145,21007,21020,21021,1376,21034,21037,21038,21041],{},[1373,21001,21002],{},"interval = \"confidence\""," dává interval spolehlivosti pro ",[1131,21005,21006],{},"střední hodnotu",[1115,21008,21010],{"className":21009},[1149],[1151,21011,21012],{"xmlns":1153},[1155,21013,21014,21018],{},[1158,21015,21016],{},[1161,21017,1603],{},[1194,21019,1603],{"encoding":1196}," při daném ",[1115,21022,21024],{"className":21023},[1149],[1151,21025,21026],{"xmlns":1153},[1155,21027,21028,21032],{},[1158,21029,21030],{},[1161,21031,1171],{},[1194,21033,1171],{"encoding":1196},[1373,21035,21036],{},"interval = \"prediction\""," širší interval pro ",[1131,21039,21040],{},"jednotlivé budoucí pozorování"," — ten musí zahrnout i rozptyl kolem regresní přímky, proto je vždy širší.",[20418,21043,21045],{"id":21044},"diagnostika-modelu","Diagnostika modelu",[1110,21047,21048,21049,1376,21052,1425,21055,21058],{},"Platnost závěrů z regresní přímky stojí na předpokladech o reziduích: ",[1131,21050,21051],{},"absenci autokorelace",[1131,21053,21054],{},"stálosti rozptylu (homoskedasticitě)",[1131,21056,21057],{},"normalitě",". V R se ověřují takto:",[3554,21060,21062],{"className":3556,"code":21061,"language":71,"meta":3558,"style":3558},"library(lmtest)\ndwtest(model)\n",[1373,21063,21064,21076],{"__ignoreMap":3558},[1115,21065,21066,21069,21071,21074],{"class":3563,"line":10},[1115,21067,21068],{"class":3741},"library",[1115,21070,1168],{"class":3569},[1115,21072,21073],{"class":3744},"lmtest",[1115,21075,3575],{"class":3569},[1115,21077,21078,21081,21083,21085],{"class":3563,"line":27},[1115,21079,21080],{"class":3566},"dwtest",[1115,21082,1168],{"class":3569},[1115,21084,786],{"class":3744},[1115,21086,3575],{"class":3569},[3554,21088,21091],{"className":21089,"code":21090,"language":3603,"meta":3558},[3601],"    Durbin-Watson test\n\ndata:  model\nDW = 3.4121, p-value = 0.9555\nalternative hypothesis: true autocorrelation is greater than 0\n",[1373,21092,21090],{"__ignoreMap":3558},[1110,21094,21095,21096,21113,21114,21131,21132,21149],{},"Durbinův–Watsonův test má ",[1115,21097,21099],{"className":21098},[1149],[1151,21100,21101],{"xmlns":1153},[1155,21102,21103,21111],{},[1158,21104,21105],{},[1277,21106,21107,21109],{},[1161,21108,4318],{},[1282,21110,1982],{},[1194,21112,5745],{"encoding":1196},": v modelu není problém s autokorelací, proti ",[1115,21115,21117],{"className":21116},[1149],[1151,21118,21119],{"xmlns":1153},[1155,21120,21121,21129],{},[1158,21122,21123],{},[1277,21124,21125,21127],{},[1161,21126,4318],{},[1282,21128,1284],{},[1194,21130,7147],{"encoding":1196},": 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, ",[1115,21133,21135],{"className":21134},[1149],[1151,21136,21137],{"xmlns":1153},[1155,21138,21139,21147],{},[1158,21140,21141],{},[1277,21142,21143,21145],{},[1161,21144,4318],{},[1282,21146,1982],{},[1194,21148,5745],{"encoding":1196}," se nezamítá.",[3554,21151,21153],{"className":3556,"code":21152,"language":71,"meta":3558,"style":3558},"library(whitestrap)\nwhite_test(model)\n",[1373,21154,21155,21166],{"__ignoreMap":3558},[1115,21156,21157,21159,21161,21164],{"class":3563,"line":10},[1115,21158,21068],{"class":3741},[1115,21160,1168],{"class":3569},[1115,21162,21163],{"class":3744},"whitestrap",[1115,21165,3575],{"class":3569},[1115,21167,21168,21171,21173,21175],{"class":3563,"line":27},[1115,21169,21170],{"class":3566},"white_test",[1115,21172,1168],{"class":3569},[1115,21174,786],{"class":3744},[1115,21176,3575],{"class":3569},[3554,21178,21181],{"className":21179,"code":21180,"language":3603,"meta":3558},[3601],"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",[1373,21182,21180],{"__ignoreMap":3558},[1110,21184,21185,21186,21203,21204,21221,21222,21149],{},"Whiteův test má ",[1115,21187,21189],{"className":21188},[1149],[1151,21190,21191],{"xmlns":1153},[1155,21192,21193,21201],{},[1158,21194,21195],{},[1277,21196,21197,21199],{},[1161,21198,4318],{},[1282,21200,1982],{},[1194,21202,5745],{"encoding":1196},": rozptyl reziduí je stálý (homoskedasticita), proti ",[1115,21205,21207],{"className":21206},[1149],[1151,21208,21209],{"xmlns":1153},[1155,21210,21211,21219],{},[1158,21212,21213],{},[1277,21214,21215,21217],{},[1161,21216,4318],{},[1282,21218,1284],{},[1194,21220,7147],{"encoding":1196},": rozptyl není stálý (heteroskedasticita). P-hodnota 0,21 je nad 0,05, ",[1115,21223,21225],{"className":21224},[1149],[1151,21226,21227],{"xmlns":1153},[1155,21228,21229,21237],{},[1158,21230,21231],{},[1277,21232,21233,21235],{},[1161,21234,4318],{},[1282,21236,1982],{},[1194,21238,5745],{"encoding":1196},[3554,21240,21242],{"className":3556,"code":21241,"language":71,"meta":3558,"style":3558},"shapiro.test(residuals(model))\n",[1373,21243,21244],{"__ignoreMap":3558},[1115,21245,21246,21249,21251,21253,21255,21257],{"class":3563,"line":10},[1115,21247,21248],{"class":3566},"shapiro.test",[1115,21250,1168],{"class":3569},[1115,21252,20716],{"class":3566},[1115,21254,1168],{"class":3569},[1115,21256,786],{"class":3744},[1115,21258,4011],{"class":3569},[3554,21260,21263],{"className":21261,"code":21262,"language":3603,"meta":3558},[3601],"    Shapiro-Wilk normality test\n\ndata:  residuals(model)\nW = 0.94818, p-value = 0.7255\n",[1373,21264,21262],{"__ignoreMap":3558},[1110,21266,21267,21268,21285],{},"Shapiro–Wilkův test má ",[1115,21269,21271],{"className":21270},[1149],[1151,21272,21273],{"xmlns":1153},[1155,21274,21275,21283],{},[1158,21276,21277],{},[1277,21278,21279,21281],{},[1161,21280,4318],{},[1282,21282,1982],{},[1194,21284,5745],{"encoding":1196},": rezidua pocházejí z normálního rozdělení. P-hodnota 0,73 opět nevede k zamítnutí — všechny tři předpoklady model splňuje.",[1110,21287,21288],{},[1760,21289],{"alt":21290,"className":21291,"src":21292},"mask-ra-diagnostika-rezidui",[1441,1764],"\u002Fwiki-assets\u002Fmask-ra-diagnostika-rezidui.png",[1110,21294,21295],{},"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.",[1103,21297,21299,21306,21337,21372,21437],{"className":21298,"dataCallout":3670},[1106,3669],[1110,21300,21302,21305],{"className":21301},[1113],[1115,21303],{"className":21304,"ariaHidden":1121},[1118,3677,1120],"Příklad: Regresní přímka",[1110,21307,21308,21309,21322,21323,21336],{},"V souboru s údaji o hodnotě produkce (v milionech Kč, proměnná ",[1115,21310,21312],{"className":21311},[1149],[1151,21313,21314],{"xmlns":1153},[1155,21315,21316,21320],{},[1158,21317,21318],{},[1161,21319,1603],{},[1194,21321,1603],{"encoding":1196},") a výši investic (ve stovkách tisíc Kč, proměnná ",[1115,21324,21326],{"className":21325},[1149],[1151,21327,21328],{"xmlns":1153},[1155,21329,21330,21334],{},[1158,21331,21332],{},[1161,21333,1171],{},[1194,21335,1171],{"encoding":1196},") 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.",[1110,21338,21339,21340,1333],{},"Výsledek: ",[1115,21341,21343],{"className":21342},[1149],[1151,21344,21345],{"xmlns":1153},[1155,21346,21347,21369],{},[1158,21348,21349,21355,21357,21360,21362,21365,21367],{},[6877,21350,21351,21353],{"accent":1121},[1161,21352,1603],{},[1165,21354,6883],{},[1165,21356,1177],{},[1282,21358,21359],{},"32,74",[1165,21361,2094],{},[1282,21363,21364],{},"2,15",[2278,21366,2280],{},[1161,21368,1171],{},[1194,21370,21371],{"encoding":1196},"\\hat y = 32{,}74 + 2{,}15\\,x",[1110,21373,20369,21374,21396,21397,21436],{},[1115,21375,21377],{"className":21376},[1149],[1151,21378,21379],{"xmlns":1153},[1155,21380,21381,21393],{},[1158,21382,21383,21389,21391],{},[1277,21384,21385,21387],{},[1161,21386,15175],{},[1282,21388,1284],{},[1165,21390,1177],{},[1282,21392,21364],{},[1194,21394,21395],{"encoding":1196},"b_1=2{,}15"," říká, že se zvýšením investic o 100 000 Kč vzroste produkce v průměru o ",[1115,21398,21400],{"className":21399},[1149],[1151,21401,21402],{"xmlns":1153},[1155,21403,21404,21433],{},[1158,21405,21406,21408,21410,21412,21414,21416,21418,21420,21422,21424,21426,21429,21431],{},[1282,21407,21364],{},[1165,21409,2598],{},[1282,21411,1284],{},[2278,21413,2280],{},[1282,21415,14993],{},[2278,21417,2280],{},[1282,21419,14993],{},[1165,21421,1177],{},[1282,21423,1298],{},[2278,21425,2280],{},[1282,21427,21428],{},"150",[2278,21430,2280],{},[1282,21432,14993],{},[1194,21434,21435],{"encoding":1196},"2{,}15\\cdot 1\\,000\\,000=2\\,150\\,000"," Kč.",[1110,21438,21439,21440,8118,21459,21507,21508,19765],{},"Dosazením libovolné hodnoty investic do empirické regresní funkce dostaneme predikci produkce, například pro třináctou firmu s investicemi ",[1115,21441,21443],{"className":21442},[1149],[1151,21444,21445],{"xmlns":1153},[1155,21446,21447,21456],{},[1158,21448,21449,21451,21453],{},[1161,21450,1171],{},[1165,21452,1177],{},[1282,21454,21455],{},"34",[1194,21457,21458],{"encoding":1196},"x=34",[1115,21460,21462],{"className":21461},[1149],[1151,21463,21464],{"xmlns":1153},[1155,21465,21466,21504],{},[1158,21467,21468,21478,21480,21486,21488,21494,21496,21498,21501],{},[1277,21469,21470,21476],{},[6877,21471,21472,21474],{"accent":1121},[1161,21473,1603],{},[1165,21475,6883],{},[1282,21477,7690],{},[1165,21479,1177],{},[1277,21481,21482,21484],{},[1161,21483,15175],{},[1282,21485,1982],{},[1165,21487,2094],{},[1277,21489,21490,21492],{},[1161,21491,15175],{},[1282,21493,1284],{},[1165,21495,2598],{},[1282,21497,21455],{},[1165,21499,21500],{},"≐",[1282,21502,21503],{},"105,81",[1194,21505,21506],{"encoding":1196},"\\hat y_{13} = b_0 + b_1\\cdot 34 \\doteq 105{,}81"," milionu Kč (se zaokrouhlenými koeficienty ",[1115,21509,21511],{"className":21510},[1149],[1151,21512,21513],{"xmlns":1153},[1155,21514,21515,21532],{},[1158,21516,21517,21519,21521,21523,21525,21527,21529],{},[1282,21518,21359],{},[1165,21520,2094],{},[1282,21522,21364],{},[1165,21524,2598],{},[1282,21526,21455],{},[1165,21528,21500],{},[1282,21530,21531],{},"105,8",[1194,21533,21534],{"encoding":1196},"32{,}74 + 2{,}15\\cdot 34 \\doteq 105{,}8",[1431,21536,21538],{"id":21537},"nelineární-a-vyšší-řády-regresních-funkcí","Nelineární a vyšší řády regresních funkcí",[1110,21540,21541,21542,21545,21546,21613,21614,21632,21633,21650],{},"Když přímka závislost nevystihuje, nabízí se další ",[1131,21543,21544],{},"lineární funkce"," — tedy funkce lineární ve svých parametrech, zapsatelné ve tvaru ",[1115,21547,21549],{"className":21548},[1149],[1151,21550,21551],{"xmlns":1153},[1155,21552,21553,21610],{},[1158,21554,21555,21557,21559,21565,21567,21573,21579,21581,21583,21585,21587,21590,21592,21598,21604,21606,21608],{},[1161,21556,19994],{},[1165,21558,1177],{},[1277,21560,21561,21563],{},[1161,21562,20009],{},[1282,21564,1982],{},[1165,21566,2094],{},[1277,21568,21569,21571],{},[1161,21570,20009],{},[1282,21572,1284],{},[1277,21574,21575,21577],{},[1161,21576,1228],{},[1282,21578,1284],{},[1165,21580,1168],{"stretchy":1167},[1161,21582,1171],{},[1165,21584,1174],{"stretchy":1167},[1165,21586,2094],{},[1165,21588,21589],{},"⋯",[1165,21591,2094],{},[1277,21593,21594,21596],{},[1161,21595,20009],{},[1161,21597,1110],{},[1277,21599,21600,21602],{},[1161,21601,1228],{},[1161,21603,1110],{},[1165,21605,1168],{"stretchy":1167},[1161,21607,1171],{},[1165,21609,1174],{"stretchy":1167},[1194,21611,21612],{"encoding":1196},"\\eta=\\beta_0+\\beta_1 f_1(x)+\\dots+\\beta_p f_p(x)"," se známými funkcemi ",[1115,21615,21617],{"className":21616},[1149],[1151,21618,21619],{"xmlns":1153},[1155,21620,21621,21629],{},[1158,21622,21623],{},[1277,21624,21625,21627],{},[1161,21626,1228],{},[1161,21628,4187],{},[1194,21630,21631],{"encoding":1196},"f_i"," a neznámými parametry ",[1115,21634,21636],{"className":21635},[1149],[1151,21637,21638],{"xmlns":1153},[1155,21639,21640,21648],{},[1158,21641,21642],{},[1277,21643,21644,21646],{},[1161,21645,20009],{},[1161,21647,4187],{},[1194,21649,20055],{"encoding":1196},". I tyto parametry se odhadují metodou nejmenších čtverců, stejně jako u přímky:",[1115,21652,21654],{"className":21653},[1149],[1151,21655,21656],{"xmlns":1153,"display":2212},[1155,21657,21658,21968],{},[21659,21660,21663,21736,21849,21908],"mtable",{"rowspacing":21661,"columnalign":21662,"columnspacing":1216},"0.25em","right left",[21664,21665,21666,21690],"mtr",{},[21667,21668,21669],"mtd",{},[7391,21670,21671],{"scriptlevel":1982,"displaystyle":1121},[1158,21672,21673,21687],{},[1158,21674,21675,21678,21684],{},[2278,21676,21677],{},"parabolick",[6877,21679,21680,21682],{"accent":1121},[2278,21681,1438],{},[1165,21683,15172],{},[2278,21685,21686],{}," regrese: ",[2242,21688],{"width":21689},"1em",[21667,21691,21692],{},[7391,21693,21694],{"scriptlevel":1982,"displaystyle":1121},[1158,21695,21696,21698,21704,21706,21712,21714,21720,21722,21724,21730],{},[1158,21697],{},[6877,21699,21700,21702],{"accent":1121},[1161,21701,1603],{},[1165,21703,6883],{},[1165,21705,1177],{},[1277,21707,21708,21710],{},[1161,21709,15175],{},[1282,21711,1982],{},[1165,21713,2094],{},[1277,21715,21716,21718],{},[1161,21717,15175],{},[1282,21719,1284],{},[1161,21721,1171],{},[1165,21723,2094],{},[1277,21725,21726,21728],{},[1161,21727,15175],{},[1282,21729,1298],{},[1209,21731,21732,21734],{},[1161,21733,1171],{},[1282,21735,1298],{},[21664,21737,21738,21785],{},[21667,21739,21740],{},[7391,21741,21742],{"scriptlevel":1982,"displaystyle":1121},[1158,21743,21744,21783],{},[1158,21745,21746,21749,21755,21758,21762,21765,21771,21774,21780],{},[2278,21747,21748],{},"polynomick",[6877,21750,21751,21753],{"accent":1121},[2278,21752,1438],{},[1165,21754,15172],{},[2278,21756,21757],{}," regrese ",[7391,21759,21760],{"scriptlevel":1982,"displaystyle":1167},[1161,21761,1110],{},[2278,21763,21764],{},"-t",[6877,21766,21767,21769],{"accent":1121},[2278,21768,3085],{},[1165,21770,15172],{},[2278,21772,21773],{},"ho stupn",[6877,21775,21776,21778],{"accent":1121},[2278,21777,3085],{},[1165,21779,15182],{},[2278,21781,21782],{},": ",[2242,21784],{"width":21689},[21667,21786,21787],{},[7391,21788,21789],{"scriptlevel":1982,"displaystyle":1121},[1158,21790,21791,21793,21799,21801,21807,21809,21815,21817,21819,21825,21831,21833,21835,21837,21843],{},[1158,21792],{},[6877,21794,21795,21797],{"accent":1121},[1161,21796,1603],{},[1165,21798,6883],{},[1165,21800,1177],{},[1277,21802,21803,21805],{},[1161,21804,15175],{},[1282,21806,1982],{},[1165,21808,2094],{},[1277,21810,21811,21813],{},[1161,21812,15175],{},[1282,21814,1284],{},[1161,21816,1171],{},[1165,21818,2094],{},[1277,21820,21821,21823],{},[1161,21822,15175],{},[1282,21824,1298],{},[1209,21826,21827,21829],{},[1161,21828,1171],{},[1282,21830,1298],{},[1165,21832,2094],{},[1165,21834,21589],{},[1165,21836,2094],{},[1277,21838,21839,21841],{},[1161,21840,15175],{},[1161,21842,1110],{},[1209,21844,21845,21847],{},[1161,21846,1171],{},[1161,21848,1110],{},[21664,21850,21851,21872],{},[21667,21852,21853],{},[7391,21854,21855],{"scriptlevel":1982,"displaystyle":1121},[1158,21856,21857,21870],{},[1158,21858,21859,21862,21868],{},[2278,21860,21861],{},"hyperbolick",[6877,21863,21864,21866],{"accent":1121},[2278,21865,1438],{},[1165,21867,15172],{},[2278,21869,21686],{},[2242,21871],{"width":21689},[21667,21873,21874],{},[7391,21875,21876],{"scriptlevel":1982,"displaystyle":1121},[1158,21877,21878,21880,21886,21888,21894,21896,21902],{},[1158,21879],{},[6877,21881,21882,21884],{"accent":1121},[1161,21883,1603],{},[1165,21885,6883],{},[1165,21887,1177],{},[1277,21889,21890,21892],{},[1161,21891,15175],{},[1282,21893,1982],{},[1165,21895,2094],{},[1277,21897,21898,21900],{},[1161,21899,15175],{},[1282,21901,1284],{},[3064,21903,21904,21906],{},[1282,21905,1284],{},[1161,21907,1171],{},[21664,21909,21910,21931],{},[21667,21911,21912],{},[7391,21913,21914],{"scriptlevel":1982,"displaystyle":1121},[1158,21915,21916,21929],{},[1158,21917,21918,21921,21927],{},[2278,21919,21920],{},"logaritmick",[6877,21922,21923,21925],{"accent":1121},[2278,21924,1438],{},[1165,21926,15172],{},[2278,21928,21686],{},[2242,21930],{"width":21689},[21667,21932,21933],{},[7391,21934,21935],{"scriptlevel":1982,"displaystyle":1121},[1158,21936,21937,21939,21945,21947,21953,21955,21961,21964,21966],{},[1158,21938],{},[6877,21940,21941,21943],{"accent":1121},[1161,21942,1603],{},[1165,21944,6883],{},[1165,21946,1177],{},[1277,21948,21949,21951],{},[1161,21950,15175],{},[1282,21952,1982],{},[1165,21954,2094],{},[1277,21956,21957,21959],{},[1161,21958,15175],{},[1282,21960,1284],{},[1161,21962,21963],{},"ln",[1165,21965,2079],{},[1161,21967,1171],{},[1194,21969,21970],{"encoding":1196},"\\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}",[1110,21972,21973,21974,21977,21978,22024,22025,2629],{},"Naproti tomu ",[1131,21975,21976],{},"nelineární funkce"," nelze do tvaru ",[1115,21979,21981],{"className":21980},[1149],[1151,21982,21983],{"xmlns":1153},[1155,21984,21985,22021],{},[1158,21986,21987,21989,21991,21997,21999,22005,22011,22013,22015,22017,22019],{},[1161,21988,19994],{},[1165,21990,1177],{},[1277,21992,21993,21995],{},[1161,21994,20009],{},[1282,21996,1982],{},[1165,21998,2094],{},[1277,22000,22001,22003],{},[1161,22002,20009],{},[1282,22004,1284],{},[1277,22006,22007,22009],{},[1161,22008,1228],{},[1282,22010,1284],{},[1165,22012,1168],{"stretchy":1167},[1161,22014,1171],{},[1165,22016,1174],{"stretchy":1167},[1165,22018,2094],{},[1165,22020,1726],{},[1194,22022,22023],{"encoding":1196},"\\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 ",[1131,22026,22027],{},"exponenciální regrese",[1115,22029,22031],{"className":22030},[1149],[1151,22032,22033],{"xmlns":1153,"display":2212},[1155,22034,22035,22067],{},[1158,22036,22037,22043,22045,22051,22053,22065],{},[6877,22038,22039,22041],{"accent":1121},[1161,22040,1603],{},[1165,22042,6883],{},[1165,22044,1177],{},[1277,22046,22047,22049],{},[1161,22048,15175],{},[1282,22050,1982],{},[1165,22052,2598],{},[2256,22054,22055,22057,22059],{},[1161,22056,15175],{},[1282,22058,1284],{},[1158,22060,22061,22063],{},[2278,22062,2280],{},[1161,22064,1171],{},[1161,22066,1333],{"mathvariant":1215},[1194,22068,22069],{"encoding":1196},"\\hat y = b_0 \\cdot b_1^{\\,x}.",[1110,22071,22072],{},[1760,22073],{"alt":22074,"className":22075,"src":22076},"mask-ra-nelinearni-krivky",[1441,1764],"\u002Fwiki-assets\u002Fmask-ra-nelinearni-krivky.png",[20418,22078,22080],{"id":22079},"v-r-parabolická-regrese","V R — parabolická regrese",[1110,22082,22083,22084,2629],{},"Na ročních ziscích firmy (šest let) se parabolická regrese odhadne přidáním kvadratického členu ",[1373,22085,22086],{},"I(x^2)",[3554,22088,22090],{"className":3556,"code":22089,"language":71,"meta":3558,"style":3558},"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",[1373,22091,22092,22127,22167,22201],{"__ignoreMap":3558},[1115,22093,22094,22097,22099,22101,22103,22105,22107,22109,22111,22113,22115,22117,22119,22121,22123,22125],{"class":3563,"line":10},[1115,22095,22096],{"class":3744},"rok",[1115,22098,4497],{"class":3741},[1115,22100,7969],{"class":3566},[1115,22102,1168],{"class":3569},[1115,22104,1284],{"class":3572},[1115,22106,1715],{"class":3741},[1115,22108,8310],{"class":3572},[1115,22110,1715],{"class":3741},[1115,22112,5393],{"class":3572},[1115,22114,1715],{"class":3741},[1115,22116,4536],{"class":3572},[1115,22118,1715],{"class":3741},[1115,22120,4524],{"class":3572},[1115,22122,1715],{"class":3741},[1115,22124,15899],{"class":3572},[1115,22126,3575],{"class":3569},[1115,22128,22129,22131,22133,22135,22137,22140,22142,22145,22147,22150,22152,22155,22157,22160,22162,22165],{"class":3563,"line":27},[1115,22130,1088],{"class":3744},[1115,22132,4497],{"class":3741},[1115,22134,7969],{"class":3566},[1115,22136,1168],{"class":3569},[1115,22138,22139],{"class":3572},"112",[1115,22141,1715],{"class":3741},[1115,22143,22144],{"class":3572}," 149",[1115,22146,1715],{"class":3741},[1115,22148,22149],{"class":3572}," 238",[1115,22151,1715],{"class":3741},[1115,22153,22154],{"class":3572}," 354",[1115,22156,1715],{"class":3741},[1115,22158,22159],{"class":3572}," 580",[1115,22161,1715],{"class":3741},[1115,22163,22164],{"class":3572}," 867",[1115,22166,3575],{"class":3569},[1115,22168,22169,22172,22174,22176,22178,22180,22182,22185,22188,22191,22193,22195,22197,22199],{"class":3563,"line":148},[1115,22170,22171],{"class":3744},"model_parabola",[1115,22173,4497],{"class":3741},[1115,22175,20522],{"class":3566},[1115,22177,1168],{"class":3569},[1115,22179,1088],{"class":3744},[1115,22181,20529],{"class":3741},[1115,22183,22184],{"class":3744}," rok",[1115,22186,22187],{"class":3741}," +",[1115,22189,22190],{"class":3566}," I",[1115,22192,1168],{"class":3569},[1115,22194,22096],{"class":3744},[1115,22196,6883],{"class":3741},[1115,22198,1298],{"class":3572},[1115,22200,4011],{"class":3569},[1115,22202,22203,22205,22207,22209],{"class":3563,"line":111},[1115,22204,20539],{"class":3566},[1115,22206,1168],{"class":3569},[1115,22208,22171],{"class":3744},[1115,22210,3575],{"class":3569},[3554,22212,22215],{"className":22213,"code":22214,"language":3603,"meta":3558},[3601],"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",[1373,22216,22214],{"__ignoreMap":3558},[1110,22218,22219,22220,22265],{},"Odhadnutá parabola ",[1115,22221,22223],{"className":22222},[1149],[1151,22224,22225],{"xmlns":1153},[1155,22226,22227,22262],{},[1158,22228,22229,22235,22237,22240,22242,22245,22247,22249,22251,22254,22256],{},[6877,22230,22231,22233],{"accent":1121},[1161,22232,1603],{},[1165,22234,6883],{},[1165,22236,1177],{},[1282,22238,22239],{},"164,6",[1165,22241,1317],{},[1282,22243,22244],{},"76,6",[2278,22246,2280],{},[1161,22248,1171],{},[1165,22250,2094],{},[1282,22252,22253],{},"32,1",[2278,22255,2280],{},[1209,22257,22258,22260],{},[1161,22259,1171],{},[1282,22261,1298],{},[1194,22263,22264],{"encoding":1196},"\\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.",[20418,22267,22269],{"id":22268},"v-r-exponenciální-regrese","V R — exponenciální regrese",[1110,22271,22272,22273,22275],{},"Nelineární funkce se v R odhadují funkcí ",[1373,22274,19780],{}," ze stejnojmenného balíčku. Bez zadaných počátečních hodnot R upozorní, že parametry nastavil na 1, a odhad dopočítá iteračně:",[3554,22277,22279],{"className":3556,"code":22278,"language":71,"meta":3558,"style":3558},"library(nls2)\nmodel_exp \u003C- nls2(zisk ~ b1 * exp(b2 * rok))\nsummary(model_exp)\n",[1373,22280,22281,22291,22327],{"__ignoreMap":3558},[1115,22282,22283,22285,22287,22289],{"class":3563,"line":10},[1115,22284,21068],{"class":3741},[1115,22286,1168],{"class":3569},[1115,22288,19764],{"class":3744},[1115,22290,3575],{"class":3569},[1115,22292,22293,22296,22298,22301,22303,22305,22307,22310,22313,22316,22318,22321,22323,22325],{"class":3563,"line":27},[1115,22294,22295],{"class":3744},"model_exp",[1115,22297,4497],{"class":3741},[1115,22299,22300],{"class":3566}," nls2",[1115,22302,1168],{"class":3569},[1115,22304,1088],{"class":3744},[1115,22306,20529],{"class":3741},[1115,22308,22309],{"class":3744}," b1",[1115,22311,22312],{"class":3741}," *",[1115,22314,22315],{"class":3566}," exp",[1115,22317,1168],{"class":3569},[1115,22319,22320],{"class":3744},"b2",[1115,22322,22312],{"class":3741},[1115,22324,22184],{"class":3744},[1115,22326,4011],{"class":3569},[1115,22328,22329,22331,22333,22335],{"class":3563,"line":148},[1115,22330,20539],{"class":3566},[1115,22332,1168],{"class":3569},[1115,22334,22295],{"class":3744},[1115,22336,3575],{"class":3569},[3554,22338,22341],{"className":22339,"code":22340,"language":3603,"meta":3558},[3601],"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",[1373,22342,22340],{"__ignoreMap":3558},[1110,22344,22345,22346,2629],{},"Stejnou křivku lze zapsat i v mocninném tvaru ",[1115,22347,22349],{"className":22348},[1149],[1151,22350,22351],{"xmlns":1153},[1155,22352,22353,22379],{},[1158,22354,22355,22361,22363,22369,22371],{},[6877,22356,22357,22359],{"accent":1121},[1161,22358,1603],{},[1165,22360,6883],{},[1165,22362,1177],{},[1277,22364,22365,22367],{},[1161,22366,15175],{},[1282,22368,1284],{},[1165,22370,2598],{},[2256,22372,22373,22375,22377],{},[1161,22374,15175],{},[1282,22376,1298],{},[1161,22378,1171],{},[1194,22380,22381],{"encoding":1196},"\\hat y=b_1\\cdot b_2^{x}",[3554,22383,22385],{"className":3556,"code":22384,"language":71,"meta":3558,"style":3558},"model_pow \u003C- nls2(zisk ~ b1 * (b2^rok))\nsummary(model_pow)\n",[1373,22386,22387,22416],{"__ignoreMap":3558},[1115,22388,22389,22392,22394,22396,22398,22400,22402,22404,22406,22408,22410,22412,22414],{"class":3563,"line":10},[1115,22390,22391],{"class":3744},"model_pow",[1115,22393,4497],{"class":3741},[1115,22395,22300],{"class":3566},[1115,22397,1168],{"class":3569},[1115,22399,1088],{"class":3744},[1115,22401,20529],{"class":3741},[1115,22403,22309],{"class":3744},[1115,22405,22312],{"class":3741},[1115,22407,8728],{"class":3569},[1115,22409,22320],{"class":3744},[1115,22411,6883],{"class":3741},[1115,22413,22096],{"class":3744},[1115,22415,4011],{"class":3569},[1115,22417,22418,22420,22422,22424],{"class":3563,"line":27},[1115,22419,20539],{"class":3566},[1115,22421,1168],{"class":3569},[1115,22423,22391],{"class":3744},[1115,22425,3575],{"class":3569},[3554,22427,22430],{"className":22428,"code":22429,"language":3603,"meta":3558},[3601],"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",[1373,22431,22429],{"__ignoreMap":3558},[1110,22433,22434,22435,22499,22500,22524],{},"Obě varianty popisují stejnou křivku (",[1115,22436,22438],{"className":22437},[1149],[1151,22439,22440],{"xmlns":1153},[1155,22441,22442,22496],{},[1158,22443,22444,22461,22463],{},[2256,22445,22446,22448,22450],{},[1161,22447,15175],{},[1282,22449,1298],{},[1158,22451,22452,22455],{},[2278,22453,22454],{},"mocninn",[6877,22456,22457,22459],{"accent":1121},[2278,22458,1603],{},[1165,22460,15172],{},[1165,22462,1177],{},[1209,22464,22465,22467],{},[1161,22466,3085],{},[1158,22468,22469,22471],{},[2278,22470,2280],{},[2256,22472,22473,22475,22477],{},[1161,22474,15175],{},[1282,22476,1298],{},[1158,22478,22479,22482,22488,22490],{},[2278,22480,22481],{},"exponenci",[6877,22483,22484,22486],{"accent":1121},[2278,22485,1438],{},[1165,22487,15172],{},[2278,22489,21963],{},[6877,22491,22492,22494],{"accent":1121},[2278,22493,15422],{},[1165,22495,15172],{},[1194,22497,22498],{"encoding":1196},"b_2^{\\text{mocninný}} = e^{\\,b_2^{\\text{exponenciální}}}",", zde ",[1115,22501,22503],{"className":22502},[1149],[1151,22504,22505],{"xmlns":1153},[1155,22506,22507,22521],{},[1158,22508,22509,22516,22518],{},[1209,22510,22511,22513],{},[1161,22512,3085],{},[1282,22514,22515],{},"0,4316",[1165,22517,3957],{},[1282,22519,22520],{},"1,540",[1194,22522,22523],{"encoding":1196},"e^{0{,}4316}\\approx 1{,}540",") a mají totožnou reziduální chybu — je to jen otázka parametrizace.",[20418,22526,22528],{"id":22527},"v-r-hyperbolická-regrese","V R — hyperbolická regrese",[1110,22530,22531,22532,2629],{},"Hyperbolická regrese se odhadne jako obyčejná lineární regrese na transformované proměnné ",[1373,22533,22534],{},"I(1\u002Fx)",[3554,22536,22538],{"className":3556,"code":22537,"language":71,"meta":3558,"style":3558},"model_hyperbola \u003C- lm(tydenni_vydaje ~ I(1 \u002F pocet_clenu))\nsummary(model_hyperbola)\n",[1373,22539,22540,22567],{"__ignoreMap":3558},[1115,22541,22542,22545,22547,22549,22551,22553,22555,22557,22559,22561,22563,22565],{"class":3563,"line":10},[1115,22543,22544],{"class":3744},"model_hyperbola",[1115,22546,4497],{"class":3741},[1115,22548,20522],{"class":3566},[1115,22550,1168],{"class":3569},[1115,22552,20477],{"class":3744},[1115,22554,20529],{"class":3741},[1115,22556,22190],{"class":3566},[1115,22558,1168],{"class":3569},[1115,22560,1284],{"class":3572},[1115,22562,4608],{"class":3741},[1115,22564,20532],{"class":3744},[1115,22566,4011],{"class":3569},[1115,22568,22569,22571,22573,22575],{"class":3563,"line":27},[1115,22570,20539],{"class":3566},[1115,22572,1168],{"class":3569},[1115,22574,22544],{"class":3744},[1115,22576,3575],{"class":3569},[3554,22578,22581],{"className":22579,"code":22580,"language":3603,"meta":3558},[3601],"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",[1373,22582,22580],{"__ignoreMap":3558},[1110,22584,22585,22586,22620,22621,22642],{},"Model ",[1115,22587,22589],{"className":22588},[1149],[1151,22590,22591],{"xmlns":1153},[1155,22592,22593,22617],{},[1158,22594,22595,22601,22603,22606,22608],{},[6877,22596,22597,22599],{"accent":1121},[1161,22598,1603],{},[1165,22600,6883],{},[1165,22602,1177],{},[1282,22604,22605],{},"2180,7",[1165,22607,1317],{},[7391,22609,22610],{"scriptlevel":1982,"displaystyle":1121},[3064,22611,22612,22615],{},[1282,22613,22614],{},"1920,0",[1161,22616,1171],{},[1194,22618,22619],{"encoding":1196},"\\hat y = 2180{,}7 - \\dfrac{1920{,}0}{x}"," vysvětluje jen 76,3 % rozptylu — u těchto dat je hyperbola podstatně horší volbou než přímka (",[1115,22622,22624],{"className":22623},[1149],[1151,22625,22626],{"xmlns":1153},[1155,22627,22628,22640],{},[1158,22629,22630,22636,22638],{},[1209,22631,22632,22634],{},[1161,22633,4759],{},[1282,22635,1298],{},[1165,22637,1177],{},[1282,22639,20677],{},[1194,22641,20680],{"encoding":1196},"). Právě k takovému porovnání slouží index determinace: nízká hodnota signalizuje, že zvolený typ funkce k datům nesedí.",[1103,22644,22646,22653,22684,22732],{"className":22645,"dataCallout":3670},[1106,3669],[1110,22647,22649,22652],{"className":22648},[1113],[1115,22650],{"className":22651,"ariaHidden":1121},[1118,3677,1120],"Příklad: Parabolická regrese",[1110,22654,22655,22656,22669,22670,22683],{},"Prodejna počítačových her nechala prodavače absolvovat kurz prodejních dovedností. Při dvaceti měřeních sledovala, kolik zákazníků navštíví prodejnu během prodejní doby (proměnná ",[1115,22657,22659],{"className":22658},[1149],[1151,22660,22661],{"xmlns":1153},[1155,22662,22663,22667],{},[1158,22664,22665],{},[1161,22666,1171],{},[1194,22668,1171],{"encoding":1196},") a jaká je toho dne tržba v tisících Kč (proměnná ",[1115,22671,22673],{"className":22672},[1149],[1151,22674,22675],{"xmlns":1153},[1155,22676,22677,22681],{},[1158,22678,22679],{},[1161,22680,1603],{},[1194,22682,1603],{"encoding":1196},"). Zároveň chtěla zjistit, zda při rostoucím počtu zákazníků stačí stávající počet prodavačů.",[1110,22685,21339,22686,1333],{},[1115,22687,22689],{"className":22688},[1149],[1151,22690,22691],{"xmlns":1153},[1155,22692,22693,22729],{},[1158,22694,22695,22701,22703,22705,22708,22710,22713,22715,22717,22719,22721,22723],{},[6877,22696,22697,22699],{"accent":1121},[1161,22698,1603],{},[1165,22700,6883],{},[1165,22702,1177],{},[1165,22704,1317],{},[1282,22706,22707],{},"60,3",[1165,22709,2094],{},[1282,22711,22712],{},"4,55",[2278,22714,2280],{},[1161,22716,1171],{},[1165,22718,1317],{},[1282,22720,8114],{},[2278,22722,2280],{},[1209,22724,22725,22727],{},[1161,22726,1171],{},[1282,22728,1298],{},[1194,22730,22731],{"encoding":1196},"\\hat y = -60{,}3 + 4{,}55\\,x - 0{,}05\\,x^2",[1110,22733,22734,22735,22753],{},"Záporný koeficient ",[1115,22736,22738],{"className":22737},[1149],[1151,22739,22740],{"xmlns":1153},[1155,22741,22742,22750],{},[1158,22743,22744],{},[1277,22745,22746,22748],{},[1161,22747,15175],{},[1282,22749,1298],{},[1194,22751,22752],{"encoding":1196},"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.",[1103,22755,22757,22764,22794,22839],{"className":22756,"dataCallout":3670},[1106,3669],[1110,22758,22760,22763],{"className":22759},[1113],[1115,22761],{"className":22762,"ariaHidden":1121},[1118,3677,1120],"Příklad: Hyperbolická regrese",[1110,22765,22766,22767,22780,22781,19765],{},"V podniku se podle interního účetnictví sledovala závislost vlastních nákladů na jednotku produkce v Kč (proměnná ",[1115,22768,22770],{"className":22769},[1149],[1151,22771,22772],{"xmlns":1153},[1155,22773,22774,22778],{},[1158,22775,22776],{},[1161,22777,1603],{},[1194,22779,1603],{"encoding":1196},") na objemu produkce v tisících kusů (proměnná ",[1115,22782,22784],{"className":22783},[1149],[1151,22785,22786],{"xmlns":1153},[1155,22787,22788,22792],{},[1158,22789,22790],{},[1161,22791,1171],{},[1194,22793,1171],{"encoding":1196},[1110,22795,21339,22796,1333],{},[1115,22797,22799],{"className":22798},[1149],[1151,22800,22801],{"xmlns":1153},[1155,22802,22803,22836],{},[1158,22804,22805,22811,22813,22815,22818,22820],{},[6877,22806,22807,22809],{"accent":1121},[1161,22808,1603],{},[1165,22810,6883],{},[1165,22812,1177],{},[1165,22814,1317],{},[1282,22816,22817],{},"96,78",[1165,22819,2094],{},[7391,22821,22822],{"scriptlevel":1982,"displaystyle":1121},[3064,22823,22824,22834],{},[1158,22825,22826,22829,22831],{},[1282,22827,22828],{},"250",[2278,22830,2280],{},[1282,22832,22833],{},"528,88",[1161,22835,1171],{},[1194,22837,22838],{"encoding":1196},"\\hat y = -96{,}78 + \\dfrac{250\\,528{,}88}{x}",[1110,22840,22841,22842,22859],{},"Záporná hodnota ",[1115,22843,22845],{"className":22844},[1149],[1151,22846,22847],{"xmlns":1153},[1155,22848,22849,22857],{},[1158,22850,22851],{},[1277,22852,22853,22855],{},[1161,22854,15175],{},[1282,22856,1284],{},[1194,22858,20387],{"encoding":1196}," v čitateli ukazuje klesající náklady na jednotku s rostoucím objemem produkce — typický projev úspor z rozsahu, který hyperbola dobře zachycuje.",[1431,22861,22863],{"id":22862},"kvalita-regresní-funkce-a-korelační-analýza","Kvalita regresní funkce a korelační analýza",[1110,22865,22866,22867,2629],{},"Kvalitu odhadnuté regresní funkce vyjadřuje ",[1131,22868,19678],{},[1115,22870,22872],{"className":22871},[1149],[1151,22873,22874],{"xmlns":1153,"display":2212},[1155,22875,22876,22944],{},[1158,22877,22878,22884,22886,22908,22910,22912,22914,22942],{},[1209,22879,22880,22882],{},[1161,22881,4759],{},[1282,22883,1298],{},[1165,22885,1177],{},[3064,22887,22888,22900],{},[2256,22889,22890,22892,22898],{},[1161,22891,6018],{},[6877,22893,22894,22896],{"accent":1121},[1161,22895,1603],{},[1165,22897,6883],{},[1282,22899,1298],{},[2256,22901,22902,22904,22906],{},[1161,22903,6018],{},[1161,22905,1603],{},[1282,22907,1298],{},[1165,22909,1177],{},[1282,22911,1284],{},[1165,22913,1317],{},[3064,22915,22916,22934],{},[2256,22917,22918,22920,22932],{},[1161,22919,6018],{},[1158,22921,22922,22924,22926],{},[1161,22923,1603],{},[1165,22925,1317],{},[6877,22927,22928,22930],{"accent":1121},[1161,22929,1603],{},[1165,22931,6883],{},[1282,22933,1298],{},[2256,22935,22936,22938,22940],{},[1161,22937,6018],{},[1161,22939,1603],{},[1282,22941,1298],{},[1161,22943,1333],{"mathvariant":1215},[1194,22945,22946],{"encoding":1196},"R^2 = \\frac{s^2_{\\hat y}}{s^2_y} = 1 - \\frac{s^2_{y-\\hat y}}{s^2_y}.",[1110,22948,22949,22950,22967,22968,22981],{},"Čím blíž je ",[1115,22951,22953],{"className":22952},[1149],[1151,22954,22955],{"xmlns":1153},[1155,22956,22957,22965],{},[1158,22958,22959],{},[1209,22960,22961,22963],{},[1161,22962,4759],{},[1282,22964,1298],{},[1194,22966,19696],{"encoding":1196}," k 1, tím silnější je závislost; v procentech udává, jakou část rozptylu závisle proměnné ",[1115,22969,22971],{"className":22970},[1149],[1151,22972,22973],{"xmlns":1153},[1155,22974,22975,22979],{},[1158,22976,22977],{},[1161,22978,1603],{},[1194,22980,1603],{"encoding":1196}," se podařilo vysvětlit zvolenou regresní funkcí. Nízký index determinace může signalizovat špatně zvolený typ regresní funkce, ne nutně absenci závislosti.",[1110,22983,22984,22985,1145,22987,23010,23011,2629],{},"Obecnou mírou těsnosti závislosti — platnou pro libovolný typ regresní funkce — je ",[1131,22986,19700],{},[1115,22988,22990],{"className":22989},[1149],[1151,22991,22992],{"xmlns":1153},[1155,22993,22994,23008],{},[1158,22995,22996,22998,23000],{},[1161,22997,14871],{},[1165,22999,1177],{},[2765,23001,23002],{},[1209,23003,23004,23006],{},[1161,23005,4759],{},[1282,23007,1298],{},[1194,23009,19724],{"encoding":1196},". Je-li zvolenou funkcí regresní přímka, index korelace je roven (až na znaménko) ",[1131,23012,19728],{},[1115,23014,23016],{"className":23015},[1149],[1151,23017,23018],{"xmlns":1153,"display":2212},[1155,23019,23020,23070],{},[1158,23021,23022,23032,23034,23068],{},[1277,23023,23024,23026],{},[1161,23025,71],{},[1158,23027,23028,23030],{},[1161,23029,1171],{},[1161,23031,1603],{},[1165,23033,1177],{},[3064,23035,23036,23046],{},[1277,23037,23038,23040],{},[1161,23039,6018],{},[1158,23041,23042,23044],{},[1161,23043,1171],{},[1161,23045,1603],{},[2765,23047,23048],{},[1158,23049,23050,23058,23060],{},[2256,23051,23052,23054,23056],{},[1161,23053,6018],{},[1161,23055,1171],{},[1282,23057,1298],{},[1165,23059,2598],{},[2256,23061,23062,23064,23066],{},[1161,23063,6018],{},[1161,23065,1603],{},[1282,23067,1298],{},[1161,23069,1333],{"mathvariant":1215},[1194,23071,23072],{"encoding":1196},"r_{xy} = \\frac{s_{xy}}{\\sqrt{s^2_x\\cdot s^2_y}}.",[1110,23074,23075,23076,23092,23093,23109],{},"Koeficient korelace nabývá hodnot od ",[1115,23077,23079],{"className":23078},[1149],[1151,23080,23081],{"xmlns":1153},[1155,23082,23083,23089],{},[1158,23084,23085,23087],{},[1165,23086,1317],{},[1282,23088,1284],{},[1194,23090,23091],{"encoding":1196},"-1"," do ",[1115,23094,23096],{"className":23095},[1149],[1151,23097,23098],{"xmlns":1153},[1155,23099,23100,23106],{},[1158,23101,23102,23104],{},[1165,23103,2094],{},[1282,23105,1284],{},[1194,23107,23108],{"encoding":1196},"+1",": znaménko určuje typ závislosti (pozitivní, nebo negativní), absolutní hodnota její sílu — čím blíž k 0, tím je závislost slabší.",[1110,23111,23112],{},[1760,23113],{"alt":23114,"className":23115,"src":23116},"mask-ra-korelace-sila",[1441,1764],"\u002Fwiki-assets\u002Fmask-ra-korelace-sila.png",[1110,23118,23119,23120,23133,23134,23152,23153,1425,23166,23179],{},"S rostoucí absolutní hodnotou ",[1115,23121,23123],{"className":23122},[1149],[1151,23124,23125],{"xmlns":1153},[1155,23126,23127,23131],{},[1158,23128,23129],{},[1161,23130,71],{},[1194,23132,71],{"encoding":1196}," se body v rozptylovém grafu víc blíží přímce; kolem ",[1115,23135,23137],{"className":23136},[1149],[1151,23138,23139],{"xmlns":1153},[1155,23140,23141,23149],{},[1158,23142,23143,23145,23147],{},[1161,23144,71],{},[1165,23146,3957],{},[1282,23148,1982],{},[1194,23150,23151],{"encoding":1196},"r\\approx 0"," je mezi ",[1115,23154,23156],{"className":23155},[1149],[1151,23157,23158],{"xmlns":1153},[1155,23159,23160,23164],{},[1158,23161,23162],{},[1161,23163,1171],{},[1194,23165,1171],{"encoding":1196},[1115,23167,23169],{"className":23168},[1149],[1151,23170,23171],{"xmlns":1153},[1155,23172,23173,23177],{},[1158,23174,23175],{},[1161,23176,1603],{},[1194,23178,1603],{"encoding":1196}," patrná jen náhodná rozptýlenost bez lineárního trendu.",[20418,23181,20421],{"id":23182},"v-r-1",[3554,23184,23186],{"className":3556,"code":23185,"language":71,"meta":3558,"style":3558},"cor(pocet_clenu, tydenni_vydaje)\n",[1373,23187,23188],{"__ignoreMap":3558},[1115,23189,23190,23193,23195,23197,23199,23202],{"class":3563,"line":10},[1115,23191,23192],{"class":3566},"cor",[1115,23194,1168],{"class":3569},[1115,23196,20442],{"class":3744},[1115,23198,1715],{"class":3741},[1115,23200,23201],{"class":3744}," tydenni_vydaje",[1115,23203,3575],{"class":3569},[3554,23205,23208],{"className":23206,"code":23207,"language":3603,"meta":3558},[3601],"[1] 0.9997441\n",[1373,23209,23207],{"__ignoreMap":3558},[1110,23211,23212,23213,23239],{},"Hodnota 0,9997 odpovídá ",[1115,23214,23216],{"className":23215},[1149],[1151,23217,23218],{"xmlns":1153},[1155,23219,23220,23236],{},[1158,23221,23222,23230,23232],{},[2765,23223,23224],{},[1209,23225,23226,23228],{},[1161,23227,4759],{},[1282,23229,1298],{},[1165,23231,1177],{},[2765,23233,23234],{},[1282,23235,20677],{},[1194,23237,23238],{"encoding":1196},"\\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.",[1103,23241,23243,23250,23253],{"className":23242,"dataCallout":3670},[1106,3669],[1110,23244,23246,23249],{"className":23245},[1113],[1115,23247],{"className":23248,"ariaHidden":1121},[1118,3677,1120],"Příklad: Koeficient korelace",[1110,23251,23252],{},"Pro stejná data o hodnotě produkce a výši investic dvanácti firem jako u regresní přímky byl spočten koeficient korelace mezi oběma proměnnými.",[1110,23254,21339,23255,23282],{},[1115,23256,23258],{"className":23257},[1149],[1151,23259,23260],{"xmlns":1153},[1155,23261,23262,23279],{},[1158,23263,23264,23274,23276],{},[1277,23265,23266,23268],{},[1161,23267,71],{},[1158,23269,23270,23272],{},[1161,23271,1171],{},[1161,23273,1603],{},[1165,23275,1177],{},[1282,23277,23278],{},"0,739",[1194,23280,23281],{"encoding":1196},"r_{xy} = 0{,}739"," — silná kladná závislost hodnoty produkce na výši investic.",[1431,23284,23286],{"id":23285},"vícenásobná-regrese-a-korelace","Vícenásobná regrese a korelace",[1110,23288,23289,23290,23303],{},"Pokud na závisle proměnnou ",[1115,23291,23293],{"className":23292},[1149],[1151,23294,23295],{"xmlns":1153},[1155,23296,23297,23301],{},[1158,23298,23299],{},[1161,23300,1603],{},[1194,23302,1603],{"encoding":1196}," působí víc vysvětlujících proměnných současně, analyzuje se zvlášť vliv každé z nich a výsledná regresní funkce se konstruuje jako součet jednoduchých regresních funkcí:",[1115,23305,23307],{"className":23306},[1149],[1151,23308,23309],{"xmlns":1153,"display":2212},[1155,23310,23311,23421],{},[1158,23312,23313,23315,23317,23323,23325,23331,23337,23339,23345,23351,23353,23355,23357,23363,23369,23371,23373,23379,23381,23387,23389,23395,23401,23403,23405,23407,23413,23419],{},[1161,23314,19994],{},[1165,23316,1177],{},[1277,23318,23319,23321],{},[1161,23320,20009],{},[1282,23322,1982],{},[1165,23324,2094],{},[1277,23326,23327,23329],{},[1161,23328,20009],{},[1282,23330,1284],{},[1277,23332,23333,23335],{},[1161,23334,1171],{},[1282,23336,1284],{},[1165,23338,2094],{},[1277,23340,23341,23343],{},[1161,23342,20009],{},[1282,23344,1298],{},[1277,23346,23347,23349],{},[1161,23348,1171],{},[1282,23350,1298],{},[1165,23352,2094],{},[1165,23354,21589],{},[1165,23356,2094],{},[1277,23358,23359,23361],{},[1161,23360,20009],{},[1161,23362,1110],{},[1277,23364,23365,23367],{},[1161,23366,1171],{},[1161,23368,1110],{},[1165,23370,1715],{"separator":1121},[2242,23372],{"width":2244},[6877,23374,23375,23377],{"accent":1121},[1161,23376,1603],{},[1165,23378,6883],{},[1165,23380,1177],{},[1277,23382,23383,23385],{},[1161,23384,15175],{},[1282,23386,1982],{},[1165,23388,2094],{},[1277,23390,23391,23393],{},[1161,23392,15175],{},[1282,23394,1284],{},[1277,23396,23397,23399],{},[1161,23398,1171],{},[1282,23400,1284],{},[1165,23402,2094],{},[1165,23404,21589],{},[1165,23406,2094],{},[1277,23408,23409,23411],{},[1161,23410,15175],{},[1161,23412,1110],{},[1277,23414,23415,23417],{},[1161,23416,1171],{},[1161,23418,1110],{},[1161,23420,1333],{"mathvariant":1215},[1194,23422,23423],{"encoding":1196},"\\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.",[20418,23425,23427],{"id":23426},"výběr-proměnných","Výběr proměnných",[1124,23429,23430,23436],{},[1127,23431,23432,23435],{},[1131,23433,23434],{},"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.",[1127,23437,23438,23441,23442,23445,23446,23449],{},[1131,23439,23440],{},"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 ",[1131,23443,23444],{},"forward"," proměnné postupně přidává, varianta ",[1131,23447,23448],{},"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.",[20418,23451,23453],{"id":23452},"postup-odhadu","Postup odhadu",[7018,23455,23456,23459,23462],{},[1127,23457,23458],{},"ověření předpokladů regresního modelu,",[1127,23460,23461],{},"samotný odhad parametrů,",[1127,23463,23464],{},"reziduální analýza výsledného modelu.",[1110,23466,23467,23468,23485,23486,8118,23488,23517,23518,23547,23548,23565],{},"Důležitost každého parametru ",[1115,23469,23471],{"className":23470},[1149],[1151,23472,23473],{"xmlns":1153},[1155,23474,23475,23483],{},[1158,23476,23477],{},[1277,23478,23479,23481],{},[1161,23480,15175],{},[1161,23482,4187],{},[1194,23484,20134],{"encoding":1196}," v modelu ověřuje ",[1131,23487,992],{},[1115,23489,23491],{"className":23490},[1149],[1151,23492,23493],{"xmlns":1153},[1155,23494,23495,23515],{},[1158,23496,23497,23503,23505,23511,23513],{},[1277,23498,23499,23501],{},[1161,23500,4318],{},[1282,23502,1982],{},[1165,23504,2629],{},[1277,23506,23507,23509],{},[1161,23508,20009],{},[1161,23510,4187],{},[1165,23512,1177],{},[1282,23514,1982],{},[1194,23516,20621],{"encoding":1196}," (proměnná je v modelu nevýznamná) proti ",[1115,23519,23521],{"className":23520},[1149],[1151,23522,23523],{"xmlns":1153},[1155,23524,23525,23545],{},[1158,23526,23527,23533,23535,23541,23543],{},[1277,23528,23529,23531],{},[1161,23530,4318],{},[1282,23532,1284],{},[1165,23534,2629],{},[1277,23536,23537,23539],{},[1161,23538,20009],{},[1161,23540,4187],{},[1165,23542,5496],{"mathvariant":1215},[1282,23544,1982],{},[1194,23546,20652],{"encoding":1196}," (proměnná je významná). Při nezamítnutí ",[1115,23549,23551],{"className":23550},[1149],[1151,23552,23553],{"xmlns":1153},[1155,23554,23555,23563],{},[1158,23556,23557],{},[1277,23558,23559,23561],{},[1161,23560,4318],{},[1282,23562,1982],{},[1194,23564,5745],{"encoding":1196}," by proměnná — a s ní spojený regresor — v modelu neměla zůstat.",[20418,23567,23569],{"id":23568},"předpoklady-modelu","Předpoklady modelu",[7018,23571,23572,23589,23622,23628,23631,23634],{},[1127,23573,23574,23575,23588],{},"Závisle proměnná ",[1115,23576,23578],{"className":23577},[1149],[1151,23579,23580],{"xmlns":1153},[1155,23581,23582,23586],{},[1158,23583,23584],{},[1161,23585,1603],{},[1194,23587,1603],{"encoding":1196}," musí být aspoň intervalového typu (ne binární, diskrétní s málo hodnotami apod.) — jinak je na místě logistická regrese.",[1127,23590,23591,23592,23621],{},"Nezávislé proměnné ",[1115,23593,23595],{"className":23594},[1149],[1151,23596,23597],{"xmlns":1153},[1155,23598,23599,23619],{},[1158,23600,23601,23607,23609,23611,23613],{},[1277,23602,23603,23605],{},[1161,23604,1171],{},[1282,23606,1284],{},[1165,23608,1715],{"separator":1121},[1165,23610,1726],{},[1165,23612,1715],{"separator":1121},[1277,23614,23615,23617],{},[1161,23616,1171],{},[1161,23618,1110],{},[1194,23620,19958],{"encoding":1196}," jsou rovněž aspoň intervalového typu, mohou být i alternativní.",[1127,23623,23624,23625,1333],{},"Nezávislé proměnné by mezi sebou neměly být příliš vysoce korelované — ",[1131,23626,23627],{},"multikolinearita",[1127,23629,23630],{},"V datech nesmí být odlehlé či extrémní hodnoty; regresní analýza je na ně citlivá a mohou vážně narušit kvalitu odhadů.",[1127,23632,23633],{},"Proměnné musí být ve vzájemně lineárním vztahu — vícenásobná lineární regrese je založená na Pearsonově koeficientu korelace, takže nelineární vztahy mezi proměnnými zůstanou neodhalené.",[1127,23635,23636,23637,23641],{},"Proměnné mají mít ",[1438,23638,23640],{"className":23639,"dataFsResolvedFilePath":10731,"href":10732},[1441],"normální rozložení","; význam tohoto předpokladu ustupuje do pozadí u dostatečně velkého datového souboru díky centrální limitní větě.",[1110,23643,23644,23645,23648],{},"Normalita se u menšího počtu pozorování ověřuje stejnými testy jako u jiných znaků (viz ",[1438,23646,5890],{"className":23647,"dataFsResolvedFilePath":4636,"href":4637},[1441],") — 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.",[20418,23650,23651],{"id":23627},"Multikolinearita",[1110,23653,23654],{},"Multikolinearita vzniká, když vysvětlující proměnné silně závisejí jedna na druhé. Je nežádoucí, protože:",[1124,23656,23657,23660,23663],{},[1127,23658,23659],{},"výsledky regrese jsou pak nespolehlivé,",[1127,23661,23662],{},"zvyšuje pravděpodobnost, že se důležitá proměnná jeví jako statisticky nevýznamná a bude z modelu vyřazena,",[1127,23664,23665],{},"směrodatné odchylky odhadnutých parametrů jsou vysoké, testová kritéria t-testů nízká, p-hodnoty vysoké.",[1110,23667,23668,23669,23672,23673,23696,23697,23715,23716,23732],{},"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 ",[1131,23670,23671],{},"VIF (Variance Inflation Factor)",": hodnoty ",[1115,23674,23676],{"className":23675},[1149],[1151,23677,23678],{"xmlns":1153},[1155,23679,23680,23693],{},[1158,23681,23682,23684,23686,23689,23691],{},[1282,23683,1284],{},[1165,23685,1287],{},[2278,23687,23688],{},"VIF",[1165,23690,1287],{},[1282,23692,4455],{},[1194,23694,23695],{"encoding":1196},"1\u003C\\text{VIF}\u003C5"," jsou varující, ",[1115,23698,23700],{"className":23699},[1149],[1151,23701,23702],{"xmlns":1153},[1155,23703,23704,23712],{},[1158,23705,23706,23708,23710],{},[2278,23707,23688],{},[1165,23709,4156],{},[1282,23711,4455],{},[1194,23713,23714],{"encoding":1196},"\\text{VIF}>5"," (přísněji ",[1115,23717,23719],{"className":23718},[1149],[1151,23720,23721],{"xmlns":1153},[1155,23722,23723,23729],{},[1158,23724,23725,23727],{},[1165,23726,4156],{},[1282,23728,3531],{},[1194,23730,23731],{"encoding":1196},">10",") značí vysokou multikolinearitu.",[1110,23734,23735],{},"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.",[20418,23737,23739],{"id":23738},"další-ukazatele-kvality-modelu","Další ukazatele kvality modelu",[1124,23741,23742,23748,23754],{},[1127,23743,23744,23747],{},[1131,23745,23746],{},"F-test"," — testuje hypotézu, že všechny regresní koeficienty jsou rovny nule, proti alternativě, že aspoň jeden v modelu být má (celková významnost modelu).",[1127,23749,23750,23753],{},[1131,23751,23752],{},"RMSE"," (odmocnina z reziduálního rozptylu) — absolutní měřítko vhodnosti funkce (na rozdíl od indexu determinace, který je relativní); nižší hodnota znamená lepší fit.",[1127,23755,23756,23759,23760,23763],{},[1131,23757,23758],{},"AIC"," (Akaikeho informační kritérium) a ",[1131,23761,23762],{},"BIC"," (Bayesovo informační kritérium) — čím nižší hodnoty obou kritérií, tím lepší model; používají se hlavně při stepwise výběru proměnných.",[20418,23765,20421],{"id":23766},"v-r-2",[1110,23768,23769],{},"Pro vícenásobnou regresi je postup v R rozšířením postupu pro regresní přímku — přibývá výběr proměnných a kontrola multikolinearity:",[3554,23771,23773],{"className":3556,"code":23772,"language":71,"meta":3558,"style":3558},"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",[1373,23774,23775,23801,23845,23871,23881,23885,23896,23907,23911,23921,23931,23935,23945,23955,23960],{"__ignoreMap":3558},[1115,23776,23777,23780,23782,23785,23787,23790,23792,23795,23797,23799],{"class":3563,"line":10},[1115,23778,23779],{"class":3744},"data",[1115,23781,4497],{"class":3741},[1115,23783,23784],{"class":3566}," read.table",[1115,23786,1168],{"class":3569},[1115,23788,23789],{"class":7974},"\"4_4.txt\"",[1115,23791,1715],{"class":3741},[1115,23793,23794],{"class":3744}," header",[1115,23796,3748],{"class":3741},[1115,23798,7944],{"class":3572},[1115,23800,3575],{"class":3569},[1115,23802,23803,23806,23808,23810,23812,23814,23816,23819,23821,23824,23826,23829,23831,23834,23836,23839,23841,23843],{"class":3563,"line":27},[1115,23804,23805],{"class":3744},"model_plny",[1115,23807,4497],{"class":3741},[1115,23809,20522],{"class":3566},[1115,23811,1168],{"class":3569},[1115,23813,1603],{"class":3744},[1115,23815,20529],{"class":3741},[1115,23817,23818],{"class":3744}," x1",[1115,23820,22187],{"class":3741},[1115,23822,23823],{"class":3744}," x2",[1115,23825,22187],{"class":3741},[1115,23827,23828],{"class":3744}," x3",[1115,23830,22187],{"class":3741},[1115,23832,23833],{"class":3744}," x4",[1115,23835,1715],{"class":3741},[1115,23837,23838],{"class":3744}," data",[1115,23840,3748],{"class":3741},[1115,23842,23838],{"class":3744},[1115,23844,3575],{"class":3569},[1115,23846,23847,23850,23852,23855,23857,23859,23861,23864,23866,23869],{"class":3563,"line":148},[1115,23848,23849],{"class":3744},"model_krok",[1115,23851,4497],{"class":3741},[1115,23853,23854],{"class":3566}," step",[1115,23856,1168],{"class":3569},[1115,23858,23805],{"class":3744},[1115,23860,1715],{"class":3741},[1115,23862,23863],{"class":3744}," direction",[1115,23865,3748],{"class":3741},[1115,23867,23868],{"class":7974}," \"both\"",[1115,23870,3575],{"class":3569},[1115,23872,23873,23875,23877,23879],{"class":3563,"line":111},[1115,23874,20539],{"class":3566},[1115,23876,1168],{"class":3569},[1115,23878,23849],{"class":3744},[1115,23880,3575],{"class":3569},[1115,23882,23883],{"class":3563,"line":96},[1115,23884,4573],{"emptyLinePlaceholder":4572},[1115,23886,23887,23889,23891,23894],{"class":3563,"line":89},[1115,23888,21068],{"class":3741},[1115,23890,1168],{"class":3569},[1115,23892,23893],{"class":3744},"car",[1115,23895,3575],{"class":3569},[1115,23897,23898,23901,23903,23905],{"class":3563,"line":82},[1115,23899,23900],{"class":3566},"vif",[1115,23902,1168],{"class":3569},[1115,23904,23849],{"class":3744},[1115,23906,3575],{"class":3569},[1115,23908,23909],{"class":3563,"line":75},[1115,23910,4573],{"emptyLinePlaceholder":4572},[1115,23912,23913,23915,23917,23919],{"class":3563,"line":8025},[1115,23914,21068],{"class":3741},[1115,23916,1168],{"class":3569},[1115,23918,21073],{"class":3744},[1115,23920,3575],{"class":3569},[1115,23922,23923,23925,23927,23929],{"class":3563,"line":72},[1115,23924,21080],{"class":3566},[1115,23926,1168],{"class":3569},[1115,23928,23849],{"class":3744},[1115,23930,3575],{"class":3569},[1115,23932,23933],{"class":3563,"line":25},[1115,23934,4573],{"emptyLinePlaceholder":4572},[1115,23936,23937,23939,23941,23943],{"class":3563,"line":65},[1115,23938,21068],{"class":3741},[1115,23940,1168],{"class":3569},[1115,23942,21163],{"class":3744},[1115,23944,3575],{"class":3569},[1115,23946,23947,23949,23951,23953],{"class":3563,"line":63},[1115,23948,21170],{"class":3566},[1115,23950,1168],{"class":3569},[1115,23952,23849],{"class":3744},[1115,23954,3575],{"class":3569},[1115,23956,23958],{"class":3563,"line":23957},14,[1115,23959,4573],{"emptyLinePlaceholder":4572},[1115,23961,23962,23964,23966,23968,23970,23972],{"class":3563,"line":60},[1115,23963,21248],{"class":3566},[1115,23965,1168],{"class":3569},[1115,23967,20716],{"class":3566},[1115,23969,1168],{"class":3569},[1115,23971,23849],{"class":3744},[1115,23973,4011],{"class":3569},[1110,23975,23976,23978,23979,23982],{},[1373,23977,19792],{}," provádí stepwise výběr podle AIC, ",[1373,23980,23981],{},"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.",[1103,23984,23986,23993,23996,23999],{"className":23985,"dataCallout":3670},[1106,3669],[1110,23987,23989,23992],{"className":23988},[1113],[1115,23990],{"className":23991,"ariaHidden":1121},[1118,3677,1120],"Příklad: Vícenásobná regrese",[1110,23994,23995],{},"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.",[1110,23997,23998],{},"Postup: odhad plného modelu → stepwise analýza podle AIC → ověření předpokladů.",[1110,24000,24001,24002,24005,24006,24008,24009,24012],{},"Diagnostika odhaleného modelu ukázala tři problémy: (1) ",[1131,24003,24004],{},"nelinearita"," — mezi některými vysvětlujícími proměnnými a cenou je zjevně jiný než lineární vztah, řešením je zkusit u nich druhou mocninu; (2) ",[1131,24007,23627],{}," mezi dvojicí proměnných popisujících vzdálenost (k silnici a ke spalovně) — doporučeno jednu z nich vynechat; (3) ",[1131,24010,24011],{},"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.",[1431,24014,5414],{"id":5413},[1103,24016,24018,24025],{"className":24017,"dataCallout":3448},[1106,3447],[1110,24019,24021,24024],{"className":24020},[1113],[1115,24022],{"className":24023,"ariaHidden":1121},[1118,3455,1120],"Koeficient korelace jen pro přímku",[1110,24026,24027,24028,24084,24085,24102,24103,24123,24124,1425,24137,1333],{},"Vzorec ",[1115,24029,24031],{"className":24030},[1149],[1151,24032,24033],{"xmlns":1153},[1155,24034,24035,24081],{},[1158,24036,24037,24047,24049,24059,24061],{},[1277,24038,24039,24041],{},[1161,24040,71],{},[1158,24042,24043,24045],{},[1161,24044,1171],{},[1161,24046,1603],{},[1165,24048,1177],{},[1277,24050,24051,24053],{},[1161,24052,6018],{},[1158,24054,24055,24057],{},[1161,24056,1171],{},[1161,24058,1603],{},[1161,24060,3434],{"mathvariant":1215},[2765,24062,24063],{},[1158,24064,24065,24073],{},[2256,24066,24067,24069,24071],{},[1161,24068,6018],{},[1161,24070,1171],{},[1282,24072,1298],{},[2256,24074,24075,24077,24079],{},[1161,24076,6018],{},[1161,24078,1603],{},[1282,24080,1298],{},[1194,24082,24083],{"encoding":1196},"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 ",[1115,24086,24088],{"className":24087},[1149],[1151,24089,24090],{"xmlns":1153},[1155,24091,24092,24100],{},[1158,24093,24094],{},[1209,24095,24096,24098],{},[1161,24097,4759],{},[1282,24099,1298],{},[1194,24101,19696],{"encoding":1196},", případně obecným indexem korelace ",[1115,24104,24106],{"className":24105},[1149],[1151,24107,24108],{"xmlns":1153},[1155,24109,24110,24120],{},[1158,24111,24112],{},[2765,24113,24114],{},[1209,24115,24116,24118],{},[1161,24117,4759],{},[1282,24119,1298],{},[1194,24121,24122],{"encoding":1196},"\\sqrt{R^2}"," — ne koeficientem korelace mezi ",[1115,24125,24127],{"className":24126},[1149],[1151,24128,24129],{"xmlns":1153},[1155,24130,24131,24135],{},[1158,24132,24133],{},[1161,24134,1171],{},[1194,24136,1171],{"encoding":1196},[1115,24138,24140],{"className":24139},[1149],[1151,24141,24142],{"xmlns":1153},[1155,24143,24144,24148],{},[1158,24145,24146],{},[1161,24147,1603],{},[1194,24149,1603],{"encoding":1196},[1103,24151,24153,24160],{"className":24152,"dataCallout":3448},[1106,3447],[1110,24154,24156,24159],{"className":24155},[1113],[1115,24157],{"className":24158,"ariaHidden":1121},[1118,3455,1120],"Významný F-test, nevýznamné t-testy",[1110,24161,24162],{},"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.",[1103,24164,24166,24173],{"className":24165,"dataCallout":3448},[1106,3447],[1110,24167,24169,24172],{"className":24168},[1113],[1115,24170],{"className":24171,"ariaHidden":1121},[1118,3455,1120],"Durbin-Watsonova statistika mimo okolí 2",[1110,24174,24175],{},"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.",[1103,24177,24179,24186],{"className":24178,"dataCallout":3448},[1106,3447],[1110,24180,24182,24185],{"className":24181},[1113],[1115,24183],{"className":24184,"ariaHidden":1121},[1118,3455,1120],"Nízký počet pozorování při stepwise výběru",[1110,24187,24188],{},"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.",[1431,24190,5604],{"id":5603},[1124,24192,24193,24198,24203,24208,24213,24218,24223],{},[1127,24194,24195],{},[1438,24196,1444],{"className":24197,"dataFsResolvedFilePath":1442,"href":1443},[1441],[1127,24199,24200],{},[1438,24201,1094],{"className":24202,"dataFsResolvedFilePath":10731,"href":10732},[1441],[1127,24204,24205],{},[1438,24206,10725],{"className":24207,"dataFsResolvedFilePath":2788,"href":2789},[1441],[1127,24209,24210],{},[1438,24211,10719],{"className":24212,"dataFsResolvedFilePath":4636,"href":4637},[1441],[1127,24214,24215],{},[1438,24216,5698],{"className":24217,"dataFsResolvedFilePath":5635,"href":5636},[1441],[1127,24219,24220],{},[1438,24221,10744],{"className":24222,"dataFsResolvedFilePath":5642,"href":5643},[1441],[1127,24224,24225],{},[1438,24226,5652],{"className":24227,"dataFsResolvedFilePath":5650,"href":5651},[1441],[1431,24229,5655],{"id":934},[1110,24231,5658,24232,5663],{},[5660,24233,5662],{},[5665,24235,24236],{},"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.",[1127,24295,24296,24297,1376,24323,1425,24349,1333],{},"Regulace měřením (spojitá veličina s normálním rozdělením): diagramy ",[1115,24298,24300],{"className":24299},[1149],[1151,24301,24302],{"xmlns":1153},[1155,24303,24304,24320],{},[1158,24305,24306,24308,24314,24316,24318],{},[1165,24307,1168],{"stretchy":1167},[6877,24309,24310,24312],{"accent":1121},[1161,24311,1171],{},[1165,24313,15130],{},[1165,24315,1715],{"separator":1121},[1161,24317,4759],{},[1165,24319,1174],{"stretchy":1167},[1194,24321,24322],{"encoding":1196},"(\\bar{x}, R)",[1115,24324,24326],{"className":24325},[1149],[1151,24327,24328],{"xmlns":1153},[1155,24329,24330,24346],{},[1158,24331,24332,24334,24340,24342,24344],{},[1165,24333,1168],{"stretchy":1167},[6877,24335,24336,24338],{"accent":1121},[1161,24337,1171],{},[1165,24339,15130],{},[1165,24341,1715],{"separator":1121},[1161,24343,6018],{},[1165,24345,1174],{"stretchy":1167},[1194,24347,24348],{"encoding":1196},"(\\bar{x}, s)",[1115,24350,24352],{"className":24351},[1149],[1151,24353,24354],{"xmlns":1153},[1155,24355,24356,24385],{},[1158,24357,24358,24360,24366,24368,24383],{},[1165,24359,1168],{"stretchy":1167},[1277,24361,24362,24364],{},[1161,24363,1171],{},[1161,24365,4187],{},[1165,24367,1715],{"separator":1121},[1277,24369,24370,24372],{},[1161,24371,4759],{},[1158,24373,24374,24376,24379,24381],{},[1161,24375,1735],{},[1161,24377,24378],{},"l",[1165,24380,1715],{"separator":1121},[1161,24382,4187],{},[1165,24384,1174],{"stretchy":1167},[1194,24386,24387],{"encoding":1196},"(x_i, R_{kl,i})",[1127,24389,24390,24391,24404,24405,24418,24419,24435,24436,24449],{},"Regulace srovnáváním (diskrétní veličina): počet neshod ",[1115,24392,24394],{"className":24393},[1149],[1151,24395,24396],{"xmlns":1153},[1155,24397,24398,24402],{},[1158,24399,24400],{},[1161,24401,7856],{},[1194,24403,7856],{"encoding":1196}," (konstantní rozsah) a ",[1115,24406,24408],{"className":24407},[1149],[1151,24409,24410],{"xmlns":1153},[1155,24411,24412,24416],{},[1158,24413,24414],{},[1161,24415,15199],{},[1194,24417,15199],{"encoding":1196}," (nekonstantní rozsah), počet neshodných produktů ",[1115,24420,24422],{"className":24421},[1149],[1151,24423,24424],{"xmlns":1153},[1155,24425,24426,24432],{},[1158,24427,24428,24430],{},[1161,24429,4192],{},[1161,24431,1110],{},[1194,24433,24434],{"encoding":1196},"np"," (konstantní rozsah) a jejich podíl ",[1115,24437,24439],{"className":24438},[1149],[1151,24440,24441],{"xmlns":1153},[1155,24442,24443,24447],{},[1158,24444,24445],{},[1161,24446,1110],{},[1194,24448,1110],{"encoding":1196}," (nekonstantní rozsah).",[1127,24451,24452],{},"Podskupiny s vymezitelnou příčinou se po jejím odstranění z výpočtu vyřadí a meze se přepočítají, dokud jsou všechny body uvnitř mezí.",[1127,24454,24455,24456,1376,24475,1376,24497,1376,24519,24543,24544,24565],{},"Indexy způsobilosti ",[1115,24457,24459],{"className":24458},[1149],[1151,24460,24461],{"xmlns":1153},[1155,24462,24463,24472],{},[1158,24464,24465],{},[1277,24466,24467,24470],{},[1161,24468,24469],{},"C",[1161,24471,1110],{},[1194,24473,24474],{"encoding":1196},"C_p",[1115,24476,24478],{"className":24477},[1149],[1151,24479,24480],{"xmlns":1153},[1155,24481,24482,24494],{},[1158,24483,24484],{},[1277,24485,24486,24488],{},[1161,24487,24469],{},[1158,24489,24490,24492],{},[1161,24491,1110],{},[1161,24493,1735],{},[1194,24495,24496],{"encoding":1196},"C_{pk}",[1115,24498,24500],{"className":24499},[1149],[1151,24501,24502],{"xmlns":1153},[1155,24503,24504,24516],{},[1158,24505,24506],{},[1277,24507,24508,24510],{},[1161,24509,24469],{},[1158,24511,24512,24514],{},[1161,24513,1110],{},[1161,24515,8597],{},[1194,24517,24518],{"encoding":1196},"C_{pm}",[1115,24520,24522],{"className":24521},[1149],[1151,24523,24524],{"xmlns":1153},[1155,24525,24526,24540],{},[1158,24527,24528],{},[1277,24529,24530,24532],{},[1161,24531,24469],{},[1158,24533,24534,24536,24538],{},[1161,24535,1110],{},[1161,24537,8597],{},[1161,24539,1735],{},[1194,24541,24542],{"encoding":1196},"C_{pmk}"," posuzují, zda statisticky zvládnutý proces vyhovuje tolerančním mezím; ",[1115,24545,24547],{"className":24546},[1149],[1151,24548,24549],{"xmlns":1153},[1155,24550,24551,24563],{},[1158,24552,24553],{},[1277,24554,24555,24557],{},[1161,24556,24469],{},[1158,24558,24559,24561],{},[1161,24560,1110],{},[1161,24562,1735],{},[1194,24564,24496],{"encoding":1196}," navíc zohledňuje vychýlení střední hodnoty.",[1127,24567,24568,24569,1333],{},"V R diagramy i indexy počítá balíček ",[1373,24570,360],{},[1431,24572,24574],{"id":24573},"statistická-regulace-procesu","Statistická regulace procesu",[1110,24576,24577,24578,24580,24581,1333],{},"Tradiční zabezpečování jakosti kontroluje výrobky až po jejich vyrobení, což je neekonomické. ",[1131,24579,24574],{}," 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 ",[1131,24582,24583],{},"statisticky zvládnutém stavu",[1110,24585,24586,24587,24590],{},"Teorie regulace vychází z ",[1131,24588,24589],{},"variability"," procesu, kterou způsobují dva druhy příčin:",[4052,24592,24593,24605],{},[4055,24594,24595],{},[4058,24596,24597,24599,24602],{},[4061,24598],{},[4061,24600,24601],{},"Náhodné příčiny",[4061,24603,24604],{},"Vymezitelné příčiny",[4165,24606,24607,24618,24629],{},[4058,24608,24609,24612,24615],{},[4170,24610,24611],{},"Povaha",[4170,24613,24614],{},"široká skupina neidentifikovatelných vlivů, každý přispívá k variabilitě malou měrou",[4170,24616,24617],{},"vlivy, které za běžných podmínek na proces nepůsobí; vyvolají nepřirozené kolísání údajů",[4058,24619,24620,24623,24626],{},[4170,24621,24622],{},"Stav procesu",[4170,24624,24625],{},"ustálený, jakost výstupů je předvídatelná, není nutné zasahovat — statisticky zvládnutý",[4170,24627,24628],{},"jakost výstupů není předvídatelná, je nutné zasáhnout — proces není statisticky zvládnutý",[4058,24630,24631,24634,24637],{},[4170,24632,24633],{},"Příklady",[4170,24635,24636],{},"psychický stav pracovníka, chvění stroje, teplota ovzduší",[4170,24638,24639],{},"změna materiálu, nezaškolená obsluha",[1110,24641,24642,24643,24646,24647,24650],{},"Vymezitelné příčiny jsou ",[1131,24644,24645],{},"sporadické"," (vznikají náhle, změny trvají krátce) nebo ",[1131,24648,24649],{},"přetrvávající"," (trvají stále nebo se mění).",[1110,24652,24653],{},[1760,24654],{"alt":24655,"className":24656,"src":24657},"mask-ilu-pricin-variability",[1441,1764],"\u002Fwiki-assets\u002Fmask-ilu-pricin-variability.png",[1110,24659,24660],{},"Regulace probíhá ve třech fázích:",[7018,24662,24663,24673,24679],{},[1127,24664,24665,24668,24669,24672],{},[1131,24666,24667],{},"Fáze přípravná"," — stanoví se sledované znaky jakosti (rozměr, hmotnost, počet vad…), délka časového intervalu mezi měřeními, ",[1131,24670,24671],{},"logická podskupina"," (skupina měření, v níž se předpokládá působení pouze náhodných příčin), typ regulačního diagramu a místa kontroly v procesu.",[1127,24674,24675,24678],{},[1131,24676,24677],{},"Fáze zabezpečování statistické zvládnutosti"," — pomocí regulačních diagramů se identifikují vymezitelné příčiny a odstraní se jejich působení.",[1127,24680,24681,24684],{},[1131,24682,24683],{},"Fáze analýzy a zabezpečení způsobilosti"," — zkoumá se, zda statisticky zvládnutý proces vyhovuje požadavkům zákazníka; k tomu slouží indexy způsobilosti (níže).",[1431,24686,24688],{"id":24687},"princip-regulačního-diagramu","Princip regulačního diagramu",[1110,24690,24691,24694],{},[1131,24692,24693],{},"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.",[1124,24696,24697,24703,24709],{},[1127,24698,24699,24702],{},[1131,24700,24701],{},"CL"," — střední přímka, odpovídá požadované (referenční) hodnotě použité charakteristiky,",[1127,24704,24705,24708],{},[1131,24706,24707],{},"UCL"," — horní akční regulační mez,",[1127,24710,24711,24714],{},[1131,24712,24713],{},"LCL"," — dolní akční regulační mez.",[1110,24716,24717],{},"Akční meze vymezují pásmo působení pouze náhodných příčin variability.",[1110,24719,24720],{},[1760,24721],{"alt":24722,"className":24723,"src":24724},"mask-rd-schema",[1441,1764],"\u002Fwiki-assets\u002Fmask-rd-schema.png",[1110,24726,24727,24730],{},[1131,24728,24729],{},"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.",[1110,24732,24733,24734,24737,24738,24741],{},"Podle charakteru regulované veličiny se diagramy dělí na diagramy pro ",[1131,24735,24736],{},"regulaci měřením"," (regulovaná veličina je spojitá náhodná veličina) a pro ",[1131,24739,24740],{},"regulaci srovnáváním"," (diskrétní náhodná veličina).",[1110,24743,24744],{},"Postup při konstrukci regulačního diagramu:",[7018,24746,24747,24750,24753,24756,24759,24762,24765,24768,24771],{},[1127,24748,24749],{},"volba regulované veličiny,",[1127,24751,24752],{},"sběr a záznam dat,",[1127,24754,24755],{},"ověření požadovaných předpokladů o datech,",[1127,24757,24758],{},"volba rozsahu logických podskupin,",[1127,24760,24761],{},"volba vhodného regulačního diagramu,",[1127,24763,24764],{},"výpočet hodnot zvoleného testového kritéria pro jednotlivé výběry,",[1127,24766,24767],{},"ověření a zajištění statistické zvládnutosti procesu,",[1127,24769,24770],{},"ověření způsobilosti procesu,",[1127,24772,24773],{},"vlastní regulace procesu.",[1431,24775,24777],{"id":24776},"regulace-měřením","Regulace měřením",[1110,24779,24780],{},"Diagramy pro regulaci měřením se používají, když je regulovaná veličina měřitelná. Požaduje se, aby:",[1124,24782,24783,24786],{},[1127,24784,24785],{},"jednotlivá měření byla vzájemně nezávislá,",[1127,24787,24788,24789,24802,24803,24816,24817,24830,24831,24844],{},"regulovaná veličina byla spojitá náhodná veličina s normálním rozdělením se střední hodnotou ",[1115,24790,24792],{"className":24791},[1149],[1151,24793,24794],{"xmlns":1153},[1155,24795,24796,24800],{},[1158,24797,24798],{},[1161,24799,1355],{},[1194,24801,3289],{"encoding":1196}," a směrodatnou odchylkou ",[1115,24804,24806],{"className":24805},[1149],[1151,24807,24808],{"xmlns":1153},[1155,24809,24810,24814],{},[1158,24811,24812],{},[1161,24813,1363],{},[1194,24815,1397],{"encoding":1196}," — tyto dva parametry charakterizují statistickou stabilitu procesu; ",[1115,24818,24820],{"className":24819},[1149],[1151,24821,24822],{"xmlns":1153},[1155,24823,24824,24828],{},[1158,24825,24826],{},[1161,24827,1355],{},[1194,24829,3289],{"encoding":1196}," je hodnota, na niž je proces nastaven, ",[1115,24832,24834],{"className":24833},[1149],[1151,24835,24836],{"xmlns":1153},[1155,24837,24838,24842],{},[1158,24839,24840],{},[1161,24841,1363],{},[1194,24843,1397],{"encoding":1196}," charakterizuje jeho přesnost.",[1110,24846,24847,24848,1376,24873,1425,24898,24935],{},"Jsou-li předpoklady splněny, volí se diagramy, které současně sledují stabilitu polohy i stabilitu rozptylu: ",[1115,24849,24851],{"className":24850},[1149],[1151,24852,24853],{"xmlns":1153},[1155,24854,24855,24871],{},[1158,24856,24857,24859,24865,24867,24869],{},[1165,24858,1168],{"stretchy":1167},[6877,24860,24861,24863],{"accent":1121},[1161,24862,1171],{},[1165,24864,15130],{},[1165,24866,1715],{"separator":1121},[1161,24868,4759],{},[1165,24870,1174],{"stretchy":1167},[1194,24872,24322],{"encoding":1196},[1115,24874,24876],{"className":24875},[1149],[1151,24877,24878],{"xmlns":1153},[1155,24879,24880,24896],{},[1158,24881,24882,24884,24890,24892,24894],{},[1165,24883,1168],{"stretchy":1167},[6877,24885,24886,24888],{"accent":1121},[1161,24887,1171],{},[1165,24889,15130],{},[1165,24891,1715],{"separator":1121},[1161,24893,6018],{},[1165,24895,1174],{"stretchy":1167},[1194,24897,24348],{"encoding":1196},[1115,24899,24901],{"className":24900},[1149],[1151,24902,24903],{"xmlns":1153},[1155,24904,24905,24933],{},[1158,24906,24907,24909,24915,24917,24931],{},[1165,24908,1168],{"stretchy":1167},[1277,24910,24911,24913],{},[1161,24912,1171],{},[1161,24914,4187],{},[1165,24916,1715],{"separator":1121},[1277,24918,24919,24921],{},[1161,24920,4759],{},[1158,24922,24923,24925,24927,24929],{},[1161,24924,1735],{},[1161,24926,24378],{},[1165,24928,1715],{"separator":1121},[1161,24930,4187],{},[1165,24932,1174],{"stretchy":1167},[1194,24934,24387],{"encoding":1196},". Výsledkem jsou vždy dva diagramy.",[20418,24937,24939,24940],{"id":24938},"diagram-xˉrbarx-r","Diagram ",[1115,24941,24943],{"className":24942},[1149],[1151,24944,24945],{"xmlns":1153},[1155,24946,24947,24963],{},[1158,24948,24949,24951,24957,24959,24961],{},[1165,24950,1168],{"stretchy":1167},[6877,24952,24953,24955],{"accent":1121},[1161,24954,1171],{},[1165,24956,15130],{},[1165,24958,1715],{"separator":1121},[1161,24960,4759],{},[1165,24962,1174],{"stretchy":1167},[1194,24964,24322],{"encoding":1196},[1110,24966,24967,24968,24990,24991,25009],{},"Regulované veličiny jsou výběrové průměry ",[1115,24969,24971],{"className":24970},[1149],[1151,24972,24973],{"xmlns":1153},[1155,24974,24975,24987],{},[1158,24976,24977],{},[1277,24978,24979,24985],{},[6877,24980,24981,24983],{"accent":1121},[1161,24982,1171],{},[1165,24984,15130],{},[1161,24986,4187],{},[1194,24988,24989],{"encoding":1196},"\\bar{x}_i"," a výběrová rozpětí ",[1115,24992,24994],{"className":24993},[1149],[1151,24995,24996],{"xmlns":1153},[1155,24997,24998,25006],{},[1158,24999,25000],{},[1277,25001,25002,25004],{},[1161,25003,4759],{},[1161,25005,4187],{},[1194,25007,25008],{"encoding":1196},"R_i"," v logických podskupinách:",[1115,25011,25013],{"className":25012},[1149],[1151,25014,25015],{"xmlns":1153,"display":2212},[1155,25016,25017,25118],{},[1158,25018,25019,25029,25031,25037,25051,25061,25063,25065,25071,25073,25084,25094,25096,25106,25116],{},[1277,25020,25021,25027],{},[6877,25022,25023,25025],{"accent":1121},[1161,25024,1171],{},[1165,25026,15130],{},[1161,25028,4187],{},[1165,25030,1177],{},[3064,25032,25033,25035],{},[1282,25034,1284],{},[1161,25036,4192],{},[6140,25038,25039,25041,25049],{},[1165,25040,6144],{},[1158,25042,25043,25045,25047],{},[1161,25044,6044],{},[1165,25046,1177],{},[1282,25048,1284],{},[1161,25050,4192],{},[1277,25052,25053,25055],{},[1161,25054,1171],{},[1158,25056,25057,25059],{},[1161,25058,4187],{},[1161,25060,6044],{},[1165,25062,1715],{"separator":1121},[2242,25064],{"width":2244},[1277,25066,25067,25069],{},[1161,25068,4759],{},[1161,25070,4187],{},[1165,25072,1177],{},[25074,25075,25076,25082],"munder",{},[1158,25077,25078,25080],{},[1161,25079,15390],{},[1165,25081,2079],{},[1161,25083,6044],{},[1277,25085,25086,25088],{},[1161,25087,1171],{},[1158,25089,25090,25092],{},[1161,25091,4187],{},[1161,25093,6044],{},[1165,25095,1317],{},[25074,25097,25098,25104],{},[1158,25099,25100,25102],{},[1161,25101,8614],{},[1165,25103,2079],{},[1161,25105,6044],{},[1277,25107,25108,25110],{},[1161,25109,1171],{},[1158,25111,25112,25114],{},[1161,25113,4187],{},[1161,25115,6044],{},[1161,25117,1333],{"mathvariant":1215},[1194,25119,25120],{"encoding":1196},"\\bar{x}_i = \\frac{1}{n}\\sum_{j=1}^n x_{ij}, \\qquad R_i = \\max_j x_{ij} - \\min_j x_{ij}.",[1110,25122,25123],{},"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.",[1110,25125,25126,25127,25153,25154,25167,25168,1425,25189,25206,25207,25220,25221,25239,25240,1333],{},"Data se zapisují do tabulky: řádek ",[1115,25128,25130],{"className":25129},[1149],[1151,25131,25132],{"xmlns":1153},[1155,25133,25134,25150],{},[1158,25135,25136,25138,25140,25142,25144,25146,25148],{},[1161,25137,4187],{},[1165,25139,1177],{},[1282,25141,1284],{},[1165,25143,1715],{"separator":1121},[1165,25145,1726],{},[1165,25147,1715],{"separator":1121},[1161,25149,1735],{},[1194,25151,25152],{"encoding":1196},"i = 1, \\dots, k"," je logická podskupina v pořadí, v jakém byla získána, sloupce obsahují ",[1115,25155,25157],{"className":25156},[1149],[1151,25158,25159],{"xmlns":1153},[1155,25160,25161,25165],{},[1158,25162,25163],{},[1161,25164,4192],{},[1194,25166,4192],{"encoding":1196}," naměřených hodnot a poslední dva sloupce ",[1115,25169,25171],{"className":25170},[1149],[1151,25172,25173],{"xmlns":1153},[1155,25174,25175,25187],{},[1158,25176,25177],{},[1277,25178,25179,25185],{},[6877,25180,25181,25183],{"accent":1121},[1161,25182,1171],{},[1165,25184,15130],{},[1161,25186,4187],{},[1194,25188,24989],{"encoding":1196},[1115,25190,25192],{"className":25191},[1149],[1151,25193,25194],{"xmlns":1153},[1155,25195,25196,25204],{},[1158,25197,25198],{},[1277,25199,25200,25202],{},[1161,25201,4759],{},[1161,25203,4187],{},[1194,25205,25008],{"encoding":1196},". Pro sestrojení diagramu je potřeba aspoň 20 podskupin. Nejprve se určí diagram ",[1115,25208,25210],{"className":25209},[1149],[1151,25211,25212],{"xmlns":1153},[1155,25213,25214,25218],{},[1158,25215,25216],{},[1161,25217,4759],{},[1194,25219,4759],{"encoding":1196},", potom diagram ",[1115,25222,25224],{"className":25223},[1149],[1151,25225,25226],{"xmlns":1153},[1155,25227,25228,25236],{},[1158,25229,25230],{},[6877,25231,25232,25234],{"accent":1121},[1161,25233,1171],{},[1165,25235,15130],{},[1194,25237,25238],{"encoding":1196},"\\bar{x}"," — u obou střední přímka a akční meze. V R se diagramy konstruují funkcí ",[1373,25241,25242],{},"qcc()",[1103,25244,25246,25253],{"className":25245,"dataCallout":3670},[1106,3669],[1110,25247,25249,25252],{"className":25248},[1113],[1115,25250],{"className":25251,"ariaHidden":1121},[1118,3677,1120],"Příklad: kontrola rozměru dílu ve 20 logických podskupinách",[1110,25254,25255,25256,25269,25270,1376,25288,25306,25307,1333],{},"Naměřená data znaku jakosti ",[1115,25257,25259],{"className":25258},[1149],[1151,25260,25261],{"xmlns":1153},[1155,25262,25263,25267],{},[1158,25264,25265],{},[1161,25266,1185],{},[1194,25268,1185],{"encoding":1196}," byla získána ve 20 logických podskupinách po 4 měřeních (",[1115,25271,25273],{"className":25272},[1149],[1151,25274,25275],{"xmlns":1153},[1155,25276,25277,25285],{},[1158,25278,25279,25281,25283],{},[1161,25280,1735],{},[1165,25282,1177],{},[1282,25284,8175],{},[1194,25286,25287],{"encoding":1196},"k=20",[1115,25289,25291],{"className":25290},[1149],[1151,25292,25293],{"xmlns":1153},[1155,25294,25295,25303],{},[1158,25296,25297,25299,25301],{},[1161,25298,4192],{},[1165,25300,1177],{},[1282,25302,7687],{},[1194,25304,25305],{"encoding":1196},"n=4","); znak je měřitelný a má normální rozdělení. Sestrojte regulační diagram ",[1115,25308,25310],{"className":25309},[1149],[1151,25311,25312],{"xmlns":1153},[1155,25313,25314,25330],{},[1158,25315,25316,25318,25324,25326,25328],{},[1165,25317,1168],{"stretchy":1167},[6877,25319,25320,25322],{"accent":1121},[1161,25321,1171],{},[1165,25323,15130],{},[1165,25325,1715],{"separator":1121},[1161,25327,4759],{},[1165,25329,1174],{"stretchy":1167},[1194,25331,24322],{"encoding":1196},[4052,25333,25334,25449],{},[4055,25335,25336],{},[4058,25337,25338,25353,25377,25401,25425],{},[4061,25339,25340],{},[1115,25341,25343],{"className":25342},[1149],[1151,25344,25345],{"xmlns":1153},[1155,25346,25347,25351],{},[1158,25348,25349],{},[1161,25350,4187],{},[1194,25352,4187],{"encoding":1196},[4061,25354,25355],{},[1115,25356,25358],{"className":25357},[1149],[1151,25359,25360],{"xmlns":1153},[1155,25361,25362,25374],{},[1158,25363,25364],{},[1277,25365,25366,25368],{},[1161,25367,1171],{},[1158,25369,25370,25372],{},[1161,25371,4187],{},[1282,25373,1284],{},[1194,25375,25376],{"encoding":1196},"x_{i1}",[4061,25378,25379],{},[1115,25380,25382],{"className":25381},[1149],[1151,25383,25384],{"xmlns":1153},[1155,25385,25386,25398],{},[1158,25387,25388],{},[1277,25389,25390,25392],{},[1161,25391,1171],{},[1158,25393,25394,25396],{},[1161,25395,4187],{},[1282,25397,1298],{},[1194,25399,25400],{"encoding":1196},"x_{i2}",[4061,25402,25403],{},[1115,25404,25406],{"className":25405},[1149],[1151,25407,25408],{"xmlns":1153},[1155,25409,25410,25422],{},[1158,25411,25412],{},[1277,25413,25414,25416],{},[1161,25415,1171],{},[1158,25417,25418,25420],{},[1161,25419,4187],{},[1282,25421,3322],{},[1194,25423,25424],{"encoding":1196},"x_{i3}",[4061,25426,25427],{},[1115,25428,25430],{"className":25429},[1149],[1151,25431,25432],{"xmlns":1153},[1155,25433,25434,25446],{},[1158,25435,25436],{},[1277,25437,25438,25440],{},[1161,25439,1171],{},[1158,25441,25442,25444],{},[1161,25443,4187],{},[1282,25445,7687],{},[1194,25447,25448],{"encoding":1196},"x_{i4}",[4165,25450,25451,25465,25480,25496,25511,25523,25537,25549,25562],{},[4058,25452,25453,25455,25458,25461,25463],{},[4170,25454,1284],{},[4170,25456,25457],{},"106",[4170,25459,25460],{},"98",[4170,25462,17756],{},[4170,25464,17756],{},[4058,25466,25467,25469,25472,25475,25478],{},[4170,25468,1298],{},[4170,25470,25471],{},"95",[4170,25473,25474],{},"94",[4170,25476,25477],{},"108",[4170,25479,10241],{},[4058,25481,25482,25484,25487,25490,25493],{},[4170,25483,3322],{},[4170,25485,25486],{},"122",[4170,25488,25489],{},"105",[4170,25491,25492],{},"103",[4170,25494,25495],{},"133",[4058,25497,25498,25500,25503,25505,25508],{},[4170,25499,7687],{},[4170,25501,25502],{},"113",[4170,25504,7709],{},[4170,25506,25507],{},"128",[4170,25509,25510],{},"135",[4058,25512,25513,25515,25517,25519,25521],{},[4170,25514,4455],{},[4170,25516,17756],{},[4170,25518,10241],{},[4170,25520,25492],{},[4170,25522,10241],{},[4058,25524,25525,25527,25529,25531,25534],{},[4170,25526,8094],{},[4170,25528,25460],{},[4170,25530,25492],{},[4170,25532,25533],{},"97",[4170,25535,25536],{},"99",[4058,25538,25539,25541,25543,25545,25547],{},[4170,25540,1726],{},[4170,25542,1726],{},[4170,25544,1726],{},[4170,25546,1726],{},[4170,25548,1726],{},[4058,25550,25551,25553,25555,25557,25560],{},[4170,25552,18390],{},[4170,25554,25507],{},[4170,25556,25495],{},[4170,25558,25559],{},"120",[4170,25561,18418],{},[4058,25563,25564,25566,25568,25570,25572],{},[4170,25565,8175],{},[4170,25567,25460],{},[4170,25569,25492],{},[4170,25571,25533],{},[4170,25573,25536],{},[1110,25575,25576,25577,25598,25599,2629],{},"Pro každou podskupinu se dopočítá výběrový průměr ",[1115,25578,25580],{"className":25579},[1149],[1151,25581,25582],{"xmlns":1153},[1155,25583,25584,25596],{},[1158,25585,25586],{},[1277,25587,25588,25594],{},[6877,25589,25590,25592],{"accent":1121},[1161,25591,1171],{},[1165,25593,15130],{},[1161,25595,4187],{},[1194,25597,24989],{"encoding":1196}," a rozpětí ",[1115,25600,25602],{"className":25601},[1149],[1151,25603,25604],{"xmlns":1153},[1155,25605,25606,25614],{},[1158,25607,25608],{},[1277,25609,25610,25612],{},[1161,25611,4759],{},[1161,25613,4187],{},[1194,25615,25008],{"encoding":1196},[4052,25617,25618,25679],{},[4055,25619,25620],{},[4058,25621,25622,25637,25660],{},[4061,25623,25624],{},[1115,25625,25627],{"className":25626},[1149],[1151,25628,25629],{"xmlns":1153},[1155,25630,25631,25635],{},[1158,25632,25633],{},[1161,25634,4187],{},[1194,25636,4187],{"encoding":1196},[4061,25638,25639],{},[1115,25640,25642],{"className":25641},[1149],[1151,25643,25644],{"xmlns":1153},[1155,25645,25646,25658],{},[1158,25647,25648],{},[1277,25649,25650,25656],{},[6877,25651,25652,25654],{"accent":1121},[1161,25653,1171],{},[1165,25655,15130],{},[1161,25657,4187],{},[1194,25659,24989],{"encoding":1196},[4061,25661,25662],{},[1115,25663,25665],{"className":25664},[1149],[1151,25666,25667],{"xmlns":1153},[1155,25668,25669,25677],{},[1158,25670,25671],{},[1277,25672,25673,25675],{},[1161,25674,4759],{},[1161,25676,4187],{},[1194,25678,25008],{"encoding":1196},[4165,25680,25681,25690,25700,25710,25720,25729,25738,25746,25755],{},[4058,25682,25683,25685,25688],{},[4170,25684,1284],{},[4170,25686,25687],{},"101,50",[4170,25689,18485],{},[4058,25691,25692,25694,25697],{},[4170,25693,1298],{},[4170,25695,25696],{},"97,25",[4170,25698,25699],{},"16",[4058,25701,25702,25704,25707],{},[4170,25703,3322],{},[4170,25705,25706],{},"115,75",[4170,25708,25709],{},"30",[4058,25711,25712,25714,25717],{},[4170,25713,7687],{},[4170,25715,25716],{},"111,75",[4170,25718,25719],{},"64",[4058,25721,25722,25724,25727],{},[4170,25723,4455],{},[4170,25725,25726],{},"97,00",[4170,25728,6408],{},[4058,25730,25731,25733,25736],{},[4170,25732,8094],{},[4170,25734,25735],{},"99,25",[4170,25737,8094],{},[4058,25739,25740,25742,25744],{},[4170,25741,1726],{},[4170,25743,1726],{},[4170,25745,1726],{},[4058,25747,25748,25750,25753],{},[4170,25749,18390],{},[4170,25751,25752],{},"126,50",[4170,25754,7690],{},[4058,25756,25757,25759,25761],{},[4170,25758,8175],{},[4170,25760,25735],{},[4170,25762,8094],{},[1110,25764,25765,25766,25779,25780,1376,25808,1376,25838,25866,25867,25889,25890,1376,25917,1376,25946,25973,25974,1333],{},"Nejprve se posoudí diagram ",[1115,25767,25769],{"className":25768},[1149],[1151,25770,25771],{"xmlns":1153},[1155,25772,25773,25777],{},[1158,25774,25775],{},[1161,25776,4759],{},[1194,25778,4759],{"encoding":1196}," na všech 20 podskupinách: ",[1115,25781,25783],{"className":25782},[1149],[1151,25784,25785],{"xmlns":1153},[1155,25786,25787,25805],{},[1158,25788,25789,25791,25794,25796,25798,25800,25802],{},[1161,25790,24469],{},[1161,25792,25793],{},"L",[1165,25795,1168],{"stretchy":1167},[1161,25797,4759],{},[1165,25799,1174],{"stretchy":1167},[1165,25801,1177],{},[1282,25803,25804],{},"15,8",[1194,25806,25807],{"encoding":1196},"CL(R)=15{,}8",[1115,25809,25811],{"className":25810},[1149],[1151,25812,25813],{"xmlns":1153},[1155,25814,25815,25835],{},[1158,25816,25817,25820,25822,25824,25826,25828,25830,25832],{},[1161,25818,25819],{},"U",[1161,25821,24469],{},[1161,25823,25793],{},[1165,25825,1168],{"stretchy":1167},[1161,25827,4759],{},[1165,25829,1174],{"stretchy":1167},[1165,25831,1177],{},[1282,25833,25834],{},"36,06",[1194,25836,25837],{"encoding":1196},"UCL(R)=36{,}06",[1115,25839,25841],{"className":25840},[1149],[1151,25842,25843],{"xmlns":1153},[1155,25844,25845,25863],{},[1158,25846,25847,25849,25851,25853,25855,25857,25859,25861],{},[1161,25848,25793],{},[1161,25850,24469],{},[1161,25852,25793],{},[1165,25854,1168],{"stretchy":1167},[1161,25856,4759],{},[1165,25858,1174],{"stretchy":1167},[1165,25860,1177],{},[1282,25862,1982],{},[1194,25864,25865],{"encoding":1196},"LCL(R)=0",". Rozpětí čtvrté podskupiny (",[1115,25868,25870],{"className":25869},[1149],[1151,25871,25872],{"xmlns":1153},[1155,25873,25874,25886],{},[1158,25875,25876,25882,25884],{},[1277,25877,25878,25880],{},[1161,25879,4759],{},[1282,25881,7687],{},[1165,25883,1177],{},[1282,25885,25719],{},[1194,25887,25888],{"encoding":1196},"R_4=64",") mez překračuje; po potvrzení vymezitelné příčiny se podskupina 4 z výpočtu vyřadí a meze se přepočítají — ",[1115,25891,25893],{"className":25892},[1149],[1151,25894,25895],{"xmlns":1153},[1155,25896,25897,25914],{},[1158,25898,25899,25901,25903,25905,25907,25909,25911],{},[1161,25900,24469],{},[1161,25902,25793],{},[1165,25904,1168],{"stretchy":1167},[1161,25906,4759],{},[1165,25908,1174],{"stretchy":1167},[1165,25910,1177],{},[1282,25912,25913],{},"13,26",[1194,25915,25916],{"encoding":1196},"CL(R)=13{,}26",[1115,25918,25920],{"className":25919},[1149],[1151,25921,25922],{"xmlns":1153},[1155,25923,25924,25943],{},[1158,25925,25926,25928,25930,25932,25934,25936,25938,25940],{},[1161,25927,25819],{},[1161,25929,24469],{},[1161,25931,25793],{},[1165,25933,1168],{"stretchy":1167},[1161,25935,4759],{},[1165,25937,1174],{"stretchy":1167},[1165,25939,1177],{},[1282,25941,25942],{},"30,27",[1194,25944,25945],{"encoding":1196},"UCL(R)=30{,}27",[1115,25947,25949],{"className":25948},[1149],[1151,25950,25951],{"xmlns":1153},[1155,25952,25953,25971],{},[1158,25954,25955,25957,25959,25961,25963,25965,25967,25969],{},[1161,25956,25793],{},[1161,25958,24469],{},[1161,25960,25793],{},[1165,25962,1168],{"stretchy":1167},[1161,25964,4759],{},[1165,25966,1174],{"stretchy":1167},[1165,25968,1177],{},[1282,25970,1982],{},[1194,25972,25865],{"encoding":1196},". Diagram rozpětí je teď zvládnutý, lze tedy posoudit diagram ",[1115,25975,25977],{"className":25976},[1149],[1151,25978,25979],{"xmlns":1153},[1155,25980,25981,25989],{},[1158,25982,25983],{},[6877,25984,25985,25987],{"accent":1121},[1161,25986,1171],{},[1165,25988,15130],{},[1194,25990,25238],{"encoding":1196},[1110,25992,24939,25993,26010,26011,1376,26042,1376,26075,26108,26109,26122,26123,1376,26150,1376,26179,26206],{},[1115,25994,25996],{"className":25995},[1149],[1151,25997,25998],{"xmlns":1153},[1155,25999,26000,26008],{},[1158,26001,26002],{},[6877,26003,26004,26006],{"accent":1121},[1161,26005,1171],{},[1165,26007,15130],{},[1194,26009,25238],{"encoding":1196}," bez čtvrté podskupiny dává ",[1115,26012,26014],{"className":26013},[1149],[1151,26015,26016],{"xmlns":1153},[1155,26017,26018,26039],{},[1158,26019,26020,26022,26024,26026,26032,26034,26036],{},[1161,26021,24469],{},[1161,26023,25793],{},[1165,26025,1168],{"stretchy":1167},[6877,26027,26028,26030],{"accent":1121},[1161,26029,1171],{},[1165,26031,15130],{},[1165,26033,1174],{"stretchy":1167},[1165,26035,1177],{},[1282,26037,26038],{},"102,01",[1194,26040,26041],{"encoding":1196},"CL(\\bar{x})=102{,}01",[1115,26043,26045],{"className":26044},[1149],[1151,26046,26047],{"xmlns":1153},[1155,26048,26049,26072],{},[1158,26050,26051,26053,26055,26057,26059,26065,26067,26069],{},[1161,26052,25819],{},[1161,26054,24469],{},[1161,26056,25793],{},[1165,26058,1168],{"stretchy":1167},[6877,26060,26061,26063],{"accent":1121},[1161,26062,1171],{},[1165,26064,15130],{},[1165,26066,1174],{"stretchy":1167},[1165,26068,1177],{},[1282,26070,26071],{},"111,68",[1194,26073,26074],{"encoding":1196},"UCL(\\bar{x})=111{,}68",[1115,26076,26078],{"className":26077},[1149],[1151,26079,26080],{"xmlns":1153},[1155,26081,26082,26105],{},[1158,26083,26084,26086,26088,26090,26092,26098,26100,26102],{},[1161,26085,25793],{},[1161,26087,24469],{},[1161,26089,25793],{},[1165,26091,1168],{"stretchy":1167},[6877,26093,26094,26096],{"accent":1121},[1161,26095,1171],{},[1165,26097,15130],{},[1165,26099,1174],{"stretchy":1167},[1165,26101,1177],{},[1282,26103,26104],{},"92,34",[1194,26106,26107],{"encoding":1196},"LCL(\\bar{x})=92{,}34",". Mez teď překračují průměry podskupin 3 a 19. Po potvrzení vymezitelné příčiny se vyřadí obě najednou a meze diagramu ",[1115,26110,26112],{"className":26111},[1149],[1151,26113,26114],{"xmlns":1153},[1155,26115,26116,26120],{},[1158,26117,26118],{},[1161,26119,4759],{},[1194,26121,4759],{"encoding":1196}," se přepočítají bez podskupin 3, 4 a 19: ",[1115,26124,26126],{"className":26125},[1149],[1151,26127,26128],{"xmlns":1153},[1155,26129,26130,26147],{},[1158,26131,26132,26134,26136,26138,26140,26142,26144],{},[1161,26133,24469],{},[1161,26135,25793],{},[1165,26137,1168],{"stretchy":1167},[1161,26139,4759],{},[1165,26141,1174],{"stretchy":1167},[1165,26143,1177],{},[1282,26145,26146],{},"12,29",[1194,26148,26149],{"encoding":1196},"CL(R)=12{,}29",[1115,26151,26153],{"className":26152},[1149],[1151,26154,26155],{"xmlns":1153},[1155,26156,26157,26176],{},[1158,26158,26159,26161,26163,26165,26167,26169,26171,26173],{},[1161,26160,25819],{},[1161,26162,24469],{},[1161,26164,25793],{},[1165,26166,1168],{"stretchy":1167},[1161,26168,4759],{},[1165,26170,1174],{"stretchy":1167},[1165,26172,1177],{},[1282,26174,26175],{},"28,06",[1194,26177,26178],{"encoding":1196},"UCL(R)=28{,}06",[1115,26180,26182],{"className":26181},[1149],[1151,26183,26184],{"xmlns":1153},[1155,26185,26186,26204],{},[1158,26187,26188,26190,26192,26194,26196,26198,26200,26202],{},[1161,26189,25793],{},[1161,26191,24469],{},[1161,26193,25793],{},[1165,26195,1168],{"stretchy":1167},[1161,26197,4759],{},[1165,26199,1174],{"stretchy":1167},[1165,26201,1177],{},[1282,26203,1982],{},[1194,26205,25865],{"encoding":1196}," — žádná z 17 zbývajících podskupin mez nepřekračuje.",[1110,26208,26209,26210,26227,26228,1376,26259,1376,26292,26325],{},"Konečný diagram ",[1115,26211,26213],{"className":26212},[1149],[1151,26214,26215],{"xmlns":1153},[1155,26216,26217,26225],{},[1158,26218,26219],{},[6877,26220,26221,26223],{"accent":1121},[1161,26222,1171],{},[1165,26224,15130],{},[1194,26226,25238],{"encoding":1196}," na stejných 17 podskupinách má ",[1115,26229,26231],{"className":26230},[1149],[1151,26232,26233],{"xmlns":1153},[1155,26234,26235,26256],{},[1158,26236,26237,26239,26241,26243,26249,26251,26253],{},[1161,26238,24469],{},[1161,26240,25793],{},[1165,26242,1168],{"stretchy":1167},[6877,26244,26245,26247],{"accent":1121},[1161,26246,1171],{},[1165,26248,15130],{},[1165,26250,1174],{"stretchy":1167},[1165,26252,1177],{},[1282,26254,26255],{},"99,76",[1194,26257,26258],{"encoding":1196},"CL(\\bar{x})=99{,}76",[1115,26260,26262],{"className":26261},[1149],[1151,26263,26264],{"xmlns":1153},[1155,26265,26266,26289],{},[1158,26267,26268,26270,26272,26274,26276,26282,26284,26286],{},[1161,26269,25819],{},[1161,26271,24469],{},[1161,26273,25793],{},[1165,26275,1168],{"stretchy":1167},[6877,26277,26278,26280],{"accent":1121},[1161,26279,1171],{},[1165,26281,15130],{},[1165,26283,1174],{"stretchy":1167},[1165,26285,1177],{},[1282,26287,26288],{},"108,73",[1194,26290,26291],{"encoding":1196},"UCL(\\bar{x})=108{,}73",[1115,26293,26295],{"className":26294},[1149],[1151,26296,26297],{"xmlns":1153},[1155,26298,26299,26322],{},[1158,26300,26301,26303,26305,26307,26309,26315,26317,26319],{},[1161,26302,25793],{},[1161,26304,24469],{},[1161,26306,25793],{},[1165,26308,1168],{"stretchy":1167},[6877,26310,26311,26313],{"accent":1121},[1161,26312,1171],{},[1165,26314,15130],{},[1165,26316,1174],{"stretchy":1167},[1165,26318,1177],{},[1282,26320,26321],{},"90,80",[1194,26323,26324],{"encoding":1196},"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.",[1110,26327,26328],{},[1760,26329],{"alt":26330,"className":26331,"src":26332},"mask-rd-priklad1-meze",[1441,1764],"\u002Fwiki-assets\u002Fmask-rd-priklad1-meze.png",[1110,26334,26335,26336,26338,26339,26341],{},"V R se diagramy sestrojí funkcí ",[1373,26337,25242],{}," z balíčku ",[1373,26340,360],{},". Data jsou tabulka, v níž řádek odpovídá logické podskupině a sloupce jednotlivým měřením:",[3554,26343,26345],{"className":3556,"code":26344,"language":71,"meta":3558,"style":3558},"library(qcc)\ndata \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"R\")      # diagram R\nqcc(data, type = \"xbar\")   # diagram x̄\n",[1373,26346,26347,26357,26380,26403],{"__ignoreMap":3558},[1115,26348,26349,26351,26353,26355],{"class":3563,"line":10},[1115,26350,21068],{"class":3741},[1115,26352,1168],{"class":3569},[1115,26354,360],{"class":3744},[1115,26356,3575],{"class":3569},[1115,26358,26359,26361,26363,26365,26367,26370,26372,26374,26376,26378],{"class":3563,"line":27},[1115,26360,23779],{"class":3744},[1115,26362,4497],{"class":3741},[1115,26364,23784],{"class":3566},[1115,26366,1168],{"class":3569},[1115,26368,26369],{"class":7974},"\"3_2.txt\"",[1115,26371,1715],{"class":3741},[1115,26373,23794],{"class":3744},[1115,26375,3748],{"class":3741},[1115,26377,7944],{"class":3572},[1115,26379,3575],{"class":3569},[1115,26381,26382,26384,26386,26388,26390,26392,26394,26397,26400],{"class":3563,"line":148},[1115,26383,360],{"class":3566},[1115,26385,1168],{"class":3569},[1115,26387,23779],{"class":3744},[1115,26389,1715],{"class":3741},[1115,26391,15894],{"class":3744},[1115,26393,3748],{"class":3741},[1115,26395,26396],{"class":7974}," \"R\"",[1115,26398,26399],{"class":3569},")      ",[1115,26401,26402],{"class":15704},"# diagram R\n",[1115,26404,26405,26407,26409,26411,26413,26415,26417,26420,26422],{"class":3563,"line":111},[1115,26406,360],{"class":3566},[1115,26408,1168],{"class":3569},[1115,26410,23779],{"class":3744},[1115,26412,1715],{"class":3741},[1115,26414,15894],{"class":3744},[1115,26416,3748],{"class":3741},[1115,26418,26419],{"class":7974}," \"xbar\"",[1115,26421,15701],{"class":3569},[1115,26423,26424],{"class":15704},"# diagram x̄\n",[1110,26426,26427,26428,26431],{},"Funkce vykreslí diagram se střední přímkou a akčními mezemi a body mimo meze zvýrazní. Podskupina s potvrzenou vymezitelnou příčinou se vyřadí z dat (například ",[1373,26429,26430],{},"data[-4, ]",") a diagram se sestrojí znovu.",[20418,26433,24939,26435],{"id":26434},"diagram-xˉsbarx-s",[1115,26436,26438],{"className":26437},[1149],[1151,26439,26440],{"xmlns":1153},[1155,26441,26442,26458],{},[1158,26443,26444,26446,26452,26454,26456],{},[1165,26445,1168],{"stretchy":1167},[6877,26447,26448,26450],{"accent":1121},[1161,26449,1171],{},[1165,26451,15130],{},[1165,26453,1715],{"separator":1121},[1161,26455,6018],{},[1165,26457,1174],{"stretchy":1167},[1194,26459,24348],{"encoding":1196},[1110,26461,24967,26462,26483,26484,26502,26503,26528],{},[1115,26463,26465],{"className":26464},[1149],[1151,26466,26467],{"xmlns":1153},[1155,26468,26469,26481],{},[1158,26470,26471],{},[1277,26472,26473,26479],{},[6877,26474,26475,26477],{"accent":1121},[1161,26476,1171],{},[1165,26478,15130],{},[1161,26480,4187],{},[1194,26482,24989],{"encoding":1196}," a výběrové směrodatné odchylky ",[1115,26485,26487],{"className":26486},[1149],[1151,26488,26489],{"xmlns":1153},[1155,26490,26491,26499],{},[1158,26492,26493],{},[1277,26494,26495,26497],{},[1161,26496,6018],{},[1161,26498,4187],{},[1194,26500,26501],{"encoding":1196},"s_i"," v logických podskupinách. Podmínky použití jsou stejné jako u ",[1115,26504,26506],{"className":26505},[1149],[1151,26507,26508],{"xmlns":1153},[1155,26509,26510,26526],{},[1158,26511,26512,26514,26520,26522,26524],{},[1165,26513,1168],{"stretchy":1167},[6877,26515,26516,26518],{"accent":1121},[1161,26517,1171],{},[1165,26519,15130],{},[1165,26521,1715],{"separator":1121},[1161,26523,4759],{},[1165,26525,1174],{"stretchy":1167},[1194,26527,24322],{"encoding":1196},", logické podskupiny ale sestávají z většího počtu měření. Data se zapisují do obdobné tabulky.",[3554,26530,26532],{"className":3556,"code":26531,"language":71,"meta":3558,"style":3558},"data \u003C- read.table(\"3_2.txt\", header = TRUE)\nqcc(data, type = \"S\")      # diagram s\nqcc(data, type = \"xbar\")   # diagram x̄\n",[1373,26533,26534,26556,26578],{"__ignoreMap":3558},[1115,26535,26536,26538,26540,26542,26544,26546,26548,26550,26552,26554],{"class":3563,"line":10},[1115,26537,23779],{"class":3744},[1115,26539,4497],{"class":3741},[1115,26541,23784],{"class":3566},[1115,26543,1168],{"class":3569},[1115,26545,26369],{"class":7974},[1115,26547,1715],{"class":3741},[1115,26549,23794],{"class":3744},[1115,26551,3748],{"class":3741},[1115,26553,7944],{"class":3572},[1115,26555,3575],{"class":3569},[1115,26557,26558,26560,26562,26564,26566,26568,26570,26573,26575],{"class":3563,"line":27},[1115,26559,360],{"class":3566},[1115,26561,1168],{"class":3569},[1115,26563,23779],{"class":3744},[1115,26565,1715],{"class":3741},[1115,26567,15894],{"class":3744},[1115,26569,3748],{"class":3741},[1115,26571,26572],{"class":7974}," \"S\"",[1115,26574,26399],{"class":3569},[1115,26576,26577],{"class":15704},"# diagram s\n",[1115,26579,26580,26582,26584,26586,26588,26590,26592,26594,26596],{"class":3563,"line":148},[1115,26581,360],{"class":3566},[1115,26583,1168],{"class":3569},[1115,26585,23779],{"class":3744},[1115,26587,1715],{"class":3741},[1115,26589,15894],{"class":3744},[1115,26591,3748],{"class":3741},[1115,26593,26419],{"class":7974},[1115,26595,15701],{"class":3569},[1115,26597,26424],{"class":15704},[20418,26599,24939,26601],{"id":26600},"diagram-xirklix_i-r_kli",[1115,26602,26604],{"className":26603},[1149],[1151,26605,26606],{"xmlns":1153},[1155,26607,26608,26636],{},[1158,26609,26610,26612,26618,26620,26634],{},[1165,26611,1168],{"stretchy":1167},[1277,26613,26614,26616],{},[1161,26615,1171],{},[1161,26617,4187],{},[1165,26619,1715],{"separator":1121},[1277,26621,26622,26624],{},[1161,26623,4759],{},[1158,26625,26626,26628,26630,26632],{},[1161,26627,1735],{},[1161,26629,24378],{},[1165,26631,1715],{"separator":1121},[1161,26633,4187],{},[1165,26635,1174],{"stretchy":1167},[1194,26637,24387],{"encoding":1196},[1110,26639,26640,26641,26666,26667,2629],{},"Používá se za stejných podmínek jako ",[1115,26642,26644],{"className":26643},[1149],[1151,26645,26646],{"xmlns":1153},[1155,26647,26648,26664],{},[1158,26649,26650,26652,26658,26660,26662],{},[1165,26651,1168],{"stretchy":1167},[6877,26653,26654,26656],{"accent":1121},[1161,26655,1171],{},[1165,26657,15130],{},[1165,26659,1715],{"separator":1121},[1161,26661,4759],{},[1165,26663,1174],{"stretchy":1167},[1194,26665,24322],{"encoding":1196},", 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 ",[1131,26668,26669],{},"klouzavé rozpětí",[1115,26671,26673],{"className":26672},[1149],[1151,26674,26675],{"xmlns":1153,"display":2212},[1155,26676,26677,26804],{},[1158,26678,26679,26693,26695,26698,26704,26706,26718,26720,26722,26724,26726,26728,26730,26732,26734,26736,26738,26740,26742,26744,26746,26760,26762,26774,26788,26802],{},[1277,26680,26681,26683],{},[1161,26682,4759],{},[1158,26684,26685,26687,26689,26691],{},[1161,26686,1735],{},[1161,26688,24378],{},[1165,26690,1715],{"separator":1121},[1161,26692,4187],{},[1165,26694,1177],{},[1161,26696,26697],{"mathvariant":1215},"∣",[1277,26699,26700,26702],{},[1161,26701,1171],{},[1161,26703,4187],{},[1165,26705,1317],{},[1277,26707,26708,26710],{},[1161,26709,1171],{},[1158,26711,26712,26714,26716],{},[1161,26713,4187],{},[1165,26715,1317],{},[1282,26717,1284],{},[1161,26719,26697],{"mathvariant":1215},[1165,26721,1715],{"separator":1121},[2242,26723],{"width":21689},[1161,26725,4187],{},[1165,26727,1177],{},[1282,26729,1298],{},[1165,26731,1715],{"separator":1121},[1282,26733,3322],{},[1165,26735,1715],{"separator":1121},[1165,26737,1726],{},[1165,26739,1715],{"separator":1121},[1161,26741,1735],{},[1165,26743,1715],{"separator":1121},[2242,26745],{"width":2244},[1277,26747,26748,26754],{},[6877,26749,26750,26752],{"accent":1121},[1161,26751,4759],{},[1165,26753,15130],{},[1158,26755,26756,26758],{},[1161,26757,1735],{},[1161,26759,24378],{},[1165,26761,1177],{},[3064,26763,26764,26766],{},[1282,26765,1284],{},[1158,26767,26768,26770,26772],{},[1161,26769,1735],{},[1165,26771,1317],{},[1282,26773,1284],{},[6140,26775,26776,26778,26786],{},[1165,26777,6144],{},[1158,26779,26780,26782,26784],{},[1161,26781,4187],{},[1165,26783,1177],{},[1282,26785,1298],{},[1161,26787,1735],{},[1277,26789,26790,26792],{},[1161,26791,4759],{},[1158,26793,26794,26796,26798,26800],{},[1161,26795,1735],{},[1161,26797,24378],{},[1165,26799,1715],{"separator":1121},[1161,26801,4187],{},[1161,26803,1333],{"mathvariant":1215},[1194,26805,26806],{"encoding":1196},"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}.",[1110,26808,26809,26810,1425,26827,26853,26854,26879,26880,26897],{},"Regulované veličiny jsou hodnoty ",[1115,26811,26813],{"className":26812},[1149],[1151,26814,26815],{"xmlns":1153},[1155,26816,26817,26825],{},[1158,26818,26819],{},[1277,26820,26821,26823],{},[1161,26822,1171],{},[1161,26824,4187],{},[1194,26826,20805],{"encoding":1196},[1115,26828,26830],{"className":26829},[1149],[1151,26831,26832],{"xmlns":1153},[1155,26833,26834,26850],{},[1158,26835,26836],{},[1277,26837,26838,26840],{},[1161,26839,4759],{},[1158,26841,26842,26844,26846,26848],{},[1161,26843,1735],{},[1161,26845,24378],{},[1165,26847,1715],{"separator":1121},[1161,26849,4187],{},[1194,26851,26852],{"encoding":1196},"R_{kl,i}","; nejdříve se určí střední přímka a meze diagramu ",[1115,26855,26857],{"className":26856},[1149],[1151,26858,26859],{"xmlns":1153},[1155,26860,26861,26877],{},[1158,26862,26863],{},[1277,26864,26865,26867],{},[1161,26866,4759],{},[1158,26868,26869,26871,26873,26875],{},[1161,26870,1735],{},[1161,26872,24378],{},[1165,26874,1715],{"separator":1121},[1161,26876,4187],{},[1194,26878,26852],{"encoding":1196},", potom diagramu ",[1115,26881,26883],{"className":26882},[1149],[1151,26884,26885],{"xmlns":1153},[1155,26886,26887,26895],{},[1158,26888,26889],{},[1277,26890,26891,26893],{},[1161,26892,1171],{},[1161,26894,4187],{},[1194,26896,20805],{"encoding":1196},". Data jsou jeden vektor naměřených hodnot:",[3554,26899,26901],{"className":3556,"code":26900,"language":71,"meta":3558,"style":3558},"data \u003C- read.table(\"3_3.txt\", header = TRUE)\nqcc(data[, 1], type = \"xbar.one\")\n",[1373,26902,26903,26926],{"__ignoreMap":3558},[1115,26904,26905,26907,26909,26911,26913,26916,26918,26920,26922,26924],{"class":3563,"line":10},[1115,26906,23779],{"class":3744},[1115,26908,4497],{"class":3741},[1115,26910,23784],{"class":3566},[1115,26912,1168],{"class":3569},[1115,26914,26915],{"class":7974},"\"3_3.txt\"",[1115,26917,1715],{"class":3741},[1115,26919,23794],{"class":3744},[1115,26921,3748],{"class":3741},[1115,26923,7944],{"class":3572},[1115,26925,3575],{"class":3569},[1115,26927,26928,26930,26932,26934,26936,26938,26940,26942,26944,26946,26948,26951],{"class":3563,"line":27},[1115,26929,360],{"class":3566},[1115,26931,1168],{"class":3569},[1115,26933,23779],{"class":3744},[1115,26935,2664],{"class":3569},[1115,26937,1715],{"class":3741},[1115,26939,4605],{"class":3572},[1115,26941,2681],{"class":3569},[1115,26943,1715],{"class":3741},[1115,26945,15894],{"class":3744},[1115,26947,3748],{"class":3741},[1115,26949,26950],{"class":7974}," \"xbar.one\"",[1115,26952,3575],{"class":3569},[1431,26954,26956],{"id":26955},"regulace-srovnáváním","Regulace srovnáváním",[1110,26958,26959],{},"Diagramy pro regulaci srovnáváním se používají, sledují-li se počty neshodných produktů nebo počty neshod na produktech — regulovaná veličina je diskrétní náhodná veličina.",[4052,26961,26962,26975],{},[4055,26963,26964],{},[4058,26965,26966,26969,26972],{},[4061,26967,26968],{},"Sleduje se",[4061,26970,26971],{},"Konstantní rozsah podskupin",[4061,26973,26974],{},"Nekonstantní rozsah podskupin",[4165,26976,26977,27012],{},[4058,26978,26979,26982,26997],{},[4170,26980,26981],{},"počet neshod na produktech (např. vady na stejných tabulích skla)",[4170,26983,26984],{},[1115,26985,26987],{"className":26986},[1149],[1151,26988,26989],{"xmlns":1153},[1155,26990,26991,26995],{},[1158,26992,26993],{},[1161,26994,7856],{},[1194,26996,7856],{"encoding":1196},[4170,26998,26999],{},[1115,27000,27002],{"className":27001},[1149],[1151,27003,27004],{"xmlns":1153},[1155,27005,27006,27010],{},[1158,27007,27008],{},[1161,27009,15199],{},[1194,27011,15199],{"encoding":1196},[4058,27013,27014,27017,27034],{},[4170,27015,27016],{},"počet neshodných produktů ve výběru (např. neshodné kusy ze série na výrobní lince)",[4170,27018,27019],{},[1115,27020,27022],{"className":27021},[1149],[1151,27023,27024],{"xmlns":1153},[1155,27025,27026,27032],{},[1158,27027,27028,27030],{},[1161,27029,4192],{},[1161,27031,1110],{},[1194,27033,24434],{"encoding":1196},[4170,27035,27036],{},[1115,27037,27039],{"className":27038},[1149],[1151,27040,27041],{"xmlns":1153},[1155,27042,27043,27047],{},[1158,27044,27045],{},[1161,27046,1110],{},[1194,27048,1110],{"encoding":1196},[20418,27050,24939,27052],{"id":27051},"diagram-cc",[1115,27053,27055],{"className":27054},[1149],[1151,27056,27057],{"xmlns":1153},[1155,27058,27059,27063],{},[1158,27060,27061],{},[1161,27062,7856],{},[1194,27064,7856],{"encoding":1196},[1110,27066,27067,27068,27086,27087,27100,27101,27126,27127,27140],{},"Regulovanou veličinou ",[1115,27069,27071],{"className":27070},[1149],[1151,27072,27073],{"xmlns":1153},[1155,27074,27075,27083],{},[1158,27076,27077],{},[1277,27078,27079,27081],{},[1161,27080,7856],{},[1161,27082,4187],{},[1194,27084,27085],{"encoding":1196},"c_i"," je počet neshod na produktech v ",[1115,27088,27090],{"className":27089},[1149],[1151,27091,27092],{"xmlns":1153},[1155,27093,27094,27098],{},[1158,27095,27096],{},[1161,27097,4187],{},[1194,27099,4187],{"encoding":1196},"-té logické podskupině, ",[1115,27102,27104],{"className":27103},[1149],[1151,27105,27106],{"xmlns":1153},[1155,27107,27108,27124],{},[1158,27109,27110,27112,27114,27116,27118,27120,27122],{},[1161,27111,4187],{},[1165,27113,1177],{},[1282,27115,1284],{},[1165,27117,1715],{"separator":1121},[1165,27119,1726],{},[1165,27121,1715],{"separator":1121},[1161,27123,1735],{},[1194,27125,25152],{"encoding":1196},"; v každé podskupině je stejný počet ",[1115,27128,27130],{"className":27129},[1149],[1151,27131,27132],{"xmlns":1153},[1155,27133,27134,27138],{},[1158,27135,27136],{},[1161,27137,4192],{},[1194,27139,4192],{"encoding":1196}," 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.",[1103,27142,27144,27151],{"className":27143,"dataCallout":3670},[1106,3669],[1110,27145,27147,27150],{"className":27146},[1113],[1115,27148],{"className":27149,"ariaHidden":1121},[1118,3677,1120],"Příklad: bodové vady na pásech látky",[1110,27152,27153,27154,27171,27172,1333],{},"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 ",[1115,27155,27157],{"className":27156},[1149],[1151,27158,27159],{"xmlns":1153},[1155,27160,27161,27169],{},[1158,27162,27163],{},[1277,27164,27165,27167],{},[1161,27166,7856],{},[1161,27168,4187],{},[1194,27170,27085],{"encoding":1196},". Sestrojte regulační diagram ",[1115,27173,27175],{"className":27174},[1149],[1151,27176,27177],{"xmlns":1153},[1155,27178,27179,27183],{},[1158,27180,27181],{},[1161,27182,7856],{},[1194,27184,7856],{"encoding":1196},[3554,27186,27188],{"className":3556,"code":27187,"language":71,"meta":3558,"style":3558},"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",[1373,27189,27190,27280,27284,27309],{"__ignoreMap":3558},[1115,27191,27192,27194,27196,27198,27200,27202,27204,27206,27208,27210,27212,27214,27216,27218,27220,27222,27224,27226,27228,27230,27232,27234,27236,27238,27240,27242,27244,27246,27248,27250,27252,27254,27256,27258,27260,27262,27264,27266,27268,27270,27272,27274,27276,27278],{"class":3563,"line":10},[1115,27193,27085],{"class":3744},[1115,27195,4497],{"class":3741},[1115,27197,7969],{"class":3566},[1115,27199,1168],{"class":3569},[1115,27201,17001],{"class":3572},[1115,27203,1715],{"class":3741},[1115,27205,4605],{"class":3572},[1115,27207,1715],{"class":3741},[1115,27209,8310],{"class":3572},[1115,27211,1715],{"class":3741},[1115,27213,4524],{"class":3572},[1115,27215,1715],{"class":3741},[1115,27217,4500],{"class":3572},[1115,27219,1715],{"class":3741},[1115,27221,15899],{"class":3572},[1115,27223,1715],{"class":3741},[1115,27225,8310],{"class":3572},[1115,27227,1715],{"class":3741},[1115,27229,4500],{"class":3572},[1115,27231,1715],{"class":3741},[1115,27233,4536],{"class":3572},[1115,27235,1715],{"class":3741},[1115,27237,4536],{"class":3572},[1115,27239,1715],{"class":3741},[1115,27241,15899],{"class":3572},[1115,27243,1715],{"class":3741},[1115,27245,5393],{"class":3572},[1115,27247,1715],{"class":3741},[1115,27249,5393],{"class":3572},[1115,27251,1715],{"class":3741},[1115,27253,5393],{"class":3572},[1115,27255,1715],{"class":3741},[1115,27257,4605],{"class":3572},[1115,27259,1715],{"class":3741},[1115,27261,15899],{"class":3572},[1115,27263,1715],{"class":3741},[1115,27265,5393],{"class":3572},[1115,27267,1715],{"class":3741},[1115,27269,4605],{"class":3572},[1115,27271,1715],{"class":3741},[1115,27273,4524],{"class":3572},[1115,27275,1715],{"class":3741},[1115,27277,15899],{"class":3572},[1115,27279,3575],{"class":3569},[1115,27281,27282],{"class":3563,"line":27},[1115,27283,4573],{"emptyLinePlaceholder":4572},[1115,27285,27286,27289,27291,27294,27296,27298,27300,27302,27304,27307],{"class":3563,"line":148},[1115,27287,27288],{"class":3744},"q_c",[1115,27290,4497],{"class":3741},[1115,27292,27293],{"class":3566}," qcc",[1115,27295,1168],{"class":3569},[1115,27297,27085],{"class":3744},[1115,27299,1715],{"class":3741},[1115,27301,15894],{"class":3744},[1115,27303,3748],{"class":3741},[1115,27305,27306],{"class":7974}," \"c\"",[1115,27308,3575],{"class":3569},[1115,27310,27311,27313,27315,27317],{"class":3563,"line":111},[1115,27312,20539],{"class":3566},[1115,27314,1168],{"class":3569},[1115,27316,27288],{"class":3744},[1115,27318,3575],{"class":3569},[3554,27320,27323],{"className":27321,"code":27322,"language":3603,"meta":3558},[3601],"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",[1373,27324,27322],{"__ignoreMap":3558},[1110,27326,27327,27328,27357,27358,27381,27382,27404],{},"Průměrný počet vad na pás je ",[1115,27329,27331],{"className":27330},[1149],[1151,27332,27333],{"xmlns":1153},[1155,27334,27335,27354],{},[1158,27336,27337,27339,27341,27343,27349,27351],{},[1161,27338,24469],{},[1161,27340,25793],{},[1165,27342,1177],{},[6877,27344,27345,27347],{"accent":1121},[1161,27346,7856],{},[1165,27348,15130],{},[1165,27350,1177],{},[1282,27352,27353],{},"3,4",[1194,27355,27356],{"encoding":1196},"CL = \\bar{c} = 3{,}4",", horní mez ",[1115,27359,27361],{"className":27360},[1149],[1151,27362,27363],{"xmlns":1153},[1155,27364,27365,27378],{},[1158,27366,27367,27369,27371,27373,27375],{},[1161,27368,25819],{},[1161,27370,24469],{},[1161,27372,25793],{},[1165,27374,1177],{},[1282,27376,27377],{},"8,93",[1194,27379,27380],{"encoding":1196},"UCL = 8{,}93"," a dolní mez ",[1115,27383,27385],{"className":27384},[1149],[1151,27386,27387],{"xmlns":1153},[1155,27388,27389,27401],{},[1158,27390,27391,27393,27395,27397,27399],{},[1161,27392,25793],{},[1161,27394,24469],{},[1161,27396,25793],{},[1165,27398,1177],{},[1282,27400,1982],{},[1194,27402,27403],{"encoding":1196},"LCL = 0",". Žádný pás meze nepřekračuje — proces je zvládnutý.",[1110,27406,27407],{},[1760,27408],{"alt":27409,"className":27410,"src":27411},"mask-rd-priklad2-c",[1441,1764],"\u002Fwiki-assets\u002Fmask-rd-priklad2-c.png",[20418,27413,24939,27415],{"id":27414},"diagram-uu",[1115,27416,27418],{"className":27417},[1149],[1151,27419,27420],{"xmlns":1153},[1155,27421,27422,27426],{},[1158,27423,27424],{},[1161,27425,15199],{},[1194,27427,15199],{"encoding":1196},[1110,27429,27067,27430,27464,27465,27483],{},[1115,27431,27433],{"className":27432},[1149],[1151,27434,27435],{"xmlns":1153},[1155,27436,27437,27461],{},[1158,27438,27439,27445,27447,27453,27455],{},[1277,27440,27441,27443],{},[1161,27442,15199],{},[1161,27444,4187],{},[1165,27446,1177],{},[1277,27448,27449,27451],{},[1161,27450,7856],{},[1161,27452,4187],{},[1161,27454,3434],{"mathvariant":1215},[1277,27456,27457,27459],{},[1161,27458,4192],{},[1161,27460,4187],{},[1194,27462,27463],{"encoding":1196},"u_i = c_i\u002Fn_i"," je průměrný počet neshod přepočítaný na jeden produkt z logické podskupiny; rozsah podskupin ",[1115,27466,27468],{"className":27467},[1149],[1151,27469,27470],{"xmlns":1153},[1155,27471,27472,27480],{},[1158,27473,27474],{},[1277,27475,27476,27478],{},[1161,27477,4192],{},[1161,27479,4187],{},[1194,27481,27482],{"encoding":1196},"n_i"," není konstantní, a proto se bod od bodu mění i meze.",[1110,27485,27486,27487,27490],{},"Za ",[1373,27488,27489],{},"sizes"," se dosadí vektor rozsahů jednotlivých logických podskupin, resp. rozměr jejich jednotek:",[3554,27492,27494],{"className":3556,"code":27493,"language":71,"meta":3558,"style":3558},"data \u003C- read.table(\"3_4.txt\", header = TRUE)   # počty suků a rozměry prken\nqcc(data[, 1], type = \"u\", sizes = data[, 2])\n",[1373,27495,27496,27522],{"__ignoreMap":3558},[1115,27497,27498,27500,27502,27504,27506,27509,27511,27513,27515,27517,27519],{"class":3563,"line":10},[1115,27499,23779],{"class":3744},[1115,27501,4497],{"class":3741},[1115,27503,23784],{"class":3566},[1115,27505,1168],{"class":3569},[1115,27507,27508],{"class":7974},"\"3_4.txt\"",[1115,27510,1715],{"class":3741},[1115,27512,23794],{"class":3744},[1115,27514,3748],{"class":3741},[1115,27516,7944],{"class":3572},[1115,27518,15701],{"class":3569},[1115,27520,27521],{"class":15704},"# počty suků a rozměry prken\n",[1115,27523,27524,27526,27528,27530,27532,27534,27536,27538,27540,27542,27544,27547,27549,27552,27554,27556,27558,27560,27562],{"class":3563,"line":27},[1115,27525,360],{"class":3566},[1115,27527,1168],{"class":3569},[1115,27529,23779],{"class":3744},[1115,27531,2664],{"class":3569},[1115,27533,1715],{"class":3741},[1115,27535,4605],{"class":3572},[1115,27537,2681],{"class":3569},[1115,27539,1715],{"class":3741},[1115,27541,15894],{"class":3744},[1115,27543,3748],{"class":3741},[1115,27545,27546],{"class":7974}," \"u\"",[1115,27548,1715],{"class":3741},[1115,27550,27551],{"class":3744}," sizes",[1115,27553,3748],{"class":3741},[1115,27555,23838],{"class":3744},[1115,27557,2664],{"class":3569},[1115,27559,1715],{"class":3741},[1115,27561,8310],{"class":3572},[1115,27563,27564],{"class":3569},"])\n",[20418,27566,24939,27568],{"id":27567},"diagram-npnp",[1115,27569,27571],{"className":27570},[1149],[1151,27572,27573],{"xmlns":1153},[1155,27574,27575,27581],{},[1158,27576,27577,27579],{},[1161,27578,4192],{},[1161,27580,1110],{},[1194,27582,24434],{"encoding":1196},[1110,27584,27585,27586,1238,27601,27614],{},"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 ",[1115,27587,27589],{"className":27588},[1149],[1151,27590,27591],{"xmlns":1153},[1155,27592,27593,27599],{},[1158,27594,27595,27597],{},[1161,27596,4192],{},[1161,27598,1110],{},[1194,27600,24434],{"encoding":1196},[1115,27602,27604],{"className":27603},[1149],[1151,27605,27606],{"xmlns":1153},[1155,27607,27608,27612],{},[1158,27609,27610],{},[1161,27611,1110],{},[1194,27613,1110],{"encoding":1196}," je pravděpodobnost, že vyrobený produkt je neshodný.",[1110,27616,27617,27618,2629],{},"Pro konstantní rozsah ",[1115,27619,27621],{"className":27620},[1149],[1151,27622,27623],{"xmlns":1153},[1155,27624,27625,27629],{},[1158,27626,27627],{},[1161,27628,4192],{},[1194,27630,4192],{"encoding":1196},[3554,27632,27634],{"className":3556,"code":27633,"language":71,"meta":3558,"style":3558},"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",[1373,27635,27636,27662],{"__ignoreMap":3558},[1115,27637,27638,27640,27642,27644,27646,27649,27651,27653,27655,27657,27659],{"class":3563,"line":10},[1115,27639,23779],{"class":3744},[1115,27641,4497],{"class":3741},[1115,27643,23784],{"class":3566},[1115,27645,1168],{"class":3569},[1115,27647,27648],{"class":7974},"\"3_7.txt\"",[1115,27650,1715],{"class":3741},[1115,27652,23794],{"class":3744},[1115,27654,3748],{"class":3741},[1115,27656,7944],{"class":3572},[1115,27658,15701],{"class":3569},[1115,27660,27661],{"class":15704},"# počty vadných tabletů v sériích po 100 kusech\n",[1115,27663,27664,27666,27668,27670,27672,27674,27676,27678,27680,27682,27684,27687,27689,27691,27693,27695],{"class":3563,"line":27},[1115,27665,360],{"class":3566},[1115,27667,1168],{"class":3569},[1115,27669,23779],{"class":3744},[1115,27671,2664],{"class":3569},[1115,27673,1715],{"class":3741},[1115,27675,4605],{"class":3572},[1115,27677,2681],{"class":3569},[1115,27679,1715],{"class":3741},[1115,27681,15894],{"class":3744},[1115,27683,3748],{"class":3741},[1115,27685,27686],{"class":7974}," \"np\"",[1115,27688,1715],{"class":3741},[1115,27690,27551],{"class":3744},[1115,27692,3748],{"class":3741},[1115,27694,19010],{"class":3572},[1115,27696,3575],{"class":3569},[20418,27698,24939,27700],{"id":27699},"diagram-pp",[1115,27701,27703],{"className":27702},[1149],[1151,27704,27705],{"xmlns":1153},[1155,27706,27707,27711],{},[1158,27708,27709],{},[1161,27710,1110],{},[1194,27712,1110],{"encoding":1196},[1110,27714,27715,27716,27752],{},"Regulovanou veličinou je počet neshodných produktů v logické podskupině přepočtený na jednotku, ",[1115,27717,27719],{"className":27718},[1149],[1151,27720,27721],{"xmlns":1153},[1155,27722,27723,27749],{},[1158,27724,27725,27731,27733,27735,27741,27743],{},[1277,27726,27727,27729],{},[1161,27728,1110],{},[1161,27730,4187],{},[1165,27732,1177],{},[1161,27734,4192],{},[1277,27736,27737,27739],{},[1161,27738,1110],{},[1161,27740,4187],{},[1161,27742,3434],{"mathvariant":1215},[1277,27744,27745,27747],{},[1161,27746,4192],{},[1161,27748,4187],{},[1194,27750,27751],{"encoding":1196},"p_i = np_i\u002Fn_i","; rozsahy podskupin nemusí být konstantní.",[1110,27754,27486,27755,27757],{},[1373,27756,27489],{}," se dosadí vektor rozsahů logických podskupin:",[3554,27759,27761],{"className":3556,"code":27760,"language":71,"meta":3558,"style":3558},"data \u003C- read.table(\"3_6.txt\", header = TRUE)   # počty vadných tabletů a rozsahy sérií\nqcc(data[, 1], type = \"p\", sizes = data[, 2])\n",[1373,27762,27763,27789],{"__ignoreMap":3558},[1115,27764,27765,27767,27769,27771,27773,27776,27778,27780,27782,27784,27786],{"class":3563,"line":10},[1115,27766,23779],{"class":3744},[1115,27768,4497],{"class":3741},[1115,27770,23784],{"class":3566},[1115,27772,1168],{"class":3569},[1115,27774,27775],{"class":7974},"\"3_6.txt\"",[1115,27777,1715],{"class":3741},[1115,27779,23794],{"class":3744},[1115,27781,3748],{"class":3741},[1115,27783,7944],{"class":3572},[1115,27785,15701],{"class":3569},[1115,27787,27788],{"class":15704},"# počty vadných tabletů a rozsahy sérií\n",[1115,27790,27791,27793,27795,27797,27799,27801,27803,27805,27807,27809,27811,27814,27816,27818,27820,27822,27824,27826,27828],{"class":3563,"line":27},[1115,27792,360],{"class":3566},[1115,27794,1168],{"class":3569},[1115,27796,23779],{"class":3744},[1115,27798,2664],{"class":3569},[1115,27800,1715],{"class":3741},[1115,27802,4605],{"class":3572},[1115,27804,2681],{"class":3569},[1115,27806,1715],{"class":3741},[1115,27808,15894],{"class":3744},[1115,27810,3748],{"class":3741},[1115,27812,27813],{"class":7974}," \"p\"",[1115,27815,1715],{"class":3741},[1115,27817,27551],{"class":3744},[1115,27819,3748],{"class":3741},[1115,27821,23838],{"class":3744},[1115,27823,2664],{"class":3569},[1115,27825,1715],{"class":3741},[1115,27827,8310],{"class":3572},[1115,27829,27564],{"class":3569},[1431,27831,27833],{"id":27832},"indexy-způsobilosti","Indexy způsobilosti",[1110,27835,27836,27837,27856,27857,27875],{},"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 ",[1115,27838,27840],{"className":27839},[1149],[1151,27841,27842],{"xmlns":1153},[1155,27843,27844,27853],{},[1158,27845,27846,27848,27851],{},[1161,27847,25793],{},[1161,27849,27850],{},"S",[1161,27852,25793],{},[1194,27854,27855],{"encoding":1196},"LSL"," a horní meze ",[1115,27858,27860],{"className":27859},[1149],[1151,27861,27862],{"xmlns":1153},[1155,27863,27864,27872],{},[1158,27865,27866,27868,27870],{},[1161,27867,25819],{},[1161,27869,27850],{},[1161,27871,25793],{},[1194,27873,27874],{"encoding":1196},"USL",". Způsobilost se zkoumá až pro proces, který je podle regulačních diagramů statisticky zvládnutý (třetí fáze regulace).",[20418,27877,27879,27896],{"id":27878},"cpc_p-index-způsobilosti",[1115,27880,27882],{"className":27881},[1149],[1151,27883,27884],{"xmlns":1153},[1155,27885,27886,27894],{},[1158,27887,27888],{},[1277,27889,27890,27892],{},[1161,27891,24469],{},[1161,27893,1110],{},[1194,27895,24474],{"encoding":1196}," — index způsobilosti",[1110,27898,27899,27900,2629],{},"Podíl mezi délkou tolerančního intervalu a délkou intervalu, ve kterém by za normálního rozdělení mělo ležet skoro všech 99,73 % hodnot znaku, tedy ",[1115,27901,27903],{"className":27902},[1149],[1151,27904,27905],{"xmlns":1153},[1155,27906,27907,27913],{},[1158,27908,27909,27911],{},[1282,27910,8094],{},[1161,27912,1363],{},[1194,27914,27915],{"encoding":1196},"6\\sigma",[1115,27917,27919],{"className":27918},[1149],[1151,27920,27921],{"xmlns":1153,"display":2212},[1155,27922,27923,27959],{},[1158,27924,27925,27931,27933,27957],{},[1277,27926,27927,27929],{},[1161,27928,24469],{},[1161,27930,1110],{},[1165,27932,1177],{},[3064,27934,27935,27951],{},[1158,27936,27937,27939,27941,27943,27945,27947,27949],{},[1161,27938,25819],{},[1161,27940,27850],{},[1161,27942,25793],{},[1165,27944,1317],{},[1161,27946,25793],{},[1161,27948,27850],{},[1161,27950,25793],{},[1158,27952,27953,27955],{},[1282,27954,8094],{},[1161,27956,1363],{},[1161,27958,1333],{"mathvariant":1215},[1194,27960,27961],{"encoding":1196},"C_p = \\frac{USL - LSL}{6\\sigma}.",[1110,27963,27964,27981,27982,27995,27996,1333],{},[1115,27965,27967],{"className":27966},[1149],[1151,27968,27969],{"xmlns":1153},[1155,27970,27971,27979],{},[1158,27972,27973],{},[1277,27974,27975,27977],{},[1161,27976,24469],{},[1161,27978,1110],{},[1194,27980,24474],{"encoding":1196}," srovnává jen délky, nevšímá si, kde uprostřed tolerance proces leží — centrovaný i silně vychýlený proces se stejným ",[1115,27983,27985],{"className":27984},[1149],[1151,27986,27987],{"xmlns":1153},[1155,27988,27989,27993],{},[1158,27990,27991],{},[1161,27992,1363],{},[1194,27994,1397],{"encoding":1196}," mají stejné ",[1115,27997,27999],{"className":27998},[1149],[1151,28000,28001],{"xmlns":1153},[1155,28002,28003,28011],{},[1158,28004,28005],{},[1277,28006,28007,28009],{},[1161,28008,24469],{},[1161,28010,1110],{},[1194,28012,24474],{"encoding":1196},[1110,28014,28015],{},"Doplňkové charakteristiky využití tolerančního intervalu:",[1124,28017,28018,28052,28140],{},[1127,28019,28020,8118,28023,28051],{},[1131,28021,28022],{},"míra využití tolerančního intervalu",[1115,28024,28026],{"className":28025},[1149],[1151,28027,28028],{"xmlns":1153},[1155,28029,28030,28048],{},[1158,28031,28032,28044,28046],{},[7391,28033,28034],{"scriptlevel":1982,"displaystyle":1121},[3064,28035,28036,28038],{},[1282,28037,15489],{},[1277,28039,28040,28042],{},[1161,28041,24469],{},[1161,28043,1110],{},[2278,28045,2280],{},[1161,28047,15496],{"mathvariant":1215},[1194,28049,28050],{"encoding":1196},"\\dfrac{100}{C_p}\\,\\%"," — na kolik procent je toleranční interval využíván sledovaným znakem,",[1127,28053,28054,28057,28058,28075,28076,1425,28108,1715],{},[1131,28055,28056],{},"robustnost procesu",": rezerva, kterou máme v tolerančních mezích, než index ",[1115,28059,28061],{"className":28060},[1149],[1151,28062,28063],{"xmlns":1153},[1155,28064,28065,28073],{},[1158,28066,28067],{},[1277,28068,28069,28071],{},[1161,28070,24469],{},[1161,28072,1110],{},[1194,28074,24474],{"encoding":1196}," nabyde hodnotu 1 — rovná se menší hodnotě z výrazů ",[1115,28077,28079],{"className":28078},[1149],[1151,28080,28081],{"xmlns":1153},[1155,28082,28083,28105],{},[1158,28084,28085,28087,28089,28091,28093,28095,28097,28099,28101,28103],{},[1161,28086,25819],{},[1161,28088,27850],{},[1161,28090,25793],{},[1165,28092,1317],{},[1165,28094,1168],{"stretchy":1167},[1161,28096,1355],{},[1165,28098,2094],{},[1282,28100,3322],{},[1161,28102,1363],{},[1165,28104,1174],{"stretchy":1167},[1194,28106,28107],{"encoding":1196},"USL-(\\mu+3\\sigma)",[1115,28109,28111],{"className":28110},[1149],[1151,28112,28113],{"xmlns":1153},[1155,28114,28115,28137],{},[1158,28116,28117,28119,28121,28123,28125,28127,28129,28131,28133,28135],{},[1165,28118,1168],{"stretchy":1167},[1161,28120,1355],{},[1165,28122,1317],{},[1282,28124,3322],{},[1161,28126,1363],{},[1165,28128,1174],{"stretchy":1167},[1165,28130,1317],{},[1161,28132,25793],{},[1161,28134,27850],{},[1161,28136,25793],{},[1194,28138,28139],{"encoding":1196},"(\\mu-3\\sigma)-LSL",[1127,28141,28142,8118,28145,1238,28185,28199],{},[1131,28143,28144],{},"podíl zmetků",[1115,28146,28148],{"className":28147},[1149],[1151,28149,28150],{"xmlns":1153},[1155,28151,28152,28182],{},[1158,28153,28154,28161,28163,28165,28168,28170,28172,28174,28180],{},[1277,28155,28156,28158],{},[1161,28157,1180],{},[1161,28159,28160],{},"z",[1165,28162,1177],{},[1282,28164,1298],{},[1161,28166,28167],{"mathvariant":1215},"Φ",[1165,28169,1168],{"stretchy":1167},[1165,28171,1317],{},[1282,28173,3322],{},[1277,28175,28176,28178],{},[1161,28177,24469],{},[1161,28179,1110],{},[1165,28181,1174],{"stretchy":1167},[1194,28183,28184],{"encoding":1196},"P_z = 2\\Phi(-3C_p)",[1115,28186,28188],{"className":28187},[1149],[1151,28189,28190],{"xmlns":1153},[1155,28191,28192,28196],{},[1158,28193,28194],{},[1161,28195,28167],{"mathvariant":1215},[1194,28197,28198],{"encoding":1196},"\\Phi"," je distribuční funkce normovaného normálního rozdělení.",[20418,28201,28203,28224],{"id":28202},"cpkc_pk-index-způsobilosti-s-ohledem-na-vychýlení",[1115,28204,28206],{"className":28205},[1149],[1151,28207,28208],{"xmlns":1153},[1155,28209,28210,28222],{},[1158,28211,28212],{},[1277,28213,28214,28216],{},[1161,28215,24469],{},[1158,28217,28218,28220],{},[1161,28219,1110],{},[1161,28221,1735],{},[1194,28223,24496],{"encoding":1196}," — index způsobilosti s ohledem na vychýlení",[1110,28226,28227],{},"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:",[1115,28229,28231],{"className":28230},[1149],[1151,28232,28233],{"xmlns":1153,"display":2212},[1155,28234,28235,28305],{},[1158,28236,28237,28247,28249,28251,28253,28303],{},[1277,28238,28239,28241],{},[1161,28240,24469],{},[1158,28242,28243,28245],{},[1161,28244,1110],{},[1161,28246,1735],{},[1165,28248,1177],{},[1161,28250,8614],{},[1165,28252,2079],{},[1158,28254,28255,28257,28277,28279,28281,28301],{},[1165,28256,1168],{"fence":1121},[3064,28258,28259,28271],{},[1158,28260,28261,28263,28265,28267,28269],{},[1161,28262,25819],{},[1161,28264,27850],{},[1161,28266,25793],{},[1165,28268,1317],{},[1161,28270,1355],{},[1158,28272,28273,28275],{},[1282,28274,3322],{},[1161,28276,1363],{},[1165,28278,1715],{"separator":1121},[2278,28280,14985],{},[3064,28282,28283,28295],{},[1158,28284,28285,28287,28289,28291,28293],{},[1161,28286,1355],{},[1165,28288,1317],{},[1161,28290,25793],{},[1161,28292,27850],{},[1161,28294,25793],{},[1158,28296,28297,28299],{},[1282,28298,3322],{},[1161,28300,1363],{},[1165,28302,1174],{"fence":1121},[1161,28304,1333],{"mathvariant":1215},[1194,28306,28307],{"encoding":1196},"C_{pk} = \\min\\left(\\frac{USL-\\mu}{3\\sigma},\\ \\frac{\\mu-LSL}{3\\sigma}\\right).",[1110,28309,28310,28311,28324,28325,28355,28356,28377,28378,1333],{},"Vyjde-li některý z obou podílů záporný, položí se roven nule; to nastane, když střední hodnota ",[1115,28312,28314],{"className":28313},[1149],[1151,28315,28316],{"xmlns":1153},[1155,28317,28318,28322],{},[1158,28319,28320],{},[1161,28321,1355],{},[1194,28323,3289],{"encoding":1196}," leží mimo toleranční interval, a proces pak není pod statistickou kontrolou. U centrovaného procesu jsou oba podíly stejné a ",[1115,28326,28328],{"className":28327},[1149],[1151,28329,28330],{"xmlns":1153},[1155,28331,28332,28352],{},[1158,28333,28334,28344,28346],{},[1277,28335,28336,28338],{},[1161,28337,24469],{},[1158,28339,28340,28342],{},[1161,28341,1110],{},[1161,28343,1735],{},[1165,28345,1177],{},[1277,28347,28348,28350],{},[1161,28349,24469],{},[1161,28351,1110],{},[1194,28353,28354],{"encoding":1196},"C_{pk} = C_p","; čím víc je proces vychýlený, tím víc je ",[1115,28357,28359],{"className":28358},[1149],[1151,28360,28361],{"xmlns":1153},[1155,28362,28363,28375],{},[1158,28364,28365],{},[1277,28366,28367,28369],{},[1161,28368,24469],{},[1158,28370,28371,28373],{},[1161,28372,1110],{},[1161,28374,1735],{},[1194,28376,24496],{"encoding":1196}," menší než ",[1115,28379,28381],{"className":28380},[1149],[1151,28382,28383],{"xmlns":1153},[1155,28384,28385,28393],{},[1158,28386,28387],{},[1277,28388,28389,28391],{},[1161,28390,24469],{},[1161,28392,1110],{},[1194,28394,24474],{"encoding":1196},[20418,28396,28398,1425,28419,28442],{"id":28397},"cpmc_pm-a-cpmkc_pmk-indexy-vztažené-k-cíli",[1115,28399,28401],{"className":28400},[1149],[1151,28402,28403],{"xmlns":1153},[1155,28404,28405,28417],{},[1158,28406,28407],{},[1277,28408,28409,28411],{},[1161,28410,24469],{},[1158,28412,28413,28415],{},[1161,28414,1110],{},[1161,28416,8597],{},[1194,28418,24518],{"encoding":1196},[1115,28420,28422],{"className":28421},[1149],[1151,28423,28424],{"xmlns":1153},[1155,28425,28426,28440],{},[1158,28427,28428],{},[1277,28429,28430,28432],{},[1161,28431,24469],{},[1158,28433,28434,28436,28438],{},[1161,28435,1110],{},[1161,28437,8597],{},[1161,28439,1735],{},[1194,28441,24542],{"encoding":1196}," — indexy vztažené k cíli",[1110,28444,28445,28446,28459,28460,28473,28474,28517,28518,2629],{},"Pokud má proces zadaný cílový střed ",[1115,28447,28449],{"className":28448},[1149],[1151,28450,28451],{"xmlns":1153},[1155,28452,28453,28457],{},[1158,28454,28455],{},[1161,28456,1575],{},[1194,28458,1575],{"encoding":1196}," (ne nutně střed tolerance), nahradí se ",[1115,28461,28463],{"className":28462},[1149],[1151,28464,28465],{"xmlns":1153},[1155,28466,28467,28471],{},[1158,28468,28469],{},[1161,28470,1363],{},[1194,28472,1397],{"encoding":1196}," odmocninou ze střední čtvercové odchylky od cíle ",[1115,28475,28477],{"className":28476},[1149],[1151,28478,28479],{"xmlns":1153},[1155,28480,28481,28514],{},[1158,28482,28483,28486,28488],{},[1161,28484,28485],{},"τ",[1165,28487,1177],{},[2765,28489,28490],{},[1158,28491,28492,28498,28500,28502,28504,28506,28508],{},[1209,28493,28494,28496],{},[1161,28495,1363],{},[1282,28497,1298],{},[1165,28499,2094],{},[1165,28501,1168],{"stretchy":1167},[1161,28503,1355],{},[1165,28505,1317],{},[1161,28507,1575],{},[1209,28509,28510,28512],{},[1165,28511,1174],{"stretchy":1167},[1282,28513,1298],{},[1194,28515,28516],{"encoding":1196},"\\tau = \\sqrt{\\sigma^2+(\\mu-T)^2}",", která trestá i vychýlení od ",[1115,28519,28521],{"className":28520},[1149],[1151,28522,28523],{"xmlns":1153},[1155,28524,28525,28529],{},[1158,28526,28527],{},[1161,28528,1575],{},[1194,28530,1575],{"encoding":1196},[1115,28532,28534],{"className":28533},[1149],[1151,28535,28536],{"xmlns":1153,"display":2212},[1155,28537,28538,28650],{},[1158,28539,28540,28550,28552,28576,28578,28580,28592,28594,28596,28598,28648],{},[1277,28541,28542,28544],{},[1161,28543,24469],{},[1158,28545,28546,28548],{},[1161,28547,1110],{},[1161,28549,8597],{},[1165,28551,1177],{},[3064,28553,28554,28570],{},[1158,28555,28556,28558,28560,28562,28564,28566,28568],{},[1161,28557,25819],{},[1161,28559,27850],{},[1161,28561,25793],{},[1165,28563,1317],{},[1161,28565,25793],{},[1161,28567,27850],{},[1161,28569,25793],{},[1158,28571,28572,28574],{},[1282,28573,8094],{},[1161,28575,28485],{},[1165,28577,1715],{"separator":1121},[2242,28579],{"width":2244},[1277,28581,28582,28584],{},[1161,28583,24469],{},[1158,28585,28586,28588,28590],{},[1161,28587,1110],{},[1161,28589,8597],{},[1161,28591,1735],{},[1165,28593,1177],{},[1161,28595,8614],{},[1165,28597,2079],{},[1158,28599,28600,28602,28622,28624,28626,28646],{},[1165,28601,1168],{"fence":1121},[3064,28603,28604,28616],{},[1158,28605,28606,28608,28610,28612,28614],{},[1161,28607,25819],{},[1161,28609,27850],{},[1161,28611,25793],{},[1165,28613,1317],{},[1161,28615,1355],{},[1158,28617,28618,28620],{},[1282,28619,3322],{},[1161,28621,28485],{},[1165,28623,1715],{"separator":1121},[2278,28625,14985],{},[3064,28627,28628,28640],{},[1158,28629,28630,28632,28634,28636,28638],{},[1161,28631,1355],{},[1165,28633,1317],{},[1161,28635,25793],{},[1161,28637,27850],{},[1161,28639,25793],{},[1158,28641,28642,28644],{},[1282,28643,3322],{},[1161,28645,28485],{},[1165,28647,1174],{"fence":1121},[1161,28649,1333],{"mathvariant":1215},[1194,28651,28652],{"encoding":1196},"C_{pm} = \\frac{USL-LSL}{6\\tau}, \\qquad C_{pmk} = \\min\\left(\\frac{USL-\\mu}{3\\tau},\\ \\frac{\\mu-LSL}{3\\tau}\\right).",[20418,28654,28656],{"id":28655},"interpretace","Interpretace",[4052,28658,28659,28686],{},[4055,28660,28661],{},[4058,28662,28663,28683],{},[4061,28664,28665,28666],{},"Hodnota ",[1115,28667,28669],{"className":28668},[1149],[1151,28670,28671],{"xmlns":1153},[1155,28672,28673,28681],{},[1158,28674,28675],{},[1277,28676,28677,28679],{},[1161,28678,24469],{},[1161,28680,1110],{},[1194,28682,24474],{"encoding":1196},[4061,28684,28685],{},"Způsobilost procesu",[4165,28687,28688,28717,28760],{},[4058,28689,28690,28714],{},[4170,28691,28692],{},[1115,28693,28695],{"className":28694},[1149],[1151,28696,28697],{"xmlns":1153},[1155,28698,28699,28711],{},[1158,28700,28701,28707,28709],{},[1277,28702,28703,28705],{},[1161,28704,24469],{},[1161,28706,1110],{},[1165,28708,1287],{},[1282,28710,1284],{},[1194,28712,28713],{"encoding":1196},"C_p \u003C 1",[4170,28715,28716],{},"dosahovaná přesnost je menší než předepsaná — proces je nezpůsobilý",[4058,28718,28719,28743],{},[4170,28720,28721],{},[1115,28722,28724],{"className":28723},[1149],[1151,28725,28726],{"xmlns":1153},[1155,28727,28728,28740],{},[1158,28729,28730,28736,28738],{},[1277,28731,28732,28734],{},[1161,28733,24469],{},[1161,28735,1110],{},[1165,28737,1177],{},[1282,28739,1284],{},[1194,28741,28742],{"encoding":1196},"C_p = 1",[4170,28744,28745,28746,28759],{},"dosahovaná přesnost je rovna předepsané — proces je způsobilý, ale sebemenší zvětšení ",[1115,28747,28749],{"className":28748},[1149],[1151,28750,28751],{"xmlns":1153},[1155,28752,28753,28757],{},[1158,28754,28755],{},[1161,28756,1363],{},[1194,28758,1397],{"encoding":1196}," jej posune na nezpůsobilý",[4058,28761,28762,28786],{},[4170,28763,28764],{},[1115,28765,28767],{"className":28766},[1149],[1151,28768,28769],{"xmlns":1153},[1155,28770,28771,28783],{},[1158,28772,28773,28779,28781],{},[1277,28774,28775,28777],{},[1161,28776,24469],{},[1161,28778,1110],{},[1165,28780,4156],{},[1282,28782,1284],{},[1194,28784,28785],{"encoding":1196},"C_p > 1",[4170,28787,28788],{},"dosahovaná přesnost je větší než předepsaná — proces je způsobilý",[1110,28790,28791,28792,28813,28814,1333],{},"U indexu ",[1115,28793,28795],{"className":28794},[1149],[1151,28796,28797],{"xmlns":1153},[1155,28798,28799,28811],{},[1158,28800,28801],{},[1277,28802,28803,28805],{},[1161,28804,24469],{},[1158,28806,28807,28809],{},[1161,28808,1110],{},[1161,28810,1735],{},[1194,28812,24496],{"encoding":1196}," se v praxi požaduje víc než jen hodnota nad 1: s rozvojem technologií roste nárok na rezervu, a běžně se dnes vyžaduje hodnota alespoň ",[1115,28815,28817],{"className":28816},[1149],[1151,28818,28819],{"xmlns":1153},[1155,28820,28821,28826],{},[1158,28822,28823],{},[1282,28824,28825],{},"1,5",[1194,28827,28828],{"encoding":1196},"1{,}5",[1110,28830,28831],{},[1760,28832],{"alt":28833,"className":28834,"src":28835},"mask-rd-cp-panely",[1441,1764],"\u002Fwiki-assets\u002Fmask-rd-cp-panely.png",[1110,28837,28838],{},[1760,28839],{"alt":28840,"className":28841,"src":28842},"mask-rd-cpk-off-centre",[1441,1764],"\u002Fwiki-assets\u002Fmask-rd-cpk-off-centre.png",[20418,28844,28846],{"id":28845},"výpočet-v-r","Výpočet v R",[1110,28848,28849,28850,28853,28854,28857,28858,28861,28862,1425,28879,1376,28896,28899,28900,28913],{},"Indexy způsobilosti počítá ",[1373,28851,28852],{},"process.capability()"," z výstupu regulačního diagramu ",[1373,28855,28856],{},"q","; ",[1373,28859,28860],{},"spec.limits"," jsou toleranční meze ",[1115,28863,28865],{"className":28864},[1149],[1151,28866,28867],{"xmlns":1153},[1155,28868,28869,28877],{},[1158,28870,28871,28873,28875],{},[1161,28872,25793],{},[1161,28874,27850],{},[1161,28876,25793],{},[1194,28878,27855],{"encoding":1196},[1115,28880,28882],{"className":28881},[1149],[1151,28883,28884],{"xmlns":1153},[1155,28885,28886,28894],{},[1158,28887,28888,28890,28892],{},[1161,28889,25819],{},[1161,28891,27850],{},[1161,28893,25793],{},[1194,28895,27874],{"encoding":1196},[1373,28897,28898],{},"target"," cílová hodnota ",[1115,28901,28903],{"className":28902},[1149],[1151,28904,28905],{"xmlns":1153},[1155,28906,28907,28911],{},[1158,28908,28909],{},[1161,28910,1575],{},[1194,28912,1575],{"encoding":1196},". Pro velikost výrobku v mm s tolerančními mezemi 100 a 110 mm a cílovou hodnotou 105 mm:",[3554,28915,28917],{"className":3556,"code":28916,"language":71,"meta":3558,"style":3558},"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",[1373,28918,28919,28929,28952,28967,28989],{"__ignoreMap":3558},[1115,28920,28921,28923,28925,28927],{"class":3563,"line":10},[1115,28922,21068],{"class":3741},[1115,28924,1168],{"class":3569},[1115,28926,360],{"class":3744},[1115,28928,3575],{"class":3569},[1115,28930,28931,28933,28935,28937,28939,28942,28944,28946,28948,28950],{"class":3563,"line":27},[1115,28932,23779],{"class":3744},[1115,28934,4497],{"class":3741},[1115,28936,23784],{"class":3566},[1115,28938,1168],{"class":3569},[1115,28940,28941],{"class":7974},"\"3_8.txt\"",[1115,28943,1715],{"class":3741},[1115,28945,23794],{"class":3744},[1115,28947,3748],{"class":3741},[1115,28949,7944],{"class":3572},[1115,28951,3575],{"class":3569},[1115,28953,28954,28956,28958,28961,28963,28965],{"class":3563,"line":148},[1115,28955,1171],{"class":3744},[1115,28957,4497],{"class":3741},[1115,28959,28960],{"class":3566}," as.matrix",[1115,28962,1168],{"class":3569},[1115,28964,23779],{"class":3744},[1115,28966,3575],{"class":3569},[1115,28968,28969,28971,28973,28975,28977,28979,28981,28983,28985,28987],{"class":3563,"line":111},[1115,28970,28856],{"class":3744},[1115,28972,4497],{"class":3741},[1115,28974,27293],{"class":3566},[1115,28976,1168],{"class":3569},[1115,28978,1171],{"class":3744},[1115,28980,1715],{"class":3741},[1115,28982,15894],{"class":3744},[1115,28984,3748],{"class":3741},[1115,28986,26419],{"class":7974},[1115,28988,3575],{"class":3569},[1115,28990,28991,28994,28996,28998,29000,29003,29005,29007,29009,29011,29013,29015,29017,29019,29022,29024,29027,29029,29032,29034,29036,29038,29040],{"class":3563,"line":96},[1115,28992,28993],{"class":3566},"process.capability",[1115,28995,1168],{"class":3569},[1115,28997,28856],{"class":3744},[1115,28999,1715],{"class":3741},[1115,29001,29002],{"class":3744}," spec.limits",[1115,29004,3748],{"class":3741},[1115,29006,7969],{"class":3566},[1115,29008,1168],{"class":3569},[1115,29010,15489],{"class":3572},[1115,29012,1715],{"class":3741},[1115,29014,17939],{"class":3572},[1115,29016,1174],{"class":3569},[1115,29018,1715],{"class":3741},[1115,29020,29021],{"class":3744}," target",[1115,29023,3748],{"class":3741},[1115,29025,29026],{"class":3572}," 105",[1115,29028,1715],{"class":3741},[1115,29030,29031],{"class":3744}," std.dev",[1115,29033,3748],{"class":3741},[1115,29035,3756],{"class":3566},[1115,29037,1168],{"class":3569},[1115,29039,1171],{"class":3744},[1115,29041,4011],{"class":3569},[1110,29043,29044,29045,1376,29048,1376,29051,1376,29054,1425,29057,29060,29061,1425,29063,29065,29066,29087,29088,29111],{},"Výpis obsahuje řádky ",[1373,29046,29047],{},"Cp",[1373,29049,29050],{},"Cp_l",[1373,29052,29053],{},"Cp_u",[1373,29055,29056],{},"Cp_k",[1373,29058,29059],{},"Cpm"," s hodnotou indexu a 95% intervalem spolehlivosti. ",[1373,29062,29050],{},[1373,29064,29053],{}," jsou dílčí poměry k dolní a horní mezi, jejich minimum je ",[1115,29067,29069],{"className":29068},[1149],[1151,29070,29071],{"xmlns":1153},[1155,29072,29073,29085],{},[1158,29074,29075],{},[1277,29076,29077,29079],{},[1161,29078,24469],{},[1158,29080,29081,29083],{},[1161,29082,1110],{},[1161,29084,1735],{},[1194,29086,24496],{"encoding":1196},". Index ",[1115,29089,29091],{"className":29090},[1149],[1151,29092,29093],{"xmlns":1153},[1155,29094,29095,29109],{},[1158,29096,29097],{},[1277,29098,29099,29101],{},[1161,29100,24469],{},[1158,29102,29103,29105,29107],{},[1161,29104,1110],{},[1161,29106,8597],{},[1161,29108,1735],{},[1194,29110,24542],{"encoding":1196}," a doplňkové charakteristiky se dopočítají ze vzorců výše:",[3554,29113,29115],{"className":3556,"code":29114,"language":71,"meta":3558,"style":3558},"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",[1373,29116,29117,29144,29169,29206,29236,29294,29308,29359],{"__ignoreMap":3558},[1115,29118,29119,29122,29124,29126,29128,29130,29132,29134,29136,29138,29140,29142],{"class":3563,"line":10},[1115,29120,29121],{"class":3744},"mu",[1115,29123,4497],{"class":3741},[1115,29125,3745],{"class":3566},[1115,29127,1168],{"class":3569},[1115,29129,1171],{"class":3744},[1115,29131,15848],{"class":3569},[1115,29133,380],{"class":3744},[1115,29135,4497],{"class":3741},[1115,29137,3756],{"class":3566},[1115,29139,1168],{"class":3569},[1115,29141,1171],{"class":3744},[1115,29143,3575],{"class":3569},[1115,29145,29146,29148,29150,29152,29154,29156,29158,29160,29162,29164,29166],{"class":3563,"line":27},[1115,29147,27855],{"class":3744},[1115,29149,4497],{"class":3741},[1115,29151,19010],{"class":3572},[1115,29153,28857],{"class":3569},[1115,29155,27874],{"class":3744},[1115,29157,4497],{"class":3741},[1115,29159,17939],{"class":3572},[1115,29161,28857],{"class":3569},[1115,29163,1575],{"class":3744},[1115,29165,4497],{"class":3741},[1115,29167,29168],{"class":3572}," 105\n",[1115,29170,29171,29174,29176,29178,29180,29182,29184,29186,29188,29190,29192,29195,29198,29200,29202,29204],{"class":3563,"line":148},[1115,29172,29173],{"class":3744},"tau",[1115,29175,4497],{"class":3741},[1115,29177,4003],{"class":3566},[1115,29179,1168],{"class":3569},[1115,29181,380],{"class":3744},[1115,29183,6883],{"class":3741},[1115,29185,1298],{"class":3572},[1115,29187,22187],{"class":3741},[1115,29189,8728],{"class":3569},[1115,29191,29121],{"class":3744},[1115,29193,29194],{"class":3741}," -",[1115,29196,29197],{"class":3744}," T",[1115,29199,1174],{"class":3569},[1115,29201,6883],{"class":3741},[1115,29203,1298],{"class":3572},[1115,29205,3575],{"class":3569},[1115,29207,29208,29210,29212,29214,29216,29218,29221,29223,29225,29227,29229,29231,29234],{"class":3563,"line":111},[1115,29209,29047],{"class":3744},[1115,29211,4497],{"class":3741},[1115,29213,8728],{"class":3569},[1115,29215,27874],{"class":3744},[1115,29217,29194],{"class":3741},[1115,29219,29220],{"class":3744}," LSL",[1115,29222,3862],{"class":3569},[1115,29224,3434],{"class":3741},[1115,29226,8728],{"class":3569},[1115,29228,8094],{"class":3572},[1115,29230,22312],{"class":3741},[1115,29232,29233],{"class":3744}," sigma",[1115,29235,3575],{"class":3569},[1115,29237,29238,29241,29243,29245,29248,29250,29252,29255,29257,29259,29261,29263,29265,29268,29270,29272,29274,29276,29278,29280,29282,29284,29286,29288,29290,29292],{"class":3563,"line":96},[1115,29239,29240],{"class":3744},"Cpmk",[1115,29242,4497],{"class":3741},[1115,29244,15869],{"class":3566},[1115,29246,29247],{"class":3569},"((",[1115,29249,27874],{"class":3744},[1115,29251,29194],{"class":3741},[1115,29253,29254],{"class":3744}," mu",[1115,29256,3862],{"class":3569},[1115,29258,3434],{"class":3741},[1115,29260,8728],{"class":3569},[1115,29262,3322],{"class":3572},[1115,29264,22312],{"class":3741},[1115,29266,29267],{"class":3744}," tau",[1115,29269,1174],{"class":3569},[1115,29271,1715],{"class":3741},[1115,29273,8728],{"class":3569},[1115,29275,29121],{"class":3744},[1115,29277,29194],{"class":3741},[1115,29279,29220],{"class":3744},[1115,29281,3862],{"class":3569},[1115,29283,3434],{"class":3741},[1115,29285,8728],{"class":3569},[1115,29287,3322],{"class":3572},[1115,29289,22312],{"class":3741},[1115,29291,29267],{"class":3744},[1115,29293,4011],{"class":3569},[1115,29295,29296,29299,29301,29303,29305],{"class":3563,"line":89},[1115,29297,29298],{"class":3744},"miravyuziti",[1115,29300,4497],{"class":3741},[1115,29302,19010],{"class":3572},[1115,29304,4608],{"class":3741},[1115,29306,29307],{"class":3744}," Cp\n",[1115,29309,29310,29313,29315,29317,29319,29321,29323,29325,29327,29329,29331,29333,29335,29337,29339,29341,29343,29345,29347,29349,29351,29353,29355,29357],{"class":3563,"line":82},[1115,29311,29312],{"class":3744},"robustnost",[1115,29314,4497],{"class":3741},[1115,29316,15869],{"class":3566},[1115,29318,1168],{"class":3569},[1115,29320,27874],{"class":3744},[1115,29322,29194],{"class":3741},[1115,29324,8728],{"class":3569},[1115,29326,29121],{"class":3744},[1115,29328,22187],{"class":3741},[1115,29330,5393],{"class":3572},[1115,29332,22312],{"class":3741},[1115,29334,29233],{"class":3744},[1115,29336,1174],{"class":3569},[1115,29338,1715],{"class":3741},[1115,29340,8728],{"class":3569},[1115,29342,29121],{"class":3744},[1115,29344,29194],{"class":3741},[1115,29346,5393],{"class":3572},[1115,29348,22312],{"class":3741},[1115,29350,29233],{"class":3744},[1115,29352,3862],{"class":3569},[1115,29354,3865],{"class":3741},[1115,29356,29220],{"class":3744},[1115,29358,3575],{"class":3569},[1115,29360,29361,29364,29366,29368,29370,29372,29374,29376,29378,29380,29383],{"class":3563,"line":75},[1115,29362,29363],{"class":3744},"Pz",[1115,29365,4497],{"class":3741},[1115,29367,8310],{"class":3572},[1115,29369,22312],{"class":3741},[1115,29371,3868],{"class":3566},[1115,29373,1168],{"class":3569},[1115,29375,3865],{"class":3741},[1115,29377,3322],{"class":3572},[1115,29379,22312],{"class":3741},[1115,29381,29382],{"class":3744}," Cp",[1115,29384,3575],{"class":3569},[1431,29386,5414],{"id":5413},[1124,29388,29389,29392,29452,29543,29609],{},[1127,29390,29391],{},"Počítat indexy způsobilosti pro proces, který není statisticky zvládnutý — způsobilost se zkoumá až ve třetí fázi regulace.",[1127,29393,29394,29395,29412,29413,29430,29431,1333],{},"Posuzovat jen ",[1115,29396,29398],{"className":29397},[1149],[1151,29399,29400],{"xmlns":1153},[1155,29401,29402,29410],{},[1158,29403,29404],{},[1277,29405,29406,29408],{},[1161,29407,24469],{},[1161,29409,1110],{},[1194,29411,24474],{"encoding":1196}," u vychýleného procesu — ",[1115,29414,29416],{"className":29415},[1149],[1151,29417,29418],{"xmlns":1153},[1155,29419,29420,29428],{},[1158,29421,29422],{},[1277,29423,29424,29426],{},[1161,29425,24469],{},[1161,29427,1110],{},[1194,29429,24474],{"encoding":1196}," polohu střední hodnoty nezohledňuje, vychýlení zachytí až ",[1115,29432,29434],{"className":29433},[1149],[1151,29435,29436],{"xmlns":1153},[1155,29437,29438,29450],{},[1158,29439,29440],{},[1277,29441,29442,29444],{},[1161,29443,24469],{},[1158,29445,29446,29448],{},[1161,29447,1110],{},[1161,29449,1735],{},[1194,29451,24496],{"encoding":1196},[1127,29453,29454,29455,29468,29469,29482,29483,29468,29498,29511,29512,29525,29526,29539,29540,29542],{},"Zaměnit diagram ",[1115,29456,29458],{"className":29457},[1149],[1151,29459,29460],{"xmlns":1153},[1155,29461,29462,29466],{},[1158,29463,29464],{},[1161,29465,7856],{},[1194,29467,7856],{"encoding":1196}," s diagramem ",[1115,29470,29472],{"className":29471},[1149],[1151,29473,29474],{"xmlns":1153},[1155,29475,29476,29480],{},[1158,29477,29478],{},[1161,29479,15199],{},[1194,29481,15199],{"encoding":1196}," nebo diagram ",[1115,29484,29486],{"className":29485},[1149],[1151,29487,29488],{"xmlns":1153},[1155,29489,29490,29496],{},[1158,29491,29492,29494],{},[1161,29493,4192],{},[1161,29495,1110],{},[1194,29497,24434],{"encoding":1196},[1115,29499,29501],{"className":29500},[1149],[1151,29502,29503],{"xmlns":1153},[1155,29504,29505,29509],{},[1158,29506,29507],{},[1161,29508,1110],{},[1194,29510,1110],{"encoding":1196}," — při nekonstantním rozsahu podskupin se volí ",[1115,29513,29515],{"className":29514},[1149],[1151,29516,29517],{"xmlns":1153},[1155,29518,29519,29523],{},[1158,29520,29521],{},[1161,29522,15199],{},[1194,29524,15199],{"encoding":1196},", resp. ",[1115,29527,29529],{"className":29528},[1149],[1151,29530,29531],{"xmlns":1153},[1155,29532,29533,29537],{},[1158,29534,29535],{},[1161,29536,1110],{},[1194,29538,1110],{"encoding":1196},", a do ",[1373,29541,27489],{}," se zadává vektor rozsahů.",[1127,29544,29545,29546,29563,29564,29577,29578,29591,29592,1333],{},"Posuzovat diagram ",[1115,29547,29549],{"className":29548},[1149],[1151,29550,29551],{"xmlns":1153},[1155,29552,29553,29561],{},[1158,29554,29555],{},[6877,29556,29557,29559],{"accent":1121},[1161,29558,1171],{},[1165,29560,15130],{},[1194,29562,25238],{"encoding":1196}," dřív než diagram rozpětí — nejprve se určí a stabilizuje diagram ",[1115,29565,29567],{"className":29566},[1149],[1151,29568,29569],{"xmlns":1153},[1155,29570,29571,29575],{},[1158,29572,29573],{},[1161,29574,4759],{},[1194,29576,4759],{"encoding":1196}," (resp. ",[1115,29579,29581],{"className":29580},[1149],[1151,29582,29583],{"xmlns":1153},[1155,29584,29585,29589],{},[1158,29586,29587],{},[1161,29588,6018],{},[1194,29590,6018],{"encoding":1196},"), potom diagram ",[1115,29593,29595],{"className":29594},[1149],[1151,29596,29597],{"xmlns":1153},[1155,29598,29599,29607],{},[1158,29600,29601],{},[6877,29602,29603,29605],{"accent":1121},[1161,29604,1171],{},[1165,29606,15130],{},[1194,29608,25238],{"encoding":1196},[1127,29610,29611],{},"Vyřadit podskupinu jen podle polohy bodu — vyřazuje se až po zjištění a odstranění vymezitelné příčiny.",[1431,29613,5604],{"id":5603},[1124,29615,29616,29621,29626,29632,29637,29642,29647],{},[1127,29617,29618],{},[1438,29619,1444],{"className":29620,"dataFsResolvedFilePath":1442,"href":1443},[1441],[1127,29622,29623],{},[1438,29624,886],{"className":29625,"dataFsResolvedFilePath":2788,"href":2789},[1441],[1127,29627,29628],{},[1438,29629,29631],{"className":29630,"dataFsResolvedFilePath":10731,"href":10732},[1441],"nahodne-veliciny-a-rozdeleni",[1127,29633,29634],{},[1438,29635,141],{"className":29636,"dataFsResolvedFilePath":4636,"href":4637},[1441],[1127,29638,29639],{},[1438,29640,5629],{"className":29641,"dataFsResolvedFilePath":5627,"href":5628},[1441],[1127,29643,29644],{},[1438,29645,716],{"className":29646,"dataFsResolvedFilePath":5635,"href":5636},[1441],[1127,29648,29649],{},[1438,29650,5652],{"className":29651,"dataFsResolvedFilePath":5650,"href":5651},[1441],[1431,29653,5655],{"id":934},[1110,29655,5658,29656,5663],{},[5660,29657,5662],{},[1110,29659,29660,29661,29664],{},"MONTGOMERY, D. C. ",[5660,29662,29663],{},"Introduction to Statistical Quality Control",". 6. vyd. John Wiley & Sons, 2005.",[1110,29666,29667,29668,29671],{},"ČSN ISO 8258. ",[5660,29669,29670],{},"Shewhartovy regulační diagramy",". Praha: Český normalizační institut, 1994.",[1110,29673,29674,29675,29678],{},"KUPKA, K. ",[5660,29676,29677],{},"Statistické řízení jakosti",". Pardubice: TriloByte, 1997.",[5665,29680,29681],{},"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":27832,"depth":27,"text":27833,"children":29705},[29706,29708,29710,29712,29713],{"id":27878,"depth":148,"text":29707},"CpC_p — index způsobilosti",{"id":28202,"depth":148,"text":29709},"CpkC_{pk} — index způsobilosti s ohledem na vychýlení",{"id":28397,"depth":148,"text":29711},"CpmC_{pm} a CpmkC_{pmk} — indexy vztažené k cíli",{"id":28655,"depth":148,"text":28656},{"id":28845,"depth":148,"text":28846},{"id":5413,"depth":27,"text":5414},{"id":5603,"depth":27,"text":5604},{"id":934,"depth":27,"text":5655},{},"\u002Ftopics\u002Fregulacni-diagramy-a-indexy-zpusobilosti",{"title":10744,"description":3558},[29721,29722,29723,29724],"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":29729,"title":10719,"body":29730,"course":23,"courses":5680,"created":5681,"description":3558,"extension":5682,"meta":39541,"navigation":4572,"path":39542,"seo":39543,"sources":39544,"stem":39550,"tags":39551,"type":5692,"updated":5681,"__hash__":39552},"topics\u002Ftopics\u002Ftestovani-hypotez.md",{"type":1096,"value":29731,"toc":39514},[29732,29735,29934,29978,29982,29992,29995,30061,30111,30264,30268,30271,30365,30515,30534,30541,30630,30634,30669,30706,30744,30779,30783,30790,31008,31127,31131,31263,31317,31339,31681,31688,31776,31782,31823,32108,32117,32232,32238,32245,32250,32256,32350,32356,32382,32388,32480,32486,32536,32540,32736,32796,33158,33497,33596,33602,33830,33834,34100,34104,34107,34173,34220,34676,34680,34683,34870,34903,35125,35444,35483,35490,36147,36286,36292,36448,36454,36461,36514,36520,36693,36699,36763,36768,36953,36959,37004,37008,37011,37015,37062,37290,37306,37395,37401,37427,37431,37434,37506,37599,37668,37674,37697,38144,38151,38155,38185,38189,38439,38458,38519,38528,38684,38690,38716,38891,38895,38916,38947,38951,38975,39005,39009,39069,39127,39131,39138,39311,39313,39466,39468,39505,39507,39511],[1099,29733,10719],{"id":29734},"testování-statistických-hypotéz",[1103,29736,29738,29744],{"className":29737,"dataCallout":1108},[1106,1107],[1110,29739,29741,1122],{"className":29740},[1113],[1115,29742],{"className":29743,"ariaHidden":1121},[1118,1119,1120],[1124,29745,29746,29816,29898,29901,29904],{},[1127,29747,29748,29749,29766,29767,29784,29785,1376,29798,29815],{},"Test porovnává tvrzení ",[1115,29750,29752],{"className":29751},[1149],[1151,29753,29754],{"xmlns":1153},[1155,29755,29756,29764],{},[1158,29757,29758],{},[1277,29759,29760,29762],{},[1161,29761,4318],{},[1282,29763,1982],{},[1194,29765,5745],{"encoding":1196}," s alternativou ",[1115,29768,29770],{"className":29769},[1149],[1151,29771,29772],{"xmlns":1153},[1155,29773,29774,29782],{},[1158,29775,29776],{},[1277,29777,29778,29780],{},[1161,29779,4318],{},[1282,29781,1284],{},[1194,29783,7147],{"encoding":1196}," pomocí testového kritéria spočteného z výběru; padne-li kritérium do kritického oboru ",[1115,29786,29788],{"className":29787},[1149],[1151,29789,29790],{"xmlns":1153},[1155,29791,29792,29796],{},[1158,29793,29794],{},[1161,29795,5777],{},[1194,29797,5777],{"encoding":1196},[1115,29799,29801],{"className":29800},[1149],[1151,29802,29803],{"xmlns":1153},[1155,29804,29805,29813],{},[1158,29806,29807],{},[1277,29808,29809,29811],{},[1161,29810,4318],{},[1282,29812,1982],{},[1194,29814,5745],{"encoding":1196}," zamítáme.",[1127,29817,29818,29819,29832,29833,29850,29851,29865,29866,29883,29884,29897],{},"Rozhodnutí nese dva typy chyb: chybu I. druhu (",[1115,29820,29822],{"className":29821},[1149],[1151,29823,29824],{"xmlns":1153},[1155,29825,29826,29830],{},[1158,29827,29828],{},[1161,29829,7514],{},[1194,29831,7577],{"encoding":1196},", zamítnutí platné ",[1115,29834,29836],{"className":29835},[1149],[1151,29837,29838],{"xmlns":1153},[1155,29839,29840,29848],{},[1158,29841,29842],{},[1277,29843,29844,29846],{},[1161,29845,4318],{},[1282,29847,1982],{},[1194,29849,5745],{"encoding":1196},") a chybu II. druhu (",[1115,29852,29854],{"className":29853},[1149],[1151,29855,29856],{"xmlns":1153},[1155,29857,29858,29862],{},[1158,29859,29860],{},[1161,29861,20009],{},[1194,29863,29864],{"encoding":1196},"\\beta",", přijetí neplatné ",[1115,29867,29869],{"className":29868},[1149],[1151,29870,29871],{"xmlns":1153},[1155,29872,29873,29881],{},[1158,29874,29875],{},[1277,29876,29877,29879],{},[1161,29878,4318],{},[1282,29880,1982],{},[1194,29882,5745],{"encoding":1196},"). Hladina významnosti ",[1115,29885,29887],{"className":29886},[1149],[1151,29888,29889],{"xmlns":1153},[1155,29890,29891,29895],{},[1158,29892,29893],{},[1161,29894,7514],{},[1194,29896,7577],{"encoding":1196}," se volí předem, obvykle 0,05.",[1127,29899,29900],{},"Pro střední hodnotu normálního rozdělení slouží jednovýběrový a párový t-test; pro srovnání dvou souborů F-test (rozptyly) a dvouvýběrový t-test (střední hodnoty).",[1127,29902,29903],{},"Normalitu ověřuje Shapiro-Wilkův test, shodu s libovolným rozdělením Kolmogorov-Smirnovův test; při porušené normalitě nastupují neparametrické testy (Wilcoxonovy, Kruskalův-Wallisův, mediánový, Friedmanův).",[1127,29905,29906,29907,29920,29921,1333],{},"Rozhodnutí lze číst dvěma rovnocennými způsoby — podle polohy kritéria vůči ",[1115,29908,29910],{"className":29909},[1149],[1151,29911,29912],{"xmlns":1153},[1155,29913,29914,29918],{},[1158,29915,29916],{},[1161,29917,5777],{},[1194,29919,5777],{"encoding":1196},", nebo podle p-hodnoty vůči ",[1115,29922,29924],{"className":29923},[1149],[1151,29925,29926],{"xmlns":1153},[1155,29927,29928,29932],{},[1158,29929,29930],{},[1161,29931,7514],{},[1194,29933,7577],{"encoding":1196},[1110,29935,29936,29937,29941,29942,29946,29947,29951,29952,1376,29965,19765],{},"Testy statistických hypotéz jsou nástroj ",[1438,29938,29940],{"className":29939,"dataFsResolvedFilePath":1442,"href":1443},[1441],"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 ",[1438,29943,29945],{"className":29944,"dataFsResolvedFilePath":2788,"href":2789},[1441],"popisnou statistiku"," výběru, a z rozdělení uvedených u ",[1438,29948,29950],{"className":29949,"dataFsResolvedFilePath":10731,"href":10732},[1441],"náhodných veličin"," (normální, ",[1115,29953,29955],{"className":29954},[1149],[1151,29956,29957],{"xmlns":1153},[1155,29958,29959,29963],{},[1158,29960,29961],{},[1161,29962,1617],{},[1194,29964,1617],{"encoding":1196},[1115,29966,29968],{"className":29967},[1149],[1151,29969,29970],{"xmlns":1153},[1155,29971,29972,29976],{},[1158,29973,29974],{},[1161,29975,1163],{},[1194,29977,1163],{"encoding":1196},[1431,29979,29981],{"id":29980},"statistická-hypotéza-a-její-test","Statistická hypotéza a její test",[1110,29983,29984,29987,29988,29991],{},[1131,29985,29986],{},"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. ",[1131,29989,29990],{},"Testování hypotéz"," je proces ověření správnosti nebo nesprávnosti hypotézy pomocí výsledků získaných náhodným výběrem.",[1110,29993,29994],{},"Proti sobě stojí dvě hypotézy:",[1124,29996,29997,30020],{},[1127,29998,29999,30019],{},[1131,30000,30001,30002],{},"Nulová hypotéza ",[1115,30003,30005],{"className":30004},[1149],[1151,30006,30007],{"xmlns":1153},[1155,30008,30009,30017],{},[1158,30010,30011],{},[1277,30012,30013,30015],{},[1161,30014,4318],{},[1282,30016,1982],{},[1194,30018,5745],{"encoding":1196}," — tvrzení o parametru nebo rozdělení, které chceme ověřit.",[1127,30021,30022,30042,30043,30060],{},[1131,30023,30024,30025],{},"Alternativní hypotéza ",[1115,30026,30028],{"className":30027},[1149],[1151,30029,30030],{"xmlns":1153},[1155,30031,30032,30040],{},[1158,30033,30034],{},[1277,30035,30036,30038],{},[1161,30037,4318],{},[1282,30039,1284],{},[1194,30041,7147],{"encoding":1196}," — staví se proti ",[1115,30044,30046],{"className":30045},[1149],[1151,30047,30048],{"xmlns":1153},[1155,30049,30050,30058],{},[1158,30051,30052],{},[1277,30053,30054,30056],{},[1161,30055,4318],{},[1282,30057,1982],{},[1194,30059,5745],{"encoding":1196}," a určitým způsobem popírá její tvrzení.",[1110,30062,5867,30063,30093,30094,2629],{},[1115,30064,30066],{"className":30065},[1149],[1151,30067,30068],{"xmlns":1153},[1155,30069,30070,30090],{},[1158,30071,30072,30078,30080,30082,30084],{},[1277,30073,30074,30076],{},[1161,30075,4318],{},[1282,30077,1982],{},[1165,30079,2629],{},[1161,30081,1355],{},[1165,30083,1177],{},[1277,30085,30086,30088],{},[1161,30087,1355],{},[1282,30089,1982],{},[1194,30091,30092],{"encoding":1196},"H_0: \\mu = \\mu_0"," existují tři varianty ",[1115,30095,30097],{"className":30096},[1149],[1151,30098,30099],{"xmlns":1153},[1155,30100,30101,30109],{},[1158,30102,30103],{},[1277,30104,30105,30107],{},[1161,30106,4318],{},[1282,30108,1284],{},[1194,30110,7147],{"encoding":1196},[4052,30112,30113,30143],{},[4055,30114,30115],{},[4058,30116,30117,30137,30140],{},[4061,30118,30119,30120],{},"Tvar ",[1115,30121,30123],{"className":30122},[1149],[1151,30124,30125],{"xmlns":1153},[1155,30126,30127,30135],{},[1158,30128,30129],{},[1277,30130,30131,30133],{},[1161,30132,4318],{},[1282,30134,1284],{},[1194,30136,7147],{"encoding":1196},[4061,30138,30139],{},"Zápis",[4061,30141,30142],{},"Typ",[4165,30144,30145,30185,30225],{},[4058,30146,30147,30150,30182],{},[4170,30148,30149],{},"nerovnost",[4170,30151,30152],{},[1115,30153,30155],{"className":30154},[1149],[1151,30156,30157],{"xmlns":1153},[1155,30158,30159,30179],{},[1158,30160,30161,30167,30169,30171,30173],{},[1277,30162,30163,30165],{},[1161,30164,4318],{},[1282,30166,1284],{},[1165,30168,2629],{},[1161,30170,1355],{},[1165,30172,5496],{"mathvariant":1215},[1277,30174,30175,30177],{},[1161,30176,1355],{},[1282,30178,1982],{},[1194,30180,30181],{"encoding":1196},"H_1: \\mu \\neq \\mu_0",[4170,30183,30184],{},"dvoustranná",[4058,30186,30187,30190,30222],{},[4170,30188,30189],{},"větší",[4170,30191,30192],{},[1115,30193,30195],{"className":30194},[1149],[1151,30196,30197],{"xmlns":1153},[1155,30198,30199,30219],{},[1158,30200,30201,30207,30209,30211,30213],{},[1277,30202,30203,30205],{},[1161,30204,4318],{},[1282,30206,1284],{},[1165,30208,2629],{},[1161,30210,1355],{},[1165,30212,4156],{},[1277,30214,30215,30217],{},[1161,30216,1355],{},[1282,30218,1982],{},[1194,30220,30221],{"encoding":1196},"H_1: \\mu > \\mu_0",[4170,30223,30224],{},"jednostranná",[4058,30226,30227,30230,30262],{},[4170,30228,30229],{},"menší",[4170,30231,30232],{},[1115,30233,30235],{"className":30234},[1149],[1151,30236,30237],{"xmlns":1153},[1155,30238,30239,30259],{},[1158,30240,30241,30247,30249,30251,30253],{},[1277,30242,30243,30245],{},[1161,30244,4318],{},[1282,30246,1284],{},[1165,30248,2629],{},[1161,30250,1355],{},[1165,30252,1287],{},[1277,30254,30255,30257],{},[1161,30256,1355],{},[1282,30258,1982],{},[1194,30260,30261],{"encoding":1196},"H_1: \\mu \u003C \\mu_0",[4170,30263,30224],{},[20418,30265,30267],{"id":30266},"chyba-i-a-ii-druhu","Chyba I. a II. druhu",[1110,30269,30270],{},"Protože je úsudek odvozen z náhodného výběru, může vést ke dvěma typům chybného rozhodnutí:",[1124,30272,30273,30310],{},[1127,30274,30275,30278,30279,30296,30297,1333],{},[1131,30276,30277],{},"Chyba I. druhu"," — zamítnutí ",[1115,30280,30282],{"className":30281},[1149],[1151,30283,30284],{"xmlns":1153},[1155,30285,30286,30294],{},[1158,30287,30288],{},[1277,30289,30290,30292],{},[1161,30291,4318],{},[1282,30293,1982],{},[1194,30295,5745],{"encoding":1196},", ačkoliv ve skutečnosti platí. Pravděpodobnost ",[1115,30298,30300],{"className":30299},[1149],[1151,30301,30302],{"xmlns":1153},[1155,30303,30304,30308],{},[1158,30305,30306],{},[1161,30307,7514],{},[1194,30309,7577],{"encoding":1196},[1127,30311,30312,30315,30316,30333,30334,30351,30352,1333],{},[1131,30313,30314],{},"Chyba II. druhu"," — přijetí ",[1115,30317,30319],{"className":30318},[1149],[1151,30320,30321],{"xmlns":1153},[1155,30322,30323,30331],{},[1158,30324,30325],{},[1277,30326,30327,30329],{},[1161,30328,4318],{},[1282,30330,1982],{},[1194,30332,5745],{"encoding":1196},", ačkoliv platí ",[1115,30335,30337],{"className":30336},[1149],[1151,30338,30339],{"xmlns":1153},[1155,30340,30341,30349],{},[1158,30342,30343],{},[1277,30344,30345,30347],{},[1161,30346,4318],{},[1282,30348,1284],{},[1194,30350,7147],{"encoding":1196},". Pravděpodobnost ",[1115,30353,30355],{"className":30354},[1149],[1151,30356,30357],{"xmlns":1153},[1155,30358,30359,30363],{},[1158,30360,30361],{},[1161,30362,20009],{},[1194,30364,29864],{"encoding":1196},[4052,30366,30367,30430],{},[4055,30368,30369],{},[4058,30370,30371,30391,30410],{},[4061,30372,30373,30374],{},"Úsudek o ",[1115,30375,30377],{"className":30376},[1149],[1151,30378,30379],{"xmlns":1153},[1155,30380,30381,30389],{},[1158,30382,30383],{},[1277,30384,30385,30387],{},[1161,30386,4318],{},[1282,30388,1982],{},[1194,30390,5745],{"encoding":1196},[4061,30392,30393,2843],{},[1115,30394,30396],{"className":30395},[1149],[1151,30397,30398],{"xmlns":1153},[1155,30399,30400,30408],{},[1158,30401,30402],{},[1277,30403,30404,30406],{},[1161,30405,4318],{},[1282,30407,1982],{},[1194,30409,5745],{"encoding":1196},[4061,30411,30412,30429],{},[1115,30413,30415],{"className":30414},[1149],[1151,30416,30417],{"xmlns":1153},[1155,30418,30419,30427],{},[1158,30420,30421],{},[1277,30422,30423,30425],{},[1161,30424,4318],{},[1282,30426,1982],{},[1194,30428,5745],{"encoding":1196}," neplatí",[4165,30431,30432,30474],{},[4058,30433,30434,30437,30458],{},[4170,30435,30436],{},"Nezamítá se",[4170,30438,30439,30440],{},"správné rozhodnutí, ",[1115,30441,30443],{"className":30442},[1149],[1151,30444,30445],{"xmlns":1153},[1155,30446,30447,30455],{},[1158,30448,30449,30451,30453],{},[1282,30450,1284],{},[1165,30452,1317],{},[1161,30454,7514],{},[1194,30456,30457],{"encoding":1196},"1-\\alpha",[4170,30459,30460,30461],{},"chyba II. druhu, ",[1115,30462,30464],{"className":30463},[1149],[1151,30465,30466],{"xmlns":1153},[1155,30467,30468,30472],{},[1158,30469,30470],{},[1161,30471,20009],{},[1194,30473,29864],{"encoding":1196},[4058,30475,30476,30479,30495],{},[4170,30477,30478],{},"Zamítá se",[4170,30480,30481,30482],{},"chyba I. druhu, ",[1115,30483,30485],{"className":30484},[1149],[1151,30486,30487],{"xmlns":1153},[1155,30488,30489,30493],{},[1158,30490,30491],{},[1161,30492,7514],{},[1194,30494,7577],{"encoding":1196},[4170,30496,30439,30497],{},[1115,30498,30500],{"className":30499},[1149],[1151,30501,30502],{"xmlns":1153},[1155,30503,30504,30512],{},[1158,30505,30506,30508,30510],{},[1282,30507,1284],{},[1165,30509,1317],{},[1161,30511,20009],{},[1194,30513,30514],{"encoding":1196},"1-\\beta",[1110,30516,30517,1145,30520,30533],{},[1131,30518,30519],{},"Hladina významnosti",[1115,30521,30523],{"className":30522},[1149],[1151,30524,30525],{"xmlns":1153},[1155,30526,30527,30531],{},[1158,30528,30529],{},[1161,30530,7514],{},[1194,30532,7577],{"encoding":1196}," 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.",[1110,30535,30536],{},[1760,30537],{"alt":30538,"className":30539,"src":30540},"mask-th-chyba-i-ii",[1441,1764],"\u002Fwiki-assets\u002Fmask-th-chyba-i-ii.png",[1110,30542,30543,30544,30557,30558,30571,30572,30585,30586,3640,30599,30612,30613,1333],{},"Obrázek ukazuje, proč jde o kompromis: posunutí kritické hodnoty ",[1115,30545,30547],{"className":30546},[1149],[1151,30548,30549],{"xmlns":1153},[1155,30550,30551,30555],{},[1158,30552,30553],{},[1161,30554,7856],{},[1194,30556,7856],{"encoding":1196}," doleva zmenší ",[1115,30559,30561],{"className":30560},[1149],[1151,30562,30563],{"xmlns":1153},[1155,30564,30565,30569],{},[1158,30566,30567],{},[1161,30568,20009],{},[1194,30570,29864],{"encoding":1196},", ale zvětší ",[1115,30573,30575],{"className":30574},[1149],[1151,30576,30577],{"xmlns":1153},[1155,30578,30579,30583],{},[1158,30580,30581],{},[1161,30582,7514],{},[1194,30584,7577],{"encoding":1196},", a naopak. Pro danou hladinu ",[1115,30587,30589],{"className":30588},[1149],[1151,30590,30591],{"xmlns":1153},[1155,30592,30593,30597],{},[1158,30594,30595],{},[1161,30596,7514],{},[1194,30598,7577],{"encoding":1196},[1115,30600,30602],{"className":30601},[1149],[1151,30603,30604],{"xmlns":1153},[1155,30605,30606,30610],{},[1158,30607,30608],{},[1161,30609,7856],{},[1194,30611,7856],{"encoding":1196}," jednoznačně určena rozdělením kritéria za platnosti ",[1115,30614,30616],{"className":30615},[1149],[1151,30617,30618],{"xmlns":1153},[1155,30619,30620,30628],{},[1158,30621,30622],{},[1277,30623,30624,30626],{},[1161,30625,4318],{},[1282,30627,1982],{},[1194,30629,5745],{"encoding":1196},[20418,30631,30633],{"id":30632},"testové-kritérium-a-kritický-obor","Testové kritérium a kritický obor",[1110,30635,30636,1145,30638,30651,30652,1333],{},[1131,30637,7151],{},[1115,30639,30641],{"className":30640},[1149],[1151,30642,30643],{"xmlns":1153},[1155,30644,30645,30649],{},[1158,30646,30647],{},[1161,30648,1575],{},[1194,30650,1575],{"encoding":1196}," je statistika spočtená z výběru; aby bylo možné test provést, musí být známo jeho rozdělení za platnosti ",[1115,30653,30655],{"className":30654},[1149],[1151,30656,30657],{"xmlns":1153},[1155,30658,30659,30667],{},[1158,30660,30661],{},[1277,30662,30663,30665],{},[1161,30664,4318],{},[1282,30666,1982],{},[1194,30668,5745],{"encoding":1196},[1110,30670,30671,1145,30674,30687,30688,30705],{},[1131,30672,30673],{},"Kritický obor",[1115,30675,30677],{"className":30676},[1149],[1151,30678,30679],{"xmlns":1153},[1155,30680,30681,30685],{},[1158,30682,30683],{},[1161,30684,5777],{},[1194,30686,5777],{"encoding":1196}," je množina hodnot svědčících pro ",[1115,30689,30691],{"className":30690},[1149],[1151,30692,30693],{"xmlns":1153},[1155,30694,30695,30703],{},[1158,30696,30697],{},[1277,30698,30699,30701],{},[1161,30700,4318],{},[1282,30702,1284],{},[1194,30704,7147],{"encoding":1196},". Je zkonstruován tak, aby",[1115,30707,30709],{"className":30708},[1149],[1151,30710,30711],{"xmlns":1153,"display":2212},[1155,30712,30713,30741],{},[1158,30714,30715,30717,30719,30721,30723,30725,30727,30733,30735,30737,30739],{},[1161,30716,1180],{},[1165,30718,1168],{"stretchy":1167},[1161,30720,1575],{},[1165,30722,1492],{},[1161,30724,5777],{},[1165,30726,26697],{},[1277,30728,30729,30731],{},[1161,30730,4318],{},[1282,30732,1982],{},[1165,30734,1174],{"stretchy":1167},[1165,30736,1177],{},[1161,30738,7514],{},[1165,30740,1715],{"separator":1121},[1194,30742,30743],{"encoding":1196},"P(T \\in W \\mid H_0) = \\alpha,",[1110,30745,30746,30747,30760,30761,30778],{},"tedy aby pravděpodobnost, že výběr dá hodnotu kritéria v ",[1115,30748,30750],{"className":30749},[1149],[1151,30751,30752],{"xmlns":1153},[1155,30753,30754,30758],{},[1158,30755,30756],{},[1161,30757,5777],{},[1194,30759,5777],{"encoding":1196}," i při platné ",[1115,30762,30764],{"className":30763},[1149],[1151,30765,30766],{"xmlns":1153},[1155,30767,30768,30776],{},[1158,30769,30770],{},[1277,30771,30772,30774],{},[1161,30773,4318],{},[1282,30775,1982],{},[1194,30777,5745],{"encoding":1196},", byla rovna zvolené hladině významnosti.",[20418,30780,30782],{"id":30781},"postup-testování-hypotézy","Postup testování hypotézy",[1110,30784,30785],{},[1760,30786],{"alt":30787,"className":30788,"src":30789},"mask-ilu-postup-testovani",[1441,1764],"\u002Fwiki-assets\u002Fmask-ilu-postup-testovani.png",[7018,30791,30792,30829,30832,30848],{},[1127,30793,30794,30795,1425,30812,1333],{},"Formulace hypotéz ",[1115,30796,30798],{"className":30797},[1149],[1151,30799,30800],{"xmlns":1153},[1155,30801,30802,30810],{},[1158,30803,30804],{},[1277,30805,30806,30808],{},[1161,30807,4318],{},[1282,30809,1982],{},[1194,30811,5745],{"encoding":1196},[1115,30813,30815],{"className":30814},[1149],[1151,30816,30817],{"xmlns":1153},[1155,30818,30819,30827],{},[1158,30820,30821],{},[1277,30822,30823,30825],{},[1161,30824,4318],{},[1282,30826,1284],{},[1194,30828,7147],{"encoding":1196},[1127,30830,30831],{},"Volba testového kritéria a výpočet jeho hodnoty.",[1127,30833,30834,30835,1333],{},"Volba hladiny významnosti a sestrojení příslušného kritického oboru ",[1115,30836,30838],{"className":30837},[1149],[1151,30839,30840],{"xmlns":1153},[1155,30841,30842,30846],{},[1158,30843,30844],{},[1161,30845,5777],{},[1194,30847,5777],{"encoding":1196},[1127,30849,30850,30851],{},"Formulace závěru:\n",[1124,30852,30853,30931],{},[1127,30854,30855,30856,8118,30874,30891,30892,30912,30913,30930],{},"pokud ",[1115,30857,30859],{"className":30858},[1149],[1151,30860,30861],{"xmlns":1153},[1155,30862,30863,30871],{},[1158,30864,30865,30867,30869],{},[1161,30866,1575],{},[1165,30868,1492],{},[1161,30870,5777],{},[1194,30872,30873],{"encoding":1196},"T \\in W",[1115,30875,30877],{"className":30876},[1149],[1151,30878,30879],{"xmlns":1153},[1155,30880,30881,30889],{},[1158,30882,30883],{},[1277,30884,30885,30887],{},[1161,30886,4318],{},[1282,30888,1284],{},[1194,30890,7147],{"encoding":1196}," je testem prokázána na hladině významnosti ",[1115,30893,30895],{"className":30894},[1149],[1151,30896,30897],{"xmlns":1153},[1155,30898,30899,30909],{},[1158,30900,30901,30903,30905,30907],{},[1282,30902,15489],{},[1161,30904,7514],{},[2278,30906,2280],{},[1161,30908,15496],{"mathvariant":1215},[1194,30910,30911],{"encoding":1196},"100\\alpha\\,\\%"," (zamítáme ",[1115,30914,30916],{"className":30915},[1149],[1151,30917,30918],{"xmlns":1153},[1155,30919,30920,30928],{},[1158,30921,30922],{},[1277,30923,30924,30926],{},[1161,30925,4318],{},[1282,30927,1982],{},[1194,30929,5745],{"encoding":1196},");",[1127,30932,30855,30933,8118,30952,30969,30970,30989,30990,31007],{},[1115,30934,30936],{"className":30935},[1149],[1151,30937,30938],{"xmlns":1153},[1155,30939,30940,30949],{},[1158,30941,30942,30944,30947],{},[1161,30943,1575],{},[1165,30945,30946],{"mathvariant":1215},"∉",[1161,30948,5777],{},[1194,30950,30951],{"encoding":1196},"T \\notin W",[1115,30953,30955],{"className":30954},[1149],[1151,30956,30957],{"xmlns":1153},[1155,30958,30959,30967],{},[1158,30960,30961],{},[1277,30962,30963,30965],{},[1161,30964,4318],{},[1282,30966,1284],{},[1194,30968,7147],{"encoding":1196}," není testem prokázána na hladině významnosti ",[1115,30971,30973],{"className":30972},[1149],[1151,30974,30975],{"xmlns":1153},[1155,30976,30977,30987],{},[1158,30978,30979,30981,30983,30985],{},[1282,30980,15489],{},[1161,30982,7514],{},[2278,30984,2280],{},[1161,30986,15496],{"mathvariant":1215},[1194,30988,30911],{"encoding":1196}," ; ",[1115,30991,30993],{"className":30992},[1149],[1151,30994,30995],{"xmlns":1153},[1155,30996,30997,31005],{},[1158,30998,30999],{},[1277,31000,31001,31003],{},[1161,31002,4318],{},[1282,31004,1982],{},[1194,31006,5745],{"encoding":1196}," nezamítáme.",[1110,31009,31010,31011,31014,31015,31032,31033,31050,31051,31071,31072,28857,31089,1145,31109,31126],{},"Rovnocennou alternativou je ",[1131,31012,31013],{},"p-hodnota",": udává, nakolik jsou data slučitelná s ",[1115,31016,31018],{"className":31017},[1149],[1151,31019,31020],{"xmlns":1153},[1155,31021,31022,31030],{},[1158,31023,31024],{},[1277,31025,31026,31028],{},[1161,31027,4318],{},[1282,31029,1982],{},[1194,31031,5745],{"encoding":1196},". Čím menší p-hodnota, tím více data svědčí proti ",[1115,31034,31036],{"className":31035},[1149],[1151,31037,31038],{"xmlns":1153},[1155,31039,31040,31048],{},[1158,31041,31042],{},[1277,31043,31044,31046],{},[1161,31045,4318],{},[1282,31047,1982],{},[1194,31049,5745],{"encoding":1196},". Rozhodovací pravidlo: ",[1115,31052,31054],{"className":31053},[1149],[1151,31055,31056],{"xmlns":1153},[1155,31057,31058,31068],{},[1158,31059,31060,31062,31064,31066],{},[1161,31061,1110],{},[1165,31063,1188],{},[1161,31065,7514],{},[1165,31067,2028],{},[1194,31069,31070],{"encoding":1196},"p \\le \\alpha \\Rightarrow"," zamítáme ",[1115,31073,31075],{"className":31074},[1149],[1151,31076,31077],{"xmlns":1153},[1155,31078,31079,31087],{},[1158,31080,31081],{},[1277,31082,31083,31085],{},[1161,31084,4318],{},[1282,31086,1982],{},[1194,31088,5745],{"encoding":1196},[1115,31090,31092],{"className":31091},[1149],[1151,31093,31094],{"xmlns":1153},[1155,31095,31096,31106],{},[1158,31097,31098,31100,31102,31104],{},[1161,31099,1110],{},[1165,31101,4156],{},[1161,31103,7514],{},[1165,31105,2028],{},[1194,31107,31108],{"encoding":1196},"p > \\alpha \\Rightarrow",[1115,31110,31112],{"className":31111},[1149],[1151,31113,31114],{"xmlns":1153},[1155,31115,31116,31124],{},[1158,31117,31118],{},[1277,31119,31120,31122],{},[1161,31121,4318],{},[1282,31123,1982],{},[1194,31125,5745],{"encoding":1196}," nezamítáme. Obě cesty — kritický obor i p-hodnota — vedou vždy ke stejnému závěru; R u všech testů vrací p-hodnotu přímo.",[1431,31128,31130],{"id":31129},"jednovýběrový-t-test","Jednovýběrový t-test",[1110,31132,31133,31134,31147,31148,31180,31181,31194,31195,1425,31212,31229,31230,31248,31249,31262],{},"Test o střední hodnotě ",[1115,31135,31137],{"className":31136},[1149],[1151,31138,31139],{"xmlns":1153},[1155,31140,31141,31145],{},[1158,31142,31143],{},[1161,31144,1355],{},[1194,31146,3289],{"encoding":1196}," rozdělení ",[1115,31149,31151],{"className":31150},[1149],[1151,31152,31153],{"xmlns":1153},[1155,31154,31155,31177],{},[1158,31156,31157,31159,31161,31163,31165,31167,31169,31175],{},[1161,31158,1185],{},[1165,31160,3695],{},[1161,31162,1350],{},[1165,31164,1168],{"stretchy":1167},[1161,31166,1355],{},[1165,31168,1715],{"separator":1121},[1209,31170,31171,31173],{},[1161,31172,1363],{},[1282,31174,1298],{},[1165,31176,1174],{"stretchy":1167},[1194,31178,31179],{"encoding":1196},"X \\sim N(\\mu, \\sigma^2)",". Z výběru o rozsahu ",[1115,31182,31184],{"className":31183},[1149],[1151,31185,31186],{"xmlns":1153},[1155,31187,31188,31192],{},[1158,31189,31190],{},[1161,31191,4192],{},[1194,31193,4192],{"encoding":1196}," se určí charakteristiky ",[1115,31196,31198],{"className":31197},[1149],[1151,31199,31200],{"xmlns":1153},[1155,31201,31202,31210],{},[1158,31203,31204],{},[6877,31205,31206,31208],{"accent":1121},[1161,31207,1171],{},[1165,31209,15130],{},[1194,31211,25238],{"encoding":1196},[1115,31213,31215],{"className":31214},[1149],[1151,31216,31217],{"xmlns":1153},[1155,31218,31219,31227],{},[1158,31220,31221],{},[1209,31222,31223,31225],{},[1161,31224,6018],{},[1282,31226,1298],{},[1194,31228,19448],{"encoding":1196},"; testem se posuzuje vztah mezi zvoleným číslem ",[1115,31231,31233],{"className":31232},[1149],[1151,31234,31235],{"xmlns":1153},[1155,31236,31237,31245],{},[1158,31238,31239],{},[1277,31240,31241,31243],{},[1161,31242,1355],{},[1282,31244,1982],{},[1194,31246,31247],{"encoding":1196},"\\mu_0"," a neznámou hodnotou ",[1115,31250,31252],{"className":31251},[1149],[1151,31253,31254],{"xmlns":1153},[1155,31255,31256,31260],{},[1158,31257,31258],{},[1161,31259,1355],{},[1194,31261,3289],{"encoding":1196},". Testové kritérium",[1115,31264,31266],{"className":31265},[1149],[1151,31267,31268],{"xmlns":1153,"display":2212},[1155,31269,31270,31314],{},[1158,31271,31272,31274,31276,31296,31300,31302],{},[1161,31273,1575],{},[1165,31275,1177],{},[3064,31277,31278,31294],{},[1158,31279,31280,31286,31288],{},[6877,31281,31282,31284],{"accent":1121},[1161,31283,1171],{},[1165,31285,15130],{},[1165,31287,1317],{},[1277,31289,31290,31292],{},[1161,31291,1355],{},[1282,31293,1982],{},[1161,31295,6018],{},[2765,31297,31298],{},[1161,31299,4192],{},[1165,31301,3695],{},[1277,31303,31304,31306],{},[1161,31305,1617],{},[1158,31307,31308,31310,31312],{},[1161,31309,4192],{},[1165,31311,1317],{},[1282,31313,1284],{},[1194,31315,31316],{"encoding":1196},"T = \\frac{\\bar{x} - \\mu_0}{s}\\sqrt{n} \\sim t_{n-1}",[1110,31318,31319,31320,31338],{},"má Studentovo rozdělení o ",[1115,31321,31323],{"className":31322},[1149],[1151,31324,31325],{"xmlns":1153},[1155,31326,31327,31335],{},[1158,31328,31329,31331,31333],{},[1161,31330,4192],{},[1165,31332,1317],{},[1282,31334,1284],{},[1194,31336,31337],{"encoding":1196},"n-1"," stupních volnosti.",[4052,31340,31341,31399],{},[4055,31342,31343],{},[4058,31344,31345,31364,31383],{},[4061,31346,31347],{},[1115,31348,31350],{"className":31349},[1149],[1151,31351,31352],{"xmlns":1153},[1155,31353,31354,31362],{},[1158,31355,31356],{},[1277,31357,31358,31360],{},[1161,31359,4318],{},[1282,31361,1982],{},[1194,31363,5745],{"encoding":1196},[4061,31365,31366],{},[1115,31367,31369],{"className":31368},[1149],[1151,31370,31371],{"xmlns":1153},[1155,31372,31373,31381],{},[1158,31374,31375],{},[1277,31376,31377,31379],{},[1161,31378,4318],{},[1282,31380,1284],{},[1194,31382,7147],{"encoding":1196},[4061,31384,31385,31386],{},"Kritický obor ",[1115,31387,31389],{"className":31388},[1149],[1151,31390,31391],{"xmlns":1153},[1155,31392,31393,31397],{},[1158,31394,31395],{},[1161,31396,5777],{},[1194,31398,5777],{"encoding":1196},[4165,31400,31401,31491,31589],{},[4058,31402,31403,31427,31451],{},[4170,31404,31405],{},[1115,31406,31408],{"className":31407},[1149],[1151,31409,31410],{"xmlns":1153},[1155,31411,31412,31424],{},[1158,31413,31414,31416,31418],{},[1161,31415,1355],{},[1165,31417,1188],{},[1277,31419,31420,31422],{},[1161,31421,1355],{},[1282,31423,1982],{},[1194,31425,31426],{"encoding":1196},"\\mu \\le \\mu_0",[4170,31428,31429],{},[1115,31430,31432],{"className":31431},[1149],[1151,31433,31434],{"xmlns":1153},[1155,31435,31436,31448],{},[1158,31437,31438,31440,31442],{},[1161,31439,1355],{},[1165,31441,4156],{},[1277,31443,31444,31446],{},[1161,31445,1355],{},[1282,31447,1982],{},[1194,31449,31450],{"encoding":1196},"\\mu > \\mu_0",[4170,31452,31453],{},[1115,31454,31456],{"className":31455},[1149],[1151,31457,31458],{"xmlns":1153},[1155,31459,31460,31488],{},[1158,31461,31462,31464,31466,31478,31480,31482,31484,31486],{},[1161,31463,1617],{},[1165,31465,7501],{},[1277,31467,31468,31470],{},[1161,31469,1617],{},[1158,31471,31472,31474,31476],{},[1282,31473,1284],{},[1165,31475,1317],{},[1161,31477,7514],{},[1165,31479,1168],{"stretchy":1167},[1161,31481,4192],{},[1165,31483,1317],{},[1282,31485,1284],{},[1165,31487,1174],{"stretchy":1167},[1194,31489,31490],{"encoding":1196},"t \\ge t_{1-\\alpha}(n-1)",[4058,31492,31493,31517,31541],{},[4170,31494,31495],{},[1115,31496,31498],{"className":31497},[1149],[1151,31499,31500],{"xmlns":1153},[1155,31501,31502,31514],{},[1158,31503,31504,31506,31508],{},[1161,31505,1355],{},[1165,31507,1177],{},[1277,31509,31510,31512],{},[1161,31511,1355],{},[1282,31513,1982],{},[1194,31515,31516],{"encoding":1196},"\\mu = \\mu_0",[4170,31518,31519],{},[1115,31520,31522],{"className":31521},[1149],[1151,31523,31524],{"xmlns":1153},[1155,31525,31526,31538],{},[1158,31527,31528,31530,31532],{},[1161,31529,1355],{},[1165,31531,5496],{"mathvariant":1215},[1277,31533,31534,31536],{},[1161,31535,1355],{},[1282,31537,1982],{},[1194,31539,31540],{"encoding":1196},"\\mu \\neq \\mu_0",[4170,31542,31543],{},[1115,31544,31546],{"className":31545},[1149],[1151,31547,31548],{"xmlns":1153},[1155,31549,31550,31586],{},[1158,31551,31552,31554,31556,31558,31560,31576,31578,31580,31582,31584],{},[1165,31553,26697],{"stretchy":1167},[1161,31555,1617],{},[1165,31557,26697],{"stretchy":1167},[1165,31559,7501],{},[1277,31561,31562,31564],{},[1161,31563,1617],{},[1158,31565,31566,31568,31570,31572,31574],{},[1282,31567,1284],{},[1165,31569,1317],{},[1161,31571,7514],{},[1161,31573,3434],{"mathvariant":1215},[1282,31575,1298],{},[1165,31577,1168],{"stretchy":1167},[1161,31579,4192],{},[1165,31581,1317],{},[1282,31583,1284],{},[1165,31585,1174],{"stretchy":1167},[1194,31587,31588],{"encoding":1196},"\\lvert t \\rvert \\ge t_{1-\\alpha\u002F2}(n-1)",[4058,31590,31591,31615,31639],{},[4170,31592,31593],{},[1115,31594,31596],{"className":31595},[1149],[1151,31597,31598],{"xmlns":1153},[1155,31599,31600,31612],{},[1158,31601,31602,31604,31606],{},[1161,31603,1355],{},[1165,31605,7501],{},[1277,31607,31608,31610],{},[1161,31609,1355],{},[1282,31611,1982],{},[1194,31613,31614],{"encoding":1196},"\\mu \\ge \\mu_0",[4170,31616,31617],{},[1115,31618,31620],{"className":31619},[1149],[1151,31621,31622],{"xmlns":1153},[1155,31623,31624,31636],{},[1158,31625,31626,31628,31630],{},[1161,31627,1355],{},[1165,31629,1287],{},[1277,31631,31632,31634],{},[1161,31633,1355],{},[1282,31635,1982],{},[1194,31637,31638],{"encoding":1196},"\\mu \u003C \\mu_0",[4170,31640,31641],{},[1115,31642,31644],{"className":31643},[1149],[1151,31645,31646],{"xmlns":1153},[1155,31647,31648,31678],{},[1158,31649,31650,31652,31654,31656,31668,31670,31672,31674,31676],{},[1161,31651,1617],{},[1165,31653,1188],{},[1165,31655,1317],{},[1277,31657,31658,31660],{},[1161,31659,1617],{},[1158,31661,31662,31664,31666],{},[1282,31663,1284],{},[1165,31665,1317],{},[1161,31667,7514],{},[1165,31669,1168],{"stretchy":1167},[1161,31671,4192],{},[1165,31673,1317],{},[1282,31675,1284],{},[1165,31677,1174],{"stretchy":1167},[1194,31679,31680],{"encoding":1196},"t \\le -t_{1-\\alpha}(n-1)",[1110,31682,31683,31684,31687],{},"V R test provádí ",[1373,31685,31686],{},"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?",[3554,31689,31691],{"className":3556,"code":31690,"language":71,"meta":3558,"style":3558},"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",[1373,31692,31693,31747],{"__ignoreMap":3558},[1115,31694,31695,31697,31699,31701,31703,31706,31708,31711,31713,31716,31718,31721,31723,31726,31728,31731,31733,31735,31737,31740,31742,31745],{"class":3563,"line":10},[1115,31696,1171],{"class":3744},[1115,31698,4497],{"class":3741},[1115,31700,7969],{"class":3566},[1115,31702,1168],{"class":3569},[1115,31704,31705],{"class":3572},"12.5",[1115,31707,1715],{"class":3741},[1115,31709,31710],{"class":3572}," 13.5",[1115,31712,1715],{"class":3741},[1115,31714,31715],{"class":3572}," 11.9",[1115,31717,1715],{"class":3741},[1115,31719,31720],{"class":3572}," 12.2",[1115,31722,1715],{"class":3741},[1115,31724,31725],{"class":3572}," 13.0",[1115,31727,1715],{"class":3741},[1115,31729,31730],{"class":3572}," 14.3",[1115,31732,1715],{"class":3741},[1115,31734,31720],{"class":3572},[1115,31736,1715],{"class":3741},[1115,31738,31739],{"class":3572}," 11.8",[1115,31741,1715],{"class":3741},[1115,31743,31744],{"class":3572}," 14.0",[1115,31746,3575],{"class":3569},[1115,31748,31749,31752,31754,31756,31758,31760,31762,31764,31766,31769,31771,31774],{"class":3563,"line":27},[1115,31750,31751],{"class":3566},"t.test",[1115,31753,1168],{"class":3569},[1115,31755,1171],{"class":3744},[1115,31757,1715],{"class":3741},[1115,31759,29254],{"class":3744},[1115,31761,3748],{"class":3741},[1115,31763,7870],{"class":3572},[1115,31765,1715],{"class":3741},[1115,31767,31768],{"class":3744}," alternative",[1115,31770,3748],{"class":3741},[1115,31772,31773],{"class":7974}," \"two.sided\"",[1115,31775,3575],{"class":3569},[3554,31777,31780],{"className":31778,"code":31779,"language":3603,"meta":3558},[3601],"    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",[1373,31781,31779],{"__ignoreMap":3558},[1110,31783,31784,31786,31787,31790,31791,31794,31795,31798,31799,31822],{},[1373,31785,1617],{}," je testové kritérium, ",[1373,31788,31789],{},"df"," stupně volnosti, ",[1373,31792,31793],{},"p-value"," p-hodnota pro zvolenou alternativu a ",[1373,31796,31797],{},"mean of x"," výběrový průměr. Zde ",[1115,31800,31802],{"className":31801},[1149],[1151,31803,31804],{"xmlns":1153},[1155,31805,31806,31819],{},[1158,31807,31808,31810,31812,31815,31817],{},[1161,31809,1110],{},[1165,31811,1177],{},[1282,31813,31814],{},"0,02843",[1165,31816,1287],{},[1282,31818,8114],{},[1194,31820,31821],{"encoding":1196},"p = 0{,}02843 \u003C 0{,}05",": úprava trasy průměrnou dobu jízdy (původně 12 minut) statisticky významně změnila.",[1103,31824,31826,31833,31921,31977,32069],{"className":31825,"dataCallout":3670},[1106,3669],[1110,31827,31829,31832],{"className":31828},[1113],[1115,31830],{"className":31831,"ariaHidden":1121},[1118,3677,1120],"Příklad: Kontrola objemu lahví",[1110,31834,31835,31836,31858,31859,31877,31878,31901,31902,31920],{},"Pivovar plní lahve, deklarovaný objem je ",[1115,31837,31839],{"className":31838},[1149],[1151,31840,31841],{"xmlns":1153},[1155,31842,31843,31855],{},[1158,31844,31845,31851,31853],{},[1277,31846,31847,31849],{},[1161,31848,1355],{},[1282,31850,1982],{},[1165,31852,1177],{},[1282,31854,2949],{},[1194,31856,31857],{"encoding":1196},"\\mu_0 = 0{,}5"," l. Náhodný výběr ",[1115,31860,31862],{"className":31861},[1149],[1151,31863,31864],{"xmlns":1153},[1155,31865,31866,31874],{},[1158,31867,31868,31870,31872],{},[1161,31869,4192],{},[1165,31871,1177],{},[1282,31873,8175],{},[1194,31875,31876],{"encoding":1196},"n = 20"," lahví dal ",[1115,31879,31881],{"className":31880},[1149],[1151,31882,31883],{"xmlns":1153},[1155,31884,31885,31898],{},[1158,31886,31887,31893,31895],{},[6877,31888,31889,31891],{"accent":1121},[1161,31890,1171],{},[1165,31892,15130],{},[1165,31894,1177],{},[1282,31896,31897],{},"0,492",[1194,31899,31900],{"encoding":1196},"\\bar{x} = 0{,}492"," l, ",[1115,31903,31905],{"className":31904},[1149],[1151,31906,31907],{"xmlns":1153},[1155,31908,31909,31917],{},[1158,31910,31911,31913,31915],{},[1161,31912,6018],{},[1165,31914,1177],{},[1282,31916,18466],{},[1194,31918,31919],{"encoding":1196},"s = 0{,}015"," l. Na hladině významnosti 5 % ověřte podezření, že pivovar lahve nedoplňuje.",[1110,31922,31923,31949,31950,31976],{},[1115,31924,31926],{"className":31925},[1149],[1151,31927,31928],{"xmlns":1153},[1155,31929,31930,31946],{},[1158,31931,31932,31938,31940,31942,31944],{},[1277,31933,31934,31936],{},[1161,31935,4318],{},[1282,31937,1982],{},[1165,31939,2629],{},[1161,31941,1355],{},[1165,31943,7501],{},[1282,31945,2949],{},[1194,31947,31948],{"encoding":1196},"H_0: \\mu \\ge 0{,}5"," l (objem je v pořádku nebo větší), ",[1115,31951,31953],{"className":31952},[1149],[1151,31954,31955],{"xmlns":1153},[1155,31956,31957,31973],{},[1158,31958,31959,31965,31967,31969,31971],{},[1277,31960,31961,31963],{},[1161,31962,4318],{},[1282,31964,1284],{},[1165,31966,2629],{},[1161,31968,1355],{},[1165,31970,1287],{},[1282,31972,2949],{},[1194,31974,31975],{"encoding":1196},"H_1: \\mu \u003C 0{,}5"," l (lahve jsou nedoplněné).",[1110,31978,31979],{},[1115,31980,31982],{"className":31981},[1149],[1151,31983,31984],{"xmlns":1153},[1155,31985,31986,32066],{},[1158,31987,31988,31990,31992,32004,32008,32010,32012,32015,32017,32019,32021,32023,32025,32027,32029,32031,32043,32045,32047,32049,32051,32053,32055,32057,32059,32061,32064],{},[1161,31989,1617],{},[1165,31991,1177],{},[3064,31993,31994,32002],{},[1158,31995,31996,31998,32000],{},[1282,31997,31897],{},[1165,31999,1317],{},[1282,32001,2949],{},[1282,32003,18466],{},[2765,32005,32006],{},[1282,32007,8175],{},[1165,32009,1177],{},[1165,32011,1317],{},[1282,32013,32014],{},"2,385",[1165,32016,1715],{"separator":1121},[2242,32018],{"width":2244},[1161,32020,5777],{},[1165,32022,1177],{},[1165,32024,7484],{"stretchy":1167},[1161,32026,1617],{},[1165,32028,1188],{},[1165,32030,1317],{},[1277,32032,32033,32035],{},[1161,32034,1617],{},[1158,32036,32037,32039,32041],{},[1282,32038,1982],{},[1165,32040,1715],{"separator":1121},[1282,32042,25471],{},[1165,32044,1168],{"stretchy":1167},[1282,32046,18390],{},[1165,32048,1174],{"stretchy":1167},[1165,32050,7543],{"stretchy":1167},[1165,32052,1177],{},[1165,32054,7484],{"stretchy":1167},[1161,32056,1617],{},[1165,32058,1188],{},[1165,32060,1317],{},[1282,32062,32063],{},"1,729",[1165,32065,7543],{"stretchy":1167},[1194,32067,32068],{"encoding":1196},"t = \\frac{0{,}492 - 0{,}5}{0{,}015}\\sqrt{20} = -2{,}385, \\qquad W = \\{t \\le -t_{0,95}(19)\\} = \\{t \\le -1{,}729\\}",[1110,32070,32071,32072,10124,32090,32107],{},"Protože ",[1115,32073,32075],{"className":32074},[1149],[1151,32076,32077],{"xmlns":1153},[1155,32078,32079,32087],{},[1158,32080,32081,32083,32085],{},[1161,32082,1617],{},[1165,32084,1492],{},[1161,32086,5777],{},[1194,32088,32089],{"encoding":1196},"t \\in W",[1115,32091,32093],{"className":32092},[1149],[1151,32094,32095],{"xmlns":1153},[1155,32096,32097,32105],{},[1158,32098,32099],{},[1277,32100,32101,32103],{},[1161,32102,4318],{},[1282,32104,1982],{},[1194,32106,5745],{"encoding":1196},": na hladině významnosti 5 % se potvrdilo, že pivovar plní lahve pod deklarovaný objem.",[1110,32109,32110,32111,32113,32114,2629],{},"Ze souhrnných charakteristik bez surových dat ",[1373,32112,31686],{}," spustit nelze — kritérium a kritická hodnota se dopočítají přímo z definice pomocí ",[1373,32115,32116],{},"qt()",[3554,32118,32120],{"className":3556,"code":32119,"language":71,"meta":3558,"style":3558},"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",[1373,32121,32122,32160,32192,32222,32227],{"__ignoreMap":3558},[1115,32123,32124,32127,32129,32132,32134,32136,32138,32141,32143,32145,32147,32150,32152,32155,32157],{"class":3563,"line":10},[1115,32125,32126],{"class":3744},"xbar",[1115,32128,4497],{"class":3741},[1115,32130,32131],{"class":3572}," 0.492",[1115,32133,28857],{"class":3569},[1115,32135,6018],{"class":3744},[1115,32137,4497],{"class":3741},[1115,32139,32140],{"class":3572}," 0.015",[1115,32142,28857],{"class":3569},[1115,32144,4192],{"class":3744},[1115,32146,4497],{"class":3741},[1115,32148,32149],{"class":3572}," 20",[1115,32151,28857],{"class":3569},[1115,32153,32154],{"class":3744},"mu0",[1115,32156,4497],{"class":3741},[1115,32158,32159],{"class":3572}," 0.5\n",[1115,32161,32162,32164,32166,32168,32170,32172,32175,32177,32179,32182,32184,32186,32188,32190],{"class":3563,"line":27},[1115,32163,1617],{"class":3744},[1115,32165,4497],{"class":3741},[1115,32167,8728],{"class":3569},[1115,32169,32126],{"class":3744},[1115,32171,29194],{"class":3741},[1115,32173,32174],{"class":3744}," mu0",[1115,32176,3862],{"class":3569},[1115,32178,3434],{"class":3741},[1115,32180,32181],{"class":3744}," s",[1115,32183,22312],{"class":3741},[1115,32185,4003],{"class":3566},[1115,32187,1168],{"class":3569},[1115,32189,4192],{"class":3744},[1115,32191,3575],{"class":3569},[1115,32193,32194,32197,32199,32202,32204,32207,32209,32211,32213,32216,32218,32220],{"class":3563,"line":148},[1115,32195,32196],{"class":3744},"t_krit",[1115,32198,4497],{"class":3741},[1115,32200,32201],{"class":3566}," qt",[1115,32203,1168],{"class":3569},[1115,32205,32206],{"class":3572},"0.05",[1115,32208,1715],{"class":3741},[1115,32210,5347],{"class":3744},[1115,32212,3748],{"class":3741},[1115,32214,32215],{"class":3744}," n",[1115,32217,29194],{"class":3741},[1115,32219,4605],{"class":3572},[1115,32221,3575],{"class":3569},[1115,32223,32224],{"class":3563,"line":111},[1115,32225,32226],{"class":3744},"t\n",[1115,32228,32229],{"class":3563,"line":96},[1115,32230,32231],{"class":3744},"t_krit\n",[3554,32233,32236],{"className":32234,"code":32235,"language":3603,"meta":3558},[3601],"[1] -2.385139\n[1] -1.729133\n",[1373,32237,32235],{"__ignoreMap":3558},[1110,32239,32240],{},[1760,32241],{"alt":32242,"className":32243,"src":32244},"mask-th-t-jednostranny",[1441,1764],"\u002Fwiki-assets\u002Fmask-th-t-jednostranny.png",[1110,32246,32247,32248,2629],{},"Další dva příklady mají k dispozici surová data, takže je lze otestovat přímo ",[1373,32249,31686],{},[1110,32251,32252,32255],{},[1131,32253,32254],{},"Životnost baterií."," Výrobce udává průměrnou životnost 10 hodin, na 11 bateriích byly naměřeny hodnoty v hodinách.",[3554,32257,32259],{"className":3556,"code":32258,"language":71,"meta":3558,"style":3558},"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",[1373,32260,32261,32324],{"__ignoreMap":3558},[1115,32262,32263,32266,32268,32270,32272,32275,32277,32280,32282,32285,32287,32290,32292,32295,32297,32300,32302,32304,32306,32309,32311,32313,32315,32318,32320,32322],{"class":3563,"line":10},[1115,32264,32265],{"class":3744},"x2",[1115,32267,4497],{"class":3741},[1115,32269,7969],{"class":3566},[1115,32271,1168],{"class":3569},[1115,32273,32274],{"class":3572},"9.5",[1115,32276,1715],{"class":3741},[1115,32278,32279],{"class":3572}," 10.5",[1115,32281,1715],{"class":3741},[1115,32283,32284],{"class":3572}," 8.9",[1115,32286,1715],{"class":3741},[1115,32288,32289],{"class":3572}," 9.2",[1115,32291,1715],{"class":3741},[1115,32293,32294],{"class":3572}," 10.0",[1115,32296,1715],{"class":3741},[1115,32298,32299],{"class":3572}," 8.5",[1115,32301,1715],{"class":3741},[1115,32303,32289],{"class":3572},[1115,32305,1715],{"class":3741},[1115,32307,32308],{"class":3572}," 8.8",[1115,32310,1715],{"class":3741},[1115,32312,32294],{"class":3572},[1115,32314,1715],{"class":3741},[1115,32316,32317],{"class":3572}," 9.5",[1115,32319,1715],{"class":3741},[1115,32321,32289],{"class":3572},[1115,32323,3575],{"class":3569},[1115,32325,32326,32328,32330,32332,32334,32336,32338,32340,32342,32344,32346,32348],{"class":3563,"line":27},[1115,32327,31751],{"class":3566},[1115,32329,1168],{"class":3569},[1115,32331,32265],{"class":3744},[1115,32333,1715],{"class":3741},[1115,32335,29254],{"class":3744},[1115,32337,3748],{"class":3741},[1115,32339,3994],{"class":3572},[1115,32341,1715],{"class":3741},[1115,32343,31768],{"class":3744},[1115,32345,3748],{"class":3741},[1115,32347,31773],{"class":7974},[1115,32349,3575],{"class":3569},[3554,32351,32354],{"className":32352,"code":32353,"language":3603,"meta":3558},[3601],"    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",[1373,32355,32353],{"__ignoreMap":3558},[1110,32357,32358,32381],{},[1115,32359,32361],{"className":32360},[1149],[1151,32362,32363],{"xmlns":1153},[1155,32364,32365,32378],{},[1158,32366,32367,32369,32371,32374,32376],{},[1161,32368,1110],{},[1165,32370,1177],{},[1282,32372,32373],{},"0,006548",[1165,32375,1287],{},[1282,32377,8114],{},[1194,32379,32380],{"encoding":1196},"p = 0{,}006548 \u003C 0{,}05",": skutečná životnost se od deklarovaných 10 hodin statisticky významně liší (baterie vydrží méně).",[1110,32383,32384,32387],{},[1131,32385,32386],{},"Odpad materiálu."," Na deseti obráběných kusech byl naměřen odpad materiálu v procentech; testuje se rozdíl proti 4 % a zároveň normalita dat.",[3554,32389,32391],{"className":3556,"code":32390,"language":71,"meta":3558,"style":3558},"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",[1373,32392,32393,32444,32470],{"__ignoreMap":3558},[1115,32394,32395,32398,32400,32402,32404,32406,32408,32410,32412,32414,32416,32418,32420,32422,32424,32426,32428,32430,32432,32434,32436,32438,32440,32442],{"class":3563,"line":10},[1115,32396,32397],{"class":3744},"x3",[1115,32399,4497],{"class":3741},[1115,32401,7969],{"class":3566},[1115,32403,1168],{"class":3569},[1115,32405,15657],{"class":3572},[1115,32407,1715],{"class":3741},[1115,32409,15662],{"class":3572},[1115,32411,1715],{"class":3741},[1115,32413,15667],{"class":3572},[1115,32415,1715],{"class":3741},[1115,32417,15672],{"class":3572},[1115,32419,1715],{"class":3741},[1115,32421,15667],{"class":3572},[1115,32423,1715],{"class":3741},[1115,32425,15667],{"class":3572},[1115,32427,1715],{"class":3741},[1115,32429,15685],{"class":3572},[1115,32431,1715],{"class":3741},[1115,32433,15690],{"class":3572},[1115,32435,1715],{"class":3741},[1115,32437,15662],{"class":3572},[1115,32439,1715],{"class":3741},[1115,32441,15662],{"class":3572},[1115,32443,3575],{"class":3569},[1115,32445,32446,32448,32450,32452,32454,32456,32458,32460,32462,32464,32466,32468],{"class":3563,"line":27},[1115,32447,31751],{"class":3566},[1115,32449,1168],{"class":3569},[1115,32451,32397],{"class":3744},[1115,32453,1715],{"class":3741},[1115,32455,29254],{"class":3744},[1115,32457,3748],{"class":3741},[1115,32459,4536],{"class":3572},[1115,32461,1715],{"class":3741},[1115,32463,31768],{"class":3744},[1115,32465,3748],{"class":3741},[1115,32467,31773],{"class":7974},[1115,32469,3575],{"class":3569},[1115,32471,32472,32474,32476,32478],{"class":3563,"line":148},[1115,32473,21248],{"class":3566},[1115,32475,1168],{"class":3569},[1115,32477,32397],{"class":3744},[1115,32479,3575],{"class":3569},[3554,32481,32484],{"className":32482,"code":32483,"language":3603,"meta":3558},[3601],"    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",[1373,32485,32483],{"__ignoreMap":3558},[1110,32487,32488,32511,32512,32535],{},[1115,32489,32491],{"className":32490},[1149],[1151,32492,32493],{"xmlns":1153},[1155,32494,32495,32508],{},[1158,32496,32497,32499,32501,32504,32506],{},[1161,32498,1110],{},[1165,32500,1177],{},[1282,32502,32503],{},"0,0343",[1165,32505,1287],{},[1282,32507,8114],{},[1194,32509,32510],{"encoding":1196},"p = 0{,}0343 \u003C 0{,}05",": průměrný odpad se od 4 % statisticky významně liší (výběrový průměr 3,86 %). Shapiro-Wilkův test dává ",[1115,32513,32515],{"className":32514},[1149],[1151,32516,32517],{"xmlns":1153},[1155,32518,32519,32532],{},[1158,32520,32521,32523,32525,32528,32530],{},[1161,32522,1110],{},[1165,32524,1177],{},[1282,32526,32527],{},"0,4634",[1165,32529,4156],{},[1282,32531,8114],{},[1194,32533,32534],{"encoding":1196},"p = 0{,}4634 > 0{,}05",", předpoklad normality pro t-test je v pořádku.",[1431,32537,32539],{"id":32538},"párový-t-test","Párový t-test",[1110,32541,32542,32543,32573,32574,1238,32608,32646,32647,32660,32661,1425,32679,32699,32700,32717,32718,31262],{},"Používá se, když jsou měření závislá — na stejných objektech se měří dvě hodnoty ",[1115,32544,32546],{"className":32545},[1149],[1151,32547,32548],{"xmlns":1153},[1155,32549,32550,32570],{},[1158,32551,32552,32554,32560,32562,32568],{},[1165,32553,1168],{"stretchy":1167},[1277,32555,32556,32558],{},[1161,32557,1185],{},[1161,32559,4187],{},[1165,32561,1715],{"separator":1121},[1277,32563,32564,32566],{},[1161,32565,1561],{},[1161,32567,4187],{},[1165,32569,1174],{"stretchy":1167},[1194,32571,32572],{"encoding":1196},"(X_i, Y_i)"," a vyhodnocují se jejich diference ",[1115,32575,32577],{"className":32576},[1149],[1151,32578,32579],{"xmlns":1153},[1155,32580,32581,32605],{},[1158,32582,32583,32589,32591,32597,32599],{},[1277,32584,32585,32587],{},[1161,32586,2641],{},[1161,32588,4187],{},[1165,32590,1177],{},[1277,32592,32593,32595],{},[1161,32594,1185],{},[1161,32596,4187],{},[1165,32598,1317],{},[1277,32600,32601,32603],{},[1161,32602,1561],{},[1161,32604,4187],{},[1194,32606,32607],{"encoding":1196},"D_i = X_i - Y_i",[1115,32609,32611],{"className":32610},[1149],[1151,32612,32613],{"xmlns":1153},[1155,32614,32615,32643],{},[1158,32616,32617,32619,32621,32623,32625,32631,32633,32641],{},[1161,32618,2641],{},[1165,32620,3695],{},[1161,32622,1350],{},[1165,32624,1168],{"stretchy":1167},[1277,32626,32627,32629],{},[1161,32628,1355],{},[1161,32630,2641],{},[1165,32632,1715],{"separator":1121},[2256,32634,32635,32637,32639],{},[1161,32636,1363],{},[1161,32638,2641],{},[1282,32640,1298],{},[1165,32642,1174],{"stretchy":1167},[1194,32644,32645],{"encoding":1196},"D \\sim N(\\mu_D, \\sigma_D^2)",". Z ",[1115,32648,32650],{"className":32649},[1149],[1151,32651,32652],{"xmlns":1153},[1155,32653,32654,32658],{},[1158,32655,32656],{},[1161,32657,4192],{},[1194,32659,4192],{"encoding":1196}," dvojic se určí ",[1115,32662,32664],{"className":32663},[1149],[1151,32665,32666],{"xmlns":1153},[1155,32667,32668,32676],{},[1158,32669,32670],{},[6877,32671,32672,32674],{"accent":1121},[1161,32673,2283],{},[1165,32675,15130],{},[1194,32677,32678],{"encoding":1196},"\\bar{d}",[1115,32680,32682],{"className":32681},[1149],[1151,32683,32684],{"xmlns":1153},[1155,32685,32686,32696],{},[1158,32687,32688],{},[2256,32689,32690,32692,32694],{},[1161,32691,6018],{},[1161,32693,2283],{},[1282,32695,1298],{},[1194,32697,32698],{"encoding":1196},"s_d^2","; testuje se vztah mezi zvoleným číslem ",[1115,32701,32703],{"className":32702},[1149],[1151,32704,32705],{"xmlns":1153},[1155,32706,32707,32715],{},[1158,32708,32709],{},[1277,32710,32711,32713],{},[1161,32712,1355],{},[1282,32714,1982],{},[1194,32716,31247],{"encoding":1196}," (obvykle 0) a ",[1115,32719,32721],{"className":32720},[1149],[1151,32722,32723],{"xmlns":1153},[1155,32724,32725,32733],{},[1158,32726,32727],{},[1277,32728,32729,32731],{},[1161,32730,1355],{},[1161,32732,2641],{},[1194,32734,32735],{"encoding":1196},"\\mu_D",[1115,32737,32739],{"className":32738},[1149],[1151,32740,32741],{"xmlns":1153,"display":2212},[1155,32742,32743,32793],{},[1158,32744,32745,32747,32749,32773,32777,32779,32791],{},[1161,32746,1575],{},[1165,32748,1177],{},[3064,32750,32751,32767],{},[1158,32752,32753,32759,32761],{},[6877,32754,32755,32757],{"accent":1121},[1161,32756,2283],{},[1165,32758,15130],{},[1165,32760,1317],{},[1277,32762,32763,32765],{},[1161,32764,1355],{},[1282,32766,1982],{},[1277,32768,32769,32771],{},[1161,32770,6018],{},[1161,32772,2283],{},[2765,32774,32775],{},[1161,32776,4192],{},[1165,32778,3695],{},[1277,32780,32781,32783],{},[1161,32782,1617],{},[1158,32784,32785,32787,32789],{},[1161,32786,4192],{},[1165,32788,1317],{},[1282,32790,1284],{},[1161,32792,1333],{"mathvariant":1215},[1194,32794,32795],{"encoding":1196},"T = \\frac{\\bar{d} - \\mu_0}{s_d}\\sqrt{n} \\sim t_{n-1}.",[4052,32797,32798,32855],{},[4055,32799,32800],{},[4058,32801,32802,32821,32840],{},[4061,32803,32804],{},[1115,32805,32807],{"className":32806},[1149],[1151,32808,32809],{"xmlns":1153},[1155,32810,32811,32819],{},[1158,32812,32813],{},[1277,32814,32815,32817],{},[1161,32816,4318],{},[1282,32818,1982],{},[1194,32820,5745],{"encoding":1196},[4061,32822,32823],{},[1115,32824,32826],{"className":32825},[1149],[1151,32827,32828],{"xmlns":1153},[1155,32829,32830,32838],{},[1158,32831,32832],{},[1277,32833,32834,32836],{},[1161,32835,4318],{},[1282,32837,1284],{},[1194,32839,7147],{"encoding":1196},[4061,32841,31385,32842],{},[1115,32843,32845],{"className":32844},[1149],[1151,32846,32847],{"xmlns":1153},[1155,32848,32849,32853],{},[1158,32850,32851],{},[1161,32852,5777],{},[1194,32854,5777],{"encoding":1196},[4165,32856,32857,32954,33059],{},[4058,32858,32859,32887,32915],{},[4170,32860,32861],{},[1115,32862,32864],{"className":32863},[1149],[1151,32865,32866],{"xmlns":1153},[1155,32867,32868,32884],{},[1158,32869,32870,32876,32878],{},[1277,32871,32872,32874],{},[1161,32873,1355],{},[1161,32875,2641],{},[1165,32877,1188],{},[1277,32879,32880,32882],{},[1161,32881,1355],{},[1282,32883,1982],{},[1194,32885,32886],{"encoding":1196},"\\mu_D \\le \\mu_0",[4170,32888,32889],{},[1115,32890,32892],{"className":32891},[1149],[1151,32893,32894],{"xmlns":1153},[1155,32895,32896,32912],{},[1158,32897,32898,32904,32906],{},[1277,32899,32900,32902],{},[1161,32901,1355],{},[1161,32903,2641],{},[1165,32905,4156],{},[1277,32907,32908,32910],{},[1161,32909,1355],{},[1282,32911,1982],{},[1194,32913,32914],{"encoding":1196},"\\mu_D > \\mu_0",[4170,32916,32917],{},[1115,32918,32920],{"className":32919},[1149],[1151,32921,32922],{"xmlns":1153},[1155,32923,32924,32952],{},[1158,32925,32926,32928,32930,32942,32944,32946,32948,32950],{},[1161,32927,1617],{},[1165,32929,7501],{},[1277,32931,32932,32934],{},[1161,32933,1617],{},[1158,32935,32936,32938,32940],{},[1282,32937,1284],{},[1165,32939,1317],{},[1161,32941,7514],{},[1165,32943,1168],{"stretchy":1167},[1161,32945,4192],{},[1165,32947,1317],{},[1282,32949,1284],{},[1165,32951,1174],{"stretchy":1167},[1194,32953,31490],{"encoding":1196},[4058,32955,32956,32984,33012],{},[4170,32957,32958],{},[1115,32959,32961],{"className":32960},[1149],[1151,32962,32963],{"xmlns":1153},[1155,32964,32965,32981],{},[1158,32966,32967,32973,32975],{},[1277,32968,32969,32971],{},[1161,32970,1355],{},[1161,32972,2641],{},[1165,32974,1177],{},[1277,32976,32977,32979],{},[1161,32978,1355],{},[1282,32980,1982],{},[1194,32982,32983],{"encoding":1196},"\\mu_D = \\mu_0",[4170,32985,32986],{},[1115,32987,32989],{"className":32988},[1149],[1151,32990,32991],{"xmlns":1153},[1155,32992,32993,33009],{},[1158,32994,32995,33001,33003],{},[1277,32996,32997,32999],{},[1161,32998,1355],{},[1161,33000,2641],{},[1165,33002,5496],{"mathvariant":1215},[1277,33004,33005,33007],{},[1161,33006,1355],{},[1282,33008,1982],{},[1194,33010,33011],{"encoding":1196},"\\mu_D \\neq \\mu_0",[4170,33013,33014],{},[1115,33015,33017],{"className":33016},[1149],[1151,33018,33019],{"xmlns":1153},[1155,33020,33021,33057],{},[1158,33022,33023,33025,33027,33029,33031,33047,33049,33051,33053,33055],{},[1165,33024,26697],{"stretchy":1167},[1161,33026,1617],{},[1165,33028,26697],{"stretchy":1167},[1165,33030,7501],{},[1277,33032,33033,33035],{},[1161,33034,1617],{},[1158,33036,33037,33039,33041,33043,33045],{},[1282,33038,1284],{},[1165,33040,1317],{},[1161,33042,7514],{},[1161,33044,3434],{"mathvariant":1215},[1282,33046,1298],{},[1165,33048,1168],{"stretchy":1167},[1161,33050,4192],{},[1165,33052,1317],{},[1282,33054,1284],{},[1165,33056,1174],{"stretchy":1167},[1194,33058,31588],{"encoding":1196},[4058,33060,33061,33089,33117],{},[4170,33062,33063],{},[1115,33064,33066],{"className":33065},[1149],[1151,33067,33068],{"xmlns":1153},[1155,33069,33070,33086],{},[1158,33071,33072,33078,33080],{},[1277,33073,33074,33076],{},[1161,33075,1355],{},[1161,33077,2641],{},[1165,33079,7501],{},[1277,33081,33082,33084],{},[1161,33083,1355],{},[1282,33085,1982],{},[1194,33087,33088],{"encoding":1196},"\\mu_D \\ge \\mu_0",[4170,33090,33091],{},[1115,33092,33094],{"className":33093},[1149],[1151,33095,33096],{"xmlns":1153},[1155,33097,33098,33114],{},[1158,33099,33100,33106,33108],{},[1277,33101,33102,33104],{},[1161,33103,1355],{},[1161,33105,2641],{},[1165,33107,1287],{},[1277,33109,33110,33112],{},[1161,33111,1355],{},[1282,33113,1982],{},[1194,33115,33116],{"encoding":1196},"\\mu_D \u003C \\mu_0",[4170,33118,33119],{},[1115,33120,33122],{"className":33121},[1149],[1151,33123,33124],{"xmlns":1153},[1155,33125,33126,33156],{},[1158,33127,33128,33130,33132,33134,33146,33148,33150,33152,33154],{},[1161,33129,1617],{},[1165,33131,1188],{},[1165,33133,1317],{},[1277,33135,33136,33138],{},[1161,33137,1617],{},[1158,33139,33140,33142,33144],{},[1282,33141,1284],{},[1165,33143,1317],{},[1161,33145,7514],{},[1165,33147,1168],{"stretchy":1167},[1161,33149,4192],{},[1165,33151,1317],{},[1282,33153,1284],{},[1165,33155,1174],{"stretchy":1167},[1194,33157,31680],{"encoding":1196},[1103,33159,33161,33168,33310,33374,33460],{"className":33160,"dataCallout":3670},[1106,3669],[1110,33162,33164,33167],{"className":33163},[1113],[1115,33165],{"className":33166,"ariaHidden":1121},[1118,3677,1120],"Příklad: Snížení spotřeby paliva aditivem",[1110,33169,33170,33171,33189,33190,33208,33209,33227,33228,33261,33262,33285,33286,33309],{},"U ",[1115,33172,33174],{"className":33173},[1149],[1151,33175,33176],{"xmlns":1153},[1155,33177,33178,33186],{},[1158,33179,33180,33182,33184],{},[1161,33181,4192],{},[1165,33183,1177],{},[1282,33185,3531],{},[1194,33187,33188],{"encoding":1196},"n = 10"," vozů se změřila spotřeba před přidáním aditiva (",[1115,33191,33193],{"className":33192},[1149],[1151,33194,33195],{"xmlns":1153},[1155,33196,33197,33205],{},[1158,33198,33199],{},[1277,33200,33201,33203],{},[1161,33202,1185],{},[1161,33204,4187],{},[1194,33206,33207],{"encoding":1196},"X_i",") a po něm (",[1115,33210,33212],{"className":33211},[1149],[1151,33213,33214],{"xmlns":1153},[1155,33215,33216,33224],{},[1158,33217,33218],{},[1277,33219,33220,33222],{},[1161,33221,1561],{},[1161,33223,4187],{},[1194,33225,33226],{"encoding":1196},"Y_i","), diference ",[1115,33229,33231],{"className":33230},[1149],[1151,33232,33233],{"xmlns":1153},[1155,33234,33235,33259],{},[1158,33236,33237,33243,33245,33251,33253],{},[1277,33238,33239,33241],{},[1161,33240,2641],{},[1161,33242,4187],{},[1165,33244,1177],{},[1277,33246,33247,33249],{},[1161,33248,1185],{},[1161,33250,4187],{},[1165,33252,1317],{},[1277,33254,33255,33257],{},[1161,33256,1561],{},[1161,33258,4187],{},[1194,33260,32607],{"encoding":1196}," představují úsporu paliva. Z dat vyšla průměrná úspora ",[1115,33263,33265],{"className":33264},[1149],[1151,33266,33267],{"xmlns":1153},[1155,33268,33269,33282],{},[1158,33270,33271,33277,33279],{},[6877,33272,33273,33275],{"accent":1121},[1161,33274,2283],{},[1165,33276,15130],{},[1165,33278,1177],{},[1282,33280,33281],{},"0,4",[1194,33283,33284],{"encoding":1196},"\\bar{d} = 0{,}4"," l\u002F100 km, ",[1115,33287,33289],{"className":33288},[1149],[1151,33290,33291],{"xmlns":1153},[1155,33292,33293,33306],{},[1158,33294,33295,33301,33303],{},[1277,33296,33297,33299],{},[1161,33298,6018],{},[1161,33300,2283],{},[1165,33302,1177],{},[1282,33304,33305],{},"0,35",[1194,33307,33308],{"encoding":1196},"s_d = 0{,}35"," l\u002F100 km. Ověřte, že aditivum spotřebu statisticky významně snižuje.",[1110,33311,33312,33342,33343,33373],{},[1115,33313,33315],{"className":33314},[1149],[1151,33316,33317],{"xmlns":1153},[1155,33318,33319,33339],{},[1158,33320,33321,33327,33329,33335,33337],{},[1277,33322,33323,33325],{},[1161,33324,4318],{},[1282,33326,1982],{},[1165,33328,2629],{},[1277,33330,33331,33333],{},[1161,33332,1355],{},[1161,33334,2641],{},[1165,33336,1188],{},[1282,33338,1982],{},[1194,33340,33341],{"encoding":1196},"H_0: \\mu_D \\le 0"," (aditivum nemá vliv nebo spotřebu zvyšuje), ",[1115,33344,33346],{"className":33345},[1149],[1151,33347,33348],{"xmlns":1153},[1155,33349,33350,33370],{},[1158,33351,33352,33358,33360,33366,33368],{},[1277,33353,33354,33356],{},[1161,33355,4318],{},[1282,33357,1284],{},[1165,33359,2629],{},[1277,33361,33362,33364],{},[1161,33363,1355],{},[1161,33365,2641],{},[1165,33367,4156],{},[1282,33369,1982],{},[1194,33371,33372],{"encoding":1196},"H_1: \\mu_D > 0"," (aditivum spotřebu snižuje).",[1110,33375,33376],{},[1115,33377,33379],{"className":33378},[1149],[1151,33380,33381],{"xmlns":1153},[1155,33382,33383,33457],{},[1158,33384,33385,33387,33389,33401,33405,33407,33410,33412,33414,33416,33418,33420,33422,33424,33436,33438,33440,33442,33444,33446,33448,33450,33452,33455],{},[1161,33386,1617],{},[1165,33388,1177],{},[3064,33390,33391,33399],{},[1158,33392,33393,33395,33397],{},[1282,33394,33281],{},[1165,33396,1317],{},[1282,33398,1982],{},[1282,33400,33305],{},[2765,33402,33403],{},[1282,33404,3531],{},[1165,33406,1177],{},[1282,33408,33409],{},"3,614",[1165,33411,1715],{"separator":1121},[2242,33413],{"width":2244},[1161,33415,5777],{},[1165,33417,1177],{},[1165,33419,7484],{"stretchy":1167},[1161,33421,1617],{},[1165,33423,7501],{},[1277,33425,33426,33428],{},[1161,33427,1617],{},[1158,33429,33430,33432,33434],{},[1282,33431,1982],{},[1165,33433,1715],{"separator":1121},[1282,33435,25471],{},[1165,33437,1168],{"stretchy":1167},[1282,33439,7739],{},[1165,33441,1174],{"stretchy":1167},[1165,33443,7543],{"stretchy":1167},[1165,33445,1177],{},[1165,33447,7484],{"stretchy":1167},[1161,33449,1617],{},[1165,33451,7501],{},[1282,33453,33454],{},"1,833",[1165,33456,7543],{"stretchy":1167},[1194,33458,33459],{"encoding":1196},"t = \\frac{0{,}4 - 0}{0{,}35}\\sqrt{10} = 3{,}614, \\qquad W = \\{t \\ge t_{0,95}(9)\\} = \\{t \\ge 1{,}833\\}",[1110,33461,32071,33462,10124,33479,33496],{},[1115,33463,33465],{"className":33464},[1149],[1151,33466,33467],{"xmlns":1153},[1155,33468,33469,33477],{},[1158,33470,33471,33473,33475],{},[1161,33472,1617],{},[1165,33474,1492],{},[1161,33476,5777],{},[1194,33478,32089],{"encoding":1196},[1115,33480,33482],{"className":33481},[1149],[1151,33483,33484],{"xmlns":1153},[1155,33485,33486,33494],{},[1158,33487,33488],{},[1277,33489,33490,33492],{},[1161,33491,4318],{},[1282,33493,1982],{},[1194,33495,5745],{"encoding":1196},": aditivum prokazatelně snižuje průměrnou spotřebu paliva.",[3554,33498,33500],{"className":3556,"code":33499,"language":71,"meta":3558,"style":3558},"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",[1373,33501,33502,33531,33562,33588,33592],{"__ignoreMap":3558},[1115,33503,33504,33507,33509,33512,33514,33517,33519,33522,33524,33526,33528],{"class":3563,"line":10},[1115,33505,33506],{"class":3744},"dbar",[1115,33508,4497],{"class":3741},[1115,33510,33511],{"class":3572}," 0.4",[1115,33513,28857],{"class":3569},[1115,33515,33516],{"class":3744},"sd_d",[1115,33518,4497],{"class":3741},[1115,33520,33521],{"class":3572}," 0.35",[1115,33523,28857],{"class":3569},[1115,33525,4192],{"class":3744},[1115,33527,4497],{"class":3741},[1115,33529,33530],{"class":3572}," 10\n",[1115,33532,33533,33535,33537,33539,33541,33543,33545,33547,33549,33552,33554,33556,33558,33560],{"class":3563,"line":27},[1115,33534,1617],{"class":3744},[1115,33536,4497],{"class":3741},[1115,33538,8728],{"class":3569},[1115,33540,33506],{"class":3744},[1115,33542,29194],{"class":3741},[1115,33544,4500],{"class":3572},[1115,33546,3862],{"class":3569},[1115,33548,3434],{"class":3741},[1115,33550,33551],{"class":3744}," sd_d",[1115,33553,22312],{"class":3741},[1115,33555,4003],{"class":3566},[1115,33557,1168],{"class":3569},[1115,33559,4192],{"class":3744},[1115,33561,3575],{"class":3569},[1115,33563,33564,33566,33568,33570,33572,33574,33576,33578,33580,33582,33584,33586],{"class":3563,"line":148},[1115,33565,32196],{"class":3744},[1115,33567,4497],{"class":3741},[1115,33569,32201],{"class":3566},[1115,33571,1168],{"class":3569},[1115,33573,5364],{"class":3572},[1115,33575,1715],{"class":3741},[1115,33577,5347],{"class":3744},[1115,33579,3748],{"class":3741},[1115,33581,32215],{"class":3744},[1115,33583,29194],{"class":3741},[1115,33585,4605],{"class":3572},[1115,33587,3575],{"class":3569},[1115,33589,33590],{"class":3563,"line":111},[1115,33591,32226],{"class":3744},[1115,33593,33594],{"class":3563,"line":96},[1115,33595,32231],{"class":3744},[3554,33597,33600],{"className":33598,"code":33599,"language":3603,"meta":3558},[3601],"[1] 3.614032\n[1] 1.833113\n",[1373,33601,33599],{"__ignoreMap":3558},[1103,33603,33605,33612,33615,33760,33766],{"className":33604,"dataCallout":3448},[1106,3447],[1110,33606,33608,33611],{"className":33607},[1113],[1115,33609],{"className":33610,"ariaHidden":1121},[1118,3455,1120],"Ověřte normalitu diferencí, ne jen výsledek testu",[1110,33613,33614],{},"Realitní kancelář nechala dva odhadce ocenit osm nemovitostí (tisíce Kč):",[3554,33616,33618],{"className":3556,"code":33617,"language":71,"meta":3558,"style":3558},"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",[1373,33619,33620,33671,33722,33746],{"__ignoreMap":3558},[1115,33621,33622,33625,33627,33629,33631,33634,33636,33639,33641,33644,33646,33649,33651,33654,33656,33659,33661,33664,33666,33669],{"class":3563,"line":10},[1115,33623,33624],{"class":3744},"estA",[1115,33626,4497],{"class":3741},[1115,33628,7969],{"class":3566},[1115,33630,1168],{"class":3569},[1115,33632,33633],{"class":3572},"3282",[1115,33635,1715],{"class":3741},[1115,33637,33638],{"class":3572}," 2506",[1115,33640,1715],{"class":3741},[1115,33642,33643],{"class":3572}," 2812",[1115,33645,1715],{"class":3741},[1115,33647,33648],{"class":3572}," 5453",[1115,33650,1715],{"class":3741},[1115,33652,33653],{"class":3572}," 3263",[1115,33655,1715],{"class":3741},[1115,33657,33658],{"class":3572}," 4571",[1115,33660,1715],{"class":3741},[1115,33662,33663],{"class":3572}," 3121",[1115,33665,1715],{"class":3741},[1115,33667,33668],{"class":3572}," 2963",[1115,33670,3575],{"class":3569},[1115,33672,33673,33676,33678,33680,33682,33685,33687,33690,33692,33695,33697,33700,33702,33705,33707,33710,33712,33715,33717,33720],{"class":3563,"line":27},[1115,33674,33675],{"class":3744},"estB",[1115,33677,4497],{"class":3741},[1115,33679,7969],{"class":3566},[1115,33681,1168],{"class":3569},[1115,33683,33684],{"class":3572},"3271",[1115,33686,1715],{"class":3741},[1115,33688,33689],{"class":3572}," 2531",[1115,33691,1715],{"class":3741},[1115,33693,33694],{"class":3572}," 2799",[1115,33696,1715],{"class":3741},[1115,33698,33699],{"class":3572}," 5471",[1115,33701,1715],{"class":3741},[1115,33703,33704],{"class":3572}," 3285",[1115,33706,1715],{"class":3741},[1115,33708,33709],{"class":3572}," 4557",[1115,33711,1715],{"class":3741},[1115,33713,33714],{"class":3572}," 3139",[1115,33716,1715],{"class":3741},[1115,33718,33719],{"class":3572}," 2976",[1115,33721,3575],{"class":3569},[1115,33723,33724,33726,33728,33730,33732,33735,33737,33740,33742,33744],{"class":3563,"line":148},[1115,33725,31751],{"class":3566},[1115,33727,1168],{"class":3569},[1115,33729,33624],{"class":3744},[1115,33731,1715],{"class":3741},[1115,33733,33734],{"class":3744}," estB",[1115,33736,1715],{"class":3741},[1115,33738,33739],{"class":3744}," paired",[1115,33741,3748],{"class":3741},[1115,33743,7944],{"class":3572},[1115,33745,3575],{"class":3569},[1115,33747,33748,33750,33752,33754,33756,33758],{"class":3563,"line":111},[1115,33749,21248],{"class":3566},[1115,33751,1168],{"class":3569},[1115,33753,33624],{"class":3744},[1115,33755,29194],{"class":3741},[1115,33757,33734],{"class":3744},[1115,33759,3575],{"class":3569},[3554,33761,33764],{"className":33762,"code":33763,"language":3603,"meta":3558},[3601],"    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",[1373,33765,33763],{"__ignoreMap":3558},[1110,33767,33768,33769,8728,33786,33805,33806,33829],{},"Párový t-test sám nezamítá ",[1115,33770,33772],{"className":33771},[1149],[1151,33773,33774],{"xmlns":1153},[1155,33775,33776,33784],{},[1158,33777,33778],{},[1277,33779,33780,33782],{},[1161,33781,4318],{},[1282,33783,1982],{},[1194,33785,5745],{"encoding":1196},[1115,33787,33789],{"className":33788},[1149],[1151,33790,33791],{"xmlns":1153},[1155,33792,33793,33802],{},[1158,33794,33795,33797,33799],{},[1161,33796,1110],{},[1165,33798,1177],{},[1282,33800,33801],{},"0,2635",[1194,33803,33804],{"encoding":1196},"p = 0{,}2635","): odhadci se podle něj neliší. Shapiro-Wilkův test na diferencích ale dává ",[1115,33807,33809],{"className":33808},[1149],[1151,33810,33811],{"xmlns":1153},[1155,33812,33813,33826],{},[1158,33814,33815,33817,33819,33822,33824],{},[1161,33816,1110],{},[1165,33818,1177],{},[1282,33820,33821],{},"0,03203",[1165,33823,1287],{},[1282,33825,8114],{},[1194,33827,33828],{"encoding":1196},"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).",[1431,33831,33833],{"id":33832},"testy-o-dvou-základních-souborech","Testy o dvou základních souborech",[1110,33835,33836,33837,33863,33864,33902,33903,1425,33921,33902,33959,33977,33978,1425,34010,34042,34043,34069,34070,1333],{},"Uvažují se dva nezávislé základní soubory ",[1115,33838,33840],{"className":33839},[1149],[1151,33841,33842],{"xmlns":1153},[1155,33843,33844,33860],{},[1158,33845,33846,33852,33854],{},[1277,33847,33848,33850],{},[1161,33849,3419],{},[1282,33851,1284],{},[1165,33853,1715],{"separator":1121},[1277,33855,33856,33858],{},[1161,33857,3419],{},[1282,33859,1298],{},[1194,33861,33862],{"encoding":1196},"Z_1, Z_2"," se znakem ",[1115,33865,33867],{"className":33866},[1149],[1151,33868,33869],{"xmlns":1153},[1155,33870,33871,33899],{},[1158,33872,33873,33875,33877,33879,33881,33887,33889,33897],{},[1161,33874,1185],{},[1165,33876,3695],{},[1161,33878,1350],{},[1165,33880,1168],{"stretchy":1167},[1277,33882,33883,33885],{},[1161,33884,1355],{},[1282,33886,1284],{},[1165,33888,1715],{"separator":1121},[2256,33890,33891,33893,33895],{},[1161,33892,1363],{},[1282,33894,1284],{},[1282,33896,1298],{},[1165,33898,1174],{"stretchy":1167},[1194,33900,33901],{"encoding":1196},"X \\sim N(\\mu_1, \\sigma_1^2)"," v ",[1115,33904,33906],{"className":33905},[1149],[1151,33907,33908],{"xmlns":1153},[1155,33909,33910,33918],{},[1158,33911,33912],{},[1277,33913,33914,33916],{},[1161,33915,3419],{},[1282,33917,1284],{},[1194,33919,33920],{"encoding":1196},"Z_1",[1115,33922,33924],{"className":33923},[1149],[1151,33925,33926],{"xmlns":1153},[1155,33927,33928,33956],{},[1158,33929,33930,33932,33934,33936,33938,33944,33946,33954],{},[1161,33931,1185],{},[1165,33933,3695],{},[1161,33935,1350],{},[1165,33937,1168],{"stretchy":1167},[1277,33939,33940,33942],{},[1161,33941,1355],{},[1282,33943,1298],{},[1165,33945,1715],{"separator":1121},[2256,33947,33948,33950,33952],{},[1161,33949,1363],{},[1282,33951,1298],{},[1282,33953,1298],{},[1165,33955,1174],{"stretchy":1167},[1194,33957,33958],{"encoding":1196},"X \\sim N(\\mu_2, \\sigma_2^2)",[1115,33960,33962],{"className":33961},[1149],[1151,33963,33964],{"xmlns":1153},[1155,33965,33966,33974],{},[1158,33967,33968],{},[1277,33969,33970,33972],{},[1161,33971,3419],{},[1282,33973,1298],{},[1194,33975,33976],{"encoding":1196},"Z_2",". Z výběrů se určí ",[1115,33979,33981],{"className":33980},[1149],[1151,33982,33983],{"xmlns":1153},[1155,33984,33985,34007],{},[1158,33986,33987,33997,33999],{},[1277,33988,33989,33995],{},[6877,33990,33991,33993],{"accent":1121},[1161,33992,1171],{},[1165,33994,15130],{},[1282,33996,1284],{},[1165,33998,1715],{"separator":1121},[2256,34000,34001,34003,34005],{},[1161,34002,6018],{},[1282,34004,1284],{},[1282,34006,1298],{},[1194,34008,34009],{"encoding":1196},"\\bar{x}_1, s_1^2",[1115,34011,34013],{"className":34012},[1149],[1151,34014,34015],{"xmlns":1153},[1155,34016,34017,34039],{},[1158,34018,34019,34029,34031],{},[1277,34020,34021,34027],{},[6877,34022,34023,34025],{"accent":1121},[1161,34024,1171],{},[1165,34026,15130],{},[1282,34028,1298],{},[1165,34030,1715],{"separator":1121},[2256,34032,34033,34035,34037],{},[1161,34034,6018],{},[1282,34036,1298],{},[1282,34038,1298],{},[1194,34040,34041],{"encoding":1196},"\\bar{x}_2, s_2^2",". Testují se varianty vztahů mezi ",[1115,34044,34046],{"className":34045},[1149],[1151,34047,34048],{"xmlns":1153},[1155,34049,34050,34066],{},[1158,34051,34052,34058,34060],{},[1277,34053,34054,34056],{},[1161,34055,1355],{},[1282,34057,1284],{},[1165,34059,1715],{"separator":1121},[1277,34061,34062,34064],{},[1161,34063,1355],{},[1282,34065,1298],{},[1194,34067,34068],{"encoding":1196},"\\mu_1, \\mu_2",", resp. mezi ",[1115,34071,34073],{"className":34072},[1149],[1151,34074,34075],{"xmlns":1153},[1155,34076,34077,34097],{},[1158,34078,34079,34087,34089],{},[2256,34080,34081,34083,34085],{},[1161,34082,1363],{},[1282,34084,1284],{},[1282,34086,1298],{},[1165,34088,1715],{"separator":1121},[2256,34090,34091,34093,34095],{},[1161,34092,1363],{},[1282,34094,1298],{},[1282,34096,1298],{},[1194,34098,34099],{"encoding":1196},"\\sigma_1^2, \\sigma_2^2",[20418,34101,34103],{"id":34102},"f-test-o-rozptylech","F-test o rozptylech",[1110,34105,34106],{},"Statistika",[1115,34108,34110],{"className":34109},[1149],[1151,34111,34112],{"xmlns":1153,"display":2212},[1155,34113,34114,34170],{},[1158,34115,34116,34118,34120,34138,34140],{},[1161,34117,1163],{},[1165,34119,1177],{},[3064,34121,34122,34130],{},[2256,34123,34124,34126,34128],{},[1161,34125,6018],{},[1282,34127,1284],{},[1282,34129,1298],{},[2256,34131,34132,34134,34136],{},[1161,34133,6018],{},[1282,34135,1298],{},[1282,34137,1298],{},[1165,34139,3695],{},[1277,34141,34142,34144],{},[1161,34143,1163],{},[1158,34145,34146,34152,34154,34156,34158,34160,34166,34168],{},[1277,34147,34148,34150],{},[1161,34149,4192],{},[1282,34151,1284],{},[1165,34153,1317],{},[1282,34155,1284],{},[1165,34157,1715],{"separator":1121},[2278,34159,2280],{},[1277,34161,34162,34164],{},[1161,34163,4192],{},[1282,34165,1298],{},[1165,34167,1317],{},[1282,34169,1284],{},[1194,34171,34172],{"encoding":1196},"F = \\frac{s_1^2}{s_2^2} \\sim F_{n_1-1,\\,n_2-1}",[1110,34174,34175,34176,1425,34198,31338],{},"má Fisherovo-Snedecorovo rozdělení o ",[1115,34177,34179],{"className":34178},[1149],[1151,34180,34181],{"xmlns":1153},[1155,34182,34183,34195],{},[1158,34184,34185,34191,34193],{},[1277,34186,34187,34189],{},[1161,34188,4192],{},[1282,34190,1284],{},[1165,34192,1317],{},[1282,34194,1284],{},[1194,34196,34197],{"encoding":1196},"n_1-1",[1115,34199,34201],{"className":34200},[1149],[1151,34202,34203],{"xmlns":1153},[1155,34204,34205,34217],{},[1158,34206,34207,34213,34215],{},[1277,34208,34209,34211],{},[1161,34210,4192],{},[1282,34212,1298],{},[1165,34214,1317],{},[1282,34216,1284],{},[1194,34218,34219],{"encoding":1196},"n_2-1",[4052,34221,34222,34279],{},[4055,34223,34224],{},[4058,34225,34226,34245,34264],{},[4061,34227,34228],{},[1115,34229,34231],{"className":34230},[1149],[1151,34232,34233],{"xmlns":1153},[1155,34234,34235,34243],{},[1158,34236,34237],{},[1277,34238,34239,34241],{},[1161,34240,4318],{},[1282,34242,1982],{},[1194,34244,5745],{"encoding":1196},[4061,34246,34247],{},[1115,34248,34250],{"className":34249},[1149],[1151,34251,34252],{"xmlns":1153},[1155,34253,34254,34262],{},[1158,34255,34256],{},[1277,34257,34258,34260],{},[1161,34259,4318],{},[1282,34261,1284],{},[1194,34263,7147],{"encoding":1196},[4061,34265,31385,34266],{},[1115,34267,34269],{"className":34268},[1149],[1151,34270,34271],{"xmlns":1153},[1155,34272,34273,34277],{},[1158,34274,34275],{},[1161,34276,5777],{},[1194,34278,5777],{"encoding":1196},[4165,34280,34281,34395,34568],{},[4058,34282,34283,34311,34339],{},[4170,34284,34285],{},[1115,34286,34288],{"className":34287},[1149],[1151,34289,34290],{"xmlns":1153},[1155,34291,34292,34308],{},[1158,34293,34294,34300,34302],{},[1277,34295,34296,34298],{},[1161,34297,1363],{},[1282,34299,1284],{},[1165,34301,1188],{},[1277,34303,34304,34306],{},[1161,34305,1363],{},[1282,34307,1298],{},[1194,34309,34310],{"encoding":1196},"\\sigma_1 \\le \\sigma_2",[4170,34312,34313],{},[1115,34314,34316],{"className":34315},[1149],[1151,34317,34318],{"xmlns":1153},[1155,34319,34320,34336],{},[1158,34321,34322,34328,34330],{},[1277,34323,34324,34326],{},[1161,34325,1363],{},[1282,34327,1284],{},[1165,34329,4156],{},[1277,34331,34332,34334],{},[1161,34333,1363],{},[1282,34335,1298],{},[1194,34337,34338],{"encoding":1196},"\\sigma_1 > \\sigma_2",[4170,34340,34341],{},[1115,34342,34344],{"className":34343},[1149],[1151,34345,34346],{"xmlns":1153},[1155,34347,34348,34392],{},[1158,34349,34350,34352,34354,34366,34368,34374,34376,34378,34380,34386,34388,34390],{},[1161,34351,1163],{},[1165,34353,7501],{},[1277,34355,34356,34358],{},[1161,34357,1163],{},[1158,34359,34360,34362,34364],{},[1282,34361,1284],{},[1165,34363,1317],{},[1161,34365,7514],{},[1165,34367,1168],{"stretchy":1167},[1277,34369,34370,34372],{},[1161,34371,4192],{},[1282,34373,1284],{},[1165,34375,1317],{},[1282,34377,1284],{},[1165,34379,1715],{"separator":1121},[1277,34381,34382,34384],{},[1161,34383,4192],{},[1282,34385,1298],{},[1165,34387,1317],{},[1282,34389,1284],{},[1165,34391,1174],{"stretchy":1167},[1194,34393,34394],{"encoding":1196},"F \\ge F_{1-\\alpha}(n_1-1, n_2-1)",[4058,34396,34397,34425,34453],{},[4170,34398,34399],{},[1115,34400,34402],{"className":34401},[1149],[1151,34403,34404],{"xmlns":1153},[1155,34405,34406,34422],{},[1158,34407,34408,34414,34416],{},[1277,34409,34410,34412],{},[1161,34411,1363],{},[1282,34413,1284],{},[1165,34415,1177],{},[1277,34417,34418,34420],{},[1161,34419,1363],{},[1282,34421,1298],{},[1194,34423,34424],{"encoding":1196},"\\sigma_1 = \\sigma_2",[4170,34426,34427],{},[1115,34428,34430],{"className":34429},[1149],[1151,34431,34432],{"xmlns":1153},[1155,34433,34434,34450],{},[1158,34435,34436,34442,34444],{},[1277,34437,34438,34440],{},[1161,34439,1363],{},[1282,34441,1284],{},[1165,34443,5496],{"mathvariant":1215},[1277,34445,34446,34448],{},[1161,34447,1363],{},[1282,34449,1298],{},[1194,34451,34452],{"encoding":1196},"\\sigma_1 \\neq \\sigma_2",[4170,34454,34455,34509,34510],{},[1115,34456,34458],{"className":34457},[1149],[1151,34459,34460],{"xmlns":1153},[1155,34461,34462,34506],{},[1158,34463,34464,34466,34468,34480,34482,34488,34490,34492,34494,34500,34502,34504],{},[1161,34465,1163],{},[1165,34467,1188],{},[1277,34469,34470,34472],{},[1161,34471,1163],{},[1158,34473,34474,34476,34478],{},[1161,34475,7514],{},[1161,34477,3434],{"mathvariant":1215},[1282,34479,1298],{},[1165,34481,1168],{"stretchy":1167},[1277,34483,34484,34486],{},[1161,34485,4192],{},[1282,34487,1284],{},[1165,34489,1317],{},[1282,34491,1284],{},[1165,34493,1715],{"separator":1121},[1277,34495,34496,34498],{},[1161,34497,4192],{},[1282,34499,1298],{},[1165,34501,1317],{},[1282,34503,1284],{},[1165,34505,1174],{"stretchy":1167},[1194,34507,34508],{"encoding":1196},"F \\le F_{\\alpha\u002F2}(n_1-1, n_2-1)"," nebo ",[1115,34511,34513],{"className":34512},[1149],[1151,34514,34515],{"xmlns":1153},[1155,34516,34517,34565],{},[1158,34518,34519,34521,34523,34539,34541,34547,34549,34551,34553,34559,34561,34563],{},[1161,34520,1163],{},[1165,34522,7501],{},[1277,34524,34525,34527],{},[1161,34526,1163],{},[1158,34528,34529,34531,34533,34535,34537],{},[1282,34530,1284],{},[1165,34532,1317],{},[1161,34534,7514],{},[1161,34536,3434],{"mathvariant":1215},[1282,34538,1298],{},[1165,34540,1168],{"stretchy":1167},[1277,34542,34543,34545],{},[1161,34544,4192],{},[1282,34546,1284],{},[1165,34548,1317],{},[1282,34550,1284],{},[1165,34552,1715],{"separator":1121},[1277,34554,34555,34557],{},[1161,34556,4192],{},[1282,34558,1298],{},[1165,34560,1317],{},[1282,34562,1284],{},[1165,34564,1174],{"stretchy":1167},[1194,34566,34567],{"encoding":1196},"F \\ge F_{1-\\alpha\u002F2}(n_1-1, n_2-1)",[4058,34569,34570,34598,34626],{},[4170,34571,34572],{},[1115,34573,34575],{"className":34574},[1149],[1151,34576,34577],{"xmlns":1153},[1155,34578,34579,34595],{},[1158,34580,34581,34587,34589],{},[1277,34582,34583,34585],{},[1161,34584,1363],{},[1282,34586,1284],{},[1165,34588,7501],{},[1277,34590,34591,34593],{},[1161,34592,1363],{},[1282,34594,1298],{},[1194,34596,34597],{"encoding":1196},"\\sigma_1 \\ge \\sigma_2",[4170,34599,34600],{},[1115,34601,34603],{"className":34602},[1149],[1151,34604,34605],{"xmlns":1153},[1155,34606,34607,34623],{},[1158,34608,34609,34615,34617],{},[1277,34610,34611,34613],{},[1161,34612,1363],{},[1282,34614,1284],{},[1165,34616,1287],{},[1277,34618,34619,34621],{},[1161,34620,1363],{},[1282,34622,1298],{},[1194,34624,34625],{"encoding":1196},"\\sigma_1 \u003C \\sigma_2",[4170,34627,34628],{},[1115,34629,34631],{"className":34630},[1149],[1151,34632,34633],{"xmlns":1153},[1155,34634,34635,34673],{},[1158,34636,34637,34639,34641,34647,34649,34655,34657,34659,34661,34667,34669,34671],{},[1161,34638,1163],{},[1165,34640,1188],{},[1277,34642,34643,34645],{},[1161,34644,1163],{},[1161,34646,7514],{},[1165,34648,1168],{"stretchy":1167},[1277,34650,34651,34653],{},[1161,34652,4192],{},[1282,34654,1284],{},[1165,34656,1317],{},[1282,34658,1284],{},[1165,34660,1715],{"separator":1121},[1277,34662,34663,34665],{},[1161,34664,4192],{},[1282,34666,1298],{},[1165,34668,1317],{},[1282,34670,1284],{},[1165,34672,1174],{"stretchy":1167},[1194,34674,34675],{"encoding":1196},"F \\le F_{\\alpha}(n_1-1, n_2-1)",[20418,34677,34679],{"id":34678},"dvouvýběrový-t-test-o-středních-hodnotách","Dvouvýběrový t-test o středních hodnotách",[1110,34681,34682],{},"Volba statistiky závisí na tom, zda jsou rozptyly považovány za shodné:",[1115,34684,34686],{"className":34685},[1149],[1151,34687,34688],{"xmlns":1153,"display":2212},[1155,34689,34690,34867],{},[1158,34691,34692,34698,34700,34776,34824,34826,34828,34837,34839,34845,34847,34853,34855,34861,34863,34865],{},[1277,34693,34694,34696],{},[1161,34695,1575],{},[1282,34697,1284],{},[1165,34699,1177],{},[3064,34701,34702,34726],{},[1158,34703,34704,34714,34716],{},[1277,34705,34706,34712],{},[6877,34707,34708,34710],{"accent":1121},[1161,34709,1171],{},[1165,34711,15130],{},[1282,34713,1284],{},[1165,34715,1317],{},[1277,34717,34718,34724],{},[6877,34719,34720,34722],{"accent":1121},[1161,34721,1171],{},[1165,34723,15130],{},[1282,34725,1298],{},[2765,34727,34728],{},[1158,34729,34730,34732,34738,34740,34742,34744,34752,34754,34756,34762,34764,34766,34768],{},[1165,34731,1168],{"stretchy":1167},[1277,34733,34734,34736],{},[1161,34735,4192],{},[1282,34737,1284],{},[1165,34739,1317],{},[1282,34741,1284],{},[1165,34743,1174],{"stretchy":1167},[2256,34745,34746,34748,34750],{},[1161,34747,6018],{},[1282,34749,1284],{},[1282,34751,1298],{},[1165,34753,2094],{},[1165,34755,1168],{"stretchy":1167},[1277,34757,34758,34760],{},[1161,34759,4192],{},[1282,34761,1298],{},[1165,34763,1317],{},[1282,34765,1284],{},[1165,34767,1174],{"stretchy":1167},[2256,34769,34770,34772,34774],{},[1161,34771,6018],{},[1282,34773,1298],{},[1282,34775,1298],{},[2765,34777,34778],{},[3064,34779,34780,34800],{},[1158,34781,34782,34788,34790,34796,34798],{},[1277,34783,34784,34786],{},[1161,34785,4192],{},[1282,34787,1284],{},[1165,34789,2094],{},[1277,34791,34792,34794],{},[1161,34793,4192],{},[1282,34795,1298],{},[1165,34797,1317],{},[1282,34799,1298],{},[1158,34801,34802,34812,34814],{},[3064,34803,34804,34806],{},[1282,34805,1284],{},[1277,34807,34808,34810],{},[1161,34809,4192],{},[1282,34811,1284],{},[1165,34813,2094],{},[3064,34815,34816,34818],{},[1282,34817,1284],{},[1277,34819,34820,34822],{},[1161,34821,4192],{},[1282,34823,1298],{},[1165,34825,1715],{"separator":1121},[2242,34827],{"width":2244},[2256,34829,34830,34832,34834],{},[1161,34831,1617],{},[1161,34833,1110],{},[1165,34835,34836],{},"∗",[1165,34838,1177],{},[1277,34840,34841,34843],{},[1161,34842,1617],{},[1161,34844,1110],{},[1165,34846,1168],{"stretchy":1167},[1277,34848,34849,34851],{},[1161,34850,4192],{},[1282,34852,1284],{},[1165,34854,2094],{},[1277,34856,34857,34859],{},[1161,34858,4192],{},[1282,34860,1298],{},[1165,34862,1317],{},[1282,34864,1298],{},[1165,34866,1174],{"stretchy":1167},[1194,34868,34869],{"encoding":1196},"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)",[1110,34871,34872,34873,34902],{},"se použije, pokud jsou rozptyly ",[1115,34874,34876],{"className":34875},[1149],[1151,34877,34878],{"xmlns":1153},[1155,34879,34880,34900],{},[1158,34881,34882,34890,34892],{},[2256,34883,34884,34886,34888],{},[1161,34885,1363],{},[1282,34887,1284],{},[1282,34889,1298],{},[1165,34891,1715],{"separator":1121},[2256,34893,34894,34896,34898],{},[1161,34895,1363],{},[1282,34897,1298],{},[1282,34899,1298],{},[1194,34901,34099],{"encoding":1196}," alespoň přibližně shodné; při rozdílných rozptylech",[1115,34904,34906],{"className":34905},[1149],[1151,34907,34908],{"xmlns":1153,"display":2212},[1155,34909,34910,35122],{},[1158,34911,34912,34918,34920,34984,34986,34988,34996,34998,35120],{},[1277,34913,34914,34916],{},[1161,34915,1575],{},[1282,34917,1298],{},[1165,34919,1177],{},[3064,34921,34922,34946],{},[1158,34923,34924,34934,34936],{},[1277,34925,34926,34932],{},[6877,34927,34928,34930],{"accent":1121},[1161,34929,1171],{},[1165,34931,15130],{},[1282,34933,1284],{},[1165,34935,1317],{},[1277,34937,34938,34944],{},[6877,34939,34940,34942],{"accent":1121},[1161,34941,1171],{},[1165,34943,15130],{},[1282,34945,1298],{},[2765,34947,34948],{},[1158,34949,34950,34958,34960,34966,34968,34976,34978],{},[2256,34951,34952,34954,34956],{},[1161,34953,6018],{},[1282,34955,1284],{},[1282,34957,1298],{},[1161,34959,3434],{"mathvariant":1215},[1277,34961,34962,34964],{},[1161,34963,4192],{},[1282,34965,1284],{},[1165,34967,2094],{},[2256,34969,34970,34972,34974],{},[1161,34971,6018],{},[1282,34973,1298],{},[1282,34975,1298],{},[1161,34977,3434],{"mathvariant":1215},[1277,34979,34980,34982],{},[1161,34981,4192],{},[1282,34983,1298],{},[1165,34985,1715],{"separator":1121},[2242,34987],{"width":2244},[2256,34989,34990,34992,34994],{},[1161,34991,1617],{},[1161,34993,1110],{},[1165,34995,34836],{},[1165,34997,1177],{},[3064,34999,35000,35080],{},[1158,35001,35002,35020,35026,35028,35034,35036,35038,35040,35042,35060,35066,35068,35074,35076,35078],{},[7391,35003,35004],{"scriptlevel":1982,"displaystyle":1121},[3064,35005,35006,35014],{},[2256,35007,35008,35010,35012],{},[1161,35009,6018],{},[1282,35011,1284],{},[1282,35013,1298],{},[1277,35015,35016,35018],{},[1161,35017,4192],{},[1282,35019,1284],{},[1277,35021,35022,35024],{},[1161,35023,1617],{},[1161,35025,1110],{},[1165,35027,1168],{"stretchy":1167},[1277,35029,35030,35032],{},[1161,35031,4192],{},[1282,35033,1284],{},[1165,35035,1317],{},[1282,35037,1284],{},[1165,35039,1174],{"stretchy":1167},[1165,35041,2094],{},[7391,35043,35044],{"scriptlevel":1982,"displaystyle":1121},[3064,35045,35046,35054],{},[2256,35047,35048,35050,35052],{},[1161,35049,6018],{},[1282,35051,1298],{},[1282,35053,1298],{},[1277,35055,35056,35058],{},[1161,35057,4192],{},[1282,35059,1298],{},[1277,35061,35062,35064],{},[1161,35063,1617],{},[1161,35065,1110],{},[1165,35067,1168],{"stretchy":1167},[1277,35069,35070,35072],{},[1161,35071,4192],{},[1282,35073,1298],{},[1165,35075,1317],{},[1282,35077,1284],{},[1165,35079,1174],{"stretchy":1167},[1158,35081,35082,35100,35102],{},[7391,35083,35084],{"scriptlevel":1982,"displaystyle":1121},[3064,35085,35086,35094],{},[2256,35087,35088,35090,35092],{},[1161,35089,6018],{},[1282,35091,1284],{},[1282,35093,1298],{},[1277,35095,35096,35098],{},[1161,35097,4192],{},[1282,35099,1284],{},[1165,35101,2094],{},[7391,35103,35104],{"scriptlevel":1982,"displaystyle":1121},[3064,35105,35106,35114],{},[2256,35107,35108,35110,35112],{},[1161,35109,6018],{},[1282,35111,1298],{},[1282,35113,1298],{},[1277,35115,35116,35118],{},[1161,35117,4192],{},[1282,35119,1298],{},[1161,35121,1333],{"mathvariant":1215},[1194,35123,35124],{"encoding":1196},"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}}.",[4052,35126,35127,35184],{},[4055,35128,35129],{},[4058,35130,35131,35150,35169],{},[4061,35132,35133],{},[1115,35134,35136],{"className":35135},[1149],[1151,35137,35138],{"xmlns":1153},[1155,35139,35140,35148],{},[1158,35141,35142],{},[1277,35143,35144,35146],{},[1161,35145,4318],{},[1282,35147,1982],{},[1194,35149,5745],{"encoding":1196},[4061,35151,35152],{},[1115,35153,35155],{"className":35154},[1149],[1151,35156,35157],{"xmlns":1153},[1155,35158,35159,35167],{},[1158,35160,35161],{},[1277,35162,35163,35165],{},[1161,35164,4318],{},[1282,35166,1284],{},[1194,35168,7147],{"encoding":1196},[4061,35170,31385,35171],{},[1115,35172,35174],{"className":35173},[1149],[1151,35175,35176],{"xmlns":1153},[1155,35177,35178,35182],{},[1158,35179,35180],{},[1161,35181,5777],{},[1194,35183,5777],{"encoding":1196},[4165,35185,35186,35270,35358],{},[4058,35187,35188,35216,35244],{},[4170,35189,35190],{},[1115,35191,35193],{"className":35192},[1149],[1151,35194,35195],{"xmlns":1153},[1155,35196,35197,35213],{},[1158,35198,35199,35205,35207],{},[1277,35200,35201,35203],{},[1161,35202,1355],{},[1282,35204,1284],{},[1165,35206,1188],{},[1277,35208,35209,35211],{},[1161,35210,1355],{},[1282,35212,1298],{},[1194,35214,35215],{"encoding":1196},"\\mu_1 \\le \\mu_2",[4170,35217,35218],{},[1115,35219,35221],{"className":35220},[1149],[1151,35222,35223],{"xmlns":1153},[1155,35224,35225,35241],{},[1158,35226,35227,35233,35235],{},[1277,35228,35229,35231],{},[1161,35230,1355],{},[1282,35232,1284],{},[1165,35234,4156],{},[1277,35236,35237,35239],{},[1161,35238,1355],{},[1282,35240,1298],{},[1194,35242,35243],{"encoding":1196},"\\mu_1 > \\mu_2",[4170,35245,35246],{},[1115,35247,35249],{"className":35248},[1149],[1151,35250,35251],{"xmlns":1153},[1155,35252,35253,35267],{},[1158,35254,35255,35257,35259],{},[1161,35256,1617],{},[1165,35258,7501],{},[2256,35260,35261,35263,35265],{},[1161,35262,1617],{},[1161,35264,1110],{},[1165,35266,34836],{},[1194,35268,35269],{"encoding":1196},"t \\ge t_p^*",[4058,35271,35272,35300,35328],{},[4170,35273,35274],{},[1115,35275,35277],{"className":35276},[1149],[1151,35278,35279],{"xmlns":1153},[1155,35280,35281,35297],{},[1158,35282,35283,35289,35291],{},[1277,35284,35285,35287],{},[1161,35286,1355],{},[1282,35288,1284],{},[1165,35290,1177],{},[1277,35292,35293,35295],{},[1161,35294,1355],{},[1282,35296,1298],{},[1194,35298,35299],{"encoding":1196},"\\mu_1 = \\mu_2",[4170,35301,35302],{},[1115,35303,35305],{"className":35304},[1149],[1151,35306,35307],{"xmlns":1153},[1155,35308,35309,35325],{},[1158,35310,35311,35317,35319],{},[1277,35312,35313,35315],{},[1161,35314,1355],{},[1282,35316,1284],{},[1165,35318,5496],{"mathvariant":1215},[1277,35320,35321,35323],{},[1161,35322,1355],{},[1282,35324,1298],{},[1194,35326,35327],{"encoding":1196},"\\mu_1 \\neq \\mu_2",[4170,35329,35330],{},[1115,35331,35333],{"className":35332},[1149],[1151,35334,35335],{"xmlns":1153},[1155,35336,35337,35355],{},[1158,35338,35339,35341,35343,35345,35347],{},[1165,35340,26697],{"stretchy":1167},[1161,35342,1617],{},[1165,35344,26697],{"stretchy":1167},[1165,35346,7501],{},[2256,35348,35349,35351,35353],{},[1161,35350,1617],{},[1161,35352,1110],{},[1165,35354,34836],{},[1194,35356,35357],{"encoding":1196},"\\lvert t \\rvert \\ge t_p^*",[4058,35359,35360,35388,35416],{},[4170,35361,35362],{},[1115,35363,35365],{"className":35364},[1149],[1151,35366,35367],{"xmlns":1153},[1155,35368,35369,35385],{},[1158,35370,35371,35377,35379],{},[1277,35372,35373,35375],{},[1161,35374,1355],{},[1282,35376,1284],{},[1165,35378,7501],{},[1277,35380,35381,35383],{},[1161,35382,1355],{},[1282,35384,1298],{},[1194,35386,35387],{"encoding":1196},"\\mu_1 \\ge \\mu_2",[4170,35389,35390],{},[1115,35391,35393],{"className":35392},[1149],[1151,35394,35395],{"xmlns":1153},[1155,35396,35397,35413],{},[1158,35398,35399,35405,35407],{},[1277,35400,35401,35403],{},[1161,35402,1355],{},[1282,35404,1284],{},[1165,35406,1287],{},[1277,35408,35409,35411],{},[1161,35410,1355],{},[1282,35412,1298],{},[1194,35414,35415],{"encoding":1196},"\\mu_1 \u003C \\mu_2",[4170,35417,35418],{},[1115,35419,35421],{"className":35420},[1149],[1151,35422,35423],{"xmlns":1153},[1155,35424,35425,35441],{},[1158,35426,35427,35429,35431,35433],{},[1161,35428,1617],{},[1165,35430,1188],{},[1165,35432,1317],{},[2256,35434,35435,35437,35439],{},[1161,35436,1617],{},[1161,35438,1110],{},[1165,35440,34836],{},[1194,35442,35443],{"encoding":1196},"t \\le -t_p^*",[1110,35445,35446,35447,34509,35465,1333],{},"Postup je dvoukrokový: nejprve F-test rozhodne o shodě rozptylů, pak se podle výsledku zvolí ",[1115,35448,35450],{"className":35449},[1149],[1151,35451,35452],{"xmlns":1153},[1155,35453,35454,35462],{},[1158,35455,35456],{},[1277,35457,35458,35460],{},[1161,35459,1575],{},[1282,35461,1284],{},[1194,35463,35464],{"encoding":1196},"T_1",[1115,35466,35468],{"className":35467},[1149],[1151,35469,35470],{"xmlns":1153},[1155,35471,35472,35480],{},[1158,35473,35474],{},[1277,35475,35476,35478],{},[1161,35477,1575],{},[1282,35479,1298],{},[1194,35481,35482],{"encoding":1196},"T_2",[1110,35484,35485],{},[1760,35486],{"alt":35487,"className":35488,"src":35489},"mask-th-f-kriticky-obor",[1441,1764],"\u002Fwiki-assets\u002Fmask-th-f-kriticky-obor.png",[1103,35491,35493,35500,35650,35731,35860,35898,35971,36110],{"className":35492,"dataCallout":3670},[1106,3669],[1110,35494,35496,35499],{"className":35495},[1113],[1115,35497],{"className":35498,"ariaHidden":1121},[1118,3677,1120],"Příklad: Porovnání dvou dodavatelů součástek",[1110,35501,35502,35503,1376,35525,35551,35552,35576,35577,1376,35599,35551,35625,35649],{},"Pevnost plastových dílů: dodavatel A (",[1115,35504,35506],{"className":35505},[1149],[1151,35507,35508],{"xmlns":1153},[1155,35509,35510,35522],{},[1158,35511,35512,35518,35520],{},[1277,35513,35514,35516],{},[1161,35515,4192],{},[1282,35517,1284],{},[1165,35519,1177],{},[1282,35521,3531],{},[1194,35523,35524],{"encoding":1196},"n_1 = 10",[1115,35526,35528],{"className":35527},[1149],[1151,35529,35530],{"xmlns":1153},[1155,35531,35532,35548],{},[1158,35533,35534,35544,35546],{},[1277,35535,35536,35542],{},[6877,35537,35538,35540],{"accent":1121},[1161,35539,1171],{},[1165,35541,15130],{},[1282,35543,1284],{},[1165,35545,1177],{},[1282,35547,7772],{},[1194,35549,35550],{"encoding":1196},"\\bar{x}_1 = 82"," MPa, ",[1115,35553,35555],{"className":35554},[1149],[1151,35556,35557],{"xmlns":1153},[1155,35558,35559,35573],{},[1158,35560,35561,35569,35571],{},[2256,35562,35563,35565,35567],{},[1161,35564,6018],{},[1282,35566,1284],{},[1282,35568,1298],{},[1165,35570,1177],{},[1282,35572,8188],{},[1194,35574,35575],{"encoding":1196},"s_1^2 = 25","), dodavatel B (",[1115,35578,35580],{"className":35579},[1149],[1151,35581,35582],{"xmlns":1153},[1155,35583,35584,35596],{},[1158,35585,35586,35592,35594],{},[1277,35587,35588,35590],{},[1161,35589,4192],{},[1282,35591,1298],{},[1165,35593,1177],{},[1282,35595,6429],{},[1194,35597,35598],{"encoding":1196},"n_2 = 12",[1115,35600,35602],{"className":35601},[1149],[1151,35603,35604],{"xmlns":1153},[1155,35605,35606,35622],{},[1158,35607,35608,35618,35620],{},[1277,35609,35610,35616],{},[6877,35611,35612,35614],{"accent":1121},[1161,35613,1171],{},[1165,35615,15130],{},[1282,35617,1298],{},[1165,35619,1177],{},[1282,35621,18403],{},[1194,35623,35624],{"encoding":1196},"\\bar{x}_2 = 75",[1115,35626,35628],{"className":35627},[1149],[1151,35629,35630],{"xmlns":1153},[1155,35631,35632,35646],{},[1158,35633,35634,35642,35644],{},[2256,35635,35636,35638,35640],{},[1161,35637,6018],{},[1282,35639,1298],{},[1282,35641,1298],{},[1165,35643,1177],{},[1282,35645,25699],{},[1194,35647,35648],{"encoding":1196},"s_2^2 = 16","). Předpokládá se normalita obou rozdělení.",[1110,35651,35652,1145,35655,1376,35693,1333],{},[1131,35653,35654],{},"Krok 1 — F-test rozptylů.",[1115,35656,35658],{"className":35657},[1149],[1151,35659,35660],{"xmlns":1153},[1155,35661,35662,35690],{},[1158,35663,35664,35670,35672,35680,35682],{},[1277,35665,35666,35668],{},[1161,35667,4318],{},[1282,35669,1982],{},[1165,35671,2629],{},[2256,35673,35674,35676,35678],{},[1161,35675,1363],{},[1282,35677,1284],{},[1282,35679,1298],{},[1165,35681,1177],{},[2256,35683,35684,35686,35688],{},[1161,35685,1363],{},[1282,35687,1298],{},[1282,35689,1298],{},[1194,35691,35692],{"encoding":1196},"H_0: \\sigma_1^2 = \\sigma_2^2",[1115,35694,35696],{"className":35695},[1149],[1151,35697,35698],{"xmlns":1153},[1155,35699,35700,35728],{},[1158,35701,35702,35708,35710,35718,35720],{},[1277,35703,35704,35706],{},[1161,35705,4318],{},[1282,35707,1284],{},[1165,35709,2629],{},[2256,35711,35712,35714,35716],{},[1161,35713,1363],{},[1282,35715,1284],{},[1282,35717,1298],{},[1165,35719,5496],{"mathvariant":1215},[2256,35721,35722,35724,35726],{},[1161,35723,1363],{},[1282,35725,1298],{},[1282,35727,1298],{},[1194,35729,35730],{"encoding":1196},"H_1: \\sigma_1^2 \\neq \\sigma_2^2",[1110,35732,35733],{},[1115,35734,35736],{"className":35735},[1149],[1151,35737,35738],{"xmlns":1153},[1155,35739,35740,35857],{},[1158,35741,35742,35744,35746,35752,35754,35757,35759,35761,35763,35765,35767,35769,35771,35784,35786,35788,35790,35792,35794,35797,35800,35802,35804,35806,35819,35821,35823,35825,35827,35829,35831,35833,35835,35837,35839,35842,35844,35846,35848,35850,35852,35855],{},[1161,35743,1163],{},[1165,35745,1177],{},[3064,35747,35748,35750],{},[1282,35749,8188],{},[1282,35751,25699],{},[1165,35753,1177],{},[1282,35755,35756],{},"1,5625",[1165,35758,1715],{"separator":1121},[2242,35760],{"width":2244},[1161,35762,5777],{},[1165,35764,1177],{},[1165,35766,7484],{"stretchy":1167},[1161,35768,1163],{},[1165,35770,1188],{},[1277,35772,35773,35775],{},[1161,35774,1163],{},[1158,35776,35777,35779,35781],{},[1282,35778,1982],{},[1165,35780,1715],{"separator":1121},[1282,35782,35783],{},"025",[1165,35785,1168],{"stretchy":1167},[1282,35787,7739],{},[1165,35789,1715],{"separator":1121},[1282,35791,6408],{},[1165,35793,1174],{"stretchy":1167},[2278,35795,35796],{},"  ",[2278,35798,35799],{},"nebo",[2278,35801,35796],{},[1161,35803,1163],{},[1165,35805,7501],{},[1277,35807,35808,35810],{},[1161,35809,1163],{},[1158,35811,35812,35814,35816],{},[1282,35813,1982],{},[1165,35815,1715],{"separator":1121},[1282,35817,35818],{},"975",[1165,35820,1168],{"stretchy":1167},[1282,35822,7739],{},[1165,35824,1715],{"separator":1121},[1282,35826,6408],{},[1165,35828,1174],{"stretchy":1167},[1165,35830,7543],{"stretchy":1167},[1165,35832,1177],{},[1165,35834,7484],{"stretchy":1167},[1161,35836,1163],{},[1165,35838,1188],{},[1282,35840,35841],{},"0,256",[2278,35843,35796],{},[2278,35845,35799],{},[2278,35847,35796],{},[1161,35849,1163],{},[1165,35851,7501],{},[1282,35853,35854],{},"3,588",[1165,35856,7543],{"stretchy":1167},[1194,35858,35859],{"encoding":1196},"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\\}",[1110,35861,35862,35880,35881,1333],{},[1115,35863,35865],{"className":35864},[1149],[1151,35866,35867],{"xmlns":1153},[1155,35868,35869,35877],{},[1158,35870,35871,35873,35875],{},[1161,35872,1163],{},[1165,35874,30946],{"mathvariant":1215},[1161,35876,5777],{},[1194,35878,35879],{"encoding":1196},"F \\notin W",", rozptyly nezamítáme jako shodné — pro t-test se použije ",[1115,35882,35884],{"className":35883},[1149],[1151,35885,35886],{"xmlns":1153},[1155,35887,35888,35896],{},[1158,35889,35890],{},[1277,35891,35892,35894],{},[1161,35893,1575],{},[1282,35895,1284],{},[1194,35897,35464],{"encoding":1196},[1110,35899,35900,1145,35903,1376,35937,1333],{},[1131,35901,35902],{},"Krok 2 — dvouvýběrový t-test středních hodnot.",[1115,35904,35906],{"className":35905},[1149],[1151,35907,35908],{"xmlns":1153},[1155,35909,35910,35934],{},[1158,35911,35912,35918,35920,35926,35928],{},[1277,35913,35914,35916],{},[1161,35915,4318],{},[1282,35917,1982],{},[1165,35919,2629],{},[1277,35921,35922,35924],{},[1161,35923,1355],{},[1282,35925,1284],{},[1165,35927,1177],{},[1277,35929,35930,35932],{},[1161,35931,1355],{},[1282,35933,1298],{},[1194,35935,35936],{"encoding":1196},"H_0: \\mu_1 = \\mu_2",[1115,35938,35940],{"className":35939},[1149],[1151,35941,35942],{"xmlns":1153},[1155,35943,35944,35968],{},[1158,35945,35946,35952,35954,35960,35962],{},[1277,35947,35948,35950],{},[1161,35949,4318],{},[1282,35951,1284],{},[1165,35953,2629],{},[1277,35955,35956,35958],{},[1161,35957,1355],{},[1282,35959,1284],{},[1165,35961,5496],{"mathvariant":1215},[1277,35963,35964,35966],{},[1161,35965,1355],{},[1282,35967,1298],{},[1194,35969,35970],{"encoding":1196},"H_1: \\mu_1 \\neq \\mu_2",[1110,35972,35973],{},[1115,35974,35976],{"className":35975},[1149],[1151,35977,35978],{"xmlns":1153},[1155,35979,35980,36107],{},[1158,35981,35982,35990,35992,36012,36014,36017,36019,36021,36023,36025,36039,36047,36049,36052,36054,36056,36058,36060,36062,36064,36066,36068,36070,36082,36084,36086,36088,36090,36092,36094,36096,36098,36100,36102,36105],{},[2256,35983,35984,35986,35988],{},[1161,35985,6018],{},[1161,35987,1110],{},[1282,35989,1298],{},[1165,35991,1177],{},[3064,35993,35994,36010],{},[1158,35995,35996,35998,36000,36002,36004,36006,36008],{},[1282,35997,7739],{},[1165,35999,2598],{},[1282,36001,8188],{},[1165,36003,2094],{},[1282,36005,6408],{},[1165,36007,2598],{},[1282,36009,25699],{},[1282,36011,8175],{},[1165,36013,1177],{},[1282,36015,36016],{},"20,05",[1165,36018,1715],{"separator":1121},[2242,36020],{"width":2244},[1161,36022,1617],{},[1165,36024,1177],{},[3064,36026,36027,36035],{},[1158,36028,36029,36031,36033],{},[1282,36030,7772],{},[1165,36032,1317],{},[1282,36034,18403],{},[2765,36036,36037],{},[1282,36038,36016],{},[2765,36040,36041],{},[3064,36042,36043,36045],{},[1282,36044,25559],{},[1282,36046,6543],{},[1165,36048,3957],{},[1282,36050,36051],{},"3,651",[1165,36053,1715],{"separator":1121},[2242,36055],{"width":2244},[1161,36057,5777],{},[1165,36059,1177],{},[1165,36061,7484],{"stretchy":1167},[1165,36063,26697],{"stretchy":1167},[1161,36065,1617],{},[1165,36067,26697],{"stretchy":1167},[1165,36069,7501],{},[1277,36071,36072,36074],{},[1161,36073,1617],{},[1158,36075,36076,36078,36080],{},[1282,36077,1982],{},[1165,36079,1715],{"separator":1121},[1282,36081,35818],{},[1165,36083,1168],{"stretchy":1167},[1282,36085,8175],{},[1165,36087,1174],{"stretchy":1167},[1165,36089,7543],{"stretchy":1167},[1165,36091,1177],{},[1165,36093,7484],{"stretchy":1167},[1165,36095,26697],{"stretchy":1167},[1161,36097,1617],{},[1165,36099,26697],{"stretchy":1167},[1165,36101,7501],{},[1282,36103,36104],{},"2,086",[1165,36106,7543],{"stretchy":1167},[1194,36108,36109],{"encoding":1196},"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\\}",[1110,36111,36112,10124,36129,36146],{},[1115,36113,36115],{"className":36114},[1149],[1151,36116,36117],{"xmlns":1153},[1155,36118,36119,36127],{},[1158,36120,36121,36123,36125],{},[1161,36122,1617],{},[1165,36124,1492],{},[1161,36126,5777],{},[1194,36128,32089],{"encoding":1196},[1115,36130,36132],{"className":36131},[1149],[1151,36133,36134],{"xmlns":1153},[1155,36135,36136,36144],{},[1158,36137,36138],{},[1277,36139,36140,36142],{},[1161,36141,4318],{},[1282,36143,1982],{},[1194,36145,5745],{"encoding":1196},": pevnost součástek od obou dodavatelů se statisticky významně liší.",[3554,36148,36150],{"className":3556,"code":36149,"language":71,"meta":3558,"style":3558},"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",[1373,36151,36152,36170,36190,36205,36240,36271,36276,36281],{"__ignoreMap":3558},[1115,36153,36154,36157,36159,36161,36163,36166,36168],{"class":3563,"line":10},[1115,36155,36156],{"class":3744},"s1",[1115,36158,4497],{"class":3741},[1115,36160,18073],{"class":3572},[1115,36162,28857],{"class":3569},[1115,36164,36165],{"class":3744},"n1",[1115,36167,4497],{"class":3741},[1115,36169,33530],{"class":3572},[1115,36171,36172,36175,36177,36180,36182,36185,36187],{"class":3563,"line":27},[1115,36173,36174],{"class":3744},"s2",[1115,36176,4497],{"class":3741},[1115,36178,36179],{"class":3572}," 16",[1115,36181,28857],{"class":3569},[1115,36183,36184],{"class":3744},"n2",[1115,36186,4497],{"class":3741},[1115,36188,36189],{"class":3572}," 12\n",[1115,36191,36192,36195,36197,36200,36202],{"class":3563,"line":148},[1115,36193,36194],{"class":3744},"Fstat",[1115,36196,4497],{"class":3741},[1115,36198,36199],{"class":3744}," s1",[1115,36201,4608],{"class":3741},[1115,36203,36204],{"class":3744}," s2\n",[1115,36206,36207,36210,36212,36215,36217,36220,36222,36225,36227,36229,36231,36234,36236,36238],{"class":3563,"line":111},[1115,36208,36209],{"class":3744},"F_dolni",[1115,36211,4497],{"class":3741},[1115,36213,36214],{"class":3566}," qf",[1115,36216,1168],{"class":3569},[1115,36218,36219],{"class":3572},"0.025",[1115,36221,1715],{"class":3741},[1115,36223,36224],{"class":3744}," n1",[1115,36226,29194],{"class":3741},[1115,36228,4605],{"class":3572},[1115,36230,1715],{"class":3741},[1115,36232,36233],{"class":3744}," n2",[1115,36235,29194],{"class":3741},[1115,36237,4605],{"class":3572},[1115,36239,3575],{"class":3569},[1115,36241,36242,36245,36247,36249,36251,36253,36255,36257,36259,36261,36263,36265,36267,36269],{"class":3563,"line":96},[1115,36243,36244],{"class":3744},"F_horni",[1115,36246,4497],{"class":3741},[1115,36248,36214],{"class":3566},[1115,36250,1168],{"class":3569},[1115,36252,3595],{"class":3572},[1115,36254,1715],{"class":3741},[1115,36256,36224],{"class":3744},[1115,36258,29194],{"class":3741},[1115,36260,4605],{"class":3572},[1115,36262,1715],{"class":3741},[1115,36264,36233],{"class":3744},[1115,36266,29194],{"class":3741},[1115,36268,4605],{"class":3572},[1115,36270,3575],{"class":3569},[1115,36272,36273],{"class":3563,"line":89},[1115,36274,36275],{"class":3744},"Fstat\n",[1115,36277,36278],{"class":3563,"line":82},[1115,36279,36280],{"class":3744},"F_dolni\n",[1115,36282,36283],{"class":3563,"line":75},[1115,36284,36285],{"class":3744},"F_horni\n",[3554,36287,36290],{"className":36288,"code":36289,"language":3603,"meta":3558},[3601],"[1] 1.5625\n[1] 0.2556189\n[1] 3.587899\n",[1373,36291,36289],{"__ignoreMap":3558},[3554,36293,36295],{"className":3556,"code":36294,"language":71,"meta":3558,"style":3558},"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",[1373,36296,36297,36354,36405,36435,36440,36444],{"__ignoreMap":3558},[1115,36298,36299,36302,36304,36307,36309,36311,36313,36315,36317,36319,36321,36323,36325,36327,36329,36331,36333,36336,36338,36340,36342,36344,36346,36348,36350,36352],{"class":3563,"line":10},[1115,36300,36301],{"class":3744},"sp2",[1115,36303,4497],{"class":3741},[1115,36305,36306],{"class":3569}," ((",[1115,36308,36165],{"class":3744},[1115,36310,29194],{"class":3741},[1115,36312,4605],{"class":3572},[1115,36314,3862],{"class":3569},[1115,36316,8740],{"class":3741},[1115,36318,36199],{"class":3744},[1115,36320,22187],{"class":3741},[1115,36322,8728],{"class":3569},[1115,36324,36184],{"class":3744},[1115,36326,29194],{"class":3741},[1115,36328,4605],{"class":3572},[1115,36330,3862],{"class":3569},[1115,36332,8740],{"class":3741},[1115,36334,36335],{"class":3744}," s2",[1115,36337,3862],{"class":3569},[1115,36339,3434],{"class":3741},[1115,36341,8728],{"class":3569},[1115,36343,36165],{"class":3744},[1115,36345,22187],{"class":3741},[1115,36347,36233],{"class":3744},[1115,36349,29194],{"class":3741},[1115,36351,8310],{"class":3572},[1115,36353,3575],{"class":3569},[1115,36355,36356,36358,36360,36362,36364,36366,36369,36371,36373,36375,36377,36379,36381,36383,36385,36387,36389,36391,36393,36395,36397,36399,36401,36403],{"class":3563,"line":27},[1115,36357,1617],{"class":3744},[1115,36359,4497],{"class":3741},[1115,36361,8728],{"class":3569},[1115,36363,7772],{"class":3572},[1115,36365,29194],{"class":3741},[1115,36367,36368],{"class":3572}," 75",[1115,36370,3862],{"class":3569},[1115,36372,3434],{"class":3741},[1115,36374,4003],{"class":3566},[1115,36376,1168],{"class":3569},[1115,36378,36301],{"class":3744},[1115,36380,3862],{"class":3569},[1115,36382,8740],{"class":3741},[1115,36384,4003],{"class":3566},[1115,36386,1168],{"class":3569},[1115,36388,36165],{"class":3744},[1115,36390,22312],{"class":3741},[1115,36392,36233],{"class":3744},[1115,36394,4608],{"class":3741},[1115,36396,8728],{"class":3569},[1115,36398,36165],{"class":3744},[1115,36400,22187],{"class":3741},[1115,36402,36233],{"class":3744},[1115,36404,4011],{"class":3569},[1115,36406,36407,36409,36411,36413,36415,36417,36419,36421,36423,36425,36427,36429,36431,36433],{"class":3563,"line":148},[1115,36408,32196],{"class":3744},[1115,36410,4497],{"class":3741},[1115,36412,32201],{"class":3566},[1115,36414,1168],{"class":3569},[1115,36416,3595],{"class":3572},[1115,36418,1715],{"class":3741},[1115,36420,5347],{"class":3744},[1115,36422,3748],{"class":3741},[1115,36424,36224],{"class":3744},[1115,36426,22187],{"class":3741},[1115,36428,36233],{"class":3744},[1115,36430,29194],{"class":3741},[1115,36432,8310],{"class":3572},[1115,36434,3575],{"class":3569},[1115,36436,36437],{"class":3563,"line":111},[1115,36438,36439],{"class":3744},"sp2\n",[1115,36441,36442],{"class":3563,"line":96},[1115,36443,32226],{"class":3744},[1115,36445,36446],{"class":3563,"line":89},[1115,36447,32231],{"class":3744},[3554,36449,36452],{"className":36450,"code":36451,"language":3603,"meta":3558},[3601],"[1] 20.05\n[1] 3.65107\n[1] 2.085963\n",[1373,36453,36451],{"__ignoreMap":3558},[1110,36455,36456],{},[1760,36457],{"alt":36458,"className":36459,"src":36460},"mask-th-t-dvoustranny",[1441,1764],"\u002Fwiki-assets\u002Fmask-th-t-dvoustranny.png",[1110,36462,36463,36464,1425,36467,36469,36470,36473,36474,1425,36491,8118,36508,36510,36511,36513],{},"V R provede obě kroky ",[1373,36465,36466],{},"var.test()",[1373,36468,31686],{},". Parametr ",[1373,36471,36472],{},"var.equal"," nastavuje volbu mezi ",[1115,36475,36477],{"className":36476},[1149],[1151,36478,36479],{"xmlns":1153},[1155,36480,36481,36489],{},[1158,36482,36483],{},[1277,36484,36485,36487],{},[1161,36486,1575],{},[1282,36488,1284],{},[1194,36490,35464],{"encoding":1196},[1115,36492,36494],{"className":36493},[1149],[1151,36495,36496],{"xmlns":1153},[1155,36497,36498,36506],{},[1158,36499,36500],{},[1277,36501,36502,36504],{},[1161,36503,1575],{},[1282,36505,1298],{},[1194,36507,35482],{"encoding":1196},[1373,36509,4042],{}," znamená předpoklad shodných rozptylů (podle výsledku F-testu), ",[1373,36512,4045],{}," předpoklad rozdílných rozptylů.",[1110,36515,36516,36519],{},[1131,36517,36518],{},"Kabely A\u002FB."," Pevnost v tahu dvou výrobců (MPa, 12 kabelů od každého):",[3554,36521,36523],{"className":3556,"code":36522,"language":71,"meta":3558,"style":3558},"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",[1373,36524,36525,36591,36654,36670],{"__ignoreMap":3558},[1115,36526,36527,36529,36531,36533,36535,36538,36540,36543,36545,36548,36550,36553,36555,36557,36559,36562,36564,36567,36569,36571,36573,36576,36578,36580,36582,36585,36587,36589],{"class":3563,"line":10},[1115,36528,5942],{"class":3744},[1115,36530,4497],{"class":3741},[1115,36532,7969],{"class":3566},[1115,36534,1168],{"class":3569},[1115,36536,36537],{"class":3572},"313",[1115,36539,1715],{"class":3741},[1115,36541,36542],{"class":3572}," 299",[1115,36544,1715],{"class":3741},[1115,36546,36547],{"class":3572}," 315",[1115,36549,1715],{"class":3741},[1115,36551,36552],{"class":3572}," 312",[1115,36554,1715],{"class":3741},[1115,36556,19041],{"class":3572},[1115,36558,1715],{"class":3741},[1115,36560,36561],{"class":3572}," 308",[1115,36563,1715],{"class":3741},[1115,36565,36566],{"class":3572}," 314",[1115,36568,1715],{"class":3741},[1115,36570,17833],{"class":3572},[1115,36572,1715],{"class":3741},[1115,36574,36575],{"class":3572}," 305",[1115,36577,1715],{"class":3741},[1115,36579,19041],{"class":3572},[1115,36581,1715],{"class":3741},[1115,36583,36584],{"class":3572}," 309",[1115,36586,1715],{"class":3741},[1115,36588,36566],{"class":3572},[1115,36590,3575],{"class":3569},[1115,36592,36593,36595,36597,36599,36601,36604,36606,36609,36611,36613,36615,36617,36619,36622,36624,36627,36629,36631,36633,36635,36637,36639,36641,36644,36646,36648,36650,36652],{"class":3563,"line":27},[1115,36594,4184],{"class":3744},[1115,36596,4497],{"class":3741},[1115,36598,7969],{"class":3566},[1115,36600,1168],{"class":3569},[1115,36602,36603],{"class":3572},"307",[1115,36605,1715],{"class":3741},[1115,36607,36608],{"class":3572}," 322",[1115,36610,1715],{"class":3741},[1115,36612,17833],{"class":3572},[1115,36614,1715],{"class":3741},[1115,36616,17833],{"class":3572},[1115,36618,1715],{"class":3741},[1115,36620,36621],{"class":3572}," 311",[1115,36623,1715],{"class":3741},[1115,36625,36626],{"class":3572}," 316",[1115,36628,1715],{"class":3741},[1115,36630,36547],{"class":3572},[1115,36632,1715],{"class":3741},[1115,36634,36566],{"class":3572},[1115,36636,1715],{"class":3741},[1115,36638,36561],{"class":3572},[1115,36640,1715],{"class":3741},[1115,36642,36643],{"class":3572}," 319",[1115,36645,1715],{"class":3741},[1115,36647,17833],{"class":3572},[1115,36649,1715],{"class":3741},[1115,36651,36552],{"class":3572},[1115,36653,3575],{"class":3569},[1115,36655,36656,36659,36661,36663,36665,36668],{"class":3563,"line":148},[1115,36657,36658],{"class":3566},"var.test",[1115,36660,1168],{"class":3569},[1115,36662,5942],{"class":3744},[1115,36664,1715],{"class":3741},[1115,36666,36667],{"class":3744}," B",[1115,36669,3575],{"class":3569},[1115,36671,36672,36674,36676,36678,36680,36682,36684,36687,36689,36691],{"class":3563,"line":111},[1115,36673,31751],{"class":3566},[1115,36675,1168],{"class":3569},[1115,36677,5942],{"class":3744},[1115,36679,1715],{"class":3741},[1115,36681,36667],{"class":3744},[1115,36683,1715],{"class":3741},[1115,36685,36686],{"class":3744}," var.equal",[1115,36688,3748],{"class":3741},[1115,36690,7944],{"class":3572},[1115,36692,3575],{"class":3569},[3554,36694,36697],{"className":36695,"code":36696,"language":3603,"meta":3558},[3601],"    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",[1373,36698,36696],{"__ignoreMap":3558},[1110,36700,36701,36702,15725,36721,36724,36725,36744,36745,36762],{},"F-test shodu rozptylů nezamítá (",[1115,36703,36705],{"className":36704},[1149],[1151,36706,36707],{"xmlns":1153},[1155,36708,36709,36718],{},[1158,36710,36711,36713,36715],{},[1161,36712,1110],{},[1165,36714,1177],{},[1282,36716,36717],{},"0,7776",[1194,36719,36720],{"encoding":1196},"p = 0{,}7776",[1373,36722,36723],{},"var.equal = TRUE",". Výsledný t-test dává ",[1115,36726,36728],{"className":36727},[1149],[1151,36729,36730],{"xmlns":1153},[1155,36731,36732,36741],{},[1158,36733,36734,36736,36738],{},[1161,36735,1110],{},[1165,36737,1177],{},[1282,36739,36740],{},"0,06932",[1194,36742,36743],{"encoding":1196},"p = 0{,}06932"," — na hladině 5 % se ",[1115,36746,36748],{"className":36747},[1149],[1151,36749,36750],{"xmlns":1153},[1155,36751,36752,36760],{},[1158,36753,36754],{},[1277,36755,36756,36758],{},[1161,36757,4318],{},[1282,36759,1982],{},[1194,36761,5745],{"encoding":1196}," nezamítá, ale hodnota je těsně nad hranicí.",[1110,36764,36765],{},[1131,36766,36767],{},"Výšky chlapců a dívek v páté třídě:",[3554,36769,36771],{"className":3556,"code":36770,"language":71,"meta":3558,"style":3558},"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",[1373,36772,36773,36853,36916,36931],{"__ignoreMap":3558},[1115,36774,36775,36778,36780,36782,36784,36787,36789,36791,36793,36796,36798,36801,36803,36806,36808,36811,36813,36815,36817,36819,36821,36823,36825,36827,36829,36832,36834,36837,36839,36842,36844,36846,36848,36851],{"class":3563,"line":10},[1115,36776,36777],{"class":3744},"boys",[1115,36779,4497],{"class":3741},[1115,36781,7969],{"class":3566},[1115,36783,1168],{"class":3569},[1115,36785,36786],{"class":3572},"130",[1115,36788,1715],{"class":3741},[1115,36790,18990],{"class":3572},[1115,36792,1715],{"class":3741},[1115,36794,36795],{"class":3572}," 136",[1115,36797,1715],{"class":3741},[1115,36799,36800],{"class":3572}," 141",[1115,36802,1715],{"class":3741},[1115,36804,36805],{"class":3572}," 139",[1115,36807,1715],{"class":3741},[1115,36809,36810],{"class":3572}," 133",[1115,36812,1715],{"class":3741},[1115,36814,22144],{"class":3572},[1115,36816,1715],{"class":3741},[1115,36818,17848],{"class":3572},[1115,36820,1715],{"class":3741},[1115,36822,36805],{"class":3572},[1115,36824,1715],{"class":3741},[1115,36826,36795],{"class":3572},[1115,36828,1715],{"class":3741},[1115,36830,36831],{"class":3572}," 138",[1115,36833,1715],{"class":3741},[1115,36835,36836],{"class":3572}," 142",[1115,36838,1715],{"class":3741},[1115,36840,36841],{"class":3572}," 127",[1115,36843,1715],{"class":3741},[1115,36845,36805],{"class":3572},[1115,36847,1715],{"class":3741},[1115,36849,36850],{"class":3572}," 147",[1115,36852,3575],{"class":3569},[1115,36854,36855,36858,36860,36862,36864,36866,36868,36870,36872,36875,36877,36880,36882,36885,36887,36889,36891,36893,36895,36897,36899,36901,36903,36906,36908,36910,36912,36914],{"class":3563,"line":27},[1115,36856,36857],{"class":3744},"girls",[1115,36859,4497],{"class":3741},[1115,36861,7969],{"class":3566},[1115,36863,1168],{"class":3569},[1115,36865,25510],{"class":3572},[1115,36867,1715],{"class":3741},[1115,36869,36800],{"class":3572},[1115,36871,1715],{"class":3741},[1115,36873,36874],{"class":3572}," 143",[1115,36876,1715],{"class":3741},[1115,36878,36879],{"class":3572}," 132",[1115,36881,1715],{"class":3741},[1115,36883,36884],{"class":3572}," 146",[1115,36886,1715],{"class":3741},[1115,36888,36884],{"class":3572},[1115,36890,1715],{"class":3741},[1115,36892,17848],{"class":3572},[1115,36894,1715],{"class":3741},[1115,36896,36800],{"class":3572},[1115,36898,1715],{"class":3741},[1115,36900,36800],{"class":3572},[1115,36902,1715],{"class":3741},[1115,36904,36905],{"class":3572}," 131",[1115,36907,1715],{"class":3741},[1115,36909,36836],{"class":3572},[1115,36911,1715],{"class":3741},[1115,36913,36800],{"class":3572},[1115,36915,3575],{"class":3569},[1115,36917,36918,36920,36922,36924,36926,36929],{"class":3563,"line":148},[1115,36919,36658],{"class":3566},[1115,36921,1168],{"class":3569},[1115,36923,36777],{"class":3744},[1115,36925,1715],{"class":3741},[1115,36927,36928],{"class":3744}," girls",[1115,36930,3575],{"class":3569},[1115,36932,36933,36935,36937,36939,36941,36943,36945,36947,36949,36951],{"class":3563,"line":111},[1115,36934,31751],{"class":3566},[1115,36936,1168],{"class":3569},[1115,36938,36777],{"class":3744},[1115,36940,1715],{"class":3741},[1115,36942,36928],{"class":3744},[1115,36944,1715],{"class":3741},[1115,36946,36686],{"class":3744},[1115,36948,3748],{"class":3741},[1115,36950,7944],{"class":3572},[1115,36952,3575],{"class":3569},[3554,36954,36957],{"className":36955,"code":36956,"language":3603,"meta":3558},[3601],"    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",[1373,36958,36956],{"__ignoreMap":3558},[1110,36960,36701,36961,36980,36981,36983,36984,37003],{},[1115,36962,36964],{"className":36963},[1149],[1151,36965,36966],{"xmlns":1153},[1155,36967,36968,36977],{},[1158,36969,36970,36972,36974],{},[1161,36971,1110],{},[1165,36973,1177],{},[1282,36975,36976],{},"0,6977",[1194,36978,36979],{"encoding":1196},"p = 0{,}6977","), t-test s ",[1373,36982,36723],{}," dává ",[1115,36985,36987],{"className":36986},[1149],[1151,36988,36989],{"xmlns":1153},[1155,36990,36991,37000],{},[1158,36992,36993,36995,36997],{},[1161,36994,1110],{},[1165,36996,1177],{},[1282,36998,36999],{},"0,4883",[1194,37001,37002],{"encoding":1196},"p = 0{,}4883",": na hladině 5 % se rozdíl průměrných výšek chlapců a dívek neprokázal.",[1431,37005,37007],{"id":37006},"testy-dobré-shody-a-normalita","Testy dobré shody a normalita",[1110,37009,37010],{},"Testy dobré shody ověřují, zda datový soubor pochází ze základního souboru s určitým typem rozdělení (normální, exponenciální apod.).",[20418,37012,37014],{"id":37013},"kolmogorovův-smirnovův-test","Kolmogorovův-Smirnovův test",[1110,37016,37017,37018,37041,37042,37061],{},"Univerzální test pro spojitá rozdělení. Porovnává empirickou distribuční funkci ",[1115,37019,37021],{"className":37020},[1149],[1151,37022,37023],{"xmlns":1153},[1155,37024,37025,37039],{},[1158,37026,37027,37033,37035,37037],{},[1277,37028,37029,37031],{},[1161,37030,1163],{},[1161,37032,4192],{},[1165,37034,1168],{"stretchy":1167},[1161,37036,1171],{},[1165,37038,1174],{"stretchy":1167},[1194,37040,14854],{"encoding":1196}," s teoretickou distribuční funkcí ",[1115,37043,37045],{"className":37044},[1149],[1151,37046,37047],{"xmlns":1153},[1155,37048,37049,37059],{},[1158,37050,37051,37053,37055,37057],{},[1161,37052,1163],{},[1165,37054,1168],{"stretchy":1167},[1161,37056,1171],{},[1165,37058,1174],{"stretchy":1167},[1194,37060,1813],{"encoding":1196}," testovaného rozdělení.",[1124,37063,37064,37127,37147,37203],{},[1127,37065,37066,37083,37084,1425,37107,37126],{},[1115,37067,37069],{"className":37068},[1149],[1151,37070,37071],{"xmlns":1153},[1155,37072,37073,37081],{},[1158,37074,37075],{},[1277,37076,37077,37079],{},[1161,37078,4318],{},[1282,37080,1982],{},[1194,37082,5745],{"encoding":1196},": odchylky mezi ",[1115,37085,37087],{"className":37086},[1149],[1151,37088,37089],{"xmlns":1153},[1155,37090,37091,37105],{},[1158,37092,37093,37099,37101,37103],{},[1277,37094,37095,37097],{},[1161,37096,1163],{},[1161,37098,4192],{},[1165,37100,1168],{"stretchy":1167},[1161,37102,1171],{},[1165,37104,1174],{"stretchy":1167},[1194,37106,14854],{"encoding":1196},[1115,37108,37110],{"className":37109},[1149],[1151,37111,37112],{"xmlns":1153},[1155,37113,37114,37124],{},[1158,37115,37116,37118,37120,37122],{},[1161,37117,1163],{},[1165,37119,1168],{"stretchy":1167},[1161,37121,1171],{},[1165,37123,1174],{"stretchy":1167},[1194,37125,1813],{"encoding":1196}," jsou náhodné (data mají dané rozdělení).",[1127,37128,37129,37146],{},[1115,37130,37132],{"className":37131},[1149],[1151,37133,37134],{"xmlns":1153},[1155,37135,37136,37144],{},[1158,37137,37138],{},[1277,37139,37140,37142],{},[1161,37141,4318],{},[1282,37143,1284],{},[1194,37145,7147],{"encoding":1196},": data nemají dané rozdělení.",[1127,37148,37149,37150,1333],{},"Testové kritérium: ",[1115,37151,37153],{"className":37152},[1149],[1151,37154,37155],{"xmlns":1153},[1155,37156,37157,37200],{},[1158,37158,37159,37161,37163,37174,37176,37182,37184,37186,37188,37190,37192,37194,37196,37198],{},[1161,37160,2641],{},[1165,37162,1177],{},[1277,37164,37165,37172],{},[1158,37166,37167,37170],{},[1161,37168,37169],{},"sup",[1165,37171,2079],{},[1161,37173,1171],{},[1165,37175,26697],{"stretchy":1167},[1277,37177,37178,37180],{},[1161,37179,1163],{},[1161,37181,4192],{},[1165,37183,1168],{"stretchy":1167},[1161,37185,1171],{},[1165,37187,1174],{"stretchy":1167},[1165,37189,1317],{},[1161,37191,1163],{},[1165,37193,1168],{"stretchy":1167},[1161,37195,1171],{},[1165,37197,1174],{"stretchy":1167},[1165,37199,26697],{"stretchy":1167},[1194,37201,37202],{"encoding":1196},"D = \\sup_x \\lvert F_n(x) - F(x) \\rvert",[1127,37204,7468,37205,37249,37250,37268,37269,1333],{},[1115,37206,37208],{"className":37207},[1149],[1151,37209,37210],{"xmlns":1153},[1155,37211,37212,37246],{},[1158,37213,37214,37220,37222,37224,37226,37228,37230,37232,37238,37240,37242,37244],{},[1277,37215,37216,37218],{},[1161,37217,5777],{},[1161,37219,7514],{},[1165,37221,1177],{},[1165,37223,7484],{"stretchy":1167},[1161,37225,2283],{},[1165,37227,2629],{},[1161,37229,2283],{},[1165,37231,4156],{},[1277,37233,37234,37236],{},[1161,37235,2641],{},[1161,37237,7514],{},[1165,37239,1168],{"stretchy":1167},[1161,37241,4192],{},[1165,37243,1174],{"stretchy":1167},[1165,37245,7543],{"stretchy":1167},[1194,37247,37248],{"encoding":1196},"W_\\alpha = \\{d : d > D_\\alpha(n)\\}","; pro ",[1115,37251,37253],{"className":37252},[1149],[1151,37254,37255],{"xmlns":1153},[1155,37256,37257,37265],{},[1158,37258,37259,37261,37263],{},[1161,37260,4192],{},[1165,37262,4156],{},[1282,37264,25709],{},[1194,37266,37267],{"encoding":1196},"n>30"," se kritická hodnota aproximuje zlomkem ",[1115,37270,37272],{"className":37271},[1149],[1151,37273,37274],{"xmlns":1153},[1155,37275,37276,37287],{},[1158,37277,37278,37281,37283],{},[1282,37279,37280],{},"1,36",[1161,37282,3434],{"mathvariant":1215},[2765,37284,37285],{},[1161,37286,4192],{},[1194,37288,37289],{"encoding":1196},"1{,}36\u002F\\sqrt{n}",[1110,37291,31683,37292,37295,37296,37298,37299,1376,37302,37305],{},[1373,37293,37294],{},"ks.test()",", kde se za ",[1373,37297,1813],{}," dosadí příslušná distribuční funkce (",[1373,37300,37301],{},"\"pnorm\"",[1373,37303,37304],{},"\"pexp\"",", …) s jejími parametry:",[3554,37307,37309],{"className":3556,"code":37308,"language":71,"meta":3558,"style":3558},"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",[1373,37310,37311,37361],{"__ignoreMap":3558},[1115,37312,37313,37315,37317,37319,37321,37323,37325,37327,37329,37331,37333,37335,37337,37339,37341,37343,37345,37347,37349,37351,37353,37355,37357,37359],{"class":3563,"line":10},[1115,37314,32397],{"class":3744},[1115,37316,4497],{"class":3741},[1115,37318,7969],{"class":3566},[1115,37320,1168],{"class":3569},[1115,37322,15657],{"class":3572},[1115,37324,1715],{"class":3741},[1115,37326,15662],{"class":3572},[1115,37328,1715],{"class":3741},[1115,37330,15667],{"class":3572},[1115,37332,1715],{"class":3741},[1115,37334,15672],{"class":3572},[1115,37336,1715],{"class":3741},[1115,37338,15667],{"class":3572},[1115,37340,1715],{"class":3741},[1115,37342,15667],{"class":3572},[1115,37344,1715],{"class":3741},[1115,37346,15685],{"class":3572},[1115,37348,1715],{"class":3741},[1115,37350,15690],{"class":3572},[1115,37352,1715],{"class":3741},[1115,37354,15662],{"class":3572},[1115,37356,1715],{"class":3741},[1115,37358,15662],{"class":3572},[1115,37360,3575],{"class":3569},[1115,37362,37363,37366,37368,37370,37372,37375,37377,37379,37381,37383,37385,37387,37389,37391,37393],{"class":3563,"line":27},[1115,37364,37365],{"class":3566},"ks.test",[1115,37367,1168],{"class":3569},[1115,37369,32397],{"class":3744},[1115,37371,1715],{"class":3741},[1115,37373,37374],{"class":7974}," \"pnorm\"",[1115,37376,1715],{"class":3741},[1115,37378,3745],{"class":3566},[1115,37380,1168],{"class":3569},[1115,37382,32397],{"class":3744},[1115,37384,1174],{"class":3569},[1115,37386,1715],{"class":3741},[1115,37388,3756],{"class":3566},[1115,37390,1168],{"class":3569},[1115,37392,32397],{"class":3744},[1115,37394,4011],{"class":3569},[3554,37396,37399],{"className":37397,"code":37398,"language":3603,"meta":3558},[3601],"    Asymptotic one-sample Kolmogorov-Smirnov test\n\ndata:  x3\nD = 0.18469, p-value = 0.8847\nalternative hypothesis: two-sided\n",[1373,37400,37398],{"__ignoreMap":3558},[1110,37402,37403,37426],{},[1115,37404,37406],{"className":37405},[1149],[1151,37407,37408],{"xmlns":1153},[1155,37409,37410,37423],{},[1158,37411,37412,37414,37416,37419,37421],{},[1161,37413,1110],{},[1165,37415,1177],{},[1282,37417,37418],{},"0,8847",[1165,37420,4156],{},[1282,37422,8114],{},[1194,37424,37425],{"encoding":1196},"p = 0{,}8847 > 0{,}05",": odpad materiálu je slučitelný s normálním rozdělením se stejným průměrem a směrodatnou odchylkou.",[20418,37428,37430],{"id":37429},"shapiro-wilkův-test","Shapiro-Wilkův test",[1110,37432,37433],{},"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.",[1124,37435,37436,37456,37476],{},[1127,37437,37438,37455],{},[1115,37439,37441],{"className":37440},[1149],[1151,37442,37443],{"xmlns":1153},[1155,37444,37445,37453],{},[1158,37446,37447],{},[1277,37448,37449,37451],{},[1161,37450,4318],{},[1282,37452,1982],{},[1194,37454,5745],{"encoding":1196},": data mají normální rozdělení.",[1127,37457,37458,37475],{},[1115,37459,37461],{"className":37460},[1149],[1151,37462,37463],{"xmlns":1153},[1155,37464,37465,37473],{},[1158,37466,37467],{},[1277,37468,37469,37471],{},[1161,37470,4318],{},[1282,37472,1284],{},[1194,37474,7147],{"encoding":1196},": data nemají normální rozdělení.",[1127,37477,37478,37479,37505],{},"Testová statistika ",[1115,37480,37482],{"className":37481},[1149],[1151,37483,37484],{"xmlns":1153},[1155,37485,37486,37502],{},[1158,37487,37488,37490,37492,37494,37496,37498,37500],{},[1161,37489,5777],{},[1165,37491,1492],{},[1165,37493,2917],{"stretchy":1167},[1282,37495,1982],{},[1165,37497,1715],{"separator":1121},[1282,37499,1284],{},[1165,37501,1921],{"stretchy":1167},[1194,37503,37504],{"encoding":1196},"W \\in \\langle 0,1 \\rangle","; hodnoty blízké 1 indikují shodu s normalitou.",[1110,37507,37508,37509,37522,37523,1145,37543,37560,37561,1145,37581,37598],{},"Na rozdíl od ostatních testů v této kapitole se Shapiro-Wilkův test v praxi vyhodnocuje pouze přes p-hodnotu (tabulka kritických hodnot pro ",[1115,37510,37512],{"className":37511},[1149],[1151,37513,37514],{"xmlns":1153},[1155,37515,37516,37520],{},[1158,37517,37518],{},[1161,37519,5777],{},[1194,37521,5777],{"encoding":1196}," se běžně neudává): ",[1115,37524,37526],{"className":37525},[1149],[1151,37527,37528],{"xmlns":1153},[1155,37529,37530,37540],{},[1158,37531,37532,37534,37536,37538],{},[1161,37533,1110],{},[1165,37535,7501],{},[1161,37537,7514],{},[1165,37539,2028],{},[1194,37541,37542],{"encoding":1196},"p \\ge \\alpha \\Rightarrow",[1115,37544,37546],{"className":37545},[1149],[1151,37547,37548],{"xmlns":1153},[1155,37549,37550,37558],{},[1158,37551,37552],{},[1277,37553,37554,37556],{},[1161,37555,4318],{},[1282,37557,1982],{},[1194,37559,5745],{"encoding":1196}," nezamítáme (normalitu lze předpokládat); ",[1115,37562,37564],{"className":37563},[1149],[1151,37565,37566],{"xmlns":1153},[1155,37567,37568,37578],{},[1158,37569,37570,37572,37574,37576],{},[1161,37571,1110],{},[1165,37573,1287],{},[1161,37575,7514],{},[1165,37577,2028],{},[1194,37579,37580],{"encoding":1196},"p \u003C \\alpha \\Rightarrow",[1115,37582,37584],{"className":37583},[1149],[1151,37585,37586],{"xmlns":1153},[1155,37587,37588,37596],{},[1158,37589,37590],{},[1277,37591,37592,37594],{},[1161,37593,4318],{},[1282,37595,1982],{},[1194,37597,5745],{"encoding":1196}," zamítáme (předpoklad normality je porušen).",[3554,37600,37602],{"className":3556,"code":37601,"language":71,"meta":3558,"style":3558},"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",[1373,37603,37604,37658],{"__ignoreMap":3558},[1115,37605,37606,37608,37610,37612,37614,37616,37618,37620,37622,37624,37626,37628,37630,37632,37634,37636,37638,37640,37642,37644,37646,37648,37650,37652,37654,37656],{"class":3563,"line":10},[1115,37607,32265],{"class":3744},[1115,37609,4497],{"class":3741},[1115,37611,7969],{"class":3566},[1115,37613,1168],{"class":3569},[1115,37615,32274],{"class":3572},[1115,37617,1715],{"class":3741},[1115,37619,32279],{"class":3572},[1115,37621,1715],{"class":3741},[1115,37623,32284],{"class":3572},[1115,37625,1715],{"class":3741},[1115,37627,32289],{"class":3572},[1115,37629,1715],{"class":3741},[1115,37631,32294],{"class":3572},[1115,37633,1715],{"class":3741},[1115,37635,32299],{"class":3572},[1115,37637,1715],{"class":3741},[1115,37639,32289],{"class":3572},[1115,37641,1715],{"class":3741},[1115,37643,32308],{"class":3572},[1115,37645,1715],{"class":3741},[1115,37647,32294],{"class":3572},[1115,37649,1715],{"class":3741},[1115,37651,32317],{"class":3572},[1115,37653,1715],{"class":3741},[1115,37655,32289],{"class":3572},[1115,37657,3575],{"class":3569},[1115,37659,37660,37662,37664,37666],{"class":3563,"line":27},[1115,37661,21248],{"class":3566},[1115,37663,1168],{"class":3569},[1115,37665,32265],{"class":3744},[1115,37667,3575],{"class":3569},[3554,37669,37672],{"className":37670,"code":37671,"language":3603,"meta":3558},[3601],"    Shapiro-Wilk normality test\n\ndata:  x2\nW = 0.96022, p-value = 0.7744\n",[1373,37673,37671],{"__ignoreMap":3558},[1110,37675,37676,37677,37696],{},"U dat o životnosti baterií se normalita nezamítá (",[1115,37678,37680],{"className":37679},[1149],[1151,37681,37682],{"xmlns":1153},[1155,37683,37684,37693],{},[1158,37685,37686,37688,37690],{},[1161,37687,1110],{},[1165,37689,1177],{},[1282,37691,37692],{},"0,7744",[1194,37694,37695],{"encoding":1196},"p = 0{,}7744","), předpoklad t-testu je tedy splněn.",[1103,37698,37700,37707,37710,38077,38083],{"className":37699,"dataCallout":3670},[1106,3669],[1110,37701,37703,37706],{"className":37702},[1113],[1115,37704],{"className":37705,"ariaHidden":1121},[1118,3677,1120],"Příklad: Doba do poruchy výrobku",[1110,37708,37709],{},"Zkoušky životnosti nového výrobku daly soubor 68 hodnot doby do poruchy (v minutách). Odhadněte charakteristiky a zákon rozdělení.",[3554,37711,37713],{"className":3556,"code":37712,"language":71,"meta":3558,"style":3558},"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",[1373,37714,37715,37806,37884,37972,38006,38016,38026,38036,38046],{"__ignoreMap":3558},[1115,37716,37717,37719,37721,37723,37725,37727,37729,37731,37733,37735,37737,37739,37741,37743,37745,37747,37749,37751,37753,37755,37757,37759,37761,37763,37765,37768,37770,37772,37774,37776,37778,37780,37782,37784,37786,37788,37790,37792,37794,37796,37798,37800,37802,37804],{"class":3563,"line":10},[1115,37718,17747],{"class":3744},[1115,37720,4497],{"class":3741},[1115,37722,7969],{"class":3566},[1115,37724,1168],{"class":3569},[1115,37726,17756],{"class":3572},[1115,37728,1715],{"class":3741},[1115,37730,17761],{"class":3572},[1115,37732,1715],{"class":3741},[1115,37734,17766],{"class":3572},[1115,37736,1715],{"class":3741},[1115,37738,17771],{"class":3572},[1115,37740,1715],{"class":3741},[1115,37742,3994],{"class":3572},[1115,37744,1715],{"class":3741},[1115,37746,8310],{"class":3572},[1115,37748,1715],{"class":3741},[1115,37750,7870],{"class":3572},[1115,37752,1715],{"class":3741},[1115,37754,17788],{"class":3572},[1115,37756,1715],{"class":3741},[1115,37758,4524],{"class":3572},[1115,37760,1715],{"class":3741},[1115,37762,17797],{"class":3572},[1115,37764,1715],{"class":3741},[1115,37766,37767],{"class":3572}," 367",[1115,37769,1715],{"class":3741},[1115,37771,17809],{"class":3572},[1115,37773,1715],{"class":3741},[1115,37775,17814],{"class":3572},[1115,37777,1715],{"class":3741},[1115,37779,17819],{"class":3572},[1115,37781,1715],{"class":3741},[1115,37783,7888],{"class":3572},[1115,37785,1715],{"class":3741},[1115,37787,17828],{"class":3572},[1115,37789,1715],{"class":3741},[1115,37791,17833],{"class":3572},[1115,37793,1715],{"class":3741},[1115,37795,17838],{"class":3572},[1115,37797,1715],{"class":3741},[1115,37799,17843],{"class":3572},[1115,37801,1715],{"class":3741},[1115,37803,17848],{"class":3572},[1115,37805,7873],{"class":3741},[1115,37807,37808,37810,37812,37814,37816,37818,37820,37822,37824,37826,37828,37830,37832,37834,37836,37838,37840,37842,37844,37846,37848,37850,37852,37854,37856,37858,37860,37862,37864,37866,37868,37870,37872,37874,37876,37878,37880,37882],{"class":3563,"line":27},[1115,37809,17855],{"class":3572},[1115,37811,1715],{"class":3741},[1115,37813,17860],{"class":3572},[1115,37815,1715],{"class":3741},[1115,37817,17865],{"class":3572},[1115,37819,1715],{"class":3741},[1115,37821,17870],{"class":3572},[1115,37823,1715],{"class":3741},[1115,37825,17875],{"class":3572},[1115,37827,1715],{"class":3741},[1115,37829,7888],{"class":3572},[1115,37831,1715],{"class":3741},[1115,37833,17884],{"class":3572},[1115,37835,1715],{"class":3741},[1115,37837,7870],{"class":3572},[1115,37839,1715],{"class":3741},[1115,37841,17893],{"class":3572},[1115,37843,1715],{"class":3741},[1115,37845,17898],{"class":3572},[1115,37847,1715],{"class":3741},[1115,37849,18990],{"class":3572},[1115,37851,1715],{"class":3741},[1115,37853,17910],{"class":3572},[1115,37855,1715],{"class":3741},[1115,37857,17915],{"class":3572},[1115,37859,1715],{"class":3741},[1115,37861,17809],{"class":3572},[1115,37863,1715],{"class":3741},[1115,37865,17924],{"class":3572},[1115,37867,1715],{"class":3741},[1115,37869,17929],{"class":3572},[1115,37871,1715],{"class":3741},[1115,37873,17934],{"class":3572},[1115,37875,1715],{"class":3741},[1115,37877,17939],{"class":3572},[1115,37879,1715],{"class":3741},[1115,37881,17944],{"class":3572},[1115,37883,7873],{"class":3741},[1115,37885,37886,37888,37890,37893,37895,37897,37899,37901,37903,37905,37907,37909,37911,37913,37915,37917,37919,37921,37923,37925,37927,37929,37931,37934,37936,37938,37940,37942,37944,37946,37948,37950,37952,37954,37956,37958,37960,37962,37964,37966,37968,37970],{"class":3563,"line":148},[1115,37887,18054],{"class":3572},[1115,37889,1715],{"class":3741},[1115,37891,37892],{"class":3572}," 74",[1115,37894,1715],{"class":3741},[1115,37896,17961],{"class":3572},[1115,37898,1715],{"class":3741},[1115,37900,17966],{"class":3572},[1115,37902,1715],{"class":3741},[1115,37904,17971],{"class":3572},[1115,37906,1715],{"class":3741},[1115,37908,17976],{"class":3572},[1115,37910,1715],{"class":3741},[1115,37912,17893],{"class":3572},[1115,37914,1715],{"class":3741},[1115,37916,17985],{"class":3572},[1115,37918,1715],{"class":3741},[1115,37920,5393],{"class":3572},[1115,37922,1715],{"class":3741},[1115,37924,17994],{"class":3572},[1115,37926,1715],{"class":3741},[1115,37928,17999],{"class":3572},[1115,37930,1715],{"class":3741},[1115,37932,37933],{"class":3572}," 194",[1115,37935,1715],{"class":3741},[1115,37937,8275],{"class":3572},[1115,37939,1715],{"class":3741},[1115,37941,18015],{"class":3572},[1115,37943,1715],{"class":3741},[1115,37945,18020],{"class":3572},[1115,37947,1715],{"class":3741},[1115,37949,18025],{"class":3572},[1115,37951,1715],{"class":3741},[1115,37953,17976],{"class":3572},[1115,37955,1715],{"class":3741},[1115,37957,4524],{"class":3572},[1115,37959,1715],{"class":3741},[1115,37961,8310],{"class":3572},[1115,37963,1715],{"class":3741},[1115,37965,18042],{"class":3572},[1115,37967,1715],{"class":3741},[1115,37969,18047],{"class":3572},[1115,37971,7873],{"class":3741},[1115,37973,37974,37976,37978,37980,37982,37984,37986,37988,37990,37992,37994,37996,37998,38000,38002,38004],{"class":3563,"line":111},[1115,37975,18054],{"class":3572},[1115,37977,1715],{"class":3741},[1115,37979,7865],{"class":3572},[1115,37981,1715],{"class":3741},[1115,37983,18063],{"class":3572},[1115,37985,1715],{"class":3741},[1115,37987,18068],{"class":3572},[1115,37989,1715],{"class":3741},[1115,37991,18073],{"class":3572},[1115,37993,1715],{"class":3741},[1115,37995,18078],{"class":3572},[1115,37997,1715],{"class":3741},[1115,37999,17809],{"class":3572},[1115,38001,1715],{"class":3741},[1115,38003,18087],{"class":3572},[1115,38005,3575],{"class":3569},[1115,38007,38008,38010,38012,38014],{"class":3563,"line":96},[1115,38009,15809],{"class":3566},[1115,38011,1168],{"class":3569},[1115,38013,17747],{"class":3744},[1115,38015,3575],{"class":3569},[1115,38017,38018,38020,38022,38024],{"class":3563,"line":89},[1115,38019,15831],{"class":3566},[1115,38021,1168],{"class":3569},[1115,38023,17747],{"class":3744},[1115,38025,3575],{"class":3569},[1115,38027,38028,38030,38032,38034],{"class":3563,"line":82},[1115,38029,16531],{"class":3566},[1115,38031,1168],{"class":3569},[1115,38033,17747],{"class":3744},[1115,38035,3575],{"class":3569},[1115,38037,38038,38040,38042,38044],{"class":3563,"line":75},[1115,38039,21248],{"class":3566},[1115,38041,1168],{"class":3569},[1115,38043,17747],{"class":3744},[1115,38045,3575],{"class":3569},[1115,38047,38048,38050,38052,38054,38056,38059,38061,38063,38065,38067,38069,38071,38073,38075],{"class":3563,"line":8025},[1115,38049,37365],{"class":3566},[1115,38051,1168],{"class":3569},[1115,38053,17747],{"class":3744},[1115,38055,1715],{"class":3741},[1115,38057,38058],{"class":7974}," \"pexp\"",[1115,38060,1715],{"class":3741},[1115,38062,4600],{"class":3744},[1115,38064,3748],{"class":3741},[1115,38066,4605],{"class":3572},[1115,38068,4608],{"class":3741},[1115,38070,3745],{"class":3566},[1115,38072,1168],{"class":3569},[1115,38074,17747],{"class":3744},[1115,38076,4011],{"class":3569},[3554,38078,38081],{"className":38079,"code":38080,"language":3603,"meta":3558},[3601],"[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",[1373,38082,38080],{"__ignoreMap":3558},[1110,38084,38085,38086,38105,38106,38123,38124,38143],{},"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 (",[1115,38087,38089],{"className":38088},[1149],[1151,38090,38091],{"xmlns":1153},[1155,38092,38093,38102],{},[1158,38094,38095,38097,38099],{},[1161,38096,1110],{},[1165,38098,1287],{},[1282,38100,38101],{},"0,0001",[1194,38103,38104],{"encoding":1196},"p \u003C 0{,}0001","), zatímco Kolmogorov-Smirnovův test proti exponenciálnímu rozdělení se střední hodnotou ",[1115,38107,38109],{"className":38108},[1149],[1151,38110,38111],{"xmlns":1153},[1155,38112,38113,38121],{},[1158,38114,38115],{},[6877,38116,38117,38119],{"accent":1121},[1161,38118,1171],{},[1165,38120,15130],{},[1194,38122,25238],{"encoding":1196}," shodu nezamítá (",[1115,38125,38127],{"className":38126},[1149],[1151,38128,38129],{"xmlns":1153},[1155,38130,38131,38140],{},[1158,38132,38133,38135,38137],{},[1161,38134,1110],{},[1165,38136,1177],{},[1282,38138,38139],{},"0,8421",[1194,38141,38142],{"encoding":1196},"p = 0{,}8421","): data odpovídají spíše exponenciálnímu rozdělení než normálnímu.",[1110,38145,38146],{},[1760,38147],{"alt":38148,"className":38149,"src":38150},"mask-th-exponencialni-shoda",[1441,1764],"\u002Fwiki-assets\u002Fmask-th-exponencialni-shoda.png",[1431,38152,38154],{"id":38153},"neparametrické-testy","Neparametrické testy",[1110,38156,38157,38158,8728,38160,38184],{},"Když předpoklad normality neplatí, nahrazují t-testy jejich neparametrické obdoby — Wilcoxonovy testy posuzují ",[1131,38159,15222],{},[1115,38161,38163],{"className":38162},[1149],[1151,38164,38165],{"xmlns":1153},[1155,38166,38167,38181],{},[1158,38168,38169],{},[1277,38170,38171,38173],{},[1161,38172,1171],{},[1158,38174,38175,38177,38179],{},[1282,38176,1982],{},[1165,38178,1715],{"separator":1121},[1282,38180,4455],{},[1194,38182,38183],{"encoding":1196},"x_{0,5}",") místo střední hodnoty a nevyžadují normalitu dat.",[20418,38186,38188],{"id":38187},"wilcoxonovy-testy","Wilcoxonovy testy",[4052,38190,38191,38236],{},[4055,38192,38193],{},[4058,38194,38195,38214,38233],{},[4061,38196,38197],{},[1115,38198,38200],{"className":38199},[1149],[1151,38201,38202],{"xmlns":1153},[1155,38203,38204,38212],{},[1158,38205,38206],{},[1277,38207,38208,38210],{},[1161,38209,4318],{},[1282,38211,1982],{},[1194,38213,5745],{"encoding":1196},[4061,38215,38216],{},[1115,38217,38219],{"className":38218},[1149],[1151,38220,38221],{"xmlns":1153},[1155,38222,38223,38231],{},[1158,38224,38225],{},[1277,38226,38227,38229],{},[1161,38228,4318],{},[1282,38230,1284],{},[1194,38232,7147],{"encoding":1196},[4061,38234,38235],{},"Příkaz v R",[4165,38237,38238,38305,38372],{},[4058,38239,38240,38270,38300],{},[4170,38241,38242],{},[1115,38243,38245],{"className":38244},[1149],[1151,38246,38247],{"xmlns":1153},[1155,38248,38249,38267],{},[1158,38250,38251,38263,38265],{},[1277,38252,38253,38255],{},[1161,38254,1171],{},[1158,38256,38257,38259,38261],{},[1282,38258,1982],{},[1165,38260,1715],{"separator":1121},[1282,38262,4455],{},[1165,38264,1188],{},[1161,38266,7856],{},[1194,38268,38269],{"encoding":1196},"x_{0,5} \\le c",[4170,38271,38272],{},[1115,38273,38275],{"className":38274},[1149],[1151,38276,38277],{"xmlns":1153},[1155,38278,38279,38297],{},[1158,38280,38281,38293,38295],{},[1277,38282,38283,38285],{},[1161,38284,1171],{},[1158,38286,38287,38289,38291],{},[1282,38288,1982],{},[1165,38290,1715],{"separator":1121},[1282,38292,4455],{},[1165,38294,4156],{},[1161,38296,7856],{},[1194,38298,38299],{"encoding":1196},"x_{0,5} > c",[4170,38301,38302],{},[1373,38303,38304],{},"wilcox.test(x, alternative = \"greater\", mu = c)",[4058,38306,38307,38337,38367],{},[4170,38308,38309],{},[1115,38310,38312],{"className":38311},[1149],[1151,38313,38314],{"xmlns":1153},[1155,38315,38316,38334],{},[1158,38317,38318,38330,38332],{},[1277,38319,38320,38322],{},[1161,38321,1171],{},[1158,38323,38324,38326,38328],{},[1282,38325,1982],{},[1165,38327,1715],{"separator":1121},[1282,38329,4455],{},[1165,38331,1177],{},[1161,38333,7856],{},[1194,38335,38336],{"encoding":1196},"x_{0,5} = c",[4170,38338,38339],{},[1115,38340,38342],{"className":38341},[1149],[1151,38343,38344],{"xmlns":1153},[1155,38345,38346,38364],{},[1158,38347,38348,38360,38362],{},[1277,38349,38350,38352],{},[1161,38351,1171],{},[1158,38353,38354,38356,38358],{},[1282,38355,1982],{},[1165,38357,1715],{"separator":1121},[1282,38359,4455],{},[1165,38361,5496],{"mathvariant":1215},[1161,38363,7856],{},[1194,38365,38366],{"encoding":1196},"x_{0,5} \\neq c",[4170,38368,38369],{},[1373,38370,38371],{},"wilcox.test(x, alternative = \"two.sided\", mu = c)",[4058,38373,38374,38404,38434],{},[4170,38375,38376],{},[1115,38377,38379],{"className":38378},[1149],[1151,38380,38381],{"xmlns":1153},[1155,38382,38383,38401],{},[1158,38384,38385,38397,38399],{},[1277,38386,38387,38389],{},[1161,38388,1171],{},[1158,38390,38391,38393,38395],{},[1282,38392,1982],{},[1165,38394,1715],{"separator":1121},[1282,38396,4455],{},[1165,38398,7501],{},[1161,38400,7856],{},[1194,38402,38403],{"encoding":1196},"x_{0,5} \\ge c",[4170,38405,38406],{},[1115,38407,38409],{"className":38408},[1149],[1151,38410,38411],{"xmlns":1153},[1155,38412,38413,38431],{},[1158,38414,38415,38427,38429],{},[1277,38416,38417,38419],{},[1161,38418,1171],{},[1158,38420,38421,38423,38425],{},[1282,38422,1982],{},[1165,38424,1715],{"separator":1121},[1282,38426,4455],{},[1165,38428,1287],{},[1161,38430,7856],{},[1194,38432,38433],{"encoding":1196},"x_{0,5} \u003C c",[4170,38435,38436],{},[1373,38437,38438],{},"wilcox.test(x, alternative = \"less\", mu = c)",[1110,38440,38441,38444,38445,1333],{},[5660,38442,38443],{},"Jednovýběrový Wilcoxonův test"," (obdoba t-testu) posuzuje odchylku mediánu od konstanty ",[1115,38446,38448],{"className":38447},[1149],[1151,38449,38450],{"xmlns":1153},[1155,38451,38452,38456],{},[1158,38453,38454],{},[1161,38455,7856],{},[1194,38457,7856],{"encoding":1196},[1110,38459,38460,38463,38464,3328,38502,38515,38516,1333],{},[5660,38461,38462],{},"Jednovýběrový Wilcoxonův test na diferencích"," (obdoba párového t-testu) posuzuje odchylku mediánu rozdílu ",[1115,38465,38467],{"className":38466},[1149],[1151,38468,38469],{"xmlns":1153},[1155,38470,38471,38499],{},[1158,38472,38473,38485,38487],{},[1277,38474,38475,38477],{},[1161,38476,1171],{},[1158,38478,38479,38481,38483],{},[1282,38480,1982],{},[1165,38482,1715],{"separator":1121},[1282,38484,4455],{},[1165,38486,1317],{},[1277,38488,38489,38491],{},[1161,38490,1603],{},[1158,38492,38493,38495,38497],{},[1282,38494,1982],{},[1165,38496,1715],{"separator":1121},[1282,38498,4455],{},[1194,38500,38501],{"encoding":1196},"x_{0,5}-y_{0,5}",[1115,38503,38505],{"className":38504},[1149],[1151,38506,38507],{"xmlns":1153},[1155,38508,38509,38513],{},[1158,38510,38511],{},[1161,38512,7856],{},[1194,38514,7856],{"encoding":1196},"; v R se volá se stejnými argumenty jako výše a navíc ",[1373,38517,38518],{},"paired = TRUE",[1110,38520,38521,38524,38525,38527],{},[5660,38522,38523],{},"Dvouvýběrový Wilcoxonův test"," (obdoba dvouvýběrového t-testu) posuzuje odchylku mediánů dvou nezávislých výběrů; argument ",[1373,38526,29121],{}," odpadá. Pro výšky chlapců a dívek z příkladu výše:",[3554,38529,38531],{"className":3556,"code":38530,"language":71,"meta":3558,"style":3558},"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",[1373,38532,38533,38603,38661],{"__ignoreMap":3558},[1115,38534,38535,38537,38539,38541,38543,38545,38547,38549,38551,38553,38555,38557,38559,38561,38563,38565,38567,38569,38571,38573,38575,38577,38579,38581,38583,38585,38587,38589,38591,38593,38595,38597,38599,38601],{"class":3563,"line":10},[1115,38536,36777],{"class":3744},[1115,38538,4497],{"class":3741},[1115,38540,7969],{"class":3566},[1115,38542,1168],{"class":3569},[1115,38544,36786],{"class":3572},[1115,38546,1715],{"class":3741},[1115,38548,18990],{"class":3572},[1115,38550,1715],{"class":3741},[1115,38552,36795],{"class":3572},[1115,38554,1715],{"class":3741},[1115,38556,36800],{"class":3572},[1115,38558,1715],{"class":3741},[1115,38560,36805],{"class":3572},[1115,38562,1715],{"class":3741},[1115,38564,36810],{"class":3572},[1115,38566,1715],{"class":3741},[1115,38568,22144],{"class":3572},[1115,38570,1715],{"class":3741},[1115,38572,17848],{"class":3572},[1115,38574,1715],{"class":3741},[1115,38576,36805],{"class":3572},[1115,38578,1715],{"class":3741},[1115,38580,36795],{"class":3572},[1115,38582,1715],{"class":3741},[1115,38584,36831],{"class":3572},[1115,38586,1715],{"class":3741},[1115,38588,36836],{"class":3572},[1115,38590,1715],{"class":3741},[1115,38592,36841],{"class":3572},[1115,38594,1715],{"class":3741},[1115,38596,36805],{"class":3572},[1115,38598,1715],{"class":3741},[1115,38600,36850],{"class":3572},[1115,38602,3575],{"class":3569},[1115,38604,38605,38607,38609,38611,38613,38615,38617,38619,38621,38623,38625,38627,38629,38631,38633,38635,38637,38639,38641,38643,38645,38647,38649,38651,38653,38655,38657,38659],{"class":3563,"line":27},[1115,38606,36857],{"class":3744},[1115,38608,4497],{"class":3741},[1115,38610,7969],{"class":3566},[1115,38612,1168],{"class":3569},[1115,38614,25510],{"class":3572},[1115,38616,1715],{"class":3741},[1115,38618,36800],{"class":3572},[1115,38620,1715],{"class":3741},[1115,38622,36874],{"class":3572},[1115,38624,1715],{"class":3741},[1115,38626,36879],{"class":3572},[1115,38628,1715],{"class":3741},[1115,38630,36884],{"class":3572},[1115,38632,1715],{"class":3741},[1115,38634,36884],{"class":3572},[1115,38636,1715],{"class":3741},[1115,38638,17848],{"class":3572},[1115,38640,1715],{"class":3741},[1115,38642,36800],{"class":3572},[1115,38644,1715],{"class":3741},[1115,38646,36800],{"class":3572},[1115,38648,1715],{"class":3741},[1115,38650,36905],{"class":3572},[1115,38652,1715],{"class":3741},[1115,38654,36836],{"class":3572},[1115,38656,1715],{"class":3741},[1115,38658,36800],{"class":3572},[1115,38660,3575],{"class":3569},[1115,38662,38663,38666,38668,38670,38672,38674,38676,38678,38680,38682],{"class":3563,"line":148},[1115,38664,38665],{"class":3566},"wilcox.test",[1115,38667,1168],{"class":3569},[1115,38669,36777],{"class":3744},[1115,38671,1715],{"class":3741},[1115,38673,36928],{"class":3744},[1115,38675,1715],{"class":3741},[1115,38677,31768],{"class":3744},[1115,38679,3748],{"class":3741},[1115,38681,31773],{"class":7974},[1115,38683,3575],{"class":3569},[3554,38685,38688],{"className":38686,"code":38687,"language":3603,"meta":3558},[3601],"    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",[1373,38689,38687],{"__ignoreMap":3558},[1110,38691,38692,38715],{},[1115,38693,38695],{"className":38694},[1149],[1151,38696,38697],{"xmlns":1153},[1155,38698,38699,38712],{},[1158,38700,38701,38703,38705,38708,38710],{},[1161,38702,1110],{},[1165,38704,1177],{},[1282,38706,38707],{},"0,315",[1165,38709,4156],{},[1282,38711,8114],{},[1194,38713,38714],{"encoding":1196},"p = 0{,}315 > 0{,}05",": mediány výšek chlapců a dívek se statisticky významně neliší — stejný závěr jako u dvouvýběrového t-testu.",[1103,38717,38719,38726,38748,38859,38865],{"className":38718,"dataCallout":3670},[1106,3669],[1110,38720,38722,38725],{"className":38721},[1113],[1115,38723],{"className":38724,"ariaHidden":1121},[1118,3677,1120],"Příklad: Realitní odhadci — neparametrická alternativa",[1110,38727,38728,38729,38747],{},"U odhadů cen z párového t-testu výše normalita diferencí neplatí (",[1115,38730,38732],{"className":38731},[1149],[1151,38733,38734],{"xmlns":1153},[1155,38735,38736,38744],{},[1158,38737,38738,38740,38742],{},[1161,38739,1110],{},[1165,38741,1177],{},[1282,38743,33821],{},[1194,38745,38746],{"encoding":1196},"p = 0{,}03203","). Správnou volbou je párový Wilcoxonův test:",[3554,38749,38751],{"className":3556,"code":38750,"language":71,"meta":3558,"style":3558},"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",[1373,38752,38753,38795,38837],{"__ignoreMap":3558},[1115,38754,38755,38757,38759,38761,38763,38765,38767,38769,38771,38773,38775,38777,38779,38781,38783,38785,38787,38789,38791,38793],{"class":3563,"line":10},[1115,38756,33624],{"class":3744},[1115,38758,4497],{"class":3741},[1115,38760,7969],{"class":3566},[1115,38762,1168],{"class":3569},[1115,38764,33633],{"class":3572},[1115,38766,1715],{"class":3741},[1115,38768,33638],{"class":3572},[1115,38770,1715],{"class":3741},[1115,38772,33643],{"class":3572},[1115,38774,1715],{"class":3741},[1115,38776,33648],{"class":3572},[1115,38778,1715],{"class":3741},[1115,38780,33653],{"class":3572},[1115,38782,1715],{"class":3741},[1115,38784,33658],{"class":3572},[1115,38786,1715],{"class":3741},[1115,38788,33663],{"class":3572},[1115,38790,1715],{"class":3741},[1115,38792,33668],{"class":3572},[1115,38794,3575],{"class":3569},[1115,38796,38797,38799,38801,38803,38805,38807,38809,38811,38813,38815,38817,38819,38821,38823,38825,38827,38829,38831,38833,38835],{"class":3563,"line":27},[1115,38798,33675],{"class":3744},[1115,38800,4497],{"class":3741},[1115,38802,7969],{"class":3566},[1115,38804,1168],{"class":3569},[1115,38806,33684],{"class":3572},[1115,38808,1715],{"class":3741},[1115,38810,33689],{"class":3572},[1115,38812,1715],{"class":3741},[1115,38814,33694],{"class":3572},[1115,38816,1715],{"class":3741},[1115,38818,33699],{"class":3572},[1115,38820,1715],{"class":3741},[1115,38822,33704],{"class":3572},[1115,38824,1715],{"class":3741},[1115,38826,33709],{"class":3572},[1115,38828,1715],{"class":3741},[1115,38830,33714],{"class":3572},[1115,38832,1715],{"class":3741},[1115,38834,33719],{"class":3572},[1115,38836,3575],{"class":3569},[1115,38838,38839,38841,38843,38845,38847,38849,38851,38853,38855,38857],{"class":3563,"line":148},[1115,38840,38665],{"class":3566},[1115,38842,1168],{"class":3569},[1115,38844,33624],{"class":3744},[1115,38846,1715],{"class":3741},[1115,38848,33734],{"class":3744},[1115,38850,1715],{"class":3741},[1115,38852,33739],{"class":3744},[1115,38854,3748],{"class":3741},[1115,38856,7944],{"class":3572},[1115,38858,3575],{"class":3569},[3554,38860,38863],{"className":38861,"code":38862,"language":3603,"meta":3558},[3601],"    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",[1373,38864,38862],{"__ignoreMap":3558},[1110,38866,38867,38890],{},[1115,38868,38870],{"className":38869},[1149],[1151,38871,38872],{"xmlns":1153},[1155,38873,38874,38887],{},[1158,38875,38876,38878,38880,38883,38885],{},[1161,38877,1110],{},[1165,38879,1177],{},[1282,38881,38882],{},"0,1484",[1165,38884,4156],{},[1282,38886,8114],{},[1194,38888,38889],{"encoding":1196},"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.",[20418,38892,38894],{"id":38893},"kruskalův-wallisův-test","Kruskalův-Wallisův test",[1110,38896,38897,38898,38915],{},"Zobecnění dvouvýběrového Wilcoxonova testu, neparametrická obdoba analýzy rozptylu jednoduchého třídění. ",[1115,38899,38901],{"className":38900},[1149],[1151,38902,38903],{"xmlns":1153},[1155,38904,38905,38913],{},[1158,38906,38907],{},[1277,38908,38909,38911],{},[1161,38910,4318],{},[1282,38912,1982],{},[1194,38914,5745],{"encoding":1196},": všechny výběry pocházejí ze stejného rozdělení.",[3554,38917,38919],{"className":3556,"code":38918,"language":71,"meta":3558,"style":3558},"kruskal.test(kvantitativní_proměnná ~ faktor, data = soubor)\n",[1373,38920,38921],{"__ignoreMap":3558},[1115,38922,38923,38926,38928,38931,38933,38936,38938,38940,38942,38945],{"class":3563,"line":10},[1115,38924,38925],{"class":3566},"kruskal.test",[1115,38927,1168],{"class":3569},[1115,38929,38930],{"class":3744},"kvantitativní_proměnná",[1115,38932,20529],{"class":3741},[1115,38934,38935],{"class":3744}," faktor",[1115,38937,1715],{"class":3741},[1115,38939,23838],{"class":3744},[1115,38941,3748],{"class":3741},[1115,38943,38944],{"class":3744}," soubor",[1115,38946,3575],{"class":3569},[20418,38948,38950],{"id":38949},"mediánový-test","Mediánový test",[1110,38952,38953,38954,38971,38972,2629],{},"Má stejný účel jako Kruskalův-Wallisův test (obdoba analýzy rozptylu jednoduchého třídění, ",[1115,38955,38957],{"className":38956},[1149],[1151,38958,38959],{"xmlns":1153},[1155,38960,38961,38969],{},[1158,38962,38963],{},[1277,38964,38965,38967],{},[1161,38966,4318],{},[1282,38968,1982],{},[1194,38970,5745],{"encoding":1196},": všechny výběry pocházejí ze stejného rozdělení) a je součástí balíčku ",[1373,38973,38974],{},"agricolae",[3554,38976,38978],{"className":3556,"code":38977,"language":71,"meta":3558,"style":3558},"library(agricolae)\nMedian.test(kvantitativní_proměnná, faktor)\n",[1373,38979,38980,38990],{"__ignoreMap":3558},[1115,38981,38982,38984,38986,38988],{"class":3563,"line":10},[1115,38983,21068],{"class":3741},[1115,38985,1168],{"class":3569},[1115,38987,38974],{"class":3744},[1115,38989,3575],{"class":3569},[1115,38991,38992,38995,38997,38999,39001,39003],{"class":3563,"line":27},[1115,38993,38994],{"class":3566},"Median.test",[1115,38996,1168],{"class":3569},[1115,38998,38930],{"class":3744},[1115,39000,1715],{"class":3741},[1115,39002,38935],{"class":3744},[1115,39004,3575],{"class":3569},[20418,39006,39008],{"id":39007},"friedmanův-test","Friedmanův test",[1110,39010,39011,39012,39029,39030,39068],{},"Neparametrická obdoba analýzy rozptylu dvojného třídění s jedním pozorováním v každé podtřídě. ",[1115,39013,39015],{"className":39014},[1149],[1151,39016,39017],{"xmlns":1153},[1155,39018,39019,39027],{},[1158,39020,39021],{},[1277,39022,39023,39025],{},[1161,39024,4318],{},[1282,39026,1982],{},[1194,39028,5745],{"encoding":1196},": distribuční funkce veličin ",[1115,39031,39033],{"className":39032},[1149],[1151,39034,39035],{"xmlns":1153},[1155,39036,39037,39065],{},[1158,39038,39039,39049,39051,39053,39055],{},[1277,39040,39041,39043],{},[1161,39042,1185],{},[1158,39044,39045,39047],{},[1161,39046,4187],{},[1282,39048,1284],{},[1165,39050,1715],{"separator":1121},[1165,39052,1726],{},[1165,39054,1715],{"separator":1121},[1277,39056,39057,39059],{},[1161,39058,1185],{},[1158,39060,39061,39063],{},[1161,39062,4187],{},[1161,39064,1735],{},[1194,39066,39067],{"encoding":1196},"X_{i1}, \\dots, X_{ik}"," jsou totožné.",[3554,39070,39072],{"className":3556,"code":39071,"language":71,"meta":3558,"style":3558},"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",[1373,39073,39074,39104,39109],{"__ignoreMap":3558},[1115,39075,39076,39079,39081,39083,39085,39088,39091,39094,39096,39098,39100,39102],{"class":3563,"line":10},[1115,39077,39078],{"class":3566},"friedman.test",[1115,39080,1168],{"class":3569},[1115,39082,38930],{"class":3744},[1115,39084,20529],{"class":3741},[1115,39086,39087],{"class":3744}," faktor_A",[1115,39089,39090],{"class":3741}," |",[1115,39092,39093],{"class":3744}," faktor_B",[1115,39095,1715],{"class":3741},[1115,39097,23838],{"class":3744},[1115,39099,3748],{"class":3741},[1115,39101,38944],{"class":3744},[1115,39103,3575],{"class":3569},[1115,39105,39106],{"class":3563,"line":27},[1115,39107,39108],{"class":15704},"# jsou-li proměnné samostatné vektory (bez argumentu data):\n",[1115,39110,39111,39113,39115,39117,39119,39121,39123,39125],{"class":3563,"line":148},[1115,39112,39078],{"class":3566},[1115,39114,1168],{"class":3569},[1115,39116,38930],{"class":3744},[1115,39118,1715],{"class":3741},[1115,39120,39087],{"class":3744},[1115,39122,1715],{"class":3741},[1115,39124,39093],{"class":3744},[1115,39126,3575],{"class":3569},[1431,39128,39130],{"id":39129},"přehled-testů","Přehled testů",[1110,39132,39133],{},[1760,39134],{"alt":39135,"className":39136,"src":39137},"mask-ilu-volba-testu",[1441,1764],"\u002Fwiki-assets\u002Fmask-ilu-volba-testu.png",[4052,39139,39140,39153],{},[4055,39141,39142],{},[4058,39143,39144,39147,39150],{},[4061,39145,39146],{},"Situace",[4061,39148,39149],{},"Test",[4061,39151,39152],{},"R funkce",[4165,39154,39155,39168,39181,39193,39206,39221,39233,39246,39259,39272,39284,39299],{},[4058,39156,39157,39160,39163],{},[4170,39158,39159],{},"Jedna střední hodnota vs. zadané číslo, normální data",[4170,39161,39162],{},"jednovýběrový t-test",[4170,39164,39165],{},[1373,39166,39167],{},"t.test(x, mu = ..., alternative = ...)",[4058,39169,39170,39173,39176],{},[4170,39171,39172],{},"Rozdíl dvou závislých měření, diference normální",[4170,39174,39175],{},"párový t-test",[4170,39177,39178],{},[1373,39179,39180],{},"t.test(x, y, paired = TRUE)",[4058,39182,39183,39186,39188],{},[4170,39184,39185],{},"Shoda rozptylů dvou nezávislých normálních výběrů",[4170,39187,23746],{},[4170,39189,39190],{},[1373,39191,39192],{},"var.test(x, y)",[4058,39194,39195,39198,39201],{},[4170,39196,39197],{},"Shoda středních hodnot dvou nezávislých normálních výběrů",[4170,39199,39200],{},"dvouvýběrový t-test",[4170,39202,39203],{},[1373,39204,39205],{},"t.test(x, y, var.equal = TRUE\u002FFALSE)",[4058,39207,39208,39211,39213],{},[4170,39209,39210],{},"Shoda dat se zadaným typem rozdělení (normální, exponenciální, …)",[4170,39212,37014],{},[4170,39214,39215,1376,39218],{},[1373,39216,39217],{},"ks.test(x, \"pnorm\", mu, sigma)",[1373,39219,39220],{},"ks.test(x, \"pexp\", 1\u002Fdelta)",[4058,39222,39223,39226,39228],{},[4170,39224,39225],{},"Normalita dat",[4170,39227,37430],{},[4170,39229,39230],{},[1373,39231,39232],{},"shapiro.test(x)",[4058,39234,39235,39238,39241],{},[4170,39236,39237],{},"Medián jednoho výběru vs. konstanta, data nejsou normální",[4170,39239,39240],{},"jednovýběrový Wilcoxonův test",[4170,39242,39243],{},[1373,39244,39245],{},"wilcox.test(x, mu = c, alternative = ...)",[4058,39247,39248,39251,39254],{},[4170,39249,39250],{},"Medián diferencí dvou závislých měření, data nejsou normální",[4170,39252,39253],{},"párový Wilcoxonův test",[4170,39255,39256],{},[1373,39257,39258],{},"wilcox.test(x, y, paired = TRUE, mu = c)",[4058,39260,39261,39264,39267],{},[4170,39262,39263],{},"Mediány dvou nezávislých výběrů, data nejsou normální",[4170,39265,39266],{},"dvouvýběrový Wilcoxonův test",[4170,39268,39269],{},[1373,39270,39271],{},"wilcox.test(x, y)",[4058,39273,39274,39277,39279],{},[4170,39275,39276],{},"Více než dva nezávislé výběry, data nejsou normální",[4170,39278,38894],{},[4170,39280,39281],{},[1373,39282,39283],{},"kruskal.test(y ~ faktor, data)",[4058,39285,39286,39289,39292],{},[4170,39287,39288],{},"Více než dva nezávislé výběry, data nejsou normální (alternativa)",[4170,39290,39291],{},"mediánový test",[4170,39293,39294,26338,39297],{},[1373,39295,39296],{},"Median.test(y, faktor)",[1373,39298,38974],{},[4058,39300,39301,39304,39306],{},[4170,39302,39303],{},"Více než dva závislé výběry (dvojné třídění, jedno pozorování na podtřídu)",[4170,39305,39008],{},[4170,39307,39308],{},[1373,39309,39310],{},"friedman.test(y ~ A | B, data)",[1431,39312,5414],{"id":5413},[1124,39314,39315,39392,39398,39415,39446],{},[1127,39316,39317,39356,39357,36744,39374,39391],{},[1131,39318,39319,39320,39337,39338,39355],{},"Nezamítnutí ",[1115,39321,39323],{"className":39322},[1149],[1151,39324,39325],{"xmlns":1153},[1155,39326,39327,39335],{},[1158,39328,39329],{},[1277,39330,39331,39333],{},[1161,39332,4318],{},[1282,39334,1982],{},[1194,39336,5745],{"encoding":1196}," není důkaz, že ",[1115,39339,39341],{"className":39340},[1149],[1151,39342,39343],{"xmlns":1153},[1155,39344,39345,39353],{},[1158,39346,39347],{},[1277,39348,39349,39351],{},[1161,39350,4318],{},[1282,39352,1982],{},[1194,39354,5745],{"encoding":1196}," platí."," U kabelů A\u002FB vyšlo ",[1115,39358,39360],{"className":39359},[1149],[1151,39361,39362],{"xmlns":1153},[1155,39363,39364,39372],{},[1158,39365,39366,39368,39370],{},[1161,39367,1110],{},[1165,39369,1177],{},[1282,39371,36740],{},[1194,39373,36743],{"encoding":1196},[1115,39375,39377],{"className":39376},[1149],[1151,39378,39379],{"xmlns":1153},[1155,39380,39381,39389],{},[1158,39382,39383],{},[1277,39384,39385,39387],{},[1161,39386,4318],{},[1282,39388,1982],{},[1194,39390,5745],{"encoding":1196}," nezamítá, ale hodnota je blízko hranice; správná interpretace je „data rovnost průměrů nevyvracejí“, ne „rovnost je prokázána“.",[1127,39393,39394,39397],{},[1131,39395,39396],{},"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.",[1127,39399,39400,39407,39408,39411,39412,39414],{},[1131,39401,39402,33902,39404,39406],{},[1373,39403,36472],{},[1373,39405,31686],{}," se volí podle F-testu, ne podle výchozí hodnoty."," Výchozí nastavení R je ",[1373,39409,39410],{},"var.equal = FALSE"," (Welchova varianta); pokud F-test potvrdí shodné rozptyly, je třeba explicitně napsat ",[1373,39413,36723],{},", jinak se použije jiná statistika a jiné stupně volnosti.",[1127,39416,39417,39420,39421,39424,39425,39442,39443,1333],{},[1131,39418,39419],{},"Jednostranná vs. dvoustranná alternativa mění kritický obor i závěr."," Volba ",[1373,39422,39423],{},"alternative = \"greater\"\u002F\"less\"\u002F\"two.sided\""," musí odpovídat formulaci ",[1115,39426,39428],{"className":39427},[1149],[1151,39429,39430],{"xmlns":1153},[1155,39431,39432,39440],{},[1158,39433,39434],{},[1277,39435,39436,39438],{},[1161,39437,4318],{},[1282,39439,1284],{},[1194,39441,7147],{"encoding":1196}," v zadání, ne být ponechána na výchozí hodnotě ",[1373,39444,39445],{},"\"two.sided\"",[1127,39447,39448,39451,39452,39465],{},[1131,39449,39450],{},"Shapiro-Wilkův test se vyhodnocuje jen přes p-hodnotu",", ne porovnáním ",[1115,39453,39455],{"className":39454},[1149],[1151,39456,39457],{"xmlns":1153},[1155,39458,39459,39463],{},[1158,39460,39461],{},[1161,39462,5777],{},[1194,39464,5777],{"encoding":1196}," s tabulkovou kritickou hodnotou jako u ostatních testů v této kapitole.",[1431,39467,5604],{"id":5603},[1124,39469,39470,39475,39480,39485,39490,39495,39500],{},[1127,39471,39472],{},[1438,39473,1444],{"className":39474,"dataFsResolvedFilePath":1442,"href":1443},[1441],[1127,39476,39477],{},[1438,39478,1094],{"className":39479,"dataFsResolvedFilePath":10731,"href":10732},[1441],[1127,39481,39482],{},[1438,39483,10725],{"className":39484,"dataFsResolvedFilePath":2788,"href":2789},[1441],[1127,39486,39487],{},[1438,39488,10738],{"className":39489,"dataFsResolvedFilePath":5627,"href":5628},[1441],[1127,39491,39492],{},[1438,39493,5698],{"className":39494,"dataFsResolvedFilePath":5635,"href":5636},[1441],[1127,39496,39497],{},[1438,39498,10744],{"className":39499,"dataFsResolvedFilePath":5642,"href":5643},[1441],[1127,39501,39502],{},[1438,39503,5652],{"className":39504,"dataFsResolvedFilePath":5650,"href":5651},[1441],[1431,39506,5655],{"id":934},[1110,39508,5658,39509,5663],{},[5660,39510,5662],{},[5665,39512,39513],{},"html pre.shiki code .sP4rz, 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…",{"slug":39559,"path":39560,"title":39561,"snippet":39562},"mask-detail-predmetu","\u002Fwiki\u002Fmask-detail-predmetu","Detail předmětu — Metody aplikované statistiky","… ruhy 1. **Pravděpodobnost a rozdělení** — náhodná veličina a rozdělení pravděpodobnosti (\u003C\u003Cnahodne-veliciny-a-rozdeleni>>). 2. **Zpracování dat** — empirické charakteristiky, kvantily a třídění dat do tříd ([[po …",{"slug":39564,"path":39565,"title":39566,"snippet":39567},"mask-prednasky-veliciny-data-testy","\u002Fwiki\u002Fmask-prednasky-veliciny-data-testy","MasK — Náhodné veličiny, datové soubory a testy hypotéz","… est, Friedmanův test | ## Související stránky - Metody aplikované statistiky - \u003C\u003Cnahodne-veliciny-a-rozdeleni>> - Popisná statistika a datové soubory - [[testovani-hypotez|Testov …",{"slug":39569,"path":5651,"title":39570,"snippet":39571},"mask-r-tahak","masK — Tahák pro R","… e normalitu dat lze předpokládat, ne že data jsou normální. ## Funkce podle kapitol ### 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